13. Enhanced Oil Recovery - Fayers

Developments in Petroleum Science, 13

enhanced oil recovery

FURTHER TITLES IN THIS SERIES

1 A, GENE COLLINS GEOCHEMISTRY OF OILFIELD WATERS

2 W.H. FERTL ABNORMAL FORMATION PRESSURES

3 A.P. SZILAS PRODUCTION AND TRANSPORT OF OIL AND GAS

4 C.E.B. CONYBEARE GEOMORPHOLOGY OF OIL AND GAS FIELDS IN SANDSTONE BODIES

5 T.F. YEN and G.V. CHILINGARIAN (Editors) OIL SHALE

6 D.W. PEACEMAN FUNDAMENTALS O F NUMERICAL RESERVOIR SIMULATION

7 G.V. CHILINGARIAN and T.F. YEN (Editors) BITUMENS, ASPHALTS AND TAR SANDS

8 L.P. DAKE FUNDAMENTALS OF RESERVOIR ENGINEERING

9 K. MAGARA COMPACTION AND FLUID MIGRATION

10 M.T. SILVIA and E.A. ROBINSON DECONVOLUTION OF GEOPHYSICAL TIME SERIES IN THE EXPLORATION FOR OIL AND NATURAL GAS

11 G.V. CHILINGARIAN and P. VORABUTR DRILLING AND DRILLING FLUIDS

1 2 T. VAN GOLF-RACHT FRACTURED HYDROCARBON-RESERVOIR ENGINEERING

Developments in Petroleum Science, 1 3

Proceedings of the third European Symposium on Enhanced Oil Recovery, held in Bournemouth, U.K., September 21-23,1981

Edited by

E JOHN FAYERS Atomic Energy Establishment, Winfrith, Dorchester, England

ELSEVIER SCIENTIFIC PUBLISHING COMPANY AMSTERDAM -OXFORD -NEW YORK 1981

ELSEVIER SCIENTIFIC PUBLISHING COMPANY Molenwerf 1 P.O. Box 211, 1000 AE Amsterdam, The Netherlands

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0 Elsevier Scientific Publishing Company, 1981 All rights reserved. No part of this publication may be reproduced, stored in a retrieval system or transmitted in any form or by any means, electronic, mechanical, photocopying, recording or otherwise, without the prior written permission of the publisher, Elsevier Scientific Publishing Company, P.O. Box 330, 1000 AH Amsterdam, The Netherlands

Printed in The Netherlands

V

TABLE OF CONTENTS

Foreword . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ix

1 .

2.

3.

4.

5.

6.

7.

8.

9.

10.

CHEMICAL FLOODING

Keynote Paper: “Fundamental Aspects of Surfactant-Polymer Flooding Process” . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . D. 0. SHAH, University of Florida, USA

Surfactants for EOR Processes in High-Salinity Systems; Product Selection and Evaluation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . M. H. AKSTINAT, Institute of Petroleum Engineering, Clausthal, West Germany

Preliminary Studies of the Behaviour or Some Commercially Available Surfactants in Hydrocarbon-Brine-Mineral Systems . . . . . . . . . . . . . . . . . C. ANDREWS, N. COLLEY and R. THAVER, British Gas Corporation, London Research Station, UK

The Provision of Laboratory Data for EOR Simulation. . . . . . . . . . . . . . . . C. E. BROWN and G. 0. LANGLEY, BP Research Centre, Sunbury, UK

Experimental Study and Interpretation of Surfactant Retention in Porous Media . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . J. NOVOSAD, Petroleum Recovery Institute, Calgary, Canada

The EACN of a Crude Oil: Variations with Cosurfactant and Water Oil Ratio MIN KWAN THAM and P. B. LORENZ, US Department of Energy, Bartlesville, OK, USA

Dynamic Interfacial Phenomena Related to EOR. . . . . . . . . . . . . . . . . . . . J. H. CLINT, E. L. NEUSTADTER and T. J. JONES, BP Research Centre, Sunbury, UK

Behaviour of Surfactants in EOR Applications at High Temperatures . . . . . . L. L. HANDY, University of Southern California, Los Angeles, CA, USA

Surfactant Slug Displacement Efficiency in Reservoirs . . . . . . . . . . . . . . . . R. J. WRIGHT and R. A. DAWE, Imperial College, University of London, UK

Some Aspects of the Injectivity of Non-Newtonian Fluids in Porous Media. . . P. VOGEL and G. PUSCH, Institute. of Petroleum Engineering, Clausthal, West Germany

1

43

63

81

101

123

135

149

161

179

vi

11.

12.

13.

14.

15.

16.

17.

18.

19.

20.

Basic Rheological Behaviour of Xanthan Polysaccharide Solutions in Porous Media: Effects of Pore Size and Polymer Concentration . . . . . . . . . . . . . . . G. CHAUVETEAU and A. ZAITOUN, Institut Franqais du PCtrole, Rueil- Malmaison, France

The Chateaurenard (France) Polymer Flood Field Test. . . . . . . . . . . . . . . . A. LABASTIE, Elf Aquitaine, Boussens, Saint-Martory , France L. VIO, Elf Aquitaine, Centre de Recherche de Lacq, Artix, France

Caustic Flooding in the Wilmington Field, California, Laboratory Modelling and Field Results. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . V. S. BREIT, Scientific Software Corp., Denver, TX, USA E. H. MAYER, THUMS Long Beach Co, CA, USA J. D. CARMICHAEL, City of Long Beach Department of Oil Properties

MISCIBLE GAS DISPLACEMENT

Keynote Paper: “Miscible Displacement: Its Potential for Enhanced Oil Recovery” . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . R. J. BLACKWELL, Exxon Production Research, Houston, TX, USA

Theoretical Aspects of Calculating the Performance of COz as an EOR Process in North Sea Reservoirs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . D. S. HUGHES, J. D. MATTHEWS and R. E. MOTT, AEE Winfrith, Dor- Chester, Dorset, UK

A New Linear Displacement Model with Mass Transfer Between Phases, Adapted to C 0 2 Injection. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . C. JAIN, Institut Franqais du PCtrole, Rued-Malmaison, France (This paper will be distributed a t the Conference)

Oil Recovery by Carbon Dioxide, the results of Scaled Physical Models and Field Pilots. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T. M. DOSCHER, M. EL ARABI, S. GHARIB and R. OYEKAN, University of Southern California, Los Angeles, CA, USA

Laboratory Testing Procedures for Miscible Floods . . . . . . . . . . . . . . . . . . S. G. SAYEGH and F. G. MCCAFFERY, Petroleum Recovery Institute, Calgary, Canada

Complex Study of C 0 2 Flooding in Hungary . . . . . . . . . . . . . . . . . . . . . .

J. TOROK, Hungarian Hydrocarbon Inst., Szazhalombatta, Hungary

An Iterative Method for Phase Equilibria Calculations with Particular Appli- cation to Multicomponent Miscible Systems . . . . . . . . . . . . . . . . . . . . . . . N. VAROTSIS, A. C. TODD and G. STEWART, Heriot-Watt University, Edinburgh, UK

s. DOLESCHALL, G. ACS, v. BALINT, z. BIRO, E. FARKAS, T. PAAL,

197

213

223

237

247

n.a.

267

285

299

313

vii

2 1. Phase Equilibrium Calculations in the Near-Critical Region . . . . . . . . . . . . . 329 R. RISNES, Norsk Agip, Norway V. DALEN, J. I . JENSEN, Continental Shelf Institute, Trondheim, Norway

The Effect of Simulated COz Flooding on the Permeability of Reservoir Rocks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 351 G. D. ROSS, A. C. TODD and J . A. TWEEDIE, Heriot-Watt University, Edinburgh, UK

22.

NUMERICAL METHODS

23. Keynote Paper: “Computer Modelling of EOR Processes”. . . . . . . . . . . . . . 367 K. AZIZ, University of Calgary, Canada

24. Three-Dimensional Numerical Simulation of Steam Injection. . . . . . . . . . . . 379 P. LEMONNIER, Institut Frangais du PCtrole, Rueil-Malmaison, France

25. Special Techniques for Fully Implicit Simulators. . . . . . . . . . . . . . . . . . . . 395 J. R. APPLEYARD, I. M. CHESHIRE and R. K. POLLARD, Operatings Research Group, AERE Harwell, UK

Some Considerations Concerning the Efficiency of Chemical Flood Simulators 409 R. W. S. FOULSER, AEE Winfrith, Dorchester, Dorset, UK

27. Control of Numerical Dispersion in Compositional Simulation. . . . . . . . . . . 425 D. C. WILSON, T. C. TAN and P. C. CASINADER, Imperial College, Uni- versity of London, UK

Interphase Mass Transfer Effects in Implicit Black Oil Simulators. . . . . . . . . 441 D. BANKS and D.K. PONTING, AERE Harwell, Oxfordshire, UK

26.

28.

EXPERIMENTAL TECHNIQUES

29. A Novel Device for COz Flooding. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45 1 V. MEYN, Institute of Petroleum Engineering, Clausthal, West Germany

The Use of Slim Tube Displacement Experiments in the Assessment of Miscible Gas Projects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 467 B. J. SKILLERNE DE BRISTOWE, BP Research Centre, Sunbury, UK

Nuclear Measurements of Fluid Saturations in EOR Flood Experiments 483 N. A. BAILEY, P. R. ROWLAND and D. P. ROBINSON, AEE Winfrith, Dorchester, Dorset, UK

32. Characterisation of EOR Polymers as to Size in Solution . . . . . . . . . . . . . . 499

30.

31.

R. DIETZ, National Physical Laboratory, Teddington, UK

viii

33.

34.

35.

36.

37.

38.

39.

Visualization of the Behaviour of EOR Reagents in Displacements in Porous Media . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 511 E. G. MAHERS, R. J. WRIGHT and R. A. DAWE, Imperial College, Uni- versity of London, UK

THERMAL RECOVERY METHODS

Keynote Paper: “The Interplay Between Research and Field Operations in the Development of Thermal Recovery Methods” . . . . . . . . . . . . . . . . . . . 527 J. OFFERINGA, R. BARTHEL and J. WEIJDEMA, Shell Exploration and Production Laboratories, Rijswijk, Holland

U.S. Department of Energy R & D on Downhole Steam Generator for the Recovery of Heavy Oil . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 543 R. L. FOX, Sandia Laboratories, NM, USA J. J. STOSUR, U.S. Department of Energy, Washington, DC, USA

Steam Drive - The Successful Enhanced Oil Recovery Technology. . . . . . . . 549 T. M. DOSCHER and F. GHASSEMI, University of California, Los Angeles, CA, USA

Down Hole Steam Generation using a Pulsed Burner . . . . . . . . . . . . . . . . . 563 D. A. CHESTERS, C. J. CLARK, F. A. RIDDIFORD, BP Research Centre, Sunbury, UK

Hot Caustic Flooding. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 573 R. JANSSEN-VAN ROSMALEN and F. Th. HESSELINK, Shell Exploration and Production Laboratories, Rijswijk, Holland

UNITED STATES RESEARCH PROGRAMME

Enhanced Oil Recovery Research and Development in the United States and in the U.S. Department of Energy. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 587 J. J. G. STOSUR, U.S. Department of Energy, Washington, DC, USA

AUTHORINDEX . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 595

i x

FOREWORD

This r e s i d e n t i a l symposium i s the t h i r d i n the series of symposia which have been he ld on t h e s u b j e c t of enhanced o i l recovery ir, the United Kingdom; the o t h e r two being he ld a t Br i t ann ic House of BP i n London i n May 1977, and a t Heriot-Watt Univers i ty i n Edinburgh i n J u l y 1978.

Since 1977, when the f i r s t symposium was he ld i n London, t he annual product ion and the number of f i e l d s i n opera t ion i n t h e UK s e c t o r of t h e North Sea has roughly doubled and i t is perhaps r i g h t t o r e - i t e r a t e t he remarks of t h e Chairman of t he organis ing committee of t h e f i r s t meeting. H e s a i d t h a t , "There i s an urgent need t o dec ide which enhanced o i l recovery techniques a r e s u i t a b l e f o r use i n the North Sea. Once t h i s dec i s ion i s made, the s e l e c t e d R&D goa l s should be vigorously pursued, lead ing , hopefu l ly , t o t h e development of s p e c i f i c tailor-made techniques e f f e c t i v e i n t h e ind iv idua l f i e l d s i n t h e North Sea a rea" .

Although these remarks a r e s t i l l v a l i d today, i n the i n t e r - vening per iod throughout Europe s i g n i f i c a n t progress has been made. W e have seen an inc rease i n t h e number of p i l o t f i e l d experiments undertaken by t h e o i l indus t ry , an inc rease i n the research work c a r r i e d o u t a t u n i v e r s i t i e s , research i n s t i t u t e s and o i l company l abora to r i e s . A number of Government programmes have been i n i t i a t e d o r expanded. Against t h i s background of an increased R&D a c t i v i t y , some s i g n i f i c a n t , a l b e i t t e n t a t i v e , s t e p s i n the a p p l i c a t i o n of enhanced o i l recovery of fshore have been taken.

The cont inuing inc rease i n t h e p r i c e of o i l over t h e p a s t few years renders t h e t iming of t he p r e s e n t symposium t o be p a r t i c u l a r l y r e l evan t t o the ques t ion of improvement i n o i l recovery i n a l l t h e s e c t o r s of t h e North Sea and f o r t he provis ion of f u t u r e supp l i e s of energy t o Europe. The occasion of t h e p re sen t conference provides an i n t e r n a t i o n a l forum f o r research workers ins enhanced o i l recovery t o exchange information and t o develop an increased awareness of t he research s t u d i e s c u r r e n t l y being pursued elsewhere. I t is hoped t h a t new d i r e c t i o n s f o r research , app l i cab le t o the European Cont inenta l S h e l f , may become apparent and the f u t u r e adopt ion of enhanced o i l recovery techniques i n t h i s a r e a advanced.

This volume i s a c o l l e c t i o n of t he papers t o be presented and d iscussed a t the Symposium.

F J FAYERS Chairman, Organising Committee

September 1981

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CHEMICAL FLOODING 1

FUNDAMENTAL ASPECTS OF SURFACTANT-POLYMER FLOODING PROCESS

D. 0. SHAH

Department of Chemical Engineering and Anesthesiology, University of Florida, Gainesville, Florida 3261 I

ABSTRACT

Surfactant-polymer f l o o d i n g process o f f e r s a promising approach t o recover add i t i ona l o i l from the water f looded rese rvo i r s which may con- t a i n as much as 70% o f o r i g i n a l o i l - i n -p lace . The c a p i l l a r y number, which determines the microscopic displacement e f f i c i e n c y o f o i l , can be increased by 3 t o 4 orders o f magnitude by reducing the i n t e r f a c i a l ten- s ion (IFT) of o i l gangl ia below 10-3 dynes/cm. involved i n the m o b i l i z a t i o n and displacement o f o i l gangl ia are descr ibed inc lud ing the r o l e o f u l t r a l o w i n t e r f a c i a l tension, t he r o l e o f i n t e r f a c i a l v i s c o s i t y i n coalescence o f o i l gangl ia and formation o f t he o i l bank, the propagation o f the o i l bank, the surfactant-polymer incom- p a t i b i l i t y , the formation and f l o w o f emulsions i n porous media, the r o l e o f w e t t a b i l i t y as wel l as the i n f l uence o f surface charge dens i t y o f the r o c k / f l u i d i n t e r f a c e and o i l - b r i n e i n t e r f a c e i n o i l displacement e f f i - ciency. It i s shown t h a t t he re are two regions o f u l t r a - l o w IFT; 1) i n the low sur factant concentrat ion (0.1-0.2%) and the other i n the h igh su r fac tan t concentrat ion reg ion (2.0%-10.0%). I n the low concentrat ion systems, the u l t ra - l ow i n t e r f a c i a l tens ion occurs when the aqueous phase of the sur factant so lu t i on i s about the apparent c r i t i c a l m i c e l l e concen- t r a t i o n . And, the s a l i n i t y i s a t the c r i t i c a l e l e c t r o l y t e concentrat ion for the coacervation process. The m ig ra t i on o f sur factant from the aqueous phase t o the o i l phase v i a coacervation process appears t o be r e - sponsible f o r the u l t r a l o w i n t e r f a c i a l tension.

I n h igh sur factant concentrat ion systems, a middle phase microemul- s ion i n e q u i l i b r i u m w i th excess o i l and b r i n e forms i n a narrow s a l i n i t y range. T h e ' s a l i n i t y a t which equal volumes o f o i l and b r i n e are so lub i - l i z e d i n the middle phase microemulsion i s r e f e r r e d t o as the optimal s a l i n i t y o f the system. A t t he optimal s a l i n i t y , t he i n t e r f a c i a l tens ion a t both i n te r faces i s equal. Evidence i s presented t h a t the middle phase microemulsion a t the optimal s a l i n i t y i s a water external microemulsion formed due t o coacervation and subsequent phase separation o f m ice l l es f r a n the aqueous phase. a desired value by vary ing the s t ruc tu re and 'concentrat ion o f alcohol. The s h i f t i n optimal s a l i n i t y can be co r re la ted w i th the b r i n e s o l u b i l i t y o f the alcohol used i n a given su r fac tan t formulat ion. It was f u r t h e r observed t h a t the optimal s a l i n i t y increases w i th the o i l chain length. I n order t o form middle phase microemulsions at very h igh s a l i n i t y , ethoxylated sur factants o r alcohols can be incorporated i n t o a su r fac tan t formulat ion which can s h i f t the optimal s a l i n i t y t o as h igh as 32% NaCl concentrat ion. Such h igh s a l i n i t y formulat ions cons is t i ng o f petroleum sul fonates and ethoxylated su l fonates are r e l a t i v e l y i n s e n s i t i v e t o diva- 1 ent c a t ions.

Conceptual events

The optimal s a l i n i t y can be sh i f t ed t o

2

The coalescence r a t e o r the phase separation t ime was minimum at op-

The r a t e o f f l a t t e n i n g o f an o i l drop i n a sur factant f o r -

t imal s a l i n i t y . It was also observed t h a t the apparent v i s c o s i t y was minimal a t the optimal s a l i n i t y f o r the f l o w o f microemulsions through porous media. mulat ion increases s t r i k i n g l y i n the presence o f alcohol. It appears t h a t the presence o f alcohol promotes the mass t r a n s f e r o f su r fac tan t from the aqueous phase t o the i n te r face . The add i t i on o f alcohol also promotes the coalescence o f o i l drops, presumably due t o a decrease i n the i n t e r f a c i a l v i s c o s i t y .

t i o n o f a sur factant and polymer even i n the absence o f o i l . I n the presence o f o i l , the formation o f middle phase microemulsion i s promoted by the presence o f polymer i n the aqueous phase. The surfactant-polymer i n c o m p a t i b i l i t y i s explained i n terms o f excluded volume e f f e c t s and the maximization o f solvent f o r polymer molecules.

been discussed inc lud ing the use o f tm, d i f f e r e n t su r fac tan t slugs, two d i f f e r e n t polymer slugs, s a l i n i t y gradient design and the i n j e c t i o n o f an o i l bank t o promote o i l recovery.

The surfactant-polymer i n c o m p a t i b i l i t y can lead t o a phase separa-

Some novel concepts f o r surfactant-polymer f l ood ing process have

PRODUCTION

PRODUCTION WATER BANK WELLS

A B C D

Fig. 1 Schematic diagram o f an o i l rese rvo i r and the displacement of o i l by water o r chemical f looding.

3

A. INTRODUCTION

It i s wel l recognized t h a t the energy consumption per c a p i t a and the standard of. l i v i n g o f a soc ie ty are i n t e r r e l a t e d . o f energy, f o s s i l f u e l s o r crude o i l s p l a y an important r o l e i n prov id ing the energy supply o f t he world. It also serves as a raw mate r ia l f o r feed stocks i n chemical indust ry . I n view o f the worldwide energy c r i - sis, the importance o f enhanced o i l recovery t o increase the supply o f crude o i l i s obvious and var ious enhanced o i l recovery processes have been proposed and tested both on a l abo ra to ry scale and i n the f i e l d . For heavy o i l s , thermal processes have been used ex tens i ve l y whereas f o r l i g h t o i l s , chemical processes such as polymer f looding, caust ic f l ood - i ng , m i s c i b l e f 1 ood i ng and s u r f act ant-pol ymer f 1 oodi ng have a t t rac ted great i n t e r e s t . The major research f i n d i n g s i n the enhanced o i l recovery area have been repor ted i n recent l i t e r a t u r e and the symposia proceedings of var ious conferences dur ing the l a s t decade (1-11). focuses on the fundamental aspects o f the surfactant-polymer f l ood ing process and re1 ated phenomena.

Among various sources

The present paper

F igure 1 schemat ica l ly shows a three-dimensional view o f a petroleum

A t the end o f water-f looding, t he o i l t h a t remains i n the rese rvo i r

These o i l gangl ia are entrapped due

rese rvo i r .

i s be l ieved t o be i n the form o f o i l gangl ia trapped i n the pore s t r u c t u r e o f the rock as shown i n Figure 1A. t o c a p i l l a r y forces. However, i f a su r fac tan t so lu t i on i s i n j e c t e d t o lower the i n t e r f a c i a l tens ion o f the o i l gangl ia from i t s value o f 20-30 dynes/cm t o 10-3 dyneslcm, the o i l gangl ia can be mobi l ized and can move through narrow necks o f t he pores. Such mobi l ized o i l gangl ia form an o i l bank as shown i n F igure 16. Figures 1C and 1D schemat ica l ly show the o i l bank approaching the production wel l and the subsequent breakthrough o f t he d r i v e water. F igure 2 schemat ica l ly i l l u s t r a t e s a two- dimensional view o f the surfactant-polymer f l ood ing process.

PRODUCTION INJECTION S URFACTANT SLUG

--- -- - - - - - -

THICKENED FRESH

WATER

Fig. 2 Schematic diagram o f the surfactant-polymer f l ood ing process.

The su r fac tan t s lug i s fo l lowed by a polymer s lug f o r a proper m o b i l i t y c o n t r o l o f the process.

4

B. CAPILLARY NUMBER AND CONCEPTUAL ASPECTS OF THE PROCESS

Recently, i n an excel lent review a r t i c l e , Taber (12) has summarized various emperical dimensionless numbers proposed by several i nves t i ga to rs t o c o r r e l a t e the o i l displacement e f f i c i e n c y i n porous media. shows such a c o r r e l a t i o n reported by Foster (13) between the c a p i l l a r y number and res idua l o i l i n porous media.

F igu re 3

I 0 l 10 ~ 1 0 2 0 3 0 4 0 5 0 6 0

RESIDUAL OIL, PERCENT PORE VOLUME

Fig. 3 Dependence o f res idua l o i l sa tu ra t i on on C a p i l l a r y Number (Foster, W.R., J. Pet. Tech., p. 206, Feb. 1973).

The c a p i l l a r y number represents the r a t i o o f viscous t o c a p i l l a r y forces

! k e i i $ ? l i n g f l u i d , u i s the i n t e r f a c i a l tens ion and 4 i s t he pore volume). A t the end o f water f looding, the c a p i l l a r y number i s around 10-6 and t h i s number has t o be increased by 3 t o 4 orders o f magnitude f o r t e r t i a r y o i l recovery processes (14). condi t ions, the reduc i o n i n ' n t e r f a c i a l tens ion from a h igh value of 20 o r 30 dyneslcm t o 1 0 - i o r 10-4 dynes/cm o f f e r s such a p o s s i b i l i - ty. u l t r a - l o w i n t e r f a c i a l tens ion a t the o i l gangl ia /sur factant formulat ion i n te r face . tens ion i n promoting the mob i l i za t i on o f o i l gangl ia i n porous media. Subsequently, t he displaced o i l gangl ia must coalesce t o form an o i l bank. It i s known t h a t h igh i n t e r f a c i a l v i s c o s i t y r e s u l t s i n the format in o f s tab le emulsion (15).

uv/u+ where 11 and v are the v i s c o s i t y and v e l o c i t y of

Under p r a c t i c a l r e s e r v o i r

Therefore, the main func t i on o f t he su r fac tan t i s t o produce such an

F igure 4 schematical ly shows the r o l e o f u l t r a l o w i n t e r f a c i a l

For t h i s a very low i n t e r f a c i a l v i s c o s i t y i s des i rab le (F igure 5).

5

FOR THE MOVEMENT OF OIL THROUGH NARROW NECK OF PORES, A VERY LOW OIL / WATER

INTERFACIAL TENSION IS DESIRABLE z .OOl DYNES/CM

Fig. 4 Schematic diagran of the role of low interfacial tension in the surf actant-pol ymer flooding process.

SURFACTANT SLUG

4

DISPLACED OIL GANGLIA MUST COALESCE TO FORM A CONTINUOUS OIL BANK : FOR THIS A VERY LOW

INTERFACIAL VISCOSITY IS DESIRABLE

F i g . 5 Schematic diagran of the role of low interfacial viscosity in the surfactant-polymer flooding process.

Once an o i l bank is formed i n the porous medium, i t has to be propagated through the porous medium without increasing the entrapment of o i l at the t r a i l i ng edge of the oil bank. As shown in Figure 6 , the maintenance of ultralow interfacial tension at the o i l bank/surfactant/ slug interface i s essential for minimizing the entrapment of the oil i n the porous medium whereas the leading edge will coalesce with the o i l gang1 i a.

SURFACTANT " d Y

SLUG

COALESCENCE OF OIL GANGLIA WITH OIL BANK CAUSES FURTHER DISPLACEMENT OF OIL

F i g . 6 Schematic diagran of the role of coalescence of o i l ganglia i n the surf act ant-pol ymer flooding process.

6

Figure 7 schemat ica l ly i l l u s t r a t e s the movement o f the o i l bank, sur factant s lug and the m o b i l i t y con t ro l polymer s lug i n the porous med i um .

INTERFACES

t Since the f l o w i s through porous m e d i a , t h e e f f e c t o f dispersion for emulsif ication should b e minimized at a l l 3 interfaces. A l s o a v o i d the formation of high v i s c o s i t y structures i n the o i l - water - surfactant dispersions i n

SURFACTANT OIL SLUG

Fig. 7 Schematic i l l u s t r a t i o n o f t he e f f e c t s o f d ispers ion and emulsi- f i c a t i o n between the various slugs dur ing the sur factant -po lymer f l o a d i n g process.

Since the f l ow through the porous mediun causes d ispers ion o f these f l u i d s , emulsions w i l l be formed a t the o i l bank/surfactant s lug i n t e r - face and a mixed surfactant-polymer zone w i l l occur a t t he su r fac tan t - polymer so lu t i on i n te r face . High v i s c o s i t y - s t ruc tu res a t both these in te r faces should be avoided i n order t o improve the e f f i c i e n c y o f t h e process. the magnitude o f i n t e r f a c i a l tens ion (16). Trushenski (17) has shown t h a t surfactant-polymer i n c o m p a t i b i l i t y leading t o a phase separation o f sur factant and polymer s t r i k i n g l y reduces the e f f i c i e n c y o f t he process.

The mass t r a n s f e r o f su r fac tan t t o the o i l bank can in f l uence

PROPER CHOICE OF SURFACTANT CAN CHANGE@TO@

Fig. 8 The r o l e o f w e t t a b i l i t y and contact angle on o i l displacement.

7

Figure 8 schemat ica l ly i l l u s t r a t e s the r o l e o f w e t t a b i l i t y o f s o l i d surface on the o i l ganglia.

The choice o f su r fac tan t can in f l uence the w e t t a b i l i t y o f t he rock surface t o o i l and b r i n e (12).

Another parameter t h a t we have found (18, 19) t h a t in f luences the i n t e r f a c i a l tens ion and i n t e r f a c i a l v i s c o s i t y and o i l recovery i s t he sur face charge a t the o i l - b r i n e as wel l as rock-br ine i n te r faces . We found t h a t a h igh surface charge dens i t y leads t o a lower i n t e r f a c i a l tension, lower i n t e r f a c i a l v i s c o s i t y and higher o i l recovery (F igure 9).

High Surface Charge Densky

-Low Interfacial Tenslon - Low Interfacial Vicorlty - High Electrkal Repulsion

Between Oil Droplets (i Sand

'. . , .. . . ' .. . *... * . .*. ... * . . . . . . Low Surface Charge Density

,. . * a .

.Sand ....:.....' , High Interfacial Tension - High Interfacial V k 4 i t y -Low Ebctrical Repulsion

Between Oil Droplei a sand

Fig. 9 Schematic diagran o f the r o l e o f surface charge i n the o i l d i s - placement process.

The conceptual processes described i n Figures 3 t o 9 are supported by t h e r e s u l t s o f our s tud ies described i n the fo l lowing sections.

C. LOW SURFACTANT CONCENTRATION SYSTEMS

Figure 10 shows the i n t e r f a c i a l tens ion as a func t i on o f su r fac tan t concentrat ion i n a dodecane/brine system. '

It i s ev ident t h a t there are two reg ions o f u l t r a - l o w i n t e r f a c i a l tension (IFT). A t low sur factant concentrat ions, the system appears t o be a two-phase system, namely, o i l and b r i n e i n equ i l i b r i um w i t h each other, whereas a t h igh su r fac tan t concentrat ion systems (around 4 t o 8% su r fac tan t concentrat ion), a middle phase microemulsion e x i s t s i n e q u i l i b r i u n w i th excess o i l and br ine. microemulsion and r e l a t e d phenomena w i l l be discussed i n sect ion D.

The formation o f middle phase

0.11

0.05

0.01 '

0.005

0.001

0.0005

I I I 1 I I I I 0.0001 0.005 0.01

TRS 10-410 CONCENTRATION ( wt. %I Fig. 10 Effect o f surfactant concentration on the in ter fac ia l tension

of TRS 10-410 + IBA i n 1.5% NaCl with dodecane.

9

For low su r fac tan t concentrat ion systems, we have show t h a t t h e u l t r a l o w IFT occurs when su r fac tan t molecules migrate from the aqueous phase t o the o i l phase (19-21). F igure 11 shows the i n t e r f a c i a l t ens ion and the p a r t i t i o n c o e f f i c i e n t o f a su r fac tan t i n an octane/brine system. The u l t r a low IFT occurred around a p a r t i t i o n c o e f f i c i e n t o f u n i t y i n t h i s system (19,ZO). However, i t should be emphasized t h a t since the p a r t i t i o n c o e f f i c i e n t changes ab rup t l y i n t h i s reg ion the exact value o f p a r t i t i o n c o e f f i c i e n t can vary s i g n i f i c a n t l y around u l t r a l o w IFT. We be- l i e v e t h a t a reasonable conclusion i s t h a t lowering o f i n t e r f a c i a l ten- s ion i s observed when m ice l l es leave the aqueous phase due t o coacerva- t i o n process (19-23).

I (

5. \

c a e

$ 0

0 2

v) z W I- -1 2 ox d a

I W I-

0.W

0.W

SURFACTANT CON CENTRATION, 0.2%

-- -. \ \ .

0 5 1.0 15 2D 25 NoCl CONCENTRATION (wt.56)

Fig. 11 E f f e c t o f added e l e c t r o l y t e on i n t e r f a c i a l tens ion and surfac- t a n t p a r t i t i o n c o e f f i c i e n t o f t h e system O.TXTRS 10-80 + b r i n e + octane.

Since c m e r c i a l petroleum sul fonates i nvo l ve a d i s t r i b u t i o n o f molecular weights and isomeric s t ruc tu res we also Invest igated the i n t e r - f a c i a l tens ion using i s o m e r i c a l l y pure sulfonates. F igure 12 shows the IFT behavior as a f u n c t i o n o f s a l i n i t y , o i l 'chain length and su r fac tan t concentrat ion using petroleum sul fonates (TRS 10-80 o r TRS 10-410 and an i somer i ca l l y pure su r fac tan t UT-1). and o i l chain length e f f e c t s were s i m i l a r f o r both these classes o f sur-

It i s evident t h a t both the s a l i n l t y

10

PETROLEUM SULFONATES:

ISOMERICALLY PURE ALKYL BENZENE SULFONATES:

Fig. 12 Schematic diagram o f the e f f e c t o f s a l t concentrat ion, o i l chain length and su r fac tan t concentrat ion on the i n t e r f a c i a l tens ion o f pure and impure a1 k y l benzene sulfonates.

factants, namely, t he re i s a s p e c i f i c s a l i n i t y and s p e c i f i c o i l chain length where we ob ta in an u l t r a l o w IFT. However, the e f f e c t o f surfac- t a n t concentrat ion on IFT was d i f f e r e n t f o r commercial and i s o m e r i c a l l y pure sur factants . served t h a t the u l t r a low IFT appears when the aqueous phase i s a t t h e apparent anc f o r the sur factant remaining i n the aqueous phase. These conclusions were i n aggreement w i th osmotic pressure, l i g h t s c a t t e r i n g and spectroscopic measurements on the e q u i l i b r a t e d aqueous phase (22).

For low sur factant concentrat ion systems, we also ob-

F igure 13 i s a general ized diagran showing the IFT, phase behavior and the two c r i t i c a l e l e c t r o l y t e concentrat ions f o r both pure and ctmwner- c ia1 sur factants a t low as we l l as h igh su r fac tan t concentrat ions. By d i r e c t analys is o f sur factant concentrat ions i n each phase, we found (21) t h a t t he s a l i n i t y a t which su r fac tan t molecules leave the aqueous phase i s lower than the s a l i n i t y a t which they enter t he o i l phase. Thus, we de f ine two c r i t i c a l e l e c t r o l y t e concentrat ions, namely, CEC1, and CEC2, t o represent the e l e c t r o l y t e concentrat ions a t which the sur- f ac tan t concentrat ion begins t o decrease i n the aqueous phase and begin t o increase i n the o i l phase respect ive ly . We f u r t h e r observed t h a t t he minimun i n t e r f a c i a l tens ion occurs i n the v i c i n i t y o f t he f i r s t c r i t i c a l e l e c t r o l y t e concentrat ion. m a y p r e c i p i t a t e o r may form a coacervate phase below the aqueous phase o r i n between the aqueous and the o i l phase depending upon i t s dens i t y (21).

I n between CECl and CEC2, the su r fac tan t

11

I n low concentrat ion systems, i t i s poss ib le t h a t an extremely small volume o f middle phase may e x i s t between the o i l and b r i n e phases even though i t may not be v i s i b l e . This suggestion i s i n agreement w i th observat ion t h a t the volume o f the middle phase microemulsion increases l i n e a r l y w i th the sur factant concentrat ion and the s t r a i g h t l i n e passes through the o r i g i n (24). It should be emphasized tha t the general behav ior and i n t e r - r e l a t i o n s h i p shown i n F igure 13 i s v a l i d f o r both commerc ia l and i s o m e r i c a l l y pure sur factants (21).

Fig.

NaCl CONCENTRATION

Generalized d i a g r m o f the e f f e c t o f s a l t concentrat ion on sur- f a c t a n t p a r t i t i o n i n g , phase behavior and i n t e r f a c i a l tension.

F igure 14 shows the e f f e c t o f o i l chain length on CEC and CEC2 i n Aerosol OT/br ine/o i l systems. creases w i t h o i l chain length u n t i l i t reaches the c r i t i c a l o i l chain length (C11) above which the value o f CECl remains constant. t h e other hand, CEC2 continues t o increase w i th the o i l chain length. I n te res t i ng l y , we observed t h a t the u l t r a l o w IFT on ly occurs f o r o i l chain lengths below the c r i t i c a l o i l chain length (< C11), whereas the i n t e r f a c i a l tens ion remains h igh for o i l s above the c r i t i c a l o i l chain length (21).

ab le t o s o l u b i l i z e i n the m ice l l es whereas the o i l s having chain length above the c r i t i c a l o i l chain length are unable t o s o l u b i l i z e i n the m i c e l l a r so lu t i on . c e l l e s i s an important requirement f o r producing u l t r a l o w IFT. extensive s tud ies on i n t e r f a c i a l tens ion and p a r t i t i o n i n g o f sur factant i n r e l a t i o n t o many parameters, we have proposed the f o l l o w i n g 5 necessa- r y condi t ions t o achieve u l t r a l o w IFT's.

It i s evident t h a t the EEC! i n -

On

We propose t h a t a l l the o i l s below the c r i t i c a l o i l chain length are

Thus, i t appears t h a t s o l u b i l i z a t j o n o f o i l w i t h i n the m i - From our

12

Fig. 14

Fig. 15

E f fec t of o i l chain length on the f i r s t and second c r i t i c a l e l e c t r o l y t e concentrations of Aerosol OT.

O/o AOT I BRINE I OIL

0 DODECANE 0 TETRADECANE A HEXADECANE

I I

1 2 3

Ef fec t of o i l chain length on the i n t e r f a c i a l systems 1.0% AOT/brine/oil .

NaCl CONCENTRATION (Wt. '/o)

tension o f t h e

13

The to ta l surfactant concentration should be appreciably above the apparent anc i n the aqueous phase.

The surfactant should be soluble i n both the aqueous and the hydrocarbon phase.

Micel les i n the aqueous phase should be able t o so lub i l i ze o i l from the hydrocarbon phase.

The aqueous phase s a l i n i t y should be near the f i r s t c r i t i c a l electro- l y t e concentration (CECI).

There should be a large slope i n the surfactant pa r t i t i on coef f i c ien t curve i n the region o f the ul t ra low IFT. (i.e. a steep pa r t i t i on co- e f f i c i e n t curve fo r surfactant).

0)

- - o

E < 8 -

$ : I =,

i

=! m

0

t 7 .

0

6 -

I- W p 5 - n a 0

I-

-1 W

SPONTANEOUS EMULSIFICATION A

E 4 -

/ 3 -,/

2 -

I -

3 0.005 0.0004 0.002 0.004 0.02 0.04 . 0.2 0.4 2 4

SODIUM HYDROXIDE (NaOH) CONCENTRATION ( w t . % )

Fig. 16 A correlat ion between in te r fac ia l tension and electrophoretic mob i l i t y fo r crude oil-NaOH solutions.

14

Figure 16 shows the correlation of interfacial tension with electrophoretic mobility in crude oil /caustic systems (18,19,25,26). observed for several crude o i l s that the u l t ra low IFT occurs in the r e - gion where the electrophoretic mobility is maximum. This suggests that the maximun in surface charge density coincides w i t h the m i n i m u m i n i n - terfacial tension. T h i s correlation was also observed for the effect of sa l in i ty and surfactant concentration (19). i l l u s t r a t e s 3 components of the interfacial tension, namely, 1 ) surface concentration of the surfactant, 2) surface charge density, and 3) mutual solubilization of o i l and brine. We propose that by a d j u s t i n g any of these variables one can influence the magnitude of interfacial tension.

broaden and lower the magnitude of interfacial tension as well as increase the s a l t tolerance limit of the surfactant formulation;

We have

Figure 17 schematically

Using the conceptual approach shown i n Figure 17, we were able to

dyneskm

Fig. 17 A schematic i l lus t ra t ion of the factors affecting the magnitude of the interfacial tension.

Figure 18 shows the interfacial tension of a petroleum sulfonate TRS 10-410/n-octane/brine system when gradually the petroleum sulfonate i s replaced w i t h an ethoxylated phosphate e s t e r (Klearfac AA-270).

The Klearfac AA-270 containing a phosphate group possesses two ionic oxygen atoms and hence can generate a high surface charge density a t the interface. This presumably i s responsible for lowering the magnitude of IFT and broadening the sa l in i ty range over which the ultralow IFT occurs for the mixed surfactant systems (27) .

a ae v

2

N ON*W

co 5

99

99

9

OO

QO

0 c

y

++

++

+ II

i' oww e N F

k N

."' ..

. - '0

.- al

00

00

0 \

F

L

Y I

I I

1 I

7

N

*I

I *

c

0

0

15

W

,--

* 7 !2 D

Fig . 18 An i l l u s t r a t i o n o f the reduction and broadening o f the minimum i n i n t e r f a c i a l tension by the addit ion o f Klearfac AA-270.

16

D. HIGH SURFACTANT CONCENTRATION SYSTEMS AND THE OPTIMAL SALINITY

Many su r fac tan t formulat ions e x h i b i t extreme f low o r s t a t i c b i re f r i ngence i n a given s a l i n i t y range o r i n a given temperature range. Often these o p t i c a l l y an i so t rop i c formulat ions e x h i b i t u l t r a l o w IFT w i t h o i l . i n t e r e s t i n understanding the changes i n molecular associat ions occu r r i ng i n these systems.

Figures 19-21 i l l u s t r a t e the m ic ros t ruc tu re o f a b i r e f r i n g e n t sur factant formulat ion cons is t i ng o f 5% TRS 10-410 + 3% isobutanol and 2% NaCl br ine.

The m ic ros t ruc tu re o f such b i r e f r i n g e n t formulat ions should be o f

Fig. 19 Freeze-fracture e lec t ron micrograph o f t he an iso t rop i c system 5% TRS 10-410 + 3% Isobutanol + 2% NaCl (85501 x).

The f reeze- f racture e lec t ron microscopic technique used t o ob ta in these p i c t u r e s i s be l ieved t o preserve the m ic ros t ruc tu re o f the sanples due t o the very r a p i d coo l i ng r a t e (24). These e lec t ron micrographs c l e a r l y i n d i c a t e t h a t the b i r e f r i n g e n t formulat ions cons is t o f bubbles f i l l e d w i t h ' b r i n e and separated f r a n each other by a t h i n su r fac tan t membrane. F igure 21 c l e a r l y shows the s t r u c t u r e o f t h i s membrane cons is t i ng o f several t h i n layers. The dimension o f each laye r i s c lose t o a sur fac- t a n t b i l a y e r (approximately 70A). Therefore, I t appears t h a t when the s a l i n i t y i s increased i n the su r fac tan t formulation, t he su r fac tan t molecu les form the m u l t i l a y e r s t r u c t u r e wh i l e keeping t h e i r po la r groups i n contact with b r i n e and form such c e l l s o r f o m l i k e s tab le s t ruc tu re . We have c a l l e d these s t ruc tu res b i r e f r i n g e n t c e l l u l a r f l u i d s (24).

17

Fig. 20 Freeze-fracture electron micrograph o f the above system at 18,OOOX.

Fig. 21 Freeze-fracture electron micrograph of the above system at 30, OOOX .

18

Figure 22 shows the s i m i l a r i t y between coacervation o f a m i c e l l a r s o l u t i o n i n the absence o f o i l and the formation o f a middle phase microemulsion i n the presence o f o i l . The lower p a r t o f F igu re 22 shows t h e t r a n s i t i o n o f a b i r e f r i n g e n t su r fac tan t formulat ion t o an i s o t r o p i c coacervate phase upon add i t i on o f s a l t . formulat ion i n the presence o f an equal volume o f dodecane shows the formation o f lower phase, middle phase and upper phase microemulsions. We propose t h a t the middle phase microemulsion i s s i m i l a r t o the coacer- vated phase conta in ing some s o l u b i l i z e d o i l . Addi t ional s tud ies i n support o f these models have been repor ted elsewhere (21, 23, 24).

(x, the other hand, the same

Fig. 22 A comparison o f coacervation i n aqueous s o l u t i o n with middle phase format i o n i n s u r f act an t /o i 1 / b r i ne/al coho1 systems.

19

Figure 23 schemat ica l ly shows the mechanism o f formation o f middle phase microemulsions as s a l i n i t y i s increased.

@ oil swollen micelles (microdraplets of oil)

0 reverse micelles (microdroplets of water 1

I 2 3 4 5 6 7

Fig. 23 A schematic i l l u s t r a t i o n o f t he l + m + u t r a n s i t i o n f o r t he TRS

As one increases the s a l i n i t y , t he anc decreases, the aggregation number o f the m ice l l es increases and the s o l u b i l i z a t i o n o f o i l w i t h i n m ice l l es increases. The compression o f the e l e c t r i c a l double l aye r around m i - c e l l e s w i l l occur, hence reducing the repu ls i ve forces between the m i - c e l l e s . Thus the reduct ion i n the repu ls i ve forces and increase i n the a t t r a c t i v e forces between the m ice l l es w i l l b r i n g the m ice l l es c lose r and u l t i m a t e l y lead t o a separation o f a m i c e l l e r i c h phase forming the middle phase microemulsion. Upon f u r t h e r increase i n s a l i n i t y , the solu- b i l i z a t i o n o f o i l i n t h i s middle phase increases whereas t h a t o f b r i n e decreases. The magnitude o f i n t e r f a c i a l tens ion o f t he middle phase w i t h o i l o r b r i n e depends upon the extent o f s o l u b i l i z a t i o n o f o i l and b r i n e i n the middle phase. I n general, t he h igher the s o l u b i l i z a t i o n o f oi.1 o r b r i n e i n the middle phase microemulsion, t he lower i s t he i n t e r f a c i a l tens ion w i th respect t o these excess phases (28). The s a l i n i t y a t which equal volumes o f o i l and b r i n e are s o l u b i l i z e d i n the middle phase microemulsion i s r e f e r r e d t o as optimal s a l i n i t y f o r the su r fac tan t -o i l - b r i ne systems under given phys ica l chemical condi t ions (29, 30).

F igure 24 shows the f reeze - f rac tu re e lec t ron micrograph o f a middle phase microemulsion formed i n the system ex tens i ve l y s tud ied by Reed and Healy (28-30). It c l e a r l y shows the d i s c r e t e spher ica l s t ruc tu res embedded i n a con- t inuous aqueous phase consis tent w i th the mechanism proposed i n F igure 23. It should be pointed out t h a t o ther i qves t i ga to rs (40-47) have proposed the p o s s i b i l i t y o f bicontinuous s t r u c t u r e o r t he coexistance o f o i l external and water external microemulsions i n the middle phase. I n very h igh su r fac tan t concentrat ion systems, (15-20%) the existence o f anama- lous s t r u c t u r e which are ne i the r conventional water external o r o i l ex- t e r n a l microemulsions have been proposed t o a.ccount f o r some unusual pro- p e r t i e s o f these systems (43-46).

10-410/Isobutano1/0il /Br ine System.

F igure 25 shows t h a t the t r a n s i t i o n l + m - c u i s not on l y achieved by increas ing the s a l i n i t y but i s also poss ib le by changing any o f t he other 8 var iab les.

20

Fig. 24 Freeze-fracture electron micrograph of the middle phase o f the Exxon system at the optimal salinity.

U Oil m

m m

Brine

D Parameter Increasing

The transition I - m --c u occurs by:

1. Increasing Salinity 2. Decreasing oil chain length 3. Increasing alcohol concentration (C,, C,, C, ) 4. Decreasing temperature 5. Increasing total surfactant concentration 6. Increasing brine/oil ratio 7. Increasing surfactant solution/oil ratio 8. Increasing molecular weight of surfactanf

Fig. 25 Schematic illustration of the factors influencing the l + m + u transit ion in surf act ant /oi 1 /bri ne/al coho1 systems.

21

Thus, by choice of a suitable parameter, one can obtain the transit ion i n the structure of these microemulsions. A t optimal sa l in i ty , the partition coefficient of surfactant i n the excess o i l and brine phases i s found to be near unity and the interfacial tension between the excess oil and excess brine is also m i n i m u n (19).

The importance of the optimal s a l in i ty concept for enhanced oil recovery i s shown in the data i l lus t ra ted in Figure 26.

SURFACTANT SLUG =O.OS P.V.

FLOODING RATEm2.3 ft/day DOW PUSHER 700:

SALINITY, NaCl w t 70

Fig. 26 Effect of s a l in i ty on the capillary number and t e r t i a ry oil recovery i n sand packs.

I t i s evident that the o i l recovery is maximum at optimal s a l in i ty for the systems reported here. An excellent correlation between the capillary number and oil recovery i s also evident from Figure 26 (48). view of this observation, the surfactant formulation for a practical application should be designed such that the reservoir s a l in i ty becomes the optimal s a l in i ty under the given reservoir conditions.

In

Figure 27 shows the effect of o i l chain length on optimal sa l in i ty of the TRS 10-410 + isobutanol systems (49) and the corresponding interfacial tension at the optimal s a l in i ty for dach o i l chain length. I t was observed that as the o i l chain length increases, the optimal s a l in i ty i n - creases and the volume of the middle phase decreases. The range over which the middle phase microemulsion exists also increases as the o i l

22

Fig. 27

chain length increases. It should be pointed out t h a t from extensive studies on mixed a1 kanes, the concept o f -Equivalent A1 kane Carbon Number (EACN) has been proposed t o c o r r e l a t e the i n t e r f a c i a l tens ion o f pure alkanes w i th those o f the mixtures (50). Many l i g h t crude o i l s have been simulated by the mixtures o f pure hydrocarbons (51). Most l i g h t o i l s o r t h e EACN f o r most l i g h t crude o i l s were found t o be between C7 and c11.

Figure 28 shows the c o r r e l a t i o n o f optimal s a l i n i t y i n the presence o f various alcohols w i th t h e i r s o l u b i l i t y i n br ine. F igu re 28 sumnarizes the data obtained by three research groups (49,52, 53). It i s i n t e r e s t i n g t h a t the optimal s a l i n i t y o f a given o i l and sur- f ac tan t formulat ion l i e s near the i n t e r s e c t i o n o f the b r i n e s o l u b i l i t y . This c o r r e l a t i o n suggests t h a t i f one determines the optimal s a l i n i t y i n the presence o f 2 o r 3 alcohols, one can p r e d i c t the optimal s a l i n i t y i n the presence o f o ther alcohols from t h e i r b r i n e s o l u b i l i t y data. This i s a very usefu l c o r r e l a t i o n and e l iminates the t i m e consuming and labor ious procedure o f ob ta in ing the optimal s a l i n i t y i n the presence o f each alcohol.

E. TRANSIENT PROCESSES

There are several t r a n s i e n t processes, such as the formation and coalescence o f drops as we l l as t h e i r f l o w through porous media, t h a t a re l i k e l y t o occur i n the surfactant-polymer f l ood ing process. shows the coalescence o r phase separation t i m e o f handshaken and sonicated macroemulsions as a func t i on o f s a l i n i t y .

F igure 29

F i g . 27 E f f e c t o f o i l chain length on t h e optimal s a l i n i t y and i n t e r - f a c i a l tension a t the optimal s a l i n i t y .

Surfoclont 50% TRS 10-410 40% Amoco A A - Sulfonate

Alcohol 3 0 % 0 7 %

Brine Variable NoCl Vorioble N o C l

01 I Dodecone Wyomlng Crude O i l

WOR I 0 I 0

Ref Shah ond Hsleh, SPE 6594 Salter. SPE 6843

1.5 % Xylene Sulfonate

0. 5 %

Variable N a C l

90/10 lsopor M / H A N

I .o Puerto and Gale, SPE 5814

BRINE SALINITY ( w t % NoCl 1 B R I N E SALINITY ( w t % doc1 I BRINE S A L I N I T Y ( u t % No CI I

F i g . 28 A c o r r e l a t i o n o f optimal s a l i n i t y i n t h e presence of various alcohols wi th t h e i r s o l u b i l i t y i n br ine . N

W

2 4

16C

12c

8C E

w

l- E

4c

C

0

SONICATEO

2 4 6 SODIUM CHLORIDE CONCENTRATION, (b1T.X)

8

F i g . 29 Ef fect o f s a l i n i t y on the phase separation o r coalescence r a t e o f sonicated and hand-shaken emulsions.

25

I t i s obvious that minimal phase separation time or the f a s t e s t coalescence ra te occurs at the optimal s a l i n i t y (54) . The rapid coalescence could contribute significantly to the formation of an oil bank from the mobilized oil ganglia. This also suggest that at the optimal s a l in i ty the interfacial viscosity must be very low to promote the rapid coalescence.

sions prepared at various sa l in i t i e s flow through i t . I t is evident that the minimum pressure drop occurs at and around the optimal sa l in i ty of the surfactant formulation. T h i s also suggests that the interfacial tension is an important factor influencing the pressure drop across porous media (54 ) .

Figure 30 shows the pressure drop across a porous medium hhen emul-

L SONICATED EMULSION CONTAINING

EQUAL VOLUME OF DODECANE AND

AQUEOUS PHASE : TRS 10 -410 + IBA (5:3 W/W)

/ t + NaCl +WATER

EMULSION FLOW RATE QE (rnl/rnin)

Effect of s a l in i ty on the pressure drop-flow ra t e curves of soni cated emu1 sions.

Fig. 30

2 6

Figure 31 shows a very interesting and important correlation between the coalescence ra te in enulsions and the apparent viscosity i n the flow through porous media. emulsions in porous media coincides with minimum phase separation time a t the optimal sa l in i ty .

The minimun apparent viscosity for the flow of

SYSTEM: SONICATED EMULSION CONTAINING

TRS 10-410 t IBA(5:3 W/W) t WATER 30 + NaCl (x%) AND EQUAL VOLUME OF DODECANE 1

01 I I I I I I I 0 2 4 6

NaCl CONCENTRATiON (WT. %)

F i g . 31 A correlation between the apparent viscosity and coalescence ra te of sonicated emulsions.

This correlation between the phenomena occurring in porous media and outside the porous medium allows us to use coalescence measurements as a screening criterion for many surfactant formulations for their possible behavior i n porous media. I t i s l ike ly that a rapidly coalescing mul- sion will give a lower apparent viscosity for the flow i n porous media ( 5 4 ) .

27

Figure 32 sumnarizes a l l the phenomena occurr ing a t t he optimal s a l i n i t y i n r e l a t i o n t o enhanced o i l recovery by surfactant-polymer f l ood ing .

Oi I Recovery Efficiency

I

Apporent viscosity (or AP) of yp emulsions in porous media

Coolescence or phase-seporotion time of emulsions

Surfoctont loss in Porous Media

vo Solubilirotion of Oil and Brine in m+ microemulsions

v x v w * lnterfociol tension

Ymo VW OPTIMAL SALINITY

I / SALl NlTY -

Fig. 32 A sumnary o f var ious phenomena occurr ing a t t he optimal s a l i n i - ty i n r e l a t i o n t o enhanced o i l recovery by surfactant-polymer f l o o d i n g .

It i s ev ident t h a t the maximum i n o i l recovery e f f i c i e n c y co r re la tes we l l with t r a n s i e n t and equilibrium p roper t i es o f su r fac tan t -o i l - b r i ne systems. I n our p re l im ina ry studies, we have found t h a t t he su r fac tan t l o s s i n porous media i s also minimum a t t he optimal sa l i h , i t y presumably due t o reduc t i on i n the entrapment process f o r the sur factant phase. Therefore, the maximum i n o i l recovery at optimal s a l i n i t y might be a combined e f f e c t o f a l l these processes tak ing place a t the optimal s a l i n i t y .

Since optimal s a l i n i t y leads t o favorable condi t ions f o r optimal o i l recovery, one would l i k e t o design approaches t o a l t e r the optimal s a l i - n i t y o f a given su r fac tan t formulat ion (55-57). optimal s a l i n i t y of a mixed su r fac tan t formulat ion cons is t i ng of a pet ro- leum sut fonate and ethoxylated su l fona te (EOR-200).

Figure 33 shows the

2 8

I 1 I

SURFACTANT FORMULATION: TRS 10-410 t EOR-200 t ISOBUTANOL

5.00/0 3.0%

4

2

€OR-200 I ' C 0 4 3 2 I SURFACTANT CONCENTRATION wt.%

TRSIO-410 5

I 1 1 I

I 2 3 4

Fig. 33. Increase i n the optimal s a l i n i t y o f sur factant formulat ion by add i t i on o f EOR-200.

As one replaces petroleum sul fonates w i th the ethoxylated su l fona te t h e optimal s a l i n i t y increases and can reach as h igh as 32% NaCl br ine. I n te res t i ng l y , these formulat ions when e q u i l i b r a t e d with o i l produced middle phase microemulsions having very low i n t e r f a c i a l tension. Thus, the mixed su r fac tan t formulat ions conta in ing p e t r o l e m sul fonates and ethoxylated su l fonates o r alcohol are promising candidates f o r h igh s a l i n i t y formulat ions ( 5 5 , 5 6 ) .

Figure 34 shows the shape o f an o i l drop upon contact ing a sur fac- t a n t formulat ion cons is t i ng o f 0.05% TRS 10-80 i n 1% NaCl. It i s e v i - dent t h a t as su r fac tan t molecules migrate from the aqueous phase t o the i n t e r f a c e and subsequently t o the o i l phase the i n t e r f a c i a l tens ion decreases and the spher ica l drop g radua l l y f l a t t e n s out. This f l a t t e n i n g

29

Fig. 34. An i l l u s t r a t i o n o f t he drop f l a t t e n i n g phenomenon f o r a drop of octane i n an e q u i l i b r a t e d s o l u t r i o n o f 0.05% TRS 10-80 I n 1% NaCl .

time r e f l e c t s the r a t e a t which molecules accumulate a t the o i l - b r i n e i n te r face . As shown i n Table 1, there i s a good c o r r e l a t i o n between the f l a t t e n i n g time, IFT and the o i l recovery. The reduct ion i n the f l a t t e n - i n g t ime leads t o favorable o i l recovery ef f ic iency (16,48).

30

TABLE 1

IFT, Flattening Time,and O i l Recovery Efficiency of 0. 052TRS 10-80 in I% NaCl vs. n-octane at 25OC

SYSTEM IFT FLATTENING TIME* OIL RECOVERY+ ( m i m ) (seconds) (%OIP)

1. Fresh Oi l l l% NaCl ~50.8* * 00

II. FreshOillEquili- brated Surfactant 0.731 6600 Solution

I i 1. Fresh OillFresh Surfactant Solution

IV. EquilibratedOill% a 121 NaCl

V. Equilibrated Oi l /

0.627 480

900

Equilibrated Surfac- 0.0267 240 tant Solution

VI. EquilibratedOill Fresh Surfactant aOO209 15 Solution

61 -63

44-52

15-11

83

w

*Flattening time i s defined as the time required for the n-octane drop to gradually flatten out

* *OctanelH@, 20' C, IFT = 50.8 mNlm, "Interfacial Phenomenb', Davies and Rideal, Chapter 1, p. 17 Table I, Academic Press, N.Y. 1963.

San@ck dimension9 1. W' dia x 7" long: Permeability= 3 darcy: flow rate: 2.3 f t /day.

+

I n general, a su r fac tan t formulat ion f o r enhanced o i l recovery i n - cludes a shor t chain alcohol. The poss ib le e f f e c t o f alcohol can be t h e change i n v i scos i t y , lowering o f the i n t e r f a c i a l tension, reduc t i on i n i n t e r f a c i a l v i s c o s i t y o r change i n su r fac tan t p a r t i t i o n i n g and modifying the s o l u b i l i t y o f su r fac tan t i n o i l o r b r i n e phase. I n te res t i ng l y , we have observed t h a t the presence o f alcohol has a much more s t r i k i n g effect on the f l a t t e n i n g t i m e o f an o i l drop i n the presence o f a sur fac- t a n t formulation. As shown i n Table 2 i t compares the many i n t e r f a c i a l proper t ies, f l a t t e n i n g t i m e and o i l recovery e f f i c i e n c y i n the presence and absence o f alcohol (16). It i s evident t h a t the f l a t t e n i n g t ime decreases s t r i k i n g l y i n the presence o f alcohol suggesting t h a t t he a lcohol promotes the mass t r a n s f e r t o the i n t e r f a c e and a r a p i d reduc t i on i n the magnitude o f the i n t e r f a c i a l tension.

There are also t ime dependent changes i n the surface p roper t i es of a surfactant formulat ion. o r changes i n the aggregation process o f m ice l l es (60). Several i n v e s t i - gators have show t h a t the i n t e r f a c i a l tens ion changes w i th t i m e (61). We have also shown t h a t using several phys ica l techniques t h a t molecular assoc iat ion also changes w i th t i m e leading t o the aging e f f e c t s o f the sur factant formulation (58). o f months o r years.

This inc lude the chemical degradation (58,59),

The aging processes may occur over a per iod


32

F. SURFACTANT-POLYMER INCOMPATIBILITY

Trushenski (17) has shown t h a t surfactant-polymer i n c o m p a t i b i l i t y can lead t o a considerable reduc t i on i n the e f f i c i e n c y o f the process. The surfactant-polymer i n c o m p a t i b i l i t y manifests i t s e l f as a phase sepa- r a t i o n and a l t e r a t i o n o f the v i s c o s i t y o f t he separated phases. The entrapment o f the h igh v i s c o s i t y phase w i l l e f f e c t i v e l y remove t h a t component from the f l o o d i n g process. The mix ing o f the sur factant and polymer i n the porous medium occurs due t o both d ispers ion e f f e c t s as w e l l as excluded volume e f f e c t s f o r the f l o w o f polymer molecules i n porous media.

F igure 35 shows the e f f e c t o f mixing sur factant and a polymer solu- t i o n i n the absence o f o i l .

Fig. 35. E f f e c t o f add i t i on o f polymer on t he phase behavior o f aqueous s u r f actant so lu t ions.

It i s evident t h a t there are tho regions o f phase separation, one a t low s a l i n i t y and the other a t h igh s a l i n i t y separated by a metastable c o l l o i - da l dispersion. We r e f e r t o the separation a t the lower s a l i n i t y as r e - g ion 1 and those a t h igh s a l i n i t y as reg ion 2. The separation o f a sur- f ac tan t - r i ch phase i n r e g i o n 2 i s s i m i l a r t o t h a t i n coacervation process, h e r e a s the separation o f m ice l l es i n reg ion 1 i s induced by the presence o f po l ymer molecules. The s u r f act ant -polymer i ncompat i b i 1 i ty shows up s t r i k i n g l y i n the formation o f reg ion 1 (62).

The add i t i on o f polymer t o an oillbrinelsurfactantlalcohol system shows t h a t the format ion o f middle phase microemulsion i s promoted by the presence o f polymer (F igure 36). However, the t r a n s i t i o n middle phase t o upper phase microemulsion i s not in f luenced a t a l l by the presence o f polymer. We have f u r t h e r show (62,63) t h a t t he optimal s a l i n i t y i s n o t s i g n i f i c a n t l y in f luenced by the presence o f polymer i n the o i l l b r i n e l s u r - f ac tan t l a l coho l system.

33

1 . 0

0.8

0.6

0.4

0.2

0.0

Polymer Concentration 5% W/V TRS 10-410 - 3% w/v I B A

- O i l : n-dodecane (MOR=l .O)

2500 ppm - - - -

1500 ppm

1.0

0.8

0.6

0.4

0.2

0.0

Fig. 36. Effect of polymer concentration on the s a l i n i t y range for formation of middle-phase microemulsion.

- - - - - -

I I I I 1 I I

Figure 37 shows the schematic explanation of the surfactant polymer incompati b i 1 i t y and concomittant phase separation.



36

surfactant slug i n porous media i s l a r g e l y determined by the s a l i n i t y o f t he polymer s o l u t i o n (65). For b e t t e r m o b i l i t y con t ro l and minimal surfactant loss a two-slug design o f a su r fac tan t formulat ion was employed (23). In t h i s design, the f i r s t sur factant s luq has an optimal s a l i n i t y c lose t o the connate water s a l i n i t y and the second su r fac tan t s lug has a much lower optimal s a l i n i t y . The polymer so lu t i on s a l i n i t y i s made equal t o the optimal s a l i n i t y o f the second su r fac tan t slug. With t h i s design, h igh o i l recovery i n berea cores can be obtained even i n the presence of h igh s a l i n i t y (6% NaCl + 1% calc ium c h l o r i d e ) connate water.

e f f e c t o f m o b i l i t y c o n t r o l and su r fac tan t d ispers ion and entrappment i n porous media (65). mer so lu t i ons employs two slugs o f polymer so lu t i ons i n which the f i r s t polymer s lug i s a t the optimal s a l i n i t y o f the preceeding su r fac tan t f o r - mulat ion and the second polymer s lug i s a t a much lower s a l i n i t y .

The optimal s a l i n i t y concept i s f u r t h e r extended t o inc lude t h e

The proposed s a l i n i t y shock design o f m o b i l i t y po ly-

INJECTION

c FLOW n

PRODUCTION

A

21 t OPTIMAL SALINITY

0 c SALINITY, %NaCI

Fig. 39. Schematic representat ion o f the g raded-sa l i n i t y design o f po lymer b u f f e r s o l u t i o n f o r enhanced o i l recovery.

With t h i s unique design h igh o i l recovery and h igh su r fac tan t recovery can be obtained f o r so lub le o i l f l o o d i n g i n sandpacks, whi le the polymer consumption can be g r e a t l y reduced.

ty shock design. used was 2.1% NaCl and the rese rvo i r b r i n e was 3% NaCl p lus 1% calc ium ch lo r i de . berea cores 88% t e r t i a r y o i l recovery and 48% su r fac tan t recovery.

For aqueous micel lar-polymer f l ood ing w i th crude o i l i n Berea cores, i t has been shown (66-69) t h a t a con t ras t s a l i n i t y design o f t he p r e f l u s h micel lar-polymer f l o o d i n g process may produce a b e t t e r o i l recovery than t h a t obtained from a constant s a l i n i t y process. In t he con t ras t s a l i n i t y design, the s a l i n i t y o f the p re f l ush water i s made higher whi le the s a l i - n i t y o f the polyner s o l u t i o n i s made lower than the optimal s a l i n i t y o f the su r fac tan t formulat ion. The r a t i o n a l e o f t h i s design i s t h a t an op- t ima l s a l i n i t y p r o f i l e can be establ ished i n the v i c i n i t y o f the surfac- t a n t s lug upon mix ing o f t he i n j e c t e d f l u i d s i n the porous medium.

F igure 40 schemat ica l ly shows our r e s u l t s obtained using the s a l i n i -

By the use o f two polymer slugs we were able t o ob ta in i n

The optimal s a l i n i t y f o r t he su r fac tan t f o rmu la t i on

37

1 CHASE WATER ~ ~ ~ a ~ L u G

POLYMER SLUG 'IiASE .prrRI 0.05% NaCl

42 % 25 %

88 x 48 x Fig. 40. The e f f e c t o f s a l i n i t y shock o f polymer buffer so lu t ion an o i l

displacement e f f i c i e n c y and sur factant loss.

I t i s hoped tha t the experimental r e s u l t s presented i n t h i s paper cont r ibu te i n a small way t o increas ing our understanding of phenomena occurr ing i n porous media. It should be enphasized t h a t r e s u l t s we have obtained using laboratory scale experiments are ne i ther conducted nor intended t o be extrapolated t o the o i l f i e l d processes. t h a t the processes occurlng i n pet ro leun reservo i rs are f a r more complex than those tha t we can design and cont ro l using a laboratory setup.

It i s recognized

ACKNOWLEDGEMENTS

The author wishes t o express h i s sincere thanks and appreciat ion t o the National Science Foundation - RANN, ERDA and the Department of Energy (Grant No: DE-AC1979BC10075) and the consortium o f the fo l low ing Indus- t r i a l Associates f o r t h e i r generous support o f the Un ivers i ty o f F l o r i d a Enhanced O i l Recovery Research Program dur ing the past seven years: 1) A lber ta Research Council, Canada, 2) Pmerican Cyananid Co., 3) Ammo Production Co., 4) A t l a n t i c - R i c h f i e l d Co., 5 ) BASF-Wyandotte Co., 6 ) B r i - t i s h Petroleum Co., England, 7) Calgon Corp., 8) C i t i e s Service O i l Co., 9) Continental O i l Co., 10) E thy l Corp., 11) Exxon Production Research Co., 12) Getty O i l Co., 13) Gulf Research and Development Co., 14) Mara- thon O i l Co., 15) Mobil Research and Development Co., 16) Nalco Chemical Co., 17) P h i l l i p s Petroleum Co., 18) Shel l Development Co., 19) Standard O i l o f Ohio Co., 20) Stepan Chemical Co., 21) Sun O i l Chemical Co. 22) Texaco, Inc., 23) Union Carbide Corp., 24) Union O i l Co., 25) Westvaco, Inc., 26) Witco Chemical Co., and the Un ivers i ty o f F lor ida. He also wishes t o convey h i s sincere thanks t o h i s Colleagues i n Chemical Engi- neering, Petroleum Engineering and I n s t i t u t e f o r Energy Studies o f Stan- f o r d Un ivers i ty f o r t h e i r co l labora t ion dur ing h i s s tay a t Stanford Uni- v e r s i t y .



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Desai, N.N.; i n "Un ive rs i t y o f F l o r i d a Research on Surfactant-Polymer O i l Recovery Systems-Annual Report", pp. 127-149, Dec. 1979.

Desai, N.N., i n "Un ive rs i t y o f F l o r i d a Research on Surfactant-Polymer O i l Recovery Systems-Annual Report", pp. 135-1-48, Dec. 1980.

Hesselink, F. Th. and Faber, M.J., i n "Surface Phenomena i n Enhanced O i l Recovery," D.O. Shah, ed., pp. 861-869, Plenum Publ ish ing Co., N.Y. ( i n press).

Chou, S . I . and Shah, D.O., i n "Surface Phenomena i n Enhanced O i l Re- covery", D.O. Shah, ed., pp. 843-860, Plenum Publ ish ing Co., N.Y. ( i n press)

Paul, G.W. and Froning, H.R., J. Pet. Tech., 25, 957 (1973).

Gupta, S.P. and Trushenski, S.P.. SPE J., 2, 116 (1979)i

Nelson, R.C., "The S a l i n i t y Requirement Diagram-A Useful Tool i n Chemical Flooding Research Development1', SPE 8824, presented a t t h e SPE Improved O i l Recovery Symposium, Tulsa, OK, A p r i l 20-23, 1980.

Hirasaki, G.J., Van Dmselaar, H.R. and Nelson, R.C., "Evaluation o f . t he S a l i n i t y Gradient Concept i n Sur factant Flooding", SPE 8825, presented a t t he SPE Improved O i l Recovery Symposium, Tulsa, OK, A p r i l 20-23, 1980.



4 4

The c h a r a c t e r i s t i c d a t a p e r t a i n i n g t o a s p e c i f i c g roup of re- s e r v o i r s must be e v a l u a t e d i n o r d e r t o p rov ide a r e p r e s e n t a t i v e su rvey o f t h e boundary c o n d i t i o n s r e q u i r e d f o r bo th t h e r a p i d t es t methods and t h e p r e l i m i n a r y f l o o d i n g expe r imen t s . Conc lus ions w i t h t h e most g e n e r a l a p p l i c a b i l i t y : S i n c e t h e r e s h o u l d be no r e s t r i c t i o n t o one o i l r e s e r v o i r o n l y , t h e r e s u l t s s h o u l d be of t h e most g e n e r a l p o s s i b l e v a l i d i t y , and s u r f a c t a n t s o l u t i o n s w i t h a broad r a n g e of a p p l i c a t i o n shou ld be sough t . Hence, maximal demands shou ld be imposed on t h e f l o o - d i n g media, i n o r d e r t o e n s u r e t es t r e s u l t s which a r e a p p l i c a b - l e t o a s many o i l r e s e r v o i r s a s p o s s i b l e .

TEST PROGRAM/STANDARDIZATION

Reproduc ib le t es t c o n d i t i o n s a r e a lways r e q u i r e d f o r i n v e s t i g a - t i n g s u r f a c t a n t s , i n o r d e r t h a t v a r i o u s p r o d u c t s be a p p r a i s e d and compared. Such c o n d i t i o n s can be f u l f i l l e d o n l y by model sys t ems , s i n c e t h e p r o p e r t i e s of r e a l sys t ems ( r e s e r v o i r w a t e r , c r u d e o i l ,

Hence a t e s t program r e q u i r e s t h e d e s i g n i n g of model sys t ems , i n which a s many pa rame te r s of r e a l sys t ems a s p o s s i b l e a r e cons ide - red. S i n c e s u r f a c t a n t s a r e generally d i s s o l v e d i n w a t e r , t h e t o t a l s a l i n i t y and t h e compos i t ion of r e s e r v o i r b r i n e a r e of utmost i m - p o r t a n c e f o r t h e s e l e c t i o n of s u i t a b l e s u r f a c t a n t s . Based on s e v e r a l hundred chemica l a n a l y s e s o f . w a t e r samples from German o i l r e s e r v o i r s , a c l a s s i f i c a t i o n i n t o t h r e e b r i n e ca t ego- ries was p o s s i b l e : - t y p e AM ( l ow s a l i n i t y ) TDS <lo g.1- - t y p e BM ( i n t e r m e d i a t e s a l i n i t y ) 1 0 .g-l-’C TDS (165 g.1- - t y p e CM ( h i g h l y s a l i n e ) TDS >165 g.1-1

Observed s i g n i f i c a n t c h a r a c t e r i s t i c s of h i g h l y s a l i n e r e s e r v o i r b r i n e s a r e t h a t - many s a l t s occu r i n t h e d i s s o l v e d s t a t e a t c o n c e n t r a t i o n s ex-

- a l l wa te r samples c o n t a i n heavy me ta l i o n s , such a s Fe - t h e pH-values of b r i n e s BM and CM l i e i n a r e l a t i v e l y a c i d i c

- a l l b r i n e s show compara t ive ly h i g h s u l f a t e c o n t e n t s - a l l b r i n e s c o n t a i n large q u a n t i t i e s of Ca2+ and Mg2+ i o n s and

Trace e l emen t s 0 1 0 mg.1-l) were n o t c o n s i d e r e d . A t r e s e r v o i r p r e s - s u r e bgtween 50 and 100 b a r and r e s e r v o i r t e m p e r a t u r e s between 40 and 80 C abou t 4 g of C 0 2 d i s s o l v e s i n 100 g of wa te r . However, above 6 b a r t h e pH-value of wa te r c o n t a i n i n g CO a l r e a d y t e n d s t o - ward a c o n s t a n t v a l u e of 3 , 3 / 1 5 / , which p robab ly a l s o domina te s i n most r e s e r v o i r b r i n e s of t y p e CM. For t h e s u r f a c t a n t i n v e s t i g a t i o n s a s t a t i s t i c a l compos i t ion was a s c e r t a i n e d f o r a h i g h l y s a l i n e model r e s e r v o i r wa te r CM ( tab le 1). T h i s s t a n d a r d i z e d b r i n e CM was employed f e r a l l subsequen t tests, u n l e s s o t h e r w i s e i n d i c a t e d . The pr imary s c r e e n i n g c r i t e r i a of s u r f a c t a n t s f o r EOR p r o c e s s e s i n h i g h l y s a l i n e sys t ems may be l i s t ed a s f o l l o w s / l o / : - s o l u b i l i t y i n r e s e r v o i r b r i n e (TDS >165 g . 1 - l ) - long-term s t a b i l i t y i n t h e t e m p e r a t u r e r ange of 30-80°C - low i n t e r f a c i a l t e n s i o n s i n t h e system b r ine / c?ude o i l

r e s e r v o i r r o c k ) a r e u s u a l l y s u b j e c t t o v a r i a t i o n s .

1 1

2+ ceed ing t h e i r u s u a l s o l u b i l i t y p r o d u c t s

r a n g e ( 3 , 0 - 6 , 5 )

lower c o n c e n t r a t i o n s of Sr2+ and Ba2+.

( v < 1 m N . m - l )

45

Table 1: Composition of synthetic reservoir brine CM

Salt Concentrations in mg.1-l

NaCl

CaC12 . 6H20 MgC12 . 6H20 KC1

KBr

KJ

LiCl

NH4Cl

SrC12 . 6H20 BaC12 . 2H20 NaHC03

Na2S04 . 1 0 H 2 0

C02 injected for at least 1 h

NaCQ3 . 4H20 FeS04 . 9H20

165 000

49 349 ( 2 5 O O O ) *

12 810 ( 6 O O O ) *

750

400

20

100

350

1 681 ( 1 O O O ) *

58 ( SO)*

650

680 ( 300)*

523 ( 2 5 0 ) *

366 ( 2 0 0 ) *

TDS: 200 070 mg.1-'

*The concentration in parentheses refers to the quantity without water of crystallization

Based on these fundamental requirements a standard test program for surfactants was developed (see fig. 1).

.solubility interfociol tension stobilit y Y e 1 mN.rn-1

wrfoctont ogoinst oil in brine CM

30 'C 'T ,- nwhthenic 60 'C

1: 3 a5 Y. 1.0 '1: swfoctont water soluble

L poroninic

80 'C

Figure 1: Test program for water-soluble surfactants

Besides the aforementioned criteria suitable surfactants should show further, - low adsorption on reservoir rock - favourable partition coefficients and. ' - broad range of application.


47

Table 2 : Commercially a v a i l a b l e s u r f a c t a n t groups

Structure

Ionic surfactants R-CH,-COONa R-C,H,-S0,Na

:)CH-SO,N~

R -CH,--CH=CH-CH,-SO,Na + R'-CH,-CH-(CH,)n-CH,-SO,Na

OH

R - C H - C ~ ' $O,Na'OCH'

R-CH,-0-S0,Na

R; R,CH -O-(C,H,O),-SO,Nn

R -CH,-O-(C,H,O), -CH,COONa

R', + /R' C P

R'/ N\R,

N o n I o n i c Surfadants

R y - ~ - t ~ , ~ , ~ ) , - ~ R' H

R-C,H.-O-(C,H.O)n-H

YH, C A - Y + C '

CH, hplmlyt ic Surfac- tants

R'

R'

R' R' - m N -CH,-COO~

1. R=C,,, bei R'=H n=3-15

2. R+R=C,,,, n=3-12

R=C,,, n=7-10

De s isna t ion

Na-salts of fatty acids Alkylbenzenesulfonate

Alkane sulfonate

a-olefinsulfonate Hydroxyalkanesulfonate as byproduct

a-sulfa fatty acid ester

Fatty alcohol sulfate

Fatty alcohol ether sulfate*

Fatty alcohol ethoxylate acetate**

(luaternary ammonium salts

Primary or secondary alcohol ethoxylates

Alkylphenol ethoxylates

Amine oxides

Sulfobetains

Betains

* Fatty alcohol polyethylene glycol ether sulfate, Na-salt ** Fatty alcohol polyethylene glycol ether carboxymethylate,Na-salt

- t y p e of c r u d e ( p a r a f f i n i c , naphthenic , a romat ic o r mixed t y p e ) - c o l l o i d a l chemis t ry of c r u d e ( c o n t e n t of a s p h a l t e n e s , r e s i n s ,

- a d s o r p t i o n phenomena (composi t ion of r e s e r v o i r r o c k ) - c h a r a c t e r i s t i c s of r e s e r v o i r environment (pH, tempera ture , wet-

- d i f f u s i o n phenomena ( r a p i d d i f f u s i o n t o t h e O/W-interface).

The importance of t h e i n d i v i d u a l parameters can vary g r e a t l y depending on t h e c o n d i t i o n s of a p p l i c a t i o n , and cannot be g e n e r a l i - zed. For t h i s r e a s o n , two complex parameters w i l l be d i s c u s s e d i n d e t a i 1 .

DIFFUSION PHENOMENA

It is known from s t u d i e s on O/W systems t h a t t h e d i f f u s i o n is dependent , among o t h e r s , on t h e s t r u c t u r e of s u r f a c t a n t s /l/. Y e t , t h e d i f f u s i o n c o e f f i c i e n t of s u r f a c t a n t s i t s e l f is of d e c i s i v e imvor- tance . I n g e n e r a l , t h e f o l l o w i n g r e l a t i o n s h i p s apply:

e t c . )

t i n g c o n d i t i o n s , s a l i n i t y )

48

- t h e d i f f u s i o n c o e f f i c i e n t a l k o x y l a t i o n

- t h e d i f f u s i o n c o e f f i c i e n t t i o n of s u r f a c t a n t ( u p t o

- t h e d i f f u s i o n c o e f f i c i e n t t u r e

- t h e d i f f u s i o n c o e f f i c i e n t

decreases w i t h i n c r e a s i n g d e g r e e of

i n c r e a s e s w i t h i n c r e a s i n g concen t r a - c.m.c.) is d i r e c t l y p r o p o r t i o n a l t o tempera-

f o r d i s s o l v e d s u r f a c t a n t s is i n v e r s e l v p r o p o r t i o n a l t o t h e v i s c o s i t y of t h e s o l v e n t

l i n e a r t y p e s . - branched b lock copolymers d i f f u s e more r e a d i l y t h a n long-chain

The s t r u c t u r e of t h e p o l y e t h e r c h a i n s of s y n t h e t i c s u r f a c t a n t s can a l s o be of importance f o r d i f f u s i o n p r o c e s s e s . I t is w e l l known t h a t p o l y e t h e r c h a i n s , depending on t h e d e g r e e of a l k o x y l a t i o n , can e x i s t i n t h e s o - c a l l e d zig-zag form o r i n t h e meander form (see f i g . 3 / 2 / ) .

Zig-zag form

Meander form

-Figure 3 : Shapes of p o l y e t h e r c h a i n s / 2 /

With i n c r e a s i n g EO number, t h e w i d t h / l e n g t h c o e f f i c i e n t of t h e non- i o n i c s i n c r e a s e s , and d i f f u s i o n c o e f f i c i e n t t h u s d e c r e a s e s . By b lock ing t h e p o l y e t h e r oxygen d i p o l e f o r c e s , a change can a l s o occur i n t h e c loud p o i n t s , t h e c r i t i c a l micelle f o r m a t i o n c o n c e n t r a t i o n (c.m.c.), and t h u s t h e i n t e r f a c i a l a c t i v i t y o r s o l u b i l i t y behav io r / 3 / .

f o r h y d r a t i o n a s a r e s u l t of 0 4 H 2

ADSORPTION

For t h e q u e s t i o n of a d s o r p t i o n phenomena a s a f u n c t i o n of s u r f a c - t a n t s t r u c t u r e o r r e s e r v o i r r o c k , numerous f i n d i n g s a r e of impor- t a n c e /l, 9 ,12 , l 4 / .

GENERAL C R I T E R I A

Swf aetants

- Amphiphatic s u r f a c t a n t s a r e r e a d i l y adsorbed on hydrophobic rock s u r f a c e s , depending on t h e i r s t r u c t u r e

- The g r e a t e r t h e s o l u b i l i t y of a s u r f a c t a n t , t h e s m a l l e r is i ts a d s o r p t i o n ( g r e a t e s t a d s o r p t i o n of s u r f a c t a n t o c c u r s i n high- s a l i n i t y wa te r because of diminished s o l u b i l i t y )

- With i n c r e a s i n g t empera tu re and v i s c o s i t y of t h e s o l v e n t adsorp- t i o n d e c r e a s e s

- With i n c r e a s i n g s u r f a c t a n t c o n c e n t r a t i o n a d s o r p t i o n i n c r e a s e s

A I M : Low t o t a l a d s o r p t i o n b u t h igh r a t e of a d s o r p t i o n up t o t h e s a -

R e s e r v o i r system

- Hydroph i l i c e a s i l y wa te r -we t t ab le r o c k s : q u a r t z , c l a y - Hydrophobic, p o o r l y wa te r -we t t ab le r o c k s : c a r b o n a t e s

t u r a t i o n c o n c e n t r a t i o n

49

SPECIAL CRITERIA

Sur f a c t a n t s

- T o t a l a d s o r p t i o n d e c r e a s e s w i t h i n c r e a s i n g m o l e c u l a r mass of s u r f a c t a n t ( t h e t o t a l a r e a a c c e s s i b l e t o a d s o r p t i o n becomes smal- l e r )

- Nonionic s u r f a c t a n t s / 9 / a r e adso rbed mos t ly i n u n i m o l e c u l a r l a - y e r s , a d s o r p t i o n d e c r e a s e s w i t h increasing EO d e g r e e , b u t adso rp - t i o n i n c r e a s e s w i t h i n c r e a s i n g l e n g t h of t h e hydrocarbon c h a i n ; d e r i v a t i v e s w i t h an a l i p h a t i c hydroca rbon c h a i n a r e more s t r o n g - l y adso rbed t h a n d e r i v a t i v e s w i t h an a r o m a t i c hydrocarbon c h a i n

- I o n i c s u r f a c t a n t s a r e adso rbed f o r t h e most p a r t i n polymolecu- l a r l a y e r s ( c a t i o n i c s : a b o u t 250 l a y e r s ) .

- L i m i t i n g c o n c e n t r a t i o n : s y n t h e t i c s u r f a c t a n t s ( 0 . 0 5 - 0 . 0 7 % ) << n a t u r a l s u r f a c t a n t s ( 0 . 2 5 % ) .

R e s e r v o i r rock

- Clay : a d s o r p t i o n of u n s a t u r a t e d h y d r o c a r b o n s ( i n p a r t po lymer i - z e d ) > a r o m a t i c s > n a p h t h e n a t e s > a l k a n e s . C a t i o n i c s >>nonionics > a n i o n i c s .

- S i l i c a t e s : s l i g h t a d s o r p t i o n of n o n i o n i c s ( o i l - w e t t e d > w a t e r - w e t t e d ) , a d s o r p t i o n i n c r e a s e s w i t h t e m p e r a t u r e ; s t r o n g adso rp - t i o n of c a t i o n i c s on q u a r t z ( l o w e r e d by a d d i t i o n of n o n i o n i c s ) .

The i n c r e a s e d a d s o r p t i o n of c a t i o n i c s , i n d e p e n d e n t of t h e reser- v o i r r o c k i s t h s c l e a r l y e v i d e n t . A s a g u i d e , v a l u e s of abou t 0 , s . l o d 4 mg/cm c a n be g i v e n f o r t h e a d m i s s i b l e a d s o r p t i o n on q u a r t z s u r f a c e s .

Y

PHYSICOCHEMICAL PROPERTIES OF SURFACTANTS

P r i o r t o t e s t i n g , a few genera l ly-known r u l e s and some e m p i r i c a l d a t a from t h e c h e m i s t r y of s u r f a c t a n t s c a n be u s e d :

Good w e t t i n g a c t i o n : C -C r a n g e ( < C ,,: s m a l l micelles, low ac f iv$$y) . Branchea and s o l v a t a b l e g r o u p s s u r f ace

s h o u l d l i e close t o t h e c e n t r e of t h e molecu le .

H y d r o p h i l i c c h a r a c t e r : 3 CH2 g r o u p s P 1 OH-group -$-NH-group P -0-group (hydrogen b r i d g i n g )

3 CHp-groups

S o l u b i l i t y : n / 3 EO - b e g i n n i n g w a t e r s o l u b i l i t y n /2 EO -medium w a t e r s o l u b i l i t y 1 - 1 , 5 n EO-good water s o l u b i l i t y ( n = number of c a r b o n atoms i n hydrophob ic c h a i n ) S o l u b i l i t y d e c r e a s e s w i t h r i s i n g t e m p e r a t u r e ( - c l o u d p o i n t / t h r o u g h d e h y d r a t i o n and i n c r e a s i n g e l e c t r o l y t e c o n t e n t (see f i g . 4 / l / ) .

HLB v a l u e : W/O e m u l s i f i e r s 3 -6 Wet t ing a g e n t s 7-9 O/W e m u l s i f i e r s 8-12

/13 - 1 8/ O/W d i s p e r s i n g a g e n t s , W/O demul- s i f i e r s , s o l u b i l i z i n g a g e n t s

50

rurtactont nonylphsnol/l5 EO

in water

0 1 .o 2.0 3.0 electrolyte concentration /ma1 1-1

F i g u r e 4 : E f f e c t of e l e c t r o l y t e c o n c e n t r a t i o n and t y p e on c l o u d p o i n t TP / 7 /

On t h e b a s i s of t h i s p r e l i m i n a r y i n f o r m a t i o n , i t i s now a l r e a d y p o s s i b l e t o g e t the most i m p o r t a n t r e q u i r e m e n t s on s u r f a c t a n t s f o r EOR p r o c e s s e s / 4 , 5 / : - Enr ichment a t t h e i n t e r f a c e - Format ion of o r i e n t e d monolayers - Permanent l o w e r i n g of i n t e r f a c i a l t e n s i o n i n t h e sys t em o i l / w a -

- Tendency t o micelle f o r m a t i o n - P a r t i a l o i l s o l u b i l i t y - S t a b i l i z a t i o n of O/W e m u l s i o n s - S o l u b i l i t y o r d i s p e r s a b i l i t y i n h i g h l y s a l i n e f o r m a t i o n w a t e r - Long-term s t a b i l i t y (1-2 y e a r s ) unde r r e s e r v o i r c o n d i t i o n s - Low a d s o r p t i o n on r e s e r v o i r r o c k - Low c o s t c o u p l e d w i t h h i g h e f f e c t i v e n e s s

A l ist of p o s s i b l e b u i l d i n g s t o n e s a v a i l a b l e commerc ia l ly f o r t h e s y n t h e s i s of s u r f a c t a n t s i s g i v e n i n t a b l e 3 . These c o n s i d e r a t i o n s t h e n l e a d t o classes of p r o m i s i n g p r o d u c t s , which i n p a r t s h o u l d e x h i b i t v e r y s t r o n g i n t e r f a c i a l a c t i v i t y and a r e described i n t h e U S - l i t e r a t u r e a s e f f e c t i v e f o r EOR p r o c e s s e s (see t a b l e 4 and 5 ) .

These known surfactants a r e s u i t a b l e p r i m a r i l y f o r low s a l i n i t i e s (1 % N a C l w i t h a b o u t 100-200 ppm Ca2+ and Mg2+ o n l y ) . W i t h o u t a p o l y e t h e r c h a i n w i t h s u f f i c i e n t d i s p e r s i n g power, however, t h e so- l u b i l i t y i n h i g h sa l in i ty s y s t e m s (15-25 % NaC1, 20 000-40 000 ppm C a 2 + and Mg2+) is f o r t h e most p a r t t o o low o r t h e e lec t ro ly te sen - s i t i v i t y t o a l k a l i n e e a r t h i o n s t o o h i g h . Even i n t h e case of po- l y e t h o x y l a t e s t h e e lec t ro ly te c o n t e n t of t h e r e s e r v o i r w a t e r c a n lower t h e c l o u d p o i n t s t r o n g l y ( f i g . 4) and t h u s c a n b r i n g a b o u t a d e c r e a s e d s o l u b i l i t y as w e l l as i n c r e a s e d a d s o r p t i o n and a p a r - t i a l p a s s a g e of t h e s u r f a c t a n t i n t o t h e o i l p h a s e /6/. I n g e n e r a l t h e i n t e r f a c i a l a c t i v i t y of t h e anionics is l i k e w i s e r educed s t r o n g - l y i n water w i t h a h i g h e l e c t r o l y t e c o n t e n t / 5 / , F r e q u e n t l y a l s o s u r f a c t a n t m i x t u r e s f o r EOR p r o c e s s e s have been d e s c r i b e d and a p p l i e d . The re r ema ins u n c l e a r t h e q u e s t i o n of c h r o m a t o g r a p h i c phenomena i n t h e u s e of c o m p l i c a t e d s u r f a c t a n t m i x t u r e s i n r e s e r v o i r , i n which t h e q u i t e d i f f e r e n t components of t h e m i x t u r e c a n e x h i b i t comple t e - l y d i f f e r e n t r a t e s of m i g r a t i o n .

t e r t o (1 m N . m - 1 a t low s u r f a c t a n t c o n c e n t r a t i o n /13 /

51

T a b l e 3 : Possible b u i l d i n g s t o n e s f o r s u r f a c t a n t s

Surfactant building stones

a-olef ins oligomeric alkenes fatty acids (saturated and unsaturated) and

alkanols (alfols, 0x0-alcohols, fatty alcohols) alkylaromatics isoalkylphenols alkylamines (fatty amines) polyalkylene glycol ethers polybutylene oxide (polypropylene oxide)

derivatives, natural oils

SO,, ( ~ O , ) , C I S O , H , , H,NSO,H,Na,SO,,NaHSO,

8 8 - ), HOC,H,SO,Na, ( C H , ) , < P , (CH2)(_So2\0 c'

H,O, (N), CICHFO,H, (HNO,)

(Formaldehyde, epichlorohydrin , RO-CHSH-CH,,

1 0 /o \

aliphatic oligoamines, polyols, etc.)

Table 4 : Anion ic s u r f a c t a n t s f o r EOR p r o c e s s e s ( i n t e r n a t i o n a l l i t e r a t u r e )

Anionic surfactants

Chemical constitution Designation structural type

R'-FH-CO,R' SO,H (Na)

R-CH,-CH-R-COONa OS0,Na

R ~ C O N ~ ~ '

S0,Na R 2

H H R-C -C,H,-N-CH,SO,Na

b H 'c P N + S O , N ~

% R

R-N -R'-(OC,H,)xOSO,Na R

PH

R-CH,

RG@-o(c.H,,o)~R

(rnFXAC0) p S0,Na

,C,H,O-C-R HN' -C,H,O-C-R

\ d H C,H,(OC,H,),OC-~-CH,-CO.Na

b sop P

R-0-(CH,-CH,-0)"-P-ONa ONa

--T a-Sulfo fatty acid

OH fatty acid sulfates

esters

7

7x -77

Sulfated amide oils

Didecyldiphenyl ether

Hydroxyalkylaminosul- fonic acids

Alkenylsuccin-N-(alkyl)- phenylimidesulfonates

Dialkylamino polyether ).wv, sulfates

Alkenyl-, OH-Alkane sulfonates

disulfonates

Sulfates of iosalkyl- phenyl polyether sul- f ona tes

triethanolamine polyglycol ether sulfocar- box y la t e s

Bisfatty acid esters of

Alkanol polyether phos- -

52

Table 5: Amphoteric s u r f a c t a n t s f o r EOR p r o c e s s e s ( i n t e r n a t i o n a l l i t e r a t u r e )

Amphoteric Surfactants

Chemical Structural constitution type

Sulfobetains

Sulfobetains 4 R’ H

R’ OH R - ~ C H , - C -cH,-so,~

YH’ H,,.,,c,,,:-I]I-cH,-coo~ Betain --f.)

CH,

R-& Alkylimidazol-

HO-CH,~CH,/N\CH,~COO~ iniumbetains

Amidoalkylbe- H,,,,-c,-co-NH-(cH,):-$-cH,-coo e

-79

-.-a CH;

tains CH,

Otherwise i t is p robab ly p o s s i b l e t o i n c r e a s e , by t h e u s e of such s u r f a c t a n t m i x t u r e s , t h e packing d e n s i t y a t t h e i n t e r f a c e and t h u s t h e d e g r e e of w e t t i n g (see f i g . 5 / l o / ) ; f u r t h e r , a l s o t h e forma- t i o n of mixed micelles is p o s s i b l e ( f i g . 6 /4/).

lipophilic port of molecule

0 hydrophtlic part of mokcuie surfactant molecule

F i g u r e 5 : Inc reased packing d e n s i t y by s u r f a c t a n t m i x t u r e s a t O/W i n t e r f a c e s

When pure n o n i o n i c s a r e u s e d , such a s i s o a l k y l p h e n o l e t h o x y l a t e s , a t t a i n m e n t of s a t i s f a c t o r y i n t e r f a c i a l a c t i v i t i e s demands a h i g h e r d e g r e e of a l k o x y l a t i o n . These p r o d u c t s a r e n o t e l e c t r o l y t e - s e n s i - t i v e and have a good s o l u b i l i t y i n b r i n e ( a r u l e of thumb is t h a t a t 5OoC, o n l y n o n i o n i c s w i t h a d e g r e e of e t h o x y l a t i o n n of 10 o r more a r e s o l u b l e i n 1 0 % NaC1).

53

oure onionic surfoctont

011

t rans i t ional interface

water

L1

oi l

transitional interface

water

11 : 12 - 1.1 surfoctont mixture (anionics/nonionics I

F i g u r e 6 : a ) packing d e n s i t y of pu re a n i o n i c s u r f a c t a n t a t i n t e r - f a c e

b ) packing d e n s i t y of an ion ic -non ion ic s u r f a c t a n t a t i n t e r f a c e

EXPERIMENTAL

Under c o n s i d e r a t i o n of a s many s e l e c t i o n c r i t e r i a , physico-chemi- c a l p r o p e r t i e s and p o s s i b i l i t i e s of s u r f a c t a n t s y n t h e s i s a s pos- s ib l e more than 1 200 s u r f a c t a n t s were t e s t e d f o r t h e i r a p p l i c a - b i l i t y t o EOR p r o c e s s e s . The s c r e e n i n g of t h e s u r f a c t a n t s was c a r r i e d o u t acco rd ing t o t h e r a p i d s c r e e n i n g program a l r e a d y in - t roduced . F u r t h e r tests on a s u r f a c t a n t w e r e proposed o n l y , i f i t had pas- s ed t h e s c r e e n i n g program.

SOLUBILITY I N BRINE CM

A l l e x p e c t a t i o n s on t h e s o l u b i l i t y of s u r f a c t a n t s i n h i g h - s a l i n i t y b r i n e s were confirmed i n a l l r e s p e c t s . E s p e c i a l l y t h e s u r f a c t a n t s w i th p o l y e t h e r c h a i n s and a n i o n i c g roups have shown good s o l u b i - l i t i e s up t o t h e mark. Tab le 6 p r e s e n t s some t y p i c a l p r o d u c t s , which were s e l e c t e d on t h e b a s i s of t h e above-descr ibed s o l u b i l i - t y c r i t e r i a a .

I N T E R F A C I A L ACTIVITY

During t h e measurements of t h e i n t e r f a c i a l a c t i v i t y (Lecomte du Nouy) a s t r o n g dependence of t h e i n t e r f a c i a l t e n s i o n on t h e tempe- r a t u r e and s a l i n i t y was e s t a b l i s h e d i n t h e system o i l / w a t e r with- o u t a d d i t i o n of any s u r f a c t a n t s (see f i g . 7 ) . The expe r imen t s have shown t h a t - a l l s t a n d a r d o i l s a r e c h a r a c t e r i z e d by a t y p i c a l i n t e r f a c i a l ten-

- i n t e r f a c i a l t e n s i o n depends s t r o n g l y on t h e o i l composi t ion - naph then ic o i l shows t h e h i g h e s t v a l u e s of i n t e r f a c i a l t e n s i o n

a g a i n s t h i g h - s a l i n i t y b r i n e s - i n g e n e r a l an i n c r e a s e i n s a l i n i t y is accompanied by a d e c r e a s e i n

i n t e r f a c i a l t ens ion /A minimum i n i n t e r f a c i a l t e n s i o n w i l l be passed . T h e r e s u l t s a r e summarized i n f i g u r e 7 .

s i o n - r e l a t i o n s h i p

5 4

T a b l e 6 : Some s u r f a c t a n t s w i t h good s o l u b i l i t y , tested i n h igh - s a l i n i t y b r i n e

Chem. constitution Designation Structural type-

I - C , H , , ~ ( C , H . O J . , C H , C D , N ~ Isoalkylphenylpolyether acetates

I C , H , . ~ O ( C , H . O I , . SO, Na Diisoalkylphenylpolyether sulfates l-C,Ha,

Acylamidopolyether sulfates R j - N / ( C , H , O ) x SO,Na

(2 x = 5 ) '(C,H,O), S 0 , N a

(Esteramine polyether N ( R - C - ~ , H , - N / ( C 1 H 4 0 ) y fl '(C,H,Oly S 0 , N a ) sulfates)

( 2 y t 1 = 2 X I

i - C , , H , , ~ - C H , - ~ - C H , ~ ( O C . H , . J x OR' (Sulfone/sulfate-isoalkyl- S O , N ~ ( W n H x n)x O R phenylpolyethoxyglycerol

x - 0 - 2 0 R'= H, SO,Na,

n = 2 , 3

ether)

-CH,COONa

Ditert.-alkylphenyl poly-

Isoalkylphenylpolyethers

ethers

I f s u r f a c t a n t s were added t o t h e s t a n d a r d o i l s , c h a r a c t e r i s t i c c u r - v e s r e s u l t e d f o r t h e f u n c t i o n i n t e r f a c i a l t e n s i o n y = f ( s u r f a c - t a n t c o n c e n t r a t i o n C T ) . T h e s h a p e of t h e c u r v e s depend on - t y p e of o i l ( c o m p o s i t i o n ) - temper a t u r e - s a l i n i t y - t y p e of s u r f a c t a n t and c o n c e n t r a t i o n of s u r f a c t a n t .

T y p i c a l d i a g r a m s of s u r f a c t a n t m i x t u r e s ( a n i o n i c s - n o n i o n i c s ) are p r e s e n t e d i n f i g u r e 8 a / b . I f t h e i n t e r f a c i a l t e n s i o n r e a c h v a l u e s of < 1 mN.m , t h e accu- r a c y of t h e method of Lecomte d u Nouy i s no l o n g e r s u f f i c i e n t . Fur- t h e r t e s t s on " s u c c e s s f u l " s u r f a c t a n t s makes t h e a p p l i c a t i o n of a s p i n n i n g - d r o p - t e n s i o m e t e r (SITE) n e c e s s a r y . A " s u c c e s s f u l " s u r f a c t a n t mus t comely w i t h t h e f o l l o w i n q c r i t e r i o n : The i n t r f a c i a l t e n s i o n of a s u c c e s s f u l s u r f a c t a n t must be < 1 mN.m-f a g a i n s t a l l t h r e e s t a n d a r d o i l s i n t h e t e m p e r a t u r e r a n g e of 30-80°C. On t h e b a s i s of t h i s c r i t e r i o n a g e n e r a l t e m p e r a t u r e i n t e r f a c i a l t e n s i o n - r e l a t i o n s h i p was d e r i v e d f o r t h e s u r f a c t a n t s tes ted (see f i g . 9 ) . By t h i s i t was e v i d e n t , t h a t a n i o n i c s ( w i t h an o p t i m a l c o n t e n t of n o n i o n i c s ) w i l l e x h i b i t t h e l o w e s t i n t e r f a c i a l t e n s i o n .

-1

TEMPERATURE STABILITY

For t h e i n v e s t i g a t i q n of t h e t e m p e r a t u r e s t a b i l i t y , s u r f a c t a n t s o l u t i o n s of v a r i o u s c o n c e n t r a t i o n s i n b r i n e CM were k e p t f o r

55

12 s 10 5 8

N 20 "I

y = f(8.011 comp 1

Y against brine EM I:\ N

Y ogoinst dist woter

0 30 60 80 temperature 9/"C

2 0 t

.-I - .- 0 : . 1 v . I . I . , , -

0 30 60 80 temperot ure 8 / "C

20 t y = t(;t.oil comp I

Y agoinst brine CM

30 60 eo temperature ;t/ 'C

N naphthenic oil A aromottc oil P poroffinic oil

f o r s u c h a s u r f a c t a n t is shown

F i g u r e 7 : I n t e r f a c i a l t e n - s i o n a s a f u n c t i o n of tem- p e r a t u r e , s a l i n i t y and o i l c o m p o s i t i o n ( n a p h t h e n i c , a r o m a t i c , p a r a f f i n i c )

6 month a t a t e m p e r a t u r e of 8OoC. A f t e r t h i s t i m e t h e i n t e r - f a c i a l a c t i v i t y was com- pa red t o t h a t of a s t a n d a r d s o l u t i o n - On t h e b a s i s of t h e s e e x - p e r i m e n t s , t h e f o l l o w i n g s t a t e m e n t was p o s s i b l e : E t h e r p h o s p h a t e s - e t h e r s u l f a t e s - e t h e r c a r b o x i - m e t h y l a t e s - e t h e r s u l f o n a - tes

a r row i n d i r e c t i o n of i n c r e a s i n g s t a b i l i t y

SPECIAL FINDINGS

P o l y e t h e r s u l f a t e s , -carb- o x i m e t h y l a t e s and - su l fona - t e s of t h e f o l l o w i n g s t r u c - t u r e a r e p a r t i c u l a r l y s u i t - a b l e f o r EOR g r o c e s s e s : R ( O C 2 H 4 ) x Y - M e ( F i g . 1 0 ) .

Numerous s u r f a c t a n t s w i t h e s p e c i a l l y low v a l u e s of t h e i n t e r f a c i a l t e n s i o n may be c l a s s i f i e d a s m i x e d s u r - f a c t a n t s ( M i s c h t e n s i d e ) ( an - i o n i c / n o n i o n i c ) . The compo- s i t i o n of t h e mixed s u r f a c - t a n t i s u s u a l l y gove rned by t h e m a n u f a c t u r i n g p r o c e s s o r t h e d e g r e e of c o n v e r s i o n . I n t h i s r e s p e c t i t was ob- s e r v e d t h a t a d e g r e e of con- v e r s i o n of 50 t o 80 p e r c e n t n o n i o n i c t o a n i o n i c s u r f a c - t a n t g i v e s r ise t o p a r t i c u - l a r l y f a v o u r a b l e s u r f a c t a n t p r o p e r t i e s . A t y p i c a l ho- moloaue d i s t r i b u t i o n f o r

i n f i g u r e 11 . The f o l l o w i n g i m p o r t a n t d a t a and r e s e a r c h r e s u l t s a r e wor th men- t i o n i n g : - The d i s t r i b u t i o n c u r v e f o r t h e s u r f a c t a n t homologs ( a l k o x i l a t e s )

s h o u l d be a s b road as p o s s i b l e (more p d l d i s p e r s e ) i . e . , a l k a l i - c a t a l y z e d a l k o x i l a t i o n ( n o t L e w i s - a c i d c a t a l y z e d ) .

c r u d e t y p e ( and Y - ) . G e n e r a l r u l e s a r e

n a p h t h e n i c c r u d e s : n = 6 5 2 EO ( p a r t i a l o i l s o l u b i l i t y )

- The d e g r e e of a l k o x i l a t i o n n must be a d j u s t e d a c c o r d i n g t o t h e

p a r a f f i n i c c r u d e s : n = 4 5 2 EO HLB: 8-10

56

rn namlhanic oil A poraflinic oil x ommolic oil

y = f (c,, oil type)

suiodoni 63 tenpirniure ’ 30.C surfuianl in brine CM

10 I naphthanic oil

A poraflinic oil x oromalic oil

y = f (cT, oil type 1

surfactant 63 impKa1ua: I0.C surfoclani in brina CM

1n 1

A h h typical onionics and mixed surfactants high content

of nonionics 1

/ temperoture a/ 0;

F i g u r e 8 a : I n t e r f a c i a l t en - s i o n a s a func - t i o n of o i l com- p o s i t i o n , s u r - f a c t a n t concen- t r a t i o n and tem- p e r a t u r e (30°C) s u r f a c t a n t :

a lkoho l -po lyg ly - c o l e t h e r - ( 4 , 5 EO) -carboxme- t h y l a t e , Na-sal t

C12 /14- fa t ty

F i g u r e 8 b : same a s f i g . 7a t empera tu re 80 C 6

F i g u r e 9 : Temperature/ i n t e r f a c i a l t e n s i o n - r e - l a t i o n s h i p f o r some i m -

area of spontaneous emulsification p o r t a n t s u r f a c t a n t g roups

57

hydrophobic chain Polyether polar hydrophilic counter ion group group

R - + X + Y Q Z@

fatty OlCOhd eth yleneoxide car boxylo te OlkOll tatty ocid propyleneoxide sulfate earth alkali nonylphenol etc sulphonate ornines naphthenic ocid phosphate etc tatty ornines propionate

etc

F i g u r e l o : S u r f a c t a n t s s u i t a b l e f o r EOR p r o c e s s e s

nonionic port

Hol EO

anionic part

Hal E O - F i g u r e 11: Q u a n t i t a t i v e a n a l y s i s of i-nonylphenol-polyglycol-

e t h e r (6 E O ) - c a r b o x i m e t h y l a t e , Na s a l t , by HPLC

a romat i c c r u d e s : n = 8 & 2 EO

( P r o p o x i l a t e s a r e i n g e n e r a l less e f f e c t i v e , a s a r e EO-PO ad- d u c t s )

p a r a f f i n i c c r u d e s : C14 5 4 ( s a t u r a t e d , unbranched) naph then ic c r u d e s : C , , + 2

- The hydrophobic c h a i n R must be t a i l o r e d wi th p r e c i s i o n .

a rbmat i c rudes : a k y l r o m a t i c s i iso-C8-12-alkyl) . - C a t i o n (2 I ) : Na', K', i 'R4 o r N H 4

- The l e n g t h of t h e hydrophobic and h y d r o p h i l i c molecular p a r t s shou ld be rough ly i n t h e 1 : 1 r a t i o ( p a r t i a l o i l s o l u b i l i t y ) .

58

Example: C12,14-alkylpolyglycol e t h e r s u l f a t e - ( 4 , 5 EO), N a - s a l t

( h y d r o p h o b i c : h y d r o p h i l i c c h a i n l e n g t h = 2 , 2 nm: 2 , 3 nm)or f o r n o n y l p h e n o l p o l y g l y c o l e t h e r s u l f a t e - ( 4 EO), N a - s a l t ( h y d r o p h o b i c : h y d r o p h i l i c c h a i n l e n g t h = 2,O: 2 , l nm (see f i g . 1 2 ) .

o i l

transitional interface

water

hydrophobic part A

~~~ hydrophilic por t B

F i g u r e 1 2 : Opt imal c h a i n r a t i o of s u i t a b l e s u r f a c -

ra t io at optimum A B - 1 1 t a n t s f o r EOR p r o c e s s e s

- The d e g r e e of c o n v e r s i o n of n o n i o n i c s i n t o s u l f a t e s , c a r b o x i - m e t h y l a t e s , s u l f o n a t e s , e t c . , s h o u l d be 50-80 % ( m i x e d s u r f a c - t a n t f o r m a t i o n from n o n i o n i c s and a n i o n i c s ) .

The carac te r i s t ic b e h a v i o u r of a n i o n i c - n o n i o n i c mixed s u r f a c t a n t s w i t h t e m p e r a t u r e (minimum of i n t e r f a c i a l t e n s i o n ) c a n be e x p l a i n e d w i t h t h e h e l p of t h e p h a s e d i ag ram f o r s u c h s y s t e m s (see f i g u r e 13), whereby t h e o c c u r r e n c e of a m i s c i b i l i t y g a p is d e c i s i v e .

A

aI L

aI

11 MST=T?

0% - nonionic surfnctant + 100% 100% c a n i o n i c surfactant - 0 %

MSTK = lower cri t ical micel l- splitting - temperature

CK = cri t ical spl i t t ing -concentrat ion of mixed micelles at MSTk

CX = composition of mixed micelles

MST=T2= spl i t t ing - temperature of mixed micelles

AT = 11 -12

a,p = coexistent phases with concentrations c, and c ,

F i g u r e 1 3 : Schemat i c p h a s e d i ag ram f o r mixed s u r f a c t a n t ( a n i o n i c - n o n i o n i c ) w i t h misci- b i l i t y g a p

59

A s e p a r a t i o n i n t o w a t e r - / o i l - s o l u b l e s u r f a c t a n t s occurs when t h e m i x e d m i c e l l e s formed from anionics & nonionics reach the micelle spl i t t ing tempera ture (MST) . When t h e MST i s exceeded, v a r i o u s i n t e r e s t i n g phenomena may be observed ( s e e f i g u r e 1 4 ) ; t h e s e a r e accompanied by t r a n s p o r t p rocesses a t t h e i n t e r f a c e s .

t F i g u r e 1 4 : Phenomena a t t h e m i c e l l e - s p l i t t i n g tempera ture (MST) f o r mixed s u r f a c t a n t (nonionic-an- i o n i c )

CONCLUSIONS

With t h e t e c h n o l o g i c a l p o s s i b i l i t i e s taken i n t o c o n s i d e r a t i o n , and with t h e h e l p of a r a p i d t es t procedure , i t was p o s s i b l e t o s e - l e c t s u r f a c t a n t s s u i t e d f o r EOR p r o c e s s e s i n h i g h - s a l i n i t y systems from a l a r g e number of products . The s e l e c t e d s u r f a c t a n t s a r e an- i o n i c s and belong t o t h e c l a s s e s of polyglycolethercarboximethy- l a t e s and polyglycolethersulfonates. As a r e s u l t of t h e manufac- t u r i n g p r o c e s s , t h e s e products may be c l a s s i f i e d a s mixed s u r f a c - t a n t s ( n o n i o n i c - a n i o n i c ) . S ince mixed micelles a r e formed, t h e s e products p o s s e s s s p e c i a l temperature-dependent p r o p e r t i e s which a r e i n t e r e s t i n g f o r EOR p r o c e s s e s . I n t h e long term, ta i lor-made p r o d u c t s , e s p e c i a l l y s u r f a c t a n t m i x - t u r e s o r mixed s u r f a c t a n t s , o f f e r s p e c i a l promise from t h e economic p o i n t of view.

6 0

Nomenclature

c .m .c . - - critical micelle formation concentration CS - - salinity/concentration of salts dissolved; g. 1-1 EO - - ethylene oxide EOR - - enhanced oil recovery

phase) HLB - - hydrophilic/lipophilic HC - - hydrocarbons OOIP - - original oil in place,

PO - - propylene oxide O/W

ppm - - parts per million

- - oil/water

tertiary oil recovery

balance

%

T D S - - iota1 dissolved solids, % W/O - - water-in-oil 0 - - temperature, OC

Abbreviations for fiqures

CT - - surfactant concentration in ppm or % - - distance between surfactant molecules at inter-

face, nm A1 # A 2

L1 L2

A u - - thickness of transitional interface - - length of hydrophilic chain, nm - - length of hydrophobic chain, nm - - interfacial tension, mN.m-1 Y

6 1

1 Baba lyan , G . A . :

2 Rosch. M . :

LITERATURE

P h y s i c o c h e m i c a l p r o c e s s e s i n o i l p ro - d u c t i o n , " P u b l i s h i n g House "Nedra" , Moscow, 1974 ( i n R u s s i a n )

The c o n f i g u r a t i o n of t h e p o l y e t h y l e n e - o x i d e c h a i n of n o n i o n i c s u r f a c t a n t s ( p a r t 1 ti 2 ) ( i n German) T e n s i d e D e t e r g e n t s ( 1 9 7 1 ) , pp. 302- 313 T e n s i d e D e t e r g e n t s 9 ( 1 9 7 2 ) , pp. 23-28

3 S c h o n f e l d t , N . : " G r e n z f l a c h e n a k t i v e E t h y l e n o x i d -Adduk- te" ( I n t e r f a c e - A c t i v e E t h y l e n e Oxide Adduc t s ) , Wiss. V e r l a g s GmbH, S t u t t g a r t

S c h i c k , M . J . : "Non ion ic s S u r f a c t a n t s " , Marce l Dekker, I n c . ,. N e w York, 1967 / C h a p t e r 22

4 A k s t i n a t , M . H . : V i scous f l o o d i n g media f o r t e r t i a r y o i l r e c o v e r y i n h i g h l y s a l i n e sys t ems - s e l e c t i o n c r i t e r i a , t e s t i n g methods and e x p e r i m e n t a l r e s u l t s ( i n German) Ph. D. t h e s i s , TU C l a u s t h a l 1978

"Surf a c t a n t s and S e q u e s t r a n t s " , Noyes Da ta Corp . , Pa rk R idge , N . J . , 1977 ,

5 Gu t scho , S . J . :

6 B a l z e r , D . ; Kosswig , K . :

7 S c h i c k , M . J . :

8 Crook, E . H . ; Fordyce , D. B. ; T r e b b i , G.F.:

9 Kravchenko, J . J . :

1 0 A k s t i n a t , M.H. :

The p h a s e - i n v e r s i o n - t e m p e r a t u r e a s a c r i t e r i a f o r s e l e c t i o n of s u r f a c t a n t s f o r EOR ( i n German) T e n s i d e D e t e r g e n t s 16 ( 1 9 7 9 ) , pp. 256 - 261

S u r f a c e f i l m s o f n o n i o n i c d e t e r g e n t s I . S u r f a c e t e n s i o n s t u d y J . C o l l . S c i . 17 ( 1 9 6 2 ) , p p . 801-813

Molecu la r w e i g h t d i s t r i b u t i o n of non- i o n i c s u r f a c t a n t s / I I . P a r t i t i o n coeffi- c i e n t s o f normal d i s t r i b u t i o n and homogeneous p , t - Octy lphenoxye thox i - e t h a n o l s ( O P E S ) J . C o l l . S c i . 20 ( 1 9 6 5 ) , pp . 191-204

E f f e c t of t e m p e r a t u r e on t h e adso rp - t i o n of n o n i o n i c s u r f a c e - a c t i v e sub- s t a n c e s on s o l i d a d s o r b e n t s C o l l . J. USRR 33. ( 1 9 7 1 ) , pp. 379-381

S u r f a c e - a c t i v e a g e n t s f o r t e r t i a r y o i l r e c o v e r y : s e l e c t i o n c r i t e r i a and s e l e c t i o n methods ( i n German) T e n s i d e D e t e r g e n t s 14 ( 1 9 7 7 ) , pp . 57- 63

62

11 Rieckmann, M . : T e r t i a r y o i l r e c o v e r y methods ( i n German) Erdo14rdgas-Z. 91 (19751 , pp. 348- 359

1 2 Rud i , V.P.; Sobk iv , E.R. :

I n f l u e n c e of s u r f a c t a n t s on t h e p r o - p e r t i e s of c l a y s ( i n R u s s i a n ) K o l l o i d Zh. S ( 1 9 6 6 ) , pp. 119-122

1 3 Cash , R . L . e t a l . : S u r f a c t a n t a g i n g : a p o s s i b l e d e t r i m e n t t o t e r t i a r y o i l r e c o v e r y 50 . SPE of AIME Ann. F a l l Mtg., 28.3.- 1 .10 .1975 , D a l l a s / T x . SPE-Paper 5564

14 Trogus , F . J . e t a l . A d s o r p t i o n of mixed s u r f a c t a n t s y s t e m s 52 . SPE of AIME Ann.Fal1 Techn. Conf. & Exh., 9.-12.10.1977, Denver /Col . SPE-Paper 6845

1 5 W r i g h t , C .C . :

16 Oppenlander , K . ; A k s t i n a t , M.H.; Mur tada , H . :

The u s e of Carbon D i o x i d e i n w a t e r - f l o o d s A P I Prod . Div . P a c i f i c Coast D i s t r . Mtg., 21 . -23 .5 .1963, Los Angeles P r e p r i n t 801-39 k

S u r f a c t a n t s f o r enhanced o i l r e c o v e r y i n h i q h - s a l i n i t y s y s t e m s - c r i t e r i a f o r t h e s u r f a c t a n t s e l e c t i o n and a p p l i - c a t i o n T e n s i d e D e t e r g e n t s 17 ( 1 9 8 0 ) , pp . 57- 67

CHEMICAL FLOODING 63

PRELIMINARY STUDIES OF THE BEHAVIOUR OF SOME COMMERCIALLY AVAILABLE SURFACTANTS IN

HYDROCARBON-BRINE-MINERAL SYSTEMS

C. ANDREWS, N. M. COLLEY and R. THAVER

British Gas Corporation, London Research Station

ABSTRACT

Some commercial surfactants have been studied with a view to their usefulness for enhanced oil recovery applications. The following aspects of their behaviour have been assessed.

1.

2.

3.

The interfacial tensions were measured by the spinning drop technique. As the temperature varies, the interfacial tension of a surfactant-brine- hydrocarbon mixture passes through a minimum. Some surfactants have given interfacial tensions approaching 10-3 dynes cm-1.

Their interfacial tension behaviour with crude oil and pure alkanes.

The variation of phase inversion temperature with different variables.

Their adsorption onto rock surfaces

We have

1.

2.

3.

4.

5.

found :

The phase inversion temperature decreases with increasing salinity, the hydrocarbon and the surfactant concentration and composition remaining constant.

For constant salinity and surfactant concentration phase inversion temperature increases with increasing equivalent alkane carbon number.

The phase inversion temperature increases with ethylene oxide content of the surfactant, salinity and hydrocarbon remaining constant.

The phase inversion temperature decreases with increasing lipophilic alcohol content of the systems.

Static adsorption tests on reservoir rock show Langmuir adsorption isotherms.

Introduction

London Research Station, the corporate laboratory of British Gas became involved in enhanced oil recovery after an invitation by the Department of Energy to take part in its research programme coordinated by A.E.E. Winfrith. information available to us on the reservoirs operated by British Gas Corporation

After a review of

6 4

we decided that our resources would be most usefully employed studying micellar/polymer and miscible flooding. performed so far to identify commercially available surfactants with interfacial tensions-lowering properties to suit the conditions prevailing in our reservoirs, and to assess their sensitivity to changes in reservoir variables, lack of sensitivity being a desirable (but attainable?) ideal. Measurements of phase inversion temperature (PIT), interfacial tensions and adsorption onto mineral surfaces have been made.

This paper describes the work we have

The Reservoir

Conditions in the target reservoir are similar to those listed below:

Oil type E.A.C.N. (Reservoir) 7-a

Temperature 43oc (Stock tank) 10

Formation water 90,000 mgNaCl/litre 1,300 mgCa/litre 500 mgMg/litre

400 mgCa/litre 1,200 mgMg/litre

Flood water (sea water) 30,000 mgNaCl/litre

Chemicals

Surfactants. Samples of the surfactants listed below were obtained from Hoeschst AG . Anionics: Hostapal" BV., an alkylaryl polyglycol ether sulphate - Na salt.

( 7 ethylene oxide (e.oJunits, 50% w/w active).

Surfactant A straight chain alkyl phenol ether acetate, 4 ethylene oxide units.

6 ethylene oxide units. Surfactant B .. 1.

Non ionics: units . ) T l O O " " "(10 ethylene oxide units.)

Sapogenate* T80 tri-butyl phenylpolyglycol ether(8 ethyleae oxide

T110 '* " .- (11 ethylene

T130 '* '* (13 ethylene oxide units.)

oxide units.)

(All 100% active).

Hydrocarbons used in this work were specified to be greater than 99% pure.

Arkopal* NO60 Nonyl phenylpolyglycol ether (6 ethylene oxide units.)

* Hostapal, Sapogenate and Arkopal are trade marks of Hoechst AG.

65

Phase Inversion Temperature

The phase inversion temperature, PIT, of a hydrocarbon/brine/ surfactant system indicates the existence of a minimum interfacial tension at that temperature. Since the lowering of interfacial tension is a requirement for the mobilisation of oil trapped in constricted capillaries and all oil reservoirs are essentially isothermal, PIT represents a useful parameter for the selection of surfactant for a given reservoir. For nonionic surfactants below the PIT the surfactant partitions preferentially into the aqueous phase and the emulsion formed between the two phases is predominately 'oil-in-water'. Above the PIT, it partitions mainly into the oleic phase and forms a 'water-in-oil' emulsion (Balzer and Kosswig,l979). studies of PIT with a range of anionic carboxy methylated nonyl phenol ethyoxylate surfactants. They found:

1. and that aromatic hydrocarbons show very low values of EACN. compounds and alkanes give intermediate PITS.

2.

3. surfactants

We have extended this work to nonionic surfactants in studying the following variables on PIT. The effects of these variables must be considered if a surfactant flood is to maintain its oil mobilising properties as it passes through the reservoir. The parameters studied in this work are:

Balzer and Kosswig (1979) have carried out some parametric

PIT increases with increasing equivalent alkane carbon number (EACN) of the oil Mixtures of aromatic

PIT increases with decreasing salinity.

PIT increases with increasing number of ethylene oxide groups in ethoxylated

1. 2. Surfactant type and concentration 3. Salinity 4. Co-surfactant type and concentration 5. Phase ratio 6.

Oil type expressed as EACN.

Number of ethylene oxide units in surfactant molecule.

1. The EACN for a given reservoir oil should be constant. The EACN of our reservoir crude has been assessed from measured EACN calculated from a well stream analysis.

2. The concentration of surfactant at some point away from the injection well is likely to change because of adsorption onto the reservoir rock surfaces. Adsorption measurements are therefore important.

3. reservoir may vary from pure injection water to pure formation water.

4. Co-surfactant effectiveness may change with concentration and type.

5. Variable oil/brine ratios will occur in a reservoir as a flood proceeds. must be taken into account when performing laboratory tests.

6 . oxide content,(Shinoda 1965). Commercial surfactants are usually assigned a nominal ethylene oxide content, but actually contain a distribution of e.0. chain lengths. If PIT is dependent upon the number of e.0. units, then selective adsorbtion by reservoir rock will change PIT.

6f stock tank crude and

The salinity of the brine in contact with residual crude in a waterflooded

This

The hydrophilic/lipophylic balance of a surfactant will depend upon its ethylene

66

dynes/cm IFT, 10-L

t0-L

lo-& V t I

I I

J PIT T°C

T°C

4 ' ( I Temperature $ 4 * I

:t ivi ty

Figure 2

Adsorption

The investigation consisted of a series of experiments to measure A, the adsorptive capacity of the reservoir rock for surfactant material. on that of Somasundaran & Hannah (1979). The method of analysis for surface-active material was the titration procedure of Reid et al., (1967).

The method used was based

Interfacial Tension

Measurements were made at ambient pressure with the University of Texas drop tensiometer.

spinning

Interfacial Tension

It is necessary to augment the data obtained from PIT measurements. The inversion of emulsions occurs over a small temperature range. For this to occur with minimum energy an interfacial tension minimum is implied. A typical plot of I.F.T. against temperature is sketched in Fig.1.

Measurements have been made to determine the way IFT changes with temperature.

Methods

Phase Inversion Temperature was determined by means of electrical conductivity measurements (Baker and Kosswig 1979). non-ionic surfactant initially below the PIT the conductivity slowly increased with temperature but fell rapidly as the emulsions inverts and the aqueous phase became discontinuous and therefore non-conducting. Figure 2 shows a typical curve. More than one 'minimum' may occur for impure surfactants.

For an oil-in- water emulsion with a

67

TESTS, RESULTS AND DISCUSSION

1. Variation of PIT with EACN and determination of EACN value of the p h e n y u cyclohexyl groups.

PITS were determined on the following mixtures at the phase ratios stated (brine/oil).

Surfactant Concentration Brine Hydrocarbons Phase Ratio Results /litre brine/oil

A ~

10 Seawater n-alkanes C7-C10

A+B

T80

T80

T 80

T80

TlOO

TlOO

TlOO

5 of each Seawater n-heptane-toluene mixtures EACN 4 to 7

10 Seawater N-alkanes c6 to cll methylcyclohexane

As above after storage for 3 months at room temperature

10 30g /NaClI n-alkanes litre cg-cl1

11 ** 1. I. 50

butyl cyclohexane

phenyl heptane

phenyl octane

.. .. 50

I, .. *. ..

5: 1 Fig 3 line A

5 : l Fig 3 line B

5:l Fig 4 line A

Fig 4 line B

4 : 1 Fig 5 line A

Fig 5 line B

Fig 5 line C

Fig 5 line D

4 : l Table 1

Table 1

Table 1

Results and Discussion

The results presented in Figs 3 to 5 show a linear relationship between EACN and PIT over the EACN range studied.

68

PIT "C

70

60

50

40

30

20

PIT "C

70

60

50

40

30

20

3 4 5 6 7 8 9 10 EACN

Figure 3: Variation of PIT with EACN for two different surfactant solutions.

I I I I I I I I I I 4 5 6 7 8 9 1 0 1 1 12

EACN

Figure 4 : Variation of PIT with EACN for log /1 Sapogenate T80 in seawater.

Line D

Line A

6 7 8 9 10 1 1 12

EACN

Figure 5: Variation of PIT with EACN; pure n-alkanes, 30 g /litre NaCl

69

The EACN of butyl cyclohexane was determined relative to the Fig 5 line B and line C, phenyl heptane and phenyl octane were determined relative to Fig 5 line C. values found are listed in Table 1.

The

TABLE I

EACN found Assigned EACN of ring

butylcyclohexane 6.5 (Fig 5 Line C) 6.75 fig 5 line B 2.6

phenyl heptane 5.0(" '. ") - -2.0

phenyl octane 6.0(" " ") - -2.0

Thus we are able to assign an EACN of 3.6 to methyl cyclohexane. us to dilute stocktank crude with hydrocarbons with rings to obtain mixtures of hydrocarbon at ambient pressures having EACNs more representative of reservoir crudes. A shift of PIT of 2 to 30C was observed on storage at room temperature for 3 months of the stock 50 gms TlO/litre solution from which line B fig 4 was obtained. No further change was observed on storage for a further 5 months, nor on a freshly prepared solution stored at 40OC for 3 weeks.

At the higher concentration of T80 the dependance of PIT on EACN is reduced. The affect is not as marked in the case of T100.

The difference in slopes shown between lines A and B, Fig 3 suggest the possibility of modifying the sensitivity of a system to change in temperature by the addition of another surfactant. problems in practice.

PIT can change rapidly with EACN. (line B Fig 3) are possible and the slope can change with surfactant concentration.

This may enable

Differential adsorption within a reservoir could cause

Rates of change of PIT of up to 140C/EACN unit

Rates of change of PIT as low as 30C/EACN unit are possible (line A Fig 3).

2. Variation of PIT with surfactant concentration

Tests h e effect of increasing surfactant concentration was studied on the following mixtures.

Surfactant Concentration Brine Hydrocarbon Phase ratio Results 8 hitre g NaC111 brineloil

T80 Various 30 heptane 4 : 1 Fig 6 10 to 70 Curve 1A

octane 4 : 1 Fig 6 I. *I T80 Curve 1B

heptane 4:l Fig 6 .* I. TlOO Curve 2A

octane 4:l Fig 6 I, .I TlOO Curve 2B

I0


The results are shown in Fig 6 . Both surfactants exhibit a non-linear relationship, with PIT increasing with decreasing surfactant concentration. This is in agreement with the work of Shinoda and Arai (1964). PIT is lower at high surfactant concentrations which indicates that a high concentration flood could be less susceptible to concentration changes.

The rate of change of

PIT *C

60

50

40

30

20 I

' 16 io 40 4b ';o Qo 7 b ad Surf actant concentrat ion, g /litre

Variation of PIT with concentration of Sapogenate T80 and T100.

Figure 6:

3 . Variation of PIT with Salinity

Tests PIT'S were determined on the following mixtures. -

Surfactant Concentration Brine g /litre

Hydrocarbon Phase ratio Results brine/oil

Ta0 10 NaCl only Stock Tank 5:l Fig 7 (various Crude EACN 10 line A concentrations)

T80 10 hexane

T a0 10 heptane

4 : l Fig 7 line B

4 : l Fig 7 line C

T80 10 octane 4 : l Fig 7

line D

71

Results and discussion

The results are shown in Fig 7. For all hydrocarbons tested, the rate of change of PIT with salinity is independent of the hydrocarbon used. The decrease in PIT with increasing salinity is to be expected as the surfactant partitions more readily into the oleic phase as salinity increases (Knickerbocker et al, 1979).

PIT OC

60 .

50 -

40 -

30

\ Line A

2o 1 10 20 30 40 50 60 70 80 90

Brine concentration, g NaCl/litre.

Figure 7:,,Variation of PIT with brine salinity; /litre Sapogenate T80 solution. 10 g

4 . Variation of PIT with Alcohol (Cosurfactant) type and concentration

Tests Measurements were made on 50 g T100flitre brine. Brine concentration was - 30 g /NaCl/litre and oil EACN 7.5 at a phase ratio of 4 : l .

Alcohols studied were: (a)' iso-butanol (lipophilic)

(c) isopropanol (hydrophilic) (b) is0 pentanol( " 1

Results and discussion.

The results shown in Fig 8 agree (Knickerbocker et al, 1979), in that increasing the concentration of a lipophilic alcohol (lines A and B) will increase the partitioning of the surfactant into the oleic phase and tend to lower the PIT. opposite affect but less pronounced. Increasing the concentration of hydrophilic alcohols has the opposite effect on PIT as increasing surfactant concentration. an alcohol has to be used as a viscosity modifier then hydrophilic alcohols may be more manageable with respect to their effect on PIT than lipophilic alcohols.

with trends predicted in the literature,

The hydrophilic alcohol (line C) has the

If

72

60 PIT OC

50

40

30

50 g /litre 30 g /litre EACN 7.5

Sapogenate NaCl

10 20 30 40 50

Alcohol concentration, g /litre.

Figure 8: Variation of PIT with alcohol concentration

5. Variation of PIT with brine/oil phase ratio

Tests with phase ratio.

PITs were measured on the following mixtures to find out if PIT varied

Surfactant Concentration Brine Hydrocarbon Results

T8 0 50 g /litre 30 g Nacl n heptane Fig 9 /litre line A

T80 10 g /litre " " " n hexane Fig 9 line B

" n heptane Fig 9 .. I. .. *. *. T80 line C

** n octane Fig. 9 line D

I. .. .. .. .. T80

TlOO

Results and Discussions

The possibility that PIT would depend upon phase ratio was indicated when PITs obtained from the measurements in the spinning drop tensiometer did not correspond exactly to those made by the conductivity measurements.

The results show that PIT increases as the proportion of oleic phase increases. This is contrary to the findings of Balzer and Kosswig (1979) who reported smaller changes with the opposite slope. and Kosswig (op.cit.)

Arai (1965) reports the same effect as Balzer

7 3

Line D

Line C Line B

Line A

10 20 30 40 50

' 60 PIT "C

50

40

30

20

Volume I hydrocarbon

Figure 9: Variation of PIT with phase ratio.

6. Variation of PIT with Ethylene Oxide (eo) content of surfactant

Tests PITS were measured using a mixture of pure normal ,alkanes, EACN 7.5 - with 30 g NaCl/litre brine containing 50 g of surfactant/litre.

The surfactants used were Sapogenate T80,TlOO,T110 and T130 which contain (nominally) 8, 10, 11 and 13 ethylene oxide units respectively. Intermediate eo contents were obtained from mixtures of the adjacent surfactants as supplied and were calculated on a molar basis.


The results presented in Fig 10 show a linear relationship between PIT and the number of eo units per molecule. probably due to evaporation of the hydrocarbon during the test.

The findings are in agreement with those of Bourell et a1,(1980). in PIT is explained by the increased hydrophilic properties with increased eo content (Shinoda, 1965).

The Arkopal series of surfactants probably exhibits a similar trend but only two have been tried i.e. NO60 ( 6 eo's) and N080(8 eo's). about 30C and 70-75OC respectively at a concentration of 50 g the same brine/hydrocarbon system. greater with the Arkopal series than the Sapogenates.

Where a surfactant contains a spectrum of eo contents, selective adsorption by the reservoir rock may change its effective eo value and thus affect the PIT of the system.

The deviation from linearity above eo - 11 is The change

These gave PITS of /litre in

The effect of the number of eo units is

74

PIT "C.

tion = - 50 g 7.5

'Surfactant ethylene oxide number.

Figure 10: Variation of PIT with surfactant ethylene oxide number

7. Variation of IFT with temperature

Tests Interfacial tension measurements were made between the upper and lower phases obtained from mixtures whose PIT'S had been determined in an attempt to confirm the presence of an IFT minimum at fhe PIT.

Tests were performed with the following mixtures. ~~~

Surfactants Concentration Brine Hydrocarbons Phase ratio PIT Results

T80 10 g /litre 30 gm NAClf n hexane 4: 1 39 Fig 11 litre

*. I. ** n octane 4: 1 49.5 Fig 12

*' Crude EACN 5: 1 23.5 Fig 13

.. 1. I. T80

NO60 .. .. 1. .. *I

=10 '


The results obtained are shown in Figs 11 to 13. conductivity measurements are included in the above table. Repeat determinations of 1.F.T. were usually found to agree within 2 5%.

Figs 11 and 12 indicate that a minimum does occur at the PIT but that more than one 'minimum' can occur. This is supported by conductivity traces made during PIT measurements and is probably due to a proportion of surfactant having a different number of eo units than the stated nominal value.

The equipment available only allowed for the transfer of phases into the tensiometer at room temperature. Measurements were made at various temperatures after heating

The PITS obtained from

75

Oil : n-hexane

Surfactant : Sapogenate T80, dynes /cm Brine : 30g /litre NaCl

1Og /litre

30 34 38 42 46

Temperature, 'c Figure 11: Variation of IFT with temperature.

Oil : n-octane

Surfactant : Sapogenate T80,- Brine : 30 g /litre NaCl

log /litre.

38 42 46 50 54

Temperature OC

Figure 12: Variation of IFT with temperature.

from room temperature. phase (microemulsion) begins to develop as the equilibrium is disturbed. to make meaningful measurements the middle phase is separated from the remaining oil drop. This was achieved with some difficulty especially in the case of colourless oils.

As one increases the temperature of the sample tube a third In order

Ideally, equilbratlon, sampling and measurements should be carried out at the same temperature.

1 6

J

lo-?

Oil : Dead crude Brine : 30 g /litre NaCl

dynes;::: 1 Surfactant : Arkopal N 6 0 , l O g /litre 10-2

10-4 15 20 25 30

Temperature ,OC

Figure 13: Variation of IFT with temperature

Adsorption of Surfactants

Tests This section describes the results obtained for adsorption of Hostapal BV on reservoir material in various states of disaggregation. BV was terminated, (because optimal salinity falls outside the range of our interest), the results showed some of the-limitations of static adsorption tests.

- Although work on Hostapal

Samples of reservoir rock were taken from cores and crushed in a ball mill until the powder passed 180 sieve. 25 g of sample were taken and

distilled water or sea-water. hours 40OC. minutes, by which time, the supernatant liquid was clear. Analysis of this liquid then gave the remaining concentration of Hostapal BV. amount abstracted by the solids was calculated.

equilibrated with 50 cm3 o r various concentrations of Hostapal BV in The suspension was stirred constantly for 4

The aqueous portion ws then decanted and centrifuged for 30

Hence the

s o o 5 1 AdsorDtive I Adsorptive

capacity,A e o o 5 1

0.5 1.0 Equilibrium concn,c,g /1

0.5 1 .o Equilibrium concn., c,g / I

Figure 1 4 : Adsorption of Hostapal BV Figure 15: Adsorption of Hostapal BV Onto reservoir rock, Sample 1. onto reservoir rock,Sample 2.


The tests performed are listed below and the results presented in Figs 14 to 18. Table 2 shows a typical sets of results.

er "..a water

0.5 1 .o Equilibrium concn., c,gr /I.

Figure 16: Adsorption of Hostapal BV onto reservoir rock,Sample 3.

TABLE 2 (SAMPLE 3)

Initial surfactant Final (equilibrium) Adsorptive capacity concentration surfactant concentration,C A, g surfactantlg

g /litre g /litre rock

0.25

0.50

1.0

1.75

2.0

2.5

3.3

5.0

0.0078

0.033

0.098

0.164

0.184

0.193

0.352

0.957

0.00048

0.00092

0.0018

0.0033

0.0036

0.0046

0.0059

0.0080

18

- 4 -

-5 -

-6 -

.003

Adsorptive capacity A,

g l g

-7 -

1nA

1 I I I

I i I

0 . 5 1 .o Equilibrium concn., c, g 11

Figure 17: Adsorption of Hostapal BV onto reservoir rock, sample 4.

In c

Figure 18: Data from Figure 16 plotted logarithmically

79

All the figures show the tendency for A to tend towards a constant for a given sample as the equilibrium concentration increases. were also equilibrated with the surfactant in seawater and the results appear to show a much higher adsorptive capacity. porosity characteristics to the other samples. form as the classical adsorption isotherms.

Portions of Sample 3 (Fig 16)

Sample 3 has similar permeability and The curves have the same general

A= adsorptive capacity A = Kc where c= final concentration

K and n are constants or In A = In K + In C

The data in Table 2 (sample 3) are plotted as In A against In C in Fig 18.

There are indications in Fig 1 4 and 15 that adsorption may be proceeding in layers.

A qualitative test of the effect of particle size on the equilibrium adsorption of surfactant was performed in a similar manner to those described above. obtained are shown in Table 3.

The results

Table 3

A g l g

< 180~ 0.0036 'fine powder 0.0028 'coarse grains' 0.0022 cm size pieces 0.0002

This would appear to limit the usefulness of static adsorption and calculation of a 'worst case' total adsorption capacity of a reservoir. obtained from core flood experiments.

More useful data would be

CONCLUSIONS

Phase inversion temperature can serve as a guide to the conditions under which a non ionic surfactant will give an interfacial tension minimum.

Using the linear relationship between EACN and PIT it is possible to assign an EACN to; stock tanks crudes, and aliphatic and aliphatic cyclic hydrocarbons. It should then be possible to use cyclic hydrocarbons to lower the EACN of stock tank crude to that of reservoir crude for use in partitioning and phase studies at ambient pressure.

If the way in which the parameters which affect surfactant properties change during the course of a flood can be assessed it should be possible to design a flood which will maintain it's properties. This, however, requires detailed knowledge of the reservoir.

Acknowledgements

We would like to thank the British Gas Corporation for their permission to publish this paper.

80

BIBLIOGRAPHY

Balzar, D, and Kosswig, K.; The phase inversion temperature as a criterion for the selection of survace active agents in the tertiary production of mineral oil.

Tenside Det. 16 (1979), 5, pp 256-261.

Shinoda, K.; The comparison between the PIT system and the HLB - value system to emulsifier selection.

Comptes rendus du 5 eme Congress International de la Detergence, Barcelona, (1965), pp 275-283.

Somasundaran, P. and Hannah, S.; Adsorption of sulphonates on reservoir rocks.

SOC. Pet. Eng. Jour. August 979, pp 221-232.

Reid, V.W., Longman, G.F. and Heinerth, E.; Determinaton of anionic active detergents by two-phase titration.

Tenside Det. 4 (1967), pp 292-304.

Shinoda, K. and Arai, M. The correlation between phase inversion temperature in emulsion and clould point in solution of nonionic emulsifier.

Jour. Phys. Chem. 68 (1964), 12, pp 3485-3490.

Knickerbocker, B.M., Pesheck, C.V., Scriven, L.E. and Davis, H.T. Phase behaviour of alcohol-hydrocarbon-brine mixtures.

Bourrel, M., Salager, J.L., Schechter, R.S. and Wade, W.H. A correlation for phase behaviour of nonionic surfactants.

Jour.Colloid Interface Sci. (1980), 2, pp 451-461.


THE PROVISION OF LABORATORY DATA FOR EOR SIMULATION

C. E. BROWN and G. 0. LANGLEY

Petroleum Engineering Branch, Exploration and Production Division, BP Research Centre, Sunburyen-names

Abstract

Laboratory core tests are important in the development and assessment of EOR processes. characterise the physical processes relevant to the field, and are appropriate to their use in field simulators. relative permeability is discussed, and its extension to low tension immiscible displacement assessed. is discussed with reference to oil slug propagation along a core.

It is vital that the core data obtained

The key parameter of

The current status of these concepts

1. Introduction

Our overall aim is to obtain data from laboratory tests on core samples, to use these data for the prediction and analysis of field trial performance, and ultimately for the prediction of full field performance.

There are many problems on the way from core tests to reservoir

In this paper we will performance prediction, one of the biggest being reservoir description and identification of reservoir heterogeneity. limit our discussions to the topic of laboratory core data, and how this may be used to examine the physical processes involved in oil recovery. We will work bn the principal that if successful6,efficient displacement cannot be obtained from a core sample, then there will be little chance of obtaining success on the field scale. We will consider the theoretical aspects associated with oil bank propagation, and how the predictions are affected by the relative permeability input data. brief discussion of methods of assessing potentially useful surfactant systems and possible artifacts associated with core tests on the laboratory scale is included. immiscible floods only.

A

In this paper we will discuss low tension, Miscible flooding will not be considered.

2. Laboratory core waterflood tests

Before considering low tension flooding, we will review the more conventional waterflood case, since this often forms the basis for enhanced oil recovery methods. Waterflood tests on core samples can be used to gain information on the efficiency of displacement of oil by water from actual reservoir rock. tests are usually confined to one dimension.

Laboratory displacement

82

For stron&ywater-wet rocks the efficiency of displacement is good in the sense that the displacement appears piston-like; practically all of the oil is recovered before breakthrough of the flooding water. However, residual oil is trapped behind the waterflood front as insular globules of oil usually occupying the larger pore spaces (1). the relationship being influenced by pore structure. The scope for tertiary oil recovery may be high in this case.

This residual oil level is dependent on the initial oil saturation;

For strongly oil-wet rock the displacement does not appear to be efficient. Early breakthrough of water often occurs, and large amounts of oil are recovered after water breakthrough, at high fractional flow of water. Residual oil is less well defined in that oil is by-passed rather than trapped and occupies smaller pores and surface grooves. However, oil may continue to be produced until very low oil saturation is obtained ( 2 ) . The scope for tertiary oil recovery may be' low in this case. The contrast in the oil-wet and water-wet case is shown in Figure 1.

FIG. 1

I n order to predict waterflood performance, it would be convenient to generate a data set which could be used for the prediction of flood performance and which is a unique property of the rock.. concept of relative permeability was introduced to fulfil this role, which has now become central to conventional numerical simulation of oil recovery processes.

The

3. Relative Permeability

The basic concept of relative permeability is limited to movement of twoormore continuous phases in the same direction through

valid to extend the Darcy equation for single phase f low to the multiphase case.

porous media at a steady saturation level. It assumes that it is

8 3

The concept is most likely to hold in the case of a sample which has initially 100% saturation of the wetting phase and where the saturation of the non-wetting phase is increasing. Relative permeability data can be generated either by a steady-state method (where both phases are injected simultaneously into the core sample and permeability measurements are made at a steady-state fractional flow), or by analysing flood data (e.g. using the Johnson, Bossler method (3) based on the Buckley-Leverett theory (4)).

two ways: Some validation of the relative permeability concept comes in

1) The steady-state and flood derived data are similar

2 ) Data produced fr6m floods using different viscosity ratios give data which lie on the same curve, even though the recovery performance may be significantly different.

Figure 2 shows typical relative permeability curves for an oil flood of a water-wet rock. permeability to oil increases quite rapidly, and that to water drops rapidly. is very much less than unity indicating interference between the phases.

It is noted from Figure 2 that the relative

The sum of the relative permeabilities througbuttheir range

s o sw

3.1 Waterflooding - the oil-wet case

Parallel arguments apply to a waterflood of an oil-wet rock. Figure 3 shows typical relative permeability curves for the oil-wet case.

Provided that capillary dispersion and end-effect problems are not involved, the waterflood performance (and hence the relative permeability obtained from waterflood data), does not appear to depend on flood rate ( 5 ) . Moreover, provided that the phases remain continuous and immiscible then, in concept, the relative permeabilities should not depend on interfacial tension.

a 4

It is often suggested that the relative permeability curves will change shape as the interfacial tension is lowered, tending towards straight lines where the sum of the relative permeabilities is unity at all saturations ( 6 ) . miscible or partially miscible displacement tests where diffusion processes act to distribute the fluid components equally over the pore structure of the rock. improving the displacement efficiency. Theoretically, the flood efficiency can be improved by straightening the oil relative permeability curve to reduce the rate of change of fractional flow of water. The resulting relative permeability curves for these miscible displacements are pseudo-functions with little predictive capacity. Steady-state tests using miscible systems are likely to produce straight line relative permeability data since a mixture of the components slows in all conductive flow channels.

As mentioned earlier, an alternative viewpoint for immiscible

This view often results from the study of

Diffusion processes have the effect of

systems is that the oil drainage relative permeability curves will not change as interfacial tension is reduced. the oil recovery performance is independent of interfacial tension. Support for this view comes from the fact that increasing the capillary number (VL/y) has little effect (assuming constant viscosities) on recovery performance, provided that capillary dispersion and end-effects are negligible ( 5 ) . In addition, for oil-wet systems residual oil saturation is not a well defined quantity; provided that enough water has passed through the rock, and that end- effects are negligible. have little effect on residual oil.

The conceptual reasoning for the argument that relative permeability does not change as the capillary number increases is that the displacing fluid will preferentially occupy pore channels with higher flow capacity, irrespective of interfacial tension. More experimental work is neede& before definite conclusions can be drawn as to which relative permeability behaviour is relevant to low tension immiscible displacement.

This would require that

in any case it is very low,

Reduction of interfacial tension will therefore

3.2 Waterflooding - the water-wet case

For the case of waterflooding of a water-wet rock, the basic concepts of relative permeability are not strictly adhered t o ; pally because the non-wetting oil phase does not remain in communication. As mentioned earlier, the recovery performance of a waterflood on a water-wet core usually appears piston-like. permeability data can be generated using conventional analysis of the flood performance, apart from end-point data.

princi-

Therefore no relative

Relative permeability curves can be generated from steady-state tests, but the data can vary depending on the test method. method is to change the fractional flow in steps which results in a saturation front travelling down the sample. state test should avoid such saturation gradients in the core sample. This situation can be approached by gradually changing the fractional flow over a long period of time. permeability curves are shown in obtained by the two steady-state methods are not necessarily the same, and might not agree with that obtained from a flood.

A common

Perhaps a true steady-

Possible shapes of the relative Figure 4. The residual oil values

85

The shape of the relative permeability curves may be considered to be academic in the water-wet case, since both sets of relative permeability curves shown in Figure 4 will probably predict plug displacement if the Buckley-Leverett theory is used. However, there may be differences of predicted flood performance when using coarse grid finite difference numerical models, but this is an artifact of the model and is usually overcome by empirically altering curves of type 1 to be more like type 2. not have a satisfactory theory to combine viscous and capillary flow effects, and we usually resort to some form of pseudo functions to match observation.

The truth of the matter is that we do

The residual oil saturation obtained after a waterflood is a definite value, in that oil flow completely ceases (unlike the oil-wet case). and on flood rate. The distribution of residual oil is also dependent on flood rate (1). In addition, high flood rate can make a weakly '

water-wet rock appear oil-wet (7,8).

The residual oil level is dependent on initial oil saturation

It is noted from Figure 4 that the relative permeability to water at residual oil saturation is low, indicating that trapped oil occupies the largest pore channels. this can be advantageous since water mobility following the flood front is kept low, thus suppressing viscous fingering on the reservoir scale.

From the point of view of a field flood,

1.0

krw

sw

FIG. 5

The residual oil saturation is also dependent on interfacial tension. facial tension can also make a water-wet sample look oil-wet. Considering the changes to the water-wet relative permeability curves as the interfacial tension is lowered, it is to be expected that significant changes will occur. method (9) indicate that below an interfacial tension of 0.1 mN/m large changes in the water-wet curves occur. The tendancy is for the relative permeability curves to become straight lines, the sum of the relative permeabilities approaching unity at all saturations. As the interfacial tension is lowered during steady-state tests it is more likely that an emulsion of oil-in-water or water-in-oil will form.

The absence of imbibition in the case of very low inter-

Data obtained by the steady-state

86

As the interfacial tension decreases to very low levels the drop size is likely to become extremely small. where the same fluid system is flowing in all conductive flow channels. In this situation straight line relative permeability data might be expected, although the basic concepts of relative permeability in fact no longer apply.

A situation will be approached

Relative permeability data obtained from displacement tests have shown somewhat different results (9) . As the interfacial tension was lowered the relative permeability to water increased and that to oil decreased. At low interfacial tension (0.01 mN/m) the relative permeability curves resembled oil-wet data. proposal that oil drainage curves could be used as a first approximation for the back end of an oil bank even for a water-wet rock.

(for constant

This supports the

Curves of residual oil saturation versus V/y viscosity) can be generated by two methods:

i) Where each flood starts from the same initial oil saturation (curve A, Figure 5 ) .

Having established a residual oil saturation at low values of V/y by increasing V or decreasing y . as trapped oil is mobilised (curve B , Figure 5).

ii) we can increase V/y

The residual oil saturation will eventually decrease

4. Application of laboratory data to enhanced recovery prediction

Reduction of residual oil saturation is. a necessary but not sufficient condition for a successful tertiary recovery flood. be essential to develop and maintain an oil bank. developed, it is the mobilised oil which collects and mobilises residual oil at the front of an oil bank. Surfactant at the back of the bank prevents retrapping of the oil.

It may Once an oil bank is

We need to consider generation of secondary drainage relative permeability data, starting from the residual oil saturation left after primary imbibition, for application at the leading edge of the oil bank. Curves of the type shown in Figure 6 can be generated from steady-state tests. It has been suggested that the secondary drainage curves retrace the primary imbibition curves (10, 11, 12) but this needs confirmation, since it will depend on how the primary imbibition curves were obtained. Prediction of oil flood performance obtained using steady-state relative permeability data can be compared to oil flood data starting from residual oil saturation after the primary waterflood.

If we work on the principal that the interfacial tension at the back end of the oil slug is low enough to prevent retrapping of oil, then as suggested earlier we might use oil-wet type relative permeability curves to describe fractional flow at the back end of the bank. The relative permeability set would then look like those shown in Figure 7.

Theoretical predictions using this type of data will be discussed in the next section. of generating relevant relative permeability data for low tension floods (13 - 21), there is still a need to obtain more data to clarify the position.

Although many people have looked at the problem

a7

FIG. 6

sw

FIG. 9

AT WATER BREAKT!lROUGH

Water Arrival

88

5. OIL BANK PROPAGATION

In EOR processes the development and propagation of an oil bank is considered to be of importance; certainly the correct analysis of such phenomena is crucial to core testing. systems, analysis can only be carried out on the basis of assumptions which are difficult to validate, unless simplified systems can be studied. Curiously little work has been reported which attempts to do thin A recent paper by Gladfelter and Gupta (22) is valuable, in that it sets some experimental evidence against which current views of oil bank propagation may be weighed. One of the key findings is that a region of increased oil saturation (an oil bank) can be generated from the fractional flow properties, without invoking other mechanisms. The additional feature proposed to explain this behaviour was hysteresis of the relative permeability curves.

For highly complex EOR

The following outlines some features of oil bank propagation in two component, two phase (oil/water) displacement in cores as given by 1-D numerical simulation. This can be compared with the experimental results and Buckley-Leverett analysis of Gladfelteqand Gupta (22). into forty grid blocks, with an oil/water ratio of 3:l. simulation run, a 0.0475 pore volume slug of oil was injected at high rate into the core, which was initially set at residual oil saturation. The relative permeability hysteresis set first used was as shown as curves A and B in Figure lO(a), with the arrows indicating which limb corresponds to which directional change in water saturation. The corresponding fractional flow curves are shown in Figure 10(b). simulated is shown in Figure ll(a), showing a series of oil bank profiles as it progresses along the core. progresses with a well defined front, but the size of the bank degrades as oil is 'lost' into the following tail. Use of the same relative permeability set, but with the hysteresis directions reversed gives the behaviour shown in Figure ll(b); nisably propagated since it is quickly dispersed. lights the sensitivity of oil bank propagation behaviour to the relative permeability curves. dominant in the present examples.

The test system simulated consists of a 45 cm core, divided For each

The corresponding oil slug behaviour as

The front of the oil bank

in this the oil bank is not recog- This result high-

They also show that numerical dispersion is not

Following the procedure of Gladfelter and Gupta (22) , injection of an oil and water mixture (in the present case, 25% oil) into a core at residual oil saturation gave the results depicted in Figure ll(c); a sharp oil front is formed, but without the presence of a bank of increased oil saturation as-experimentally observed. This result is as expected, since the numerical model moves incrementally up the relative permeability curves to the imposed injection composition; overshoot this point, as can be achieved with front criteria as employed in a simple fractional flow analysis. the principal of an oil bank stabilised by relative permeability hysteresis can be demonstrated by simulating injection of an oil bank followed by injection of an oil/water mixture. The importance of an oil bank induced by hysteresis effects extends not only to the valid identification of "enhancedt1 oil, but also to the correct assignment of water-increasing or water-decreasing steady-state relative permeabilities; i.e. the presence of a transient bank may in fact involve changes in the direction reverse to that overall.

it cannot Rankine-Hugoniot shock

However,

This is shown in Figure ll(d).

89

fw

0 . 3 - - -

0,s (x/L) 1.0 c

90

91

More drastic disparity between the relative permeability curves used at the leading and trailing fronts of an oil bank can of course give stabilised bank propagation without an oil/water mixture being subsequently injected. Figure ll(e) shows this, using curves A and C of Figure lO(a). The straightening of curve A to give curve C follows the commonly assumed functional change in the relative permeability curve induced by reducing the interfacial tension. However, experimental verification of the relative permeability behaviour in eor systems is still limited, and the assumed curves may not offer a good description of the physical processes involved. displacement of oil by surfactant acts as a high rate water flood as suggested earlier (since in both cases capillary forces are dominated by viscous forces) the aqueous phase will preferentially travel through the larger pore channels. This could result in a relative permeability behaviour as shown in Figure 7, with an increased krw, but with a kro curve falling below the prior curve at high oil saturations, i.e. the low tension flood does not have the imbibition which in a water-flood case ensures the oleic phase preferentially occupies the larger pores of a water-wet medium. once more show degradation of an injected oil slug.

If the immiscible

The simulation results for this case (Fig. ll(f))

These simulation runs indicate the need to take proper account of relative permeability variations in the analysis and simulation of transient processes, and show that under certain conditions oil bank propagation will not occur. The use of assumed Ilideal" relative permeability data (i.e. straight line extrapolations) may artificially predict stable bank propagation.

6. IRREVERSIBILITY AND HYSTERESIS IN CORE TESTS

In this section some modelling approaches to describe non-identity are outlined.

Core tests can display a wide range of irreversible characteristics. Jones and Rozelle (23) consider that irreversibility results from the common "S" shaped fractional flow curve if the conventional tangent constructions are applied to waterflooding and oil flood respectively. However, in considering the Buckley-Leverett theory, it can be noted that two solutions to the problem are to be expected, since the material balance may be applied for either the waterflood or the oilflooding directions. particular stage of an EOR process must be used still holds. A more fundamental problem is whether the fractional flow curve itself is a unique function of saturation.

The conclusion that the direction appropriate to the

6. RELATIVE PERMEABILITY HYSTERESIS

6.1 Primary Hysteresis

The best documented tlhysteresisl' effects in relative permeability curves are associated with the irreversibility of the primary curves i.e. those curves which originate at initial conditions of complete saturation by a single phase. (or irreducible) phase saturations. essentially irreducible saturations can be established for both

This hysteresis gives rise to residual It is commonly assumed that

92

wetting and non-wetting phases, although the distribution and properties of these phases are by definition functions of wettability. it is usual to treat wetting and non-wetting phases asymmetrically.

Thus

The irreducible water saturation and the residual oil saturation values are expected to be dependent on the initial saturation established prior to reduction to residual. For strongly wetting phases, the residual saturation tends to be ill-defined, so this effect is of little consequence. empirical relationship which correlates initial and residual non-wetting phase saturations; phase and oil the non-wetting phase) is

For the non-wetting phase, Land (12) has proposed a semi-

the Land relationship (taking water to be the wetting

+ -1 + -1 (Sor) - (Swi) = c (1) +

where Sor = Sor/(l- swi)

swi = Soi/(l- Swi) +

with C being a constant for a given system.

Equations of this form have been used by Killough (24) to estimate hysteresis sets descending from the primary non-wetting relative permeability curve.

6.2 Secondary Hysteresis

The term secondary refers to those curves which start from the end points of the primary curves. accessible reversibly, that is in the saturation range Sw = Swi to (1-Sor). In fact, it is only within a reversible range that the term hysteresis can be truly applied. prove complex, and for relative permeability curves the lack of experimental precision and the probable dependence of data on experimental design (25) have so far prevented detailed analysis.

This region is (in principle) fully

The characterisation of any hysteretic system can

In the absence of a scientific approach, empirical relationships are generally developed on the basis of plausibility and utility. may be questioned whether the initial formulation of the multiphase flow relationships in the empirical Darcy-analogue form itself ensures that all subsequent analysis can be no more than empirical.

It

A currently favoured parameterisation of relative permeability curves uses a scaled power law relationship;

I kro = kro(Swi)*(S;)"o

krw = krw(Sor)*(S;)"w

where

* So = (l-Sor-Sw)/(l-Swi-Sor)

sw = (Sw-Swi)/(l-Swi-Sor) *

93

The secondary hysteresis can then be conveniently described by variation of the with an alternative different parameterisation scheme. parameter can be defined as

exponents, as used by Evrenos and Comer (26) A hysteresis

and similarly for the water exponents, where the superscript arrows denote increasing and decreasing water saturation. dependent on the value of Hi the hysteresis scan can occur in either direction, both types of behaviour being reported from experimental observations.

It can be noted that

The variation of the relative permeability curves for an EOR process requires detailed description if a numerical simulation of the process is to be made. For surfactant flooding, the paramaterised relative permeability curves are often modified in a systematic manner dependent on the new value of residual oil saturation (Sorc). Following this procedure with the hysteresis parameter, it is to be expected that the hysteresis becomes less pronounced as the residual

Sor = 0.2

FIG. 12

94

oil saturation is decreased (since any conceptual model of the hysteresis mechanism centres on irreversibility following loss of hydraulic connectivity during phase trapping). Paralleling other dependencies on Sorc, a logarithmic relationship between Hi and Sorc can be used, or more simply a power law expression.

( Sorc 1 a 1 - Hi (Sorc) =

( - 1 1 - Hi ( Sor I

(4 )

Two of a family of relative permeability curves using this relationship isshown in Figure 12, with the dependence of the no exponent on Sorc being

1 - no (Sorc) Sorc

1 - n Sor

- - - (5)

6 . 3 Scanning Hysteresis

Conventional oil recovery processes are usually described in terms of monotonic changes of saturation. processes aimed at mobilisation of post waterflood residual oil necessitate changes in the forms of the relative permeability curves and in the directions in which a process description scans them. In order to estimate how scanning from intermediate points of the secondary bounding curves will progress in the absence of definitive experimental evidence, parallels can be sought in other hysteretic systems. petroleum engineering experience is the capillary pressure as a function of saturation. to relative permeability 2nd to capillary pressure hysteresis, it is to be expected that mutually consistent descriptions should be possible. . In order to compare the two sets of phenomena, the relative permeabilities need to be expressed as a single variable, and the fractional flow can be considered to be a state variable which offers more hope of comparability with other hysteresis phenomena.

Enhanced oil recovery

The other hysteretic process which is well established in

Since the same physical processgives rise both

The most direct consistency relationship between capillary pressure scans and fractional flow scans would be if one set were directly mapable onto the other. However, since the fractional flow setis rigorously bounded whereas the capillary pressure set is asymptotically bounded, this can at best be an approximation. In addition, the commonly made approximation is also present in the comparison of equilibrium capillary pressure values with dynamic systems. to correlate primary capillary pressure curves with fractional flow curves have not to date proven sufficiently satisfactory to enable mapping of scanning curves from capillary pressure to fractional flow data.

A less direct appeal to consistency can be made by application

Attempts

of similar functional forms to describe both capillary pressure and fractional flow hysteresis sets. The most general theory available to describe hysteresis systems is Independent Domain Theory, as propounded by Everett (27). Unfortunately, the theory has not proved quantitatively applicable (due to the prime assumptions i.e. the existence of domains and their independence, Topp and Miller ( 2 9 ) ) , but does provide a qualitative framework in which empirical relationships can be set.

95

In recent years a number of studies have been carried out in which unsaturated flow in porous aedia has been analysed numerically using empirical analytic hysteresis functions. However, these studies have concentrated on liquid/vapour systems of interest to hydrologists rather than on liquid/liquid systems and the hysteresis relationship examined has been between the saturation and flow potential. an analogue of the empirical hysteresis function as recently used by Pickens and Gillham (29) to the fractional flow/saturation system gives

cosh(Sw/S1)a - (fi - f.)/(fi+fj)

cosh(SJS')a - (fi - f .)/(fi+f .)

Applying

I (6) fw = fi I J J

J

where S', a, f., and f. are fitting parameters which can be identified from sufficied data.

The functional form of this relationship can reproduce fractional flow curves, and scans within those curves which accord with the expected hysteretic behaviour as described by independent domain theory. However, this equation is not convenient in that the relative permeability hysteresis set cannot be explicitly separated from this representation.

applied to capillary pressure hysteresis, by which scanning curves are described by a scaled combination of the bounding curves. this to the relative permeability and fractional flow sets gives relationships of the type

A more flexible approach is to follow that which Killough (24)

Extending

c ., + + kri = kri - F(kri - kri) (7a)

fi = fi - F(fi - fi) (7b) 0 ., + +

0 1 where F = (Si - Si + a)- - l/a

(Simax - S: + a)-' -l/a

where the subscript refers to a scanning curve from point Si, the superscript arrows refer to the bounding curves, and a is a fitting parameter. Examples are shown in Figure 13.

96

The above discussion highlights the empirical way in which relative permeability hysteresis can be handled at present. important factors, such as core end effects and oil saturation residual to surfactant flooding, the position is even less well defined .

For other.

7. DISPLACEMENT TESTS FOR ASSESSING POTENTIALLY USEFUL SURFACTANT SYSTEMS

7.1 Screening tests

Any potentially useful surfactant system must be able to reduce

Having found a surfactant capable of doing interfacial tension between oil and water by a significant amount (e.g. down to lo-' mN/m). this, the next step is to conduct screening tests using glass bead or sand pack columns. core tests.

If successful, the next step is to conduct

As we have discussed, the wetting conditions of a core sample play a large part in the displacement characteristics. of considerable importance to march reservoir wetting conditions when conducting core tests. material which is carefully prepared in order to change the surface wetting as little as possible. flushing of live crude oil through the core at reservoir temperature.

It is therefore

In order to do this we use preserved core

Our present procedure involves the

The core is then left to ltageIt in contact with crude oil for several weeks. advance rate) to establish a residual oil saturation. Before injecting surfactant solution, the brine flow rate is increased to - 200 ft/day. This is essential to ensure that oil left in the core is "trapped oil" and not oil retained by core end-effects. Surfactant is then injected into the core at - 1 ft/day. Careful monitoring of the recovery performance enabled theoretical predictions to be tested. The theoretical work may show up reasons for lack of success in core flood tests or possible reasons why successful core tests may not necessarily lead to a successful field test.

A low rate waterflood is then conducted (e.g. 1 ft/day

7.2 Core scale artifacts

It is well known that laboratory tests on core samples can produce misleading information due to the small scale of the core plug in relation to reservoir scale. represents a homogeneous reservoir rock.

This is so even if the core plug

The recovery of oil from cores during laboratory waterflood tests For oil-wet cores is affected by capillary forces on the sample scale.

flooded at low rate, tests on short cores result in early water breakthrough (5). The flood front is dispersed by capillary forces (Figure 8).

97

If the core length or flood velocity is increased or the interfacial tension is decreased, then the oil recovery at water breakthrough is improved. If a low rate flood test is carried out on a core sample, e.g. to match reservoir type flow rates, then the oil recovery at water breakthrough may show an increase as the interfacial tension is decreased. However, on the reservoir scale, the reduction of interfacial tension would have no effect, according to the curves in Figure 8.

A similar situation arises in the case of residual oil saturation (i.e. after sufficient water has been passed through the core so that oil flow ceases). Capillary forces cause retention of oil at the outlet face of the core sample giving the impression of high residual oil saturation, particularly if the flood is carried out at rates representing reservoir flow rates. tension can result in significant production of this end-effect oil which would not be representative of the reservoir scale.

Reduction of interfacial

In order to improve the situation, long cores are sometimes used Small core plugs may be butted

Careful arrangement of the small plugs to reduce the influence of end-effects. together to create a long core. is necessary in order that relevant data is produced.

Turning to the water-wet case, the recovery of oil at water- breakthrough is less affected by sample length than in the oil-wet case (8). capillary forces delay water-breakthrough (Figure 9). given in Figure 9 only applies over a small region of flow rate and interfacial tension, where capillary forces completely dominate fluid distribution on the pore scale. below a certain interfacial tension, viscous forces will start to take over as the dominant factor controlling fluid distribution. of sample length, however, will have no effect on fluid distribution on the pore scale.

Water may arrive early at the outlet end of the sample but The representation

Above a certain flow velocity or

Increase

The above discussion highlights the importance of careful interpretation of laboratory data if valid information is to be produced. In our discussions we have tended to consider the extreme case of oil- wet and water-wet rocks. In practice rocks may have a variety of wetting conditions. We have also considered an ideal situation where clays within the porous media do not'effect the fluid flow characteristics. Adsorption of surfactants on to pore and clay surfaces has not been discussed. consideration of these interesting effects is outside the scope of this paper.

Indeed not all of the pore surface may have the same wetting.

Full

7.3 Simulation aspects

Preliminary analysis of core tests of EOR systems can be carried Investigation of the sensivity out with linear scaling relationships.

to particular system properties in the optiiisation of a system requires the use of more detailed simulation methods. the separation of core scale effects as discussed above demand careful study if the experimental results are to characterise the physical processes relevant to the field. In all cases the data must be considered in terms of its relevance to its intended use on input to a field simulator, with the attendant changes in scale which can only be treated mathematically. floods is provided by the greater degree of experimental accessibility,

In particular,

An additional role of the simulation of core

98

and the ability to repeat laboratory work, as contrasted with the field situation. model on the basis of laboratory results, there is no guarantee of success in the field (although, conversely, failure at the laboratory scale cannot easily be reconciled with confidence in subsequent field application). dialogue between the laboratory and the field testing can proceed, and it is therefore important that it should be able to describe the real physical processes rather than aim at mere plausibility and utility.

Despite the benefits of validation of a simulation

The simulation provides the language by which the

CONCLUSIONS

1. Despite its extensive use, the concept of relative permeability remains empirical. exercised when attempting to extend its area of applicability. particular, the relative permeability functions which are appropriate to low tension immiscible displacement are as yet uncertain.

2. The behaviour of an oil slug injected into a core provides a prototype to assess many of the assumptions which are present when core data are prepared for simulation of EOR processes. The availability of a correctly defined set of relative permeability curves, complete with hysteresis, irreversibility and system changes is of great importance to the correct modelling of an oil bank. Although in field use, such concepts may be of secondary importance to the heterogeneity, they cannot be ignored in the provision of data from core tests. Currently available simulation schemes are empirical; they require development and experimental validation.

As with any empirical quantity, great care must be In

3. Numerical schemes which essentially scan relative permeability curves demand that these curves are defined over the full saturation interval. The sensivity to these curves of oil bank stability (and presumably all multi-front systems) is such that plausibility alone is too weak a criterion for-acceptability. In addition, the behaviour of transient saturations associated with multiple shock fronts may not be adequately modelled.

Acknowledgements

Permission to publish this paper has been given by the British Petroleum Co. Ltd.

The authors wish to thank Mr. J .F . Berry and Dr. I. White who carried out the simulation work described in this paper.

List of Symbols

kr relative permeability S fractional saturation f fractional flow V superficial velocity y interfacial tension L core length x distance along core

a, C, F, fi, Hi, n, S+, S , 0 , i t - parameters, defined in the text.

99

Subscripts

o oil w water r residual i irreducible

References

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L.L. Handy and P. Datta Fluid distributions during immiscible displacement in porous media. SOC. Pet. Eng. J, Sept. 1966 page 261.

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Johnson, E.F., Bossler, D.P. and Naumann, V.O. Calculation of relative permeability from displacement experiments. Trans AIME (1959) 216, 370-372.

Buckley, S.E. and Leverett, M.C. Mechanisms of fluid displacement in sands.

L.A. Rapoport and W.J. Leas Properties of linear waterfloods. Trans AIME (1953) 198, 139 - 148. C. Bardon and D.G. Longeron Influence of very low interfacial tension on relative permeability. SOC. Pet. Eng. J, Oct 1980 page 391.

F.F. Craig Jr. 1971.,The reservoir engineering aspects of waterflooding. spe Monograph Vol. 3 H.L. Doherty Series. Page 24.

Kyte J.R. and Rapoport L.A. Linear waterflood behaviour and end effects in water-wet porous media. 213, 423 - 426. J.O. Amarefule and L.L. Handy 1981. tensions on relative oil-water relative permeabilities of consolidated porous media.

T.M. Geffen, W.W. Owens, D.R. Parrish and R.A. Morse Experimental investigation of factors affecting laboratory relative permeability measurements. vol. 192, page 99 - 110. C.R. Sandberg, L.S. Gournay and R.F. Sippel The effect of fluid-flow rate and viscosity on laboratory determinations of oil-water relative permeabilities. JPT, 1958, 36 - 43. C.S. Land. Comparison of calculated with experimental imbibition relative permeability SOC. Pet. Eng. J (Dec 1971)

M.C. Leverett Flow of oil-water mixtures through unconsolidated sands. Trans AIME (1939) 132, 149. N. Mungan Interfacial effects in immiscible liquid- liquid displacement on porous media.

A.W. Talash 1976. Experimental and calculated relative permeability data for systems containing tension additives. SPE preprint 5810.

SPE preprint 4104.

Trans AIME (1942) 146, 107 - 116.

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The effect of interfacial

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J.P. Batycky and F.G. McCaffery Low interfacial tension displacement studies. meeting of the Pet. SOC. of CIM, Calgary, Canada (June 13-16, 1978 1. H. Asar Influence of interfacial tension on gas-oil relative permeability in gas-condensate systems. University of Southern California (May 1980)

C.P. Thomas, W.K. Winter and P.D. Flemings 1977. Application of a general multiphase multicomponent chemical flood model to ternary, two-phase surfactant systems. SPE preprint 6727.

S.P. Gupta and S.P. Trushenski Micellar flooding compositional effects on oil displacement. SOC. Pet. Eng. J April 1979 116 - 128. G.A. Pope The application of fractional flow theory to enhanced oil recovery. SOC. Pet. Eng. J. (June 1980) 191 - 202. Gladfelter, R.E. and Gupta, S.P. Effects of Fractional Flow Hysteresis on Recovery of Tertiary Oil. SPE J (Dec. 1980) 508 - 520. Jones, S.C. and Rozelle W.O. Relative Permeability from Displacement Experiments. (May 1978) 807 - 817. Killough, J.E. Saturation Functions. SPE J (Feb. 1976) 37 - 48. Lin, C.Y. and Slattery, J.C. Three-Dimensional, Randomised Network Model for Two Phase Flow Through Porous Media. SPE 9803, 1981.

Evrenos, A.I. and Comer, A.G. Numerical Simulation of Hysteretic Flow in Porous Media.

Everett, D.H. and Smith, F.W. A General Approach to Hysteresis. Trans. Faraday SOC. (1954)

Topp, G.C. and Miller, E.E., Hysteretic Moisture Characteristics and Hydraulic Conductivities for Glass Bead Media. Sci. SOC. Amer. Proc. (1966) 30, 156 - 162. Pickens, J.F. and Gillham, R.W., Finite Element Analysis of Solute Transport Under Hysteretic Unsaturated Flow Conditions Water Resour. Res. (1980) - 16, 1071 - 1078.

paper 78-29-26, 29th Annual Tech.

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Graphical Techniques for Determining SPE J.

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Soil.


EXPERIMENTAL STUDY AND INTERPRETATION OF SURFACTANT RETENTION IN POROUS MEDIA

J. NOVOSAD

Petroleum Recovery Institute CNgary, Alberta, CaMda T2L 2A6

ABSTRACT

Total r e t e n t i o n of s u r f a c t a n t s i n a reservoi r during chemical f loods is probably one of the most important parameters i n t h a t it determines the economic success o r f a i l u r e of t h i s enhanced o i l recovery process. It is not, therefore , s u r p r i s i n g that a s u b s t a n t i a l research e f f o r t has been devoted t o labora tory evaluat ions of sur fac tan t r e t e n t i o n i n porous media. Generally, the systems s tudied are complex as they conta in a minimum of tw l i q u i d phases, an& no less than f i v e components: s u r f a c t a n t , cosur fac tan t , e l e c t r o y t e , water, and o i l . mental procedures f o r determining sur fac tan t adsorpt ion and t o t a l sur fac tan t r e t e n t i o n . It is shown that t h e i n t e r p r e t i o n of experimental d a t a is not s t r a i g h t forward, and that extreme caut ion must be exercised before any in te r - po la t ion o r ex t rapola t ion of adsorpt ion o r r e t e n t i o n data is attempted.

The p r i n c i p a l ob jec t ive of t h i s paper is t o analyze and evaluate experi-

Laboratory data on r e t e n t i o n of pure su l fona te (Texas # l ) , petroleum su l fona te (TRS 10-80). and synthe t ic sulfonate (FA 400) are presented. These show t h e importance of experimental condi t ions as similar experiments may yie ld s u b s t a n t i a l l y d i f f e r e n t r e s u l t s when condi t ions are var ied. Spec i f ica l ly , the effect of .phase behavior on t o t a l s u r f a c t a n t re ten t ion fs discussed and experimental procedures are out l ined so that a d i f f e r e n t i a t i o n can be made between l o s s e s of s u r f a c t a n t due t o unfavorable phase behavior and those due t o adsorpt ion a t the so l id- l iqu id in te r face . d i t i o n s may a f f e c t the measured values of sur fac tan t l o s s e s is shown by the e f f e c t of s u r f a c t a n t s lug s i z e on t h e apparent l e v e l of r e t e n t i o n and adsorption.

An example of how experimental con-

INTRODUCTION

Adsorption of s u r f a c t a n t s considered f o r enhanced o i l recovery appl ica t ions has been s tudied extensively i n t h e last few years1’6 as it has been convincingly shown that it is poss ib le t o develop sur fac tan t systems which d isp lace o i l from porous media almost completely when used i n l a r g e q u a n t i t i e s . recovery by s u r f a c t a n t s is not a quest ion of p r i n c i p l e but r a t h e r a quest ion of economics. Since s u r f a c t a n t s are mre expensive than t h e crude o i l , development of a p r a c t i c a l enhanced oil recovery (EOR) technology depends on how much sur- f a c t a n t can be economically s a c r i f i c e d i n recovering a d d i t i o n a l crude o i l from a reservoi r . been considered c r i t i c a l t o the success OT f a i l u r e of t h i s EOR process.

Effect ive o i l

Therefore, i t is q u i t e clear why sur fac tan t adsorpt ion has always

102

It w a s recognized earlier t h a t physico-chemical adsorp t ion may be only one of a number of f a c t o r s which cont r ibu te t o t o t a l s u r f a c t a n t r e t e n t i o n . Other physico-chemical mechanisms may include s u r f a c t a n t entrapment i n a n immobile o i l phase5, s u r f a c t a n t p r e c i p i t a t i o n by d iva len t ions6 caused by a separa t ion o f cosur fac tan t from surfactant ' , and s u r f a c t a n t t a t i o n due t o chromatographic separa t ion of d i f f e r e n t s u r f a c t a n t spec ies . When complications a r i s i n g from ion-exchange phenomena usua l ly involved i n sur- f a c t a n t f looding are included, i t should not come as a s u r p r i s e t h a t measured adsorpt ion isotherms d i f f e r s u b s t a n t i a l l y from those previously observed f o r simpler s u r f a c t a n t systems.

s u r f a c t a n t p r e c i p i t a t i o n

yrecipi-

A p r i n c i p a l o b j e c t i v e of t h i s work is t o eva lua te t h e experimental techniques t h a t can be used f o r measuring s u r f a c t a n t adsorpt ion and t o s tudy experimentally two mechanisms respons ib le f o r s u r f a c t a n t r e t e n t i o n . an at tempt is made t o d i f f e r e n t i a t e between t h e adsorpt ion of s u r f a c t a n t s a t the so l id- l iqu id i n t e r f a c e and 'the r e t e n t i o n of s u r f a c t a n t s due t o t rapping i n t h e immobile hydrocarbon phase which remains wi th in t h e core following a s u r f a c t a n t flood .

Speci f ica l ly ,

PLUSCRMENT OF ADSORPTION AT THE SOLID-LIQUID INTERFACE

Previous adsorp t ion measurements of s u r f a c t a n t s considered f o r enhanced o i l recovery produced adsorpt ion isotherms of unusual shapes with unexpectel fea tures . f a c t a n t r e t e n t i o n has been p lo t ted a g a i n s t t h e concentrat ion of in jec ted s u r f a c t a n t . Numerous explanat ions have been of fered f o r these peaks; such as, a formation of mixed micells6, the e f f e c t s of "s t ruc ture forming" and "s t ruc ture breaking" c a t i o n s 8 , and t h e p r e c i p i t a t i o n and consequent r e d i s s o l u t i o n of d iva len t ions2. p a r t i c u l a r s i t u a t i o n and t h e i r r e l a t i v e impartance i s d i f f i c u l t t o asses. bwever , it seems t h a t , i n view of the number of processes t h a t are taking p lace s i m l t a n e o u s l y and the l a r g e number of components present i n most of t h e systems s tudied , one should not expect smooth monotonically increas ing isotherms t h a t a r e pat terned a f t e r adsorp t ion isotherms f o r only two pure components. Also, it should be rea l ized that most experimental procedures do not y i e l d an amount of s u r f a c t a n t adsorbed but r a t h e r t h e sur face excess.

Pr imar i ly , a n adsorpt ion maximum has been observed when t o t a l sur-

Which of these e f f e c t s are responsible f o r the peaks i n a

It is shown next that a n adsorpt ion isotherm expressed i n terms of t h e sur face excess a s a func t ion of a n e q u i l i b r i u m s u r f a c t a n t concent ra t ion must, by d e f i n i t i o n , contain a maximum if t h e da ta are measured over a s u f f i c i e n t l y wide range of concentrat ions. It has been shown repeatedly t h a t , f o r adsorpt ion a t the so l id- l iqu id i n t e r f a c e , the sur face excess is the only c o n s i s t e n t l y defined experimental v a r i a b l e which should be used i n descr ib ing the p r e f e r e n t i a l uptake of one component over another i n t o the adsorbed layer'. defined by Equation (1)L:

The sur face excess is

ne =

where, no =

i

xo = i

i

i

x =

ne =

0 n o -(xi m - Xi)

t o t a l mass of the l i q u i d system (g) ,

r e l a t i v e concentrat ion of component i i n t h e bulk phase before adsorp t ion takes p lace ( f r a c t i o n ) , r e l a t i v e concentrat ion of component i i n t h e bulk phase a f t e r adsorp t ion equi l ibr ium is a t t a i n e d ( f r a c t i o n ) ,

excess of mass of component i i n t h e adsorbed phase per mass u n i t of adsorbent (g/g),

mass of adsorbent (g), m =

10 3

and a n adsorp t ion isotherm is defined as t h e sur face excess dependence on equi l ibr ium concent ra t ion of component i i n t h e bulk phase:

It should be clear from Equation (1) that t h e sur face excess must be equal t o zero f o r pure components ( x i = 0, x i = 1 ) and, therefore , a non-zero adsorp- t i o n isotherm must conta in a t least one peak. This a p p l i e s t o f u l l y miscible systems i n which adsorp t ion isotherms are meaningful over t h e e n t i r e concentra- t i o n range between pure component 1 and pure component 2 . However, s o l u b i l i t y l i m i t s of most s u r f a c t a n t s i n r e s e r v o i r br ines are reached a t low concentrat ions, and measurements of adsorpt ion above such concent ra t ion l e v e l s are meaningless a s s u r f a c t a n t p r e c i p i t a t i o n takes place. Therefore, a presence o r a n absence of a maximum i n a n adsorpt ion isotherm is dependent upon s u r f a c t a n t s o l u b i l i t y i n a br ine o r o ther continuous phase.

Equation (1) a p p l i e s a l s o t o multicomponent systems, however, such adsorption isotherms cannot be expressed graphica l ly i n a two-dimensional form without spec i fy ing a d i r e c t i o n i n which t h e adsorpt ion sur face (for three-component systems) is cut f o r viewing i n two dimensions 4. It is not p r a c t i c a l t o perform adsorp t ion experiments w i t h multicomponent systems i n such a way that the adsorpt ion sur face is c u t i n a pre-determined way s i n c e i t i s not usual ly known a p r i o r i w h a t t h e bulk composition of ind iv idua l components is going t o be a f t e r adsorp t ion has taken place.

This problem is even more complicated when designing experiments with sur- f a c t a n t mixtures which are considered f o r s u r f a c t a n t f looding as individual components of t h e mixture are d i f f i c u l t t o separa te and, consequently, the whole mixture is usua l ly t r e a t e d as a s i n g l e component. chosen a n a l y t i c a l method can determine t h e sum of s e v e r a l s u r f a c t a n t s accurately, i t has been previously shown that isotherms f o r ind iv idua l components may d i f f e r s u b s t a n t i a l l y from an o v e r a l l i ~ o t h e r m . ~

Even i f i t is assumed that a

This i s of importance f o r systems i n which each component wi th in the mixture serves a d i f f e r e n t funct ion, such a s e i t h e r achieving an u l t r a low i n t e r f a c i a l t ens ion o r improving t h e s o l u b i l i t y of o ther components. The over- a l l adsorp t ion isotherm is then not s u i t a b l e f o r pred ic t ing t h e system performance during t h e f lood because deple t ion of ind iv idua l components is not represented by t h e o v e r a l l isotherm.

Treat ing t h e mixture as a s i n g l e component br ings a d d i t i o n a l uncertainty t o adsorpt ion experiments. e x t e n t s , t h e i r equi l ibr ium concentrat ions become d i f f e r e n t from those o r i g i n a l l y present so t h a t they w i l l depend on s p e c i f i c experimental condi t ions such as the adsorbent / so lu t ion r a t i o . from one experiment t o another as equi l ibr ium concentrat ions may be moving on the adsorp t ion s u r f a c e i n d i f f e r e n t d i r e c t i o n s depending on t h e s p e c i f i c condi t ions of t h e experiment. These are t h e main reasons why experimental data from d i f f e r e n t l a b o r a t o r i e s are so d i f f i c u l t t o compare and why a grea t d e a l of caut ion should be exercised i n i n t e r p r e t i n g t h e shapes of isotherms which were determined i n experiments i n which the i n i t i a l r e l a t i v e concentrat ion of each ind iv idua l component was held constant while t h e t o t a l concentrat ion w a s varied.

As t h e ind iv idua l components a r e adsorbed t o d i f f e r e n t

The apparent adsorpt ion l e v e l may vary Subs tan t ia l ly

METHODS FOR WXjUREMENT OF ADSORPTION ISOTHERMS

There a r e t w o d i s t , i n c t l y d i f f e r e n t approaches f o r measuring adsorpt ion a t the so l id- l iqu id i n t e r f a c e . The f i r s t , a batch method, c o n s i s t s of measuring

10 4

s u r f a c t a n t concentrat ions i n t h e bulk phase before and a f t e r adsorp t ion takes p lace , and adsorpt ion is c a l c u l a t e d from Equation (1). a r e performed i n t h e bulk phase, t h e meaning of each v a r i a b l e i n Equation (1) is without ambiguity and t h e ca lcu la ted sur face excess is a v a l i d thermodynamic var iab le .

Since a l l measurements

A main disadvantage of using t h e batch method l ies i n its poor accuracy a t higher s u r f a c t a n t concentrat ions. concentrat ion due t o adsorpt ion becomes small and adsorpt ion i s obtained by subt rac t ing two numbers of s i m i l a r s ize . It has been shown with s u r f a c t a n t sys tems considered f o r enhanced o i l recovery that exceedingly accura te a n a l y t i c a l methods a r e required f o r measurement of adsorp t ion from s o l u t i o n s when s u r f a c t a n t concent ra t ions exceeds one percent .

The measured change i n bulk s u r f a c t a n t

I n t h e second method, a dynamic one, the r e t e n t i o n of s u r f a c t a n t s is determined from a flow-type experiment, and t h e l o s s e s of s u r f a c t a n t are ca l - cu la ted e i t h e r from t h e delay of t h e s u r f a c t a n t breakthrough curve, i f t h e amount of s u r f a c t a n t i n j e c t e d is so l a r g e that t h e e f f l u e n t concentrat ion reaches t h e in jec ted concentrat ion, o r from the material balance when a smaller amount of s u r f a c t a n t is i n j e c t e d (Figure 1).

It should be r e a l i z e d tha t , i f the s u r f a c t a n t concentrat ion a t t h e core o u t l e t does not reach t h e i n j e c t e d concentrat ion, then t h e adsorpt ion determined from a material balance is a t t a i n e d over a concentrat ion range t h a t extends from t h e in jec ted l e v e l a t t h e core inlet t o t h e maximum e f f l u e n t concentrat ions measured a t t h e core o u t l e t . For example, i f the i n j e c t i o n of a 20% PV sur- f a c t a n t s l u g r e s u l t s i n a maximum o u t l e t concentrat ion corresponding t o 10% of the in jec ted concentrat ion, t h e average s u r f a c t a n t concentrat ion wi th in t h e core would be approximately 55% of t h e in jec ted l e v e l . maximum o u t l e t concent ra t ion of 90% r e s u l t i n g i n t h e average concentrat ion wi th in t h e core being about 95% of t h e in jec ted concentrat ion. Therefore, the r e t e n t i o n va lues obtained from these two experiments would be r e l a t e d t o d i f f e r e n t concent ra t ion regions, and t h e r e s u l t s would not be d i r e c t l y comparable.

A l a r g e r s l u g may give a

A similar argument can be made when a d i f f e r e n t degree of separa t ion between a cosur fac tan t and a s u r f a c t a n t o c c u r s i n experiments i n which varying s l u g sizes are used. An example of such a separa t ion is shown i n Figure 2, andagain r e t e n t i o n r e s u l t s should be d i f f e r e n t s i n c e i t has been shown previously that alcohol concent ra t ions a f f e c t s u r f a c t a n t r e t e n t i o n s u b s t a n t i a l l y .

There are two a d d i t i o n a l cons idera t ions concerning measurements of adsorp- t i o n i n displacement experiments i n which a n o i l phase i s present and when i t i s displaced from a core by a s u r f a c t a n t so lu t ion . I n t h i s case , adsorpt ion cannot be determined d i r e c t l y from the de lay of t h e breakthrough curve f o r two reasons. F i r s t l y , t h e pore volume a v a i l a b l e t o the s u r f a c t a n t is changing dur ing t h e flood as o i l is displaced. This makes t h e i n t e g r a t i o n indicated i n Figure l ( a ) mre d i f f i c u l t s i n c e t h e amount of o i l recovered must be known a t each point i n t h e flood. Secondly, the p o s s i b i l i t y of s u r f a c t a n t being d i s - t r i b u t e d between t h e b r i n e and hydrocarbon phases dur ing t h e flood, i n a way that d i f f e r s from the i n j e c t e d s o l u t i o n , mst be considered. s u r f a c t a n t flow v e l o c i t y becomes dependent no t only on adsorp t ion but also on two-phase flow c h a r a c t e r i s t i c s . Unless the s u r f a c t a n t d i s t r i b u t i o n is known prec ise ly a t each s t a g e of the food, the delay i n t h e breakthrough curve may be caused by e i t h e r of t h e two phenomena, and a d i s t i n c t i o n between them cannot be made.

adsorp t ion measurements can be best performed i n batch experiments. However, s i n c e t h e i r s e n s i t i v i t y is o f t e n not s u f f i c i e n t f o r measurements of adsorpt ion

When t h i s occurs , t h e

The previous paragraphs were intended t o show t h a t thermodynamically v a l i d

10 5

from s u r f a c t a n t s o l u t i o n s of higher concentrat ions, displacement experiments must be used f o r such systems. It should, however, be r e a l i z e d that such tests measure averaged va lues of adsorp t ion over concent ra t ions that range from t h e maximum e f f l u e n t concent ra t ion t o t h e i n j e c t e d concentrat ion. The adsorption va lues are also averaged over t h e range of cosur fac tan t fsur fac tan t ratios which depend on t h e s p e c i f i c characteristics of t h e s u r f a c t a n t system.

It fol lows that even minor v a r i a t i o n s i n t h e displacement experiments can produce s u b s t a n t i a l l y d i f f e r e n t r e s u l t s i n terms of s u r f a c t a n t r e t e n t i o n and adsorpt ion. Therefore, i t is imperat ive t h a t every adsorp t ion measurement be descr ibed i n d e t a i l so t h a t t h e r e s u l t s from d i f f e r e n t l a b o r a t o r i e s can be r e a l i s t i c a l l y compared. This is not present ly t h e case, as manifested i n t h e recent paper by Meyer and S a l t e r ' who surveyed t h e l i t e r a t u r e t o determine t h e e f f e c t s of a n o i l presence on s u r f a c t a n t r e t e n t i o n and found that a n increase, a decrease, o r no e f f e c t had been observed. d i f f e r e n t experimental techniques and procedures could have been responsible f o r such divergent r e s u l t s .

It is e n t i r e l y poss ib le that the

Another phenomenon a f f e c t i n g t h e r e t e n t i o n of s u r f a c t a n t s should be t rea ted Surfac tan t s o l u b i l i t y i n r e s e r v o i r f l u i d s could possibly be grouped separa te ly .

w i t h i n t h e phase behavior categorv but , s i n c e it mav a f f e c t r e t e n t i o n of s u r f a c t a n t s so s u b s t a n t i a l l y , i t is discussed separa te ly .

I .o

Continuous o r C/% 0.5 Large Slug I n j e c t i o n

0.0 0.0 4.0 2.0

PORE VOLUME

Figure 1: Determination of Surfac tan t Retention from Displacement Experiments

It has been previously shown that t h e r e i s a n order of magnitude d i f fe rence i n the r e t e n t i o n of s u r f a c t a n t s from dispersed s o l u t i o n s and from so lu t ions i n which the s u r f a c t a n t s are t r u l y dissolved '. Even though mst in jec ted sur fac tan t s o l u t i o n s used i n adsorp t ion s t u d i e s conta in a lcohols as cosur fac tan ts i n order t o keep s u r f a c t a n t s f u l l y dissolved, t h i s ray not be the case i n the l a t e r s tages of a f lood. Alcohols propagate through the porous mediua a t d i f f e r e n t

1 0 6

!i

i? 4 - G a 3 in \ I- 3 - z

0 8 i?

8

a 3 in

v e l o c i t i e s than s u r f a c t a n t s because they d i s t r i b u t e themselves between t h e o i l and t h e b r i n e d i f f e r e n t l y than do t h e s u r f a c t a n t s (Figure 2) . Should t h i s happen, i t is l i k e l y that t h e s u r f a c t a n t l o s e s its: s o l u b i l i t y i n t h e br ine , p r e c i p i t a t e s , and l o s e s i t s a b i l i t y t o propagate through t h e core. This w i l l r e s u l t i n an apparent increase i n s u r f a c t a n t r e t e n t i o n which cannot be e a s i l y d is t inguished from e i t h e r adsorpt ion o r t rapping in t h e hydrocarbon phase. Therefore, in most experiments descr ibed in t h i s work, a lcohols were used i n excess q u a n t i t i e s thereby e l imina t ing o r s u b s t a n t i a l l y reducing t h i s p o s s i b i l i t y . In a l l cases , a lcohol concentrat ions i n t h e e f f l u e n t were monitored so that a p o t e n t i a l problem of poor s u r f a c t a n t s o l u b i l i t y could be assessed a t t h e end of eack flood.

5 -

2 -

1-

6 1-b INJECTED SOLUTION

‘0.0 0.5 1.0 1.5 2.0 PORE VOLUME

Figure 2: Cosurfactant /Surfactant Ratio a t the Core Outlet (10072 3’ I n j e c t i o n of 2% 1 / 6 Texas !!l/ n-Propanol i n 1.5‘; N a C l Brine)

The main o b j e c t i v e of t h i s work is t o determine s u r f a c t a n t r e t e n t i o n in &rea cores with t h e main emphasis being t o d i s t i n g u i s h physico-chemical adsorpt ion of s u r f a c t a n t s from l o s s e s of s u r f a c t a n t s due t o t rapping i n t h e i m o b i l e hydrocarbon phase t h a t is l e f t i n the core a f t e r a flood.

Chenical s

Three types of s u r f a c t a n t s were used dur ing t h e course of t h i s study. TXS 10-82 served a s a n example of a commercial q u a l i t y petroleum su l fona te which

10 7

is produced by a d i r e c t s u l f o n a t i o n of petroleum-based feedstocks. PDM 337 w a s a n example of a s y n t h e t i c su l fona te . and Texas 81 was a well-def ined pure s u r f a c t a n t , t h e s t r u c t u r e of which was p a t t e r n e d a f t e r typical molecules found i n petroleum-based feedstocks.

Texas # I -

PDM 337 -

TRS 10-80 -

Octane -

sodium salt o f 8-phenyla-hexadecyl-p-sulfonate w a s obtained from Pro fes so r Wade o f t h e Un ive r s i ty of Texas and has been used as rece ived . According t o Frances et a1.l1 t h e p u r i t y o f t h e sample exceeds 98%.

monoethanol amine salt o f a l k y l or thoxylene s u l f o n a t e supp l i ed by Exxon Chemicals, Houston, Texas. According t o t h e s u p p l i e r , it is 84% a c t i v e w i t h a median a l k y l chain s i z e of around C12. This s u r f a c t a n t was used a s received.

petroleum s u l f o n a t e suppl ied by Witco Chemicals. were d e s a l t e d and deo i l ed accord-ins t o t h e procedures descr ibed by Shah e t a1.12

t e c h n i c a l grade suppl ied by P h i l l i p s Petroieum Company.

Samples

Orthoxylene - b o i l i n g p o i n t range 143.5' - 144.5"C suppl ied by Matheson, Coleman and B e l l Co.

Secondary Butyl a l c o h o l - b o i l i n g p o i n t range 98" - 100°C, simplied by Eastman KDdak Company.

N a C l suppl ied by Fisher S c i e n t i f i c d i s so lved i n deionized water.

Brine

Adsorbent - B e r e a sandstone c o r e s w i t h air pe rmeab i l i t y range o f 100 t o 1 ,200 md, supp l i ed by Cleveland Q u a r r i e s .

A n a l y t i c a l Methods

The p r e c i s i o n of a n a l y t i c a l methods is of u t m s t importance i n a l l s t u d i e s of adso rp t ion a t t h e so l id - l iqu id i n t e r f a c e . The fol lowing methods have been ex tens ive ly t e s t e d and employed f o r concen t r a t ion de te rmina t ion i n t h i s work.

S u r f a c t a n t s - W Spectrophotometry (Varian 's Super Scan 3) - HF'LC u t i l i z i n g water-methanol-acetoni t r i le - sodium 3ihydro-

phosphate so lven t s ' (Waters Associates Instrument) .

Octanelo-xylenefSecondary Suty: slcohol-GC emplo>-lng Chromosorb S packing and t h e thermal conduc t iv i ty d e t e c t o r (Hewlett-Packard Instrument) .

Divalent Ions - I o n i c Flame Spectrophometry (Perkin-Elnrer Instrument) - Chelatometr ic t i t r a t i o n

E iTer inen ta l Procedures

Berea a r e s (2.5 x 2.5 cm2 c ross - sec t ion ) were c u t t o 30 CGI l e n g t h s and d r i ed i n a vacuum oven a t ll0'C f o r 24 hours. They were then s a t u r a t e d under vacuum w i t h degassed b r i n e , o i l f looded t o a connate water s a t u r a t i o n , and then water- f looded t o a r e s i d u a l o i l s a t u r a t i o n u s u a l l y i n t h e range of 30 t o 35% of pore volume.

A s u r f a c t a n t s l u g w a s i n j e c t e d i n t o t h e cores a t r e s i d u a l o i l s a t u r a t i o n a t constant rates of 2 ml/hour so that t h e apparent f r o n t a l advance rate of the f l u i d did not exceed 30 cmlday. volati le components, t h e o u t l e t l i n e w a s fed through a syr inge needle p ie rc ing t h e septum of a c o l l e c t i o n tube. c o l l e c t o r and t h e syr inge needle were automated, thus al lowing uninterrupted f looding i n experiments l a s t i n g severa l days.

I n order t o eliminate evaporat ive l o s s e s of

Synchronized movements of a f r a c t i o n

Surfac tan t f loods were performed as follows. During t h e s u r f a c t a n t flood and the subsequent b r i n e flood (no polymers o r v i s c o s i t y improving agents have been used i n t h i s work), t h e samples were co l lec ted a t two-hour i n t e r v a l s which r e s u l t e d i n 5 t o 10% of pore volume being c o l l e c t e d i n each sample. Ef f luent f l u i d s were then analyzed f o r o i l , b r ine , s u r f a c t a n t , and cosur fac tan t content . When t h e production of o i l , s u r f a c t a n t , and cosur fac tan t ceased, severa l pore volumes of a hydrocarbon phase were in jec ted i n t o t h e core i n an at tempt t o recover s u r f a c t a n t s trapped i n o i l remaining i n the core . produced by t h i s hydrocarbon flood was analyzed f o r a l l components and recovered s u r f a c t a n t s were considered t o be s u r f a c t a n t s trapped i n t h e hydrocarbon phase during t h e s u r f a c t a n t flood. In some f loods , octane w a s displaced by nonane o r decane so that a complete displacement of res idua l cil could be v e r i f i e d and a material balance 011 o i l c losed.

Liquid

After a l l s u r f a c t a n t s trapped i n t h e o i l were d isp laced , t h e core w a s flooded with a s t rong solvent such as e t h y l a lcohol or isonropyl a lcohol i n a mixture wi th b r i n e t o remove a l l remaining s u r f a c t a n t s from t h e core. required i n j e c t i o n of 5 t o 1 0 pore volumes and t h e material balance on s u r f a c t a n t c losed usua l ly between 90 t o 100% of i n j e c t e d s u r f a c t a n t . removed from t h e c o r e by alcohol so lvents is considered t o be s u r f a c t a n t adsorbed on t h e rock dur ing t h e f lood.

This

Surfac tan t

The f looding sequence descr ibed above al lows a determinat ion of t h e o v e r a l l s u r f a c t a n t r e t e n t i o n ( i . e . t h e amount of s u r f a c t a n t l o s t during the f lood) from t h e d i f fe rence between t h e amounts of s u r f a c t a n t in jec ted and recovered during the s u r f a c t a n t and subsequent b r i n e i n j e c t i o n . amount of s u r f a c t a n t trapped i n t h e o i l phase due t o unfavorable phase behavior, and t h e adsorbed s u r f a c t a n t recovered i n t h e f i n a l solvent f lood completes t h e mater ia l balance.

The hydrocarbon flood g ives a

This procedure i m p l i c i t l y assumes that t h e hydrocarbon phase does not remove This assumption was v e r i f i e d i n the following adsorbed s u r f a c t a n t from t h e core.

way:

X 75X PV of 3% s u r f a c t a n t s l u g was in jec ted i n a br ine-saturated core and followed with t h r e e a d d i t i o n a l pore volumes of br ine . determined a t 0.6 mg/g. Then, octane was continuously in jec ted and an e f f l u e n t was analyzed f o r s u r f a c t a n t s . After w r e than 5 P P o f throughput only 0.06 mg of s u r f a c t a n t per one gram of rock w a s recovered. This i n d i c a t e s that a minor amount of adsorbed s u r f a c t a n t can be recovered by the o i l , and that t h e bulk of adsorbed s u r f a c t a n t w i l l not be desorbed. However, even ch is small amount of adsorbed s u r f a c t a n t recovered by o i l is s u f f i c i e n t t o qua l i fy t h i s method f o r determinat ion of trapped s u r f a c t a n t as q u a l i t a t i v e .

Sur fac tan t l o s s was

In genera l , t h e bes t mater ia l balances were obtained i n f loods wi th TRS 10-80, andusual ly the most inaccura te results were obtained with PDM 337. It seems reasonable t o suggest t h a t a degree of s u r f a c t a n t s o l u b i l i t y i n a lcohol so lvents could expla in t h i s t r e n d , however, no measurements of s u r f a c t a n t s o l u - b i l i t i e s have been made.

1 0 9

I n order t o avoid experimental complications due t o t h e poss ib le p r e c i p i t a t i o n of s u r f a c t a n t s by d i v a l e n t ions, sodium c h l o r i d e b r i n e s were used throughout th i s study. Berea cores were pref luehed w i t h 5 t o 7 pore volumes of sodium c h l o r i d e b r i n e s i n order t o d i s p l a c e most of t h e exchangeable d iva len t ions. concent ra t ion i n t h e propagating s u r f a c t a n t s l u g (Figure 3). I n our experiments, these l e v e l s have not exceeded 90 ppm. Separate phase behavior experiments ind ica ted that such low d i v a l e n t ion concentrat ions a f f e c t e d the phase behavior of s u r f a c t a n t s o l u t i o n s i n that a minor s h i f t toward upper phase microemulsions w a s not iced, but no s u r f a c t a n t p r e c i p i t a t i o n was observed.

Even w i t h these precaut ions, t h e r e i s a n increase i n d i v a l e n t c a t i o n

loot

7 2 O O 1

PORE VOLUME

Figure 3: DivaleDt Ions Content i n the Eff luent ( In jec t ion of 75% PV of 2% 110.5 TRS 10-8OlSBA i n 1% N a C l )

It should be noted here that t h i s procedure f o r d i f f e r e n t i a t i n g trapped s u r f a c t a n t i n t h e hydrocarbon phase from t h e adsorbed sur fac tan t is not appl icable t o a l l s i t u a t i o n s . For example, i n s u r f a c t a n t systems i n which t h e sur fac tan t d i s t r i b u t i o n c o e f f i c i e n t is not a t extreme l e v e l s ( i . e . K = [ ( c s ) o i l / ( c s ) b r i n e l tends t o zero f o r lower phase microemulsions o r K + - f o r upper phase microemulsions) t h e chase b r i n e would bleed s u r f a c t a n t from the o i l phase and no s u r f a c t a n t would ever be found trapped i n the o i l .

RESLZTS Ah?) DISCUSSION

Studies of o i l recovery e f f i c i e n c y and s u r f a c t a n t r e t e n t i o n ind ica te that b e t t e r , performing processes a r e usua l ly accompanied by lower s u r f a c t a n t r e t e n t i o n even though lower r e t e n t i o n does not necessar i ly mean higher o i l recoverp.14

Since our experimental technique can d i s t i n g u i s h between s u r f a c t a n t l o s s e s due t o adsorpt ion and l o s s e s due t o unfavorable phase behavior, i t Qas thought t o be of i n t e r e s t t o perform severa l series of similar experiments and then observe how these ind iv idua l cont r ibu t ions t o t o t a l s u r f a c t a n t r e t e n t i o n are a f f e c t e d .

110

Effect of Cosurfactant on Surfac tan t Retent ion

I t has been shown than, i n systems containing no o i l ( i . e . systems containing only s u r f a c t a n t , cosur fac tan t , and b r i n e ) , poor s u r f a c t a n t solu- b i l i t y may r e s u l t i n very high s u r f a c t a n t r e t e n t i o n i n Berea cores . An a d d i t i o n a l cosur fac tan t helped t o d i s s o l v e t h e s u r f a c t a n t i n t h e br ine and the s u r f a c t a n t r e t e n t i o n w a s reduced by one order of m a g n i t ~ d e . ~ containing o i l , poor s u r f a c t a n t s o l u b i l i t y may not r e s u l t i n s u r f a c t a n t molecule aggregat ion but may lead t o a change in phase behavior i n which c a s e the s u r f a c t a n t d i s s o l v e s i n t h e upper hydrocarbon phase. s u r f a c t a n t r e t e n t i o n would increase even though s u r f a c t a n t adsorp t ion may e i t h e r not change a t a l l o r may even decrease.

I n systems

I n that case t h e

The PDM 337 s u r f a c t a n t with secondary buty l a lcohol .as a cosur fac tan t w a s se lec ted f o r t h i s p a r t of t h e study. An increasing cosur fac tan t content makes the s u r f a c t a n t s l i g h t l y -re b r i n e so luble and t h e phase behavior changes from a n upper t o a middle phase (Figure 4 ) .

SURFACTANT CONTAINING PHASE

VO.1 1/0.5 1/1.0 1/50

Figure 4: Phase Behavior of 3X PDM 337 Surfac tan t (80120 volumetric r a t i o of 1.5% k C 1 / octane f o r d i f f e r e n t surfactant lsecondary b u t y l a lcohol r a t i o s )

Sur fac tan t lcosur fac tan t r a t i o s of l:O.l, 1:0.5, 1:1, and 1:s were in jec ted i n four f loods on Berea cores t h a t had been waterflooded t o r e s i d u a l o i l sa tura t ions . The e f f l u e n t s were analyzed f o r s u r f a c t a n t , cosur fac tan t and o i l content . Typical examples of t h e da ta co l lec ted a r e shown i n Figures 5 t o 7 and the r e s u l t s of these f loods are summarized i n Table 1. This series of f loods c l e a r l y shows a l l of t h e d i f f i c u l t i e s which can be encountered when an at tempt is made t o compare adsorp t ion d a t a obtained from d i f f e r e n t displacement experiments.

111

PORE VOLUME

Figure 5:

6

5

4

s Y

g 3 3 J 0 ' 2

I

0

Surfactant and Cosurfactant Breakthrouzh Curves (Flood 112: 50% PV Inject ion of 3%, 1:5 PDM 337lSBA i n 1.5% NaCl Brine)

0 MICROEMULSION

- f$j OIL

0 BRINE

0

I 2

PORE VOLUME 3

Figure 6: Effluent Phase Behavior (Flood 112)

112

Surfacuat Surfacunr losses Due to Adsorption (c/c0)- co-surfacunc Refention ?hse BeUhvior u~uht ratio 4 1 ulr Ull

lJO.1 1.2 - 1.2 0

110.5 1.2 - 1.2 .02

111 1.0 - 1.0 0.10

115 0.7 0.7 0.21

0.3

w z u 0.2

k LL 0 z I-

K LL

0 2 0.1

0.0

Oil Recover).

I MI? (SorIf- (foul-

z z 2

52 15 17

66 10 19

85 5 22

70 8 2 1

PORE VOLUME

Figure 7: F r a c t i o n a l Flow of O i l (Flood 1 1 2 )

F i r s t , i t should be noted that, i n t h e f loods w i t h s u r f a c t a n t r a t i o s of 1 : O . l and 1:0.5, e s s e n t i a l l y no s u r f a c t a n t is contained i n t h e e f f l u e n t . This means t h a t not enough s u r f a c t a n t was i n j e c t e d t o s a t i s f y t h e adsorp t ion capaci ty of t h e rock and t h a t t h e s u r f a c e s near t h e end of the core are probably not completely adsorbed with s u r f a c t a n t . s u r f a c t a n t l c o s u r f a c t a n t r a t i o s have led t o the production of some s u r f a c t a n t ,

Floods w i t h the 1:l and 1:5

113

b u t t h e concentrat ion peaks a t the core o u t l e t s are s u b s t a n t i a l l y d i f f e r e n t from each o t h e r and, consepuently, t h e adsorpt ion values f o r the two d i f f e r e n t average s u r f a c t a n t concentrat ions are not d i r e c t l y comparable. Figure 8 shows, t h e normalized r a t i o s of s u r f a c t a n t and cosur fac tan t concen- t r a t i o n s are q u i t e d i f f e r e n t f o r t h e two f loods. Therefore, even though it may be tempting t o suggest t h a t t h e r e is enough da ta i n Table 1 t o a s c e r t a i n t h e dependence of s u r f a c t a n t adsorp t ion on a lcohol content , a c l o s e r look shows that a comparison of s u r f a c t a n t adsorpt ion f o r the four d i f f e r e n t systems cannot be nade without conducting a d d i t i o n a l experiments.

A l s o , as

The las t three c o l u m s of Table 1 conta in t h r e e i n d i c a t o r s o f t h e o i l Results show that e f f i c i e n c y i n i t i a l l y

This confirms a conclusion reported

recovery of each s u r f a c t a n t f lood. increases w i t h cosur fac tan t conten t , h w e v e r , t h e f i n a l f lood performs less e f f i c i e n t l y than t h e previous one. previously that lower s u r f a c t a n t r e t e n t i o n does not n e c e s s a r i l y lead t o t h e bes t o i l recovery e f f i c i ~ n c y . ' ~

I

5.0

4.0 Y

? I

I I I I I I I I I I ,*ol F;

0.0 0 0.5 1.0 2.0 3.0

PORE VOLUME

Figure 8: >!ormalized Cosurfactant /Surfactant Rat ios a t Core Out le t s

The Effec t of Slug S i z e on Surfactant Retent ion

A similar series of experiments w a s performed wi th TRS 10-80. The s u r f a c t a n t l c o s u r f a c t a n t r a t i o w a s var ied from 1:O.S t o 1 : l O . Typical flooding r e s u l t s a r e shown i n Figures 9 t o 11, and Table 2 s u m a r i z e s t h e d a t a obtained i n t h e s e f i v e f loods.

114

L 0 SURFACTANT A COSURFACTANT

1 PORE VOLUME

Figure 9: Surfactant and Cosurfactant Breakthrough Curves (Flood 69: SBA in 1.0% NaC1)

75% PV Injection of 2%, 1:0.5 TRS 10-80/

0 2 4 PORE VOLUME

Figure 10: Effluent Phase Behavior

115

0.3

1 0 0.2 LL 0

z 2

a 5 0.1

0.0 4

PORE VOLUME

Figure 11: Fractional Flow of O i l (Flood 69)

Table 2: Summary of Flooding Results with 3% TRS 10-80/SBA i n 1.0% NaCl/Octane System

Surf acUnc W cesurfaeunt Injected Retantien Trapped Surfacunt Adsorption ( d c , ) ,

x n y h =&It W l

1110 80 0.35 0.2 . 1s .so

115 94 0.50 0.4 0.10 0.95

113 150 0.2 - 0.15 1.0

113 7 5 0.3 0.1 0.20 0.85

Ill 75 0.5 - 0.48 0.8

110.5 75 0.6 - 0.55 1.0

1 1 6

It is i n t e r e s t i n g t o compare the s u r f a c t a n t r e t e n t i o n values observed i n f loods using a sur fac tan t /cosur fac tan t r a t i o of 1 : 3 i n which d i f f e r e n t s i z e s l u g s of i d e n t i c a l composition were in jec ted . l a r g e to enable t h e e f f l u e n t concentrat ion t o reach t h e l e v e l of t h e in jec ted concentration. The i n j e c t i o n volume i n t h e o t h e r comparable f lood w a s halved so t h a t t h e e f f l u e n t concentrat ion reached only 85% of t h e in jec ted concen- t r a t i o n . While t h e r e is a d i f f e r e n c e i n r e t e n t i o n , t h e d i f f e r e n c e i n adsorp- t i o n i s smaller. This apparent discrepancy can be explained i n terms of t h e amount of o i l trapped i n t h e hydrocarbon phase. In t h e f i r s t f lood, t h e r e is no trapped s u r f a c t a n t , while i n t h e second about one-third of the s u r f a c t a n t l o s s i s due t o unfavorable phase behavior. in forna t ion r e f l e c t i n g only o v e r a l l s u r f a c t a n t r e t e n t i o n may be very misleading.

A 150% PV s l u g w a s s u f f i c i e n t l y

This example shows c l e a r l y that

Another series o f experiments w a s performed wi th t h e pure Texas #I surfac tan t . Figures 12 t o 14 show an example of t h e experimental d a t a and Table 3 p r e s e n t s a summary of t h e r e s u l t s . I n this case, even though both o v e r a l l r e t e n t i o n and adsorp t ion increase wi th increas ing s l u g s ize , they do so a t d i f f e r e n t rates. Again, i t is t h e 106s due t o t h e phase behavior which is af fec ted more by the s i z e of t h e s u r f a c t a n t s lug.

0 SURFACTANT A COSURFACTANT

/ \ \

0.8 ' * O I p' \

0.6

c'co 0.4

0.2

0.0 0 I 2 3

PORE VOLUME

Figure 12: Sur fac tan t and Cosurfactant Breakthrough Curves (Flood 99: n-Propanol i n 1.5% NaCl)

100% PV I n j e c t i o n of 2X, 1:6 Texas <!l/

6

5

- 4 - E Y

g 3 J 0 >

2

1

0 I 0 I 0 MXROEMLILSION fQ OIL

BRINE

PORE VOLUME

Figure 13: Effluent Phase Behavior (Flood 99)

L

0.31 nn

PORE VOLUME

117

I

Figure 14: Fractional Flow of O i l (Flood 99)

118

PV Injected Rerent ion bsses h e LO Adsorption (c/co)ux Phase Behavior

.6/6 d 6 4 8

0.50 0.7 0.24 0.4 0.05

0.75 1.0 0.5 0.5 0.25

1.0 1.1 0.14 0.54 0.60

I 011 Recovery

ZROIP (Sor)fLnal (fol* x x 2

38 18 22

55 14 22

74 7 27

Experiments have beer? performed t o eva lua te t h e e f f e c t of c o s u r f a c t a n t presence w i t h i n t h e chase b r i n e on t h e r e t e n t i o n o f s u r f a c t a n t s . summarizes t h e r e s u l t s .

Table 4

Table 4: Summary of Flooding R e s u l t s w i t h 3%, 1:1.75 PDM 337lSBA i n 1.5% NaCl/Octane System

Flood Flood Retention lasses Due co M i o r p t i o n (c lco)- I Oewript ion Phase k h v i o r

WlK ma18 w/a ~ ~~~~~ ~~~ ~

86A ti0 oil i n the 1.2 1.2 0.65 core

85 Surfacunr slug only 0.8 0.15 0.5 1.0

followed by one PV of 3Z S M in brlne 0.5 0.20 0.3 0.5

82 Surfacunr

83 s.U am 85 bur at SLoyEll INJJLCTION RATE 0.8 0.L 0.4 1.0

5 36 I 79

Flood 86A contained no o i l , and adso rp t ion of 1 .2 mglg w a s observed. Flood 85 contained o i l a t r e s i d u a l o i l s a t u r a t i o n and adso rp t ion of 0.5 mgfg was determined. I n a d d i t i o n , t h e r e was a l o s s of 0.15 mgfg s u r f a c t a n t due t o phase behavior. The procedure used i n Flood 82 was t h e same a s f o r Flood 85 except t h a t i n Flood 82 t h e one PV of t h e b r i n e t h a t followed t h e s u r f a c t a n t s l u g con- t a ined 3% secondary b u t y l a l coho l . A s expected, t h e r e t e n t i o n and adso rp t ion l e v e l s a r e both lower, however, t h e amount of s u r f a c t a n t trapped in t h e oil phase d id not change appreciably. The o i l recovery w a s b e t t e r a s t he f i n a l o i l s a t u r a - t i o n is lowered from 14% PI’ i n Flood 85 t o 5% PV i n Flood 82. Another i n t e r e s t i n g a spec t observed i n t h i s experiment was t h e shape of t h e s u r f a c t a n t breakthrough curves ( s e e F igu re 15). Even though the f l o o d s were run a t t h e same i n j e c t i o n rates, t h e shape of t h e curve in Flood 82 g ives t h e impression o f a much higher l e v e l of d i s p e r s i o n than t h a t i n Flood 85. Seve ra l exp lana t ions are p o s s i b l e , bu t t h e l i m i t e d d a t a a v a i l a b l e do n o t a l low f o r a unique i n t e r p r e t a t i o n and

Table 3: Summary of Flooding Experiments with 2 X , 1:6 Texas $l/n-Propanol in 1.5% ?;aCl/Octane

1 1 9

t h e r e f o r e none is o f f e r e d . However, i t is observed that d a t a such a s these should be o f concern t o people d e a l i n g w i t h numerical models f o r chemical f l ood ing s i n c e t h e d a t a suggest t h a t t h e chemical composition of t h e s u r f a c t a n t s l u g may s u b s t a n t i a l l y a f f e c t t h e apparent d i s p e r s i o n .

t- I

0 I 2 3 4 PORE VOLUME

Figure 15: Sur fac t an t Breakthrough Curves

A r e c e n t l y publ ished paper d e s c r i b i n g s t a t i c adso rp t ion experiments , among o t h e r r e s u l t s , i n d i c a t e d t h a n a n a t t a inmen t of adso rp t ion equ i l ib r ium requ i r ed almost two weeks of c o n t a c t between a s u r f a c t a n t s o l u t i o n and a s o l i d ads0 rben t . l p l a c e du r ing displacement tests in Berea co res . Therefore , Flood 85 w a s repeated b u t a t a n i n j e c t i o n r a t e t h a t w a s t e n times lower and equal t o a n apparent f r o n t a l v e l o c i t y of 3 cm/day. It took more than 1 0 days f o r t h e sur- f a c t a n t s l u g t o propagate through t h e core. The o i l recovery was b e t t e r and a n a d d i t i o n a l 4% PV o f o i l was recovered which i s i n agreement wi th t h e previously publ ished d a t a on t h i s t ype of wperiment .15 bu t t h e l o s s o f s u r f a c t a n t by t h e phase t r app ing mechanism inc reased s u b s t a n t i a l l y wh i l e t h e adso rp t ion l o s s w a s s l i g h t l y lower. It t h e r e f o r e seems r easonab le t o suggest t h a t t h e a d d i t i o n a l r e s idence t ime f o r t h e s u r f a c t a n t i n t h e c o r e allowed i t t o be more concentrated i n t h e o i l phase, but than a n i n c r e a s e i n a d s o r p t i o n w a s n o t observed. It has been noted be fo re that , f o r s u r f a c t a n t systems which a r e no t a t op t ima l formulat ion ( i . e . not a t a middle phase c o n f i g u r a t i o n ) , t h e time requ i r ed f o r a t t a inmen t of phase equi l ibr ium may be s u b s t a n t i a l . s u r f a c t a n t r e d i s t r i b u t i o n among t h e phases may be more r e spons ib l e f o r t he time dependence of r e t e n t i o n t h a n is t h e slow a t t a inmen t of adso rp t ion equi l ibr ium a t t h e so l id - l iqu id i n t e r f a c e . This sugges t ion i s supported by previously reported r e s u l t s on a d s o r p t i o n measurements i n ba t ch experiments i n which, i n t h e absence of o i l , t h e adso rp t ion always reached equ i l ib r ium w i t h i n 24 hours.4

An at tempt has been made t o f i n d o u t i f similar phenomenon takes

The r e t e n t i o n l e v e l w a s t h e s a m e

Our experiments enable t h e sugges t ion that t h i s process of-

1 2 0

SUIPlARY

Based upon more than one hundred displacement experiments w i t h t h r e e types of s u r f a c t a n t s i n Berea cores , t h e following conclusions may be made:

1.

2.

3 .

4.

5 .

6 .

Thermodynamically v a l i d s u r f a c t a n t adsorp t ion isotherms should be determined i n ba tch experiments.

Displacement experiments y i e l d s u r f a c t a n t r e t e n t i o n va lues which involve averaging s e v e r a l var iab les . adsorpt ion is appl ied t o r e t e n t i o n d a t a obtained from displacement experiments, t h e o ther causes of s u r f a c t a n t l o s s e s must be accounted f o r so only adsorp t ion d a t a are used.

Experimental procedures that permit d i f f e r e n t i a t i n g between s u r f a c t a n t l o s s e s due t o adsorp t ion and thosc due t o unfavorable phase behavior have been developed and tes ted .

Pure s u r f a c t a n t (Texas #1) , s y n t h e t i c su l fona te (PDY 3 7 ) , and petroleum su l fona te (TRS 1@-80) g ive comparable r e s u l t s f o r r e t e n t i o n and adsorpt ion i n Berea cores.

Adsorption of s u r f a c t a n t s can be reduced by t h e s d d i t i o n of low molecular weight a lcohols (sec-butyl a lcohol , n-propano'.? . For t h e t h r e e s u r f a c t a n t s s tud ied , adsorpt ion l e v e l s d i d not exceed 1.2 mg/g. t o unfavorable phase behavior o r some o ther mechanism should be suspected.

I f any theory developed f o r

I f t h e o v e r a l l r e t e n t i o n i s higher , sur fac tan t l o s s e s due

ACKNOWLEDGEMENTS

The author wishes t o acknowledge t h e a s s i s t a n c e and dedica t ion of Laurie Baxter and G a i l Parker who performed t h e p r e c i s e experiments necessary f o r t h i s paper. Sincerely acknowledged a r e Bev Moore and G a i l Donaldson f o r typing t h i s manuscript.

REFERENCES

1.

2.

3.

MEYERS, K. 0. and SALTER, S. J.; "The Effec t of Oil-Brine Rat io on Surfac tan t Adsorption from Microemulsion", paper SPE 8989 presented a t the SPE 55th Annual F a l l Meeting, Dallas, Texas (September 21-24, 1980).

CELIK, M. S., GOYAL, A., MANEV, E. and SOMASUNDURAN, P.; "The Role of Sur fac tan t P r e c i p i t a t i o n and Redissolut ion i n t h e Adsorption of Sulfonate on Minerals", paper SPE 8263 presented a t t h e SPE 54th Annual F a l l Meeting, Las Vegas, Nevada, (September 23-26, 1979).

KRUMRINE, P. A., CAMPBELL, T. C. and FALCONER, J. S.; "Surfactant Flooding I: The Effec t of Alkal ine Additives on IFT, Surfac tan t Adsorption, and Recovery Efficiency", paper SPE 8298 presented a t the 5 t h Symposium on O i l f i e l d and Geothermal Chemistry, Stanford, Cal i forn ia (May 28-30, 1980).

1 2 1

4.

5 .

6 .

7.

8.

9.

10 .

11.

12.

13.

14.

15.

NOVOSAD, J.; "Adsorption of Pure S u r f a c t a n t and Petroleum Sulfonate a t t h e Solid-Liquid I n t e r f a c e " , Proceedings o f t h e 3rd I n t e r n a t i o n a l Conference on Sur face and Colloid Sciences he ld i n Stockholm, Sweden, (August 20-25, 1979) , Plenum Pub l i sh ing , New York (1981).

GLOVER, C. J., PUERTO, M. C., MAERTER, J. M. and SANDVIK, E. I.; "Sur fac t an t Phase Behavior and Re ten t ion i n Porous Media", (June 1979) SPEJ 2, 183-193.

TROGUS, F. J . , SCHECHTER, R. S. and WADE, W. H . ; "A h'ew I n t e r p r e t a t i o n of Adsorpt ion Maxima and Minima", (June 1979) J. Colloid Sci . 70, 293-305.

GALE. W. W. and SANDVIK. E. I.: "Ter t i a rv S u r f a c t a n t Floodinn: Petroleum Su l fona te Composition - Efficac; Studies" , (1973) SPEJ 2, 191-199.

SOMASUNDARAN, P. and HANNA, H. S.; "Adsorption of Su l fona te s on Reservoir Rocks", paper SPE 7059 p resen ted a t t h e 5 t h Symposium on Improved Methods f o r O i l Recovery he ld i n Tulsa, Oklahoma,(April 16-19, 1978).

SIRCAR, S. , NOVOSAD, J. and MYERS, A. L.; "Adsorption from Liquid Mixtures on S o l i d s : p e r a t u r e Coef f i c i en t s " , (May 1572) I & EC Fundamentals ll, 249-254.

GILLILAND, W. E. and CONLEY, F. R. ; "Surfactant Waterflooding".

FRANCES, E. I., DAVIS, H. T., MILLER, W. G . and SCRIVEN, L. E.; "Phase Behavior of a Pure Alkyl Aryl S u l f o n a t e Sur fac t an t " , p re sen ted a t t h e 175 th ACS Na t iona l Meeting, Anaheim, C a l i f o r n i a (March 13-17, 1978).

SHAH, D. 0. and WALKER, R. D. ; "Research on Chemical O i l Recovery Systems", Semi-Annual Report , Un ive r s i ty of F l o r i d a , G a i n e s v i l l e (June 1977).

ZORNES, D. R., WILLHITE, G. P. and MICHXICK, M. J.; "An Experimental I n v e s t i g a t i o n I n t o t h e Use of HPLC f o r t h e Determinat ion of Petroleum Sulfonates" , (June 1978) SPEJ 18, 207-218.

TRUSHENSKI, S. P. , DAUBEN, D. L. and PARRISH, E. R.; %Micellar Flooding -Fluid P ropaga t ion , I n t e r a c t i o n and Mobil i ty" , (1974) SPEJ l4, 633-644.

HEALY', R. N., REED, R. L. and CARPENTER, C. W.; "A Laboratory Study of Nicroemulsion Flooding", (1975) SPEJ 15, 87-100.

Thermodynamics of Excess P r o p e r t i e s and Their Tem-



THE EACN OF A CRUDE OIL: VARIATIONS WITH COSURFACTANT AND WATER OIL RATIO

MIN KWAN THAM and PHILIP BOALT LORENZ

U.S. Department of Energy Bartlesville Energy Technology Center

ABSTRACT

The EACN concept, which allows the subs t i tu t ion of a crude o i l by an alkane or an alkane mixture for phase volume or i n t e r f ac i a l tension studies, has been gen- e ra l ly accepted. I n t h i s paper, it was shown tha t such parameters as alcohol type, crude o i l composition, and water-oil-ratio could have an e f f ec t on the EACN of a crude o i l . the causes fo r t h i s aberration. components was thought t o be another. is i n progress.

The pa r t i t i on behavior of the alcohol was traced as one of Interaction of surfactant with heavy crude o i l

Experiments t e s t ing the l a t e r hypothesis

INTRODUCTION

The term Equivalent Alkaf_e3Carbon Number (EACN), was coined by the researcn &--.up from University of Texas i n t e r f a c i a l properties of any o i l with a surfactant can be modeled by the behav- i o r of alkanes. Thus, heptane, heptylbenzene, and butyl cyclohexane a l l exhibit "optimum" conditions, i.e., minimum in t e r f ac i a l tension (IFT) fo r the same combinations of surfactant, cosurfactant, and salt concentration. I n general, the benzene r ing appeared t o have EACN = 0 , and the cyclohexane r ing EACN = 3. addition, the EACN of a mixture of hydrocarbons follows the simple mixing ru le ,

. This concept a r i s e s from the observation tha t the

Inl-3

(Em)mixture = 11 xi EACNi, ---(l)

i where X i s the mole f rac t ion of component i.

i 4

This concept was later found t o be applicable t o crude o i l s and pseudo crudes , whereby an alkane or alkane mixture can be found t o model the IFT behavior of a crude o i l . An important finding of t he i r s is tha t the EACN of an o i l (crude, pseudocrude, o r hydrocarbon) is independent of the surfactant formulation, and tha t t h i s equivalence always holds. Crude o i l , being dark i n color and usually qui te viscous, can make equilibrium attainment very slow and phase volume observa- t i on d i f f i cu l t . Replacing the crude with hydrocarbon w i l l f a c i l i t a t e screening of surfactant formulation, and therefore, the EACN concept is a very valuable one.

Recently, the Texas group and Glinsmann5, extended the concept of equivalent optimal s a l i n i t y t o high concentration surfactant systems (> 2%). the EACN of a crude o i l i s independent of the alcohols and surfactants i n the formulations.

Here, also,

12 4

As p a r t of our support ing reseagch program f o r t h e DOE micellar-polymer p i l o t test i n Nowata County, Oklahoma , w e determined t h e EACN of t h e Delaware-Childers (D.C.) o i l from t h a t f i e l d , using s e v e r a l s u r f a c t a n t systems, and a t e r - o i l - r a t i o s (WOR). It w a s found t h a t t h e EACN w a s n o t a cons t an t v a l u e . This paper r e p o r t s t h e r e s u l t s i n our i n v e s t i g a t i o n on t h e probable causes f o r t h i s v a r i a - t i on .

Glinsmann's method of measuring t h e EACN of a n o i l was followed, i n which t h e opt imal s a l i n i t i e s of a s u r f a c t a n t system wi th a series of a lkanes w e r e de t e r - mined. By comparing t h e opt imal s a l i n i t y of t h e crude o i l w i th t h e same sur- f a c t a n t system, optimal s a l i n i t i ~ ! " ~ t h e one used h e r e w a s t h e equa l s o l u b i l i z a t i o n from phase volume measurements.

Various s u r f a c t a n t systems were s tud ied f i r s t , w i th s p e c i a l emphasis on t h e e f f - e c t of a l coho l type, becay&213tudies have shown t h e s t r o n g in f luence of a l coho l s on phase behavior and IFT . The e f f e c t of crude o i l components was then s tud ied . F i n a l l y , t h e e f f e c t of WOR w a s a l s o s tud ied .

Y

5

CN w a s determined. Of t h e d i f f e r e n t c r i t e r i a o d e f i n i n g 6

EXPERIMENTAL Materials

The s u r f a c t a n t s used (and t h e i r p rope r t i e s ) a r e l i s t e d i n Table I. They were used without p u r i f i c a t i o n .

The alkanes were pure-grade hydrocarbon from P h i l l i p s Chemical Company. phenyl dodecane w a s from Eastman Kodak Company.

Procedure

For phase-volume s t u d i e s , s u r f a c t a n t s o l u t i o n s were mixed wi th o i l i n g l a s s tubes ( p r e c i s i o n bo re t o 0.474 5 0.001 cm i . d . ) , and shaken f o r one minute i n a mech- a n i c a l shaker (40 Hz). Except where noted otherwise, t h e WOR w a s set a t u n i t y . The tubes were kep t i n a n a i r ba th a t 30' f o r e q u i l i b r a t i o n . Usually, one week t o s i x months were requ i r ed f o r complete e q u i l i b r a t i o n . Some of t h e solut ions-- e s p e c i a l l y those wi th high viscosity--were shaken a second t i m e t o ensu re thorough mixing.

The

Table I. P r o p e r t i e s of S u r f a c t a n t s

(b) Floodaid 141 TRS 10-410(a) Suntech I

TY Pe Blend of petroleum sulfon- Petroleum Su l fona te s of

93" propylene tetramer a t e s mixed wi th Cosurfactant 122

s u l f ona te mixed xylenes and

% Active 45 62 65

Equivalent WeAght 450

Equivalent wide

D i s t r i b u t i o n Weight

418 372

400-450 344-390 (80%) (92%)

(a) Witco Chemical Company. (b)

(c)

An experimental s u l f p g a t e (Sample No. I, Suntech Lot 768511) prepared by

Amoco Cosurfactant 122 i s a mixture of e thoxylated a l coho l s . Suntech Tech, Inc.

125

Phase volumes were measured with a cathetometer. Standard correction for the round-bottom end of the glass tubes, and for the oil and water menisci, were obtained by weight measurements. Solubilization calculations were fashioned after the work of Glinsmann. The following assumptions were made in the calculations: (a) all the surfactant and cosurfactant is in the surfactant phase (this is an incorrect assumption as can be seen later, but the effect on the phase volumes is negligible); (b) the volumes are additive. In the present work, surfactant and electrolyte concentrations refer to the concentration in the aqueous phase.

Some experiments were performed with crude oil components. oil into distillates and heavy ends were done at 400°F and 10 -Egg. Vacuum. Analysis for acids and bases was by column liquid chromatography determination was by pentane precipitation. with a gas chromatograph.

Distillation of crude

. Asphatene Alcohol concentrations were measured

RESULTS AND DISCUSSION Optimal Salinities

The optimal salinities for a number of systems with normal alkanes are plotted in The observed behavior is the same a8 that reported in the literature

carbon chain length, (2) water solubility of the cosurfactant (the solubilities are in the order IBA < TAA < Amoco 122), and (3) concentration of the water soluble cosurfactant.

that is, the optimal salinity increases with increases in (1) hydro-

/ 5 7 0 T i I 000 I- 3s 10- 410, 1.8% Amoco 122 ( E l

0 4% Suntech I, 2% TAA (A) z - ' \ U 600 8 o o G . 0 % Amoco 122 (D)

i i!

400

Y Z Y O FA 141 (F ) z

U v)

-I 200 U I

c I

I ooc;' , I

80 * I I I I I I I 7 8 9 10 I I 12 13 14

ALKANE CARBON NUMBER

Figure 1. tiary amyl alcohol; IBA = isobutyl alcohol:

Optimal salinity of surfactant systems with normal alkanes. TAA = ter- Amoco 122 - Amoco Cosurfactant 122.

12 6

The observed l i n e a r re1 t nship of I n (S ) versus alkane carbon number (ACN) w a s reported by SalagergYfg, who found t h t t the s lopes f o r a l l the sulfonate systems were 0.16 5 0.01. The value f o r the 5 percent TRS 10-410 - 3 percent isobutyl alcohol (IBA) system obtained by least square f i t is 0.17, which is i n good agreement with h i s values. However, the s lopes were 0.11 f o r t e r t i a r y amyl alcohol and 1.8 percent f o r cosurfactant 122, and 0.14 with 1.0 percent cosur-, fac tan t 122. This i s i n contradict ion t o the pred ic t ion of Salager 's equation , which predic t s s lope independent of the alcohol. The slopes f o r the Suntech and Floodaid sur fac tan t were 0.12 and 0.28, respect ively.

*

Effect of Surfactant Formulations on the EACN of Delaware-Childers O i l

The EACN of D. C. o i l w a s determined by comparing its optimal s a l i n i t y with t h a t of the alkanes f o r a given sur fac tan t formulation. tems w e r e used t o determine the constancy of its EACN. su l t s .

The severa l sur fac tan t sys- Table I1 shows the re-

Table 11. The optimal s a l i n i t y and EACN of D. C. o i l with d i f f e r e n t sur fac tan t formulations

Surfactant system Optimal s a l i n i t y

meq/l N a C l EACN

A 4% Suntech I 2% Ter t ia ry amyl alcohol ( T W

B 5% TRS 10-410 3% TAA

C 5% TRS 10-410 3% Isobutyl alcohol

D 5% TRS 10-410 1% Amoco 122

E 5% TRS 10-410 1.8% Amoco 122

680 9.5

19 7 9.3

193 10.9

410 6.15

590 6.2

F 12% FA 141* 222 7.7

* Sulfonate content equivalent t o 7.6% TRS 10-410 o r Suntech I

The spread of 4.7 u n i t s i n the values ind ica tes t h a t EACN as usual ly determined is not a constant quantity. From Figure 1 and Table 11, i t is necessary t o conclude t h a t the current ly accepted concept apply only over a narrow range of conditions.

Thus, Systems A and B y with f a i r l y s imi la r sur fac tan ts , give near ly i d e n t i c a l EACN values. Also, i n Systems D and E , a twofold v a r i a t i o n i n alcohol concen- t r a t i o n has no inf luence on EACN. But the t r a n s i t i o n from C t o B t o D (with a s igni f icant increase i n water s o l u b i l i t y of the cosurfactant a t each s tep) shows tha t the cosurfactant species has a major inf luence on the r e s u l t s . There are two propert ies of System F t h a t could contr ibute t o i t s d i f f e r e n t EACN value: a wide d i s t r i b u t i o n of equivalent weight and a d i f f e r e n t type of alcohol.

The EACN of an o i l w a s determined by comparing the optimal s a l i n i t y of the o i l with those of alkanes. The v a r i a t i o n i n EACN observed above, necessar i ly re f - l e c t s differences i n propert ies between the o i l and alkanes. i n t e r e s t t o study the e f f e c t of sur fac tan t formulation on the EACN of a number of o i l s .

It is therefore of

12 7

EACN of Several o i l s With Systems C and F

Surfactants Systems C and F were used t o compare the b h System C was chosen because i t has been widely s tudied 5*artna, and because the optimal s a l i n i t i e s , phase behavior and EACN of most of the o i l s s tudied with t h i s system followed a "regular" pat tern. f o r its " i r regular i t ies" . these systems with a number of o i l s . i n the EACN between the two systems, even though the deviat ion i s not as large as the D. C. o i l case. Bradford o i l shows an even smaller difference. These var ia t ions among the various crude o i l s may be compared with the differences i n the crude o i l composition (Table I V ) . Bradford o i l i s high i n paraf f in , and D. C . o i l contains a la rger quant i ty of heavy b28es and acids . pounds are known t o complex with the sulfonates .

of d i f f e r e n t o i l s .

On the o ther hand, System F w a s chosen Table 111 lists the optimal s a l i n i t i e s and EACN of

The E l Dorado o i l r e s u l t s show differences

These heavy corn-

Table 111. Optimal s a l i n i t i e s and EACN of crude o i l s and crude oil f rac t ions

System C .

S* EACN

System F

S* EACN

E l Dorado o i l 169 10.0 261 8.3

Bradford o i l 19 6 11.0 425 10.1

Bradford D i s - 130 8.2 t i l lates

19 7 7.3

Bradford heavy- ends + decanea 238 12.4 (20) 615 11.4 (15.8)

D. c. O i l 193 10.9 222 7.7

D. C . dig- t i l l a te 103 6.7 132.5 5.8

D. C. heavy- ends + decanea 185 10.6 (12.5) 295 8.7 (4.6)

(a) Equal weight r a t i o of heavy ends and decane

The behavior of the components of these crude o i l s is q u i t e revealing. t i l la tes show a downward s h i f t i n EACN as compared with t h a t of the whole crudes, as expected. In te res t ing ly , the l a r g e differences between Bradford and D. C. o i l s with respect t o the sur fac tan t Systems C and P disappeared. Both show a d i f fe r - ence of 0.9 u n i t s with the two systems, as compared t o 0.9 and 3.2 f o r the whole Bradford and D. C. o i l s , respectively. Y e t , the f a c t t h a t the d i s t i l l a t e s having d i f f e r e n t EACN with d i f f e r e n t sur fac tan t systems indica tes t h a t there are cer ta in components i n the d i s t i l l a t e s behaving d i f f e r e n t l y from the alkanes, which are the standards. alkanes and other series of compounds i s not exact . a l k y l benzene and a l k y l cyclohexane series t h a t are grea te r , the f a r t h e r one moves away from EACN of 8. t h a t the deviat ion can be q u i t e l a r g e when less conventional materials are used. The mixing of benzene with phenyl dodecane ( t o give an EACN of 8) shows normal EACN with System C.

The dis-

Actually, it has been recognized tQat the equivalence between There are deviat ions i n the

Table V presents some f u r t h e r d a t a on t h i s , showing

A downward s h i f t i n EACN with System E, similar t o t h a t

12 8

Table I V . Crude o i l p roper t ies

Delaware-Chllders o i l Bradford o i l E l Dorado o i l

G r a v i t y " AP I Nitrogen, percent 0.07

X Aromatic through f r a c t i o n l za 4.04

X Acids17 2.17

1.58 X Bases

X Total Asphaltenes 1.46

X Paraf f in through cu t 7

31.9

17

34.6

44.3 36.0

0.01 0.07

3.82 5.50

0.13 - 0.3 - 0.02 -

64.0 55.3

(a) Cut temperature 437°F a t 40 nun Hg. (corresponding t o molecular weight of 280). (b) Cut temperature 392°F (corresponding t o molecular weight of 150).

Table V. Optimal s a l i n i t i e s and EACN of akyl benzenes

.System C *System E s, EACN s, EACN

Benzene - phenyl dodecane 110 7.9 360 1.9 mixture, 1:2 molar r a t i o

Phenyl dodecane 145 9.0 557 5.9

with crude o i l s was ob e ved. the simple sca l ing l awgsg f o r both sur fac tan t systems. Under t h i s l a w , phenyl dodecane should have an EACN of 12. value and cannot be explained t o t a l y by the smaller deviat ion previously reported f o r the case without alcohol . The data on the heavy ends in Table 111 are a l o t more "irregular". cal experlmental purposes, it was necessary t o cu t t h e v iscos i ty by mixing with equal weights of decane. Equation ( l ) , an assumption was necessary on the molecular weight (MU). No value of MU could be found t h a t was consis tent with the EACN values , even f o r "regular" System C. t o an alkane of carbon No. 32, but gave EACN 20 f o r t h e Bradford heavy ends and 12.5 f o r those from D. C. The weight f r a c t i o n s of d i s t i l l a t e s and heavy ends from D. C. o i l (which l o s t only 4 wt-X I n d i s t i l l a t i o n ) required MW 254 (EACN 18) €or consistency with the whole-oil EACN. equation (1) only with MW = 160 (EACN - 11.3) f o r heavy ends. It is obvious t h a t heavy ends are not equivalent at a l l t o alkanes even with System C; and t h e discrepancy between Systems C and E are very large.

Alcohol Par t i t ion ing and Its Effect on EACN

W e have shown earlier t h a t replacing i sobuty l alcohol with Amoco 122 i n a sur fac t - an t formulation causes a downward s h i f t i n EACN. It is therefore of i n t e r e s t t o study the par t i t ion ing behavior of these alcohols, because alcohol p a r t i t i o n i n g is known t o be the prime determlnant of the phajts-&h2yior, i n t e r f a c i a l tension, and optimal s a l i n i t y of a surfactant-oi l system ' .

On the o ther hand, phenyl dodecane does not observe

The observed EACN d i f f e r s grea t ly from this

€

For prac t i -

To ge t the EACN of t h e heavy ends by themselves from

The d i s t i l l a t i o n temperature suggested a MJ of 450, which corresponds

The EACN of the decane mixture obeyed

12 9

Since determination of alcohol concentrations in crude oil poses considerable problem due to its wide boiling range--choosing the right column is difficult-- only the partition coefficients in hydrocarbons were measured. that the large differences in behavior of alkanes and allcyl benzenes would be reflected in the alcohol partitioning and suggest one cause for the difference between alkanes and crude oils. listed in Table VI. under other conditions are given for illustration. not very sensitive to salinity up to 3 percent; the table shows that the same value was obtained for Co-surfactant 122 in pure water and in System E at optimal salinity of 3.4 percent. The differences between the partition coefficients of Amoco 122 in octane and phenyl dodecane is striking. strong preferential partitioning of the heavier alcohol compounds (components 2 and 3) into the oleic phase of the phenyl dodecane system (Table VII). comparison with octane, the aqueous alcohol concentration in phenyl dodecane is lowered. position and concentration on the optimal salinity and EACN. It is certain, however, such changes will make the effort to estimate a "true EACN" impossible. That is, it is not possible to modify the definition of EACN to account for thig2 change in alcohol concentration. In agreement with the findings of Tosh, s& the presence of surfactant did not affect the alcohol partitioning behavior for the systems studied.

It was suspected

The results of the partitioning experiments are The numbers are relevant only at optimal salinity, but data

Partition coefficients are

In addition, there is a

Thus, in

It is not known what will be the effect of this change of alcohol com-

,

Table VI. Partition coefficients of alcohols ~ ~~~~~

Octane Phenyl dodecane

3% IBA 0.3ga 0.32b'd

1.8% Amoco 0.6aaSd 5.5C'd 122

a = alcohol originally in deionized water. b - alcohol originally in 0.9% NaC1. c = alcohol originally in 3.3% NaC1. d - in the presence of 5% TRS 10-410 at optimal salinity.

Table VII. Distribution of alcohol components, System E

Alcohol concentration, %

Phase Component 1 Component 2 component 3

Upper 0.26 0.25 0.15 Octane Middle 0.5 0.84 0.53

Lower 0.3 0.24 0.25

Partition coefficient - 0.8 Alcohol concentration, %

Phase Component 1 Component 2 Component 3

Upper 0.26 0.44 0.4 Phenyl Middle 0.6 0.69 0.69 dodecane Lower 0.19 <o . 01 <o. 01

Partition coefficient - 5.5

130

Solubilization a t Optimal Sa l in i ty

+-s v) - 2.0- >” \ > Y

The g&)ilization a t optimal s a l i n i t y , being re la ted t o the in t e r f ac i a l tension Under optimal condition (vo/vs) = (vw/vs) = (v/vs)S* The value decreases with increases i n alkane carbon

Hsieh and Shah” found a correlation between (V/Vs)s* and alkane

density. Puerto and Gale” related (V/Vs)s* and the s ide chain lgngth of an a lkyl

orthoxylene sulfonate. Figure 2 is a p lo t bf (V/V ) * versus alkane carbon number

l inear i ty w a s @served a l so i n the so lubi l iza t ion of alkanes i n micelles , according to Klevens structure, and other charac te r i s t ics of the solubizates. Reed and Healy had a l so noted some pa ra l l e l developments between o i l and water so lubi l i ty and so lubi l i - zation i n micelles. I n t h i s work, we found tha t the data fo r crude o i l s and crude o i l d i s t i l l a t e s a l so f a l l on the alkane l ine. This shows tha t with System C , o i l s modeled by optimal s a l i n i t y are a lso modeled by the degree of solubilization.

, is an in te res t ing property t o examine further.

for System C. Within experimental e r ror , the p lo t is s$ l i nea r fo r alkanes. Such

, who studied so lubi l iza t ion as a function of molar v o l v s ,

\ 5% TRS. 10-410 - 3% IBA

I I I I I I I

7 .O

6 .O

5 .O

4.0

3.0

0

\

o Alkane 0 Bradford oil 0 D.C. oi l . Bradford - light 0 0.C.-light ends

o Alkane 0 Bradford oil

. Bradford - light 0 0.C.-light ends

0 0 D.C. oi l

\

ends

4

Figure 3 I s a similar p lo t f o r System F. w a s observed. anes (not shown), which shows tha t t h i s relationship is qu i t e general. case, the crude o i l s and d i s t i l l a t e s do not f a l l on the l ine.

Again a l i nea r relationship f o r alkanes In f ac t , Systems D and E a l so give t h i s l i nea r re la t ion with alk-

I n t h i s I f the EACN values-

131

"."

8.0.

7 . 0 .

6 . 0 .

5 . 0 .

determined with System C are used, the f i t is much b e t t e r . degree of s o l u b i l i z a t i o n might give mre consis tent values of EACN than optimal s a l i n i t y . Even so, D. C. o i l does not f i t the cor re la t ion very w e l l , perhaps due t o its high content of acids , bases, and asphaltenes.

This suggests t h a t

4.0.

3.0.

2.0'

\

0- - - - +'. \ \ -

o Alkane D Bradford oil A D.C. o i l

0 D. C. -l ight ends

-

Bradford - light ends

-

-

\ \ \ \ \ \ \

- 12% FA 141

I . I I I I I I I

EACN

Figure 3. (V/Vs)s* versus equivalent alkane carbon number Q

Effect of Water-Oil-Ratio on EACN

The e f f e c t of water-oil-ratio (WOR) can be seen from Figure 4. by increasing the WOR from 1 t o 2, the pos i t ion of the octane and D. C. o i l l i n e s are interchanged. than 8, by simply increasing the WOR. re la ted t o alcohol par t i t ion ing . data of Table V I I . which would mean t h a t less of component l w o u l d be extracted from the aqueous phase. increase.

there i s no such f rac t iona t ion with octane, and presumably with other alkanes, the increase i n EACN is as expected.

It is noted t h a t

That is the EACN of crude o i l changed from 7.7 t o higher It is p laus ib le t h a t the WOR e f f e c t is

Consider the case of phenyl dodecane, with the Increase of WOR reduces the proportion of the o i l phase,

The proportion of water-soluble component i n the aqueous phase,would According t o Figure 1, t h i s should lead t o an increase i n S Since

4 .

132

30C

*," 20c

I oc 0

A Octane o D.C. oi l

I 2 WOR

3

Figure 4. Variation of optimal s a l i n i t y with water-oil-ratio

CONCLUSIONS

The EACN concept was found t o be i n e r ro r +hen sys t em involving ethoxylated alcohols and/or aromatics were used. Alcohol par t i t ion ing is found t o be an important fac tor causing t h i s deviation. components of the crude o i l might have contributed pa r t i a l ly t o t h i s "abnormal" behavior. applying the EACN concept.

The higher boiling, non-hydrocarbon

W e would l i k e t o advise caution when This is under investigation.

ACKNOWLEDGMENT

The authors wish t o acknowlege the help of J. B. Green and J. Lacina fo r the analyses on crude o i l s components.

Am

EACN

S*

vO

vs

vW

0

NOMWCLATURe

Alkane carbon number.

Equivalent alkane carbon number.

Optimal s a l i n i t y f o r phase behavior, meq/l NaC1.

Volume of o i l solubilized i n the surfactant phase.

Volume of surfactant i n the surfactant phase.

Volume of water solubilized i n the surfactant phase.

Volume of water o r o i l solubilized per un i t volume of surfactant a t optimal s a l in i ty .

133

REFERENCES

Cash, R. L., Cayias, J. L., Fournier, R. G., Jacobson, J. K., Schares, T., Schechter, R. S., and Wade, W. H. i a l Tension," Paper 5813 presented a t the SPE Symposium on Improved oil Recovery, held i n Tulsa, Okla., March 22-24, 1976.

Cayias, J. L., Schechter, R. S., and Wade, W. H.: Petroleum Sulfonates f o r Producing Low I n t e r f a c i a l Tensions between Hydro- carbon and Water," J. Coll. In t . Sci., 59, 31-38 (1977).

Cash, L., Cayias, J. L., Fournier, G., MaCalllster, D., Schares, T., Schechter, R. S., and Wade, W. H.: Scaling Rules t o Binary Hydrocarbon Mixtures," J. Coll. I n t . Sci., 59, 39- 44 (1977).

Cayias, J. L., Schechter, R. S., and Wade, W. B.: f o r Low I n t e r f a c i a l Tension," SPE J., l6, 351-357 (1976).

Glinsmann, G. R.: "Surfactantflooding with Microemulsions Formed I n s i tu - Ef fec t of O i l Characteristics." Annual F a l l Technical Conference and Exhibition of the SPE-AIME, held i n Las Vegas, Nevada, September 23-26, 1979.

Walker, C. J., Burtch, F. W., Thomas, R. D., and Lorenz, P. B.: Micellar Polymer Flood Pro jec t i n Nowata County." 68 (1976).

Lorenz, P. B., and Tham, M. K.: Polymer P i l o t Test." O i l and G a s J. To be published.

Reed, R. L. and Healy, R. N.: "Physicochemical Aspects of Microemulsion Flooding - A Review," i n Improved O i l Recwery by Surfactant and Polymer Flooding.

Salager, J. L., Morgan, J. C., Schechter, R. S., and Wade, W. H.: mum Formulation of SurfactantfWaterfOil Systems f o r Minimum I n t e r f a c i a l Tension o r Phase Behavior."

"Modeling Crude O i l s f o r Low Interfac-

"The U t i l i z a t i o n of

"The Application of Low I n t e r f a c i a l

"Modeling Crude O i l s

Paper SPE 8326 presented a t the 54th

"ERDA's O i l and Gas J., 74, 60-

"Calcium Effec t i n the DOE Surfactant-

Shah, D. 0. and Schechter, R. S., eds., Academic Press (1977).

"Opt i -

SPE J., 2, 107-115 (1979).

(10) Jones, S. C. and Dreher, K. D.: "Cosurfactants i n Micellar System Used f o r Ter t ia ry O i l Recwery." SPE J., l6, 161-167 (1976).

(11) Salteli, S. J.: "The Influence of Type and Amount of Alcohol on Surfactant- Oil-Brine Phase Behavior and Properties." 52nd Annual F a l l Technical Conference and Exhibit of the SPE-AIME, i n Denver, Colorado, October 9-12, 1977.

Paper 6843, presented a t the

(12) Hsieh, W. C. and Shah, D. 0.: "The Effec t of Chain Length of O i l and Alcohol As W e l l Aa Surfactant t o Alcohol Ratio on the Solubi l izat ion, Phase Behavior, and I n t e r f a c i a l Tension of OilfBrinefSurf actantfAlcoho1 Systems." Paper SPE 6594, presented a t the SPE-AIME In terna t iona l Sppo- sium on O i l f i e l d and Geothermal Chemistry, La J o l l a , Cal i fornia , June 27- 28, 1977.

(13) Wade, W. H., Morgan, J. C., Jacobson, J. K., Salager, J. L., and Schechter, R. S.: " I n t e r f a c i a l Tension and Phase Behavior of Surfactant Systems." SPE J., la, 242-252 (1978).

(14) Baviere, M., Schechter, R., and Wade, W. H.: "The Influence of Alcohols on Microemulaion Composition." J. Coll. In t . Sci., &&, 266-279 (1981).

134

(15) Dominguez, J. G., Willhite, G. P., and Green, D. W.: "Phase Behavior of Microemulsion Systems with Emphasis on Effects of Paraffinic Hydrocarbon and Alcohols," in Solution Chemistry of Surfactants. Vol. 2, Gttal, K. L., ed., Plenum, New York, pp. 673-697 (1979).

(16) Malmberg, E. W.: "Large-Scale Samples of Sulfonates for Laboratory Studies in Tertiary Oil Recovery, Preparation and Related Studies," Report No. FE-2605-20, National Technical Information Service, U. S. Department of Commerce, Springfield, Virginia (1979).

(17) Green, J. B. and Hoff, R. J.: "Liquid Chrometography on Silica Using Mobile Phases Containing Aliphatic Carboxylic Acids I1 - Applications in Fossil Fuel Characterization," J. Chrom. 2, 231-250 (1981).

(18) Salager, J. L.: "Physico-Chemical Properties of Surfactant-Water-Oil Mixtures---Phase Behavior, Microemulsion Formation and Interfacial Ten- sion." Ph.D. Dissertation, The University of Texas at Austin, 1977.

(19) Miller, C. A. and Fort, T. Jr.: "Low Interfacial Tension and Miscibility Studies for Surfactant Tertiary Oil Recovery Processes." DOE/BC/10007-4, National Technical Information Service, U.S. Department of Commerce, Springfield, Virginia 22161 (1979).

Report No.

(20) Clementz, D. M. and Gerbacia, W. E.: "Deactivation of Petroleum Sulfon- ates by Crude Oils." J. Pet. Tech., pp. 1091-1093, September 1977.

(21) Puerto, M. C. and Gale, W. W.: "Estimation of Optimal Salinity and Solu- bilization Parameters for Alkylorthoxylene Sulfonate Mixtures." SPE J., - 17, 193-200 (1977).

(22) Tosch, W. C., Jones, S. C., and Adamson, A. W.: "Distribution Equilibria in a Micellar Solution System." J. Coll. Int. Sci., 31, 297-306 (1969).

(23) Healy, R. N., Reed, R. L., and Stenmark, D. G.: "Multiphase Microemulsion Systems." SPE J., 2, 147-160 (1976).

(24) Huh, C.: "Interfacial Tensions and Solubilizing Ability of a Microemul- sion Phase That Co-exists With Oil and Brine." J. Coll. Int. Sci., 2, 408-426 (1979).

(25) Fleming, P. D., 111, Vinatieri, J. E., and Glinsmann, G. R.: "Theory of Interfacial Tension in Multicomponent Systems." 1531 (1980).

J. Phys. Chem., 84, 1526-

(26) Klevens, H. B.: "Solubilization." Chem. Rev., 1-74, 1950.


DYNAMIC INTERFACIAL PHENOMENA RELATED TO EOR

J. H. CLINT, E. L. NEUSTADTER and T. J. JONES

The British Petroleum Company Limited, BP Research Centre, Chertsey Road, Sunbutyen-Tharnes, Middlesex, TWI 6 7 WV

ABSTRACT

The relevance of dynamic interfacial tension and interfacial rheology to EOR is discussed. A technique developed by BP, the "Drop Volume Dynamic Tensiometer" allows dynamic interfacial tension to be determined over a wide range of rate of fractional area change. The behaviour of aqueous surfactant systems against crude oil is very different for fresh systems compared with systems where the phases have been pre-equilibrated. to EOR systems is illustrated with examples of surfactants which give widely different oil displacement profiles.

A new method for the measurement of interfacial dilatational rheological parameters of oil/water interfaces is described. This is the pulsed drop experiment which has experimental advantages over the interfacial trough method and allows parameters to be determined over a wider range of frequencies. interfacial dilatational rheology on coalescence phenomena is illustrated with data for water-in-oil demulsifiers.

The ease of oil bank formation is influenced by the kinetics of coalescence, which in turn is controlled by film drainage from between colliding droplets. For crude oil films in water, increasing interfacial shear viscosity greatly reduces the rate of thinning. For the reverse system, increasing interfacial shear viscosity can reduce coalescence rates for oil drops in water almost to zero. This would have a very adverse effect on oil bank formation.

The application of these measurements

The effect of

INTRODUCTION

In an enhanced oil recovery process, oil ganglia which have been trapped at small pore throats are released by lowering the interfacial tension, prevented from being retrapped by maintaining a low tension (dynamic) and encouraged to coalesce to form an oil bank. In all except the initial release it could be argued that it is the dynamic properties of the interface such as the dynamic interfacial tension and the interfacial rheology which will govern each individual and hence the overall process.

This paper reports some novel methods for measuring dynamic interfacial tension and interfacial dilatational rheology which work very well for crude oil-water systems. Techniques will be illustrated with results for pure oils as well as crude oils, and the significance of these data for EOR processes will be discussed.

136

DYNAMIC INTERFACIAL TENSION

This technique is essentially an extension of the drop volume method for interfacial tension and is illustrated in Figure 1.

WATER (I JACKET 'k

SEPTUM CAP

SYRINGE PUMP

FIGURE 1 - DROP VOLUME DYNAMIC TENSIOMETER

Oil from a syringe pump is pumped at an accurately known volume flow rate to a syringe needle inserted through a septum cap into a small glass cell surrounded by a water jacket. and the inside and outside diameters determined accurately. of observation an image of the tip and drops formed is obtained using a microscope and TV camera and displayed on a monitor screen.

The experiment consists very simply of measuring the number of drops formed in a fixed period of time and repeating at a whole range of volume flow rates Q. If n is the number of drops per unit time then the volume of each drop

The tip'of the syringe needle is ground flat For convenience

I

Q v = -

n ... (1)

The interfacial tension y can then be calculated using the usual formula

... ( 2 )

137

where P - P ' is the density difference between the oil and water phases, and R is the radius of the tip to which the drop is attached. inside or outside tip radius depending on the wetting conditions.

If we make the assumption that the drops are spherical then the rate of fractional area change at the time when the drop detaches can be shown to be

The latter may be the

... ( 3 )

Hence we are able to estimate both the interfacial tension and the rate of fractional area change simply by measuring the rate of formation of drops at a known volume flow rate.

Figures 2 and 3 illustrate the type of results obtained using Forties crude oil against two different surfactant systems. head sample free of any additives such as demulsifiers or corrosion inhibitors. All aqueous solutions were made up in filtered sea water. differences in the results depending on whether the oil/water systems were preequilibrated or whether they were fresh. dynamic interfacial tension on rate of fractional area change for a surfactant system "A" at 7OOC.

The crude oil used was a well

There were large

Figure 2 shows the dependence of

d I

E

FIGURE 2 - DYNAMIC INTERFACIAL TENSION -FORTIES CRUDE/SOOO PPM SURFACTANT "A" AT 7OoC

138

The difference between fresh andpre-equilibrated systems is immediately apparent. The preequilibrated tension rises rapidly at moderate rates of area increase whereas the tension of the fresh system stays remarkably low until very high rates of area change are reached where the area is roughly doubling every second. In contrast to this is the behaviour of the surfactant system "B" shown in Figure 3.

6

5 d I E

0

1

FIGURE 3 - DYNAMIC INTERFACIAL TENSION I FORTIES CRUDE/50OO PPM SURFACTANT "B" AT 70OC

This time the pre-equilibrated system gave interfacial tensions which were very small and at time9 unmeasurably so (only the one which could be measured is shown). The dashed line indicates that the tension remains low even at high rates of area change. rising rapidly with modest rates of area increase.

The interesting point about these two systems is that they give totally different oil removal profiles when tested in a model sand column test. For surfactant "A" which gave low fresh tension but high equilibrium tensions, removal of oil was rapid but incomplete. less than 2 pore volumes (PV). tensions but very low equilibrium tensions, removal of residual oil was Complete but required a very large number (15) of PV.

The tensions for the fresh system showed the normal dynamic effect

About 35 per cent of residual crude oil was removed in For surfactant "B", which gave high fresh

139

Admittedly the shape and duration of the oil displacement curve will be dependent on more than just the dynamic tension behaviour. and the degree of adsorption will also be important factors. However, the distinction between the two systems above is clear and the oil displacement behaviour is logically related to the dynamic tension properties.

Surface wettability

INTERFACIAL DILATATIONAL RHEOLOGY

For the measurement of interfacial dilatational rheology the method employed in the past has been that of dilatational modulus measurements at various frequencies using an interfacial film balance (1). The method involves propagation of longitudinal waves of the frequency of interest and measuring changes of interfacial tension with a Wilhelmy plate. These changes, together with the phase differences between them and the area changes, allow calculation of Ed# the dilatational elasticity and nd, and dilatational viscosity, at each frequency. This technique suffers from a number of disadvantages including

(a) Measurements are reliable only at fairly low frequencies where the wavelength of longitudinal waves is long compared with the distance between oscillating barrier and Wilhelmy Plate.

(b) Good results depend on the rapid response of the Wilhelmy plate and the maintenance of a well defined contact angle.

(c) The method uses large quantities of oil with a large area exposed to air allowing loss of light ends. used at temperatures much above ambient.

Also the apparatus is not easily

We have developed a new technique which uses a small drop of oil pulsed in water. Area changes are calculated from drop diameters and the tip diameter, and tension is calculated by measuring the excess pressure inside the drop with a sensitive pressure transducer. The experimental arrangement is shown in Figure 4.

CHART RECORDER

SENSITIVE PRESSURE

SYRINGE PUMP TRANSDUCER

WATER FROM THERMOSTAT

FIGURE 4 - PULSED DROP METHOD FOR INTERFACIAL DILATATIONAL RHWlLOGY

140

The oil drop is formed at a ground glass or stainless steel tip. of tip needed depends on the region of interfacial tension being investigated. the excess pressure inside the drop was measured using a transducer from SE Labs (EMI) Ltd, type SE 1150/WG. Output from the transducer is displayed on a chart recorder. Instead of the conventional oscillatory method for dilatational modulus measurements, the single pulse Fourier transform method was used (2). When the cell containing the aqueous solution of interest is sufficiently well thermostatted the drop radius (rl) is measured, a fixed volume pulse is injected from the syringe pump over a short period of time which increases the radius to r2 and then the variation of pressure with time is followed on the chart recorder. The shape of a typical pressure trace is shown in Figure 5.

The radius

TIME/MINS

E'fGURE 5 - TRANSIENT PRESSURE INSIDE DROP FOLLOWING SUDDEN EXPANSION

The equilibrium pressure after the experiment is lower than that at the beginning because the drop radius is larger. All of the pressure trace after the rapid rise is assumed to take place at a constant drop radius, the final radius r ~ . Then the interfacial tension at any time Y (t) is given by

... (4)

141

The interfacial modulus is usually written:-

t* = dy/dlnA = t' + it" ... ( 5 )

Taking Fourier transforms of the numerator and denominator coverts the perturbation time function AA(t)/A and the response time function y(t), to the frequency function. Thus:-

€*(W) =

For a perfect step function (instantaneous area change):-

Therefore:- iw f -

t*(w) = ~ A / A 1, Ay(t) [cos wt - i sin otldt

The real part gives us the dilatational elasticity:-

= Ed(w) = :[ Ay(t) sin wt dt

The lmaginary part gives the dilatational viscosity:-

AA/A

m

E" = *wnd(w) = w J: AY(t) cos wt dt W A

where w = angular frequency (radians per second).

... (6)

... (7)

... ( 8 )

... (9)

... (10)

Equations 9 and 10 can be used to calculate td and n decay curve. It is convenient to take approximately 100 readings ffom the.decay curve for use in these computations.

The method was evaluated using a model system of 10 ppm stearic acid dissolved in n-decane against distilled water adjusted to pH 2.5 to prevent ionisation of the acid. Results are shown in Figure6 for the real (elasticr damponent of the modulus and in Figure 7 for the imaginary (frequency x viscosity) component.

at any frequency from the A desk top microcomputer is adequate afthough a little slow.

142

d I

E

2 \

W

I I I I1111 I I I 1 1 1 1 1 ~ I I 1 1 1 1 1 1 I I i i i i r r 20

- -

15 -

10 -

5 -

0-

10-3 10-2 10-1 1

FREQUENCY/Hz

FIGURE 6 - REAL PART OF INTERFACIAL DILATATIONAL MODULUS FOR 10 PPM STEARIC ACID

FILLED CIRCLES - DROP METHOD IN n-DECANE/DISTIUED WATER pH 2.5 AT 25OC. OPEN CIRCLES - TROUGH METHOD.

10

8

6

I d

E

a 4 W

2

0 10-1 1

FREQUENCY/Hz

FIGURE 7 - IMAGINARY PART OF INTERFACIAL DILATATIONALMDDULUS. SYSTEM AND SYMBOLS AS FOR FIGURE 6

143

In each case the results are shown in comparison with data obtained previously using the interfacial trough technique, also using the Fourier transform method. Each set of data is the average of three separate runs. Agreement between the drop and trough methods is very good over most of the frequency range except possibly for the values of E " at intermediate frequencies.

The shapes of the curves of E ' and E" are very close to those expected for a single relaxation mechanism. This is illustrated more strikingly in Figure 8 where a Cole-Cole plot ( E " against E l ) is shown. A single relaxation mechanism has a semi-circular Cole-Cole plot and the data from interfacial trough experiments clearly follow a semi-circle quite closely. Again agreement with pulsed drop data is encouragingly good considering the great difference between the two techniques. The implication is that the techniques measure real dilatational parameters and not artefacts.

4 I

E

0 5 10 15 20

E ' / ~ N m-l

FIGURE 8 - COLE-COLE PLOT FOR INTERFACIAL DILATATIONAL MODULUS. 10 PPM STEARIC ACID IN n-DECANE/DISTILLED WATER pH 2.5.

OPEN CIRCLES - TROUGH METHOD. FILLED CIRCLES - DROP METHOD

The single relaxation mechanism implied by Figures 6 , 7 and 8 is presumably diffusion of the stearic acid from the interface into the bulk decane phase. The maximum in C'' which corresponds to the inflection point in E ' occurs at U = 0 . 0 0 2 5 Hz which is an angular frequency w = 2nu = 0.0157 s-'. This is the characteristic frequency of the relaxation process. 'I = l/w = 64 sec. This would seem to be a very reasonable relaxation time for a diffusion controlled mechanism in a dilute system [c = 10 p p = 3.5 x 10-5 mol am-31.

The relaxation time

1 4 4

The main advantages of the drop method over the trough method are

(a) The system can be enclosed so that loss of light ends from crude oils is avoided.

The system can easily be thermostatted at high temperatures. (b)

(c) The system is compact and very small quantities of materials are used.

EFFECT OF INTERFACIAL RHEOLCGY ON COALESCENCE PHENOMENA

The pulsed drop method has not yet been used to investigate coalescence phenomena. However, as an illustration of how interfacial dilatational rheology is involved in coalescence processes which are essential to oil bank formation, dilatational parameters for the Forties crude oil/formation water interface can be quoted which were determined by the trough method. oil demulsifiers was investigated. function of frequency and as a Cole-Cole plot in Figure 10.

The influence of various water-in Results are shown in Figure 9 for E " as a

rl

Ei

w

6

0 - FORTIES/FORMATION WAT

- +10 PPM DEM 1113 5

4 A - +10 PPM RP 968 0 - + 5 PPM CC 6601

3

2

1

0 1

FREQUENCY/Hz

FIGURE 9 - EFFECT OF VARIOUS DEMULSIFIERS ON IMAGINARY (VISCOUS) COMPONENT OF INTERFACI~RILATATIONAt MODULUS

FORTIES CRUDE/FORMATION WATER AT 25OC

1 4 5

0 2 4 6 8 10 12

E'/~N m-l

FIGURE 10 - COLE-COLE PLOT FOR SYSTBMS IN FIGURE 9. SYMBOLS AS IN FIGURE 9.

The interface without additives gives two separate peaks indicating two different relaxation mechanisms are involved. can calculate relaxation times for the two processes of 87 sec and 4 sec. These are compared with relaxation times for systems with low concentrations of three water-in-oil demulsifiers in the table below.

From the positions of the peak maxima we

Relaxation Time (Seconds)

87 4 1 Forties crude/formation water

+ 5 ppn CC 6601

+10 ppm RP 968 22

+10 ppn DEM 1113 9

4.5

The major effect of the &emulsifiers is to remove the relaxation process characterised by a long relaxation time. to mean more rapid film drainage (3) and therefore more rapid coalescence.

These demulsifiers are also found to reduce the interfacial shear viscosity of the crude oil/water interface. at some frequencies the dilatational viscosity is reduced whereas at other, normally higher, frequencies the dilatational viscosity can be greatly increased. At this stage the mechanistic implications of these observations are not fully understood. Further work on this topic is planned.

Shorter relaxation times are expected

However, from Figure 9 it can be seen that

146

MEASUREMENT OF DRAINAGE RATES FOR SINGLE OIL FILMS IN WATER

Direct evidence for the influence of interfacial shear rheology on the kinetics of drainage of thin films has been obtained by measuring the thickness of crude oil films in distilled water. measure thickness of oil films in air ( 3 ) , but having the whole cell filled with water. Measurements of the intensity of light reflected from the single oil film were used to calculate film thickness as a function of time. Results for Iranian Heavy crude and for Forties crude in distilled water are shown in Figure 11.

The technique was the same as that used to

4

0

0 0.5 1 .o 1.5 2.0

(t/min) -4

FIGURE 11 - FILM DRAINAGE - CRUDE OIL FILMS IN DISTILLED WATER AT 25OC

For the Iranian Heavy case the thickness is proportional to t-+ in accordance with the Stephan-Reynolds equation indicating that drainage is essentially from between two rigid interfaces. drainage curve is not a straight line and indicates much more rapid drainage of the film than can be accounted for by the lower bulk viscosity of Forties oil. more fluid compared with the Iranian Heavy case. out by measurements of interfacial shear viscosity at the crude oil/water interface. Figure 12 were obtained. Iranian Heavy/distilled water interface builds up to quite high values whereas that for the Forties/distilled water interface remains low.

In contrast the Forties crude in water film

This implies that the Forties crude/distilled water interface is much These implications are borne

Using the biconical bob shear rheometer the results shown in Over a period of hours the shear viscosity of the

The reverse system, drainage of water films from between colliding oil droplets, is relevant to oil bank formation. Because crude oil is opaque it is not possible to perform experiments analogous to the single oil film drainage measurements outlined above. However, there is clear evidence in the literature for the reduction of coalescence rates for crude oil drops in water when interfacial shear viscosity is increased ( 4 ) .

.6

4

E

P \ * v)

v) H

E 8

3

a 2 a

3

w X v)

H V

B z

. 4

. 2

FORTIES

I I

H 0 1 2 3 4 5

INTERFACE AGE/HOURS

FIGURE 12 - CRUDE OIL/WATER INTERFACIAL, SHEAR VISCOSITIES AT 25OC Clearly an important quality of an EOR surfactant will be the maintenance of low interfacial shear viscosity as an aid to oil bank formation.

1.

2 .

3 .

4 .

5.

6 .

CONCLUSIONS

A dynamic drop volume technique can be used to determine dynamic interfacial tension in crude oil/water systems as a function of rate of fractional area change.

For different surfactant systems which have markedly different oil removal profiles from sand columns, dynamic interfacial tension behaviour can be completely different.

A pulsing drop method has been devised which can measure the interfacial dilatational rheological parameters for oil/water systems. The results agree well with those determined using an interfacial trough. Both systems can be used with the single step pulse Fourier transform method.

For a pure system of stearic acid in n-decane against distilled water at pH 2.5, the complex dilatational modulus gives a semi-circular Cole- Cole plot indicating that relaxation at the interface is due to a single mechanism, presumably diffusion to and from the interface.

For a Forties crude/oil formation water interface, two separate relaxation processes are detected, presumably diffusion and molecular rearrangement. Water in crude oil demulsifiers remove the mechanism with the longer relaxation time.

Drainage of crude oils films in water can be followed by reflectance measurements of thickness. interfacial shear viscosity.

Drainage rate depends critically on

148

NOMENCLATURE

Area of interface (ma) Volumetric flow rate (m3 s-1) Tip radius (m) Volume of drop (m3)

Acceleration due to gravity (m s - ~ ) Number of drops per unit time (s-l) Excess pressure inside drop (Nm-2) Time (s)

Interfacial tension (Nrn-l) Complex interfacial dilatational modulus (Nm ) Real part of dilatational modulus (Nm-1) Imaginary part of dilatational modulus (Nm-l) Interfacial dilatational elasticity (Nm-1) Interfacial dilatational viscosity (Ns m-l) Frequency (cyclic) (Hz) Density (kg N 3 ) Relaxation time ( 8 )

Angular frequency (s-1)

-1

A

R V

Q

9 n AP t

Y € *

E '

€ "

Ed Ild

P 'I

w

U

ACKNOWLEDGEMENT

Permission to publish this paper has been glven by The British Petroleum Company Limited.

REFERENCES

GRAHAM, D.E., JONES, T.J., NEUSTADTER, E.L. AND WHITTINGHAM, K.P. "Interfacial Rheological Properties of Crude Oil Water Systems", 3rd International Conference on Surface and Colloid Science, Stockholm, 1979, Plenum Press, in the press.

LOGLIO, G., TESEI, U. AND CINI, R "Spectral Data of Surface Viscoelastic Modulus Acquired Via Digital Fourier Transformation" J. Colloid Interface Sci, (1979), 71, 316.

CALLAGHAN, I.C. AND NEUSTADTER, E.L. "Foaming of Crude Oils: A Study of Non-Aqueous Foam Stability" Chemistry and Industry, 17.1.81, p 53.

WASAN, D.T., McNAMARA, J.J., SHAH, S.M., SAMPATH, K. AND ADERANGI, N. "The Role of Coalescence Phenomena and Interfacial Rheological Properties in Enhanced Oil Recovery: An Overview" J. Rheology, (19791, 23, 181.


BEHAVIOR OF SURFACTANTS IN EOR APPLICATIONS AT HIGH TEMPERATURES

LYMAN L. HANDY

Department of Petroleum Engineering University of Southern carifornrb

ABSTRACT

Temperature sepsitive properties of some anionic and nonionic surfactants used in EOR operations have been measured. thermal stability. kinetics. The stability can, therefore, be quantitatively expressed in terms of the half-life of the surfactant. At 180°C half-lifes for petroleum sulfonates varied from 1 to 11 days. data can be used to predict half-lifes at other temperatures. nonionics is known to be affected by temperature. dehydrate and become less soluble. rock minerals. This problem increases with increasing temperature. Adsorption is temperature dependent although the experimental results for the anionics were obscured by precipitation. decrease with increasing temperature at low concentrations but to increase with temperature at high concentrations. ured as a function of temperature. Mixtures of sulfonates, however, have all sham an order of magnitude reduction in interfacial tension at temperatures in excess of 120%.

Of particular interest is the Those surfactants we investigated decomposed by first order

Activation energies were measured and these Solubility of

At the cloud point they Anionics appear to form precipitates with

Adsorption of nonionics were observed to

Interfacial tensions have also been meas- The results vary with the surfactant.

INTRODUCTION

Much of the unrecovered oil in the United States occurs in heavy oil deposits, mostly in California. known to occur in Venezuela, Mexico, Canada and elsewhere. the viscosity must be reduced by orders of magnitude. accomplish this objective is to heat the oil in-place. either steamflooding or in situ combustion. quently used process. chemical additives which will improve the process. steam is that it tends to finger through the formation and to override the oil. Various organic chemicals have been investigated for use with steam as flow diverters to minimize gravity override. Surfactants are being evaluated as possible additives which will reduce the residual oil saturation in that portion of the reservoir which is flooded only with hot water during steam drive. Although the temperature requirements for chemicals to be used at steam tempira- tures are much more rigorous, high temperatures are also encountered in the deeper reservoirs which are currently being considered for enhanced oil recovery. This has introduced additional requirements with respect to the temperature compatibility of chemicals used in these reservoirs.

Large accumulations of heavy oil are also To recover this oil

The only feasible way to This can be done by

Steam injection is the most fre- This has given rise to the investigation of various

One of the problem with

150

In the present paper we are concerned, primarily, with surfactants, but problems are also encountered with polymers at high reservoir temperatures. Four aspects of the effect of temperature are considered: the effect on the stability of the surfactants, the effect on solubility, the effect on water-oil interfacial tensions and, finally, the effect on adsorption onto the solid matrix.

THERMAL STABILITY

A limited number of studies have been reported in the literature on the stability of surfactants suitable for oilfield operations at temperatures in excess of 100°C. Data have also been reported by others for the petroleum sulfonate, TRS 10-80, but no temperatures were stated for those experiments.2 results were presented for anionic and nonionic surfactants. included sodium dodecylbenzene sulfonate, an acidic Dowfax sulfonate and several petroleum sulfonates. The petroleum sulfonates included TRS 10-80 manufactured by Witco and Petrostep 465 manufactured by Stepan Chemical Corporation. Dowfax 240 was from Dow Chemical Company. The nonionic was an alkylphenoxypolyethanol manufactured under the trademark of Igepal CO-850 by GAF.

The most extensive of these is that of Handy et al.’

In our earlier report The anionics

The surfactants were mixed at various concentrations without salt and aged at elevated temperatures in Teflon containers in Parr Acid Digestion bombs. Particular care was taken to eliminate air from the bombs. Long term aging tests were conducted in sealed borosilicate glass vials. In comparing our work with that of others, a major factor is the method used for chemically analyzing for the active surfactant. which involves a dye transfer between two phases. difficult to detect in this procedure. The bond which ruptures during high temperature aging is the sulfur-aromatic ring bond. lengths at 220-240 nm and 260-280 nm. tures, the absorption at these characteristic wavelengths is decreased. The decrease in the concentration of the active surfactant can be measured quantitatively from the change in the peak heights. Concentrations were determined from a comparison of peak heights with those observed for solutions of known concentration. because these compounds also have a disubstituted aromatic ring. of the Epton titration has been proposed by Mukerjee which is reported to be more quantitative than the original method.

The most common procedure is the Epton titration,

We used instead W spectrophotometry. We found the end points

Disubstituted aromatic rings have a characteristic absorption wave When the sulfur-aromatic ring bond rup-

The alkylphenoxypolyethanols could also be analyzed by W absorption A modification

We have not tested that procedure.

The decomposition reaction for the petroleum sulfonates is the following:

ArSO; + 2H20 ArH + SO; + H30=

It would be possible, therefore, to monitor the reaction from a measurement of the pH.

Representative data from reference 1 are given on Figures 1 and 2. The plot of the logarithm of concentration versus time was linear. was also observed to be linear. behavior. anionics is first order. order kinetics is

pH versus time The other anionic surfactants gave similar

These results indicate that the decomposition reaction for the The decomposition rate for a reaction following first

- dC/dt = kt

151

c = c c-kt or log c = - -kt + log co 0 2.303

In these equations C is concentration in moles per liter; C is the initial concentration; t is time in days and k is the rate constant in days-'. The rate constant is determined from the slope of the semilog plot. One can also show that when C/Co - 4, the elapsed time is equal to the half-life of the surfactant.

0

TRS 10-a0 C, = 243 x IU3M

70

I 0 99 OI 144 Ism 240

HEATING TIME (HRS)

Fig. 1-Concentration of TKS 10-80 as function of heating time at 149°C and 204°C

Fig. 2 - pH of TRS 10-80 as function of heating time at 140'C

If one has rate constants at several different temperatures one can determine the activation energy for the reaction. With the activation energy one can determine rate constants and half-lifes at other temperatures. This is particularly useful in estimating the stability of surfactants at lower temperatures for which the decomposition rates are low and long times would be required to measure the half-lifes. constant versus the reciprocal of the absolute temperature for TRS 10-80. This plot is typical of those obtained for the surfactants which were tested. In the equation

Figure 3 is a plot of the log of the rate

-E a log a 2.303 RT +

Ea is the activation energy in cals/mole; R is 1.987 cals and T I s the absolute temperature in OK. From the slope of the plot one can determine the activation energy.

152

A summary of decomposition data for several surfactants is given in Table 1. At 180°C Petrostep 465 is the most stable of the surfactants we investigated. Because of its high activation energy relative to the other surfactants, this surfactant would have a half-life of about 16 years at 100°C. None of the surfactants have adequate stability for use at normal steam temperatures. These results would be expected to be representative for aryl sulfonates, but better stabilities have been informally reported for alkyl sulfonates.

SOLUBILITY

Quantitative data on the effect of temperature on the solubility of petroleum sulfonates have not been reported, but evidence has been cited by several authors that precipitation of the sulfonates occurs at the higher temperatures in natural sandstones. * s 5 , This occurs not as a

I 1 I 1

TRS 10-80 I

w

0.7

0.5

0.21 I 1 1 I I 2.0 21 ?A? 2.3 2.4 28

f IO~PK-IJ

Fig,. 3 - The rate constant (k)

as tunction of -(OK-') f o r 'IKS 10-80

1 T

result of a direct temperature effect on the solubility of the surfactants but, apparently, as a result of an interaction with minerals in the porous media. Reed has measured a significant increase in the solubility of rock minerals at steam temperatures.' divalent cations. increasing temperature. decreases the solubility of the sulfonates.

The petroleum sulfonate ions form precipitates with These precipitates are likely to decrease in solubility with

In general, the presence of salt in the solutions

TABLE 1

SUMMARY OF DECOMPOSITION DATA FOR SURFACTANTS

Mol. Wt. Temp. "C t$(days) Ea(kcals) Surfactant

NaDDBS 348.5 130 180 150 180

Dowfax 2AO 500 177

TRS 10-80 415 149 204.5 180

6.13 .22

1.75

5.6(W)

13.6

6.9(pH)

17.4 3.0 7.0

24.0 24.0 26.0 26.0

NA

12.4 12.4 12.4

Petrostep 465 130 444 25.2 465 157 108 25.2

180 11 25.2

Igepal 1100 130 .75 8.84 CO-850 180 .22 8.84

Ziegler observed tur- bidity in the produced fluid from a Berea sand pack when sodium dodecylbenzene sulfonate solutions were injected at a concentration of 1400 pmols/liter. However, data in Figure 4 show that surfactant precipitated out of a 0.2 molar salt solution could be redissolved when distilled water was injected and when the temperature was increased. In this experiment the sand pack was flushed with 1374 pmols/liter surfactant In 0.2 M NaC1. Then the pack was flushed with salt solution only, with distilled water and. finallv. Fig. 4-Desorotion curve for NaDDBS with distilled wate; at 180'C. Distilled water redissolved sulfonate precipitated out of, brine and an increase in temperature to 180'C did redissolve sulfonate still precipitated at 40°C after the distilled waterflood.

The solubility of nonionic surfactants is not as sensitive to salt concentration as that of the anionic surfactants. On the other hand, the solubility of the alkylphenoxypolyethanols shows a marked sensitivity to temperatures. At very specific temperatures called the cloud points, the ethoxy groups in these compounds lose associated water and the solubility decreases abruptly to form precipitates. The cloud point is a function of the molecular weight of the surfactant, the electrolyte composition and the concentration of the surfactant. Cloud points as a function of concentration for Igepal CO-850 are shown in Table 2.

TABLE 2

SUMMARY OF PHYSICAL AND SORPTION PROPERTIES

FOR IGEPAL CO-850

Molecular Weight - 1,100 CMC = 100 w l / L

Cloud Points

cn trunOl/L) Cloud Point ("C)

73 366 640

>180 113 106

Sorption Properties

Temperature Keq A k l k2 AHo ("C) (dm'/pmol) (pmol/m2) (dm'/pmol.h) (hours-') (Id).

45 5.78~ 0.524 1.2 x 0.21 -40.2

70 2.09 x lo-' 0.705 1.5 x 0.72

95 7.34 x lo-' 0.831 2.5x10-' 3.41

154

isotherms were also measured E 28' I I I I I I I I I ' by the conventional static - - method at 25OC and 95OC. - 2 4 - - Dynamic and static adsorption 9 - - data were obtained for sodium o 20- -

NoCl = 0 2 Y

dodecylbenzene sulfonate x - (NaDDBS) and Igepal CO-850. $ 16: 0 -

EFFECT OF TEMPERATURE ON SURFACTANT ADSORPTION

If low concentration surfactants are to be used in combination with steamflooding or hot waterflooding in a reservoir. the effect of temperature on adsorption becomes a matter of considerable importance. could be combined with heat transport through the reservoir. The surfactant concentration shock could either lead or trail the temperature shock. will be presented later which shows that interfacial tensions are reduced at higher temperatures. If this is the case, one would prefer to have the surfactant front remain in the heated portion of the reservoir. In steamflooding, however, it is well-established that the steam overrides the oil. The water transporting the surfactant is likely to be moving primarily in a heated region immediately below the steam zone. In that case the surfactant will be moving in a hot portion of the reservoir under isothermal conditions. mechanism prevails in the reservoir, adsorption isotherms will be required for the prevailing temperature at which the surfactant is being transported. Consequently, we have made an initial effort to determine adsorption Isotherms as a function of temperature for an anionic and a nonionic surfactant.

Surfactant transport

Data

Whichever

An abundance of data exists in the literature for adsorption of various surfactants onto various substrates at room temperature. normally obtained by equilibrating the surfactant solutions with the solid surfaces. difficult problem.

These data were

Measuring adsorption isotherms at steam temperatures is a much more

Ziegler et al. obtained data using a dynamic, chromatographic transport procedure. ' packed in a core holder. The core was saturated with brine or distilled water and placed in an oven to maintain the temperature at the desired value. Surfactant solution was injected, starting at low concentrations. The pore volumes of solution required to move the surfactant through the core were measured. From chromatographic transport theory the quantity of surfactant adsorbed at this concentration could be calculated.

The porous medium was a disaggregated. fired Berea sandstone,

The surfactant concentration in the injected solution was increased stepwise and the volumes required to move each concentration step through the core was measured. the BET method. From these data the adsorption isotherm

The surface area of the sand had been measured by a variation of

As discussed earlier, the NaDDBS has a low solubility in 0.2 molar NaCl and also tended to precipitate at the higher temperatures when in contact with the Berea sandstone. Consequently, only adsorption isotherms obtained by the static method are reported for NaDDBS. These data are shown at 25OC and 9SoC for concentrations up to 70 pmols/L on Figure 5. The results show

155

that adsorption decreases with increasing temperature as one would expect. Data obtained in the absence ot salt show less temperature dependence. of the precipitation problem, no dynamic data are reported for NaDDRS. results o t desorption experimenLs are shown in Figure 4, but the slugs of surfactant being produced after reducing Lhe salt Concentration or after increasing the temperature had been explained earlier as being more the result of dissolving precipitated surlactant than desorption or adsorbed surfactant. The slug produced after increasing Llie temperature, however, may have resulted in part from decreased adsorption at elevated temperatures. consistent with the limited static data showing a decrease in adsorption with temperature.

Because 'Thc

This would be

The experiments with Igepal CO-850 were complicated by the cloud point,

Static results are given in Figure 6 . which is characteristic of this class of surfactants, and by the instability of this surfactant at high temperatures. Equilibration time for the (v 28 95OC curve was limited to E

three hours. Degradation NeCl : O O M was a serious problem if significantly longer times were used. The results show a slight temperature depend- i ence. Figure 7 is an example I! 16 - of results obtained by the dynamic method for Igepal CO-850. Surfactant was injected at an initial con-

and at two incremental concentration higher than the i~

initial. Consistent with a 2

pore volumes of injected surfactant required to pro-

' ' 1 1 1 1 1 1 1 1

-

LEGEND

+ 25% ; oa - centration of 67 pmols/L 2

-9- 95%

Langmuir-type isotherm, the O0 0 20 4 0 60 80 m 1 1 1 1 1 1 1 ~

SURFACTAM CONCENTRATION, M I 1 O6

Fig. 6 - Static adsorption isotherms for Igepal CO-830

duce the incremental step in concentration decreased with increasing concentration. Dynamic data were obtained at 45°C. 70°C and 95°C. Data were not obtained at higher temperatures because of the limit established by the cloud point's. Degradation of Igepal is not a problem in the dynamic procedure because the surfactant is at an elevated temperature only while moving < through the core. 0

The dynamic adsorption isotherms for Igepal are given qn Figure 8. concentrations adsorption decreases with temperature, but adsorption increases with temperature for concent.rations in excess of about 200 pmols/L. This effect is also associated

At low

I 1 I I I I I I I

0 0 0 0 0

LEGENO

-+- Co = 6?uM, v = 139 m/h - -c- CO = 331uM, v 1 137 m/h - : 597uM, v = 139 m/h

kl : I8 a LhMOLE- h

T = 9 5 % NaCI = O O M

PORE VOLUMES INJECTED

0 2

0 0 o 4 a 12 16 x ) 24 28 32

Fig. 7 - Breakthrough curves for Igepal CO-850

156

with the cloua point. As the ethoxide groups lose their associated water, the surfactant becomes less soluble and would be expected to separate out onto the solid phase more readily. Langmuir constants for Igcpal are given in Table 2.

The

The results of the dynamic method with Igepal indicate that the method is suitable for determining adsorption isotherms at elevated temperatures, but the surfactants, Igepal and NaDDBS, were not suitable for testing the procedure at temperatures in excess of 100°C because of solubility problems.

EFFECT OF TEMPERATURE ON INTERFACIAL TENSIONS

Few results have been reported giving interfacial tensions of.oil- surfactant solutions as functiohs of temperature. '*'*' These data are required for any process using surfactants in reservoirs but, particularly, for the high temperatures associated with steamflooding. We have used two methods for measuring interfacial tensions as functions of temperature

0 loo 300 500 SURFACTANT COWCLNTRMIOII, H I

Fig. 8- Dynamic adsorption isotherms for Igepal CO-850

and pressure. minimum interfacial tension that can be measured on the pendent drop equipment is about 0.1 mN/m and that is with low precision. gives data below 0.001 mN/m. equilibrium between the surfactant solution and the oil, the pendent drop procedure is also less suitable than the spinning drop. method a drop can be suspended at the most for one-half hour. hand, a drop can be maintained indefinitely in a spinning drop apparatus. Normally, equilibrium times for surfactant solutions and refined oils are small. The problem arises with caustic solutions and crude oils. indicated that equilibrium for these systems has not been established even in matter of days. method, we have obtained data by both procedures.

temperatures to 2OO0C and preseures to 30 drop equipment is such that it is a simple matter to construct an air bath around the capillary tubes which contain the spinning drop. operate at thermostat temperatures. sealing the capillary tubes at the above temperatures and pressures. can be easily drilled out of the tubes to permit using them again. Our equipment is easy and inexpensive to build, but it does not have the versatility of that developed at the Technical University of Clausthal. operates at higher pressures and temperatures and permits the exchange of fluids in the rotating capillary during the experiments.

An important factor in measuring interfacial tensions by either the pendent drop or the spinning drop method is the density difference between the water and the oil. This becomes particularly critical when measuring interfacial tensions at elevated temperatures.

These are the-pendent drop and the spinning drop methods. The

The spinning drop reportedly If time is an important factor in establishing

In the pendent drop On the other

Some reports have

Although the spinning drop would appear to be the preferred

We have modified the spinning drop equipment of Gash and Parrish for use at The design of the spinning

No bearings need to An epoxy was found that was effective in

The epoxy

Their apparatus

The density of water decreases more rapidly with

157

temperature than that for oil. Consequently, the density difference between water and oil can become quite small at higher temperatures. estimating these densities can have a significant effect on the calculated interfacial tensions. phase is a crude oil. become greater than that of the water. used under those circumstances. and can be generated easily for the surfactant and brine solutions. Densities for repined oils and pure hydrocarbons were determined using data from "Petroleum Refinery Engineering."' * To correct crude oil densities for temperature, the volume correction factors from ASTM D-206-36, Group 1, were used. Density data for water and three crude oils taken from El-Gassier et al. are shown in Figure 9.

A small error in

This problem becomes particularly acute when the oil For some crudes the density of the oil m y , in fact,

The spinning drop equipment cannot be Density data are readily available for water

Kepresentative data obtained by the spinning drop method are shown on Figure 10. ' TKS 10-80 in various concentrations of salt. The concentration of the TRS 10-80 was kept constant at 0.5 g/L. dependence on temperature up to 18OoC, but they are affected substantially by the salt concentration. The lowest interfacial tensions were observed at salt concentrations of 5.0 g/L. The lower curves on this figure are duplicate runs and show reasonable agreement. representative crude oil also showed little effect of temperature.

Interfacial tensions were measured between mineral oil No. 9 and

The interfacial tensions shared little

Interfacial tensions for TRS 10-80 against a

10 0

5.0 fo-doa $4 vs'. w&u in^

NQ9

-X- API CWOE 6rP,4PIFRUqE , , , , ' ' 0.7

10 50 loo I50 x)o 250

TEMPERATURE, "c

Fig. 9-Effect o f temperature on density of water and crude o i l s

z ID r/L MOCI

*Lo1) fi WaCl

0 3 o m s o l 2 o ~ m o ~ TEMPERATURE, 'Ic

Fig. 10- Effect of salt concentration and temperature on interfacial tension of 0.5 g/L TRS 10-80 versus mineral oil No. 9

The interfacial tension between the nonionic surfactant, Igepal DM-730 and a 15.9OAF'I California crude oil showed a marked minimum when plotted versus temperature as shown on Figure 11." similar data were obtained with the surfactant in presence of salt. facial tension minima for the nonionics coincided with the cloud point for the particular surfactant concentration. in the surfactant solubility, it is not surprising that the interfacial tension

No salt was present in this example but The inter-

Since the cloud point indicates a decrease

158

decreases at tliis temperature. 'L'lie 100.0 decrease in transparency 0 1 Llie aqiieous phase at the cloud point was 500 a limiting factor in measuring interfacial tensions of nonionics as a I'unction 0 1 temperature by either tlic spinning drop or the pendent drop met hod.

A more detailed study of the efrects of surfactant concentration, E salt concentration and temperature on > 1.0 interfacial tension against a crude E oil was made with the pendent drop b equipment. Although this equtpment is not capable OP measuring the ultra low tensions it can show, at least qualitatively, the trend of the effect of these variables. Representative data 0.0 are shown on Figure 12. The surfactant in this case was TRS 10-80 and the oil was CaliPornia Wheeler.Ridge crude with an API gravity of 15.9".

results are interesting in that they

0.2

The temperature was 177OC. ?'he 10 50 100 I50 200 TEMPERATURE, OC

indicate an optimum surfactant and salt concentration at 177°C to obtain a minimum interfacial tension. Similar minima were observed for lower temperatures but the minlmum interfacial tension increased with decreasing temperature. At 93°C the

INTERFACIAL TENSION CONTOURS I77.C

Y

0.5

v = 0.005 nN/m 0 c,

0.02 1 1 I 1 1 1 1 0. I 0.5 ID 20 30

NoCl CONCENTRATION (WT %)

Fig. 11- Effect of surfactant concent rat ion and temperature on interfacial tension between IHS 10-80 and criltle otl. NaCl = 0.0 g/L

minimum intertacial tension was 0.1 mN/m as compared t o 0.005 mN/m at 177OC.

Additional data have been obtained using a mixture of surfactants against yure hydrocarbons and mineral oils. The equivalent alkane carbon number, FACN, for the surfactant mixtures was calculated as recommended by Jacobson et a1.I5 As shown in Vigure 13, these mixtures stiow an abrupt decrease in interfacial tension at temperatures in excess of 120°C. The experiments are being extended to obtain data for several hydrocarbons and, thereby, evaluate the relation between the change in interfacial tensions with temperature and the FACN concept .

CONCLUSIONS

Fig. 12 - Interfacial tensions as The results of our experi- functions of NaCl and TKS 10-80 mental work and data reported by concentrations at 177OC others suggests conclusions about

159

the behavior or surfacLants a t I .o elevated temperature. Some ol these conclusions are quite as specific and dependable for the systems to which they apply. Many

a2 are tentative. Certainly more 4 work is required to extend the nuinber of sureactants wtiicla liavc been evaluated at high tempcra- tures.

5 a 05

Ei

Y E

1. The surfactants investigated 1 02 were observed to decompose by first order kinetics. Therefore, & I)I

stability of a surfactant at a f oo( given temperature is its Iialf- life. Activation energies were determined for several surfactants. Stabilities can be esti-

higher or lower temperatures than those used in the experiments.

a quantitative measure of the

rn

mated from these energies at 00;

1 I 1 1 1 I MIXTURE OF ANIONIC SURFACTANT VS

N-OOD€W

SURFACTANT

PETROSTEP 465 . PETROSTEP 450 . NeCI CONC g/L

0 2 0

- TRS 10-80

FIR. 13- Interfacial tensions as Ciinc- tions o f temperature and salt concentration for lsurfactant mixtures against n- dodcca nc

2 . The anionic petroleum sulfonates were observed to be more stable than the nonionics. The stabilitv of the best sulfonate would be only marginally acceptable at temperatures to 180°C but other surfactants need,to be evaluated. of the surfactants tested would be adequately stable at normal reservoir temperatures .

All

3. tures as a result of an interaction with solubilized rock minerals which show limited solubility at elevated temperatures. The solubility of the nonionics decreases abruptly at the characteristic cloud point. tration at which these surfactants can hr uscad at higher temperatures.

Evidence suggests that the sulfonates may be precipitated at steam tempera-

This limits the concen-

4. on adsorption. dodecylbenzene sulfonate and for Igepal CO-850, but the effect is not as substantial as one might have expected. Additional data are required with other surfactants in consolidated sandstones.

Dynamic and static methods were used for evaluating the temperature effect The data suggest that adsorption decreases for both sodium

5. A substantial amount of data is being accumulated relating interfacial tension and temperature. For specific types of petroleum sulfonates some data indicate little effect of temperature on interfacial tensions. On the other hand, pendent drop data do suggest a significant decrease in interfacial tension with temperature for optimum salt and surfactant concentrations. Other results show a decrease in interfacial tension with temperature for mixtures of sulfonates against pure hydrocarbon or mineral oil. The nonionic, Igepal DM-730, showed a sharp minimum in the int'erfacial tension at a specific temperature. That temperature appears to be related to the cloud point.

160

REFEKENCES

HANDY, L. L., AMAEFULE, J. O., ZIECLER, V. M., and ERSHAGHI, I.; "Thermal Stability of Surfactants for Reservoir Application", paper SPE 7867 presented at SPE Fourth Intl. Symposium on Oilfield and Geothermal Chemistry, Houston, Jan. 22-24, 1979.

ISAACS, E. E., PROWSE. D. R., and RANKINE, J. P.; "The Role of Surfactant Additives in the In Situ Recovery of Bitumen from Oil Sands", Paper No. 81-32-13, presented at the 32nd Annual Technical Meeting of the Petroleum Society of ClM, Calgary, May 3-6, 1981.

MUKERJEE, P.; "Use of Ionic Dyes for the Analysis of Ionic Surfactants and Other Ionic Organic Compounds", Analytical Chemistry (May 1956) 2 (5) 870.

ZIECLER, V. M. and HANDY, L. L.; "Effect of Temperature on Surfactant Adsorption In Porous Media", SOC. Pet. Engr. Jour. (April 1981) 21 (2) 218-226.

CELIK, M., GOYAL, A., MANEV, E., and SOMASUNDARAN, P.; "The Role of Surfactant Precipitation and Redissolution in the Adsorption of Sulfonate on Minerals", paper SPE 8263 presented at the SPE 54th Annual Technical Conference and Exhibition, Las Vegas, Sept. 23-26, 1979.

REED, M. G . ; Injection," J. Pet. Tech. (June 1980) 941-949.

GOPALAKRISHNAN, P., BOREIS, S. A., and CAMBARNOUS, M.; "An Enhanced Oil Recovery Method -- Injection of Steam with Surfactant Solutions", Report of Group d'Etude IFP-IMF Sur lee Milieux Poreux Toulouse (1977).

SANDVIK. E. I., GALE, W. W.. and DENEKAS, M. 0 . ; "Characterization of Petroleum Sulfonates", SOC. Pet. Engr. Jour. (June 1977) 184-192.

McCAFFERY, F. G.; "Measurement of Interfacial Tensions and Contact Angles at High Temperature and Pressure", J. of Canadian Petroleum Technology (July 1972).

GASH, B., and PARRISH, D. R.; "A Simple Spinning-Drop Interfacial Tensiometer", J. Pet. Technology (January 1977) 30-31.

BURKOUSKY, M. and MAX. C.; "Applications for the Spinning Drop Technique for Determining Low Interfacial Tension", Tenside Detergents (1978) 15 (5)

"Gravel Pack and Formation Sandstone Dissolution During Steam

247-251.

1.

2.

3.

4.

5.

6.

7.

8.

9.

10.

11.

12. NELSON, W. L. ; "Petroleum Refinery Engineering", (1958) 157-161.

13. HANDY, L. L., EL-GASSIER, M. and ERSHAGHI, I.; "Interfacial Tension Properties of Surfactant-Oil Systems Measured by a Modified Spinning Drop Method at High Temperatures", paper SPE 9003 presented SPE Fifth Intl. SvaDosium on Oilfield and Geothermal Chemistry, Stanford University, May 28-30, 1980.

14. ZEKRI, A.; Personal Communication.

15. JACOBSON, J. K., MORGEN, J. C., SCHECHTEX, R. S., and WADE, W. H.; "Low Interfacial Tensions Involving Mixtures of Surfactants", SOC. Pet. Engr. Jour. (1976) 122-128.


SURFACTANT SLUG DISPLACEMENT EFFICIENCY IN RESERVOIRS; TRACER STUDIES IN 2-D LAYERED MODELS

ROBERT J. WRIGHT, RICHARD A. DAWE and COLIN G. WALL

Petroleum Engineering Section, Imperial College, London SW7 2AZ

ABSTRACT

The ef fec ts of layering within porous material with regard t o basic flow

mechanisms and chemical dispersion have been investigated. Experiments

have been performed within unconsolidated glass bead packs.

variables controlled were layer permeability and dimensions, f lu id

viscosity and flow rate; gravity and capillary pressure influences were

eliminated by using model f lu ids of matched density and complete misc-

i b i l i t y . The importance of channeling and crossflow ef fec ts a re emph-

asized by the resu l t s , and the behaviour of non-unit mobility r a t io

displacements i s predictable using re la t ive ly simple conceptual/mathem-

a t i c a l models. The dispersion of chemical tracers between layers has

a l so been modelled mathematically and the r e s u l t s have been applied t o

laboratory t e s t s on heterogeneous cores.

The

162

INTRODUCTION

I t is well known that the natural heterogeneity of petroleum reservoir material is one of the major problems i n chemical E.O.R. processes. Of particular consequence are the non-random variations i n permeability to be found within porous rocks. Layering structures are a common feature of sandstones and their e f f ec t s have been reviewed i n recent l i t e r a tu re w i t h reference to f lu id flow (1) and dispersion mechanism ( 2 ) . The efficiency of surfactant slugs is probably the most l ike ly application of these considerations; however the fundamental problems are ocnmnon to a l l E.O.R. processes. We have investigated layered models, both conceptual/ mathematical and physical (v isua l ) . Experimentally, flow mechanisms and dispersion e f fec ts have been monitored using dye tracers. Displace- ments have been of an ideal miscible type and therefore represent perfect microscopic displacement efficiency. The properties peculiar t o surfact-

, ants such as adsorption, phase equilibrium and emulsification charact- e r i s t i c s have been excluded i n the present work. We are taking the approach tha t the gross f lu id flow and dispersion e f fec ts w i t h i n heterogeneous media shoald be be t te r understood before laboratory core-flood resu l t s and data from linear homogeneous packs can be applied t o the reservoir system. W e have attempted t o view miscible and immiscible displacement mechanisms on a common basis s i n c e the two concepts merge i n ultra-low-tension systems.

The experimental work discussed here involved idealized layered models of packed Ballotini. The flow mechanics of displacements a t various (favourable and unfavourable) mobility r a t io s were recorded by photo- graphing dye tracer boundaries under conditions of flow ra t e fo r which diffusion/dispersion e f fec ts were small. To quantify dispersion phenomena we have considered equiviscous miscible displacements, and we describe here numerical predictions w i t h one example application. Conceptual models were developed, based on simple two layer-channel interactions. This approach follows contributions within the l i t e r a tu re on dispersion (2 ) & (3) and crossflow (4 ) & ( 5 ) i n such model systems.

FLOW PATTERNS I N LAYERED MEDIA

I t has been found useful t o consider simple two-channel conceptual m o d e l s i n order t o account for crossflow behauiour i n multilayered and s t r i a t ed media. CrosSflow directions and approximate magnitudes can be demon- s t ra ted mathematically by considering the variation of flow p o t e n t i a l along the axes of the channels. Figure l(i) i l l u s t r a t e s two para l l e l channels composed of homogeneous and continuous porous media; a high permeability channel (a) and a less permeable channel (b). The displacement of f l u id (1) by f lu id ( 2 ) within this model ( in the x direction) has resulted i n two displacement boundaries ( a t Xa and q). The instantaneous pressure prof i les a re plotted fo r two d i f fe ren t viscosity ra t ios ; displacing f lu id the more viscous i n F ig . l ( i i ) and the less viscous i n F i g . l ( i i i ) .

163

Fig.

1 (ii)

l(iii)

t Y

Fluids Prom I n t o - p 2 Location. Crossflowing Channel:- Channe 1 : - P 1

>1 (2) a b

X (1) b a

(1) E (2 ) b a

X (1) E (2) a b

"b

"b <1

1

P ii

0 1

P R -

0 X + x 4 L

Figure 1.

(i) Displacement i n dual channel m o d e l

(ii) Pressure P r o f i l e s f o r

!J2 > p1

(iii) Pressure P r o f i l e s f o r

p2 < p1

This assumes no c a p i l l a r y pressure, dispers ion, g r a v i t y or ccmpressibi l i ty e f f e c t s ; also f o r t h e moment, no crossflow between t h e channels (as i f separated by an i m p e r m e a b l e b a r r i e r ) . It is, however, a usefu l method for represent ing local croltsflow tendencies as ind ica ted by pressure drops (at f ixed x) between the channel axes. C r o s s f l o w would therefore be s t r o n g e s t around the displacement f r o n t s andoccurs i n t h e d i rec t ions ind ica ted i n Table 1.

Table 1.

164

Experimental.

Displacements w e r e performed i n a v i sua l model composed of g lass beads packed t o form a cent ra l (high permeability) layer surrounded by l e s s permeable packing. width of 10 cm., the length of the flow model was 20 an, the permeability r a t io s between layers was 2.8, and porosity was approximately 38%. Constant flow ra t e s were used and matched density aqueous solutions were employed. Glycerol/water mixtures and sod im chloride o r sodium sulphate solutions were used. The photographs (Plates 1 - 3 ) i l l u s t r a t e displacement pa t te rns with fluorescent t racers under three d i s t i n c t conditions of viscosity r a t io ; p2/p1 = 0.22 (Plate 1 1 , 1.0 (Plate 21, and 3 . O (Plate 3) . Roughly 0 . 2 pare volumes of displacing f lu id has been in j - ected, and flow is i n a l l cases from l e f t t o r igh t .

Channel widths were around 1 cm within a t o t a l model

P la te 1: unfavourable mobili t ies

P la te 2: equal mobili t ies

P la te 3: favourable mobilities

The d i f fe ren t displacement boundary pa t te rns and the consequent differences i n displacement efficiency can be explained to sane extent by the ax ia l pressure gradients of Figs. l(ii) and ( i i i ) , b u t the dominant influence is crossflow as de ta i led i n Table 1. Hence, when displacing f lu id is less viscous (more mobile) the leading "finger" within the high permeability channel advances rapidly due to crossflow i n t o the finger a t its base and out 06 the channel around i ts leading t i p . the shape of the finger by swelling i ts f ron t and squeezing i ts base. For "favourable" viscosity r a t i o s these conditions a re reversed; penetration in to the high permeability channel is retarded, the advancing Cusp being squeezed i n a t the f ron t (with some t r ace r dispersed ahead as a th in plume) and widened a t i ts base where it joins the main displacement front. boundary; loca l f ingering i n the forme<>case and a sharp s tab i l ized boundary i n the latter favourable mobil+&y case.

Crossflow is seen t o a l t e r

Smaller scale differences a r e apparent around the main displacement

165

Quantitative Results: Unfavourable Mobility Ratio Continuous Displacement

Crossflow can be quantified i n the two channel conceptual model described above by means of a numerical crossflow index:-

kt (Ax)2 = A . - ka

. - d '

where A is the crossflow boundary surface area per u n i t volume of channel ( a ) , kt is the effective cross permeability between the channel axes, ka Is the permeability of channel (a ) , fractional distance and d is the separation of the channel axes.

For equal width straight layers of isotropic media,d is equal to the layer width and

Ax is the numerical inter-node

2 A = - kt - -

d * ka 1 + ka/kb

Fig. 2 i l lust ra tes calculated instdtaneous channel (a) pressure profiles for xa = 0.5, xb layer aspect ratios given below:-

0 when p2/ pl = 0.1, for the mossflow indexes and

d & Curve a (Ax = 0 . 0 2 ) layer z (kb 4, -

1 o.Ooo1 2 . 0

2 0.01 0.2

3 0.1 0.06

4 1.0 0.02

These span the extremes of practically no crossfhw (curve 1) t o near m a x i m u m crossflow (almost zero resistance to flaw between channel centres, curve 4 ) .

Figure 2.

Possible pressure distributions along channel (a ) .

0 1

Numerical cdkculations of distance/time tracks have been performed based on incremental advances of a displacement front (Ax = 0.02) and estimation of pressure gradients, hence displacement velocities (as a function Of frontal position). For various values of "a" displacemant tracks were calculated for viscosity ratios of 0 . 5 (Fig.3),0.1 (Fig. 4) and 0.01 (Fig.5).

166

I L

02 '

0.1 *

E l I

Figure 3.

lJ2/Pl = 0.5

Figure 4.

P 2 h 1 = 0.1

Figure 5.

lJ2/lJ1 = 0.01

Figs. 3 - 5 : Time/Distance tracks fo r displacement f ron t within high permeability ChdMel; numerical calculations.

Clearly, fo r mobility natios near unity crossflow is unimportant and displacement ve loc i t ies a re constant with t i m e . The l imiting l i nea r tracks f o r high a are approached qu i t e closely fo r moderate values of viscosity ratios and layer aspect-ratio. to crossflow index when d/L > 0.1 and p2/p1 < 0.1, a s a general guide.

The behaviour is only sens i t ive

167

Experiment kakD d/L

0 1

* 2 1 2 . 8 1.::: * 3

0 4

Experimental Results.

Flow v i s u a l i z a t i o n experiments were conducted with matched dens i ty f l u i d p a i r s having " adverse" v i s c o s i t y ratios. The packed bead models were as described above. Experiments were dis t inguished by t h e parameters given

'2/'1

} 0.33

0 . 2 2

below:-

Figure 6.

Relat ive Front Posi t ions.

.IS

xb - L

.I

45

a a

"Mean f ront" pos i t ions were est imated from colour photcgraphs taking i n t o account dispers ion and local f ingering. When p l o t t e d versus time,approximately s t r a i g h t l i n e t racks were obtained; data scatter being not too serious. The r e s u l t s i n terms of t h e leading f r o n t displacement (xa) and t h e main f r o n t (a) are p l o t t e d on Fig. 6, along with the numerically pred ic ted curves using t h e parameters given i n Table 2. of experiment and cd lcu la t ions is encouraging. However, these predict ions are based on equating xb/L to t h e dimensionldss t i m e (of Figs.3 - 5) which is not expected to be a good approximation i n a l l cases. I t is noticeable that t h e r e is a s i g n i f i c a n t dependence on v i s c o s i t y ratio: i n t e r e s t i n g f e a t u r e of m o s t experiments is the r e l a t i v e l y f a s t i n i t i a l pene t ra t ion i n t o t h e high permeabi l i ty layer , a d e t a i l contradicted by the n m e r i c a l r e s u l t s . (6) f o r vtscous f inger ing i n randomly var iab le porous media.

The cor re la t ion

An

Simi lar f indings are descr ibed by Peaceman and Rachford

168

Discussion of Analytical Methods.

I t is useful t o consider a t t h i s point the effectiveness of an analytical solution method based on 1-dimensional flow theory and "pseudo" re la t ive permeability functions ( 7 ) . These are be t te r described as synthetic functions since they a re derived by adding together the e f fec ts of the individual layer properties. The re la t ive permeabiliw t o displacing (2) and displaced (1) phases a re plotted versus saturation of phase ( 2 ) on Fig. 7 for the model parameters of experiments 3 and 4. Use of these functions is ideally res t r ic ted to immiscible (no diffusion) processes; however they can be applied to miscible processes when the ef fec t of dispersion is negligible. A useful feature of the present displacements is tha t they should give resu l t s which are similar t o perfect ultra-low- tension displacements (having negligible capillary pressures and 100% microscopic displacement efficiency).

Predicted saturation/distance prof i les based on the above functions using the viscosity r a t io s of i n t e re s t a re given on Fig. 8 . distributions a re not found i n practice even when local fingering is taken in to account: however it is only the averaged displacements w i t h i n the f a s t (S2 = 0 - 0.14) and s l o w (S2 = 0.14 - 1.0) flowing regimes which w i l l be considered (dotted l i n e s ) . The r a t i o of displacement ra tes

These extended

1.0

0.5

t 5,

0 0 s, 1

- 0 X / L - 0.5 1.0

Fig. 7. Relative permeabilities. Fig. 8 . Theoretical saturation distributions.

are predicted t o be 8.5 for a viscosity r a t i o of 0.33 and 12.9 for a viscosity r a t io of 0.22. greater than those indicated i n Fig. 6 . It is thought therefore tha t 1- dimensional flow theory exaggerates the e f f ec t of mobility r a t i o for reasons concerning crossflow mechanism. I t may therefore be possible, using low tension displacements w i t h i n layered media which a re significantly be t te r than those provided by analytical 1-dimensional methods.

These re la t ive ra tes a re about a factor of two

convenient approrimations,to obtain predictions fo r miscible and

m t i u t i v e &sui t s : Favourable Mobility Ratio Continuous Displacement.

Crossflow is the principle mechanism by which a displacement f ront may be s tab i l ized against the influence of local permeability variations. The dual-channel pressure prof i les discussed above can be used to explain t h i s flow mechanism and the "shock front" concept of 1-dimensional displacement theory ( 5 ) .

169

In sane preliminary work we used a packed bead model containing four f a s t flow channels (permeability r a t i o 13:l) of d i f fe ren t width. The r e su l t s r e f l e c t a considerable influence of gravity since the displacing f lu id was more dense and was flowed ve r t i ca l ly upward. traced displacement fronts ( f u l l l ines) i n re la t ion to the layer bound- a r i e s (dashed) for three stages ( f rac t iona l pore volrrmes injected indicated). Here l.12/l.11 = 5, Ap = 0.113 g/cm3; while on Fig. 10 are the observations fo r p2/p1 = 10,Ap = 0.149 9/cm3. Predictions based on synthetic r e l a t ive permeabilities fo r t h i s model lead t o the single shock fronts shown (dotted). l a t t e r case (1.8 x 10-3cm/sec, a s compared with 0.91 xlO-’an/sec) and the e f f e c t of t h i s is t o compensate t o some extent for the e f fec t of a higher viscosity r a t io .

Pig. 9 i l l u s t r a t e s

The super f ic ia l flow ra t e was greater i n the

Fig. 9. Fig. 10

Shock f ront formation is c lear ly not observed. boundary appear t o increase i n amplitude with increase i n channel diameter (the f a r r i gh t channel is r ea l ly a half-channel since there is a no-flow boundary a t its s ide ) . ment there is l i t t l e change i n the f ronta l shape with t ime.

I t has been found t h a t the basic charac te r i s t ics of such s tab i l ized displacement patterns can be approximated by considering dual-channel pressure prof i les . viscous crossflow (but not gravity) is allowed for. The Stabil ization

The osc i l la t ions of f ronta l

In the case of the higher viscosity r a t i o displace-

Figure 11 i l l u s t r a t e s the form of such prof i les when

Figure 11.

Pressure p ro f i l e s for favourable mobili t ies with crossflow.

Phenanenon, which tends t o discourage channeling i n t o the high permeability zone) depends upon the crossflow which i t s e l f is governed by the region between the two prof i les . by a t r iangle enabling an expression t o be derived fo r a s tab i l ized separation “6”( =xa - q), assuming the velokities of the two f m n t e are

The geometry of t h i s region can be approximated

170 IT. E. DANFORTM

I’aye (1). Three “Stateu of Activation”. . . . . . . . . . . . . . . . . . . . . . . . . . 193 (2). Thermal Activation.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 193 (3). Decay of Enhanced Emission.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 196 (4). Activation by Reverse Current.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 197 (5). Effects of Products from Nearby Cathodes.. . . . . . . . . . . . . . . . . . . 198

3. Mechanisms of Disappearance. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 199 a. General . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 199 b. Electrolysis. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 199 c. S p u t t e r i n g , . , . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 200 d. vapora at ion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 201

4. Optical Phenomena in Crystalline Thorium Oxide., . . . . . . . . . . . . . . . . . . 5. Electrical Conductivity of Thorium Oxide.. . . . . . . . . . . . . . . . . . . . . . . . .

b. Crystalline Specimens. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 206 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 210

202 204

a. Powdered or Sintered Specimens.. . . . . . . . . . . . . . . . . .

I. INTRODUCTION

The appearance of thorium oxide on the scene of high-powered tube engineering has been gradual over the past three decades, and was naturally accelerated by World War 11. In general, it may be said to be used in applications where barium-strontium oxide falls short in some aspect of ruggedness and where the extra heating power required by the thoria cathode is not impracticable. The present paper describes certain practical applications of thorium oxide emitters, outlines the outstanding problems and the types of research and development which are under way, and presents those rather fragmentary theoretical developments which research workers have succeeded in achieving a t the present writing. Even more than with barium oxide, the theory is still only semiquantitative, and decisive experiments are lacking.

Comparing the thorium oxide situation with that of barium oxide one finds that less work with theoretical intent has been done in the former case. This is due to the fact that the latter has occupied a far more important commercial position for over a quarter of a century. Actually it may appear that, as a subject of research in semiconductor thermionics, the thorium oxide system is more amenable to quantitative understanding than is the barium oxide emitter.

11. THORIUM OXIDE AND PRACTICAL ELECTRONICS 1. Preliminary

The introduction of thorium oxide into the field of practical electronics came about because of its metallurgical as well as its thermionic properties.’ As a refractory material, insoluble in tungsten, quantities of the order of one percent are added to tungsten to control recrystallization

171

maxima covering the scatter of d a t a are p l o t t e d on Figure 13,along with crosses indica t ing t h e separat ions based on t h e p o s i t i o n a t which the channel is completely occupied by displacing f l u i d . Theoret ical curves applying to our model, and o ther permeabi l i ty ratios ( indicated on t h e curves) are included. These g ive t h e equi l ibr ium s t a b i l i z e d f r o n t a l separat ions pred ic ted using t h e above equations. Assuming t h e b a r s t o be acceptable a s an experimental estimate of t h i s parameter (remembering t h a t no p is ton- l ike f r o n t is observed i n t h e high permeabi l i ty channel) then the usefulness of t h e mathematical approximation is supported. should be viewed i n r e l a t i o n to the predic t ions of 1-dimensional flow theory based on t h e synthe t ic r e l a t i v e permeability funct ions f o r these models, Fig. 7 shows these f o r experiments 7 and 8 . The a n a l y t i c a l so lu t ion i n d i c a t e s a s i n g l e shock f r o n t through the whole system f o r v i s c o s i t y ratios g r e a t e r than 2.82, i.e. 6 = 0. Our experimental r e s u l t s c l e a r l y demonstrate t h a t t h i s is not t h e case and w i l l be of more serious consequence to displacement e f f i c i e n c y as Layer (or other channel) diameters increase.

This

5

b

3 +

I .b

b b

b m 8

b. . b

. .

Figure 12. Frontal Separat ions, Experiment NOS. 0 5 , 0 6 , + 7, 0 8 .

Figure 13. Viscosi ty R a t i o Ef fec t , experimental (bars) and theoretical ( l i n e s ) .

172

SLUG DISPLACEMENTS

I t has been found t h a t continuous in jec t ion t e s t s model well the development of displacement boundaries a t f ron t and rear of a "slug" up t o the time when overtaking occurs. and channelling ahead i n a similar way t o the displacements discussed abbve involving continuous injection. rmbili ty r a t i o displacement of typical pattern. of Plate 5 shows a s t ab i l i zed form a t i ts front. similar liquid,without dye,exhibiting a typical equiviscous displacement.

P la te 4 shows a low v iscos i ty slug fingering

Behind the slug we have a favourable The high viscosity slug It is pushed by a

P la te 4 P la te 5

The permeability r a t i o was a s before (2.8) and the viscosity r a t io s involved i n the displacement of f l u i d (1) by f l u i d ( 2 ) by f l u i d (3) were for Plate 4, p3:p2:p1 = 3:1:3, and fo r P la te 5 , 4.6:4.6:1.

Although the volumes of these slugs a re about 20% of the pore volume, loss of slug in t eg r i ty occurs. The low viscosity slug (Plate 6) is continuing to be squeezed from the low permeability medium i n t o the f a s t flow channel; however the slug is 'near being divided i n t o three portions. viscosity slug (Plate 7) has been s p l i t by the chase f l u i d which has channelled through and is crossflowing out of the high permeability layer, par t icu lar ly near the f ront o f the slug.

The high

Pla te 6. Plate 7.

The breakdown of slug in t eg r i ty could possibly be res i s ted by chemicals, added t o the chase fluid.designed spec i f ica l ly to r e s i s t cer ta in crossflow processes and the mixing of out-of-sequence f lu ids . could be the in-situ ge l l ing polymers which a re sens i t ive to s a l i n i t y environment ( 8 ) . This is a poss ib i l i t y which w i l l be investigated i n future modelling work.

For surfactaht slugs the f l u i a red is t r ibu t ions discussed above w i l l be combined oith considerable adsorption, dispersion, mass-transfer and gravity e f fec ts . Capillary pressure e f f ec t s could a l so be important even though in t e r f ac i a l tensions may be low, since mobilized o i l banks w i l l be pa r t ly o r wholly composed of discontinuous o i l whose flow w i l l be highly non-Newtonian. ( 9 ) .

An example

17 3

DISPERSION I N LAYERED MEDIA

The s tabi l i ty of chemical slugs w i t h i n channelled porous media can be strongly affected by diffusion/dispersion processes. a two-layer mode1,following the approach of Lake and IiraSaki ( 2 ) and Koonce and Blackwell ( 3 ) for chemical dispersion and Satman and Zolotukhin (10) for the analogous problem i n heat transfer.

To scale these effects it is useful to define a transverse dispersion number ( 2 ) :

Eere we consider

1 4 G . 3 , d2 V

N~~ =

where L and d are the length and width of the system, Kt is the Mansverse dispersion doefficient, V is the superficial flow rate permeability layer.

Lateral dispersion is insignificant when N T D < 0 . 2 , while when N T D > ~ composition is practically constant over any cross-section through the system and the behaviour can be represented by a single effective longitudinal dispersion coefficient ( 2 ) . We examine here the intermediate range of NTD, between 0 . 2 and 5 , which could apply to comon field conditions i f d is of the order of lm and to laboratory core tests i f layers of a few mrn width are present within the porous m e d i u m .

We consider flow parallel to the layers and tracer dispersion normal to this direction (longitudinal dispersion coefficient is zero). The lateral dispersion coefficient has been taken to be constant,independent of concentration, position and flow rate. For reservoir r a t e s , i t is generally found to be of the order of the molecular diffusion coefficient (11).

i n the high

Figure 14 shows computed isoconcentration contours .(at 0..1 intervals) within a two layer system, the upper one (between Y values 0.5 and 1.0) flowing from l e f t t o right, the lower tracer by lateral dispersion from the a t u n i t concentration is dispersed as dimensionless t i m e : -

T K t = t - - d2

where T is the absolute time from the

is stagnant but receives injected permeable layer. Tracer injected shown a t three values of the

NTD _.

14

s t a r t of the displacement.

It is of interest to obtain convenient analytical approximations to the mean tracer concentration within a given cross-section of the flow channel (and of the non-flowing matrix). Figure 15 shows numerical points and analytical curves representing the distribution of average concentration w i t h distance i n the flow direction (normalized for t = 0 . 2 ) The analytical approximations were derived wing solutions to the zero- concentration-boundary-condition case ( 1 2 ) , evaluated for short dimensionless times. Expressions of s i d l a r form are applicable to other channel geanetries (e.g. cylindrical) provided times are short. The approximations derived for the heat transfer problem (10) involve also a square root of time dependence; however these integral solutions are very complex because they are intended to cope w i t h a large time range. Our approximation is:-

T I t l E = O -05

S

I I?

I- .-,

? -

I I I I 1

-m 0-1 1.2 0.9 0.4 0.5 0.8 0.7 0-1 0.) I FRRCTIONAL OISTRNCE IN FLOY OlRECTlON

T I t l E = O - 10 I

I

S I?

> I 3 ‘ Z

O Z 25

I 5 0.1 0.2 0.9 0.4 0.s 0.a 0.1 0.m 0.) I

* m

a t

N

FRRCTIONAL OISTRNCE IN FLOY OlRECTlON

Figure 14. Isoconcentration contours i n two layer system.

175

COnPUlEO 0 T=O.OS

.? A 1.0.10 + 1=0.15 0

f 0

lu . 0

FITTED c; 1 -2l'"I 1-1 I - x 11-3 _ I -

I I I 1 I I I I I -1 a.1 O.? 0 . 3 0.1 0 4 0.6 0.1 0.a 0-S I

FRRCTIONRL OISTRNCL

Figure 15. Cross-sectional averaged concentrations i n flow channel.

E = 1 - 2 . 0 t+ (1 - (1 - XI+) where is the average i n j e c t e d tracer concentration within the cross sec t ion (a t X) of the flowing channel; X is t h e f r a c t i o n a l d i s tance equal to x/V.i . A similar method can be used t o approximate t h e averaged Concentrations within t h e non-flowing matrix (Em) f o r the t w o equal-capacity layers here considered:-

Em = 2 . 0 t+ (1 - x% .

Applications to a Multichannel Problem.

One approach t o a multichannel problem is to consider each individual channel as i n t e r a c t i n g with a surrounding matrix which possesses the s u i t a b l y averaged p r o p e r t i e s of t h e rest of the porous body. Generally a non-zero flow rate w i l l apply to t h e ex terna l matrix i n c o n t r a s t t o t h e s tagnant case as above. This n e c e s s i t a t e s considerat ion of the problem as one of r e l a t i v e flow rates using moving co-ordinate methods.

Tracer e f f l u e n t p r o f i l e s have been analysed i n terms of var ious models intended t o account f o r heterogeneity (13) , (141, (15). Laboratory tracer tests on layered reservoi r materials are of i n t e r e s t f o r t w o reasons; f i r s t , conventional methods f o r character iz ing dispers ion co- e f f i c i e n t s f o r miscible displacement and r e l a t i v e permeabi l i ty funct ions for l o w tension immiscible d i s p l a c e m n t may be unre l iab le ; second, such laboratory Systems can model similar problems on t h e reservoir scale.

To estimate mass t r a n s f e r rates f o r t h e channels (e.g. l ayers ) within a heterogeneous core sample displacement flow tests of d i f f e r e n t rates have to be compared. Unfortunately, very l i t t l e r a w d a t a of this kind is to be found within t h e petroleum l i t e r a t u r e . Our main source is t h e high q u a l i t y recent work of Spence and WatJcins (16). Handy (17) has used dual tracers to evaluate d i f fus ion e f f e c t s and w e have begun tests on layered sand- s tones using u l t r a - v i o l e t absorpt ion monitoring techniques.

176

Using the above approximations, and the assumption that flow within the matrix surrounding any given channel-"i" is approximated by the mean velocity oif the whole displacement (v), a method of effluent curve anal- y s i s has been derived (18). a t its moment of breakthrough a t the effluent end of the single channel

:t difgerent rates, we can estimate the fractional cross section of the channel (6jS) and i ts effective mass transfer coefficient (M ) thus:-

Thus i f the fractions of displacing fluid

j", (f (1) and f j (2)) ,are known from two experiments (1 and 2) performed

j

V j = L/T,, L being the length of the test core.

j ( 2 P j (2) = v

W T j (1)

M t = 4Kt/d2 for a layer.

These expressions can be applied to effluent eanposition values measured shortly after the f i r s t detected breakthrough of displacing phase from the multichannel system. This characterizes the fastest flow channel(s) of the sample. allow for the ( t i m e dependent) contitbutions from a l l the faster-flowing channels. of'.-) and the individual ("breakthrough") channel "j" contribution can be obtained using the following h1gorithm:-

Subsequent tracer measurenmnts have t o be processed to

The gross composktion measured i n one experiment is F(a functibn

The effluent profile is analyzed forward i n time as presented above for T C Lfi ; while for T > L f i s u p s are taken backward I n time redbfining F as the concentration of displaced fluid. Asatisfactory analysis can be performed with a proQramable calculator (a program suitable for an "BP 41C" Is available from the authors). Small t i m e steps should be avoided since errors due mainly to intralayer longitudinal dispersion, ignored i n the present analybls w i l l become impartant; ten t o twenty steps for each effluent curve have been found t o be satisfactory.

177

based on some of the tracer composition prof i les of Spence Example resu l t s and Watkins a re indicated on Figures 16 - 18. Mass transfer coefficient distribution over the cross section of t h e samples is given on Figure 16 for a sandstone and a carbonate. M values of lo-' and 1 0 - 4 could be interpreted i n terms of layers of &out 2 . 0 cm and 0 . 5 an width respectively. Figure 1 7 gives the "no dispersion" velocity prof i les of the porous media. functions (Fig. 18) applying to the idea l "no dispersion" case o r t o the idea l near-zero-interfacial tension immiscible displacement case. Pred- ic t ions of mobility r a t io e f fec ts could therefore be made using conventional 1-dimensional displacement theory. However, fo r Righly heterogeneous media allowance fo r crossflow ef fec ts , as discussed above, should be included.

The l a t t e r can be represented as re la t ive permeability

-

Figure 16.

Mass t ransfer coeffkcient distributions ~ ~ 1 1 lines:"Sandstone SS2" Dashed lines : "Carbonate B 17"

Figure 17.

Velocity distributions.

Figure 18.

Miscible type re la t ive penneabilities .

coNcLus10Ns

Surfactant E.O.R. slugs w i l l be susceptible t o layer and streak permeab- i l i t y heterogeneities found within reservoirs due t o disturbance of flow patterns and increased dispersion. Mathematical approximations have been found which a re capable of modelling the channelling and crossflow ef fec ts present i n non-unit mobility ratio displacements. loss of in tegr i ty due to flow mechanism has been observed in slugs of around 20% pore volume. depending on the width of layers. possible to model khese phenamena analytically to match numerical simulations and to analyze tracer test data.

Experimentally,

Diffusion/disper$ion ef fec ts can be large, For short dimensionless times it is

178

ACKNOWLEDGEMENTS

Dr. M. Allmen is thanked f o r performing t h e dispers ion computations and Mr. M. Hughes f o r technica l help. W e are g r a t e f u l t o t h e Department of Energy f o r f i n a n c i a l support.

L.

2.

3.

4.

5.

6.

7.

8.

9.

10.

11.

12.

13.

14.

15.

16.

17.

18.

REFERENCES

WEBBER, K., Influence On Fluid Flow of Conrmon Sedimentary S t ruc tures I n Sand Bodies., S.P.E. Paper 9247

LAKE, 11. & HIRASAKI. G. , Taylor 's Dispersion I n S t r a t i f i e d Porous Media., S.P.E. Paper 8436.

KCONCE. T. & BLAQCWELL, R., Idea l ized Behaviour of Solvent Banks i n S t r a t i f i e d Reservoirs., S0c.Pet.Eng.J. (Dec. 1965) 2 , ( 6 ) , 318 - 328.

HAWTWORNE, R., The E f f e c t of Capi l lary Pressure I n a Multilayer Model of Porous Media. S0c.Pet.Eng.J. (Dec. 1975) Is, 467 - 476.

WRIGHT, R. & DAWE.R., An Examination Of The Multiphase Darcy Model Of Fluid Displacement I n Porous Media. Rev.Inst.Fr.du Pe t ro le (Nov-Dec 1980) - 35, (N0.6) 1011 - 1024.

PEACEMAN. D. & RACZiFORD, H., Numerical Calculat ion of Multidimensional Miscible Displacement. S0c.Pet.Eng.J. (Dec 1962) 2, 327 - 340.

€EARN. C., Simulation Of S t r a t i f i e d Waterflooding By Pseudo Relative Permeability Curves, ( Ju ly 19711, g, 805 - 813.

MACK, J., Process Technology Improves Oil Recovery, O i l & G a s J.(Oct.1979) 77, No. 40, 67 - 71.

EGBOGAII, E. , WRIGHT, R. & DAWE, R., A Model Of O i l Ganglion Movement In

- Porous Media, S.P.E. Paper 10115.

SATMAN, A. & ZOLOTWHIN, A. , Application of the Time-Dependent Overal l Heat Transfer Coeff ic ien t Concept t o Heat Transfer Problems I n Porous Media, S.P.E. Paper 8909.

Media, S0c.Pet.Eng.J. (March 1963) 2, 70 - 84.

CRANK, J., The Mathematics of Diffusion, Oxford Univ. Press. 1975,Sec.4.3.

KOVAL, E. , A Method For Predic t ing The Performance Of Unstable Miscible Displacements I n Heterogeneous Media, S0c.Pet.Eng.J. (June 196312,145-154.

JOHNSON, C. & SWEENEY, S. , Quanti ta t ive Measurements Of Flow Heterogen- e i t y I n Laboratory Core Samples And Its E f f e c t On Fluid Flow Characteri- stics, S.P.E. Paper 3610:

ROSMAN, A. & SIMON, R., Flow Heterogeneity I n Reservoir Rocks, S.P.E. Paper 5631.

SPENCE, A. & WATKINS, R., The E f f e c t o f Miscfoscopic Core Heterogeneity On Miscible Flood Residual O i l Sa tura t ion , S.P.E. Paper 9229.

HANDY, L., An Evaluation O f Diffusion E f f e c t s I n Miscible Displacement, Trans. AIME (1959) 216, 61 - 65.

WRICBT, R. et. al . , Heterogeneous Porous Media; A Miscible Displacement Model;- to be submitted f o r publ icat ion.

PERKINS, T. & JOHNSON, O., A Review of Diffusion and Dispersion i n POrOUS


SOME ASPECTS OF THE INJECTIVITY OF NON-NEWTONIAN FLUIDS IN POROUS MEDIA

PETER VOGEL and GUNTER PUSCH

Institut fur Tiefbohrkunde und Erdolgewinnung, Technical University Clausthal. West Germany

ABSTRACT

In existing numerical models, the rheological behaviour of

polymer solutions is commonly described by the power law,

which is not satisfactory at very low shear rates and at

relatively high shear rates. An improvement of the

mathematical description was achieved by using the

Carreau viscosity equation and deriving a filter law

for porous media. The validity over a wide range of shear

rates was proven by experimental results obtained from

flood tests in sand packs with one typical product each of

the three polymer classes (PAA, HEC, BPS) used in enhanced

oil recovery.

On the basis of typical reservoir data, the behaviour of

an injection well during polymer injection is investigated

by calculating the pressure profile around a wellbore.

From these data, conclusions are drawn for the selection of

polymers according to their rheological properties.

180

I NTRODUCT I ON

Flooding with viscous media has aroused increasing

interest in the field of enhanced o i l recovery. Numerous pilot projects are currently in progress or have already

been terminated / 1 ,2 / . The importance which is at present

attached to this field of research is thus evident.

Chiefly aqueous polymer solutions are employed as viscous

flooding media. A characteristic feature of these polymer

solutions is that the decisive parameter for the description

of their flow properties, the viscosity, varies as' a function

of the shear rate. In general, the solutions exhibit

pseudoplastic behaviour, that is, a decrease of the viscosity

with augmenting shear stress.

In the field of enhanced oil recovery, the viscous

behaviour of polymer solutions in porous media has

become of vital importance as far as their injectivity is

concerned. The investigations were initiated by the following

two questions:

- How can the viscosity values indicated in a rheogramme be

- Can these polymer solutions be injected into the reservoir applied to flow processes in porous media?

without exceeding the fracturing pressure of the rock?

In the following, a method which allows a calculation of the

injectivity of polymer solutions on the basis of the

rheogrammes and of the knowledge of the characteristic

reservoir data is presented.

CHARACTERIZATION OF THE POLYMERS EMPLOYED

Information about the flow behaviour of non-NEWTONian fluids

is provided by their rheogramme, that is, the plot of the

viscosity as a function of the shear rate; this is both

important and experimentally easy to obtain. All of the

considerations discussed in the following are based

exclusively on the information gained therefrom.

To begin, the rheogrammes of the polymer solutions used here

are presented. The liquids employed are aqueous solutions

181

Figure 1: Viscosity behaviour of a polysaccharide solution

Figure 2: viocosity behaviour of a hydroxyethylcelluloae solution

182

100 I

Figure 3: Viscosity behaviour of a polyacrylamide solution

(original brine with a salt concentration of 100 g/l;

reservoir temperature of 5OoC) of a typical, representative

product in each of the three classes of polymers used in

enhanced oil recovery.

comparable additional oil recovery (p' of additional oil per

m3 of polymer solution consumed) in flooding tests were thereby selected.

Figure 1 shows the rheogramme for a polysaccharide, figure 2

that for a hydroxyethylcellulose, and figure 3 that for a

polyacrylamide solution. A double logarithmic scale has

been chosen for the graphic representation.

The three curves display characteristic features in common:

A plateau occurs in the range of low shear rate; a linear

decrease is observed at higher values.

For the calculation of the flow behaviour of these non-

NEWTONian fluids, an analytical expression for the dependence

of the viscosity on the shear rate, which represents the

experimental values of the rheogramme over a wide range of shear rate, is of special importance.

The preceding figures show that the four-parameter equation

found by CARREAU /3/

Polymer solutions which yield a mutually

183

( 1 )

provides a good fit to the experimentally determined

rheogramme for the polymer solutions under investigation here.

The significance of the parameters in the CARREAU equation,

as well as a simple method for determining them, are briefly

explained. n o denotes the viscosity at the shear rate 0 = 0,

and can be determined directly from the horizontal portion of

the curve in the range of very low shear rates. By means of

supplementary measurements performed in the range of high

shear rates, values indicative of rl- are obtained. n-1 is

the slope of the linearly decreasing part of the curve. The

plateau for the range of low shear rate and the linearly

decreasing part of the curve intersect at a point whose

abscissa is approximately equal to 1/X.

In the following, the essential steps in the development of

a filter law for CARREAU fluids mdescrihed. The power law

frequently employed in previous publications is considerably

simpler to handle analytically, and is therefore preferred for

the treatment of concrete problems. For the polymer solutions

investigated in this work, however, a power-law dependence of

the viscosity on the shear rate does not describe the

experimentally observed behaviour with sufficient accuracy.

Consequently, sizable errors can result in the description of

the flow processes in porous media, as will be shown by means

of an example. For a wide range of shear rates, an extension,

as described in this work with respect to the viscosity model,

is indispensable.

A F I LTER LAW FOR CARREAU FLUIDS

Filter laws for non-NEWTONian fluids are known only for a few

special cases / 4 , 5, 6, 7/. The procedure common to their

derivations is as follows: First the capillary flow is

treated analytically for the liquid in question, in order to

obtain a filter law with the use of an appropriate capillary

bundle model.

This procedure is adopted in the following as well; a filter

184

law is thereby derived for CARREAU fluids, and the porous

medium is replaced by a capillary bundle which is

hydrodynamically equivalent with respect to porosity and

permeabi 1 ity .

0

Figure 4: Straight capillaric model of a porous medium

The simplest capillary model of a porous medium /a, 9/

consists of a bundle of circular cylindrical capillaries of

equal radius R. Figure 4 illustrates this concept.

A comparison of the DARCY filter law with the law of HAGEN-

POISEUILLE yields the "hydraulic equivalenceradius" for this

simple model:

By means of this concept, the

related to the capillary flow

can be treated accordingly.

flow through a porous medium is

of the liquid in question and

On the basis of this theory, a filter law for CARREAU fluids

can be derived. The procedure is justified by experimental

results. In the following considerations, it is

remarkable that no empirical corrections are required.

It is necessary first to calculate the flow behaviour of

CARREAU fluids in capillaries; for this purpose the velocity

profile and the averaqe velocity of the capillary flow must be

known. For the derivation, a circular cylindrical capillary

185

-1.

Figure 5: Flow throuqh a circular tube

of radius R and lensth L is considered - Figure 5 - and a cylindrical coordinate system is introduced. The z-axis and

the capillary axis are identical; the direction of .flow is

taken to be that of the positive z-axis.

The differential equation for the radial velocity

distribution v(r) is

( 3 )

whereby po - pL denotes the applied pressure difference. This differential equation is transcendental in the

derivative of the function being souqht, v(r); this fact

proved to be a considerable problem in the further course of

the calculations.

The introduction of the wall shear rate 0 , as a parameter is decisive for the solution of this problem. The calculation

/ l o / finally yields an analytical expression for the average

velocity during capillary flow. By means of the hydraulic

equivalence radius, this expression can be easily transformed

to a filter law. In the case of the capillary bundle model

used, the one-dimensional filter law takes the following

form :

186

In order to save space, the following substitutions have been

made :

With the exception of a correction factor, the external form

of this filter law is identical to that of the DARCY law.

This factor depends on the parameters of the CARREAU equation

and on the maximal shear rate 9, occurring in the capillary

bundle model. The maximal shear rate is obtained from the

transcendental equation

which admits an iterative solution according to the BANACH

fixed-point theorem.

The algorithm necessary for the numerical solution of

equations (4) and ( 6 ) requires the following steps:

After the parameters of the CARREAU equation, as well as the

permeability and porosity of the porous medium have been

determined, qR is calculated from ( 6 ) for predetermined

values of the pressure gradient, and the corresponding filter

velocity is determined from ( 4 ) .

COMPARISON OF THEORETICAL AND EXPERIMENTAL RESULTS

The theoretical results are verified by experiment; no

empirical correction factors are thereby required.

In order to carry out the required flood experiments, an

apparatus similar to that already used by DARCY was

employed. Sand packs of 50 percent porosity and 5 D

permeability, compacted by vibration, served as porous media.

If the DARCY equation is solved for the viscosity, the

result is

( 7 )

With the use of the present results, the effective viscosity

in the porous medium was determined directly from the

measured data according to ( 7 ) on the one hand, and by means

of the previously derived filter law, on the other hand.

188

For comparison, polysaccharide and hydroxyethylcellulose,

which exhibit a dominantly linear, decreasing range in their

rheourammes, were treated as power-law fluids.

o OBSERVED VALUES - CALCULATE0 - C A R R E N MODEL ----- CALCULATED-POWER -LAW MODEL

A

100- I 80.

c

D u

VELOCITY Im/d) 10 .

.Z .4 .'s .e 1'. i'.z t i 1:s *

Figure 6: Effective viscosity for flow of polysaccharide

solution in porous media'

W

t L u

K w

t 0 OBSERVED VALUES - CALCULATED - CARREAU MODEL - --- CALCULATED -POWER -LAW-MODEL

A

500. 400. \

\

\ \ \ 300. \

\ '.

VELOCITY ( m/dl 100 -

. Z .C .6 .8 1. 1.2

\ 500. 400. \

\ \ \ 300. \

\ '.

VELOCITY ( m/dl 100 -

. Z .C .6 .8 1. 1.2

Figure 7: Effective viscosity for flow of hydroxyethyl-

cellulose solution in porous media

189

100 t 0

- OBSERVED VALUES CALCULATED -CARREAU HODEL

Figure 8: Effective viscosity for flow of polyacrylamide

solution in porous media

From the filter law for power-law fluids, the effective

viscosity in a porous medium was likewise calculated.

Figures 6, 7, and 8 show the dependence of the viscosity on the filter velocity and compare the experimental and

theoretical results.

For the CARREAU model, the deviation between the experimental

and theoretical results is less than 10 percent for the

polysaccharide and polyacrylamide solutions, and less than

15 percent for the hydroxyethylcellulose solution. Hence

the agreement between theory and experiment can be regarded

as qood.

The power-law model describes the dependence of the viscosity

on the filter velocity with sufficient accuracy in the case of polysaccharide, whereaa considerable deviation occurs for hydroxyethylcellulose. These examples demonstrate the

advantages of the new filter law for the questions under

investigation.

CALCULATION OF THE INJECTIVITY BEHAVIOUR

During enhanced oil recovery, the pseudoplastic behaviour of the polymer solutions used exerts a pronounced influence on their injectivity. Once the questions concerning filtration .

190

adsorption, stability, etc. have been clarified for a given

reservoir in the course of the product selection procedure, the

question of the injectivity of the polymer solution involved

remains to be answered by the reservoir engineer. A t this

juncture, an important decision of whether or not a selected

product is suitable for field application must be made; this

is a vital cirterion because of the high financial risk

involved. A method must be provided for predicting the behaviour

in the field on the basis of laboratory data; thus a criterion

for decision must be established.

In the following, the flowing pressure and radial

distribution of pressure around the injection well are

calculated for an injector in a radially symmetric reservoir

and for a predetermined injection rate, with the use of the

filter law just presented.

The multitude of influential parameters necessitates a

restriction to a typical case encountered in practice. The

following, realistic, qeometrical and physical reservoir

data are employed for the model calculations:

Reservoir:

Permeability K = 1000 mD

Porosity d = 0.24

Effective reservoir thickness h = 4 m

Well :

Cased with 7" diameter and ideally perforated in the

reservoir zone

r = 0.069 m Wellbore radius

Injection rate q = 100 m3 /d

Depth = 1000 m

W

FORMULATION OF THE SELECTION CRITERION

From the standpoint of reservoir engineering, the essential

criterion for the injectivity of a polymer solution is that

the fracturing pressure of the rock must not be exceeded during

the injection. The predetermined injection rate and the

average reservoir pressure also affect the decision. For a

depth of 1000 m and under the assumption that the average

reservoir pressure corresponds to the hydrostatic pressure ,

191

a value of 5 = 100 bar results. The order of magnitude of

the fracturinu qradient typical for sedimentary rocks lies

between 0.18 and 0.24 bar per metre of depth. For the

injector under consideration here, this results in a maximal

bottom-hole flowing pressure of 180 to 240 bar: hence the bottom

hole flowing pressure may exceed the average reservoir pressure

by a maximum of 80 to 140 bar durinq polymer injection.

Furthermore, a radially symmetric reservoir is thereby

assumed. The ranue of influence of the injector is selected

at re = 200 m; the reservoir pressure of 100 bar is assumed

to prevail at the outer boundary. Thus, the following criterion

for decision is obtained: The polymer solution is injectable

provided the pressure drop over a distance of 200 m from the

bore hole does not exceed 80 to 140 bar.

CALCULAT IONAL PROCEDURE

The object of the calculation is to determine the relationship

between the pressure gradient and the distance from the well.

This function is subsequently integrated.

Because of the complicated structure of the filter

law previously derived, the entire calculation is performed

numerically.

As a result of its structure, the filter law just developed

allows only the determination of the corresponding filter

velocity for given values of the pressure gradient. With

reference to / l l / , the following procedure is adopted for

determining the locally prevailing pressure gradient. From

the equation of continuity the following expression is

obtained for the radial velocity distribution:

whereby r denotes the distance from the wellbore axis. This

provides a possibility of determining the distance from the

well corresponding to given values of the pressure gradient

by means of the filter law and equation ( 8 ) .

The calculation starts with the determination of the pressure

192

gradient at the bore hole. For this purpose, two values of

the pressure gradient, of which one is smaller and one larqer

than that prevailing at the well, are initially assumed. By

nesting of intervals a sequence of pressure gradient

values is constructed in such a way'that the values

of the radius determined from the filter law and equatisn ( 8 )

converge toward the wellbore radius. The procedure is

truncated as soon as the wellbore radius has been approached

with the required accuracy. The value of the pressure

gradient corresponding to the radius thus determined is then

taken as the pressure gradient at the well.

Subsequently, this value is decreased stepwise, and the

corresponding values of the radius are determined from the

filter law and equation ( 8 ) . Thus, a tabular representation

of the pressure gradient as a function of the distance from

the well is obtained. .The calculation of the total pressure drop is subsequently performed by means of numerical

integration.

400.

3mi

32 0-

200:

2(O:

-

1 POLYSACCHARIOE 2 POLYACRYLAMIDE 1 POLYSACCHARIOE 2 POLYACRYLAMIDE

360.- 3 HYDROXYETHYLCELLULOSE

-

0. 30. 60. 90. 120. 150. 180. 210. DISTANCE (M 1

Figure 9: Calculated pressure profile during polymer injection

193

RESULTS OF THE MODEL CALCULATION

In figure 9, the pressure difference occurring during

injection, as referred to the pressure at the injection well,

is plotted as a function of the distance from the well for

the three polymer solutions under investigation. Moreover,

the maximal values of 80 and 140 bar for the injection over-

pressure are indicated. According to the criterion

formulated here, the polymer solutions are suitable for

injection provided the pressure difference remains less than

80 to 140 bar over a distance up to 200 m from the injection

well. This condition is fulfilled for the polysaccharide,

and partially fulfilled for the polyacrylamide in this case.

In contrast, the hydroxyethylcellulose exhibits a decidedly

deviating behaviour. The pressure difference, as referred

to the well, already amounts to 140 bar at a distance of

about 20 m, and increases to more than 350 bar over a

distance of 200 m. It must be emphasized that this is a

model calculation, whereby the effects described are

attributed solely to the dependence of the viscosity on the

filtration velocity.

If, in a practically relevant case, the model calculations

indicate that the maximal permissible injection pressure will

be exceeded, the concentration of the polymer solution to be

used must be reduced; the viscosity is thus decreased. The

parameters of the CARREAU equation are then determined from

the rheogramme, and the calculation is repeated with the use

of these values.

A further possibility is the purely theoretical plotting of

rheogrammes for injectable fluids by the variation of

parameters in the CARREAU equation.

CONCLUSIONS

The rheological behaviour of aqueous polymer solutions is

well described by the CARREAU model.

for such fluids is described and experimentally verified.

With.the use of the new filter law, the radial pressure

distribution around the injection well during the injection

A filter law derived

19 4

of polymer solution is calculated. A polymer solution is

judged as suitable for injection as far as the bottom hole

flowing pressure does not exceed the fracturing pressure of

the rock at the bottom of the hole. Among the products

investigated here, the polysaccharide solution fully, and

the polyacrylamide solution conditionally satisfies this

criterion under the given conditions.

NOMENCLATURE

h K

L

n

P -

Po - PL q r

r e

rW R

V

V f

P

YR

‘10

‘1, h

d

‘1

Formation thickness

Permeability

Length

Power-law index

Average pressure

Pressure drop

Injection rate

Radial coordinate

External boundary radius

Wellbore radius

Radius of the tube

Velocity

Filtration velocity

Shear rate

Shear rate at the tube wall

viscosity

Zero-shear-rate viscosity

Infinite-shear-rate viscosity

Time constant

Porosity

REFERENCES

1 CHANG, H. L.;

Polymer Flooding Technology - Yesterday and Tomorrow J. Pet. Tech. (Aug. 197818 1113 - 1128

2.

3 .

4 .

5.

6 .

7.

8.

9.

195

GRODDE, K.H., SCHAEFER, W.;

"Experience with the Application of Polymer to Improve

Water Flood Efficiency in Dogger Reservoirs of the

Gifhorn Trough, Germany"

Erdoel-Erdgas-Zeitschrift 94 (July 1978) 7 , 252 - 259

CARREAU, J.P.;

'Rheological Equations from Molecular Network Theories"

Ph.D. Thesis, Univ. of Wisconsin, Madison 1968

BIRD, R.B., STEWART, W.E., LIGHTFOOT, E.N.;

"Transport Phenomena"

J. Wiley a. Sons, New York (19601, 206 - 207

SADOWSKI, T.J.;

"Non-Newtonian Flow Through Porous Media"

Trans. SOC. Rheol. 9 (1965) 2, 251 - 271

SADOWSKI, T.J., BIRD, R.B.;

"Non-Newtonian Flow Through Porous Media"

Trans. SOC. Rheol. 9 (1965) 2 , 243 - 250

PARK, H.C., HAWLEY, M a c . , BLANKS, R.F.;

"The Flow of Non-Newtonian Solutions Through Packed Beds"

Polym. Eng. Scie. (1975) 15, 761 - 773

SCHEIDEGGER, A.E.;

"Theoretical Models of Porous Matter"

Producers Monthly 17 (Aug. 1953) 10. 17 - 23

SCHEIDEGGER, A.E.;

"The Physics of Flow Through Porous Media"

University of Toronto Press (19631, 115 - 117

10. VOGEL, P.;

"Untersuchungen zur Berechnung des FlieSverhaltens wlSriger

Polymerl6sungen in Sandpackungen"

Ph.D. Thesis, TU Clausthal 1980, West Germany

11. BONDOR, P.L., HIRASAKI, G.J.r T H A M r M . J . ;

"Mathematical Simulation of Polymer Flooding in Complex

Re s e rvo i r s " SOC. Pet. Eng. J. (Oct. 19721, 369 - 382


CHEMICAL FLOODING 19 I

BASIC RHEOLOGICAL BEHAVIOR OF XANTHAN POLYSACCHARIDE SOLUTIONS IN POROUS MEDIA:

EFFECTS OF PORE SIZE AND POLYMER CONCENTRATION

G. CHAWETEAU and A. ZAITOUN

Institut Francais du Pktrole, B.P. 31 I , 92500 Rueil Malmaison - France

ABSTRACT

The basic rheological behavior of xanthan polysaccharide solut ions has been extensively invest igated by varying polymer concentration, pore s i z e and the chemical nature of porous media. The rheological character izat ion of solut ions has sham t h a t xanthan macromolecules behave l i k e r i g i d rods i n the s a l i n i t y conditions selected. A l l microgels were carefu l ly removed from solut ions i n order t o study the behavior f a r away from i n j e c t i o n wells.

I n f ine cy l indr ica l pores, mobility reduction a t low shear r a t e s was found t o be constant and lower than the Newtonian v iscos i ty a t low shear r a t e s , except for pore diameters smaller than macromolecule length. Water permeability was not reduced a f t e r polymer flow, showing t h a t the rheological behavior was not influenced by re ten t ion o r adsorption phenomena. reduction and r e l a t i v e v iscos i ty decreases a s pore s i z e decreases and polymer concentration increases. of a depleted layer i n which polymer concentration and thus v i r c o s i t y i s smaller than i n the bulk. on chemical nature and pore shape. A model based on t h i s physical hypothesis i s proposed f o r ca lcu la t ing mobility reduction a s a function of pore s i z e and polymer solut ion propert ies . experimental r e s u l t s .

I n various unconsolidated porous media, such as packs of g lass beads, carborundum par t ic les and.sand grains , the same behavior i s observed. The mobility reduction i r l e s s than i n la rge c a p i l l a r i e s and decreases with pore size. Moreover, the depleted layer e f f e c t decreases with shear r a t e u n t i l i t vanishes a t high f low rates . e f fec t ive shear r a t e s i n pore throa ts of porous media as a funct ion of average veloci ty .

The experiments car r ied out i n Fontainebleau sandstones having d i f fe ren t permea- b i l i t i e s confirm t h i s observation and show t h a t pore throa t diameters i n consolidated porous media a re la rger than predicted by the usual cap i l la ry models.

In a l l types of porous media, no d i l a t a n t behavior was detected even a t the highest flow r a t e s .

The prac t ica l appl icat ions of t h i s study f o r EOR are 1) w t h a n solut ions are be t te r sweeping f l u i d s i n heterogeneous reservoi rs than conventional f l u i d s h v i n g the same average v iscor i ty ; 2) they can be ured i n l e s s permeable forma- t ions than previously claimed; 3) very good i n j e c t a b i l i t y i s expected for microgel- f ree solut ions.

The r a t i o between mobility

This i s explained by the exis tence near the pore wal l

This deplet ion i s due to s t e r i c e f f e c t s and does not depend

The model's predict ions a r e i n agreement with

A comparison between flow curves and rheograms gives an estimation of

198

INTRODUCTION

Both hydrolyzed polyacrylamide and xanthan polysaccharide solutions are candidates for enhancing oil recovery.

Up to now, hydrolyzed polyacrylamides have undoubtedly been more extensively studied in the laboratory and used in field applications. However, the macromolecular flexibility of this type of polymer causes several detrimental effects (1): 1) The viscosity decreases sharply as salinity increases, due to the screening of charged groups, particularly in the presence of bivalent ions. 2) The dilatant behavior at high flow rates which decreases injectability. behavior isdue to the coil-stretch transition of macromolecules in converging zones of porous media (2 ) . 3 ) The mechanical degradation which occurs when hydrodynamic forces on the stretched molecules overcome the strength of carbon-carbon bonds ( 3 ) . Moreover, the hydrolysis of acrylamide groups at high temperatures, observed even in neutral conditions ( 4 1 , can lead to precipitation in the presence of calcium ions. So their use is limited to low salinity and temperature reservoirs.

The rigid rodlike conformation of xanthan polysaccharide molecules in most reservoir conditions enables the problems mentioned above to be avoided. is almost insensitive to salinity, except in a very low salinity range, and neither dilatant behavior nor mechanical degradation has been observed in oil recovery conditions. salinity reservoirs. available on the market has excluded xanthan polysaccharides from many field applications. microgels and cellular debris, particularly in powders, is well documented (5). The influence of these microgels on their flow behavior has been extensively studied in well-defined porous media (6). facturing processes, particularly for fermentation broths, reduce to a great extent the risks of well plugging, so that xaqthan solutions could be widely used in the near future.

These newly manufactured polymers contain so few microgels that they will be adsorbed or retained at a short distance from the injection well. conditions, most of the oil to be recovered which is located far from the injection well will be swept by a polymer solution without microgels. the basic rheological properties of such a solution in porous media is very important from a practical point of view.

The first experiments carried out in porous media with a microgel-free solution (7) showed that the apparent viscosity or mobility reduction is less than the viscosity determined in a viscometer, mainly at the lowest shear rates in the Newtonian regime, Further experiments, performed with a well-characterized polymer solution and well-defined porous medium, showed that this phenomenon was related to the existence of a depleted effects (8) . concentration depleted-layer phenomenon on the sweeping properties of xanthan solutions.

This

The viscosity

So this polymer is potentially very attractive, particularly for high But, up to now, the poor quality of most industrial products

The poor solubility of some products and the existence of both

However, recent improvements in manu-

In these

Thus knowing

layer near the wall, due to steric The present investigation aims to study the influence of polymer and rock permeability in order to estimate the effects of this

POLYMER SOLUTIONS

The xanthan polymer used is a sample manufactured in a fermentation-broth form by RhBne-Poulenc laboratories with a fermentation process specially designed to avoid microgel formation. All solutions were obtained by dilution with salted water, clarified and filtered at very low shear rate to remove any possible remaining microgel - with a method previously described (6). against bacterial attack.

Its molecular weight should be close to 0.8 x lo6.

The addition of 400 ppm NaNg protected solutions In the conditions chosen (salinity = 5 g/l NaC1, pH = 7,

199

8 = 30°C), the polymer molecule was shown t o behave l i k e a r i g i d rod having a 0.62 pm length and 16.5 1 diameter ( 8 ) .

BULK RHEOLOGICAL PROPERTIES

Shear flow

Viscosi ty measurements were performed with a s e r i e s o f g l a s s capi l la ry viscometers, previously descr ibed, over a wide shear r a t e range (0.1 polymer concentrations (25 t o 2400 ppm) using Rabinowitch-Mooney correct ion f o r power-law f l u i d s . The p l o t s of shear v i scos i ty versus shear r a t e i n log-log coordinates (Fig.1) show how so lu t ions behave i n pure shear flow. The following can be observed:

1) A Newtonian regime, a t very low shear r a t e s , i n which r e l a t i v e v iscos i ty 7, which i s the r a t i o between polymer solut ion and br ine v i s c o s i t i e s i s independent of shear r a t e and equal t o q r o .

2) A t r a n s i t i o n zone, character ized by a c r i t i c a l shear r a t e , equal t o the inverse of a r o t a t i o n a l re laxa t ioh time ir.

3) A shear-thinning regime, i n which r e l a t i v e v i s c o s i t y decreases with shear r a t e according t o a power l a w whose exponent is 2 m.

Over the shear r a t e range t e s t e d , the experimental data f i t very wel l with the

t o 3000 s-1) for various

Cerreau model A ( 9 ) . I

'1 r o

'3" 7r = [1+ ( T r X Y )

100:

50-

20- +

lo:

5-

2

' L 1

Figure 1.

Viscosity-shear r a t e curves f o r var ious polymer concentration

2 0 0

Converging flow

An estimate of viscous f r i c t i o n i n converging flows can be made by measuring the apparent r e l a t i v e v iscos i ty i n a model consis t ing of successive short c a p i l l a r i e s separated by cy l indr ica l expansionsfm! which the geometry is shown i n Figure 2 .

Figure 2.

Influence of converging flow zones on apparent v i scos i ty

The capi l la ry radius was chosen s u f f i c i e n t l y small so a s t o avoid any i n e r t i a e f f e c t For shear r a t e s l e s s than a c r i t i c a l value t o the shear v i scos i ty , meaning t h a t r e l a t i v e v i s c o s i t i e s a r e equal i n both converging and shear flow. ForY > yf, the apparent v i scos i ty becomes greater than shear v i scos i ty . This increased viscous f r i c t i o n occurring i n converging flow near the entrance t o the c a p i l l a r y is explained by the s t rong or ien ta t ion of the rods i n the flow d i rec t ion when the product of re laxa t ion time by elonga- t i o n r a t e is s u f f i c i e n t l y high (2) (10). viscos i ty is very s m a l l , compared t o t h a t obtained with polyacrylamide so lu t ion with the same flow conditions (2 ) . Indeed, the polyacrylamide molecule is both s t re tched and or ien ta ted i n the flow d i rec t ion by the converging flow. s t re tch ing degree ( the s t re tched length may be ;O times the i n i t i a l c o i l diameter) explains the magnitude of the viscous f r i c t i o n increase with polyacrylamide, thus involving d i l a t a n t behavior.

i n our expe imental conditions. o*= 600 s-i, the apparent v i scos i ty i n the model was found t o be equal

However, this increase i n apparent

The high

20 1

WALL EFFECT I N FLOW THROUGH FINE CAPILLARIES

The e f f e c t s of pore s i z e on apparent v i scos i ty were f i r s t invest igated i n a very simple system, namelywith a well-characterized rodl ike polymer solut ion flowing through f ine cy l indr ica l c a p i l l a r i e s , in order t o make the in te rpre ta t ion easier .

Experimental f a c i l i t y

Nuclepore membranes were selected for these experiments because t h e i r pores have a well-defined cy l indr ica l shape. corresponding t o nominal diameters (ranging between 0.4 and 12 pm) were determined by electron microscopy (81, and the average diameters a r e given i n Figure 3.

The average diameters and a r e a l pore dens i t ies

4--+

3-

2-

-3

-2

_ _ _ _ _ 500prn Copillories - Nuclepore Membmnes

A s e r i e s of six f i l t e r holders, each one containing f i v e membranes separated by nylon gr ids , was used t o obtain s u f f i c i e n t pressure drops measured by oil-water manometers. The thickness of the Nuclepore membranes is constant and approximately equal t o 10 p m , so that the c a p i l l a r y length t o radius r a t i o l /r given i n Figure 3 depends on pore diameter.

Results and discussion

The r e s u l t s of flow experiments a re shown i n Figure 3. versus shear r a t e i s plot tedas a dashed l ine. var ia t ions of r e l a t i v e apparent v i scos i ty measured during flow through membranes having d i f f e r e n t pore diameters.

The most importcmt r e s u l t is t h a t i n the Newtonian regime the apparent viscosi ty in f i n e pores is found t o be lower than i n bulk solut ions and decreases with pore

Bulk r e l a t i v e v iscos i ty The sol id- l ine curves show the

202

diameter, except f o r t h e smallest one whose diameter (0.28 pm) i s l e s s than molecule length (0.62 pm). In t h i s l a s t case the macromolecules a r e re ta ined on the upstream s ide of the membrane, causing an extra-pressure drop and thus a curve upturn i n low shear range. A t the highest shear r a t e s , the macromolecules a re or ien ted by hydrodynamic forces and can e a s i l y pass through the membranes. flow, showing t h a t flow proper t ies were not dis turbed by adsorpt ion or re ten t ion phenomena. va l id i n the Newtonian regime even f o r cy l indr ica l pores having d i f f e r e n t length to-radius r a t i o s . A t higher shear r a t e s , the entrance e f f e c t s can increase apparent v i s c o s i t y i n r e l a t i v e l y short c a p i l l a r i e s (111, and the shear r a t e dependence must be s tudied with models having s imi la r geometric shapes such as glass- bead packs ( see below).

This decrease preted ( 8 ) by the exis tence of a depleted layer near the pore.wal1. This deple- t i o n i s due t o t h e s t e r i c hindrances which reduce the probabi l i ty t h a t the macromolecular center of mass may be a t a dis tance less than one macromolecular h a l f - length from the wal l a s shown i n Figure 4. Thus, t h e polymer concentration w i l l increase from zero a t wal l contact up t o bulk concentrat ion a t a dis tance close t o half the length of a macromolecule. Such a depleted-layer has been theoret- i c a l l y predicted f o r both c o i l polymers (12) and rodl ike p a r t i c l e s (131, and i t physical ly explains the apparent s l i p a t the w a l l predicted f o r concentrated solut ions (14). i t y due to the polymer i s l e s s near the wal l than i n the bulk, causing a lower overa l l apparent v i s c o s i t y i n f i n e pores than i n the bulk. as pore diameter decreases.

A coaxial two-fluid flow model has been proposed t o schematize polymer so lu t ion flow (Fig. 4) . The bulk so lu t ion with a r e l a t i v e v i s c o s i t y q r b flows i n the center of the c a p i l l a r y i n s i d e a rad ius equal t o ( r - 5 ) . A depleted so lu t ion having a r e l a t i v e v iscos i ty ' Iw flows i n an annulus having thickness 5 surrounding the bulk solut ion.

In a l l experiments, the water permeability was unchanged a f t e r polymer

It must be noted t h a t a comparison between apparent v i s c o s i t i e s i s

i n apparent v i scos i ty a s pore diameter decreases has been i n t e r -

A s a consequence of t h i s depleted layer , the increase i n viscos-

This e f f e c t increases

The ve loc i ty i s zero a t the wal l and equal i n both

Allowed hsitiom of Rods

Ir

Figure 4

Schemetic v i e w of polymer so lu t ion flow through f i n e pores with a depleted layer e f f e c t

203

tY 0

the bulk solution and the depleted solution at a distance r From this model, an analytical equation has been derived to relative viscosity 'Irp as a function of pore diameter 2 r:

rlrw 4 rlrFJ = 1 - (1- 1/p ) (1- 6/r )

where p' Trb' '1,

Apparent viscosity

rP

-6 from the axis. calculate apparent

0.40

(2)

3.90

Very good agreement between the experimental apparent relative viscosity in the Newtonian zone (Fig. 3) and the predictions of this model was found in choosing the following values for depleted layer characteristics:

8 = 0.3 pm 'I, 1.77

The value of 6 is close to half the length of a macromolecule (L/2 = 0.31pm), and the value of qrw is consistent with the physical hypothesis proposed. Moreover WBERT and TIRRELL (15) have recently proposed a calculation based on the finitely extendable nonlinear elastic dumbbell as a molecular model and the exclusion of all molecule configurations intersecting the walls. agreement is found between their calculations and our experimental findings.

Thus, the relation between the diameter dependence of apparent viscosity and the depleted- layer phenomenon seems to be very well established. Moreover, the same behavior was recently observed with polyacrylamide solutions when there are no effects of adsorption on flow properties ( 1 ) .

Good

FLOW THROUGH UNCONSOLIDATED POROVS MEDIA

Pore size dependence

Calibrated glass beads having different diameters (see Table 1) were packed to obtain porous media having similar pore shapes but different pore sizes. flow experiments were performed with a 400 ppm xanthan solution, and the absence

The

TABLE I

diameter

200-250

40-50

I 20-3.0

10-20 I&

Perme- ability k km2)

137

36

8.4

2.4

0.66

0.21

0.11

0.40 I 3.75

0.41 I 2.97

index

0.185

0.180 1 1.7 I 43 I 0.175

0.160

0.130

0.110 1 1 0.080

of permeability reduction after polymer flow was checked for .very bead pack to ascertain the absence of any adsorbed layer effect.

2 0 4

XP5gA NoCl

The flow-experiment r e s u l t s a re qui te s imilar t o those observed i n flow through cy l indr ica l pores (Fig. 5 ) . The apparent v i scos i ty i n the Newtoqian zone is

4. .

3'

2-

.

I,

1 l S l -4

12 41 Glass Beod Pocks I0161 .3

1361 1841

IOZ1

10 111

-2 - - - .Bulk Sheor Vscosity -Apparent Viscosity

\ .-- '. (k) Permeobilily m prn'

. . . a * . . . 8 , , . . . . ' ' . -1

Figure 5.

Pore s i z e dependence of apparent v i scos i ty i n flow through glass-bead packs

found to be lower than the bulk v iscos i ty and decreases with average pore s i z e evaluated by pack permeability as shown i n Figure 5. The maximum wall shear r a t e i n the average pore throa t diameter was calculated by:

- 0 . 5 ? = 4 x 4 v (8 k 0 -5 (3 1

Where a is a shape parameter c h a r a c t e r i s t i c o f the pore s t ructure . a should be one for a bundle of c a p i l l a r i e s having the same diameters. media, the value of P i s experimentally determined as being t h a t which gives the same c r i t i c a l y c corresponding to the onset of shear-thinning behavior for both the shear viscosity-shear r a t e curve and the apparent viscosity-shear r a t e curve i n the porous medium under consideration. equal t o 1 .7 for packs of large spheres having the same diameter (8). It decreases with the pore size-molecule length r a t i o and increases a s pore s t ruc ture heterogeneity increases. This i s the case when the bead-diameter d i s t r i b u t i o n becomes wider o r when the consolidation degree of sands

Due t o the s t a t i s t i c a l homothety of bead packs, the shear r a t e dependence of the depleted-layer media. As expected, the rod or ien ta t ion with $hear decreases the depleted layer e f f e c t a s the flow r a t e increases , and apparent v i scos i ty becomes independent of pore s i z e a t high shear r a t e s ( y 7 3000 s-1). apparent v i scos i ty overcomes the shear viscosi ty . lncrease i n viscous f r i c t i o n i n converging zones of porous media where the macromolecules a r e or ien ta ted i n the d i rec t ion of flow (Fig. 2).

The value of For porous

The a value was found t o be

giving sandstones increases (8).

e f f e c t can be deduced from flow experiments i n t h i s type of porous

A t the highest flow r a t e s , the This can be explained by the .

205

As shown by results obtained with polymer flow through Nuclepore membranes, Equation (2) gives the relation between apparent viscosity and pore diameter. Thus an effective diameter can be calculated for each glass bead pack from the apparent viscosity measured. This effective diameter corresponds to an average hydrodynamic diameter of pore throats where polymer flows. mean pore size is proportional to the square root of the permeability for homothetic porous media. from the polymer apparent viscosity is plotted versu from the simplest capillary model, 2 r = 2 (8 k 0-1)8". All the points corresponding to experiments performed with glass-bead packs are lined-up on the first bissectrix. So the average hydrodynamic diameter of pore throats is approxirmrte- ly equal to 2 (8 k 0-1)0.5 for homogeneous bead packs.

Additional points deduced from experiments carried out in sand packs (8) are also lined-up on the same curve.

polymer concentration effects

On the other hand the

In Figure 9, the effective pore-throat diameter deduced ore diameter calculated

The influence of polymer concentration was systematically studied by using a Carborundum pack having a permeability equal to 0.1 pm2, a porosity equal to 0.48 and an effective pore diameter of 2.6pm. The polymer concentration was varied from 200 ppm to 1600 ppm, and the absence of permeability reduction was checked after every polymer flow experiment.

7 rP r)r

102r102 -10

I

1 lo '"%2 . . ' . . ' Figure 6. y'(seC-'1

The depleted-layer effect as a function of shear rate at different polymer concentrations incarborundum packs

206

Both shear v i s c o s i t i e s i n dashed l i n e s and apparent v i s c o s i t i e s i n s o l i d l i n e s a re p lo t ted i n Figure 6.

The f i r s t observation i s t h a t the general behavior i s q u i t e s imilar t o t h a t observed i n glass-bead packs. s i t i v e t o the pore shape and chemical nature of porous media. consis tent with the s t e r i c o r i g i n of the phenomenon.

The depleted-layer e f f e c t appears t c be insen- This r e s u l t i s

Moreover, the magnitude of the e f f e c t , i . e . the r a t i o between apparent v i s c o s i t y and shear v i scos i ty , increases sharply with the polymer concentration, a t low shear r a t e s (Fig. 7 ) .

60-

40-

20-

'7rP '7r I I I 1

XP 5911 NaCl pH=7 8 = 3 0 ° C

Corborundum Packs

/ /

1

-40

0 0 400 800 1200 1600

Figure 7.

The inf luence of polymer concentration on the magnitude of depleted layer e f f e c t

C ( ppml

A t the highest concentration t e s t e d ( c = 1600 ppm), the apparent v i s c o s i t y

( t l r p

This polymer concentration e f f e c t could a l s o be predicted. d iv is ion by

= 17.5) i s less than one t h i r d of bulk shear v i s c o s i t y ( 'Irb

V r b and inversion, Equation (2) can be wr i t ten :

= 62).

Indeed, a f t e r both

For dilute solutions, the thickness constant so that:

qrb’ qrp =

where k = (1 - 6 l 4 is a positive

Grain diameter Dg(pLm)

207

of the depleted layer 6 is expected to be

k + (1 - k ) P (5)

porosity Apparent Perme- viscosity

abi1i3 rP k ( p

constant, always less than 1 for a given

-

porous medium. with p = ‘lrb .

rlw

In the concentration range tested, the Cb/Cw ratio is expected to be constant (13). Since the viscosity of these polymer solutions is roughly an exponential function of polymer concentration (81, the qrb/f)r,ratio increases very sharply with polymer concentration, thus explaining the concentration dependence observed for the depleted-layer effect.

&As a consequence , the depleted-layer effect incresses iinearly

14.3 4.4

FLOW THROUGH SANDSTONES Permeability effects

As shown above, the depleted-layer effect depends only on pore size for a given polymer solution. bility deduced from the simplest capillary model

However, the well-known relation between pore size and permea-

(6) -1 0.5

2rc= 2 (8 k 0 is valid only for homothetic unconsolidated packs.

For natural porous media such as sandstones, this relation is no longer valid, and electron microscopy observations (16)hsve shown that pore throat diameters are generally larger than those calculated by Equation (6). As a consequence, the influence of permeability cannot be predicted by a simple model.

TABLE I1

Flow through sand packs and sandstones (XP solution, 9, = 4.0, 2 m = 0.22)

I 8 0 - 1 ~ ~ 5.0 I 0.38 I 3.5 Sand I Sand 2

0.119

I 0.0373 1 0.084 I 2.95 I Ssnd;tone

I 0.0206 I 0.075 I 2.83 I I Sand:tone I 0.0096 I 0.056 I 2.69

I 0.0033 I 0.056 I 2.49 I

~ ~~

Shear- 1 Shear-rate I Pore-thros;] thinning constant diameter

0.165 2.5 21

0.165 1.4 15.7

0.087 I 4.2 I 13.6 I 0.062

0.060

0.056 I 9.1 I 6.0 I

208

some cores of quartzit ic Fontainebleau sandstones having permeabilities ranging from 3x10'3 to 0.4p1d (Table 11) were selected t o obtain a quantitative evaluation of the depleted-layer effects. A l l the cores were preflushed by a hydro- chloric acid solution t o remove the sl ight quantity of iron contained i n the sample i n order t o avoid possible interaction8 with the polymer. After polymer flow experiments, the i n i t i a l permeability of each core was exactly restored, even for the less permeable sample (3.3 x 10-3)Id).

The experimental resul ts shown i n Figure 8 are similar t o those observed i n unconsolidated porous media. The apparent viscosity t s l e s s than in the bulk i n the Newtonian zone, which indicater a depleted-layer effect that increases as permeability decreases.

%

4

3

2

1

7)r

4

3

2

1 loo 10' 103 104

y(sec-1) Figure 8.

The depleted layer effects in flow through Fontainebleau Sandrtoner

using polymersolution characterist ics in the bulk ( '1 b = 4) and near the wall ( 8 = 0.3 p and q d l . 7 7 1 , deduced from experimantr vfth Nuclepore membranes, Equation (2) giver the effective diameter of pore throats 2 r am a fuoction of permabili ty for Fontainebleau sandstones (Table 11). A8 e d c t e d , t U a ef+ r-tive diameter 2 rp is always larger than 2 rc; and the r a t i o rp/rc increaaes as $-me.- b i l i t y &creaser, as shown in Figure 9, in which experimental point8 corresponding to 8andrtones are plotted as solid circler. secondary crystall ization process which explains the decrease in permeability for Fontainebleau sandrtoner. The r a t i o rp/rc should be no l y one for Fontainebleau

high as 3 in very low permubili ty range There remulta are conrir tmt w i t h Dullien's observations, but are =re accurate because of the mathod

valuer is obrerved a8 permeability docreares (Table 111, f rom the pore dimetar heterogeneity increase with the consolidation pSOC888.

This trend is wruistent with the

rand Pack8 having the same grain diameter (10<k~2Opm P 1, but reacher values as (lO'3<k<!~1O'3pd).

and the use Of homogeneour 8.rie8 Of smdstoner. MOS.OVOX', an inaea8e i n a as could be expected

209

I I I I I I

- --I Fontainebieau Sandstones 2 r ~ = 3 5 ( 2 r , ) ~ ~ ’ /

(8.4)

20-1 0.3601, / p . 0 )

i 3 0 . 1 1 ) I Sandpacks I 1. Sandstones I

(k)Permeability in p m 2

1 V .I

i 2 5 16 20 5‘ 100 2r or 2&mi

Figure 9.

Comparison of pore throat diameters detenrdned by polymer injection method with measured or calculated pore diameter

i n various porous media

From a practical point of view, these r e su l t s show tha t xanthan solutions can pass very eas i ly through even the low permeability zones of reservoirs. The lowest l imit for use of such xanthan solutions should correspond to pore throat diameters equal to_ycromolecular length ( k O . 6 pm) , i . e . t o permeability much lower than 10 bleau sandstones. Practically, the use of such polymers is never limited by polymer dimensions.

p d for sandstones having a structure similar t o Fontaine-

Ddrodvnamic retention

The f i r s t type of hydrodynamic retention, which is related to thermodpamic effects (17) and thus does not depend on pore-molecule re la t ive dimensions, was found to be almost negligible for these unthan solutions having rodlibe molecules. As theoretically expected, the entropy difference. due t o molecular alignment are too small to induce large concentration differences between the different zones

2 10

of the porous medium. In high permeability sandstones, the concentration differences observed after sudden flow-rate changes (from Newtonian to shear-thinning regimes,namely from 6 to 700 sec’l) werE very small (m/q<I%), in comparison with those observed in dilatant regime with coiled polymers .(la) (19) (20) (1).

The second type of hydrodynamic retention, which depends on pore-molecule relative dimensions end which can be explained by the slow accumulation of polymer molecules in the zones of porous media where pore-throat diameters can be smaller than molecular size, was observed in very - low - permeability sandstones (k = 3 and 9 x 10-3 pro2). and kept constant in the shear-thinning regime, large concentration decreases in the effluent have been noted and the apparent viscosity was found to increase slowly as indicated by the arrows in Figure 8.

Indeed, when the flow rate has been suddenly increased

CONCLUSIONS

The basic rheological behavior of xanthan solutions in porous media has been studied with solutions without microgels, i.e. as they are in reservoirs far away from the injection wells. Indeed, the microgels contained in injected solutions are retained in a zone located around the injection well.

The main conclusions of these investigations are the following:

1) The apparent viscosity of polymer solutions flowing through fine pores is always less than bulk shear viscosity at low shear rates in the Newtonian regime and decreases as pore size decreases. This phenomenon is interpreted by the existence near the pore wall of a depleted layer where average polymer concentration and viscosity are lower than in the bulk.

2) An analytical equation derived from a schematization of polymer solution flow as a two-fluid concentric flow is proposed to predict apparent viscosity as a function of pore size and polymer solution characteristics. F l o w experiments performed In well-calibrated cylindrical pores established the validity of this equation and provided the characteristics of the depleted layer. particularly, its thickness close to the half-length of the macromolecule is consistent with our interpretation of the origin of the depleted layer.

3 ) The depleted-layer effect decreases as shear rate increases so that, at the highest shear rates, the apparent viscosity becomes independent of pore size. Moreover, the rodlike conformation of xanthan molecules minimizes viscous friction in zones of converging flow inside the porous structure, so that w dilatant behavior is observed even at the highest flow rates such as those existing around the injection well. The injectability of microgel-free xanthan solutions should be excellent.

4 ) The depleted-layer effect is also observed in Nuclepore membranes, glass bead packs, Carborundum and sand packs,and Sandstones. Thus, this effect seems to be independent of the pore shape and chemical nature of porous media. consistent with the steric origin of this phenomenon.

5) The magnitude of the depleted-layer effect increases sharply with the polymer concentration, as predicted by our model, so that this effect becomes very significant from a practical point of view,

6) The magnitude of the depleted-layer effect increases as sandstone permeability decreases: Microgel-free ranthan solutions can pass easily, with a small apparent viscosity and without any permeability reduction, through sandstones having very low permeabilities.

This is

211

7) The average hydrodynamic diameter of pore throats be deduced by measuring the apparent viscosity of a well-known polymer solution in the Newtonian regime. ing pore structure.

8 ) The effect of the depleted layer, which decreases apparent viscosity mainly in low permeability zones, enables xanthan solutions to sweep. o i l better in heterogeneous formations than conventional fluids having a viscosity that is independent of pore size.

in a given sandstone can

Thus polymer injection is a new method for investigat-

Acknowledments

This research was supported by the Association de Recherches sur les Techniques d'Exploitarion du Petrole ( ARTEP , and Rh6ne-Poulenc Industries provided the polymer sample. Delaplace and R. Tabary who performed laboratory experiments. .

The authors wish to acknowledge the contribution of Ph.

1.

2.

3.

4.

5.

6.

7.

8.

9.

REFERENCES

CHAUVETEAU, G.; Coil Polymer Solution Flow Through Porous Media in Oil Recovery Conditions", paper SPE 10 060 presented at the Annual Technical Conference and Exhibition, San Antonio, Oct. 4-7, 1981.

CHAUVETEAU, G. and MOAN, M.; "The Onset of Dilatant Behavior in Non-Inertial Flow of Dilute Polymer Solutions through Channels with Varying Cross Sections", Journal de Physique-Lettres, 42 (1981) L-201 - L-204. GHONIEM, S., MOAN, M. , CHAUVETEAU, G. and WOLFF, C.; "Mechanical Degradation of Semi-Dilute Polymer Solutions in Laminar Flowr",accepted for publication in Journal of Canadian Chemical Engineering.

MULLER, G., FENYO, J.C., and SELEGNY, E.; "High Molecular weight Hydro- lyzed Polyacrylamides. J. Awl. Pol. Sci., (19801, 25, 627-633.

MULLER, G. ; Aqueous Solutions",

KOHLER, N. , and CHAUVETEAU, G. ; in Porous Media: Preferential Use of Fermentation Broth", J. Pet. Techn. (Feb. 1981) 23, 349-358.

CHAUVETEAU, G., and KOIILER, N.; charide Solutions on Their Flow Behavior Through Various Porous Media", Paper SPE 9295 presented at the 55th Annual Technical Conference and Exhibition, Dallas, Sept. 21-24, 1980.

CHAUVETEAU, G.; macromolecules de taille non negligeable devant les dimensions des pores", C.R. Aced. Sci. Paris, (Feb. 19791, 288, 107-110.

CHAUVETEAU, G. ; Influence of Pore Size on Rheological Behavior", in Journal of Rheology, 1981.

C W U , P. J. ; "Rheological Equations from Molecular Network Theories", Trans. soc. Rheol., (19721, 16, 99-127.

9'Molecular Interpretation of the Different Properties of

I11 Effects of Temperature on Chemical Stability",

"Thermal stability of High Molecular weight Polyacrylamide Polymer Bulletin (to be published).

"Xanthan Polysaccharide Plugging Behavior

"Influence of Microgels in Xanthan Polysac-

"Ecoulement laminaire en milieu poreux de solutions de

"Rodlike Polymer Solution Flow through Fine Pores: Submitted for publication

2 12

10.

11.

12.

13.

14.

15.

16.

17.

18.

19.

20.

HOA, N.T., CHAUVETEAU, G. , GAUDU, R. , and ANNE-ARCHARD, D.; "Relation entre le champ de vitesse dlelongation et l'apparition d'un comportement dilatant d'une solution de pol-re diluee dans un Ccoulement convergent non-inertiel", Submitted for publication in C.R. Acad. Sci. (1981).

MOAN, M. , CHAUVETEAU, G. , and GHONIEM, S.; "Entrance Effects in Capillary Flow of Dilute and Semi-Dilute Polymer Solutions", J. Non.Newt. Fluid. &&. , (19791, 5, 463-474. JOANNY, J.F., LEIBLER, L., and DE GENNES, P.G.; "Effects of Polymer Solutions on colloid stability", J. of Pol. sc. (19791, 17, 1073-1084.

AUVRAY, L.; "Solutions de macromolecules rigides : Effete de paroi, de confinement et d'orientation uar un dcoulement", (Janv. 19811, VOl. 42, 79-95.

DE GENNES , P.G. ; C.R. Acad. Sci. Paris, (April 9, 19791, 288, B y 219-220.

AUBERT, J.H. , and TIRRELL, M. ; "Effective Viscosity of Dilute Polymer Solutions near Interfaces", ACS P olymer Preprint (1981) 22, 1, 82-83.

Journal de Physique

"Ecoulements viscosimetriques de polylderes enchevetres".

BATBA, V.K., and DULLIEN, F.A.L. ; "Correlation between Pore Structure of sandstones and Tertiary Oil Recovery", soc. Pet. Erin. J. (Oct. 19731, 13, 256-258.

METZNER, A.B. ; "Flow of Polymeric Solutions and Emulsions through Porous Media", in "Improved Oil Recovery by Surfactant and polvmer Floodinn", Acad. Press. Inc. , New-York (1977) , 439-451. CHAUVETEAU, G. , and KOHLER, N. ; for Laboratory Evaluation", Recovery Meeting, April 22-24 (1974).

WILLHITE, G.P., and DOHINGUEZ, J.C. ; %Mechanisms of Polymer Retention in

"Polymer Flooding: the Essential Elements Paper S R 4745, presented at the Improved Oil

Porous Media",in Jmroved Oil Recovery by Surfactmt and Polymer Floodinq, Acad. Press. Inc. New-York (1977) ,511-553.

CHAUVETEAU , G. ; "The Effects of Rheological Properties and Polymer-Rock Dimension-Sensitive Interactions on Polyacrylamide Solution Flow through Porous Media", SOC. Rheol. Meeting, Houston, (1978) Oct. 22-26.


THE CHATEAURENARD (FRANCE) POLYMER FLOOD FIELD TEST

A. LABASTIE and L. VIO

Elf Aquitaine ( M u c t i o n )

Abstract

A polymer flood is operated by Elf Aquitaine in the Chateaurenard (France) field, located in the Paris Basin.

The pilot is developped with one injector and seven producers, in a layer of unconsolidated sand, 5 meters thick, at a depth of 600 m ; the 44 ha pattern enclosea a very important pore volume (700 000 m3). The oil is paraffinic and has a viscosity of 40 cPo at reservoir tenperkture (30OC).

The water being almost fresh (0,4 g/l TDS) it has been decided to use hydro- polyacrylamides. Several commercial products have been tested, mainly for viscosity and injectivity ; a liquid polymer, dissolved in produced water, is presently being used for the pilot. The water must be carefully treated before dissolution to avoid polymer degradation and formation plugging.

The injection has been started in 1977 and on account of the quantities injected so far, we have not yet seen any response in the sir main producers (which are at a distance of 400 to 500 m from the injector). But the seventh intermadiate producer, drilled at a shorter distance (280 m) from the injector, has shown vexy interesting results with a sharp decrease of the WOR (WOO tons of tertiaq oil have been produced) ; this response is due to the effect of nobility control, maybe amplified by a local reservoir heterogeneity.

Field deBcriDtion

The Chateaurenard field, outlined in Fig. 1, is part of the Neocomian (Lower Cretaceous) oil reservoirs, found in the southern part of the Paris Basin ; it is located 100 km SSE of Paris, and the oil eone extends over an area of 20 km2.

2 14

Fig. 1 - Map of Chateaurenard field

2 15

Ge ol o m

There are three distinct structures, separated by North-South faults with throws of 15 to 20 m. Situated at a depth of about 600m, the reservoir is formed of three layers of unconsolidated sands separated by shale as depicted on the type - log of Fig. 2 ; the dip of these layers is very slight, about l o . The reservoir concerned by the polymer injection is formed by the two upper levels (R1 and R 2 , belonging to the Hauterivian stage of the Neocomian) of the central structure ; these two levels can be considered as a single reservoir, because the clay layer between them is discontinuous and does not form a tight barrier. The reservoir forms a roughly triangular monocline whose closures are a fault in the east and the wedgeout of the sands in the south.

The deposit of these sands is in the form of submarine channels ; this sedimentation type gives massifs with sharp lateral variations of facies.

T Y P E LOG

CHATEAUR€NARD - St. FIRMIN. CHUtLLLS FIELDS -.

Gamma-Ray Laieroloa

Fig. 2 - Type l og

2 16

Characteristics of R1/R2 reservoir : fluid properties

The reservoir is formed by uadonsolidated sand, with some amount of clay(2 to 15 k). The average total thickness in the pilot area is 5 metres, with a porosity of 30 $. This sandstone is relatively fine but with a wide g r a i n sine distribution (80 to 3 5 0 p Y The average permeabilitg is 1 Darcy (1)m ), but with rather large and unforeseeable variations on account of the channel type sedimentation system.

The fluids are a relatively viscous oil (40 cPo at 30OC, reservoir temperature) of paraffinic type and without dissolved gas, and an almost fresh water ; the relevant characteristics are indicated in the folhing table :

ained (average 150k),

Depth, m (ft) Porosity, $ Permeability, mD Clay content, % Initial water saturation, $ Residual oil saturation, $ Current field avera e oil saturation, $ Temperature, OC ( O P T

Oil gravity, g/cm3 (OAPI) Oil viscosity, aa.s (CPO) Water salinity (TDS), p m Water hardness (Ca + Mgp, ppm

600 (1970) 30

1000 2 to 15 30 30 55 30 (86)

40 (40) 400 70

089 (27)

Production history

The field was discovered in 1958, initial oil in place was estimated at 11 Mm3 (69 millions bbl), with half f o r R1/R2 reservoir. I n 1980, cumulative production was 26 $ of OOIP, mainly through the action of an edge water drive. Because of very small dip a relative permeability curve3 water appeared early in the production and water cut increased quickly ; in 1980, its average value for the field was 89 $. Peak oil production .reached 267 000 m3 in 1964 ; 1980 production was 95 000 m3.

le and adverse mobility ratio (see kn Fig. 3 the

- Relative permeabilities

2 17

POLYMER PILOT DESIGN

Pattern selection

The Chateaurenard field has been developped with an average well spacing of 400 m, and for this polymer pilot it has been decided to use this spacing. The R1/R2 was intergsting for this test, because of the two layers with a discontinuous separation, maybe responsible of poor sweeping efficiency ; but it was necessary that the two layers were not separated at the polymer injectca: well.

After several interference tests, a seven spots pattern has been selected, with one injector (CR 9 bis) and six mpin producers (CR 3 - CR 6 - CR 12 - CR 16 - CR 19 Bis - CR 21 bis) at distances of 400 to 500 meters from the injector ; a seventh intermediate producer (CR 56) has been drilled at a shorter distance from the injector, in order to get an earlier response. This pattern is outlined in Fig. 4.

-Clay isopachs (separation R1 - R2)

Fig. 4 - Polymer pilot pattern

The surface area of this pattern is 44 ha (110 acres), and it encloses a pore volume of 700 000 m3. The mobility ratio is very adverse and before polymer flood, after many years of waterflooding, the oil saturation was still 55 $.

Polymer choice and slug design

The water being almost fresh and the temperature low, hydrolyzed polyacrylamides were selected. To dissolve polymer in produced water was the easiest for field operations, but it can Be detrimental for polyacrylamides stability (1). So we have studied the degradation of polymer in presence of oxygen and iron (little amounts are present in produced water). It has shown that we must avoid the presence of both iron and oxy en, but that little amounts of one of them is not detrimental (see Fig. 5 - 67.

2 18

Fig. 6 - Afte r 2 hours Chemical ctegraduation of polyacrylamides : v i s c o s i t y ($ of i n i t i a l viscoswy

funct ion of Fe and 02 content

2 19

Commercial products were tested mainly for viscosity and injectivity. The injectivity test is a constant flow rate test through a 5,umilliporeR filter , with pressure drop measurement ; the pore size (5p) is similar to the one of Chateaurenard reservoir, and the flow rate is chosen to give same shear rates as in the field flood. This is important because a plugging behaviour can be hidden if the fbw rate is to high, due to microgel deformations in impoktant pressure gradients (2) . This test seems a good screening procedure f o r comparison of products, even if sandpacks floods may be necessary for further investigation. Some results are given in Fig. 7 as an example.

AP millibrn

l i l i r i 5. 64711 I f

. I (liqiil) I (liqiil)

A Sl(prlrr.2lk ritlltticl) . G~(pmhr,ii ritcitiw)

0 5 m 16 ZO ' t i w . h

It has been found that dry polymers (powder) need a retention of several hours after dissolution to become satisfactory on injectivity test. In this example, products A and C1 are good, products B and C2 are not satisfactory (plugging behaviour) ; product A is used for this operation.

Polymer concentration and slug size have been determined by performance predictions with a reservoir model ; a slug of 0,33 PV with 700 ppm polymer has been chosen.

The polymer slug will be followed by water injection, with viscosity decrease designed to prevent deleterious effects of viscous fingering (3).

Surface installations

The polymer solution is prepared with produced water, available in great quantities but not clean : it is contaminated by iron (Fe" and Fe+++), residual oil (1000 ppm), oxygen (< 1 ppm) and clay particles. Removal of oil, clay and insoluble iron is carried out in a flotator using nitrogen, which also strips the water of oxygen traces ; a nitrogen blanket prevents anay oxygen entry. After treatment, the water is $ood for polymer dissolution, with low amounts of oil (< 3 ppm), oxygen (<0,01 ppm) and iron (< 5 ppm). A bacteria killing agent is added to the water, that is filtered before polymer dissolution.

2 20

At the beginning of the operation, dry powder polymer was used, with residence time between dissolution and injection to get good injectivity characteristics. It has been changed for liquid polymer (emulsion), easier to handle and good for injection immediately after dissolution. The fluid flow diagram of Fig. 8 outlines the equipment, that is designed for first dissolution of polymer in a concentrated master solution, and then final dilution ; polymer solution is 5rfiltered at the wellhead before injection, without any problem.

lil

151 I* (IWW TIM

t t t t l i t q c c

PILOT PERFORMANCE : FIRST RESULTS

The polymer injection has begun in 1977. Until 1979, the flow rate was 135 m3/day (850 bbl/day) ; since 1980, it has been increased to 250 m3/day (1 600 bbl/day) ; no injectivity problems were encountered with polymer solution. A slug of 235 000 m3 is to be injeM, with decreasing concentration at the rear front to prevent fingering, followed by water.

Up to 'une 15, 172 700 m3 of polymer solution have been injected (24,7 $ pore volume?.

The six main producers have not yet shown any response, which is normal on account of quantities injected so far.

However, the seventh internlediate producer (CR 56) , has given very interesting results (see-fig. 9). This well, drilled at a distance of 280 m from the injector CR9 bis, has been put into production in 1978. Untgll mid 1979, the water cut was about 90 $, as in the other well of this area, then we observed a sharp decrease to 20 $ of the water cut, which is only 55 $ now (increasing).

9000 tons of tertiary oil have been produced.

The time of oil bank breakthrough is in accordance with our predictions, but it is not possible to explain such an oil cut assuming an homo eneous repar- tition of permeabilities and saturations before polymer flodd fsee predicted and observed production in Fig. 9).

221

A very poorly waterflooded zone (of lower permeability) has been reached by polymer flood, due to mobility control effect. This very good result would have not been possible without mobility control, so it must be attribuBed to the effect of polymer injection. However, this effect has been very important because 6f a local Eeservoir heterogeneity, so such a result cannot be generalized.

But with this channel rtype sedimentation system, some other poorly water-d zones may

We have now to wait for the response of other producers to have a good idea of polymer flodding performance in this field.

exist, which can be swept by polymer flood in good conditions.

h

07

0s

0.2

0

b b -.. .

b

b * b

b b b

CONCLUSIONS

1 - The polymer solution is prepared without problem using produced water,

2 - The solution is easily injected and does not show any plugging behaviour. 3 - A,significant decrease of WOR has been observed in the closest producer

well ; a poorly waterflooded gone has been swept by polymers, due to mobility control effect. go00 tone of tertiary oil have been produced.

which is carefully treated.

222

REFERENCES

1 - G. Chauveteau et N. Kohler - Conditions de stabilit6 des solutions de polymkres lors d'une injection sup champs.

International Symposium on hydrocarbon exploration, drilling and production technics (Paris, 10 - 12 dec. 1975).

2 - G. Chauveteau - The effect of rheological properties and polymer rock dimension sensitive interactions on polyacrylamide solution flow through porous media - 49th Annual Meeting of the Society of Rheology (1978).

3 - E. L. Claridge - A method of design of graded viscosity banks - Paper SPE 6848 presented at 52nd SPE Annual Fall Meeting (Oct. 1977).


CAUSTIC FLOODING IN THE WILMINGTON FIELD, CALIFORNIA LABORATORY, MODELING, AND FIELD RESULTS

VERNON S. BREIT

Scientific Software Cotporntion

EDWARD H. MAYER

THUMS Long Beach Company

JOHN D. CARMICHAEL

City of Long Beach Department of Oil PToperties'

ABSTRACT

A caus t i c enhanced water f lood t e s t i s being conducted i n the Ranger Reservoir o f the Long Beach Uni t , Wilmington F ie ld , C a l i f o r n i a by t h e Department o f O i l Proper t ies o f the City o f Long Beach and i t s f i e l d contractor , THUMS Long Beach Company, i n assoc iat ion w i th the Uni ted States Department o f Energy. The purpose o f the p i l o t demonstration i s t o evaluate the e f f i c i e n c y o f t h e caust ic displacement mechanism i n the environment o f a s t r a t i f i e d , heterogeneous, h igh o i l v i s c o s i t y rese rvo i r where primary waterf lood recovery i s r e l a t i v e l y poor. The t e s t area i s located i n the Ranger Zone o f Fau l t Block V I I w i t h i n the Wilmington F ie ld . The p i l o t t e s t i nvo l ves t h e i n j e c t i o n o f caus t i c s o l u t i o n i n t o a modi f ied staggered l i n e d r i v e we l l pa t te rn cons is t i ng o f e igh t i n j e c t i o n we l l s which surround eleven a c t i v e producers i n an area o f approximately n inety- three acres.

Laboratory i nves t i ga t i ons conducted j o i n t l y by THUMS and the Department o f O i l Proper t ies i nd i ca ted t h a t Ranger Zone crude could be r e a d i l y emuls i f ied i n the presence o f water conta in ing as low as 0.1% by weight sodium hydroxide. Addi t ional o i l was recovered i n core f l o o d s when 1.0 weight percent sodium c h l o r i d e was added t o the a1 k a l i ne so lu t i on .

The r e s u l t s o f t h e l abo ra to ry core t e s t work and t e s t s o f t h e r e a c t i o n between a l k a l i n e so lu t i ons and rese rvo i r sands used i n r e s e r v o i r s imulat ions i nd i ca ted o i l r a t e response and t o t a l incremental o i l recovery are ve ry dependent upon t h e caust ic concentrat ion and caust ic s lug size. A l k a l i n e consumption ca lcu lated t o be very large.

1. Now w i th X t r a Energy Corporation, Signal H i l l , C a l i f o r n i a .

2 2 4

This paper sumnarizes the r e s u l t s o f the caust ic core f l oods which were performed t o evaluate the entrainment mechanism o f o i l displacement and labo ra to ry t e s t s t o evaluate the long term consumption o f hydroxide ions by the rese rvo i r sands. The past performance o f the f i e l d and the rese rvo i r s imulat ion history-match o f t h a t past performance are discussed. The predic ted f u t u r e performance o f the f i e l d f o r both continued water f looding and a caust ic f l o o d i s sumnarized.

A l k a l i n e f a c i l i t i e s were completed and placed i n operation on March 27, 1980. Pre- f lush i n j e c t i o n consisted o f 11.5 m i l l i o n b a r r e l s o f softened f resh water w i th an average o f 0.96 weight percent s a l t . The p re - f l ush amounted t o approximately 10 pore volume percent. A l ka l i ne s o l u t i o n conta in ing 0.4 weight percent sodium o r t h o s i l i c a t e and 1.0 weight percent s a l t i n softened water i s being i n jec ted .

INTRODUCTION

The Wilmington F i e l d i s the l a rges t f i e l d i n Ca l i f o rn ia , F ig . 1. It has seven basic rese rvo i r zones w i th crudes t h a t genera l l y have a r e l a t i v e l y low g rav i t y , h igh v i s c o s i t y and h igh organic ac id content. The recovery e f f i c i e n c y f o r the waterf lood i n the Ranger Zone o f the Wilmington F i e l d has been low due p r i m a r i l y t o a h i g h l y unfavorable m o b i l i t y r a t i o between water and o i l and s i g n i f i c a n t rese rvo i r s t r a t i f i c a t i on.

FIGURE 1 - FIELD LOCATION MAP

225

lQor

I.-@

I I@@:

s : B 3 - 5 z : " , .

S I L

The concept o f a c t i v a t i n g the na tu ra l sur factants present i n the crude o i l by contact w i t h a l k a l i n e water, although l i m i t e d t o rese rvo i r s w i t h s u i t a b l e crude o i l s , has p o t e n t i a l economic advantages over commercial sur factant f looding owing t o the h igh cost o f the su r fac tan ts and t h e low cost o f a l k a l i n e mater ia ls . Several mechanisms have been postu la ted f o r t he improved o i 1 recovery r e s u l t i n g from a l k a l i n e waterf looding. Included among these are e m u l s i f i c a t i o n and entrainment, w e t t a b i l i t y reversa l , and emu1 s i f i c a t i o n and entrapment1 The re1 a t ionship between these poss ib le mechanisms i s necessar i ly more complicated i n caust ic water f looding than sur factant i n j e c t i o n due t o the complexity o f the a l ka l i - c rude o i l r e a c t i o n which would take p lace i n the rese rvo i r .

LABORATORY STUDIES

, I . 1 ' , , ~.bor.iory namuitm dynamical ly d r i ven t o 0 Phi. w,.r minimum water sa tu ra t i on

using Ranger Zone crude - CORE SAMPLt NO.21 o i l . The samples were

then water dr iven at a Q r a t e vary ing from s i x

f e e t per day p r i o r t o water breakthrough t o one f o o t per day a f t e r water

9 i reduct ion was done t o

0 1 ' 1 ' core). The cores were waterf looded t o res idual

Hi.., ; o i l sa tu ra t i on (see Fig. 3' , , # A 1 I 2). Then the cores were

again dynamical ly dr iven I- I - t o minimum water - 9'

s. I OIL m v = sa tu ra t i on using crude I o i l . The enhanced I o r a l k a l i n e water d r i v e I t e s t s were then

s ia n n be u 6s re performed. These t e s t s

A C.nti. S * r l l r - --- S*l"l.,i.. I..*,. -

A - --

do ! # P $0

1% Ir - breakthrough ( the

I :A avoid excessive pressure

0 , gradients w i t h i n the f l

I - w - 0,,1

1 I .

'L' )*on m u A N . c L I O U

I

- I

I

. ' I a I * I * ' a 1 . ' 0 -

Laboratory i nves t i ga t i ons have been performed f o r t h i s a1 k a l i n e p i l o t p r o j e c t t o prov ide comparison core f l o o d t e s t s between water f lood and a l k a l i n e f l o o d recovery and de f i ne the extent o f caust ic consumption by the rese rvo i r rock. The comparative core f l oods were performed w i t h preserved core ma te r ia l which was c u t p a r a l l e l t o the core axis. The plugs measured approximately two inches i n diameter by f i v e inches long. The long term a l k a l i n e comsumption t e s t s were performed w i th sand packs * i c h were prepared i n L u c i t e columns and va r ied i n length from s i x t o twelve inches w i t h a diameter o f approximately one and a h a l f inches.

Comparative Core Flood Studies

Frozen preserved core samples were jacketed on cor ing i n p l a s t i c tub ing. I n the l abo ra to ry the plugs were placed i n a modi f ied Hassler sleeve apparatus, thawed and confined a t 1600 p s i overburden oressure. The cores were heated t o rese rvo i r temoerature o f 125'F and

226

1. I n j e c t water t o breakthrough o r a pre-determined wa te r /o i l r a t i o ;

2. I n j e c t a pre- f lush conta in ing 1% sodium ch lo r i de b r ine i n softened water; and

3. Fol low w i t h an a l k a l i n e - s o f t water s o l u t i o n conta in ing sodium c h l o r i d e a t a concentrat ion o f 1%. ( D i f f e r e n t a l k a l i n e concentrat ions were used i n the various t e s t s performed . )

F igure 2 shows a t y p i c a l response t o t h i s t ype entrainment mechanism a1 k a l i n e waterf looding. (S ix ty- two comparative core f lood t e s t s were performed.) On the average, improvement i n o i l recovery was approximately 10 pore volume percent. No strong c o r r e l a t i o n was found between improvement i n o i l recovery and the concentrat ion of a l k a l i in jected. Therefore, a l l o f the core f l o o d t e s t s were combined and analyzed t o ob ta in a more s t a t i s t i c a l l y meaningful average core response t o a l k a l i n e f looding. These t e s t s were used t o ob ta in r e l a t i v e pe rmeab i l i t y t o o i l and water f o r both the water f lood and the a l k a l i n e f l o o d performance (Fig. 3). These r e l a t i v e pe rmeab i l i t y phenomena were used i n rese rvo i r s imulat ion matches o f i n d i v i d u a l core

FIGURE 3 - OIL/WATER RELATIVE PERMEABILITY

227

t e s t s . They then were scaled f o r the two-dimensional s lug s ize op t im iza t i on cases and f o r a three-dimensional model o f the p i l o t area f o r the caust ic f l o o d p r e d i c t i o n cases.

Long Term A l k a l i n e Consumption I n Reservoir Sands

The e f f e c t o f a l k a l i n e consumption i s a c r i t i c a l economic considerat ion. As a r e s u l t , studies were undertaken i n an attempt t o de f i ne the magnitude o f the caust ic consumption which can be expected t o occur i n an a l k a l i n e f l o o d i n the Ranger Zone o f Fau l t Block VII. The t e s t s conducted included s t a t i c e q u i l i b r i u m tests , reve rs ib le adsorption chemical consumption tests , s e n s i t i v i t y o f caust ic consumption t o f l o w rate, and long-term f l o w tes ts . I n the l a t t e r type t e s t s sand packs were prepared, and f o l l o w i n g water f looding t o breakthrough, s o f t wa te r -a l ka l i so lu t ions w i th 1% sodium ch lo r i de were i n j e c t e d i n t o t h e sand packs f o r per iods ranging between 30 and 104 days. S t a t i c periods o f varying length fo l lowed a f t e r which the a1 k a l i n e i n j e c t i o n was resumed. The o u t l e t caus t i c concentrat ions were measured d a i l y dur ing the e n t i r e f l o w t e s t . It was evident from the t e s t s t h a t t he consumption o f a l k a l i n e ma te r ia l i s a long term phenomenon. The number o f pore volumes o f i n j e c t i o n requi red f o r concentrat ion o f output s o l u t i o n t o reach t h e concentrat ion o f t he i n j e c t e d s o l u t i o n ranged upward t o 38 pore volumes. Reducing the f l o w r a t e o f t h e i n j e c t i o n increased the number o f pore volumes requi red t o reach an e f f l u e n t concentrat ion n e a r l y equal t o the i n l e t concentrat ion. The upper curve o f F ig . 4 shows t y p i c a l r e s u l t s f o r long term a l k a l i n e consumption r e s u l t s where t h e amount o f consumption, i n terms o f mass per u n i t volume i s p l o t t e d versus t h e concentrat ion residence t ime product. The consumption l abo ra to ry work i s described i n more d e t a i l i n t he "Fourth Annual Report" o f t h i s p r o j e c t prepared f o r the U. S. Department o f Energy.2'

FIGURE 4 - LONG TERM ALKALINE COMSUMPTION RELATIONSHIPS

228

RESERVOIR DESCRIPTION

The Wilmington f i e l d i s located i n the south-western p o r t i o n o f Los Angeles, C a l i f o r n i a as shown i n Fig. 1. It i s the l a rges t f i e l d i n C a l i f o r n i a and one o f t h e major f i e l d s i n North America. Cumulative o i l production t o date i s i n excess o f 1 b i l l i o n barre ls .

The f i e l d i s an asymnetrical a n t i c l i n e w i t h a north-west south-east ax is broken by a ser ies o f transverse normal f a u l t s . The f a u l t s d i v ide the rese rvo i r i n t o pools and have proven t o be e f f e c t i v e b a r r i e r s t o f l u i d and pressure comnunication. Dips rang: from a maximum o f 20" on the northern f l a n k t o approximately 60 on the southern f l a n k . The e n t i r e s t ruc tu re i s eleven mi les long and th ree mi les wide under ly ing approximately 13,000 acres. Produci.ng zones i n the F i e l d (Tar, Ranger, Upper Terminal, Lower Terminal, Union Pac i f i c , Ford, and 237) l i e between the depths o f 2,000 and 7,000 f e e t subsea and range i n age from l a t e Miocene t o Pliocene. The upper fou r zones conta in ing low g rav i t y , h igh v i s c o s i t y crude are the major o i l reservo i rs . The r e s e r v o i r rock i n a l l zones i s sandstone w i t h d i f f e r e n t degrees o f consol idat ion and var ied s i l t and c l a y content. The p i l o t pa t te rn area i s i n the eastern p o r t i o n o f t h e Long Beach Un i t o f Wilmington F i e l d between the Juniper0 and Temple Avenue Fau l t s i n the Ranger zone and i s shown i n F ig . 5.

FIGURE 5 - PATTERN AREA SCHEMATIC

The modi f ied l i n e d r i v e con f igu ra t i on of t he pa t te rn represents a t y p i c a l waterf lood we1 1 pa t te rn f o r t he Ranger Zone o f the Long Beach Un i t . Ranger i s t he l a r g e s t and most p r o l i f i c o f t he U n i t ' s rese rvo i r s . It consis ts o f several d i s t i n c t i n t e r v a l s o r subzones separated by impermeable shale sections (see Fig. 6). Each subzone i s an i n teg ra ted sequence of shales and unconsolidated t o semi-consolidated, p o o r l y sorted, medium-to-f i n e grained sands. These s i x subzones l i e a t depths of 2,600 t o 3,400 f e e t w i t h a net th ickness o f 305 fee t . The p roper t i es o f each zone are sumnarized i n Table 1. Productive subzones under ly ing the p i l o t area conta in crudes w i t h a wide range o f

229

SIMULATION YOWL LAYERS RANQEI ZONE - PILOT AREA

TABLE 1 - RESERVOIR CHARACTERISTICS BY ZONE

Ranger Poros i ty* Perm* Net Pay Net Volume Subzone ( f r a c t i o n ) (md) ( f e e t ) (Acre Feet) t0 2 60 2 70 109 9341

F .274 321 52 4578

H .246 179 41 3647

X .265 173 48 4339

G .289 220 29 2655

64 .270 131 26 2331

FIGURE 6 - TYPE LOG * Based on 1600 P S I Conf in ing Pressure Core

Analysis Data and Special Logging Programs.

phys ica l proper t ies. The general c h a r a c t e r i s t i c s o f these p roper t i es are: an o i l g r a v i t y range o f 14'-27' API ; t h e o i l g r a v i t y w i t h i n a subzone depends upon s t r u c t u r a l p o s i t i o n w i t h t h e h igher subzone g r a v i t y a t the h igh s t r u c t u r e pos i t i ons and low g r a v i t i e s a t the lower s t r u c t u r e pos i t i ons . From subzone t o subzone the o i l g r a v i t y depends upon geological age w i th the lower (o lde r ) subzones conta in ing higher g r a v i t y crude and t h e upper subzones conta in ing the lower g r a v i t y crude.

PRODUCTION HISTORY

I n i t i a l development i n the p i l o t area began irr August 1967. A t t h e t ime o f the development, pressure gradients ex is ted across the p a t t e r n w i t h t h e average rese rvo i r pressure being approximately 85% o f hyd ros ta t i c . This phenomenon i s due t o comnunication between the p i l o t and o lde r producing areas i n t h e v i c i n i t y . Waterf looding operations began concurrent ly w i th development. The modi f ied three producing row l i n e d r i v e f l o o d pa t te rn was aided by per iphera l aqu i fe r i n j e c t i o n . The i n i t i a l development o f t he p a t t e r n was completed i n e a r l y 1975. O i l p roduct ion f o r t he p i l o t p a t t e r n area as o f September 30, 1980 was 11,490,000 STB. Cumulative water i n j e c t i o n by the e igh t surrounding i n j e c t i o n we l l s was 55,000,000 STB. O f t h i s amount, t he p i l o t area had produced 38,000,000 STB o f water. (Performance o f the confined pa t te rn i s shown i n F ig . 7.)

2 30

FIGURE 7 - PATTERN AREA OF PERFORMANCE HISTORY

RESERVOIR SIMULATION HODELIN6

The formulat ion o f t he caust ic s imulat ion model has been repor ted i n an e a r l i e r paper by B re i t , e t al3. For enhanced waterf looding, t h e s imulator accounts f o r t he i n j e c t i o n and production o f up to s i x d i f f e r e n t a c t i v e agents i n an aqueous phase. Any o r a l l o f these agents may be caust ic o r polymer type f l u i d s o r a combination o f these types o f f l u i d s . The pr imary displacement e f f e c t s o f a caust ic f l u i d are represented by changes i n r e l a t i v e pe rmeab i l i t i es to o i l and water. This s i m p l i f i e d approach permi ts the modeling o f enhanced recovery p ro jec ts without the necess i ty o f determining the exact mechanisms o f t he displacement i n minute d e t a i l . The model also accounts f o r the consumption o f ac t i ve ma te r ia l w i t h i n a caust ic s lug by three d i f f e r e n t mechanisms: The i n t e r a c t i o n between a caust ic s lug and format ion water t o form p r e c i p i t a t e s o f d i va len t cations, t he instantaneous o r e q u i l i b r i u m adsorption o f caus t i c so lut ion, and the long term k i n e t i c a l l y c o n t r o l l e d i n t e r a c t i o n between caust ic and t h e rock ma t r i x i t s e l f . The pe rmeab i l i t y changes r e s u l t i n g from the d i va len t i o n p r e c i p i t a t i o n were not considered i n the s imulator work f o r t h e Range V I I p i l o t .

The s imu la t i on work was based on the use o f t h e r e l a t i v e pe rmeab i l i t y curves produced i n the l abo ra to ry experiments shown i n Fig. 2, an instantaneous caus t i c consumption o f 0.42 pounds and a maximum long term consumption o f 0.84 pounds per cubic foot . The match o f t h e l abo ra to ry response f o r core experiment No. 21 using these parameters i s shown i n Fig. 2.

231

Caustic Flood Optimization Study

A small area o f the FQ subzone, Fig. 5, including two injectors was selected for s l u g optimization studies us ing the N-HANCE reservoir simulation model. Injection was scaled from the planned f ie ld injection ra te of 34,000 STB per day. The reservoir and waterflood characterist ics of this area are sumnarized i n Table 2.

TABLE 2 - ALKALINE SLUG OPTIMIZATION STUDIES BASE MTA FOR STUDY AREA

Reservoir Pore Volume o f Study Area In i t i a l Oil in Place (TOIP) 1,231,000 STB Waterflood Oil Recovery:

TO 5-01-79 562,000 STB % TOIP 45.65 e PV 29.91

Waterflood O i l Recovery 5-01-79 To economic limit of 150 WOR (11-01-85) 84,000 STB

Cumulative Waterflood Oil Recovery 646,800 STB % TOIP 52.54 % PV 34.42

Injection Rate 5-01-79 on to End 4,806 B/D (7.5 PV%/Yr.*)

Preflush Injection - 1.0% Sa l t in Softened Water Solution (390 Days) 1,874,340 STB

% PV 99.75 Start of Alkaline Injection 5-24-50

1,879,000 RB

Performance of t h i s area of the f i e ld and simulator was characterized by rapid water breakthrough followed by a gradual r i s e i n WOR to i t s current average value of 50. Injection surveys have confirmed that over half the injection water i n these two injectors has entered the Fo subzone leaving it at a much higher average water saturation than lower zones. Results of the optimization study runs are sumnarized in Table 3. In a l l b u t one case, discussed subsequently, the re la t ive permeability adjustment was made l inearly between a1 kaline and waterflood behavior depending on the active alkaline concentration in each ce l l . The low alkaline concentration of 0.4 weight percent in the largest pore volume slug, 60%, produced the greatest amount. of incremental o i l . However, this. increase i n production tended to be at low rates, continuing on to l a t e i n the l i f e of the producers being modeled. In contrast, the higher concentration, smaller slug volume cases produced a m r e rapid oil ra te response as can be seen in Fig. 8. T h i s figure also i l l u s t r a t e s the effect of long term caustic consumption on the projected results.

As can be seen by the results of the three 0.8 weight percent alkali cases, the incremental o i l recovery increases approximately 50% when no long term consumption is assumed to be present. In addition, the o i l ra te reaches a m a x i m u m value approximately 15% higher in the absence of long term consumption.

The re la t ive success of an alkaline flood will be m r e dependent on the o i l recovery at wells f a r removed from the injection rows than of the wells d i rec t ly adjacent to the injectors, because those areas

232

TABLE 3 - ALKALINE SLUG OPTIMIZATION S N D I E S O I L RECOVERY M T A

Economic Incremental O i l Recovery

Descr ip t ion Consumption MST Bbl. Date M Bbl. % TOIP % PV

Waterflood - 84.8 11-01 -85 - - -

A l k a l i n e Long O i l Recovery L i m i t Above Water Flood s1 ug Term (150 WOR)

Pro-Rated A l k a l i n e Re la t i ve Permeabi l i ty Adjustment 3s PV % Accelerated 114.0 - - 89.2 7.25 4.75 0.4% A l k a l i Rate r Accelerated 137.9 9-01-86 53.1 4.31 2.83 0.8% A l k a l i Rate TFVT-- Constant 143.5 6-05-86 58.7 4.77 3.12 0.8% A l k a l i Rate r None 159.8 7-01-86 75.0 6.09 3.99 0.8% A l k a l i

Accelerated 122.1 12-06-85 37.3 3.03 1.99 1.0% A l k a l i Rate 7TFv-T- None 142.3 10-21-85 57.5 4.67 3.05 1.0% A l k a l i

Variable* Rate flinimum ’Threshold A l k a l i n e Re la t i ve Permeabi l i ty Adjustment

0.4% A l k a l i Rate

* 0.4% o r t h o s i l i c a t e f o r f i r s t 1.5 years, 1.0% f o r next 1.0 year, 0.8% f o r 1.0

6 PV % Accel e r a t ed 162.0 2-16-88 77.5 6.30 4.12

% Accelerated 226.0 - - 141.2 11.47 7.51

year, 0.4% f o r 1.0 year and 0.2% f o r 2.0 years.

FIGURE 8 - OIL PRODUCTION RATES SLUG SIZE OPTIMIZATION

233

near the i n j e c t o r s have been more completely swept. The amount o f caus t i c t h a t can be t ransmi t ted through these c loser areas wi thout being consumed i s o f considerable i n t e r e s t . The lower the long term consumption the greater i s t he transmission o f t he caus t i c through the area mear the i n j e c t o r s and out i n t o the r e s t o f the rese rvo i r , (Fig. 9) . This long term consumption i s .dependent upon both the concentrat ion o f the caust ic i n an area and i t s residence time. Increased transmission r a t e s could a lso be expected f o r constant concentrat ion s lug i n j e c t i o n s at accelerated i n j e c t i o n rates.

FIGURE 9 - ACTIVE ALKALI TRANSMITTED THROUGH OPTIMIZATION STUDY AREA

Two add i t i ona l v a r i a t i o n s from the constant concentrat ion cases a l ready discussed were run. F i r s t , a va r iab le concentrat ion case was run i n which the a l k a l i n e content was va r ied from t h e 0.4 weight percent c u r r e n t l y being i n j e c t e d i n the f i e l d t o a maximum o f 1.0 weight percent and then tapered back t o a concentrat ion o f 0.2 weight percent. Tota l a l k a l i i n j e c t e d was the same as i n the p r i o r runs however. Although t h i s run d i d show some minor accelerat ion i n the o i l r a t e response, the cumulative production and the caust ic moving ou ts ide the area were both d isappoint ing i n comparison t o the constant concentrat ion i n j e c t i o n cases.

S im i la r l y , another run was made i n which the change t o the enhanced recovery r e l a t i v e pe rmeab i l i t y curves w i t h i n the model was made at a minimum threshold a1 k a l i concentrat ion which corresponded t o the decrease i n i n t e r f a c i a l tens ion from the l abo ra to ry experiments. This case d i d show a considerably greater o i l production and a s i g n f i c a n t l y higher o i l product ion r a t e than the l i n e a r s h i f t i n from

permeab i l i t y curves. Currently, we are unable t o determine which o f normal wa te r /o i l r e l a t i v e pe rmeab i l i t y curves t o caust ic r e 9 a t i v e

234

these two re la t i ve -pe rmeab i l i t y s h i f t techniques more accurate ly represents t r u e r e s e r v o i r phenomena. Owing t o the f a c t t h a t t he greatest cumulative o i l production was achieved f o r the continuous i n j e c t i o n o f 0.4 weight percent a l k a l i and the equipment l i m i t a t i o n s on i n j e c t i o n concentrat ion and i t s r a t e i n the f i e l d , the 0.4 weight percent constant concentrat ion cases were selected f o r p r e d i c t i o n o f the performance o f the e n t i r e p i l o t area.

Performance Match o f t h e P i l o t Area

The h i s t o r i c a l performance o f the pa t te rn area was matched using a black o i l r e s e r v o i r s imulat ion model conta in ing 1770 g r i d c e l l s i n seven layers, two w i t h i n the Fo subzone, and one layer. i n each o f t he remaining subzones. The model included areas t o both the nor th and south o f t he pat tern, Fig.5.

The i n j e c t i o n i n t o each subzone was spec i f i ed on the basis o f surveys o f the i n j e c t i o n wells. The performance shown i n Fig. 7 was matched by c o n t r o l l i n g t h e amount o f f l u i d which migrated o f f t he pa t te rn area t o the no r th and south, and by minimal changes i n the t runca t ion o f r e l a t i v e pe rmeab i l i t y curves between the pa t te rn and the areas t o the nor th and south.

Predic ted Performance o f t h e P i l o t Area

O i l recovery p r e d i c t i o n cases were run f o r continued waterflood operat ion and f o r t he two caust ic f l o o d cases. One o f these used the prorated a l k a l i n e f l o o d r e l a t i v e pe rmeab i l i t y adjustment, Case I, and the other t h e minimum threshold a l k a l i n e r e l a t i v e pe rmeab i l i t y adjustment, Case 11, o u t l i n e d i n an e a r l i e r section. The r e s u l t s of these p red ic t i ons are sumnarized i n Table 4 and F ig . 10. The

m I

B

I I

FIGURE 10 - OIL PRODUCTION RATES, WATERFLaOD AND CAUSTIG FLOOD CASE I AND CASE I1

235

TABLE 4 - PATTERN AREA PREDICTED PERFORMME THROUGH OECEMBER, 1994

~~ ~

Subzone Waterflood A l k a l i Case I A l k a l i Case I 1 Cum O i l Cum O i l Cum O i l

MSTB MSTB MSTB

4390 4497 4758 2871 2990 3048 1742 1751 1762 H

X 3560 3580 3622 (i 1787 1791 1795 64 699 706 715

F0

TOTAL lnmQ 1m l??OU

predic ted performance of the a l k a l i n e f l ood i n comparison t o continued water f lood i n j e c t i o n i s d isappoint ing. The runs i n d i c a t e t h a t those we l l s i n the f i r s t row o f producers away from the i n j e c t i o n we l l s do respond t o caus t i c i n j e c t i o n . However, these were we l l swept by the i n j e c t i o n water p r i o r t o caust ic i n j e c t i o n leav ing l ess o i l t o respond t o i n j e c t i o n o f caust ic . Add i t i ona l l y , throughout the h i s t o r y o f t he f i e l d , the Fo subzone has taken over h a l f o f the i n j e c t e d water. I n t h e p r e d i c t i o n cases h a l f t he caust ic water continued t o f l o w i n t o t h i s F subzone. Late i n the l i f e o f the f i e l d , s i g n i f i c a n t par ts o f the o i f product ion from the we l l s w i t h i n the pa t te rn i s occurr ing from zones lower than the Fo subzone. As a consequence, the increase o r incremental product ion i n the Fo subzone i s overwhelmed o r masked by the production from lower zones.

m L u s I o I I s

The f i e l d performance t o date and the predic ted performance from the s imu la t i on s tud ies i n d i c a t e t h a t t he re are many complicating f a c t o r s t o t h e successful app l i ca t i on o f a l k a l i n e f l o o d i n g i n a heterogeneous rese rvo i r . The labo ra to ry core t e s t s have confirmed the a p p l i c a b i l i t y o f a l k a l i n e f l o o d i n g t o Ranger Zone crude and r e s e r v o i r rock. However, the h igh degree o f consumption ind icated by l abo ra to ry work and s imulat ion r e s u l t s can be a c o n t r o l l i n g f a c t o r i n the success o f any caust ic i n j e c t i o n p ro jec t . Actual f i e l d r e s u l t s are needed t o c a l i b r a t e t h e consumption parameters t o f i e l d condi t ions.

Min imizat ion of t h i s consumption appears poss ib le by i n j e c t i n g the a l k a l i n e s o l u t i o n a t a higher concentrat ion and/or i n j e c t i n g at a h igher r a t e t o minimize t h e residence t ime i n t h e rese rvo i r . Furthermore, the s imulat ion experience has ind icated the d e s i r a b i l i t y o f c o n t r o l o f t he placement o f i n j e c t i o n f l u i d by subzone ( v e r t i c a l l y ) f o r a more e f f i c i e n t a l k a l i n e i n j e c t i o n p ro jec t .

2 36

REFERENCES

1. Johnson, C.E.: "Status o f Caustic and Emulsion Methods". J- Pet. Tech. (January, 1976) 85-94.

2. "Caustic Waterf looding Demonstration Pro ject , Ranger Zone, Long Beach Unit, Wilmington F ie ld , C a l i f o r n i a . Annual Report f o r the Period June 1979 - May, 1980." Report SAN/12047-4. Prepared f o r DOE by the City o f Long Beach, Department o f O i l Proper t ies and THUMS Long Beach Company under Contract No. E-AC-03-76ET-12047.

3. B re i t , V.S., Mayer, E.H., and Carmichael, J.D.: "An E a s i l y Applied Black O i l Model o f Caustic Waterflooding". SPE Paper No. 7999, Presented at the 1979 C a l i f o r n i a Regional Meeting of SPE o f AIME, Ventura, Ca l i f o rn ia , A p r i l 18-20, 1979.

MISCIBLE GAS DISPLACEMENT 2 3 1

MISCIBLE DISPLACEMENT: ITS STATUS AND POTENTIAL FOR ENHANCED OIL RECOVERY

R. J. BLACKWELL

Exxon Reduction Research Company

Miscible flooding continues to be one of the most intriguing enhanced oil recovery methods because of its potential for recovering all of the oil flushed by solvent; and one of the most exasperating, because only in rare instances have actual field performances come anywhere close to the high recovery efficiencies potentially possible from this process.

History

The concept of miscible flooding is quite old. recognized by the petroleum industry well over 50 years ago and several papers were published in the 1920's describing early research in this area. During the 1930's and early 1940's. interest in enhanced recovery techniques was low; however, following the end of World War 11, there was a dramatic increase in research directed toward improving our knowledge of what might be called the "physics and chemistry of fluid flow in porous media" and toward the development of the three basic areas of enhanced oil recovery--thermal, chemical, and miscible. Investigations into the use of miscible flooding techniques to improve oil recovery was a significant part of this increased effort.

It was an exciting era. fluids could be used for miscible flooding. Almost every available fluid including alcohols, ketones, propane, butane, LPG, nitrogen, carbon dioxide, methane and mixtures of many of the a ove were tested. Some of the first research was on completely misciblel~q (frequently called f irst-contact miscible) systems in which all mixtures of the solvent and oil form a single phase fluid. However, two multiple-contact methods of a hieving miscible displacements4 the high pressure or vaporizing gas method were also developed during the 1950's. fluid which is initially not miscible with the crude, but is able to generate a solvent bank within the porous medium during the displacement process. the high-pressure gas process, the injected gas is enriched with intermediate and higher molecular weight components vaporized from the first crude contacted. If the phase behavior of tht! gas oil system is favorable, a self sustaining solvent bank is formed le in the reservoir. In the mriched-gas process, the enriching components in the injected gas transfer to the crude oil and generate a solvent bank consisting of a modified crude oil. (possibly excluding some asphaltenes) is flushed from the region contacted.

Its potential was generally

Laboratory tests were conducted to determine which

5 and the enriched gas process, Both of the latter involve injection of a

In

ing a small volume of denuded crude as residual

In this process, essentially all of the oil

238

Following the discovery of these three basic approaches and the development of methods for determining the cond1tior.s that each must meet in order to have a miscible displacement, attention was turned (about 1954) to determining the conditions required for effective use of each method in field applications. Initially, the primary objective was to design miscible floods using the smallest amount of LPG or enriched gas possible. ments of the amount of mixing that occurs as fluids flow through porous medin were needed and several companies including Exxon initiated work in this area. At about the same time, we and other research laboratories began our first experimental and theoretical studies of viscous fingering. It rapidly became apparent that, although the effects of mixing must be considered in any attempt to predict miscible flood performance, it was viscous fingering or solvent channeling that would likely dominate the behavior of a miscible flood.

In order to do this, measure-

Viscous fingering was studied in long models, short models, narrow models and wide models. or glass bead packs, and in models containing various permeability heterogeneities. viscous fingering and to quantify its effects, a number of floods were run in each model using fluid systems with different oil/solvent viscosity ratios, viscosity levels and fluid densities. At the beginning of this period, some people hoped that viscous fingering would turn out to be a "laboratory artifact" in the sense that it would be less of a problem in the field than it was in laboratory floods. solvent channeling was a serious problem in field applications and at least as detrimental there as it was in laboratory floods.

Tests were conducted in Hele-Shaw models, in homogeneous sand

In order to establish the physical principles responsible for

However as confirmed later in many field tests,

Nevertheless, there was a general air of optimism during the middle 50's. Many believed that the remaining problems (such as viscous fingering) would soon be solved and that miscible flooding would usher in a new era of high enhanced oil recoveries. tests were initiated. OOIP were obtained in many of these tests. only fell far short of original expectations but were far from being economically attractive.

Because of this optimism, a number of field However, incremental oil recoveries of only 5 to 10%.

These incremental recoveries not

The earlier optimism turned suddenly into pessimism.

The principal reason for the poorer than anticipated recovery efficiencies was severe channeling of the solvent banks. cause of this channeling was reservoir heterogeneities such as permeability variations in different strata, fractures, etc. However, viscous fingering and gravity overriding were invariably major factors--either causing solvent channeling or aggravating the channeling associated with reservoir heterogeneity.

In some instances, the dominant

It is perhaps worthwhile to point out that viscous fingering and the closely rela ed gravity overridg phenomenum had been recognized sometime earlier. Hill in 1952 and Dietz ment fronts and established the critical rate concept for the control of viscous fingering by gravity segregaticn. Unfortunately, practical production rates can be achieved in only a llmif d number of reeervoirs without exceeding the critical rate; hence the incentib trolling solvent channeling was and remains quite high.

f in 1953 discussed gravity stabilization of displace-

for developing other methods of con-

239

Several papers and patents were published during the late 50's and early 60's describing methods that might increase thz reservoir volye swept by the solvent bank. One of the methods was gas-ucter injection which later became known as the WAG process. Several other methods, including the use of polymers, were also investigated. Unfortunately, none appeared particularly attractive at that time; and with the growing disenchantment with miscible flooding, research in mobility control methods dropped to a low level. By default, the WAG approach became the generally "accepted" method for mobility control, but one with obvious deficiencies. In the middle 1970's, several laboratories renewed their research activity in this area and several new patents and papers describing the addition of various surfactants and other modifications to the WAG process have appeared recently. I regret to say however, that in my opinion, no dramatic break- throughs have occurred to date and our ability to control solvent channeling has not changed much since 1960.

Another was thc use of foaming agents.

Nevertheless, miscible flooding technology has advanced significantly during the past two decades. studies have provided additional insight into the dynamics of miscible displacement processes, particularly in the area of C02 - miscible flooding. Numerical methods for simulating process performance have been developed along with better techniques for arriving at the critically important reservoir descriptions used for analysis of field results and in making predictions of the performance and economic viability of a miscible flood in a specific field.

Results from both field applications and laboratory

Field Applications

Miscible gas projects have provided the industry with valuable field data and operating experience during the past 15 years, particularly in the use of C02. Although detailed flood performance information is available from only a few of these projects, the results generally lead one to the same conclusions reached in 1950's--that is, high displacement efficiencies can be achieved in the regions flushed by solvent, but high volumetric sweep efficiencies are possible only if solvent channeling can be controlled effectively.

The early breakthrough of C02 in the largest miscible-C02 flood in the United States, the 30,000 acre Sacroc project in the Kelly-Snyder field of West Texas, provides a dramatic illustration of the problem. C02 injection was initiated in this project in January 1972. year after injection of less than 2% HCPV of CO November 1972, it became necessary to curtail d2 injection when C02 production exceeded the capacity of the esisting gas plants to extract the C02 from produced gas. describes in detail efforts to maintain control of CO production. Two important steps were taken. First, the WAG ratio was increased from its initial value of about 0.5:l to 3:1, and then second, a zonal injection program was initiated to provide an improved distribution of the gas and water into all zones and thereby imprme the overall sweep efficiency. but manageable problem throughout the flood. N rertheless, the extra investment and operating costs involved in recovery, purifying, and reinjecting the produced C02 were significant factors in the 1977 decision to reduce the volume of C02 injected from 20% HCPV as planned originally to about 12% HCPV. corresponding reduction in the estimated incremental oil recovery was from 107 million STB (8.1XOOIP) to 88 million STB (or 6.7XOOIP).

Breakthrough occurred in June of the same In and increased rapidly.

A paper by Kane

2

C02 channeling and production cont iued to be an exasperating

The

2 4 0

In general, the performance of Sacroc and other field experience obtained to date suggests that incremental oil recoveries (over that. possible by water flooding) will most often fall in the range of only 6 to 30 percent of the original-oil-place (OOIP), less frequently in the 10 to 15% range, and will rarely exceed 15% OOIP.

Current Laboratory Research

At the present time, there are a number of industrial and university laboratories actively engaged in miscible displacement research. years these research efforts have emphasized work on CO there has been a limited amount of work on the use of ogher gases such as nitrogen, flue gas and C02 enriched with intermediate hydrocarbons such as propane, butane, etc. As mentioned earlier, several laboratories are investigating different methods for improving volumetric sweep.

Several laboratories are engaged in fundamental studies of phase behavior and C02 flood performance often including measurements of the composition, density and viscosity of individual equilibrium phases of fluids produced during laboratory floods in slim tubes, or through reservoir cores. Equi- librated samples taken from PVT cells are also being analyzed and compared with he slim tube results. A recent U. S. Department of Energy report by Orr et a1 The report describes their comprehensive study of the complex phase behavior of a particular C02- crude oil system in some detail and carefully delineates the reservoir conditions under which liquid-liquid, liquid-liquid-vapor and liquid-vapor equilibrium mixtures were observed. analysis procedure which permits the characterization of the hydrocarbons present in the various fluid combinations described above throughout the CI1 - C36 range (as well as the usual Cl - Cl0 range). Similar studies are being carried out in other laboratories using other C02 - crude oil systems. scaled experimental and theoretical studies of the interactions of phase . behavior, viscous fingering, gravity segregation, rock lithology and heterogeneity, and the relationship between oil remobilization and rock wettability.

Research efforts to develop better mobility control techniques were mentioned earlier. The use of foams is again being investigated and some encouraging laboratory and field test results have recently been reported. I remain skeptical that foam injection, as such, is the solution to the problem of viscous fingering, I feel additional research is merited. the greatest strides in micellar-polymer technology have been made as the result of fundamental studies of the basic mechanisms involved. Similar comprehensive studies are needed using several C02, crude oi?., brine and classes of surfactants at pressures above and below the minimum miscibility pressure and temperatures spanning the range from 20' to 100°C.

In recent flooding, although

5 is an excellent example of this type of study.

It also describes their chromatographic

Nevertheless, there is a need for additional carefully

Even though

In recent years,

Mathematical Simulation

Although worthwhile improvements in our numerical technique. for simulating miscible floods have occurred during the past 15 years, further improvements are greatly needed. The ideal computer program for modelling miscible C02 displacements, for example, must simulate the generation of the miscible rolvent bank, the potential precipitation of a solid (asphaltene) phase, and predict the amount and compositions of the various phases present in every

241

grid block each time step. immobile immiscible hydrocarbon liquid phases (each containing over 30 components), and carbonated water. The simulator must be able to model block-to- block flow of both miscible and immiscible phases, and correctly model the dispersion or mixing of the miscible components transfer of components tetween immiscible phases.

Compositional simulators with sophisticated phase behavior packages and other simulators with specialized capabilities have been developed to model miscible gas processes. Current compositional simulators can model most of the physical and chemical phenomena involved in a miscible flood; unfortunately, none provide all of the features that one might desire. Numerical dispersion remains a serious problem for the grid block sizes typically required in most reservoir studies; viscous fingering is difficult to model and is usually approximated empirically using a mixing parameter model; and computing costs are normally high because of the overall complexity of the simulator. sequently, fully compositional models are frequently not as practical for field wide reservoir engineering studies as they are for special studies such as the simulation of the flood performance of a cross section or a small reservoir pattern area. A particularly important application is their use in conjunction with laboratory tests. This type of application is not only a good way to test the capability of the computer program, but it is also a good way to test our understanding of the chemical and physical processes involved in a miscible gas flood.

Greatly simplified compositional simulators are frequently used for reservoir performance predictions, comparison of different gas injection programs, etc. These simplified simulators normally use a limited number of gas and pseudo components to represent the injected gas, and the natural gas and crude oil (including the asphaltenes).

The number and composition of the required pseudo-oil components can be determined by comparing reservoir model results obtained by use of the simplified computer program with those obtained using a fully compositional simulator. sensitivity studies of flood performance for various geological models of the reservoir, optimization of the WAG ratios, and large scale or field wide stud ies . Other types of simulators, such as modified black oil simulators, are also frequently useful for specialized applications. specialized simulators requires that the user understand the limitations of the various simulators since interpretation of results fs often complicated by the simplying assumptions used. includes comparisons of the advantages and disadvantages of the principal types of "miscible" simulators.

Any grid block may contain a number of mobile and

Con-

Typical applications of the resulting simplified model include

Effective use of these

A recent paper by Todd

RESERVOIR DESCRIPTION

The need for a reliable description of reservoir geology and other re !rvoir engineering data can hardly be overemphasized. the chemistry and physics involved in a miscible displacement, nor how precisely we are able to model these phenomena mathematically, it is not possible to make useful reservoir performance predictions of miscible processes without having a reliable reservoir description. It must be recognized that a much better reservoir description is required for predicting miscible

No matter how well we mow

2 4 2

flood performance than is normally required for a comparable study of a water flood in the same field. scription can lead to significant differences in prediction of miscible flood performance and project economics; whereas, these same changes in reservoir description may be unimportant when predicting the performance and economics of a waterflood.

In the past, the amount, type, and quality of routinely available reservoir description data have been dictated primarily by reservoir engineering needs for conventional primary and secondary recovery processes. Many of the same types of data are needed for predicting miscible flood performance.

Useful geological input includes the depositional environment of the reservoir. Depositional environment data and information on subsequent diagenetic changes of rock matrix can be particularly valuable in predicting continuity of permeable zones, shale deposits or tight streaks, and the frequency and distribution of the openings (or windows) through these impermeable layers. Ac- quisition of this additional reservoir description data can be both difficult and costly, but its acquisition and careful interpretation is absolutely necessary.

Surprisingly small changes in the reservoir de-

EOR Potential For Miscible Processes

United States: the future potential of miscible gas processes and other enhanced recovery processes in the United States. phase behavior concepts used to predict miscible flood performance are well known, one might assume that the incremental oil recovery from miscible flooding could be easily estimated and that the incremental oil volumes predicted by the various studies would be similar in niagnitude with perhaps some differences in timing. the uncertainties in volumetric sweep caused by inadequate reservoir description data, in the estimates of the incremental oil recovery possible over waterflooding and in the economic assumptions used. recovery over that possible from waterflooding, range from an "almost assured" 2 billion barrels* to "possibly optimistic" estimates of over 30 billion barrels. Our own estimates for the incremental reserves that can reasonably be added by the year 2000 fall into the 3 to 5 billion range. estimates will turn out to be far too conservative.

Despite this apparent conversatism, I believe that the United States and possibly Canada will begin to see significant production from miscible gas processes during this decade. Miscible processes have the most potential of the various enhanced oil recovery processes for near-term production of light oil and could begin to make its contribution felt by the mid-1980's. timing for this increased production will be critically dependent on near term investments and development of C02 supplies.

A recent study by Frost and Sullivan" includes a breakdown of their projections of expenditures for enhanced oil recovery in the United States during the 10- year period 1979-88. will grow at a rate of about 25% per year from a level of about $0.7 billion per year in 1980 to $1.4 billion per year in 1984 and should reach a level of about $2.5 billion per year (of which $2.1 billion is for injected gases) in 1988.

During the past decade, there have been numerous studies of

Since the basic displacement mechanisms and

However, this is not what one finds primarily because of

Estimates of the incremental

Hopefully, these

But

F6S predicts that expenditures for miscible gas processes

The total expenditure allotted to miscible gas processes during the

*2 x 109 barrels

243

10-year period was $13.75 billion or 36% of the $38 billion projected for all EOR processes. equipment and services as well as the cost of the injected fluids.

These estimates include projections for oil field

Plans are gearing completion for three new pipelines which will bring over one billion(l0 scf/day of C02 to the Permian basin in West Texas from formations in Colorado and New Mexico. two pipelines in early 1983.

Current plans call for completion of the first

If we assume that injection of 10 k scf of CO barrel of enhanced oil recovery production, tfen C02 from these pipelines would result in an oil production rate of 100 k B/D. current U. S. production (currently about 70 k B/D) from all miscible gas projects.

will provide approximately one

This would more than double

Most of the near term activity will continue to be concentrated in West Texas, but new miscible gas projects are also being considered for several other regions of the U. S., including Louisiana and the Mid-continent area. Most will employ CO with LPG. reservoirs containing high gravity crudes because of miscibility pressure restrictions. For example, nitrogen will be used by Exxon in the 15400 foot, 285'F Jay and Black Jack Creek Fields in Florida. However, in some areas of the U. S. (e.g. in offshore reservoirs) or in Canada, acquisition of adequate supplies of COP at a reasonable cost may not be possible and miscible hydrocarbon gases may be used despite their high cost. Production of 100 k BID is not anticipated outside the Permian Basin of West Texas, until the late 1980's or early 1990's.

Canada: In a recent (March 1980) study12 of the potential of enhanced oil recovery in Canada, it was estimated that miscible gas processes could increase oil recovery by 1.885 billion barrels, 1.352 from hydrocarbon miscible and 0.533 from CO . This base case estimate was made for an assumed oil price of $20 per barref although higher prices ($25 and $100) were used in sensitivity studies. government and the province of Alberta which were in place or announced in lY78. betveen the federal and provincial governments have been completed.

although some projects will use nitrogen or methane enriched 2 The use of nitrogen will usually be limited to deep high temperature

The study utilized the tax and royalty regulations of the federal

Consequently, the study will need to be updated when current negotiations

The study found that the base case estimate of 1.885 billion barrels is extremely sensitive to small changes in the values assumed for recovery efficiency, operating costs, etc. For example, a reduction of only 15% in the assumed recovery efficiency reduced the estimated recovery to 0.476 billion barrels. marginally profitable (high risk) oil is included in the base case estimate. Past experience dictates that without significant increases in oil price, very few projects with marginal screening study economics remain as economically attractive prospects after more detailed studies have been completed. reason is that early recovery estimates almost invariably drop as reservoir geology becomes better defined.

This reduction of almost 75% indicates that a significant volume of

One

Thus the potential for miscible flooding in Canada remains highly uncertain but it appears likely that an incremental production of about 1 billion barrels of oil could be achieved if current technical, economic, and political problems can be resolved.

2 4 4

North Sea: processes frequently starts when a field is still in the early stages of its productive life. potential of various EOR methods in the North Sea have already progressed past the screening stage and more detailed engineering studies are currently in progress for a number of fields.

In recent years, consideration of potential applications of EOR

Thus it is not surprising that the evaluations of the

Although several reservoirs should be good miscible C02 flood candidates, the volume of C02 available is limited. in the North Sea may, in fact, use hydrocarbon gases rather than C02.

Until the C02 supply problem is resolved, it is premature to estimate probable incremental recoveries that can be attributed to future use of miscible gas processes.

Hence, the first miscible gas projects

Other Areas: or planned miscible-gag projects, the two largest miscible gas projects are in Libya and Algeria. in Libya was started in 1969 and has been producing at approximately 100 k BID. producing at approximately 60 k B/D. in various parts of the world with a total production rate of perhaps 500- 1000 BID.

Although North America may have the largest number of existing

Both are hydrocarbon miscible. The Intisar D project

The Hassi Messaoud project in Algeria was started in 1964 and has been There are several other small project

The ultimate potential for the use of EOR processes in the North Sea remains to be determined. initiated in North Sea fields before the end of the decade. Plans for a miscible C02 project onshore in a depleted East Midland oil field and a miscible hydrocarbon project offshore have already been announced. stand that consideration is being given to a surfactant flooding pilot offshore. Undoubtedly, other projects will follow but the bulk of EOR activity in the North Sea will probably not occur until the next decade.

However, I anticipate that several EOR projects will be

Similarly I under-

I am optimistic about the future potential of EOR. shortage of trained scientists and engineers in the area. is increasing rapidly and the outlook for solving the remaining technical problems and designing economically attractive projects is promising. I feel that the thousands of man-years of research that the industry has devoted to the development of enhanced recovery technology are finally beginning to bear fruit. are expanding rapidly throughout the world. increasingly optimistic about EOR potential. the optimism of the 50's and that of the 80's; EOR technology of the 80's is more mature than it was then. capability and limitations of the various methods and the role that EOR can realistically be expected to play in our efforts to meet the world's energy needs.

Currently there is a However, the number

Interest and activity in applying miscible gas and other EOR processes The Industry is once again becoming But there is a difference between

We have a much better understanding of the

I recognize that significant and chal1engit:g problems remain to be solved, but I am confident that the solution to many of these problems can be found and that substantial volumes of EOR production will become economically feasible in the future. Miscible gas processes should make a significant contribution to this ob jec tive .

1.

2.

3.

4.

5.

6 .

7 .

8.

9.

10.

11.

12.

13.

2 4 5

REFERENCES

Everett, J. P. et al: "Liquid-Liquid Displacement in Porous Media as Affected by the Liquid-Liquid Viscosity Ratio and Liquid-Liquid Miscibility,"

Henderson, J. H.: "A Laboratory Investigation of Displacement From Porous Media by A Liquified Petroleum Gas" Trans., AIME 198 (1953) 33.

Whorton, L. P., and Kieschnick, W. F.: "A Preliminary Report on Oil Recovery by High-Pressure Gas Injection," Drilling and Production Pract. ApI. 1950, 247.

Stone, H. L. and Crump. J. S.: "The Effect of Gas Composition Upon Oil Recovery by Gas Drive,"

Hill, S.: "Genie Chemique," Chem. Eng. Sci. (1952) I. NO. 6, p. 246.

Dietz, D. N.:

Caudle, B. H., and Dyes, A. B.: Gas-Water Injection," Trans., AIME. 213, (1958), 281.

Kane, A. V., Sacroc Unit-Kelly Snyder Field," SPE 7091, Presented at Fifth Symposium on Improved Methods for Oil Recovery in Tulsa, Okla., April 1978.

Orr, F. M., Taber, J. J. et al,

Trans., AIME 198 (1950) 215.

Trans., AIME (1956) 207, 105.

Proc., Acad. Scie. Amst. B. (1953) 56, 83

"Improving Miscible Displacement by

"Performance Review of a Large Seale C02-WAG Project

"Displacement of Oil by Carbon Dioxide," U. S. DOEfETf12082-9, May 1981.

Todd, M. R.: "Modeling Requirements for Numerical Simulation of CO Recovery Processes," SPE 7998, presented at the 1979 Regional Meetlng of the SPE (AIME) in Ventura, Calif., April 1979.

-, "#38 Billion Projected for Enhanced Recovery in '80s": Petroleum Engineer International pages 98-100, Feb. 1981.

Prince, J. Philip, "Enhanced Oil Recovery Potential in Canada", Energy Research Institute ISBNO-0-920522-09-2, March 1980.

Chierici, G. L.: "Enhanced Oil Recovery Techniques: State of the Art and Potential" presented at Seminar on Improved Techniaues For the Ex-

Canadian

traction of Primary Forms of Energy sponsored by United Nations Economic Commission for Europe, Vienna, Austria, Nov. 1980.


MISCIBLE GAS DISPLACEMENT 247

THEORETICAL ASPECTS OF CALCULATING THE PERFORMANCE OF COZ AS AN EOR PROCESS IN NORTH SEA RESERVOIRS

DAVID S. HUGES, JOHN D. MATTHEWS, ROBERT E. MOTT

AEE Winfrith, Dorchester, Dorset, DT2 8DH

ABSTRACT

This paper examines some aspects of calculating the performance of COf as a prospective enhanced oil recovery agent in North Sea reservoirs. The paper falls into two areas.

First the problems of predicting the phase behaviour of CO2 with reservoir oils are examined. Although experimental PVT data are available for C02-hydrocarbon systems, these are at lower pressures than prevail in the North Sea. The Peng-Robinson and Generalised Redlich-Kwong equations of state are compared for existing experimental data, and their predictions for miscibility are reviewed for North Sea reservoir conditions. problems of pseudo-components and interaction coefficients are discussed in this context.

Some of the

Second, results are presented of 3-D compositional simulations for a simplified reservoir model based on the Forties Field. The few component equilibrium factors in this model are adjusted to match the equation of state implications discussed above. Current reservoir conditions are found to give an immiscible Cop-displacement. Good sweep efficiencies are obtained in the watered-out reservoir from the immiscible COq-displacement calculations. This occurs because: (i) local displacement efficiency is good as a result of pi1 swelling and transfer of hydrocarbons into the gas stream and (ii) volumetric sweep is good with component exchange between gas and oil reducing viscosity and density differences. The reservoir pressure is then increased to achieve an MCM displacement. Three-dimensional results are obtained which compare the performance of the miscible and immiscible displacement processes. The immiscible results are slightly more attractive, but modelling approximations in both cases may be giving a false impression of the real comparability.

INTRODUCTION

This paper examines some of the problems of predicting oil displacement behaviour by CO2 in the context of typical North Sea field characteristics. For this purpose we have considered both immiscible and miscible CO2 drive in a conceptual reservoir simulation with properties akin to the Forties field.

The first part of the paper is concerned with problems of predicting phase behaviour using equations of state based on the Peng-Robinson and Generalised Redlich-Kwong formulations. of its superior prediction of fluid densities.

Some preference for the latter is given because The use of the Redlich-Kwone

248

equat ion i n a few pseudo-component formulat ion i s i l l u s t r a t e d , w h i c h then d i c t a t e s the choice of an equ i l ib r ium K-factor c o r r e l a t i o n f o r use i n a compositional r e s e r v o i r s imula t ion code. I n the case of t he F o r t i e s f i e l d t h e minimum m i s c i b i l i t y p re s su re is p red ic t ed t o be j u s t above t h e ope ra t ing p res su re , which implies oppor tun i ty t o consider both immiscible o r misc ib l e C02-flooding of the r e s e r v o i r , fol lowing the p re sen t convent ional water f lood.

The second p a r t of t he paper examines both immiscible and misc ib l e o i l displacement by C02 i n a conceptual 5-spot p a t t e r n wi th p r o p e r t i e s akin t o thc F o r t i e s f i e l d . f o r immiscible displacement based on a v e r t i c a l two-dimensional scream-tube sec t ion . A near optimum process i s then evaluated i n a f u l l three-dimensional model. The p red ic t ed immiscible COz-drive i s found t o be more a t t r a c t i v e than expected due t o i t s o i l swe l l ing and mass t r a n s f e r behaviour. Miscible ca l cu la - t i ons f o r t h i s same three-dimensional model have a l s o been undertaken using the Todd and Longstaff mixing approximation i n the s imula t ion code. d i f f e r e n c e s i n recovery e f f i c i e n c y between these two types of displacement a r e bel ieved t o be w i t h i n the unce r t a in ty of t he methods used. i n f luenc ing the r e l a t i v e sweep e f f i c i e n c i e s under immiscible and misc ib l e d r ive a r e discussed.

Various a l t e r n a t i v e COpJwater i n j e c t i o n s t r a t e g i e s a r e compared

The

The f a c t o r s

PVT PROPERTIES OF C02 AND RESERVOIR OILS

Choice of Equation of S t a t e

When p r e d i c t i n g PVT p r o p e r t i e s of r e s e r v o i r f l u i d s from a thermodynamic equat ion of s t a t e , a t y p i c a l approach i s t o use a two cons t an t cubic equat ion based on the Redlich-Kwong equa t ion (Ref I ) which gives a s a t i s f a c t o r y compromise between s i m p l i c i t y and accuracy. The two equat ions which a r e most commonly used, e s p e c i a l l y i n a p p l i c a t i o n s t o C02 systems, a r e the Peng-Robinson (PR) equat ion (Ref 2) and t h e General ised Redlich-Kwong (GRK) equat ion i n a form f i r s t proposed by Zudkevitch and J o f f e (Ref 3 ) .

The Peng-Robinson equat ion t akes t h e form

p = - RT - a(T) 9

\ rb v'(v+b) + b(v-b)

2 2 2 a. = 0.45724 ai R Tci/Pci , bi = 0.07780 R Tci/Pci ,

ai = I + m ( 1 - Tr 1 1.

( 3 )

(4)

(5) 2 m = 0.37464 + 1 . 5 4 2 2 6 ~ - 0 . 2 6 9 9 2 ~ .

The o t h e r symbols have t h e i r convent ional d e f i n i t i o n s which a r e given a t t h e end of t h e paper.

,

249

I n the GRK equa t ion

p = - - RT a

v-b T'v (v+b) ,

and the mixing r u l e s (2) a r e used t o c a l c u l a t e a and b. R a i and S&i a r e temperature dependent func t ions which a r e c a l c u l a t e d f o r each component by f i t t i n g t o the vapour p re s su re and s a t u r a t e d l i q u i d d e n s i t y of t he component a t t h e given temperature. For s u p e r c r i t i c a l temperatures Qa and a r e assumed t o take the same va lues as a t the c r i t i c a l temperature.

The vapour p re s su re and s a t u r a t e d l i q u i d d e n s i t y are normally der ived from c o r r e l a t i o n s i n terms of c r i t i c a l p r o p e r t i e s , normal b o i l i n g po in t and a c e n t r i c f a c t o r , a long wi th a l i q u i d d e n s i t y a t a s i n g l e r e fe rence temperature. The a l t e r n a t i v e procedures suggested by Yarborough (Ref 4) and Coats (Ref 5 ) g ive broadly similar r e s u l t s .

The i n t r o d u c t i o n of t he %parameters is the most s i g n i f i c a n t d i f f e r e n c e between the two equa t ions . I n t h e PR equa t ion the c r i t i c a l Z-factor is n e c e s s a r i l y 0.307 f o r a l l components, whereas f o r l i q u i d hydrocarbons the c r i t i c a l 2 - f ac to r i s known t o be between 0.20 and 0.26. Thus the PR equat ion n e a r l y always unde rp red ic t s t he d e n s i t y of hydrocarbon l i q u i d s . For example, a t 100°C the d e n s i t y of decane is underpredicted by 6% and the d e n s i t y of pentadecane by 12%.

The use of t he %parameters i n t h e GRK equa t ion overcomes t h i s problem ( a t the c o s t of a l o s s of s i m p l i c i t y ) and t h i s equa t ion g e n e r a l l y g ives good p r e d i c t i o n s of l i q u i d d e n s i t i e s i f t he %parameters are chosen appropr i a t e ly .

I n t e r a c t i o n C o e f f i c i e n t s

I n bo th equa t ions the mixing r u l e f o r parameter 'a ' employs b ina ry i n t e r a c t i o n c o e f f i c i e n t s 6 i - which must be determined empi r i ca l ly . I n t e r a c t i o n c o e f f i c i e n t s f o r p a i r s of hyirocarbon components are g e n e r a l l y zero o r ve ry smill (except f o r methane-heavy hydrocarbon p a i r s ) b u t non-zero c o e f f i c i e n t s f o r hydrocarbon-C02 b i n a r i e s are e s s e n t i a l i f accu ra t e p r e d i c t i o n s are t o be obtained, and the choice of i n t e r a c t i o n c o e f f i c i e n t s i s a major, problem when applying an equa t ion of s t a t e t o C02/hydrocarbon mixtures . t o t h i s problem i s t o d e r i v e the i n t e r a c t i o n c o e f f i c i e n t s from d a t a on b ina ry mixtures , b u t t he p r e s s u r e s i n t h e s e b ina ry systems are u s u a l l y much lower than found i n r e s e r v o i r s , and t h e r e is some evidence t h a t t he r e s u l t i n g va lues are n o t opt imal f o r multi-component systems a t h ighe r p re s su res . have found t h a t an i n t e r a c t i o n c o e f f i c i e n t of 0.10 f o r a l l C02-hydrocarbon b i n a r i e s g i v e s reasonable r e s u l t s i n the PR equa t ion f o r t e r n a r y and multi-component systems, while b ina ry d a t a suggest r a t h e r l a r g e r c o e f f i c i e n t s (eg. 0.13 f o r bu tane ) .

A more sys t ema t i c approach f o r C02-hydrocarbon mixtures has been proposed by Turek e t a1 (Ref 6 ) f o r t he GRK equat ion. A second i n t e r a c t i o n c o e f f i c i e n t f o r C02-hydrocarbon b i n a r i e s was introduced by modifying the mixing r u l e f o r t he parameter 'b ' i n equa t ion ( 2 ) , t o read

The convent ional approach

We

j ' b = 1 Z ( 1 + Dij) (bi + b . ) xi x . . 3

2 50

Component

‘6

c7

c8

cIo

‘14

This reduces t o equa t ion (2) when D i j = 0. were assumed t o be r e s p e c t i v e l y q u a d r a t i c and cubic func t ions of hydrocarbon a c e n t r i c f a c t o r , and a l s o Ra and f o r s u p e r c r i t i c a l C02 were assumed t o be quadra t i c func t ions of temperature. The polynomial parameters were then determined by a r e g r e s s i o n a n a l y s i s u s ing phase e q u i l i b r i u m d a t a on f i f t e e n C02-hydrocarbon b i n a r i e s .

These developments t o the GRK equa t ion have emphasised a c c u r a t e p r e d i c t i o n s of phase behaviour r a t h e r than d e n s i t i e s ; no d e n s i t y d a t a were used i n the r eg res s ion a n a l y s i s . f i t t i n g t o b ina ry d a t a is the ove rp red ic t ion of C02 d e n s i t i e s a t high p res su res ; f o r example, a t 100°C the d e n s i t y of C02 is ove rp red ic t ed by 10% a t 200 b a r s and by 19% a t 300 ba r s . equat ion a r e accu ra t e t o w i t h i n 5%, even a t high p res su res . form of the GRK equa t ion is t o be used t o c a l c u l a t e d e n s i t i e s i n a compositional s imulator , some compensating adjustment of the R’s is needed.

These i n t e r a c t i o n c o e f f i c i e n t s

A consequence of the changes t o t h e C02-parameters from

C 0 2 4 e n s i t i e s p red ic t ed by the PR Thus,if t h i s

Mole p e r c e n t

3.06

4.95

4.97

30.21

5.04

Comparison of P r e d i c t i o n s f o r C O ~ / S y n t h e t i c O i l Systems

Component

c2

c3

c4

c5

To i l l u s t r a t e some of t h e s e p o i n t s , t he PR and GRK equa t ions have been used t o p r e d i c t s a t u r a t i o n p res su res and de r i s i t i e s of mixtures of Cog wi th the I0 component s y n t h e t i c o i l whose composition i s given i n Table 1 . Experimental d a t a on t h i s system a t 48.9OC and 65.6OC i s given by Turek e t a l . The c a l c u l a t i o n s were c a r r i e d ou t u s ing the VOLE phase e q u i l i b r i u m code (Ref 7) developed a t AEE Winfr i th . C02-interaction c o e f f i c i e n t s and &parameters were taken from Reference 6 , and i n t e r a c t i o n c o e f f i c i e n t s f o r a l l hydrocarbon p a i r s were set t o ze ro except f o r C I - C I O and Cl-Ci4, where a va lue of 0.01 was used i n o r d e r t o match the observed bubble p o i n t s of the o r i g i n a l o i l . used an i n t e r a c t i o n c o e f f i c i e n t of 0.10 f o r a l l C02-hydrocarbon p a i r s .

I n t e r a c t i o n c o e f f i c i e n t s between C 1 , C2 and C3 wi th C6’ taken from Katz and F i rozabad i (Ref 8). except t h a t t he C I - C I O and C I - C ~ ~ c o e f f i c i e n t s had t o b e inc reased by 0.01 t o f i t t he observed bubble p o i n t of the o r i g i n a l o i l a t 65.6W. However, t he p red ic t ed bubble p o i n t was then i n e r r o r by 21: a t 48.9OC.

I n the c a l c u l a t i o n s wi th the GRK equa t ion the

The PR c a l c u l a t i o n s

hydrocarbons were

Mole p e r c e n t

34.67

3. 13

3.96

5 . 9 5

4.06

TABLE I

COMPOSITION OF SYNTHETIC O I L (Ref 6 )

251

Predicted sa tura t ion pressures a r e shown i n Figure 1 . q u i t e w e l l with the measurements except t h a t the predicted c r i t i c a l points occur a t a ra ther higher C02 concentration. The PR predict ions a re ra ther less accurate , espec ia l ly a t the lower temperature, although some improvement could probably be made by ad jus t ing individual in te rac t ion coef f ic ien ts .

The GRK r e s u l t s agree

L 0 !i

n

MEASURED 414'C 6M.C BUOBLE POINT 0 0

DEW POINT 0

CALCULATED

PR EOUAlION - - - GRK EOUAllON -

* 1 1 I I I 0 0.I ' 0.4 0.6 0 6 1.0

MOLE FRACTION Cq

FIG. 1. SAIURAIION PRESSURES IN THE COz- SYNlHElIC OIL SYSIEM.

700r MEASURED 0

CALCULATED

CREOUAIION - - - CRK EOUATION -

b \

t I I I I I 0 0-2 0.4 0 .6 0.6 1.0

MOLE FRACTION CO2

FIG. 2. DENBlllES OF SATURATED FLUID IN ;HE COz - SYNTHEIIC OIL SYSTEM I&8.9'C 1

Density predict ions a t 48.9OC are shown i n Figure 2. accurate a t low C02 concentrations, but a t high C02-concentration the densi ty is overpredicted by lo%, s ince the densi ty of pure C02 i s overestimated. The PR equation underpredicts d e n s i t i e s by 5 o r 6% a t 48.9OC. and by 3 o r 4% a t 65.6OC. found t h a t while l i q u i d dens i t ies a r e underpredicted by the PR equation, the f r a c t i o n a l changes i n volume due to the addi t ion of COq t o o i l a re represented q u i t e wel l . From these r e s u l t s , and o ther ca lcu la t ions on synthe t ic o i l mixtures, i t appears t h a t ne i ther equation is capable of accurate predict ions of oilIC02 mixtures across the e n t i r e composition range. This implies t h a t some f i t t i n g of parameters t o experimental data is needed i f accurate predict ions of densi ty and phase behaviour a r e t o be obtained simultaneously.

The GRK equation is

This i s cons is ten t with the work of Sigmund e t a1 (Ref 9) . who

252

Pseudo Component Representat ion of Reservoir O i l s

The a p p l i c a t i o n of an equa t ion of s ta te t o s y n t h e t i c o i l s is r e l a t i v e l y s t r a igh t fo rward as i n d i v i d u a l components can be i d e n t i f i e d and r ep resen ted as such i n the t h e o r e t i c a l model. However, the heavy f r a c t i o n s of r e s e r v o i r f l u i d s con ta in so many d i f f e r e n t isomers t h a t i t i s impossible t o i d e n t i f y them i n d i v i d u a l l y , and i t is necessary t o d i v i d e the heavy f r a c t i o n s (normally Cg and above) i n t o pseudo components, each pseudo component r ep resen t ing a group of components having similar p r o p e r t i e s . of parameters f o r t hese pseudo components i s a seve re problem when applying an equa t ion of s ta te t o r e s e r v o i r o i l s , and is p a r t i c u l a r l y s i g n i f i c a n t i n C 0 2 / 0 i l systems, where the heavy f r a c t i o n s have a s t r o n g i n f l u e n c e on the phase behaviour a t high p res su re .

The s e l e c t i o n

A comnon approach is t o d i v i d e the heavy f r a c t i o n i n t o groups, each of which has i n d i v i d u a l components whoge b o i l i n g p o i n t l ies w i t h i n a c e r t a i n range. This is p a r t i c u l a r l y convenient i f a d i s t i l l a t i o n a n a l y s i s has been c a r r i e d o u t on the o i l , as one pseudo component can be assigned t o each ' c u t ' i n the d i s t i l l a t i o n . S p e c i f i c g r a v i t y , average b o i l i n g p o i n t and molecular weight a r e normally determined f o r each ' c u t ' , bu t the equa t ion of s ta te model r e q u i r e s 'pseudo' c r i t i c a l p r o p e r t i e s as inpu t . Various c o r r e l a t i o n s have been proposed f o r determining these p r o p e r t i e s ; f o r example those o f Cavet t (Ref 10) and Whitson (Ref 1 1 ) which are most convenient as they use s p e c i f i c g r a v i t y and average b o i l i n g p o i n t as c o r r e l a t i n g parameters.

A f u r t h e r problem i s the s e l e c t i o n of i n t e r a c t i o n c o e f f i c i e n t s f o r t hese pseudo components. The sys t ema t i c approach t o C02-hydrocarbon i n t e r a c t i o n c o e f f i c i e n t s desc r ibed e a r l i e r has the advantage t h a t i t i s p o s s i b l e t o use t h e func t iona l dependence on a c e n t r i c f a c t o r t o e x t r a p o l a t e the pseudc components. This r o u t e has been followed i n -the p r e s e n t work f o r t he GRK equat ion, while f o r the PR equa t ion a value of 0.1 was used f o r a l l C02-hydrocarbon p a i r s . I n bo th cases the i n t e r a c t i o n c o e f f i c i e n t between methane and the h e a v i e s t f r a c t i o n s (c](j+) w a s ad jus t ed t o match the observed bubble p o i n t of t he o r i g i n a l o i l w i thou t C02. small (around 0.05) f o r the GRK equa t ion , b u t when applying the PR equa t ion t o North Sea o i l s , i t has always been found necessary t o use l a r g e methane- heavy hydrocarbon i n t e r a c t i o n c o e f f i c i e n t s (up t o 0.4) t o f i t t he observed bubble p o i n t s ; these c o e f f i c i e n t s v a r i e d considerably between d i f f e r e n t o i l s and d i d not fol low any obvious sys t ema t i c t r end .

This c o e f f i c i e n t w a s always

Ca lcu la t ions on North Sea o i l s have shown t h a t t he GRK equa t ion p r e d i c t s t he d e n s i t y of o i l without C02 t o w i t h i n a few p e r cen t ; while the PR equa t ion underest imates o i l d e n s i t y by between 10 and Z O X , depending on the c o r r e l a t i o n used t o c a l c u l a t e pseudo component p r o p e r t i e s . However, t o o b t a i n a c c u r a t e d e n s i t i e s w i th the CRK equa t ion i t was necessary t o use the measured d e n s i t y of each ' c u t ' when c a l c u l a t i n g the 0-parameters.

Assessing the va r ious methods f o r c a l c u l a t i n g PVT p r o p e r t i e s f o r C02/reservoir o i l systems is d i f f i c u l t because of t he l ack of experimental d a t a on o i l s f o r which a comprehensive a n a l y s i s of t he h e a v i e r f r a c t i o n s is a l s o ava i l ab le . the s t a g e where i t can g ive r e l i a b l e a p r i o r i p r e d i c t i o n s ( i e . without f i t t i n g t o experimental d a t a ) of t hese p r o p e r t i e s . I n any case i t may prove s impler t o make a few PVT measurements on COZ/oil mixtures , than t o c a r r y o u t t he d e t a i l e d composi t ional a n a l y s i s r equ i r ed f o r i n p u t t o a p r e d i c t i v e equa t ion of s t a t e model.

F u r t h e r work is needed t o develop the equa t ion of s t a t e method t o

253

Predict ion of PVT Propert ies of CO?/Forties O i l Mixtures

A t the present time, no experimental phase behaviour da ta a r e avai lable f o r C02 and North Sea o i l s . s t a t e ca lcu la t ions have been performed t o generate PVT information f o r COZ/Forties o i l mixtures, and t o derive da ta f o r a model with a small number of pseudo components with approximately the same e s s e n t i a l propert ies . 3 and 4 show calculated sa tura t ion pressures and swelling fac tors f o r COq/ F o r t i e s o i l , using the a l te rna t ive PR and GRK equations i n an 18-component model i n the VOLE code (swelling f a c t o r is defined as the volume of o i l plus CO2 a t s a t u r a t i o n pressure r e l a t i v e t o volume of o r i g i n a l o i l a t i t s sa tura t ion pressure) . Both the Whitson and Cavett cor re la t ions were used f o r es t imat ing the proper t ies of the twelve pseudo components t o represent the C6+ f rac t ion . The two GRK ca lcu la t ions pred ic t s imi la r sa tura t ion pressures , while the two PR ca lcu la t ions give s i g n i f i c a n t l y d i f f e r e n t sa tura t ion pressures , depending on which cor re la t ion is used f o r the pseudo component proper t ies . It i s t o be expected t h a t the GRK predict ions a re less s e n s i t i v e t o the pseudo component c o r r e l a t i o n because of the subsequent matching t o the measured density using the *parameters. swelling f a c t o r s as a funct ion of Cop concentration. f a c t o r s f o r sa tura ted o i l a t a typ ica l pressure of 200 bars vary considerably, with values of 1.50 and 1.72 f o r the PR ca lcu la t ions , and 1.58 and 1.64 from the GRK equation.

In the absence of such data , d e t a i l e d equation of

Figures

The various methods give similar predict ions f o r the o i l However, the swelling

These ca lcu la t ions have shown some s i g n i f i c a n t differences between d i f f e r e n t methods f o r pred ic t ing the PVT proper t ies of reservoi r oil/CO2 mixtures. choice of cor re la t ion f o r pseudo component proper t ies appears t o be a t l e a s t as important as the choice of equation of state. t o resolve the posi t ion.

The

Experilqental data a r e needed

G4K + WHITSON - GRK i CAVETT - --- PR + WHITSON -*-• PR + CAVETT * * . - - .

01 I I 1 1

0 0.2 0 4 0.6 0.8 MOLE FRACTION C 0 2

FIG. 3. CALCULATED SATURATION PRESSURES OF FORTIES OIL - C02 MIXTURES

2 5 4

1.8

a P 1 . 6 u 4 U

WHITSON - CAVETT ---- (RESULTS ARE SIMILAR FOR EACH EQUATION OF STATE) CRS CORRELATION * * - * *

1

0.2 0 . 4 0.6 0 . 8

MOLE FRACTION COP

FIG. 4. CALCULATED SWELLING OF SATURATED FORTIES OIL CO2 MIXTURES

The equations of s t a t e were used t o es t imate minimum m i s c i b i l i t y pressure (MMP), using a s implif ied model of the multi-step process leading to mult iple contact misc ib i l i ty . In the numerical procedure adopted i n the VOLE code a t Winfrith, the f l u i d composition a t each s tage is determined by mixing o r i g i n a l o i l with the gas phase from the previous s t a t e i n a multi-step process. For t ies w a s predicted by both PR and GRK models t o be between 210 and 220 bars , compared with a f igure of 240 bars from the l a t e s t cor re la t ion of Holm and Josendal (Ref 12). In the For t ies f i e l d the reservoi r pressure w a s i n t i a l l y 220 bars , but has f a l l e n t o around 180 bars . Thus the ca lcu la t ions suggest t h a t C02-injection i n F o r t i e s would give r i s e t o an i k s c i b l e displacement, but the pressure i s only j u s t below the MMP.

The MMP f o r

Few Component Representation of F o r t i e s O i l

To r e a l i s t i c a l l y represent the PVT behaviour of reservoi r o i l s some 15 t o 40 d i f f e r e n t components (or pseudo components) a r e needed. However, when using a compositional s imulator , i t is e s s e n t i a l t o reduce the number of components so t h a t computing cos ts a r e acceptable. When mathematically s imulat ing a COP flood, the methane and C02 a re normally kept as s ing le components, and between two and four pseudo components a re used t o represent the CT-f rac t ion of the o i l . results unless c e r t a i n parameters have been adjusted t o f i t da ta from experiments, o r from more de ta i led calculat ions. analysis using an equation of s t a t e phase equi l ibr ium code i n which the Q-parameters (or c r i t i c a l p roper t ies i n the PR equation), and i n t e r a c t i o n coef f ic ien ts a r e adjusted u n t i l a good match is obtained. component model within a compositional s imulator , there is l i t t l e t o choose between d i f f e r e n t equations of s t a t e ; i n a l l cases i t should be possible t o obtain an accurate representat ion by tuning appropriate parameters. the few component equation of s t a t e model becomes a sophis t ica ted cor re la t ion with a wider range of v a l i d i t y than the K-value approach.

It is unl ikely t h a t such a coarse representat ion w i l l give accurate

This can be done by non-linear regression

When used i n a few

In essence,

255

In an i d s c i b l e C 0 2 f lood two main recovery mechanisms operate. swelling of the o i l through so lu t ion of C02 and evaporation of c e r t a i n components from the o i l i n t o the produced gas stream. t ions using an equation of s t a t e compositional simulator which has recent ly been developed have demonstrated t h a t these phenomena could be accurately represented i n a few component model. C02 f lood i n a one-dimensional geometry. representat ion of the reservoi r o i l , and the second a 6-component representat ion i n which the parameters were obtained by an averaging procedure chosen t o give the same values of the equation of s t a t e 'a ' and 'b' coef f ic ien ts . After some minor adjustments of the methane-heavy hydrocarbon in te rac t ion coef f ic ien ts , the 6-component and 18-component predict ions of densi ty , v i scos i ty and bubble points agreed everywhere t o within I o r 2%. The o i l composition used was s imi la r t o t h a t found i n the For t ies reservoi r , and the s i x components se lec ted were COP, C1, C2-C5, c6-C1Os Cll-C19 and C20+.

Figure 5 shows the o i l recovery and GOR as a funct ion of the amount of Cog in jec ted , f o r the two d i f f e r e n t representat ions. There is close agreement between the two cases, with o i l recoveries d i f f e r i n g by a t most 0.5%. The recoveries of individual components a r e a l s o i n c lose agreement. r e s u l t s suggest t h a t a s i x component model can give an adequate representat ion of the PVT proper t ies of the f l u i d s , so long as the parameters have been adjusted t o match da ta from experiments o r more de ta i led calculat ions.

They a r e the

One-dimensional calcula-

Two calculat ions were performed f o r a The f i r s t used an 18-component

These

18 COMPONENT MOOEL 0 - l o o r 6 COMPONENT MOOEL -

u 4

z 2

90

O 80 a

5 B 10 0

0

8

8 & 5 0

6 0 w >

0.6 1.0 1.2

LOO0 - d >

a 2000 ~

ul

1000

C O 2 INJECTEO ( I N I T I A L HVOROCARBON PORE VOLUME)

FIG. 5. PREDICTED PERFORMANCE OF ONE DIMENSIONAL DISPLACEMENT OF FORTIES OIL AT 210 BAR C02

THE DISPLACEMENT OF OIL BY C02 I N A CONCEPTUAL RESERVOIR

Calculat ions of o i l displacement by C02 have been performed using a s implif ied three dimensional conceptual reservoi r with proper t ies broadly similar t o those found i n the For t ies f i e l d (Ref 13). A repeated 5-spot p a t t e r n has been assumed i n a 100 m thick sandstone with uniform porosi ty of 27% and permea- b i l i t i e s of 400 mD i n the hor izonta l d i r e c t i o n and 40 mD i n the v e r t i c a l d i rec t ion . a typ ica l value of 700 metres. res idua l o i l from waterflooding was 30%.

The assumed w e l l separat ion between an i n j e c t o r and a producer was The connate water s a t u r a t i o n was 23% and the

Water v i scos i ty was 0.42 cp.

256

The assumption of homogenetity i n the 5-spot pa t te rn allows eight-fold symmetry t o be invoked and a three-dimensional representat ion of a symnetry s e c t o r was used i n the calculat ions. a r e a l mesh p a t t e r n was adopted, based upon uni t mobility p o t e n t i a l flow. a r e a l mesh consisted of 4 stream tubes with 12 subdivisions along each tube the subdivisions being se lec ted t o give equal areas i n the s h o r t e s t stream tube (see Figure 7); t h i s reduces the t i m e s t e p penalty which occurs i n e x p l i c i t calculat ions of sa tura t ions . were assumed, the thickness of the uppermost layers (6 .7 and 13.3m) being smaller than t h a t of the lower layers (20 m) t o allow gravi ty overr ide t o be followed whi l s t economising on the number of meshes. t h i s bas ic mesh arrangement f o r the current comparative exercise was examined by performing mesh refinement ca lcu la t ions i n two dimensions.

Before undertaking ca lcu la t ions of o i l displacement by CO2 in jec t ion , i t was f i r s t necessary t o define the s t a t e of the model reservoi r a f t e r waterflopding. Calculations of waterflood behaviour were performed assuming the 5-spot pa t te rn t o be produced a t a constant r a t e of 5000 m3/day (31000 BPD) with an equal in jec t ion of water i n t o each i n j e c t o r . assuming t h a t the sandstone was predominantly water wet, and the Corey approximation (Ref 1 4 ) was used t o obtain water r e l a t i v e permeabi l i t ies . Imbibition o i l r e l a t i v e permeabi l i t ies were derived by applying the Land concept of reduced f r e e sa tura t ions (Ref 15) t o the Corey drainage approximation. With the r a t h e r coarse leve l of mesh d e f i n i t i o n described above, i t was not thought necessary t o include the marginal e f f e c t s associated with the use of capi l la ry pressure curve, but the calculated d i s t r i b u t i o n of water sa tura t ions a r i s i n g from the model is expected t o be typ ica l of a possible condition f o r a CO2 displacement process.

The calculat ions of waterflood behaviour were performed using the compositional simulator described l a t e r . 1800 days, with a recovery of 51% of the o i l i n place. 50% a t 2100 days when the recovery is 59% of the o i l i n place. condition, most of the unswept o i l was confined t o the two outer stream tubes around the production w e l l . Some underriding of o i l by water had occurred so t h a t the top two layers contained about ha l f of the unswept o i l . This condition when the water cu t reached 50% has been used a s the s t a r t i n g point f o r the CO2 displacement ca lcu la t ions , s ince t h i s may be a typ ica l l imi t ing s i t u a t i o n f o r off-shore water handling.

To reduce mesh or ien ta t ion e f f e c t s , a curv i l inear This

In the v e r t i c a l cross sec t ion , 6 v e r t i c a l l ayers

The broad adequacy of

Relat ive permeabi l i t ies were derived

Breakthrough of water occurs a t the producer a f t e r The water cut rises t o

A t t h i s

Modelling Assumptions Adopted i n Immiscible and Miscible Displacement Calculations

Displacement of o i l by Cop i n the model reservoi r has been s tudied under i d s c i b l e and miscible conditions by performing ca lcu la t ions f o r pressures j u s t below and j u s t above the minimum m i s c i b i l i t y pressure. t iona l Reservoir Simulator, CRS, (Ref 16) used f o r the multi-dimensional immiscible displacement ca lcu la t ions employs equi l ibr ium K-value cor re la t ions f o r ca lcu la t ing phase behaviour, with an equation of state f o r dens i t ies . s i x component representat ion of For t ies o i l described e a r l i e r w a s used i n the study, the parameters i n the K-value cor re la t ion being adjusted t o match the sa tura t ion pressure and swelling fac tors of oil/CO2 mixtures predicted by the de ta i led equation of s t a t e model (see Figure 4), and t o match measured o i l dens i t ies and v i s c o s i t i e s .

The miscible ca lcu la t ions were car r ied out using the Todd and Longstaff mixing model (Ref 17). This is a model f o r a two component, o i l and so lvent , system which assumes d i r e c t m i s c i b i l i t y of the phases. assumption of an e f f e c t i v e o i l v i scos i ty and densi ty , and an e f f e c t i v e gas v iscos i ty and densi ty , using a mixing parameter, w, which has t o be defined by

The Intercomp Composi-

The

The method r e l i e s on the

257

empirical means. f o r t h i s mixing model. ca lcu la t ion and incorporat ing the Todd and Longstaff equations. and C02 proper t ies were entered i n tabular form. Todd and Longstaff calculated the o i l displacement f o r an a r e a l bead pack system which gave good agreement with experimental da ta obtained by Lacey (Ref 18). Good agreement with Lacey's r e s u l t s was a l s o obtained i n the present work using the modified CRS model with a curv i l inear gr id and w = 0.67. There i s , however, no experimental evidence t h a t the mixing model is cor rec t f o r a v e r t i c a l cross sec t ion geometry and the e f f e c t i v e dens i t ies assumed i n the model may not be va l id .

Whilst Todd and Longstaff recommend a value of w = 0.67 f o r a rea l s tud ies , Warner (Ref 19) has recommended a value of w = 0.8 f o r v e r t i c a l cross sect ions and f o r 3-dimensional ca lcu la t ions . In the present s tud ies , a value W = 0.7 was used f o r most of the ca lcu la t ions , but some ca lcu la t ions were a l s o performed using w = 0.5 and w = 1.0 t o assess the s e n s i t i v i t y of the r e s u l t s t o changes i n t h i s fac tor .

The r e l a t i v e permeability treatment i n the models f o r miscible and immiscible displacement a r e very d i f f e r e n t . For immiscible displacement, three phase r e l a t i v e permeabi l i t ies a r e evaluated using Stone's second method (Ref 20). In t h i s approach, the water r e l a t i v e permeability i s a funct ion of the water s a t u r a t i o n only and the gas r e l a t i v e permeability is a funct ion of the gas s a t u r a t i o n only. The o i l r e l a t i v e permeability i s a funct ion of both water and gas sa tura t ions and is given by

The CRS code was modified to provide a s u i t a b l e vehicle This involved bypassing the phase equi l ibr ium

Unmixed o i l Using a value of W = 0.67,

r l r 1

r - (9)

Each of the r e l a t i v e permeabi l i t ies i n immiscible displacement a r e subject t o three-phase hys te res i s e f f e c t s a s the flow regimes change (Ref 21). In a gas dr ive the gas becomes mobile a t an i n i t i a l s a t u r a t i o n of about 0.05,whereas when gas is displaced a trapped gas s a t u r a t i o n of 0.30 i s typica l (Ref 2 2 ) . Fai lure t o account f o r the hys te res i s i n gas r e l a t i v e permeabi l i t ies r e s u l t s i n opt imis t ic recoveries , s ince l i t t l e gas is trapped. The CRS code was therefore modified t o allow f o r gas hys te res i s e f f e c t s . permeabi l i t ies were obtained by applying the Land method (Ref 15) t o the drainage curve calculated from the Corey approximation (Ref 1 4 ) . gas s a t u r a t i o n .(SgF) defined by Land is f i r s t computed a s a funct ion of the cur ren t gas s a t u r a t i o n (S ) and the highest value of gas sa tura t ion previously reached within each gr id f l o c k (Sgmax). The equations a r e

Gas r e l a t i v e

The "free"

I s* - 0.5 [s*g - S*gr +/(s*g - s* l 2 + 4(S* - s*gr)/c gF gr g

where s - s

A value of C = 1.86 was obtained from Equation 10 by s u b s t i t u t i n g a trapped gas sa tura t ion (S ) of 0.30 when the maximum gas s a t u r a t i o n had reached 0.77 ( i e 1- sWc): considered t o be small and were ignored.

gr Hysteresis e f f e c t s i n the o i l and water r e l a t i v e permeabi l i t ies were

258

The r e l a t i v e permeability treatment i n the Todd and Longstaff miscible model i s based upon the assumption t h a t o i l and solvent behave as a s ing le phase. consistency with the waterflood. t h i s s i n g l e hydrocarbon/C02 phase uas given the same r e l a t i v e permeability (krhC) as t h a t of o i l i n water. This implies a res idual hydrocarbon/C02 s a t u r a t i o n a f t e r water dr ive of 0.30. The separate o i l and gas r e l a t i v e permeabi l i t ies were then obtained by making the l i n e a r as sump t ion.

For

S

(13) kro = - So S krhc

g

Hysteresis e f f e c t s i n gas r e l a t i v e permeability were not included i n the miscible ca lcu la t ions , i t being argued t h a t o i l and gas behave as the same phase under miscible conditions.

Two-Dimensional Studies

A number of comparative imniscible displacement ca lcu la t ions have been performed using a v e r t i c a l , two dimensional model t o examine various C02-injection s t r a t e g i e s a f t e r waterflood. This v e r t i c a l model consis ted of the second longest of the four stream tubes i n the mesh scheme i d e n t i f i e d previously. Continuous in jec t ion of C02 (Case a ) was used a s the bas i s of comparison. following a l t e r n a t i v e s t r a t e g i e s were then examined f o r 0.22 PV of in jec ted C02 followed by chase water u n t i l the produced water reaches 90%.

The

Case b In jec t ion of a s ing le s lug of C02 over the f u l l height of the sec t ion

Case c Alternat ing 100 day in jec t ions of Cog and water across the f u l l height of the sec t ion

Case d Simultaneous i n j e c t i o n of C02 i n t o the lower half of the sec t ion and water i n t o the upper half

Alternat ing 100 day in jec t ions of C02 and water, with the COP i n j e c t i o n r e s t r i c t e d t o the lower ha l f of the sec t ion and water i n j e c t i o n r e s t r i c t e d t o the upper h a l f .

Case e

Cases d and e , i f p rac t icable , would both require dual completions with the in jec ted C02 flowing down a c e n t r a l pipe and water through a surrounding annulus. i n d e t a i l . corrosion problems associated with a l t e r n a t i n g C02 and water in jec t ion .

The r e s u l t s of these ca lcu la t ions a re i l l u s t r a t e d i n Figure 6 . the asymptotic value of o i l recovery is 45% of the t a r g e t , with only 15% of the o i l being recovered when 0.22 PV of C02 is in jec ted . a f t e r 0.22 PV COP i n Case b increases o i l production t o 34%, f o r two reasons, namely more of the swollen o i l i s displaced, and some of the C02 is moved t o become e f f e c t i v e i n o ther p a r t s of the reservoi r . Al ternat ing water with the C02 i n Case c reduces the peak value of C02 s a t u r a t i o n a t ta ined i n any gr id block, so t h a t the amount of C02 trapping i s a l s o reduced. A s a r e s u l t , more of the Cog can be mobilised during the subsequent chase water flood and the recovery increases t o 39%.

The p r a c t i c a l problems of dual completions have not been considered However, separat ion of C02 and water w i l l considerably reduce the

With Case a,

Inclusion of chase water

259

In each of the above cases , there is a s i g n i f i c a n t amount of gravi ty override. By i n j e c t i n g C02 i n t o the lower half of the reservoi r with water i n t o the upper h a l f , Case d, gas overr ide is reduced and the o i l recovery i s increased to 59% of the ta rge t . r e s t r i c t i n g the gas to the lower half of the reservoi r and water to the upper h a l f , Case e , produces a f u r t h e r s l i g h t improvement i n o i l recovery t o 62% of the ta rge t .

Alternat ing the gas and water i n j e c t i o n s , whi l s t

0 1ooo

l lYE (DAYS)

FlG.5 COMPARISON OF OIL RECOVFRIES FOR DIFFERENT If4JECTION SlHATEGIES

The ca lcu la t ions f o r C02 i n j e c t i o n i n t o a v e r t i c a l two dimensional model reservoi r have been repeated f o r miscible displacement conditions. Table 2 , the results showed the same trends as those f o r i m i s c i b l e displacement, with Case e again producing the highest l eve l of o i l recovery.

As shown i n

The miscible displacement ca lcu la t ions produced o i l recoveries s l i g h t l y below the immiscible values. This trend i n difference between miscible and immiscible displacement was observed i n a l l of the calculat ions reported i n t h i s paper. The ca lcu la t iona l models described e a r l i e r f o r the two processes involve very d i f f e r e n t physical concepts. A s is discussed l a t e r , current l imi ta t ions i n represent ing these physical concepts a r e thought t o be the reason f o r the somewhat lower calculated o i l recoveries f o r the miscible condition.

Areal sweep e f f e c t s were examined f o r both miscible and immiscible displacement of o i l when a t o t a l of 0.22 PV of C02 is in jec ted , with a l t e r n a t i n g 100 day s lugs of gas and water , followed by chase water. For these ca lcu la t ions , a two dimensional a r e a l model was used with a s i n g l e mesh block i n the v e r t i c a l d i rec t ion . The immiscible and miscible displacements showed o i l recoveries of 61% and 54% of the t a r g e t o i l respect ively. The r e s u l t i n g a r e a l dis t r ibu- t ions of o i l f o r the two processes a re i l l u s t r a t e d i n Figure 7. seen t h a t i n the immiscible case the C02 has been e f f e c t i v e f o r a grea te r d i s tance from the i n j e c t o r than i n the miscible case. consequence of the d i f f e r e n t treatments f o r gas and o i l r e l a t i v e permeabilities i n the two models, which produce d i f f e r e n t values f o r the res idua l gas

It can be

This result i s a d i r e c t

2 6 0

TABLE 2

COMPARISON OF IMMISCIBLE AND MISCIBLE DISPLACEMENT I N A VERTICAL, TWO DIMENSIONAL CROSS SECTION FOR A TOTAL INJECTION OF 0.22 PV OF CO2

Strategy

a

b

c Alternat ing 100 day in jec t ions of C02 and water, followed by chase water

Simultaneous in jec t ion of C02 i n t o lower half of reservoi r and water i n t o upper half followed by chase water

In jec t ion of C02 i n t o lower half of reservoi r and water i n t o upper ha l f with a l t e r n a t i n g - 100 day cycles between C02 and water i n j e c t i o n , followed by chase water

Single s l u g i n j e c t i o n of C02

Single s l u g of C02 followed by chase water

d

e

. -

~ ~~~~

O i l Recovery (2 of Target)

Immiscible

15

34

39

59

62

Miscible

12

29

39

51

52

sa tura t ions . representat ion of gas displacement processes which needs f u r t h e r theoret ica development coupled with experimental information.

The high a r e a l sweep ef f ic iency obtained with the immiscible displacement is caused by two e f f e c t s :

This h ighl ights an important f a c t o r i n the mathematical

( i ) component exchange between o i l and gas reduces the i n i t i a l v i scos i ty r a t i o of 20:l t o 3.2:1

( i i ) up t o one t h i r d of the gas dissolves i n the o i l keeping gas sa tura t ions low and hence maintaining low gas mobi l i t i es .

The e f f e c t of varying the Todd and Longstaff mixing parameter was examined i n the two dimensional s tud ies . 1.0 f o r a l t e r n a t i n g 100 day in jec t ions of Cop and water over the f u l l height of the sect ion. followed by chase water, a r e shown i n Table 3.

TABLE 3

Results of ca lcu la t ions f o r w = 0 . 5 , 0.7 and

It might have

EFFECT OF VARYING TODD AND LONGSTAFF M I X I N G PARAMETER ON OIL RECOVERY FOR WATER ALTERNATING WITH GAS I N TWO DIMENSIONAL STUDIES

( X of t a r g e t )

Ver t ica l Cross Section

Areal Model 44 54 63

261

IMMISCIBLE MISCIBLE

KEY I EOUIVALENT

HVDROCARBON

SATURATION

SO * 0 6 0.07- 0.16 - 0.21-

0.15 0.24 0.33

F I G 7 RESIOUAL HYDROCARBON OlSTRlBUTlON RESULTING FROM 2000 OAY WAG I N AREAL MODEL

been expected that the sensitivity to the value of w would be different in the horizontal and vertical planes, because in the latter the effective densities will influence the override behaviour. This has not occurred in an obvious manner, although the direct link between effective viscosities and densities in the Todd and Longstaff model may not be realistic.

Three-Dimensional Calculations

Calculations of immiscible and miscible displacement of oil have been performed using the three-dimensional conceptual reservoir model described earlier. These calculations were performed assuming the Cop-injection strategy which produced the highest oil recovery in two dimensional studies; ie. injection of C02 restricted to the lower half of the reservoir and water injection restricted to the upper half with alternating 100 day injections of C02 and water, followed finally with chase water across the full height of the column. The results are presented in Figure 8. immiscible displacement was 56% of the oil remaining after waterflood, compared with 51% for miscible displacement. rise immediately after initiation of CO2-injection,but decreased to a level of 50% for about 1000 days before it increased rapidly once more. processes imply a need to handle high water-cuts, but not as high as would be incurred from continued injection of water without C02.

The distributionsof hydrocarbon in the vertical cross section along the second longest streamtube areshown in Figure 9 . gravity on the recovery and show the additional penetration made by the C02

The calculated oil production for

In both cases the water cut continued to

Thus both

These illustrate the effects of

262

FIC. 8. COMPARISON OF IMMISCIBLE AN0 MISCIBLE DISPLACEMENTS FOR THE THREE OlMENSlONAL RESERVOIR MOOEL

(b) MISCIIL DISPLACEMENT

FIG. 9. MSTWEUTIONS OF HYDROCARBON IN A VERTICAL CROSS SECTION OF THE THREE DIMENSIONAL MODEL (HYOROCARBON MASS AS PERCENT WATER FLOOD RESICUAL)

263

during immiscible displacement. immiscible and miscible cases with the previous two-dimensional cross section calculations, and this indicates that selection of that model was a good basis for comparing general injection strategies.

These results are broadly similar for both

Modelling Factors Influencing the Calcu1atio:is

The higher oil recovery calculated for immiscible displacement compared with miscible displacement was unexpected. in the simulation models which need further theoretical and experimental investigation.

However, there are a number of features

Although hysteresis has been introduced into the gas relative permeabilities for the immiscible calculation, the model adopted has certain limitations. The treatment used has considered variations in trapping of the gas phase only, whereas a full treatment should consider all non-wetting phases. However, this introduces new problems in estimating the proportions of oil and gas that are trapped, and there is no experimental evidence to resolve this problem. The relative permeability treatment for the immiscible case, which assumes distinct gas and oil phases, should also change as the displacement process approaches miscibility. cases, only a single C02/hydrocarbon phase exists, and there is no equivalent to the hysterises in trapping of CO2 assumed in the immiscible relative permeability model.

The mixing model used for the miscible calculations is designed to provide effective viscosities in the presence of viscous fingering, whereas the effects of viscous fingering are ignored in the multicomponent immiscible model.. Immiscible viscous fingering may well be important, particularly when miscibility conditions are approached. Predicted recoveries from the immiscible model are therefore likely to be optimistic.

The method of calculating effective oil and solvent densities in the Todd and Longstaff model has not been validated. an important characteristic of miscible gas displacement processes and there is a need to develop and validate an independent mixing model for effective densities. influence on fingering in the areal plane.

In the mixing model for the miscible

Gravity override is

Gravity override may be a partially stabilising

The assumption of instantaneous equilibration over the whole grid block with the multicomponent model causes immiscible predictions to be optimistic. This phenomenon is particularly emFhasised in a coarse mesh arrangement, since it allows substantial amounts of C02 to dissolve in the oil ahead of the displacement front, causing the oil to swell artificially and consequently increasing the mobility ratio. Similarly, the formation of free gas behind the front is inhibited by the coarse mesh mixing.

Oil recoveries with both processes are slightly optimistic because no allowance has been made for the solubility of CO2 in water. of water blocking, preventing the CO2 from contacting some of the oil has also been neglected.

The effect

All of the above factors require more detailed quantatative analysis supported by experimental measurements to allow more definitive comparisons to be made.

2 6 4

Nomenclature

a,b

C

D

K

K r

m

P

R

S

T

V

X

a

6

w

n

Parameters i n equations of s t a t e

Imbibition trapping constant

Binary in te rac t ion coef f ic ien t f o r the parameter 'b'

Vapour-liquid equi l ibr ium p a r t i t i o n coef f ic ien t

Relat ive permeability

Character isat ion constant i n PR equation

Pressure

Universal gas constant

Saturat ion (S* e f f e c t i v e sa tura t ion)

Absolute temperature

Molar volume

Mole f r a c t i o n

Parameter i n PR equation

Binary in te rac t ion coef f ic ien t f o r the parameter 'a'

Acentric fac tor ; empirical mixing par-ameter

Parameter i n GRK equation.

Subscripts

C r i t i c a l property

Free

gas

c r i t i c a l gas

hydrocarbon

components

maximum

o i 1

reduced property

water

connate water

265

Acknowledgement

The work r epor t ed i n t h i s paper has been funded by the Department of Energy. The au tho r s acknowledge the advice given by D r F J Fayers. D r T P Fishlock and >lr R I Hawes and the h e l p of M r I R Hawkyard i n undertaking computations.

References

I .

2.

3.

4.

5.

6.

7.

8.

9 .

10.

1 I .

12.

13.

REDLICH, 0. and KWONG, J.N.S., "On the Thermodynamics of So lu t ions . V. An Equation of S t a t e . F u g a c i t i e s of Gaseous Solut ions" , (February 1949), 44, 233-244.

PENG, D.Y. and ROBINSON, D.B. , "A New Two-Constant Equation of State" , Ind. Eng. Chem. Fundam. (1974) 15, 59-64.

ZUDKEVITCH, D. and JOFFE, J . , "Cor re l a t ion and Product ion of Phase E q u i l i b r i a w i th the Redlich-Kwong Equation of State" , AIChE J n l (19731,

Chemical Reviews.

16, 112-119.

YARBOROUGH, L.; "Applicat ion of a General ised Equation of S t a t e t o Petroleum Reservoir Fluids" , i n "Equations of S t a t e i n Engineering", Advances i n Chemistry S e r i e s , 182, American Chemical Soc ie ty , Washington DC. (1979) , 385-435.

COATS, K.H.; "An Equation of S t a t e Compositional Model", Soc.Pet.Eng.Jn1. (October 1980). 363-376.

TUREK, E.A. e t a l ; "Phase E q u i l i b r i a i n Carbon Dioxide - Multicomponent Hydrocarbon Systems: Experimental Data and an Improved P r e d i c t i o n Technique", paper SPE 9231 presen ted a t the SPE Annual F a l l Technical Conference and Exh ib i t i on , Dallas, September 21-24 1980.

MOTT, R.E., "Development and Evaluat ion of a Method f o r Ca lcu la t ing the Phase Behaviour of Multi-Component Hydrocarbon Mixtures from an Equation of State" , AEEW - R 1331 (1980) .

KATZ, D.L. and FIROZAEADI, A; "P red ic t ing Phase Behaviour of Condensatel Crude-Oil Systems us ing Methane I n t e r a c t i o n Coeff ic ients" . J. Pe t . Tech. (November 1978), 1649-1655.

-

SIGMUND, P.M. e t a l p "Laboratory C02 Floods and. t h e i r Computer Simulation", paper PDlO(5) p re sen ted a t the 10th World Petroleum Congress, Bucharest , 1979.

CAVETT, R.H., "Physical Data f o r D i s t i l l a t i o n Ca lcu la t ions - Vapour-Liquid Equilibrium", Proc. 27 th API Mid-year Meeting, San Francisco, 1962.

WHITSON, C.H., "Charac t e r i z ing Hydrocarbon P lus Fract ions" , paper EUR 183 presen ted a t the European Offshore Petroleum Conference and Exh ib i t i on , London, October 1980.

HOLM, L.WI and JOSENDAL, V.A. , "E f fec t of O i l Composition on Miscible Type Displacement by Carbon Dioxide", paper SPE 8814, presen ted a t the 1st SPE/DOE Symposium on Enhanced O i l Recovery, Tulsa , A p r i l 1980.

HILLIER, G.R.K, COBB R.M., DIMMOCK, P.A.. "Reservoir Development Planning f o r t he F o r t i e s Field" , Paper EUR 9 8 presen ted a t European Offshore Petroleum Conference and Exh ib i t i on , London, October 1978.

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COREY, A.T., "The In te r - re la t ion Between Gas and O i l Relat ive Permeabilities", Producer's Monthly Vol X I X , I , Nov 1954.

LAND, C.S., "Calculation of Imbibition Relat ive Permeability f o r Two and Three Phase Flow From Rock Properties", Trans AIME (1968) , 243, 149- 156.

NOLEN, J.S., "Numerical Simulation of Compositional Phenomena i n Petroleum Reservoirs", SPE Reprint Ser ies No I I , Numerical Simulation (1973) , p 269-284.

TODD, M.R. and LONGSTAFF, W . J . , "The Development, Testing and Application of a Numerical Simulator f o r Predict ing Miscible Flood Performance", J. Pet . Tech. (July 1972), 874-882.

LACEY, J . W . , FARIS, J . E . , BRINKMAN, F.H., "Effect of Bank Size on O i l Recovery i n High Pressure Gas-Driven LPG-Bank Process", J.Pet.Tech (August 1961). 806-816.

WARNER, H.R., "An Evaluation of Miscible C02 Flooding i n a Waterflooded Sandstone Reservoir", J. Pet . Tech (Oct 1977), 1339-1347.

STONE, H.L., "Estimation of Three Phase Relat ive Permeability and Residual O i l Data", J. Can. Pet. Tech. (Oct 1973), 12, 53-61.

BREIT, V.S. and GRAUE, D . J . , "Scaling of Flow Parameters f o r Miscible Gas Flood Simulation Studies", Paper SPE/DOE 9804, Presented a t the Second J o i n t Symposium on Enhanced O i l Recovery, Tulsa, Apri l 1981.

HOLMGREN, C.R. and MORSE, R.A., "Effect of Free Gas Saturat ion on O i l Recovery by Waterflooding" Trans AIME (1951) . 192, 135-140.


OIL RECOVERY BY CARBON DIOXIDE THE RESULTS OF SCALED PHYSICAL MODELS AND FIELD PILOTS

TODD M. DOSCHER, MAHGUIB EL ARABI, SIAVASH GHARIB and RICHARD OYEKAN

Department of Petroleum Engineering, Universiq of Southern clllifornia. Los Angeles, Cdifornia 90007

I. ABSTRACT

C o n s i d e r a b l e e f f o r t s h a v e b e e n expended in t h e p a s t d e c a d e on t h e p o t e n t i a l u s e of c a r b o n d i o x i d e f o r t h e r e c o v e r y of r e s i d u a l c r u d e oil, however t h e r e s u l t s of f i e l d p i l o t o p e r a t i o n s have i n d i c a t e d t h a t very l a r g e q u a n t i t i e s of carbon d iox ide are requ i r ed to r ecove r t h e r e s i d u a l oil.

Sca led p h y s i c a l model s t u d i e s have been under taken i n an a t t e m p t t o de t e rmine whether t h e l a r g e r a t i o s of i n j e c t e d carbon d iox ide t o produced crude o i l . observed i n f i e l d demons t r a t ion p r o j e c t s , are t o be expec ted or a r e due t o some d e f e c t s in t h e a p p l i c a t i o n of t h e p rocess i n t h e f i e l d . The r e s u l t s of t h i s s t u d y h a v e r a t h e r u n e q u i v o c a l l y i n d i c a t e d t h a t t h e h i g h r a t i o s of i n j e c t e d carbon d iox ide t o recovered c rude o i l should i n f a c t be expected.

The expe r imen t s have a l s o shown t h a t a very he ightened e f f i c i e n c y of t h e p r o c e s s c a n b e a c h i e v e d by u s i n g a s l u g of c a r b o n d t o x t d e f o l l o w e d by water. However, t h e r e s u l t s need t o be q u a l i f i e d by n o t i n g t h a t t h e prototype r e s e r v o i r s used i n t h e s e s t u d i e s are very f a v o r a b l e f o r t h e use of CO2*

The recovery mechanism appea r s t o b e c h i e f l y t h e s o l u t i o n of carbon d i o x i d e i n t h e oil, i t s s w e l l i n g and c o n s e q u e n t i n c r e a s e i n m o b i l i t y , and then t h e d isp lacement of t h e swo l l en , mobi le o i l by a gas d r i v e ( i f carbon d iox ide is i n j e c t e d con t inuous ly ) or by water i f a s l u g of carbon d iox ide is f o l l o w e d by t h e l a t t e r . The e f f i c i e n c y o f t h e p r o c e s s is t h w a r t e d by t h e high m o b i l i t y of t h e carbon d iox ide which l e a d s t o v i scous f i n g e r i n g and i ts low d e n s i t y , compared t o water, which l e a d s t o g r a v i t y seg rega t ion .

Exper iments have i n d i c a t e d t h a t n i t r o u s oxide , which a l s o d i s p l a y s a h igh s o l u b i l i t y i n o r g a n i c compounds, is as e f f e c t i v e as carbon d iox ide i n t h e s e model s tud ie s .

11. INTRODUCTION

Much of t h e opt imism concern ing t h e p o t e n t t a l of carbon d ioxide i n r ecove r ing r e s i d u a l c rude o i l has been based on s l i m t ube experiments. A 50 t o 100 f o o t l e n g t h of 3/8 i nch tub ing is packed w i t h sand, f i l l e d wi th crude oil and d i s p l a c e d w i t h carbon d iox ide a t a h igh p res su re , which changes but l i t t l e between e n t r a n c e and o u t l e t because of t h e h igh pe rmeab i l i t y of t h e system. A t y p i c a l r e s u l t of a s l i m t ube exper iment is shown i n F igure 1. On t h e same p l o t is shown t h e v a r i a t i o n i n d e n s i t y and v i s c o s i t y of t h e carbon d iox ide as a f u n c t i o n of t h e p re s su re .

268

5 . 6 . 7

t h e p r e d i c t a b i l i t y of a "minimum m i s c i b i l i t y p r e s s u r e " ; t h a t p r e s s u r e a t which 95% of t h e o i l con ta ined in t h e s l i m t ube is recovered b e f o r e carbon d iox ide breakthrough. There appeared t o be an i m p l i c i t sugges t ion t h a t good recovery would be achieved as long as t h e d i sp lacemen t p r e s s u r e was equa l t o o r g r e a t e r t h a n t h i s v a l u e . G a r d n e r , et .al .8 however showed t h a t t h e h i g h r e c o v e r i e s o b t a i n e d i n s l i m t u b e s is r e l a t e d t o t h e a t t a i n m e n t of a low phys ica l d i s p e r s i o n c o e f f i c i e n t (D/vL), and i t can b e r e a d i l y shown t h a t t h e d i s p e r s i o n c o e f f i c i e n t s achieved in s l i m t ubes a r e very d i f f e r e n t from t h e d i s p e r s i o n c o e f f i c i e n t s o b t a i n e d in r e a l r e s e r v o i r s 9 . Ea r l i e r work on v i scous f i n g e r i n g of cour se showed t h a t s t a b l e p i s t o n - l i k e d isp lacement of one f l u i d by a n o t h e r is e f f e c t e d w h e t h e r t h e f l u i d s a r e m i s c i b l e o r n o t ; even d e s p i t e an adve r se m o b i l i t y r a t i o i f t h e d i ame te r of t h e f low sys tem approaches t h e t h i c k n e s s of t h e f i n g e r s t h a t can be gene ra t ed in t h e sys tem u n d e r s t u d y l o . The j u x t a p o s i t i o n of t h e p h y s i c a l p r o p e r t i e s of c a r b o n d i o x i d e w i t h t h e s l i m t u b e r e c o v e r y as a f u n c t i o n of p r e s s u r e in F i g u r e 1 c e r t a i n l y sugges t s t h a t t h e i n c r e a s i n g recovery is due t o g r a d u a l l y decreasing adve r se m o b i l i t y and g r a v i t y r a t i o s .

E a r l i e r i n v e s t i g a t o r s have d e f i n e d 1 * 2 s 3 * 4 , and t h e n d e b a t e d ,

' O O t A

. \

4 0 0 800 1200 1600

PRCSSURC. PSI

Fig. 1: THE EFFECT OF PRESSURE ON THE DISPLACEMENT OF A 45' CRUDE I N A SLIM TUBE

Warner ' ' s t u d i e d t h e n u m e r i c a l s i m u l a t i o n of c a r b o n d i o x i d e d isp lacement of r e s i d u a l c rude o i l w i th a model t h a t depended on t h e mixing of t h e carbon d iox ide w i t h t h e o i l f o r i t s m o b i l i z a t i o n and t r anspor t . No o i l bank was developed i n t h e s e s i m u l a t i o n s and t h e parameter t h a t e x e r c i s e d t h e c h i e f c o n t r o l o v e r t h e p r o c e s s was t h e g r a v i t y s e g r e g a t i o n of t h e i n j e c t e d carbon d iox ide i n t h e wa te r - f i l l e d r e s e r v o i r . Warner 's n u m e r i c a l r e s u l t s would have s t i l l been poore r had he inc luded t h e very f i n e g r i d t h a t C l a r i d g e l 2 had e a r l i e r shown was n e c e s s a r y f o r v i s c o u s f i n g e r i n g t o b e p rope r ly e x h i b i t e d in a numer ica l model.

The p h a s e b e h a v i o r a s d e s c r i b e d in t h e c u r r e n t l i t e r a t u r e , e.g., Reference 8, shows t h e e x i s t e n c e of a m i s c i b i l i t y gap13 in carbon dioxide- c r u d e o i l s y s t e m s . As t h e c a r b o n d i o x i d e c o n t e n t of t h e s y s t e m is increased , t h e s o l u t i o n of carbon d iox ide in t h e c rude f r a c t i o n a t e s i n t o two o r more phases. One is a s o l u t i o n of carbon d iox ide i n t h e heavy components of t h e c rude . F o r v i r t u a l l y a l l c r u d e o i l s t h a t h a v e been s t u d i e d and r e p o r t e d i n t h e l i t e r a t u r e , t h e s o l u b i l i t y is a b o u t 60 mol p e r c e n t c a r b o n d i o x i d e . The s e c o n d p h a s e is t h e m i x t u r e of t h e l i g h t componen t s of t h e crude and t h e excess carbon d iox ide in t h e system. The l a t t e r phase remains

269

a h i g h l y m o b i l e f l u i d a n d c a n b e e x p e c t e d t o f i n g e r t h r o u g h t h e r e s e r v o i r j u s t as wou ld any low v i s c o s i t y f l u i d . Even i n t h e a b s e n c e of v i s c o u s f i n g e r i n g , a Buckley L e v e r e t t a n a l y s i s 1 4 of t h e i n j e c t i o n of s o l v e n t i n t o a w a t e r e d o u t r e s e r v o i r shows t h a t e a r l y b r e a k t h r o u g h o f a m o b i l e s o l v e n t should be expected.

The f i e l d p e r f o r m a n c e o f t e r t i a r y p i l o t o p e r a t i o n s have i n d i c a t e d t h a t i n d e e d c a r b o n d i o x i d e c a n m o b i l i z e and d i s p l a c e r e s i d u a l c r u d e o i l . The S a c r o c t e r t i a r y i l o t r e c o v e r e d 3% of t h e r e s i d u a l o i l a t a CO /OIL r a t i o of 36 MSCF/BbllP. A t L i t t l e Creek, M i s s i s s i p p i , a s much as 60% 0% t h e o i l conta ined i n a p i l o t p a t t e r n may have been recovered a t a r a t i o of 27.6 MSCF/Bb116. A t L i c k Creek , A r k a n s a s , a p i l o t o p e r a t i o n i n t h e Meakin s a n d i n d i c a t e s t h e r a t i o o f r e c o v e r e d o i l t o i n j e c t e d c a r b o n d i o x i d e w i l l b e 28.4 MSCF/Bbl, a n d t h e l a s t a v a i l a b l e f i u r e s f o r t h e Two F r e d s f i e l d i n West Texas i n d i c a t e a r a t i o of 18 MSCF/Bblq6.

I f t h e s e r a t i o s are p r o j e c t e d t o be v a l i d f o r f u l l s c a l e opera t ion , t h e n t h e e c o n o m i c v i a b i l i t y o f c a r b o n d i o x i d e i n j e c t i o n p r o j e c t s f o r t h e recovery of r e s i d u a l o i l must be re-examined. Even r e - i n j e c t i o n of produced carbon d ioxide , a f t e r r e q u i r e d p u r i f i c a t i o n and dry ing , and account ing f o r i n t e r e s t c h a r g e s due t o t h e d e l a y b e t w e e n i n j e c t i n g c a r b o n d i o x i d e and r e c o v e r i n g t h e c r u d e 01, t h e c i t e d r a t i o s of c a r b o n d i o x i d e i n j e c t e d t o produced o i l would add ove r $20 t o t h e c o s t of r ecove r ing a b a r r e l of o i l by t h e i n j e c t i o n of carbon dioxide.

These s t u d i e s were c a r r i e d o u t i n an a t t e m p t t o de t e rmine whether

s u c h h i g h c a r b o n d i o x i d e / o i l r a t i o s a r e t o b e e x p e c t e d o r a r e due t o s p e c i f i c p e c u l i a r i t i e s of t h e p i l o t and demons t r a t ion tests from which they have emenated.

111. RESULTS OF THE EXPERIMENTAL STUDIES

The expe r imen ta l work was c a r r i e d o u t i n p h y s i c a l l y s c a l e d models of a d i r e c t l i n e d r i v e p a t t e r n , see T a b l e 1. The d e t a i l s of t h e s c a l i n g p r o c e d u r e s t h a t have b e e n u s e d a n d t h e c o n s t r u c t i o n of t h e r e q u i r e d h i g h p r e s s u r e ( t o 5000 psi .) , high t empera tu re ( t o 250'F.) equipment is desc r ibed elsewhere9..

TABLE 1.

PARAMETER MODEL VALUE PROTOTYPE VALUE

PERMEABILITY, MDS. 3.000 20. INJECTION PATTERN LINE DRIVE LINE DRIVF SPACING, INJECTOR TO PRODUCER, FT. 3.08 462.

RESERVOIR THICKNESS, FT. 0.1875 28.2

The r e s e r v o i r chosen f o r t h i s p a r t i c u l a r set of exper iments , i t can be seen , w a s one of r e l a t i v e l y low permeab i l i t y . Th i s was done t o minimize t h e e f f e c t s of g r a v i t y s e g r e g a t i o n and v l s c o u s f i n g e r i n g and thus secu re a r e l a t i v e l y f a v o r a b l e performance.

2 70

A. The P r o d u c t i o n H i s t o r y of R e s i d u a l O i l Recovery by Carbon Dioxide

F i g u r e s 2 t h r o u g h 4 p r e s e n t a t y p i c a l p r o d u c t i o n h i s t o r y f o r t h e d i s p l a c e m e n t of r e s i d u a l c r u d e o i l by s u b - c r i t i c a l c a r b o n d i o x i d e a t 1400 p s i a n d 73OF. I t is r e a d i l y s e e n t h a t water a l o n e is p r o d u c e d a t f i r s t ; i t i s t h e o n l y m o b i l e p h a s e i n t h e r e s e r v o i r f o l l o w i n g a water f l o o d . C a r b o n d i o x i d e a p p e a r s a t t h e p r o d u c i n g e n d o f t h e s y s t e m a f t e r t h e i n j e c t i o n o f a b o u t 0.2 of a p o r e volume, and c r u d e oil p r o d u c t i o n is i n i t i a t e d s i m u l t a - n e o u s l y w i t h t h a t of c a r b o n d i o x i d e .

COa INJECTED IPV)

Fig. 2. PRODUCTtON HISTORY FOR A TYPICAL C 0 2 DIS LACEMENT 45°A.P.I.CRUDE, S0=0.21. P11400 PSI. T=73 g

CO, INJECTED (PV1

F i g - 3 . CUMULATIVE RECOVERY OF OIL AND WATER FOR FXG. 2

The p r o d u c t i o n r a t e of oil r e a c h e s a maximum v a l u e w i t h i n 0.2 t o 0.3 o f a p o r e v o l u m e f o l l o w i n g b r e a k t h r o u g h , b u t t h e r a t i o o f oil t o c a r b o n d i o x i d e in t h e e f f l u e n t c o n t i n u o u s l y d e c r e a s e s a f t e r i t s f i r s t appearance.

271

Fig. 4. PRODUCTION RATE HISTORY FOR FIG. 2

The recovery of t h e r e s i d u a l o i l is never comple te even wi th t h e i n j e c t i o n of s e v e r a l p o r e v o l u m e s o f c a r b o n d i o x i d e , a n d t h i s i s t r u e even which a comple te ly m i s c i b l e hydrocarbon (dodecane) i s s u b s t i t u t e d f o r t h e crude o i l .

I t i s i n f o r m a t i v e t o n o t e t h a t t h e a v e r a g e m o l a r c o n c e n t r a t i o n of c a r b o n d i o x i d e in t h e o i l p h a s e w i t h i n t h e model , c a l c u l a t e d by mater ia l ba lance , r eaches a v a l u e of wel l over 0.6 by t h e time carbon d ioxide breaks t h r o u g h in t h e e f f l u e n t , F i g u r e 5. The i m p o r t a n c e of t h i s o b s e r v a t i o n i n c o n n e c t i o m w i t h t h e r e l a t i o n s h i p o f p h a s e b e h a v i o r t o r e c o v e r y w i l l b e d i scussed l a t e r .

Fig. 5 . AVERAGE MOLAR CONCENTRATION OF CARBON D I O X I D E IN OIL PHASE FOR EXPERIMENT DESCRIBED BY FIGURE 2.

The e f f i c i e n c y o f t h e r e c o v e r y p r o c e s s , e x p r e s s e d i n terms of MSCF/Bbl, i s shown i n F i g u r e 6 f o r v a r i o u s i n i t i a l s a t u r a t i o n s of c r u d e o i l . I t i s s e e n t h a t t h e C 0 2 / 0 1 1 r a t i o s are i n d e e d in t h e r a n g e of 20 t o 30 MSCF/Bbl when r e s i d u a l s a t u r a t i o n s of less than 30% are be ing recovered.

272

I

F i g . 6. THE EFFICIENCY OF OIL RECOVERY BY CARBON D I O X I D E AS A FUNCTION OF INITIAL OIL SATURATION, P=1400 PSI , T - 73OF.

B. E f f e c t of Tempera ture and P r e s s u r e

T h e t e m p e r a t u r e a n d p r e s s u r e a f f e c t t h e d i s p l a c e m e n t of o i l by carbon d i o x i d e i n two i m p o r t a n t a s p e c t s . The f i r s t is r e l a t e d t o t h e f a c t t h a t t h e s e p a r a m e t e r s a f f e c t t h e p h y s i c a l p r o p e r t i e s , v i s c o s i t y and d e n s i t y , which, i n t u r n , a f f e c t f l u i d f l o w i n c l u d i n g t h e d i s p l a c e m e n t of one f l u i d by another . The second is t h e e f f e c t of t e m p e r a t u r e and p r e s s u r e on t h e s o l u - b i l i t y of t h e c a r b o n d i o x i d e i n t h e c r u d e o i l .

From c h e m i c a l t h e r m o d y n a m i c s i t i s known t h a t f o r t h e c a s e w h e r e t h e r e i s n o n e t v o l u m e c h a n g e a t t e n d a n t upon m i x i n g , s o l u b i l i t y of o n e l i q u i d i n a n o t h e r is n o t a p p r e c i a b l y a f f e c t e d by p r e s s u r e , and is i n c r e a s e d by t e m p e r a t u r e . T h i s i n d e e d ' w a s found t o b e t h e case f o r t h e s o l u b i l i t y of l i q u i d c a r b o n d i o x i d e i n h y d r o ~ a r b o n s l ~ . The s o l u b i l i t y of s u p e r c r i t i c a l c a r b o n d i o x i d e i n h y d r o c a r b o n s i n c r e a s e s w i t h i n c r e a s i n 8 p r e s s u r e a n d d e c r e a s e s w i t h i n c r e a s i n g t e m p e r a t u r e . The s o l u b i l i t y of c a r b o n d i o x i d e i n t h e p r i n c i p a l c r u d e oil u s e d i n t h i s s t u d y is shown i n F i g u r e s 7 and 8.

Pool 1 A\ I

Fig. 7. SOLUBILITY OF CARBON D I O X I D E I N 450 CRUDE, SCF/BbL

273

If P a

W i t h t h i s b a c k g r o u n d i n h a n d , s o m e t w e n t y r u n s were c o n d u c t e d t o e v a l u a t e t h e e f f e c t of t e m p e r a t u r e and p r e s s u r e on t h e d i s p l a c e m e n t of c r u d e o i l by c a r b o n d i o x i d e as r e v e a l e d i n t h i s p h y s i c a l l y s c a l e d m o d e l s t u d y . Both c r u d e o i l and a m i s c i b l e hydrocarbon (dodecane) were used a t r e s i d u a l a n d h i g h i n i t i a l s a t u r a t i o n s , a t t e m p e r a t u r e s t o 130°F., a n d o v e r t h e p r e s s u r e r a n g e of 650 ps i . t o 2650 p s i .

The e f f e c t of p r e s s u r e on t h e r e c o v e r y of t h e 45OA.P.I. c r u d e o i l a t s u b - c r i t i c a l t e m p e r a t u r e s is shown i n F i g u r e 9 f o r b o t h r e s i d u a l and h igh i n i t i a l s a t u r a t i o n s . It is a p p a r e n t t h a t t h e e f f e c t of p r e s s u r e a t a sub- c r i t i c a l t e m p e r a t u r e i s v e r y a i g n i f i c a n t i f t h e p r e s s u r e is less t h a n t h e s a t u r a t i o n v a l u e ( a b o u t 900 p s i a t 75OF.), b u t a f u r t h e r p r e s s u r e i n c r e a s e a b o v e t h e s a t u r a t i o n v a l u e h a s o n l y a m i n o r e f f e c t o n r e c o v e r y . F o r t h i s h i g h i n i t i a l o i l s a t u r a t i o n , t h e r e c o v e r y i n c r e a s e s f r o m a meager 20% t o o v e r 6 0 % upon i n c r e a s i n g t h e p r e s s u r e f r o m 6 5 0 p s i . t o 1,000 p s i , b u t i n c r e a s e s f rom 63% t o o n l y 71% when t h e p r e s s u r e is i n c r e a s e d a n o t h e r 1000 p a l t o 2 0 0 0 p s i .

The d r a m a t i c i n c r e a s e i n t h e recovery as t h e p r e s s u r e is i n c r e a s e d f r o m 6 5 0 p s i t o 1000 p s i a t 75OF. p a r a l l e l s a m a r k e d i n c r e a s e i n t h e d e n s i t y of carbon d e n s i t y f rom 0.11 t o 0.74 g/CC. The d e n s i t y of t h e carbon d i o x i d e i n c r e a s e s f r o m 0.22 t o 0.70 t o 0.76 a s t h e p r e s s u r e i n c r e a s e s f r o m 1 1 5 0 t o 2 1 5 0 p s i . a n d f i n a l l y t o 2 6 5 0 p s i . T h i s t r a n s l a t e s t o a d e n s i t y d i f f e r e n c e b e t w e e n d i s p l a c i n g f l u i d a n d d i s p l a c e d f l u i d ( w a t e r ) o f 0.78, 0.30, and 0.24 g/cc. A s i m p l e f o r c e b a l a n c e t h e n shows t h a t t h e same d e g r e e of g r a v i t y s e g r e g a t i o n t h a t o c c u r s a t a p r e s s u r e of 2150 p s i c a n be achieved

274

a t 1 1 5 0 p s i o n l y by i n c r e s i n g t h e r a t e by a f a c t o r of t h r e e . Hence , t h e p o o r e r e f f i c i e n c y a t 1 1 5 0 p s i as c o m p a r e d t o t h a t a t 2 1 5 0 p s i i s p r o b a b l y due p r i m a r i l y t o a g r e a t e r d e g r e e of g r a v i t y s e g r e g a t i o n a t t h e l o w e r p r e s s u r e . Between 2150 p s i and 1650 p s i , t h e small d i f f e r e n c e i n recovery i s p r o b a b l y due t o t h e c o m b i n e d e f f e c t of s m a l l d i f f e r e n c e s i n b o t h s o l u b i l i t y and g r a v i t y s e g r e g a t i o n .

leiend 0 A 0 0 1 - S P n r v r e W ) ZOO0 lo00 800 1870 1180 lo00 21BO

0.21 0.21 0.11 0.18 0.18 0.18 0.18

CO, INJECTED WVI

Fig.9. THE EFFECT OF PRESSURE ON RECOVERY

OF CRUDE O I L BY CARBON D I O X I D E AT 73'F*

A t a s u p e r - c r i t i c a l t e m p e r a t u r e t h e e f f e c t o f p r e s s u r e on t h e r e c o v e r y of r e s i d u a l c r u d e o i l i s s i m i l a r t o i t s e f f e c t a t s u b - c r i t i c a l v a l u e s a l t h o u g h t h e r e c o v e r y l e v e l s a r e s o m e w h a t less t h a n a t t h e l o w e r t e m p e r a t u r e , F i g u r e 10.

COa INJECTED (PV)

Fig . 10. THE EFFECT OF PRESSURE ON RECOVERY OF CRUDE OIL AT 130°F*

275

To f u r t h e r s tudy t h e r o l e of d e n s i t y on t h e d isp lacement of carbon d ioxide , a set of expe r imen t s were performed over a range of t empera tu res and p r e s s u r e s where t h e d e n s i t y could be main ta ined r e l a t i v e l y cons t an t by m a n i p u l a t i n g t h e s e two p a r m e t e r s . A t 1400 p s i . a n d 75’F. t h e d e n s i t y of c a r b o n d i o x i d e i s 0.82, as i t i s a t 2700 p s i . a n d 125OF. e v e n though t h e t e m p e r a t u r e s a r e be low and a b o v e t h e c r i t i c a l t e m p e r a t u r e , r e s p e c t i v e l y . The r e s u l t s of two runs , one a t each of t h e fo rego ing sets of parameters , is shown i n F i g u r e 11 a n d i t i s r e a d i l y s e e n t h a t t h e r e s u l t s of t h e two r u n s can be superimposed on each o ther .

--I I

COi INJECTED (PVI

Fig. 11. THE COMPENSATING EFFETS OF TEMPERATURE AND PRESSURE

ON THE DISPLACEMENT OF RESIDUAL CRUDE O I L

To g a i n s t i l l f u r t h e r i n s i g h t i n t o t h e d isp lacement of crude o i l by carbon d iox ide , t h e e f f e c t of p r e s s u r e on t h e d isp lacement of a comple te ly m i s c i b l e hydrocarbon was i n v e s t i g a t e d as a f u n c t i o n of p re s su re , F igure 12.

, It is appa ren t t h a t t h e e f f e c t of p r e s s u r e is t h e same f o r t h e d isp lacement of dodecane a s i t i s f o r t h a t o f c r u d e o i l ; i t is t h e r a t e of change of s o l u b i l i t y w i t h p r e s s u r e t h a t a f f e c t s t h e r a t e of change of recovery wi th p r e s s u r e whether t h e d i s p l a c i n g f l u i d is r i s c i b l e or not.

--I

U

COa INJECTED IPV)

Fig. 12 . THE EFFECT OF PRESSURE ON THE DISPLACEMENT OF DODECANE BY CARBON D I O X I D E

276

C. E f f e c t of I n j e c t i o n Rate

Exper iments were conducted a t p r o t o t y p e v e l o c i t i e s v a r y i n g f rom 0.05 t o 0.4 f o o t p e r day. F i g . 1 3 s h o w s t h a t i n c r e a s i n g t h e v e l o c i t y o v e r t h e i n d i c a t e d range r e s u l t s i n a s l i g h t improvement i n recovery. However, t h e e f f e c t is s e n s e d o n l y i n t h e la ter l i f e of t h e f lood .

Some e x p e r i m e n t s were c o n d u c t e d a t s t i l l l o w e r r a t e , b u t g r a v i t y s e g r e g a t i o n d o m i n a t e d t h e s y s t e m a n d t h e c r u d e o i l r e c o v e r y d e c r e a s e d r a p i d l y .

80

COa INJECTION IPV)

Fig. 13. THE EFFECT OF VELOCITY (OR INJECTION RATE) ON THE RECOVERY OF CRUDE O I L BY CARBON DIOXIDE

D. The E f f e c t of I n i t i a l Oil S a t u r a t i o n .

T h e i n i t i a l o i l s a t u r a t i o n h a s a v e r y d i r e c t e f f e c t o n b o t h t h e f r a c t i o n a l o i l r e c o v e r y , a n d t h e r e s u l t i n g c a r b o n d i o x i d e / o i l r a t i o , see Fig. 14. The o i l recovery is o n l y 50% of t h e r e s i d u a l s a t u r a t i o n b u t c l i m b s t o 80% of t h e i n i t i a l o i l s a t u r a t i o n when t h e l a t t e r is 80%.

%(PVl .77 .63 29, 2 3 1 1 1 I I I -

0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2D CO, INJECTED IPV)

Fig. 14 . THE EFFECT OF INITIAL OIL SATURATION ON OIL RECOVERY

277

The d i f f e r e n c e I n t h e e f f i c i e n c y of t h e d i s p l a c e m e n t is d i r e c t l y r e l a t e d t o t h e f a c t t h a t when a low o i l s a t u r a t i o n is displaced, much of t he i n j e c t e d c a r b o n d i o x i d e is b e i n g u s e d m e r e l y t o d i s p l a c e t h e water i n t h e r e s e r v o i r (.which is n e c e s s a r y b e f o r e t h e c a r b o n d i o x i d e can c o n t a c t and d i s s o l v e i n t h e c r u d e o i l ) . When t h e i n i t i a l o i l s a t u r a t i o n is above t h e r e s i d u a l v a l u e , b o t h o i l and water a r e p r o d u c e d t h r o u g h o u t t h e run. The f low of o i l , e s p e c i a l l y a f t e r carbon d iox ide breakthrough, is much h ighe r than would be p red ic t ed from t h e relative pe rmeab i l i t y r e l a t i o n s h i p f o r t h e o i l -wa te r system; t h i s l eads t o t h e conclusion t h a t t h e mob i l i t y of t h e o i l i n which carbon d iox ide has d i s so lved has been increased. It IS obviously t h e v i s c o s i t y r educ t ion and, perhaps, most impor t an t ly , t h e s w e l l i n g of t h e crude o i l phase which causes t h i s i n c r e a s e i n mobil i ty . The s w e l l i n g of t he 45' c r u d e oil u s e d i n t h i s s t u d y is shown i n F i g u r e 1 5 i t is s u b s t a n t i a l .

The C 0 2 / 0 I L r a t i o is only about 7 MSCF/Bbl f o r an I n i t i a l s a t u r a t i o n of 0.77, but i nc reases to a va lue of 15 MSCF/Bbl when t h e i n i t i a l s a t u r a t i o n is d ropped t o 0.29.

Fig. 15. THE SWELLING FACTOR OF A 45°A.P.I. CRUDE BY CO2

E. The E f f e c t of O i l ComDosition

Four d i f f e r e n t " o i l s " were u s e d t o s t u d y t h e e f f e c t of o i l c o m p o s i t i o n : dodecane , wh ich is c o m p l e t e l y m i s c i b l e , hexadecane which d i s p l a y s a m i s c i b i l i t y gap, t h e 4S0A.P.I. c r u d e , a n d a s o l u t i o n of a 14O A.P.I. c r u d e i n t h e 45O c rude . The r e s u l t s a re shown i n F i g u r e 16.

The o v e r a l l recovery is h ighes t when carbon d iox ide is completely m i s c i b l e w i t h t h e o i l phase, viz., dodecane. However, only a s l i g h t l y lower 011 r e c o v e r y is a c h i e v e d when h e x a d e c a n e is s u b s t i t u t e d f o r t h e dodecane. T h e r e is i n f a c t v i r t u a l l y no d i f f e r e n c e i n t h e r e c o v e r y of t h e o i l phase , as long as i t s v i s c o s i t y is less than 6 c e n t i p o i s e s , m i s c i b l e o r not, during t h e i n j e c t i o n of t h e f i r s t 0.5 p o r e vo lume of c a r b o n d i o x i d e . The s l i g h t d i f f e r e n c e s i n r e c o v e r y t h a t d e v e l o p upon t h e i n j e c t i o n of more ca rbon d iox ide are perhaps b e s t understood by r e f e r r i n g t o t h e experiment using a mix tu re of 14O and 45O crude o i l s .

278

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This mix tu re had a v i s c o s i t y of 20 c e n t i p o i s e s and a g r a v i t y of 35'; i ts recovery by cont inuous carbon d iox ide i n j e c t i o n was no t i ceab ly l e s s than t h e r e c o v e r y w i t h t h e o t h e r o i l s wh ich had a v i s c o s i t y of l ess t h a n 6 cen t ipo i se s . Exacerbated v i scous f i n g e r i n g , lower s o l u b i l i t y and s w e l l i n g probably a l l c o n t r i b u t e t o t h e lower recovery f o r t h e more v i s c o u s c rude . I t is i n f o r m a t i v e t o note , Fig. 17, t h a t most of t h e o i l t h a t is recovered has t h e same g r a v i t y as t h a t of t h e m i x t u r e . Only a t t h e t a i l end of t h e recovery is t h e r e some evidence of t h e l i g h t e r f r a c t i o n be ing p r e f e r e n t i a l l y r ecove red . Because o f t h e f r a c t i o n a t i o n of t h e s y s t e m i n t o two or more phases when t h e carbon d iox ide con ten t of t h e sys tem exceeds a mol f r a c t i o n of 0.6 t o 0.7, t h e m o b i l e p h a s e c o n t a i n i n g a l a r g e f r a c t i o n of c a r b o n d i o x i d e a n d a s m a l l f r a c t i o n o f t h e l i g h t e n d s of t h e c r u d e o i l i s b e i n g p r e f e r e n t i a l l y produced. Add i t iona l work has shown t h a t when a l i v e c rude oil i s u s e d , t h e r e s u l t s a r e n o t s i g n i f i c a n t l y d i f f e r e n t f r q m t h o s e t h a t have been desc r ibed f o r t h e dead crude. Although a good p a r t of t h e methane appears t o be s t r i p p e d from t h e c rude as t h e carbon d iox ide d i s s o l v e s i n i t , it a l s o appears t h a t f r a c t i o n a t i o n occurs a t a somewhat lower molar concen- t r a t i o n of c a r b o n d i o x i d e and a more v o l a t i l e oil is p r o d u c e d somewhat e a r l i e r . However t h e o v e r a l l r e c o v e r y d o e s n o t seem t o b e s u b s t a n t i a l l y a f f e c t e d by t h e presence of moderate amounts of methane i n t h e c rude o i l .

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F. The E f f e c t of S lug S i z e

The e f f e c t of u s ing s l u g s of carbon d iox ide on t h e recovery of r e s i d u a l c r u d e oil was s t u d i e d , and t h e r e s u l t s a r e p r e s e n t e d i n F i g u r e s 18 and 19. The 4 5 O c r u d e was u s e d i n a l l t h e s e e x p e r i m e n t s , a n d t h e r e s i d u a l o i l s a t u r a t i o n w a s c o n s i s t e n t l y brought down t o 0.21 p.v. be fo re i n i t i a t i n g t h e test. I t is impor t an t t o n o t e i n t h e fo l lowing d i scuss ion , t h a t t h e comparisons t h a t w i l l be made on t h e e f f i c i e n c y of t h e v a r i o u s s l u g s w i l l be f o r a ----- l i m i t e d volume of t o t a l f l u i d i n j e c t e d , carbon d iox ide o r carbon d iox ide and water.

F o r o p e r a t i n g c o n d i t i o n s of 1000 p s i . a n d 73OF. t h e oil r e c o v e r y i n c r e a s e s l i n e a r l y w i t h a n i n c r e s e i n s l u g s i z e f r o m 0.11 t o 0.22 p o r e volume f o r a t o t a l i n j e c t i o n of 1.0 t o 1.2 pore volumes. However, when t h e s i z e o f t h e s l u g i s i n c r e a s e d a b o v e 0.22 p o r e vo lume , and t h e t o t a l f l u i d i n j e c t e d i s k e p t c o n s t a n t a t a b o u t o n e p o r e volume, t h e r e c o v e r y d o e s n o t i n c r e a s e any f u r t h e r . A s a m a t t e r of f a c t , a s l o n g a s t h e t o t a l f l u i d i n j e c t e d is l i m i t e d t o 1.2 P.v., t h e recovery a c t u a l l y dec reases as t h e s l u g s i z e is i n c r e a s e d above a va lue of 0.22.

L ;1 3 o at

FLUID INJLCTED. PV

Fig. 18. THE EFFECT OF SLUG SIZE ON THE RECOVERY OF RESIDUAL CRUDE O I L 1400 PSI , 73OF.

- 0.1 0.2 a3 0.4 as 0.6 0.7 ae a9 11)

FLUID INJECTED, PV

Fig. 19 THE EFFECT OF SLUG SIZE ON THE RECOVERY OF RESIDUAL CRUDE O I L 18 PSI, 130°F*

2 80

Over the range of temperatures and p r e s s u r e s i n v e s t i g a t e d i n t h e s tudy of t h e s l u g s of c a r b o n d i o x i d e , 7 3 O t o 130°F., and f r o m 1000 p s i t o 1800 psi., t h e optimum s l u g s i z e showed no c o n s i s t e n t change; i t ranged from 0.20 t o 0.26 p o r e volume. I t is h y p o t h e s i z e d t h a t t h e opt imum s l u g s i z e i s t h a t volume of c a r b o n d i o x i d e wh ich c a n b e i n j e c t e d i n t o t h e s y s t e m w i t h o u t e s t a b l i s h i n g a f r e e and cont inuous s a t u r a t i o n throughout t h e e n t i r e model. Once such a mobile gas s a t u r a t i o n is e s t a b l i s h e d , any f u r t h e r i n j e c t i o n of carbon d iox ide r e s u l t s i n t h e development of a (dense) gas d r ive , which is r e l a t i v e l y i n e f f i c i e n t i n d i s p l a c i n g t h e s w o l l e n c r u d e o i l . On t h e o t h e r hand, i f carbon dioxide i n j e c t i o n is h a l t e d b e f o r e a f r e e gas phase satura- t i o n is e s t a b l i s h e d throughout t h e model, then t h e swo l l en crude o i l phase, rendered mobile by t h e i n c r e a s e i n i ts pore volume s a t u r a t i o n , w i l l be much more e f f i c i e n t l y d i sp l aced by a r e l a t i v e l y v i scous f l u i d , v i z , water.

The i n c r e a s e d e f f i c i e n c y of s l u g s of c a r b o n d i o x i d e i n r e c o v e r i n g r e s idua l crude o i l is wel l i l l u s t r a t e d by t h e r e s u l t s of t h i s work which are p l o t t e d i n F igu re 20. Again, i t m u s t be noted t h a t t h e r e s e r v o l r prototype m o d e l l e d i n t h i s work i s o n e wh ich s h o u l d show up c a r b o n d i o x i d e a t i t s very bes t .

The e f f i c i e n c y of t h e u l t i m a t e displacement can be inc reased s l i g h t l y i f t he v i s c o s i t y of t h e chase wa te r is inc reased by t h e a d d i t i o n of a g lyco l o r a polymer. I f , f o l l o w i n g t h e i n j e c t i o n of a n opt imum s l u g of c a r b o n d i o x i d e , n i t r o g e n is i n j e c t e d ; t h e n t h e r e s u l t i n g r e c o v e r y of o i l is markedly reduced. The n i t r o g e n is an i n e f f i c i e n t d i s p l a c i n g f l u i d ; moreover I t s t r i p s some of t h e d i s s o l v e d c a r b o n d i o x i d e f r o m s o l u t i o n I n t h e c r u d e o i l , thereby de fea t ing t h e e n t i r e process , see F igure 21.

4

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Fig. 20. THE EFFICIENCY OF SLUGS OF CARBON DIOXIDE I N RECOVERING RESIDUAL CRUDE OIL

G. N i t rous Oxide

I

r n o r d e r t o g a i n f u r t h e r c o r r o b o r a t i o n f o r t h e h y p o t h e s i s t h a t i t is t h e s w e l l i n g of t h e r e s i d u a l crude o i l is t h e key f a c t o r i n t h e recovery of t h e la t ter by t h e i n j e c t i o n of carbon dioxide, a s e a r c h . w a s made f o r o t h e r s u b s t a n c e s t h a t wou ld d i s s o l v e t o t h e same e x t e n t and s w e l l t h e c r u d e o i l equ iva len t ly : n i t r o u s oxide has been desc r ibed t o be v i r t u a l l y equ iva len t t o c a r b o n d i o x i d e i n many p h y s i c a l p r o p e r t i e s 1 8 . E x p e r i m e n t s p roved t h a t n i t r o u s o x i d e p e r f o r m e d i n t h e p h y s i c a l mode l s i n a v i r t u a l l y i d e n t i c a l manner t o carbon dioxide. ( I t is a f a r more expensive substance.)

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, I

00 01 07 0 3 04 05 06 07 08 09 I0 I t I 2

Fig. 21. THE INEFFICIENCY OF NITROGEN AS A CHASE FLUID AFTER A C02 SLUG

IV. CONCLUSIONS

P h y s i c a l l y s c a l e d model s t u d i e s of t h e d i s p l a c e m e n t and r e c o v e r y of c r u d e O i l by c a r b o n d i o x i d e y i e l d r e s u l t s wh ich a r e c o n s i s t e n t w i t h t h e r e s u l t s of f i e l d demonstr t ion and p i l o t p r o j e c t s . and c o n s i s t e n t w i th the p r i n c i p l e s of f l u i d f low and phase behavior.

C o n t i n u o u s i n j e c t i o n of c a r b o n d i o x i d e w i l l r e c o v e r a s i g n i f i c a n t f r a c t i o n of a wa te r f lood r e s i d u a l o i l s a t u r a t i o n , b u t t h e r e s u l t i n g carbon d i o x i d e / o i l r a t i o s w i l l b e above 20 MSCF/B, and may be as high as 30.

The use of s l u g s of carbon d iox ide fo l lowed by water w i l l e f f e c t i v e l y reduce the r e s u l t i n g carbon d i o x i d e / o i l r a t i o w i t h o u t s e r i o u s l y a f f e c t i n g t h e amount of o i l t h a t can be recovered by t h e i n j e c t i o n of a t o t a l of about one p o r e vo lume of f l u i d . A l though v a l u e s a p p r o a c h i n g 5 MSCF/B have been achieved i n t h e s e model s t u d i e s , i t is caut ioned t h a t t h e model used was a very f avorab le one, viz., l o w pe rmeab i l i t y , uniform and l inea r . Even minor h e t e r o g e n e i t y i n a f i e l d o p e r a t i o n w i l l e n c o u r a g e c h a n n e l i n g , and t h e dec rease i n t h e v i scous t o g r a v i t y f o r c e s encountered I n r a d i a l f low away from t h e w e l l bo res w i l l encourage g r a v i t y segregat ion.

The performance of t h e displacement experiments l e a d s t o t h e conclusion t h a t t h e mechanism by which carbon d iox ide d i s p l a c e s r e s i d u a l crude o i l is comprised of t h r e e s e q u e n t i a l s t eps : 1) t h e immisc ib l e displacement of t he oi l -occluding, mobile water, 2) t h e s o l u t i o n of carbon dioxide i n t h e crude o i l and i t s subsequent s w e l l i n g t h a t develops o i l phase mob i l i t y , and 3) t he immisc ib l e displacement of t h e mobile s o l u t i o n of carbon dioxide i n o i l by t h e con t inu ing f low of carbon d iox ide or water.

Although t h e r e s i d u a l s a t u r a t i o n of t h e o i l phase (a s o l u t i o n of carbon d i o x i d e i n o i l ) c a n b e l o w e r e d by c o n t i n u i n g t h e f l o w of c a r b o n d i o x i d e , r e s u l t i n g i n some c o n t i n u i n g e v a p o r a t i o n of c r u d e o i l f r a c t i o n s , t h e

2 8 2

r e s u l t i n g i n c r e m e n t a l carbon d i o x i d e / p r o d u c e d o i l r a t i o s w i l l b e v e r y high. The more p r a c t i c a l l i m i t t o t h e r e c o v e r y i s r e a c h e d when t h e r e s i d u a l s a t u - r a t i o n of t h e low v i s c o s i t y o i l p h a s e t o t h e subsequent g a s o r water d r i v e i s approached.

N i t r o u s oxide , which d i s s o l v e s i n and swells c r u d e o i l s s i m i l a r l y , is as e f f e c t i v e as c a r b o n d i o x i d e i n r e c o v e r i n g c r u d e o i l . The s u b s t i t u t i o n of n i t r o g e n f o r water as a c h a s e f l u i d i n j u r e s t h e r e c o v e r y b e c a u s e t h e g a s is n o t as good a d i s p l a c i n g a g e n t f o r t h e s w o l l e n c rude .

The complex p h a s e b e h a v i o r of carbon d i o x i d e w i t h c r u d e o i l a p p e a r s t o c o n t r i b u t e l i t t l e t o t h e recovery p r o c e s s ; t h e e f f e c t of t h e f r a c t i o n a t i o n of t h e c r u d e i n t h e p r e s e n c e o f c a r b o n d i o x i d e r e s u l t s i n s o m e s l i g h t a d d i t i o n a l r e c o v e r y a t t h e t a i l end of t h e f l o o d .

S l i m t u b e e x p e r i m e n t s s i n c e t h e y do n o t c o r r e c t l y model t h e d i s p e r s i o n c o e f f i c i e n t s a n d t h e r e l a t i o n s b e t w e e n g r a v i t y a n d v i s c o u s f o r c e s do n o t p r o v i d e a d e q u a t e i n s i g h t i n t o a r e s e r v o i r r e c o v e r y process . The s o - c a l l e d minimum m i s c i b i l i t y p r e s s u r e a s i n t e r p r e t e d f r o m s u c h e x p e r i m e n t s i s a c t u a l l y t h e p r e s s u r e above which no s i g n i f i c a n t i n c r e a s e i n recovery w i l l b e achieved. The r e c o v e r y mechanism is s t i l l e f f e c t i v e a t l o w e r p r e s s u r e s .

ACKNOWLEDGEMENTS

The work on t h i s p r o j e c t w a s s u p p o r t e d by t h e U n i t e d S t a t e s Department of E n e r g y , G a r y E n e r g y Co., a n d e n d o w m e n t f u n d s a t t h e U n i v e r s i t y of Southern C a l i f o r n i a .

REFERENCES

1. Beeson, D. M., and O r t l o f f , C.D., ' !Laboratory I n v e s t i g a t i o n of t h e Water- Dr iven Carbon D i o x i d e P r o c e s s f o r O i l Recovery", TRANS AIME (1959) 216, 388- 91 2. Holm, Law., "Carbon D i o x i d e f o r S o l v e n t F l o o d i n g f o r I n c r e a s e d O i l Recovery", TRANS AIME (1959) 216, 225-231 3. R a t h m e l l , J.J., S t a l k u p , F.I., a n d H a s s i n g e r , R.C., "A L a b o r a t o r y I n v e s t i g a t i o n of M i s c i b l e D i s p l a c e m e n t by C02", SPE 3483, 4 6 t h A n n u a l Meeting of SPE of AIME (1971) 4. Holm, L.W., and J o s e n d a h l , V.A., "Mechanism of O i l D i s p l a c e m e n t by Carbon Dioxide", JPT (1974) , 1417-1438. 5. D u n n y s h k i n , I.I., a n d N a m o i t , A., " S t u d y of C o n d i t i o n s of P e t r o l e u m M i s c i b i l i t y w i t h Carbon Dioxide", N e f t . Khoz., (1978) , v. 3, 59-61 6. N a t i o n a l P e t r o l e u m Counci l , "Enhanced O i l Recovery - An A n a l y s i s of t h e P o t e n t i a l f o r Enhanced O i l Recovery f rom Known F i e l d s i n t h e U n i t e d S t a t e s - 1976 t o 2000, Washington, D.C., (1976) 7. Y e l l i g , W.F. a n d M e t c a l f e , R.S., " D e t e r m i n a t i o n a n d P r e d i c t i o n of C O P Minimum M i s c i b i l i t y Pressure" , JPT, (1980) , 160-168. 8. G a r d n e r , J . W . , Orr, P.M., a n d P a t e l , P.D., "The E f f e c t of P h a s e B e h a v i o r on CO2 Flood Disp lacement Ef f ic iency" , SPE 8367, 5 4 t h Annual Meet ing of SPE of AIME, Las Vegas, (1979) 9. E l Arabi , M., PbD. D i s s e r t a t i o n , U n i v e r s i t y of S o u t h e r n C a l i f o r n i a , J u n e 1981. 10. O f f e r i n g a , J., a n d v a n d e r P o e l , C., " D i s p l a c e m e n t of O i l From P o r o u s Media by M i s c i b l e Liquids" , TRANS AIME (1954) 201, 310-317 11. W a r n e r , H. R., Jr., "An E v a l u a t i o n of W i s c i b l e C02 F l o o d i n g i n Water f looded Sands tone R e s e r v o i r s " , JPT, (1979), 1339-1347

283

12. C l a r i d g e , E.L., " D i s c u s s i o n of t h e Use of C a p i l l a r y T u b e N e t w o r k s i n R e s e r v o i r Peformance S t u d i e s " , SPEJ (1972) , 352-61 13. G l a s s t o n e , S., T e x t Book of P h y s i c a l Chemis t ry , p. 713, D. Van Nostrand, New York, 1940. 14. D o s c h e r , T. a n d G h a r i b , S., " P h y s i c a l l y S c a l e d M o d e l s S i m u l a t i n g t h e Disp lacement of R e s d i u a l Oil by M i s c i b l e CO2 i n L i n e a r Geometry", SPE 8896. 5 0 t h Annual C a l i f o r n i a Regional Meet ing of SPE of AIME (1980) 1 5 , Kane , A.V., " P e r f o r m a n c e Review of a L a r g e S c a l e C a r b o n Dioxide-WAG P r o j e c t , SACROC U n i t - K e l l y S n i d e r F i e l d , SPE 7091, SPE I m p r o v e d O i l F i e l d Recovery Symposium, T u l s a 1978 16. Gruy F e d e r a l , Inc. , " T a r g e t R e s e r v o i r s f o r C O P M i s c i b l e F l o o d i n g " , U.S.Department of Energy, Washington, D.C., (1980) 17. Kamath , K.I., C o m b e r i a t i , J.R., a n d Z a m m e r i l l i , A.M., "The R o l e of R e s e r v o i r T e m p e r a t u r e i n Carbon D i o x i d e F l o o d i n g " , P a p e r N4, p r e s e n t e d a t t h e U.S.Department of Energy Symposium, T u l s a , Oklahoma 1979 18. G e r r a r d , W., S o l u b i l i t y of Gases and L i q u i d s , A Graphic A n a l y s i s , Plenum P r e s s , N e w York (1976) . S e e a l s o , H i l d e b r a n d , J.H., a n d S c o t t , R.L., T h e S o l u b i l i t y of Non-Elec t ro ly tes , Reinhold , New York (1950).



LABORATORY TESTING PROCEDURES FOR MISCIBLE FLOODS

S. G. SAYEGH and F. G. McCAFFERY*

Petroleum Recovery Institute, Chlgury. Alberta, Gnuah T2L 2A6

ABSTRACT

The o b j e c t i v e of t h i s paper is t o provide a s ta te-of- the-ar t review and c r i t ique of labora tory t e s t i n g procedures f o r miscible f looding f o r researchers irr the f i e l d . An a d d i t i o n a l a i m of the paper is t o give reservoir and production engineers i n s i g h t i n t o those procedures, 80 that they may apprec ia te t h e i r p o t e n t i a l s and l i m i t a t i o n s , and be b e t t e r a b l e t o evaluate laboratory results i n l i g h t of t h e i r f i e l d experience.

The t o p i c s t r e a t e d include s ingle- and multiple-contact phase behavior and physical p roper t ies measurements, and involve slim-tube and core displacement t e s t s . General objec t ives f o r each type of test are l i s t e d , recommended p r a c t i c e s are out l ined , and many examples from the l i t e r a t u r e are referenced. I n addi t ion , general screening criteria are presented for the s e l e c t i o n of s u i t a b l e candidate r e s e r v o i r s f o r miscible flooding.

IXTRODUCTIOY

One of the p r i n c i p a l enhanced recovery methods cur ren t ly under consideration f o r l i g h t o i l r e s e r v o i r s is miscible f looding with carbon dioxide and/or hydrocarbon solvents . The process is complex and involves many parameters t h a t have t o be optimized so t h a t a flood can lead t o a technica l and economic success. Some of the f a c t o r s that have t o be s tudied are t h e reservoir geology, o i l and oi l -solvent phase behavior, o i l solvent displacement characteristics, waterflood performance, as w e l l as r e s e r v o i r engineering aspec ts such as solvent production and o i l i n j e c t i o n s t r a t e g i e s , expected performance under both water and solvent f looding, apd economics.

In t h i s paper, laboratory t e s t i n g procedures f o r miscible flooding w i l l be discussed. These w i l l include the measurement of the phase behavior and dis- placenent data of reservoi r crude oi l -solvent systems, and how such data may be used in evaluat ing the s u i t a b i l i t y of a solvent flood f o r a p a r t i c u l a r appl i - cat ion. The o b j e c t i v e of t h i s paper is t o provide a state-of-the-art review and c r i t i q u e f o r researchers i n the f i e l d . An a d d i t i o n a l aim of t h e paper is to give reservoi r and production engineers ins ight i n t o laboratory t e s t i n g procedures SO

that they may apprec ia te t h e i r p o t e n t i a l s and l i m i t a t i o n s and thus be b e t t e r a b l e t o evaluate laboratory results i n l i g h t of t h e i r f i e l d experience.

* Present address: Occidental Research Cozporation, I rvine, Cal i f . 92713, U.S .A.

For o ther

286

ze.:irvs of the E i s c i b l e f looding process and i t s f i e l d a p p l i c a t i o n s , the reader is r s f e r r e d to t h e works by Holm’, Stalkup2, Dosher et a1.3, and M~ngan‘’~. Burnett and DamC have reviewed screening tests f o r a v a r i e t y of enhanced o i l recover:* processes ,

PROCESS DESCRIPTION AND GENERAL SCREENING CRITERIA

I n a miscible f lood t h e solvent contac ts t h e o i l and a mixing zone is formed. t o so lvent , without an i n t e r f a c e . For economic reasons, t h e so lvent i s usua l ly not i n j e c t e d cont inuously, but o f t e n i n the form of a s l u g t y p i c a l l y about 20-30% of t h e hydrocarbon pore volume (HCPV). The s l u g is then followed by a chase f l u i d , usua l ly water or l e a n gas, t o d r i v e it through t h e r e s e r v o i r towards the production w e l l s . a l t e r n a t i n g w i t h water, c o m n l y c a l l e d t h e water-alternating-gas (WAG) process. Al te rna t ive ly , water may be co-injected with t h e so lvent . These latter i n j e c t i o n modes help c o n t r o l t h e high mobil i ty of the solvent .

I n t h e mixing zone, t h e r e is a gradual change in composition from o i l

The s l u g may be i n j e c t e d i n small por t ions

It is r a r e l y technica l ly or economically f e a s i b l e t o i n j e c t a solvent that is d i r e c t l y miscible with t h e o i l . Instead, m i s c i b i l i t y is genera l ly achieved through what are known as t h e m l t i p l e - c o n t a c t m i s c i b i l i t y (MCM) mechanisms7-13. Two such mechanisms can occur when gaseous or s u p e r c r i t i c a l s o l v e n t s a r e used: a condensation mechanism and a vaporizat ion mechanism. When s u b c r i t i c a l so lvents a r e used a t p ressures above t h e i r bubble poin t , the process is one of l iqu id- l i q u il e x t r a c t ion1 ’ 1 5 .

The high o i l recovery i n misc ib le f loods is a t t r i b u t e d t o the following fac tors :

- high microscopic displacement e f f ic iency - o i l e x t r a c t i o n by so lvent - l o r i n t e r f a c i a l t ens ion - o i l swel l ing - o i l v i s c o s i t y reduct ion - blowdown recovery

The so lvents used (C02 and hydrocarbons) are general ly less dense and viscous than the o i l s . through it . solvent breakthrough, poor sweep ef f ic iency , and low o i l recovery. a good candidate r e s e r v o i r f o r hor izonta l miscible f looding should have t h e fo l lov ing characteristics:

This causes t h e solvent t o over r ide t h e o i l and f i n g e r These are adverse f a c t o r s i n hor izonta l f loods and lead t o e a r l y

I n general ,

- t h i n pay zone, up t o 5 m - good hor izonta l cont inui ty - r e l a t i v e l y homogeneous - low vert ical- to-horizontal permeabi l i ty r a t i o - Zot f rac tured - contains undersaturated o i l - contains no f r e e gas s a t u r a t i o n - contains no mobile water

?ins solvent should be chosen such that i t :

- achieves m i s c i b i l i t y w i t h t h e o i l a t r e s e r v o i r condi t ions - is cheap - is r e a d i l y a v a i l a b l e

287

For v e r t i c a l downward displacements, t h e requirements are somewhat l e s s cons t ra in ing :

- t h e r e s e r v o i r should not conta in permeabi l i ty b a r r i e r s t o v e r t i c a l flow - t h e displacement should be c a r r i e d out a t a s u i t a b l e rate such that the

flood is g r a v i t y s t a b l e

PHASE BEHAVIOR MEASUREMENTS

Phase behavior measurements are c a r r i e d o u t f o r severa l purposes:

- t o c h a r a c t e r i z e t h e o i l - so lvent system - t o determine t h e mechanism by which m i s c i b i l i t y is achieved - t o f ine- tune t h e phase behavior packages i n compositional s i rmla tors

I n genera l , t h e phase behavior s t u d i e s involve t h e fol lowing measurements:

- s o l u b i l i t i e s - mult ip le phase formation, including both l i q u i d and s o l i d phases - d e n s i t i e s - o i l swel l ing - v i s c o s i t i e s

Phase Behavior Measurement Equipment

High pressure phase equi l ibr ium experimental techniques f o r a v a r i e t y of a p p l i c a t i o n s have recent ly been reviewed by Eubank e t a1.16 connection wi th C02 and hydrocarbon systems were described by other , researchers . 17-26

Apparatuses used i n

A connuon type of apparatus c o n s i s t s of a windowed cel l whose volume may be manipulated by means of a p is ton o r mercury from a p o s i t i v e displacement pump. The c e l l is placed i n a t h e n m s t a t e d oven f o r temperature cont ro l . The des i red components of t h e mixture are loaded i n t o t h e cell and then mixed. Mixing is usua l ly done wi th a magnetically-coupled stirrer, by rocking the c e l l , o r by c i r c u l a t i n g t h e f l u i d s . observa t ions of t h e coexis t ing phases may be c a r r i e d out . phases may a l s o be withdrawn f o r d e n s i t y and v i s c o s i t y measurements, and f o r compositional analyses . t o determine bubble and dew poin ts , and volumetric proport ions of coexis t ing phases as func t ions of pressure.

Once equi l ibr ium has been reached, v i s u a l Samples of these

Constant composition expansions may a l s o be car r ied out

The apparatus descr ibed by LeeP3 and Sayegh e t a1.26 has two interconnected This g ives a greater f l e x i b i l i t y of opera t ion and permits the measure- cells .

ment of v i s c o s i t y without using a separa te viscometer. D. Robinson (personal communication) a t t h e Universi ty of Alberta has t h e c e l l constructed e n t i r e l y from sapphire. This permits unhindered v i s u a l observat ion of t h e e n t i r e con- t e n t s of the c e l l . of D. Robinson have t h e i r sampling l i n e s d i r e c t l y connected t o gas chromatographs f o r analysis. The apparatus described by Orr et al .24 d i f f e r s from t h e o t h e r s i n t h a t it resembles a continuously s t i r r e d tank reac tor .

The apparatuses of Orr e t al .24, of Connor and Pope25, and

288

Phase Behavior Tes ts to Character ize t h e Crude O i l

Typical tests f o r the charac te r iza t ion of the crude o i l involve the measurement of i t s composition, molecular weight, d e n s i t y , v i s c o s i t y , compressi- b i l i t y , bubble poin t , formation volume f a c t o r , g a s - o i l r a t i o , d i s t i l l a t i o n curve, d i f f e r e n t i a l l i b e r a t i o n , constant volume deple t ion , and constant composition expansion charac t e r i s tics.

These tests are genera l ly c a r r i e d out a t r e s e r v o i r temperature using, f o r example, ASTM standard procedures and are preferab ly c a r r i e d out with bottom- hole samples. the production l i f e t i m e of a r e s e r v o i r , and be c a r r i e d out on samples from t h e d i f f e r e n t producing zones o r horizons of a pool t o determine i f t h e r e are any v a r i a t i o n s i n o i l p roper t ies . This is e s p e c i a l l y Important where t h e r e s e r v o i r pressure f a l l s below t h e o r i g i n a l bubble point of t h e o i l .

Tes t ing of o i l p r o p e r t i e s should be p e r i o d i c a l l y repeated during

Standingl’l and Henry e t a1.28 presented d e s c r i p t i o n s of bottomhole sampling

The w e l l should be produced procedures. I n general , t h e sampling w e l l should be se lec ted so that it is representa t ive of t h e average r e s e r v o i r condi t ions. a t a slow r a t e dur ing sampling t o minimize pressure drawdown e f f e c t s and t h e r e s u l t a n t phase changes. Also, s u f f i c i e n t sampling time should be allowed t o ensure t h a t the sample bomb i s f i l l e d with f r e s h oil.

Large volumes of r e s e r v o i r f l u i d s a r e necessary t o c a r r y out a complete laboratory study of a misc ib le flood. Thus, i t is unreasonable t o use bottom- hole samples f o r a l l these tests. The normal procedure is t o take l a r g e samples of separa tor o i l and gas, then recombine them t o natch the p r o p e r t i e s of the bottomhole sample. 25

Phase Behavior Tests t o Character ize t h e Crude Oil-Solvent System

The general phase behavior of hydrocarbon f l u i d s have been wel l re- ~ i e w e d . ~ ” ~ ~ severa l author^^'^'^^'^^, whi le most of t h e recent ly published s t u d i e s have d e a l t with t h e phase behavior of C02-011 systems.ll p12’14p18’23’24’26p30-38 r e f l e c t s t h e growing i n t e r e s t i n using C02 as a misc ib le f looding agent .

Data f o r hydrocarbon f loods of r e s e r v o i r crudes were presented by

This

The following d iscuss ion w i l l concentrate on C02-reservoir crude o i l systems s ince these are of most i n t e r e s t t o the industry. crude o i l s stems are o f t e n presented i n the form of te rnary phase d ia - grans .9p12yY4y24 Such a representa t ion provides a convenient form f o r t h e v i s u a l i z a t i o n of t h e com o s i t i o n a l path during a constant temperature and pressure d i s lacementl 11g7 and f o r determining t h e mechanism of achieving misc ib i l i ty .% It should, however, be remembered t h a t t h e te rnary representa t ion is not thermodynamically r igorous and hence should not be in te rpre ted l i t e r a l l y . Nore accura te pred ic t ions of t h e displacement pa th may be made using a quaternary diagram. ’

A second type of test is the constant conposi t ion e ~ p a n s i o n . ~ ’ ~ ~ ’ ~ ~ ’ ~ ~ T n i s provides information on the phase betavior of the C02-011 sys tem i n t h e var ious loca t ions of the r e s e r v o i r where the pressure may vary. For example, a t c o c i i t i o n s where m l t i p l e l i q u i d phases appear. t h e s l u g could break down, while asp;laltene p r e c i p i t a t i o n could leqd t o a reduct ion i n r e s e r v o i r permeability.

The phase diagrams of C02-

289

The d e n s i t y , swe l l ing f a c t o r , and v i s c o s i t y of the C02-saturated 0i118’26’31

a r e u s u a l l y measured i n g a r a l l e l w i th t h e phase-envelope measurements descr ibed above. Connor and Pope2 r e c e n t l y presented such d a t a f o r hydrocarbon-oi l systems. t h e o i l causing i t t o swell and t h u s t o reduce its d e n s i t y and v i s c o s i t y . Carbon d iox ide is gene ra l ly more e f f e c t i v e i n t h i s regard than hydrocarbon s o l v e n t gases . j6 A t very high p res su res , t h e d e n s i t y and v i s c o s i t y curves could s ta r t i n c r e a s i n g because the e f f e c t o f p r e s s u r e on t h e f l u i d p r o p e r t i e s predominates over t h e e f f e c t of so lven t d i s s o l u t i o n .

I n gene ra l , as t h e p re s su re inc reases , more so lven t g a s d i s s o l v e s i n t o

Phase Behavior T e s t s t o Determine t h e Mechanism of Mult iple- Contact M i s c i b i l i t y

The tests mentioned p rev ious ly are a l l s t a t i c , s ingle-contact tests. The tests descr ibed i n t h i s s e c t i o n are designed t o s imula t e t h e dynamic, mult iple- c o n t a c t p rocess occur r ing i n a r e s e r v o i r between t h e i n j e c t e d s o l v e n t and the r e s e r v o i r crude o i l . These tests are c a r r i e d o u t i n a c o n t r o l l e d manner i n a PVT c e l l , t hus t h e process parameters are w e l l de f ined .

The f i r s t type of test is t h e gene ra t ion o f a Benham p l o t by a stagewise approximation o f t h e continuous mult iple-contact process.’ 2’ ’ 9’ 24’ 25’ 39 procedure, a c e r t a i n p ropor t ion of o i l and so lven t are mixed i n a PVT c e l l and allowed t o reach equ i l ib r ium. The p ropor t ions and p r o p e r t i e s o f t h e r e s u l t a n t vapor and l i q u i d a r e then measured. I f a condensation process occurs , t h e vapor phase is then purged and a f r e s h ba t ch o f s o l v e n t is introduced i n t o t h e c e l l . On t h e o t h e r hand, t h e l i q u i d phase is purged i f , based on changes i n phase volume, a v a p o r i z a t i o n process is involved, and a f r e s h ba t ch o f o i l is i n t r o - duced i n t o t h e c e l l . i n t h e c e l l , a t which po in t MCM has been a t t a i n e d .

In t h i s

The e n t i r e process is repeated u n t i l only one phase appears

The drawback of t h i s method is t h a t i t is a s tagewise process , which only approximates t h e continuous c o n t a c t s i n a r e s e r v o i r . As such, i t is i m p l i c i t l y assumed t h a t t h e o i l and so lven t i n t h e r e s e r v o i r have enough time t o reach equi l ibr ium. This is probably a reasonable assumption i n many cases s ince r e s e r v o i r flow rates are q u i t e low, but i f s e v e r e channel l ing, f i n g e r i n g , o r g r a v i t y seg rega t ion occur i n t h e r e s e r v o i r , t r u e equ i l ib r ium may n o t be a t t a i n e d and t h e p r e d i c t i o n w i l l be o p t i m i s t i c . Another problem as soc ia t ed w i t h des ign ing t h i s t ype of batchwise experiment is t h e choice of volumetr ic r a t i o s of gas-to-liquid con tac t ed i n each s t e p . m o b i l i t i e s of t h e hases and flow rates should be taken i n t o account t o determine

Resenroir parameters such as t h e

a r e a l i s t i c r a t i o . 3 9

The procedure desc r ibed by O r r et a1.24 is a v a r i a t i o n of t h e above method I n such a n expe r i - i n t h a t t h e n u l t i p l e c o n t a c t s are c a r r i e d o u t cont inuously.

ment, t h e rate of so lven t i n j e c t i o n i n t o t h e c e l l would have t o be c a r e f u l l y s e l e c t e d t o o b t a i n meaningful r e s u l t s .

LABORATORY DISPLACEMENT TESTS

Laboratory displacement tests provide important information on t h e behavior These of r e s e r v o i r f l u i d / s o l v e n t systems under dynamic displacement cond i t ions .

tests a r e of two types: sl im-tube and co re displacements . It i s important t o c a r r y o u t both types of tests i n a l abora to ry s tudy s i n c e each one provides d i f f e r e n t information necessary f o r t h e eva lua t ion of a f i e l d app l i ca t ion . Each type of t e s t w i l l now be discussed i n f u r t h e r d e t a i l .

Slim-Tube Displacement Tests

Slim-tube displacement tests are l abora to ry tests that are c a r r i e d o u t i n a n i d e a l i z e d porous medium. As such, they may be thought of a s being an i n t e r - mediate approximation t o r e s e r v o i r f l oods , l y i n g between t h e wre r e a l i s t i c co re f loods and t h e more i d e a l i s t i c mult iple-contact PVT c e l l tests. A s l i m - tube test is c a r r i e d o u t p r imar i ly t o determine i f a solvent ach ieves m i s c i b i l i t y w i th a n o i l a t a c e r t a i n temperature and pressure. involving a series of runs ' cou ld be done w i t h e i t h e r o r both o f t h e fol lowing o b j e c t i v e s :

A l a b o r a t o r y i n v e s t i g a t i o n

- minimum m i s c i b i l i t y p r e s s u r e (ME') determinat ion - s o l v e n t s c reen ing

Orr et al.24 have made a summary o f sl im-tube displacement appa ra tuses used by va r ious i n v e s t i g a t o r s . z o n t a l l y c o i l e d s t a i n l e s s steel tub ing . The tube i s 10-20 m long, about 5 mu i n t e r n a l diameter , and packed wi th f i n e g l a s s beads o r s ands t o a po ros i ty o f about 30% and t o a pe rmeab i l i t y of 3-15 urn2. o i l , then flooded with C O P . The e f f l u e n t from t h e slim-tube passes through a s i g h t g l a s s f o r visual obse rva t ion , is sampled f o r a n a l y s i s , and is then f l a shed t o a t m s p h e r i c p re s su re through a backpressure r e g u l a t o r . Produced l i q u i d and gas phases are metered s e p a r a t e l y . The d a t a obtained from t h e test inc lude e f f l u e n t c o l o r , number of phases , composition and g a s - o i l r a t i o , as w e l l as o i l recovery and p r e s s u r e drop a c r o s s the coil--each as a func t ion of t h e volume o f so lven t i n j e c t e d .

The s l i m tube is normally cons t ruc t ed from hori-

The c o i l is f i r s t s a t u r a t e d w i t h

The b a s i c assumption i n sl im-tube tests i s that t h e displacement is p i s ton - l i k e and t h a t l i t t l e o r no f i n g e r i n g o c c u r s . - This is due i n p a r t to t h e uniform- i t y of t h e packing and t h e dampening e f f e c t of t h e t u b e ' s w a l l s . t h e c r i t e r i a f o r m i s c i b i l i t y being achieved i n a carbon d iox ide f lood a re :

Accordingly,

- no appearance o f a methane bank p r i o r to . breakthrough - l a t e so lven t breakthrough ( a t around 0.8 pore volumes of so lven t i n j e c t e d ,

- a s m o t h t r a n s i t i o n from o i l t o so lven t i n t h e mixing zone without t h e o r l a t e r )

a m e a r a n c e of a n i n t e r f a c e .. - high u l t i m a t e recovery ( g r e a t e r than 95% of t h e o r i g i n a l oi l - in-place, . OOIP)

On t h e o t h e r hand, a n i m i s c i b l e displacement is cha rac t e r i zed by:

- t h e appearance of a methane bank p r i o r t o solvent breakthrough - e a r l y breakthrough - t h e obse rva t ion o f a n i n t e r f a c e between t h e o i l - r i c h and solvent-r ich

- low u l t i m a t e recovery phases i n t h e mixing zone

A l l of t h e above-noted symptoms of a n immiscible displacement should appear i f t he p re s su re is w e l l below t h e MEip. This a l s o depends t o some ex ten t on t h e c h a r a c t e r i s t i c s of t h e s l i m tube i t s e l f ( tube diameter , uniformity of bead s i z e and packing). It would be i n s t r u c t i v e t o c a r r y o u t two i n i t i a l displacements t o c h a r a c t e r i z e t h e p a r t i c u l a r s l i m tube being used. conducted under d e f i n i t e l y immiscible cond i t ions us ing n i t rogen , f o r example, a s t h e f lood ing agen t , while t h e second f lood would involve f i r s t - c o n t a c t m i s c i b l e cond i t ions us ing benzene, f o r example, as the d i s p l a c i n g agent . For f u r t h e r d i s c u s s i o n s , t h e r e a d e r is r e f e r r e d t o o t h e r publ ished works.24' 31'40'41 y 4 2

The f i r s t f lood could be

2 9 1

A v a r i e t y of s l i m tube lengths have been used by var ious researcher^.^^ would appear t h a t mult iple-contact m i s c i b i l i t y is achieved f a i r l y e a r l y i n the l i f e of t h e displacement (within t h e f i r s t two meters) , o therwise a high o i l recovery would not be obtained. (about 10) required i n PVT cel l , mult iple-contact experiments12’19’25 although, as mentioned previously, such experiments are open t o i n t e r p r e t a t i o n . On the o t h e r hand, Yel l ig15 concluded t h a t longer lengths (2.5 - 5 m) were required t o develop m i s c i b i l i t y when carbon dioxide was i n the l i q u i d form. Thus, a s l i m tube length between 10-20 1 is recommended. The rate a t which slim-tube d is - placements are run a f f e c t s t h e s t a b i l i t y of t h e displacement f r o n t and the time allowed f o r contact between t h e o i l and so lvent . For t h i s reason, displacement rates are b e s t kept a t less than 1 0 m/day. minimizes t h e pressure drop across t h e slim tube, which provides f o r good d e f i n i t i o n of t h e minimum m i s c i b i l i t y pressure.

I t

This is supported by t h e lower number of contac ts

The use of r e l a t i v e l y low rates a l s o

Benham e t a1.8 have presented c o r r e l a t i o n s f o r t h e minimum enrichment of dry gas (by LPG) required t o achieve m i s c i b i l i t y , while Jacobson43 s tudied the cont r ibu t ion of a c i d gases t o m i s c i b i l i t y . Other researchers1 O S 3 l ’40’41 ’42’44 have inves t iga ted t h e e f f e c t of t h e d i f f e r e n t process var iab les on t h e carbon dioxide MMP. I n general , t h e ME’ increases wi th decreasing o i l g rav i ty and i ts C5 t o C30 content , and w i t h increas ing temperature and molecular weight of t h e o i l C5+ f r a c t i o n . Hydrogen s u l f i d e and LPG i n t h e carbon dioxide decrease t h e I W , while n i t rogen and methane increase it.

In a d d i t i o n t o studying dynamic m i s c i b i l i t y condi t ions , t h e r e s u l t s of slim-tube experiments may be used t o c a l i b r a t e compositional s imulators . 39’45’46 Wang and L ~ c h e ~ ~ inves t iga ted the r e l a t i v e e f f i c i e n c y of d i f f e r e n t water- a l te rna t ing-gas cyc les and concluded t h a t the t o t a l o i l recovery w a s i n s i g n i f i - can t ly a f f e c t e d by the i n j e c t i o n sequence provided t h a t t h e t o t a l amount of carbon dioxide i n j e c t e d remained t h e same.

I n summary, slim-tube displacement tests are an extremely usefu l t o o l f o r

Caution must be exercised when t ransposing the studying t h e m i s c i b i l i t y r e l a t i o n s h i p between o i l and solvent systems under cont ro l led dynamic condi t ions. r e s u l t s of such s t u d i e s t o r e s e r v o i r systems s i n c e t h e e f f e c t s of t h e reservoi r rock p r o p e r t i e s (homogeneity, relative permeabi l i ty , w e t t a b i l i t y , and pore geometry) have not been taken i n t o account, hence displacement tests on reservoi r rocks must follow. a n attempt t o provide more d e t a i l e d i n s i g h t i n t o t h e displacement behavior as it may occur i n t h e r e s e r v o i r i n regions contacted by t h e solvent .

The following s e c t i o n d e a l s w i t h core displacement tests i n

Core Displacement Tests

Following slim-tube displacement tests t o confirm t h e establishment of m i s c i b i l i t y w i t h t h e o i l f o r a given solvent a t appropr ia te reservoi r condi t ions of temperature and pressure, core f looding measurements are general ly recommended. Such tests can be used t o evaluate a v a r i e t y of displacement phenomena t h a t have bear ing on the miscible f looding process. These include.

- recovery mechanisms9’1 9 - d i f f u s i o n and d ispers ion c o e f f i c i e n t s , and dead-end pore volume^^^-^^ - miscible and compositional s imulator tuning48’ 64 - chromatographic separa t ion of components1 ’48 - water, o i l , and gas r e l a t i v e p e r r n e a b i l i t i e ~ ~ ” ~ ~ - rock i n t e r a c t i o n s wi th gas and b r i n e - dynamic oi l -solvent phase behavior 5 8 - e f f e c t of t h e following f a c t o r s on displacement e f f i c i e n c y o r o i l recovery:

292

. rock

. s o l v e n t type’ 4’60 . water s a t u r a t i o n (secondary o r t e r t i a r y f lood ing mode)59’60’63rC5 . phase behavior (mul t i l e l i q u i d and s o l i d phases)32 . displacement pressure” ’’ . so lven t i n j e c t i o n r a t e l 5 ’ 6 ’ . f lood ing mode (cont inuous so lven t i n j e c t i o n , so lven t s l u g s i z e WAG, water-solvent c o i n j e c t i o n , C02-foam and C02-polymer i n j e c t i o n ) b 2 ’ 6 3 . blowdown . low i n t e r f a c i a l tension66

A c o r e displacement appa ra tus c o n s i s t s of a co re ho lde r i n which the co re is placed under a conf in ing p res su re . The c o r e is connected t o r e s e r v o i r o i l and b r ine , i n j e c t i o n water, and so lven t con ta ine r s . The. c o r e i s flooded a t r e s e r v o i r temperature and p r e s s u r e w i t h t h e s e f l u i d s i n t h e proper sequence, and t h e f l u i d product ion and p res su re drops are monitored. t h e core’s e f f l u e n t s can be made through a s i g h t g l a s s .

V i s u a l obse rva t ion of

It is recommended that c o r e from t h e a c t u a l r e s e r v o i r be used i n t h e d i s - placement tests. mechanis t ic s t u d i e s . The s e l e c t i o n of r e s e r v o i r c o r e s f o r t hese tests is a n important procedure which r e q u i r e s a n understanding o f t h e geology of t h e e n t i r e r e s e r v o i r . The c o r e s should be sampled from t h e pay zone of i n t e r e s t and chosen t o properly r e p r e s e n t t h e main rock types occur r ing i n t h e r e s e r v o i r . Cores wi th l a r g e h e t e r o g e n e i t i e s such as f r a c t u t e s , vugs, and l amina t ions would tend t o g ive r e s u l t s that exaggerate t h e e f f e c t s of t h e h e t e r ~ g e n e i t i e s . ~ ~ S t u d i e s of Rosman and Simon66, and Eatycky e t a1.67 have, however, shown t h a t t he hetero- gene i ty exh ib i t ed by i n d i v i d u a l c o r e segments dec reases when t h e segments are bu t t ed toge the r t o form a longer c o r e assembly.

Although ou tc rop c o r e s may a l s o be used f o r c e r t a i n

F u l l diameter , v e r t i c a l co res may be used f o r eva lua t ing v e r t i c a l f l o o d s wh i l e , f o r h o r i z o n t a l f l oods , h o r i z o n t a l p lugs have t o be d r i l l e d o u t of t he f u l l diameter co re . These plugs a r e t y p i c a l l y 2-3 cm i n diameter and 6-10 cm long. s u f f i c i e n t l y long assembly f o r t h e displacement t e s t , p a r t i c u l a r l y i f t h e development of m u l t i p l e con tac t m i s c i b i l i t y i s involved. To ach ieve good c a p i l l a r y c o n t a c t between t h e c o r e s , t h e co re f a c e s can be machined square on a l a t h e , and t h e r e is t h e o p t i o n o f p l ac ing f i l t e r paper between t h e c o r e f a c e s p r i o r .to mounting them i n a tiraxial c o r e holder . It is recommended t h a t t h e plugs be chosen such that they come from t h e same f a c i e s i n t h e r e s e r v o i r , and t h a t they have similar and r e p r e s e n t a t i v e porosi ty-permeabi l i ty c h a r a c t e r i s t i c s Combining plugs from d i f f e r e n t f a c i e s and wi th widely varying p r o p e r t i e s makes the i n t e r p r e t a t i o n of t h e displacement r e s u l t s d i f f i c u l t and o f quest ionable value as i n p u t d a t a f o r s imula to r p r e d i c t i o n s of f i e l d performance.

About 20 p lugs should be bu t t ed toge the r i n a co re holder t o g ive a

The co res a v a i l a b l e f o r t e s t i n g may be i n t h e preserved state o r , more l i k e l y , are i n a n aged cond i t ion . I f preserved, t h e co res can be used d i r e c t l y i n t h e displacement experiments. Non-preserved co re needs t o be cleaned thoroughly by e x t r a c t i o n or displacement w i t h s o l v e n t s such a s toluene-methano166, mounted dry i n a co re holder , and then have i t s w e t t a b i l i t y and i n i t i a : o i l s a t u r a t i o n r e -e s t ab l i shed by con tac t w i th the r e s e r v o i r f l u i d s .

A t y p i c a l t e s t procedure u t i l i z e d wi th cleaned, non-preserved co re involves evacuat ing, s a t u r a t i n g w i t h r e s e r v o i r lsrine, and then f lood ing w i t h crude o i l u n t i l t h e water s a t u r a t i o n approaches t h e connate water s a t u r a t i o n . I f t h i s procedure cannot provide a s u f f i c i e n t l y low i n i t i a l water s a t u r a t i o n , then methods u t i l i z i n g gas flow and/or evaporat ion can be Following placement of crude o i l i n t h e core , it is l e f t t o age f o r s e v e r a l days f o r t h e purpose of

293

re -es tab l i sh ing t h e o r i g i n a l ~ e t t a b i l i t y ~ ~ . flooded wi th i n j e c t i o n water down t o r e s i d u a l o i l s a t u r a t i o n . r e l a t i v e permeabi l i ty may be ca lcu la ted from t h e pressure drop and production h i s t o r y of t h e waterflood. F ina l ly , t h e core i s solvent flooded. I f the solvent f lood is t o be a secondary one, t h e waterflood s t e p is then na tura l ly o m i t t e d .

After aging, t h e core is water- The water-oi l

The d i s t i n c t advantages of using non-preserved core are its ease of handling during t h e d r i l l i n g of plugs, and t h e a b i l i t y t o examine t h e cores and measure t h e i r p r o p e r t i e s (such as a i r permeabi l i ty and poros i ty) p r i o r t o the f lood tests. The disadvantage of using aged c o r e is t h a t one is seldom sure of t h e adequacy of t h e measures taken t o r e s t o r e t h e c o r e t o its o r i g i n a l state.

A prime reason f o r a t tempting t o r e s t o r e t h e r e s e r v o i r wet t ing condi t ion i n t h e c o r e relates t o t h e reported t rapping o r s h i e l d i n g of o i l by mobile water i n water-wet It is genera l ly bel ieved that mixed o r intermediately w e t systems provide optimum t e r t i a r y recovery e f f i c i e n c i e s w i t h solvent floods.

RECAPITULATION

The f i r s t s t e p i n t h e implementation of a f ie ld-sca le miscible flood is t h e s e l e c t i o n of s u i t a b l e candidate r e s e r v o i r s and so lvents . A set of technical screening criteria has been provided t o a i d i n t h e se lec t ion . These should be augmented by o t h e r l i m i t a t i o n s and/or incent ives (e.g. economic) s p e c i f i c t o each loca le .

Once t h e prel iminary s e l e c t i o n has been made, labora tory tests can be car r ied out t o reduce t h e t e c h n i c a l and economic u n c e r t a i n t i e s assoc ia ted with f i e l d tests. The labora tory tests should be supplemented with geological ( reservoi r d e s c r i p t i o n ) and computer s imulat ion studies'.

Laboratory tests have been categorized i n t o s ta t ic and dynamic measurements, and d i f f e r e n t types of tests that may be c a r r i e d o u t under each category have been l i s t e d . S t a t i c phase behavior tests enable t h e measurement o f t h e proper t ies of t h e o i l , so lvent , and t h e i r mixtures under cont ro l led condi t ions. Slim tube tests determine t h e dynamic m i s c i b i l i t y c h a r a c t e r i s t i c s of t h e oi l -solvent system. F i n a l l y , c o r e displacement tests he lp determine t h e e f f e c t of t h e process condi t ions and rock p r o p e r t i e s on t h e displacement e f f i c i e n c y i n t h e swept zone of the reservoi r .

ACKNOIJLEDQ4ENI'S

The au thors wish t o express t h e i r thanks t o P.M. Sigmund f o r consul ta t ions, and t o B. Moore f o r . t y p i n g t h e manuscript.

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HUTCHINSON, JR., C.A. and BRAUN, P.H.; "Phase R e l a t i o n s of Misc ib l e Displacement i n O i l Recovery", A.1.Ch.E. J. (1961), 7 (l), 64.

BENHAM, A.L., DOWDEN, W.E., and KUNZMAN, W . J . ; * 'Miscible Flood Displacement - P r e d i c t i o n o f M i s c i b i l i t y " , Trans. AIME (1960) 219, 229.

FATIWELL, J.J., STALKUP, F.I., and HASSINGER, R.C.; "A Laboratory I n v e s t i - g a t i o n o f Misc ib l e Displacement by Carbon Dioxide", paper SPE 3483, prepared f o r 46 th Annual F a l l Meeting o f t h e SOC. o f P e t . Eng. o f A I I E , New Orleans, Louis iana (October 3-6, 1971).

HOLM, L.W. and JOSENDAL, V.A.; "Effect o f O i l Composition on Miscible-Type Displacement by Carbon Dioxide", paper SPE 8814, presented a t t h e F i r s t J o i n t SPE/DOE Symp. on Enhanced O i l Recovery, Tu l sa , Oklahoma (Apri l 20-23, 1980) ,

METCALFE, R.S. and YARBOROUGH, L.; "The E f f e c t of Phase E q u i l i b r i a on t h e C 0 2 Displacement Mechanism", SOC. P e t . Eng. J. (August 1979), 242.

GARDNER, J .W. , ORR, F.M., and PATEL, P.D.; 'The E f f e c t o f Phase Behavior on Cog Flood Displacement Eff ic iency", paper SPE 8367, p re sen ted a t t h e 5 4 t h Annual F a l l Technical Conference and Exh ib i t i on o f t h e SOC. o f P e t . Eng. o f AIME, Las Vegas, Nevada (September 23-26, 1979).

WANG, G.C .; "Microscopic I n v e s t i g a t i o n o f Cog Flooding Process", SPE/DOE paper no. 9788, p re sen ted a t t h e 1981 SPE/DOE Second J o i n t Symposium o n Enhanced O i l Recovery o f t h e SOC. o f P e t . Eng., Tu l sa , Oklahoma (Apri l 5-8, 1981).

HUANG, E.T.S. and TRACm, J.H.; "The Displacement o f Residual O i l by Carbon Dioxide", paper SPE 4735, p re sen ted a t Improved O i l Recovery Symposium o f t h e SOC. o f Pe t . Eng. of AIME, Tulsa, Oklahoma (Apr i l 22-24, 1974) .

YELLIG, W .F.; "Carbon Dioxide Displacement of a West Texas Reservoir O i l " , paper SPE/DOE 9785, presented a t t h e 1981 SPE/DOE Second J o i n t Symp. on Enhanced O i l Recovery of t h e SOC. o f Pe t . Eng., Tu l sa , Oklahoma (Apr. 5-8,1981).

EIJB.UK, P.T., HALL, K.R., and HOLSTE, J .C. ; "A Review o f Experimental Techniques f o r Vapor-Liquid E q u i l i b r i a a t ltigh Pressure" , Proceedings o f 2nd I n t e r n a t i o n a l Conference on Phase E q u i l i b r i a and Fluid P r o p e r t i e s i n t h e Chemical I n d u s t r y , West B e r l i n (Ilareh 17-21, 1981), Dechema, F rankfu r t / Main, 675.

STANDING, M.B. ; "Volumetric and Phase Behavior o f O i l F i e l d Hydrocarbon Systems", SOC. o f P e t . Eng. o f AIME, D a l l a s , Texas, E igh th P r i n t i n g (1977).

2 9 5

WELKER. J .R. and DUNLOP, D.D.; "Physical P r o p e r t i e s of Carbonated O i l s " , J . Pet . Tech. (August 1963) 873.

MENZIE, D.E. and NIELSEM, R.F.; "A Study of t h e Vaporizat ion of Crude O i l by Carbon Dioxide Repressuring", J . Pet . Tech. (November 1963). 1247.

SCHNEIDER, G., ALWANI, Z., HORVATH, E., and FRANCK, E.U.; "Phasengleich- w ich te und k r i t i s c h e Erscheinungen i n b ina ren Mischsystemen b i s 1500 ba r C02 m i t n-Octan, n-Undecan, n-Tridecan und n-Hexan", Chemie-1ng.-Tech. (1967) 2 ( l l ) , 649. .

JACOBY, R.H. and YARBOROUGH, L.; "PVT Measurements on Petroleum Reservoir F l u i d s and t h e i r Uses", Ind. Eng. Chem. (October 1967), 48.

YARBOROUGH, L. and VOGEL, J.L.; "A New System f o r Obtaining Vapor and Liquid Sample Analyses t o F a c i l i t a t e t h e Study of Multicomponent Mixtures o f Elevated Pressures" , Chem. Eng. Prog. Symp. Ser . (1967) 63 (811, 1.

LEE, J .I .; " V i s c o s i t i e s of Carbon Dioxide-Sulfur Dioxide Mixtures and t h e E f f e c t of Methane on S u l f u r Dioxide-Oil Misc ib i l i t y" , Research lbte RN-9, Petroleum Recovery I n s t i t u t e , Calgary, Alberta (March 1979).

ORR, J R . , F.M., SILVA, M.K., LIEN, C.L., and PELLETIER, 11.T.; "Laboratory Experiments t o Evaluate F i e l d P rospec t s f o r C02 Flooding", paper SPE 9534 p resen ted a t 1980 Soc. o f Pe t . Eng. of AIME Eas te rn Regional Meeting, Morgantown, West Vi rg in i a (November 5-7, 1980).

CONNOR, H.J . and POPE, A.E.; "Development of Experimental Phase Equ i l ib r i a f o r Miscible Hydrocarbon Enhanced O i l Recovery", Pe t . Soc. of C I M , paper no. 81-32-41, presented a t 32nd Annual Meeting of t h e Pet . SOC. o f C I M , Calgary, A lbe r t a (May 3-6, 1981).

SAYEGH, S.G., NAJMAN, J., and HLAVACEK, B.; "Phase Equilibrium and Fluid P r o p e r t i e s of Pembina Cardium Stock-Tank Oil-Methane-Carbon Dioxide-Sulfur Dioxide Mixtures", Pe t . SOC. of CIM, paper 81-32-14, presented a t 32nd Annual Technical Meeting o f t h e Pe t . Soc. of CIM, Calgary, Alberta (May 3-6, 1981).

HENRY, R.L., FEATHER, G.L., SMITH, L.R., and FUSSELL, D.D.; " U t i l i z a t i o n of Composition Observat ion Wells i n a West Texas C02 P i l o t Flood", paper SPE/WE 9786, presented a t t h e 1981 SPE/DOE Second J o i n t Symp. on Enhanced O i l Recovery of t h e Soc. of Pe t . h g . , Tulsa , Oklahoma (Apri l 5-8, 1981).

McCAIN, JR . , W .D .; "The P r o p e r t i e s of Petroleum Fluids", Petroleum Pub l i sh ing Company, Tulsa, Oklahoma (1973).

RUTHERFORD, W.W.; " M i s c i b i l i t y Re la t ionsh ips i n t h e Displacement of Oil by Light Hydrocarbons", SOC. P e t . Eng. J. (December 1962) 340.

HOLM, L.W .; "Carbon Dioxide Solvent Flooding f o r Increased O i l Recovery", Pe t . Trans. A P E (1959) 216, 225.

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31. HOLM, L.W. and JOSEXDAL, V.A.; "Mechanisms of O i l Displacement by Carbon Dioxide", J. Pe t . Tech. (December 1974) 1427.

32. SHELTON, J.L. and YARBOROUGH, L.; "Multiple Phase Behavior i n Porous Media During COP o f Rich-Gas Flooding", J . Pe t . Tech. (September 1977) 1171.

Reservoir O i l Systems", SOC. Pe t . Eng. J . (February 1978) 20. 33. SIMON, R., ROSMAN, A., and LWi, E.; "Phase Behavior P r o p e r t i e s of C02-

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LEE, J.I. and SIGMUND, P.M.; 'Phase Behavior and Displacement S t u d i e s of Carbon Dioxide-Hydrocarbon Systems", Research Report RR-37, Petroleum Recovery I n s t i t u t e , Calgary, A lbe r t a (September 1978).

LEE, J .I. ; " M i s c i b i l i t y of Carbon Dioxide-Sulfur Dioxide-Hydrocarbon Systems", Research Note RN-8, Petroleum Recovery I n s t i t u t e , Calgary, A lbe r t a (August 1978) .

LEE, J. I.; "Ef fec t iveness of Carbon Dioxide Displacement Under Misc ib l e and Imni sc ib l e Conditions", Research Report RR-40, Petroleum Recovery I n s t i t u t e , Calgary, A lbe r t a (March 1979) .

ORR, JR. , F.M., W, A.D., and LIEN, C.L.; 'Thase Behavior o f C02 and Crude O i l i n Low Temperature Reservoirs", paper SPE 8813, -presented a t t h e F i r s t J o i n t SPEIDOE Symp. on Enhanced O i l Recovery, Tulsa , Oklahoma (Apri l 20-23, 1980).

TUREK, E.A., METCALFE, R.S., YARBOROUGH, L., and ROBINSON, J R . , R.L.; "Phase E q u i l i b r i a i n Carbon Dioxide-Multicomponent Hydrocarbon Systems: Experimental Data and a n Improved P r e d i c t i o n Technique", paper SPE 9231, p re sen ted a t t h e 55 th Annual F a l l Technical Conference and E x h i b i t i o n o f t h e SPE o f AIME, Dallas, Texas (September 21-24, 1980) .

METCALFE, R.S., FUSSELL, D.D., and SHELTON, J.L.; "A M u l t i c e l l Equi l ibr ium Sepa ra t ion Model f o r t h e Study o f M u l t i p l e Contact M i s c i b i l i t y i n Rich Gas Drives", SOC. P e t . Eng. J . (June 1973) , 147.

YELLIG, W.F. and METCALFE, R.S.; ' 'Determination and P r e d i c t i o n of COP Minimum M i s c i b i l i t y P res su res" , paper SPE 7477, presented a t t h e 53rd Annual F a l l Technical Conference and Exh ib i t i on of t h e SOC. of P e t . Eng. of A m , Houston, Texas (October 1-3, 1978).

IETCALFE, R.S .; "Effect o f I m p u r i t i e s on Minimum M i s c i b i l i t y P r e s s u r e s and Minirmm Enrichment Leve l s f o r CO2 and Rich Gas Displacement". paper SPE 9230, presented a t t h e 55 th Annual F a l l Technical Conference and E x h i b i t i o n o f t h e SOC. o f P e t . Eng. o f AIME, Dallas, Texas (September 21-24, 1980).

JOHNSON, J.P. and WLLIN, J.S.; '?leasurement and C o r r e l a t i o n o f CO2 M i s c i b i l i t y Pressures" , pape r SPE 9790, p re sen ted a t t h e 1981 SPEIDOE Second J o i n t Symposium o n Enhanced O i l Recovery o f t h e SOC. of P e t . Eng. of AIME, Tulsa , Oklahoma (Apri l 5-8, 1981).

JACOBSON, H.A.; "Acid Gases and Their Con t r ibu t ion t o M i s c i b i l i t y " , J. Can. P e t . Tech. (April-June, 1972) 56.

CRONQUIST, C.; "Carbon Dioxide Dynamic M i s c i b i l i t y w i th L igh t Reservoir O i l s " , p r e sen ted a t 4 t h Annual DOE Enhanced O i l Recovery Symposium, Tulsa , Oklahoma (August 29-31, 1978).

SIGMUND, P.M., A Z I Z , K., LEE, J.I., NGHIEM, L.X., and IEHR.4, R.; ' h b o r a t o r y C02 Floods and The i r Computer Simulation", p re sen ted a t t h e World Petroleum Congress, Bucharest , Rumania (September 1979).

WILLIAMS, C.A., ZANA, E.N., and HUMPHRYS, G.E.; "Use of t h e Peng-Robinson Equation of S t a t e t o P r e d i c t Hydrocarbon Phase Behavior and M i s c i b i l i t y f o r F lu id Displacement", paper SPE 8817, presented a t t h e F i r s t J o i n t SPEIDOE Symposium on Enhanced O i l Recovery, Tulsa , Oklahoma (Apr i l 20-23, 1980).

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IJANG, G.C. and LOCKE, C.D.; "A Laboratory Study o f t h e E f f e c t s of C02 I n j e c t i o n Sequence on T e r t i a r y O i l Recovery". SOC. Pe t . Eng. 3. (August 1980) 278.

LEACH, M.P. and YELLIG, W.F.; "Compositional Model S t u d i e s - CO2 O i l - Displacement Mechanisms", SOC. Pet . Eng. J . (February 1981). 89.

BLACKWELL, R.J .; "Laboratory Study o f Microscopic Di spe r s ion Phenomena", SOC. Pe t . Eng. J. (1962) L, 69.

PERKINS, T.K. and JOHNSTON, O.C.; "A Review o f Di f fus ion and Dispersion i n Porous Media", SOC. Pet . Eng. J. (1962) 1, 77.

VAN DER POEL, C.; "Effect o f Lateral D i f f u s i v i t y on Misc ib l e Displacement i n Hor i zon ta l Reservoirs", SOC. Pet . Eng. J. (1962) L 93.

COATS, K.H. and SMITH, B.D.; "Dead-End Pore Volume and Dispersion i n Porous Fledia", Soc. Pet . Eng. J . , (March 1964) 73.

BRIGHAM, W.E.; '%ixing Equat ions i n Shor t Laboratory Cores", SOC. Pe t . Eng. J. (February 1974) 91.

BAKER, L.E.; "Ef fec t s of Dispersion and Dead-End Pore Volume i n Miscible Flooding", SOC. P e t . Eng. J . (June 1977) 219.

YELLIG, W.F. and BAKER, L.E.; "Factors Af fec t ing Miscible Flooding Dispersion Coef f i c i en t s " , Pe t . SOC. of CIM paper no. 80-31-06, presented a t 31st Annual Technical Meeting, Pe t . SOC. of C I M , Calgary, Alberta (May 25-28, 1980).

SPENCE, J R . , A.P. and WATKINS, R.W.; 'The Ef fec t of Microscopic Core Heterogenei ty on Miscible Flood Residual Oil Saturat ion", paper SPE 9229, p re sen ted a t t h e 55 th Annual F a l l Technical Conference and Exhibi t ion of t h e SOC. o f Pe t . Eng. o f A M E , Dallas, Texas (September 21-24. 1980).

SCHNEIDER, F.N. and OWENS, W.W.; "Relat ive Pe rmeab i l i t y S tud ie s o f Gas-Water Flow Following Solvent I n j e c t i o n i n Carbonate Rocks", SOC. P e t . Eng. J. (February 1976) 23.

HENRY, R.L. and METCALFE, R.S.; "Mul t ip l e Phase Generation During C02 Flooding", paper SPE 8812, presented a t t h e F i r s t J o i n t SPE/DOE Symposium on Enhanced O i l Recovery, Tulsa , Oklahoma (Apri l 20-23, 1980).

STALKUP, F.I.; "Displacement of O i l by Solvent a t High Water Saturat ion", SOC. Pe t . Eng. J . , (December 1970) 337.

SHELTON, J.L. and SCHNEIDER, F.N.; "The E f f e c t s of Water I n j e c t i o n on Misc ib l e Flooding Methods Using Hydrocarbons and Carbon Dioxide", SOC. Pet . Eng. J. (June 1975) 217.

NATRINS, R.W.; "A Technique f o r t h e Laboratory lleasurement of Carbon Dioxide Unit Displacement E f f i c i ency i n Reservoir Rock", paper SPE 7474, presented a t t h e 53rd Annual f a l l Technical Conference and e x h i b i t i o n of t h e Sac. of P e t . Eng. of AINE, Houston, Texas (October 1-3, 1978).

HELLER, J.P., TABOR, J.J. and LOCKE, C.D.; "Mobility Control f o r COP Floods - A L i t e r a t u r e Survey", U.S. Dept. of Energy Pub l i ca t ion no. DOE/MC/10689-3 (1980).

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CIIRISTIAN, L.D., SHIRER, J .A . , KIMBLE, E.L., and DLAClrJJELL, R.J.; "Planning a T e r t i a r y O i l Recovery P r o j e c t for J a y - L i t t l e Escambia Creek F i e l d Unit", paper SPE/DOE 9805, presented a t t h e 1981 SPE/DOE Second J o i n t Symposium on Enhanced O i l Recovery of t h e SOC. o f P e t . Eng., Tulsa , Oklahoma (Apri l 5-8, 1981).

RANDALL, T.E., WANSLEEBEN, J. and SIGMUND, P.M.; "Physical Model, West Wilmar Rich Gas P i l o t " , P e t . Soc. of C M paper no. 51-32-16, presented a t t h e 32nd Annual Technical Meeting of t h e P e t . Soc. of CIM, Calgary, A lbe r t a (May 3-6, 1981).

ROSMAN, A. and ZANA, E.; "Experimental S t u d i e s o f Low I n Displacement by C02 In j ec t ion" ; paper SPE 6723, presented a t t h e 52nd Annual F a l l Technical Conference and Exh ib i t i on o f t h e Soc. of Pe t . Eng. gf AIME, Denver, Colorado (October 9-12, 1977).

ROSMAN, A. and SIMON, R.; "Flow Heterogenei ty i n Reservoir Rocks", J. P e t . Tech. (December 1976) 1427.

BATYCKY, J.P., M I R K I N , M . I . , JACKSON, C.H., and BESSERER, G.J . ; "Miscible and Immiscible Displacement S t u d i e s on Carbonate Reservoir Cores", J. Can. P e t . Tech. (1981) 20 (l), 104.

GRIST, D.M., LANGLEY, G.O., and NEUSTADTER, E.L.; "The Dependence of Water Pe rmeab i l i t y on Core Cleaning Methods i n t h e Case of Some Sandstone Samples", J. C a n P e t . Tech. (April-June 1975) 48.

CUIEC, L., LONGERON, D . and PACSIXSZKY, J.; "On t h e Necessi ty o f Respect ing Reservoir Condi t ions i n Laboratory Displacement Studies" , paper SPE 7785, presented a t t h e Middle Eas t O i l Technical Conference of t h e Soc. of P e t . Eng. , Manama, Bahrain (March 25-29, 1979).

HARVEY, JR., M.T., SHELTOM, J.L., and KELM, C.H.; "Field I n j e c t i v i t y Experiences With Misc ib l e Recovery P r o j e c t s Using A l t e r n a t e Rich-Gas and Water In j ec t ion" , J. P e t . Tech., (September 1977) 1051.


COMPLEX STUDY OF COZ FJBODING IN HUNGARY

SANDOR DOLESCHALL, GABOR ACS, &VA FARKAS,

Hungarian Hydrocarbon Institute

TIBOR PAAL, JANOS TOROK

V A L ~ R BALINT

General Contracting and Designing Office for the Oil Industry, “Olajterv ”

ZOLTAN B I R ~

lhznsdanubian Oil and Gas Roduction Company

ABSTRACT

A systematic program o f carbonated natura l gas f l ood ing has been c a r r i e d ou t i n Hungary, based on laboratory PVT and displacement studies, fol lowed by composi- t i o n a l mathematical s imu la t i on and. f i e l d experiment on depleted rese rvo i r .

PVT stud ies have proved t h a t gas con ta in ing 81 mole % carbon d iox ide can be used f o r EOR purposes. The s tud ies covered the vo lumetr ic and phase behaviour o f carbonated natura l gas f l ood ing under f i e l d cond i t i ons and the r e s u l t s proved t h a t such f l ood ing was e f f i c i e n t even i f the gas i s n o t pure carbon dioxide. Based upon t h e o r e t i c a l cons iderat ions a technologica l scheme has been developed t o increase the sweep e f f i c i e n c y .

A ten-component, three-phase mathematical model developed t o simulate carbon d iox ide f l ood ing i s s u i t a b l e f o r t r e a t i n g s ing le - and multi-phase systems. The d i f f e r e n c e equations handle the systems w i t h d i f f e r e n t number o f phases I n a un i form way, thus the generation and disappaerance o f phases can be fol lowed by the model wi thout d i f f i c u l t i e s .

The computer model was used t o simulate p a r t i a l l y m isc ib le carbonated natura l gas f l o o d i n g i n t h e western area o f t h e Budafa o i l f i e l d . The production h i s t o r y match and p r e d i c t i o n agreed wel l w i t h the f i e l d data.

INTRODUCTION

The o i l resources o f Hungarian rese rvo i r s cover o n l y a small p a r t o f the country’s demand, and the import of crude o i l imposes a considerable economic burden on a country developing i t s indust ry . Apart from the need- to search f o r new o i l f i e l d s , it became ev ident as long ago as the f i f t i e s t h a t it was important t o consider secondary and l a t e r t h e t e r t i a r y recovery methods. Among the o the r p o s s i b i l i t i e s t h e e f f e c t o f carbon d iox ide was a l s o studied, and

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very soon most a t t e n t i o n focused on the questions o f C02 f l ood ing because i n Hungary t h e occurrence o f natura l carbon d iox ide i n h igh carbon d iox ide content natura l gases i s more o f t e n found and t o a greater ex ten t than the world average. Some r e s u l t s o f C02 f l ood ing i n Hungary can be found i n Ref. 1 .

PVT AND PHASE BEHAVIOUR MEASUREMENTS

F e a s i b i l i t y s tud ies o f t h e a p p l i c a t i o n p o s s i b i l i t i e s o f carbon d iox ide and carbonated natura l gases s ta r ted i n 1955 w i th a se r ies o f PVT measurements. The very f i r s t PVT stud ies proved t h a t carbonated natura l gas a l t e r s the v i s c o s i t i e s and vo lumetr ic p roper t i es o f crudes w i t h very d i f f e r e n t d e n s i t i e s i n a favourable way compared w i t h t h e e f f e c t o f lean o r wet natura l gases under t h e same condi t ions, mainly i f t h e carbon d iox ide content o f t h e d isso lved gas i s above 60 mole 5 . Based upon the r e s u l t s o f more d e t a i l e d PVT measurement, sets o f curves have been developed t o p r e d i c t t h e s o l u b i l i t y , swe l l i ng and v i s c o s i t y o f monophase r e s e r v o i r oi l--carbonated na tu ra l gas systems. The actual PVT p roper t i es o f t h e o r i g i n a l gas saturated o i l were chosen as a reference s t a t e t o e l i m i n a t e t h e poss ib le large e r r o r s coming from the unknown parameters o f such very complex systems, and o n l y t h e change o f t he given p roper t i es was co r re la ted w i t h the d isso lved carbon d iox ide conten t . I n t h i s way simple, easy t o use equations w i t h good accuracy have been developed. For example, t he p r e d i c t i o n o f v i s c o s i t i e s o f saturated and undersaturated crudes under d i f f e r e n t cond i t i ons i s poss ib le w i t h the use o f on l y one measured v i s c o s i t y value.

I t has been proved t h a t i n t h e case o f Hungarian crude o i l s , bearing i n mind the actual rese rvo i r condit ions, t h a t no complete m i s c i b i l i t y occurs even i f t he d isso lved gas i s pure carbon d iox ide.

I n t h e course of t h e thorough examination o f t he PVT data "unusual" behaviour was observed. Repeated measurements i n a windowed PVT c e l l revealed the presence o f a carbon d iox ide r i c h second l i q u i d phase which e x i s t s w i t h i n a d e f i n i t e pressure-temperature range above a c e r t a i n gas--oil r a t i o . Th is reg ion depends upon t h e t o t a l composition o f t he system and the phenomenon i s connected w i t h t h e r e s t r i c t e d s o l u b i l i t y o f carbon d iox ide i n rese rvo i r o i l s . P a r t i t i o n o f l i g h t and intermediate hydrocarbons between the r e s e r v o i r o i l and the second l i q u i d phase has been proven - i n agreement w i th o the r expe- r ience. I n the case o f c e r t a i n Hungarian crude o i l s r e v e r s i b l e p r e c i p i t a t i o n o f semi-sol id p a r t i c l e s has a l s o been observed bu t mostly under such circumstances which cannot be rea l i zed i n actual rese rvo i r s . I t i s i n t e r e s t i n g t h a t these phenomena occur i n the presence o f carbonated natura l gases, too, even i f they a re r e l a t i v e l y r i c h I n l i g h t hydrocarbon f r a c t i o n . The existence o f t he mentioned mult iphase systems had t o be considered i n planning vapour-- l iquid e q u i l i b r i u m studies.

The aim o f these s tud ies i s t o determine exact K values according t o the need o f compositional mathematical s imulat ion. Equ i l i b r i um r a t i o s had been determined f o r c h a r a c t e r i s t i c r e s e r v o i r oi l--carbonated natura l gas as wel l as rese rvo i r oil--water--carbonated natura l gas systems and a method f o r e s t i - mation was developed. As a r e s u l t o f add i t i ona l measurements and comparison of experimental w i t h computed data us ing d i f f e r e n t equations o f s t a t e it i s concluded t h a t f u r t h e r improvements a re necessary both f o r t h e development o f general ized K f unc t i ons and equations o f s t a t e together w i t h the improvement o f i n t e r a c t i o n c o e f f i c i e n t s .

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30 1

Judging by the r e s u l t s o f o the r studies, t h e i n t e r f a c i a l tens ion decreases w i t h increas ing carbon d iox ide content i n gas--oil--water systems. Volumetric and phase behaviour as well as water content and hydrate forming cond i t i ons o f carbonated natura l gases i n Hungary were a l s o s tud ied and the r e s u l t i n g data used t o formulate general ized re la t i onsh ips .

Experimental data on s o l u b i l i t y , swe l l i ng and v i s c o s i t y o f t y p i c a l rese rvo i r waters - saturated w i t h carbonated natura l gases having d i f f e r e n t composition, even i n t h e presence o f calcium carbonate and r e s e r v o i r rocks conta in ing c lay minera ls - together w i t h vapour-- l iquid e q u i l i b r i u m r a t i o s supplied f u r t h e r in format ion enabl ing a b e t t e r understanding o f t h e mechanism o f carbonated natura l gas f looding. I t has been pointed o u t t h a t because o f t he i n t e r a c t i o n o f carbonated water and rese rvo i r rocks c e r t a i n c l a y minera ls con t rac t and t h i s may improve the e f f i c i e n c y o f the process i n p rac t i ce .

A PVT model was used t o f o l l o w the change o f t h e vo lumetr ic and phase behaviour and the e q u i l i b r i u m composit ion o f phases i n the course o f f looding. This model contained water-, o i l - and gas-phases under r e s e r v o i r cond i t i ons w i t h a r a t i o corresponding t o t h e actual sa tu ra t i on a t a given, depleted f i e l d . The pressure was increased t o the o r i g i n a l r e s e r v o i r pressure d i r e c t l y by t h e i n j e c t i o n gas. In another se t o f experiments the f i n a l pressure was reached step by step, t he vapour phase g radua l l y being changed by t h e i n j e c t i o n gas a t each i n t e r - mediate pressure u n t i l e q u i l i b r i u m composition was approached. These experiments were repeated f o r d i f f e r e n t f i e l d cond i t i ons us ing i n j e c t i o n gases w i th d i f f e r e n t carbon d iox ide content. I n t e r p r e t a t i o n o f t he r e s u l t s revealed the Importance o f t h e dynamic pressure-increase process being appl ied f o r carbonated natura l gas f looding, t he r o l e o f the l i g h t hydrocarbon f r a c t i o n present and supported the conclusion prev ious ly drawn on t h e bas is o f PVT s tud ies o f mono-and two- -phase systems.

Taking i n t o considerat ion the composition o f t he g radua l l y displaced gas, it has been concluded t h a t it i s no t poss ib le i n p r a c t i c e t o replace a l l the f ree and d isso lved gas by a carbon d iox ide s lug o f reasonable s ize. I t has a l so been found t h a t despi te the d i l u t i o n o f t h e s lug by hydrocarbon gas i n the pores, r e l a t i v e l y s i g n i f i c a n t vapor i za t i on o f t he o i l takes place i f the carbon d iox ide content o f t he f r e e gas phase i s above a c e r t a i n c r i t i c a l concentrat ion. This c r i t i c a l value, which depends upon t h e pressure, temperature and the c h a r a c t e r i s t i c s o f t he o i l , can a l so be exceeded by using carbonated natura l gases f o r t he i n jec t i on . These observations confirmed i n d i r e c t l y t h e idea about t h e probable formation o f a m i s c i b l e f r o n t i n the r e s e r v o i r under dynamic cond i t i ons dur ing carbonated na tu ra l gas f looding.

As t o the vo lumetr ic p roper t i es and v i s c o s i t i e s o f t he e q u i l i b r i u m l i q u i d phases no substant ia l d i f f e rence could be found on comparing the e f f e c t o f a carbon d iox ide s lug and a l a rge r volume o f carbonated natura l gas w i th higher carbon d iox ide content.

LABORATORY DISPLACEMENT STUDIES

Fol lowing encouraging PVT r e s u l t s dynamical laboratory s tud ies were c a r r i e d ou t t o examine the e f f i c i e n c y o f C02

displacement processes. The l i n e a r model used f o r t h e measurements was 1 m long and 25 mm i n diameter. Nonconsolidated r e s e r v o i r sandstone cores and r e s e r v o i r f l u i d were used f o r these displacement tes ts . Th i s technique i s s u i t a b l e f o r s tudy ing product ion h i s t o r i e s , as well as var ious forms o f C02 f l o o d i n g and the actual mechanism o f t h e process.

302

As a f i r s t s tep t h e e f f e c t o f carbonated water was examined. Carbonated water sa tu ra ted a t r e s e r v o i r p ressure and tempera ture was i n j e c t e d i n t o t h e p r e v i - ous l y water f looded core . Carbon d i o x i d e appeared i n t h e e f f l u e n t a f t e r i n j e c t i n g one pore volume o f sa tu ra ted water . To reach t h e i n j e c t e d e q u i l i b r i u m concen t ra t i on o f t h e carbonated water i n t h e e f f l u e n t 4-8 pore volumes o f sa tu ra ted water were necessary. Consequently, t h e a d d i t i o n a l o i l was produced w i t h a r a t h e r h i g h water c u t . The a d d i t i o n a l o i l was 5-7 % o f t h e o r i g i n a l o i l an p lace . Because o f t h e i n j e c t i o n o f a l a r g e volume o f water and t h e modest a d d i t i o n a l o i l recovery, t h i s method i s uneconomic.

To inc rease t h e amount o f i n j e c t e d carbon d iox ide , ove rsa tu ra ted water was used i n t h e nex t s e r i e s o f exper iments. The a d d i t i o n a l o i l reached 10 % o f 0 . i .p . and favourab le e f f e c t s o f f r e e gas s a t u r a t i o n were observed, t oo . However even i n t h i s case, 3-5 pore volumes o f carbonated water were used t o o b t a i n t h i s r e s u l t .

Gaseous carbon d i o x i d e was i n j e c t e d i n t o t h e model when s tudy ing t e r t i a r y recovery methods f o r dep le ted r e s e r v o i r s . Two d i f f e r e n t i n i t i a l s a t u r a t i o n c o n d i t i o n s were used as average r e s e r v o i r c o n d i t i o n s f o r m o d e l l i n g p r o d u c t i o n h i s t o r i e s : - t h e dep le ted r e s e r v o i r has a h i g h gas s a t u r a t i o n , -25-35 %; - t h e dep le ted r e s e r v o i r has a low gas s a t u r a t i o n and h i g h water s a t u r a t i o n ,

-50-60 $.

The pressure was increased t o t h e o r i g i n a l r e s e r v o i r p ressure by i n j e c t i n g carbon d i o x i d e gas. A f t e r t h e pressure bu i ld -up , d i f f e r e n t s i z e s o f C02 s l u g s were i n j e c t e d and fo l l owed by r e s e r v o i r water f l o o d i n g . The a d d i t i o n a l o i l recovery as a f u n c t i o n o f s l u g s i z e was s tud ied . The probab le op t ima l s l u g s i z e was about 0.2 PV. Using t h i s , t h e a d d i t i o n a l o i l recovery was 12-16 % o f t h e o r i g i n a l o i l i n p l a c e f o r systems hav ing a h i g h i n i t i a l gas s a t u r a t i o n and 8-12 % f o r t h e case o f h i g h i n i t i a l water s a t u r a t i o n . The a d d i t i o n a l o i l recovery was always r e l a t e d t o t h e r e s i d u a l o i l s a t u r a t i o n o f t r a d i t i o n a l water f l o o d i n g .

A l l o f t h e dynamic displacement t e s t s , mentioned above were performed w i t h p r a c t i c a l l y pu re carbon d i o x i d e . Tes ts were conducted us ing carbonated n a t u r a l gases, t oo . The r e s u l t s showed t h a t t h e use o f ca rbo ra ted n a t u r a l gases hav ing a CO con ten t above 80 mole $, g i v e n o t worse, b u t b e t t e r r e s u l t s i n most cases i f t h e proper d isp lacement techno logy i s used.

2

Complex f l o w c o n d i t i o n s and physico-chemical processes e x i s t i n r e s e r v o i r o i l - - r e s e r v o i r water--carbon d i o x i d e - - r e s e r v o i r rock systems. The parameters i n f l u e n c i n g t h e e f f e c t i v e n e s s o f C02 f l o o d i n g must be i n d i v i d u a l l y determined f o r each p r o j e c t . I f t h e w e t t a b i l i t y o f r e s e r v o i r rock changes f rom water-wet t o o i l - w e t t h e favourab le e f f e c t s o f f r e e gas s a t u r a t i o n and t h e l a t e r water f l o o d i n g a r e reduced. T h i s change of w e t t a b i l i t y depends upon many f a c t o r s - among o thers , on t h e q u a n t i t y o f i n j e c t e d C02 (2 ) .

I f carbon d i o x i d e i s i n j e c t e d i n t o t h e dep le ted o i l r e s e r v o i r it i n t e r a c t s w i t h t h e r e s e r v o i r f l u i d and component mass t r a n s f e r s t a r t s among t h e phases. As a r e s u l t o f t h i s process t h e o i l phase w i l l be r i c h e r i n components hav ing h i g h e r mo lecu la r we igh ts . I n extreme cases some o f t h e components w i t h i n t e r f a c i a l a c t i v e c h a r a c t e r i s t i c s may adsorb on t h e rock sur face , t he reby changing t h e w e t t a b i l i t y p r o p e r t i e s o f t h e system and lead ing t o t h e rock becoming more o i l - w e t . A l though t h e carbon d i o x i d e c o n t e n t o f t h e o i l phase decreases t h e v i s c o s i t y o f c rude r i c h i n h i g h mo lecu la r components and s w e l l s t h e o i l - phase a p o s s i b l e inc rease i n t h e o i l - w e t c h a r a c t e r coun te rac ts these favourab le e f f e c t .

303

Re la t i ve permeabi l i ty curves f o r saturated carbonated water systems were a l so measured. The character o f r e l a t i v e permeabi l i ty curves j u s t i f i e d the e f f e c t mentioned above. Under some circumstances the porous medium became more o i l -we t . Decreasing o i l and increas ing water pe rmeab i l i t i es could be observed i n c e r t a i n sa tu ra t i on ranges, depending upon the CO content o f t h e gas used. The increase i n res idual o i l sa tu ra t i on was a l so observed w i th increas ing The bases o f comparison were the r e l a t i v e curves o f hydrocarbon gas saturated s y s terns.

2 C02 content.

COMPUTER MODEL

A three-phase, ten-component mathematical model has been developed t o study carbon d iox ide displacement experiments and to p r e d i c t performances (3, P a r t I . ) . The governing d i f f e r e n t i a l equations o f the compositional model w r i t t e n i n a usual form a re as fo l lows:

k j f j - C . = d i v [ 5 2 (grad p j + $9 grad z) + @zSjSjDj , igrad C j Aj J t i

j

+ 9 i i = l,Z, ..., I0

j = gas, o i l , water

The bas is o f t he c a l c u l a t i o n s i s t he assumption t h a t local thermodynamic e q u i l i b r i u m e x i s t s dur ing displacement. I n t h i s way, t h e re la t i onsh ips corre- la ted w i th laboratory PVT and e q u i l i b r i u m measurements can d i r e c t l y be employed. I n accordance w i t h the laboratory measurements, the formation f l u i d o f Budafa o i l f i e l d was considered as a ten-component system. The components are: seven hydrocarbon components /C,, C2, C3, C4, C5, C6, C /, nitrogen, carbon d i x i d e and water.

As t he water phase e x i s t s everywhere i n t h e formation, and dur ing the water i n j e c t i o n a g rea t amount of carbon d iox ide i s t o be transported by water, the s o l u t i o n o f t he carbon d iox ide component i n the water phase cannot be neglected. Besides three-phase regions, two-, moreover one-phase regions occur dur ing the processes, thus a method has been developed t h a t a l lows one t o e a s i l y ca l cu la te a change i n the number o f phases. The three-phase e q u i l i b r i u m was in te rp re ted as the simultaneous existence o f two two-phase equ i l i b r i ums .

To s i m p l i f y t he e q u i l i b r i u m ca lcu la t i ons the f o l l o w i n g assumptions were made: - the gas and o i l phases do no t con ta in a water component, - the d isso lved gas i n t h e water phase cons is t s o f carbon d iox ide only . /When

checking the c a l c u l a t i o n s the d isso lved gas i n t h e water phase contained methane, as well , bu t t h e l i t t l e in f luence o f t h i s on the phase equ i l i b r i um made it reasonable t o neglect it./

7+

304

When c a l c u l a t i n g the phase equi l ibr ium, f l ash ca lcu lat i .ons a re used t o determine the mole f r a c t i o n s o f t he phases; however, t he c a l c u l a t i o n o f three-phase e q u i l i b r i u m make i t necessary t o so lve a coupled system o f two nonl inear a l - gebraic equations. Occasional ly, mainly when the number o f phases changes, convergence problems o f i t e r a t i v e techniques occur. The system was transformed i n t o one nonl inear a lgeb ra i c equation, and a numerical procedure combining the Newton-method and the method o f halving, ensure f a s t convergence i n every case. The densi ty o f t he gas phase i s ca l cu la ted using the Redlich-Kwong equation o f s ta te. When determining dens i t i es o f t h e f l u i d phases the labo- r a t o r y c o r r e l a t i o n s a re appl ied. I n accordance w i t h these c o r r e l a t i o n s the formation volume f a c t o r i s ca l cu la ted as a func t i on o f the d isso lved g a s / f l u i d r a t i o f o r both f l u i d phases. Thus the q u a n t i t y o f t he dissolved gas has t o be known. Because the composit ion o f t he phases i s known, the d isso lved gas /o i I r a t i o can be determined from the composit ion o f t he o i l phase by normal f l a s h ca l cu la t i on . As f o r t he dissolved gas/water r a t i o , i t was assumed t h a t water i n i t s normal s t a t e i s f r e e o f gas.

I n order t o check the PVT and e q u i l i b r i u m c a l c u l a t i o n s laboratory pressure- -build-up measurements were simulated by a one-volume element model. Very good matches could be achieved by modifying the molecular weight o f t he C7+ component by 5 $.

FIELD EXPERIMENT

A f t e r some p i l o t t e s t s the f i r s t large-scale process was s ta r ted i n the western area o f t he Budafa o i l f i e l d i n 1972. The area i s a sec t i on o f t he Lower-Pan- nonian /Lower-Pliocene/ Budafa rese rvo i r which cons is t s o f f ou r separable sequences o f s t r a t a o f t he same hydrodynamic system. The formations are heterogeneous v e r t i c a l l y and h o r i z o n t a l l y . The e f f e c t i v e formation th ickness va r ies from 1-2 m t permeabi l i ty 0.1 pm . The sandstone formations occu r r i ng a t an average depth o f 850 m have a temperature o f 64 OC. The i n i t i a l pressure level judging by the hyd ros ta t i c cond i t i on a t the beginning o f product ion was 9800 kPa. The producgd crude i s o f an i n ermed a t e - p a r a f f i n character, i t s average densi ty a t 20 C being 0.817.10' kg/mf. The r e s e r v o i r o i I was i n i t i a l l y saturated, the two upper sequences o r i g i n a l l y had an extens ive gas cap. Th is accumulation was unfavourable from the p o i n t o f view o f t e r t i a r y recovery because the o i l zones o f the two lower layers were s i t u a t e d under the gas caps o f t he two upper I ayers.

Production was begun i n J u l y o f 1937. Fol lowing the r a i d increase i n the number o f wells, crude product ion amounted t o 89,800 m /year i n t941 which was the peak product ion o f t h i s area. The energy o f the formation decreased because o f t he h igh product ion leve l and r e s t r i c t e d egge water d r i ve . I n order t o overcome the energy reduction, 139 m i l l i o n m hydrocarbon gas was in jec ted i n t o the r e s e r v o i r from 1942 t o 1958. During the primary and secondary displacements the s o l u t i o n gas dr ive, t he energy o f gas caps and, t o a s l i g h t extent, edge water d r i v e worked wh i l e the formation pressure decreased t o an average level o f 2900 kP3, which was considered as an

3 abandon pressure. A t o t a l o f 1 m i l l i o n m o i l and 600 m i l l i o n m gas was produced. The average recovery e f f i c i e n c y was 22.6 $.

30 m. The average p o r o s i t y i s 21 $, t he average hor izonta l 9

!?

305

I

306

A t t h e beg inn ing o f t e r t i a r y recovery t h e o i l zones o f t h e area had a h i g h gas s a t u r a t i o n . T e r t i a r y recovery by carbonated n a t u r a l gas was r e a l i z e d by u s i n g 41 i n j e c t i o n , 71 p r o d u c t i o n and 9 o b s e r v a t i o n w e l l s . When des ign ing t h e technology, t h e e x i s t i n g w e l l s i n t h e area were taken i n t o account, and t h e system c o u l d be c h a r a c t e r i z e d by an i r r e g u l a r m u l t i - s p o t p a t t e r n . The we l l p a t t e r n used i s shown i n F i g . 1.

I n t h e f i r s t phase o f t h e t e r t i a r y recovery, carbonated n a t u r a l gas was i n j e c t e d i n t o t h e fo rma t ion d u r i n g which c o n t r o l l e d p r o d u c t i o n was r e a l i z e d . The carbonated n a t u r a l gas used was produced f rom a h i g h pressure r e s e r v o i r d iscovered i n t h e a c t u a l area o f Budafa. T h i s gas - hav ing a carbon d i o x i d e con ten t o f 81 m l e % and l i g h t hydrocarbons - was i n j e c t e d i n t o t h e low pressure o i l r e s e r v o i r by means o f n a t u r a l energy. The carbon d i o x i d e appeared i n t h e p roduc t i on w e l l s 1-2 months a f t e r t h e beg inn ing o f i n j e c t i o n . Data r e l a t i n g t o i n j e c t i o n and p roduc t fon3 ra tes /F ig . 2/ show t h a t t h e GOR amounted t o a ve ry h i g h l eve l /3000-5000 m /m / d u r i n g t h e i n j e c t i o n . T h i s disadvan- tageous e f f e c t was caused by t h e h i g h gas s a t u r a t i o n d a t i n g back t o t h e p r imary and secondary recovery . No o i l bank fo rma t ion cou ld be observed i n any o f t h e p r o d u c t i o n w e l l s . Gas and l i q u i d f l o w always occur red s imu l - taneous ly i n t h e l aye rs . I n o r d e r t o d i m i n i s h t h e h igh GOR va lue o f t h e produced f l u i d , water i n j e c t i o n was s t a r t e d a t t h e gas -o i l c o n t a c t o f t h e two upper l a y e r s i n t h e autumn o f 1974, and t h e whole a rea was water f l ooded f rom t h e summer o f 1975. A t t h a t t i m e t h e averag? pressure o f t h e r e s e r v o i r was 10,900 kPa, t h e water i n j e c t i o n r a t e f500 m /day.

GOR response t o water f l o o d i n g was observed f rom t h e end o f 1974 when t h e cha rac te r o f p r o d u c t i o n changed remarkably. Along w i t h i nc reas ing o i l p ro - d u c t i o 3 r y t e , t h e g a s / o i I r a i o decreased f rom t h e p rev ious years ’ l eve l o f 5000 m /m t o about 600 m3/$. The changed c o n d i t i o n s can be seen i n F i g . 2.

The carbon d i o x i d e c o n t e n t o f t h e produced gas remained above 65 mole % d u r i n g t h e water i n j e c t i o n , which made i t e v i d e n t t h a t i n j e c t i o n o f a d d i t i o n a l c rbonated n a t u r a l gas was n o t necessary. U n t f I 1 s t January 1981, 694 m i l l i o n m carbonated n a t u r a l gas and 3.013 m i l l i o n m water had been i n j e c t e d i n t o t h e fo rmat ion . I t should be ment ioned t h a t t h e g r e a t e r p a r t o f t 9 e i n j e c t e d gas was used t o f i l l up t h e gas caps. By January 1981, 173,000 m o i l and

3 1.072 m i l l i o n m water had been produced and t h e average recove ry e f f i c i e n c y had been 27.5 %, t h u s t e r t i a r y recovery r e s u l t e d i n a d d i t i o n a l o i l o f 3.9 %. T h i s amount o f a d d i t i o n a l o i l i s , however, an average va lue . For example, t h e a d d i t i o n a l o i l f rom Sec t ion I I . q u i t e cons ide rab le i n t h a t t h e e a r l i e r va lue was ‘12.7 % 0 . i .p . The method has proved t o be success fu l f o r one- layer, r e l a t i v e l y homogeneous s e c t i o n s hav ing low water s a t u r a t i o n , and t h e e f f e c - t i v e n e s s was poor, about 1-2 % f o r t h e m u l t i - l a y e r s fo rma t ion under t h e gas caps. The d isp lacement i s s t i l l c o n t i n u i n g . The f i n a l amount o f a d d i t i o n a l o i l expected i s 5.7 I. The p r o d u c t i o n o f a d d i t i o n a l o i l proved t o be econom- i c a l l y worth wh i l e .

3

HISTORY MATCH AND PREDICTION

The f i e l d exper iment was analysed by s i m u l a t i o n o f performance h i s t o r y (3, P a r t I I.). The r e s e r v o i r i s t h i n , heterogeneous, laminated and n e a r l y h o r i z o n t a l , t h u s an a rea l model was used and t h e e f f e c t s o f c a p i l l a r i t y and g r a v i t a t i o n were neg lec ted . Because of t h e complex pe t rog raph ic and h e t e r - ogeneous s a t u r a t i o n cond i t i ons , t h e Budafa-West m u l t i - l a y e r r e s e r v o i r

307

L ----

I

n

Grp

FIGURE 2 Butlofa-West Unit performcnce history

308

c o n s t i t u t e s a compl ica ted system. For t h i s reason an e a s i l y separable, one- - l a y e r s e c t i o n o f t h e r e s e r v o i r was examined be long ing t o t h a t a rea where t h e h ighes t amount o f o i l o r i g i n a t e d from. /Pr imary and secondary displacement r e s u l t e d i n 45.2 % f o r t h i s s e c t i o n . / The s e c t i o n i s shown i s F i g . ‘I as Sec t ion 1 1 .

Because o f computer r e s t r i c t i o n /an ICT 1905 computer w i t h a memory o f 32 Kwords was used/, we cou ld n o t desc r ibe a l l t h e i n j e c t i o n and p r o d u c t i o n w e l l s o f t h e sec t i on ; o u r i n t e n t i o n was t o o b t a i n an o v e r a l l p i c t u r e o f t h e process. / I t i s t o be noted t h a t d e t a i l e d da ta on fo rma t ion parameters were a l s o i naccess ib le . / The s e c t i o n was cons idered t o be o f cons tan t th ickness , h o r i z o n t a l , and t h e average rock parameters and i n i t i a l s a t u r a t i o n r e f e r r i n g t o t h e beg inn ing o f t h e t e r t a r y recovery were used. We wished t o make use o f a l l t h e measured data, t h e r e f o r e on t h e bases o f averag ing t h e d i s t a n c e s o f t h e i n j e c t i o n and p roduc t i on w e l l s o f t h e s e c t i o n an e i g h t h o f a f i v e - s p o t element was con- s t ruc ted . The i n j e c t i o n and t h e p r o d u c t i o n da ta o f t h e model were c a l c u l a t e d from t h e cumu la t i ve da ta o f t h e s e c t i o n u s i n g t h e pore volume r a t i o o f t h e s e c t i o n and those o f t h e e i g h t h o f t h e f i v e - s p o t element.

R e l a t i v e p e r m e a b i l i t y curves f o r three-phase carbonated systems were no t a v a i l a b l e . Based upon l a b o r a t o r y measurements and pub l i shed da ta a s imp le fo rm o f paramet r ic r e l a t i v e p e r m e a b i l i t y curves were cons t ruc ted , and parameters o f t h e curves were determined by h i s t o r y matching. Pressure and p r o d u c t i o n da ta o f 5.5 years /2.5 years o f gas i n j e c t i o n , 3 years o f water i n j e c t i o n / were used. I t seemed t h a t no parameter group can be chosen t o s imu la te e a r l y breakthrough o f carbon d iox ide . A n a l y s i s o f h o r i z o n t a l p e r m e a b i l i t y d i s t r i - b u t i o n i n t o v e r t i c a l d i r e c t i o n us ing con t inuous c o r e samples o f t h e r p s e r v o i r examined showed t h a t 20 % o f t h e p e r m e a b i l i t y da ta were above 0.31 pm d i f f e r e d remarkably f rom t h e average va lue . The f l o o d i n g process i s very s t r o n g l y i n f l uenced by t h e presence o f h i g h p e r m e a b i l i t y zones. The he te r - ogene i t y was taken i n t o account i n a s imp le way, t h e t h i c k n e s s was d i v i d e d i n t o a good and a poor p e r m e a b i l i t y l aye r .

The r e s u l t s o f t h e h i s t o r y match can be seen i n F i g . 3 . The computed average pressures d i f f e r e d f rom t h e measured ones by o n l y about 5 %. A f t e r hav ing good r e s u l t s on t h e h i s t o r y match f o r Sec t i on I I , t h e model was app l i ed t o t h e o t h e r 5 s e c t i o n s o f t h e area. 15-25 s i m u l a t i o n s were used t o reach t h e f i n a l r e s u l t s f o r each case. We had t o assume i n t h e mode l l ing , t h a t no f l o w boundar ies e x i s t e d between t h e s e c t i o n s though, as i s t o be expected, t h i s i s n o t t h e case. T h i s f a c t was proved by t h e c a l c u l a t i o n s . To some e x t e n t we had t o mod i fy t h e i n j e c t e d gas t o g e t t h e good pressure h i s t o r y match. However, these m o d i f i c a t i o n s were equa l i zed f rom t h e v i e w p o i n t o f t h e whole area, and a c a l c u l a t e d gas l o s s o f o n l y 6 % r e s u l t e d .

The r e s u l t s o f h i s t o r y matching a r e summarized i n F i g . 4 . The c a l c u l a t i o n s were performed i n 1978. The f i g u r e shows p r e d i c t i o n s u n t i l 1983 toge the r w i t h t h e a c t u a l p roduc t i on parameters o f t h e l a s t t h r e e years .

which

CONCLUSIONS

A f t e r thorough and ex tens i ve s t u d i e s economic f i e l d - w i d e t e r t i a r y displacement by carbon d i o x i d e c a r r i e d o u t i n Hungary. t h e three-phase system can be model led w i t h good accurarcy us ing t h e l a b o r a t o r y c o r r e l a t i o n s . The CO d isp lacement has proved t o be success fu l f o r one- layer, r e l a t i v e l y homogeneous s e c t i o n s hav ing low water s a t u r a t i o n .

Vo lumet r ic and phase behaviour o f

2

309

FIGURE 3. Comparison of measured and cornouted data B u d o f o - W e s t unit S e r t ; o n II .

b c

/ /'

/ / ,

r01.r

- .mom\ .-

FIGURE L. Comparison of measured a n d computed data B u d a f a - W e s t unit

311

U t i l i z a t i o n of t h e l oca l p o t e n t i a l proved, i n t h i s case, t o be a s u b s t a n t i a l f a c t o r i n a c h i e v i n g economic a d d i t i o n a l o i l p r o d u c t i o n the reby overcoming t h e e f f e c t s o f un favourab le r e s e r v o i r c o n d i t i o n s .

NOMENCLATURE

C

D

9

K

k

P

9 S

t

-

mass c o n c e n t r a t i o n

d i f f u s i v i t y

g r a v i t a t i o n a l a c c e l e r a t i o n

p e r m e a b i l i t y t enso r

r e l a t i v e p e r m e a b i l i t y

p ressu re

mass s i n k p e r u n i t volume p e r u n i t t ime

sa t u r a t i on

t i m e

depth

v i s c o s i t y

d e n s i t y

p o r o s i t y

Subsc r ip t s

i r e f e r s t o i t h component

j r e f e r s t o j t h phase

REFERENCES

1. Ba'n, A . , Ba' l in t , V., Do lescha l l , S., Zabrodin, P. I., Torok, J. : "Pr imenen i je u g l e k i s l o v o gaza v dob iche n e f t i " / " A p p l i c a t i o n o f carbon d i o x i d e i n o i l p roduc t ion" / , Nedra Publ . Co., Moscow, 1977

2. Ba ' l in t , V., Paa'l, T.: "A nedves i t6s i a ' l l apo t 6s az a'ramla'si je l lemzo'k va'ltoza'sa CO da l t e l i t e t t f lu idum-rendszerek por6zus kozegben Va l6 a'ra- moltata 'sakor~-/"Changes o f we t tab i I i t y c o n d i t i o n s and f l o w c h a r a c t e r i s t i c s f o r f l o w i n g carbon d i o x i d e sa tu ra ted f l u i d system i n porous media"/, KColaj 6s Foldga'z, Nov. 1979

3. Acs, G., DoIeschaI I , S., B i r 6 , Z., Farkas c . : "HBromfa'zisu, kompozic i6s model l 6s alkalmaza'sa a Budafa-nyugat t e l e p sz6n-dioxidos muvel6s6nek le - ira'sa'ra" /"A three-phase, compos i t iona l model and i t s a p p l i c a t i o n f o r d e s c r i b i n g CO d isp lacement o f t h e Budafa-West rese rvo i r " / , P a r t I , Ko'olaj 6s Folzga'z, Jan. i981; P a r t I I, Ko'olaj 6s Foldga'z, Feb. 1981



AN ITERATIVE METHOD FOR PHASE EQUILIBRIA CALCULATIONS WITH PARTICULAR APPLICATION TO

MULTICOMPONENT MISCIBLE SYSTEMS

NIKOS VAROTSIS, ADRIAN C. TODD, GEORGE STEWART

Petroleum Engineering Department, Heriot- Watt University

ABSTRACT

An equation of state based method is used to establish phase behaviour and properties for mixtures of injection gases and reservoir fluids with specific application to multicomponent miscible systems including CO

The modified Soave-Redlich-Kwong or the Peng-Robinson or a version of the Redlich-Kwong equation of state can be selected to be used in the model. iteration method used requires a minimum number of variables for which simultaneous iteration is required and an algorithm based on the Broyden's modification of the full Newton step gives consistent phase properties and rapid convergence even near the very sensitive for a miscible displacement critical point area.

The model has been tested against published data including simple binaries, ternaries and multicomponent mixtures of reservoir oil and C02 injection gases. Good agreement between the predicted and the experimental values has been found together with a minimum number of iterations required to solve each problem.

The paper discusses briefly the specific use of the model in an experimental phase behaviour study for UK oil-C02 systems and as an integral part of a compositional reservoir simulator.

2'

The

INTRODUCTION

One of today's more promising oil recovery techniques is miscible C02 flooding. The use of CO investigated $or miscible displacement, for immiscible displacement of reservoir oil, for producing well stimulation and for carbonated water flooding.

The current industry interest in co flooding is mainly concentrated on the mass transfer effect that takes place begween the injected CO oil inside the reservoir. The co extracts hydrocarbons from the oil phase and at the same time co2 is absorbed into the liquid phase up to the moment that miscibility is achieved. injection of CO at the very sensitive critical point. A method is needed, first to calculate the saturation conditions for the mixtures of the injected gases and reservoir oils from which a prediction of the miscible pressure can be made and second to carry out the isothermal flash calculations for different pressures so that the phase behaviour of the system can be studied in detail. described which using any of the Peng-Robinson, modified Soave-Redlich-Kwong and

to improve oil recovery is not a new idea since C02 has been

phase and the reservoir 2

2

The study and prediction of oil recovery involving requires a knowledge of the vapour-liquid equilibria especially

2 .

Such a model will be

314

a version of the Redlich-Kwong equations of state can give predictions of the vapour-liquid equilibria of multicomponent mixtures and especially good and rapid convergence in the critical point region where most of the methods according to the literature fail to converge.

An extrapolation technique is used to improve the initial estimates for the

2 consequative calculations of the saturation pressure of a reservoir oil-CO mixture across the phase envelope and up to the crLtica1 point. Although the model has been specifically applied to CO -oil systems is obviously applicable to any injected gas or flowing system.

2

MISCIBILITY MECHANISMS - DIFFERENT MODELLING APPROACHES

Two of the most important and promising gas injection enhanced oil recovery practices are C02 flooding and lean gas injection.

The major mechanisms to improve the oil recovery in a carbon dioxide flooding are vaporization and condensation. phase and the oil rich phase and the initially immiscible phases gradually become miscible as they are enriched in intermediate and even heavy hydrocarbons and C02 respectively. the reservoir fluid results finally in an one phase miscible fluid. ment of miscibility can be visualised conceptually with a ternary diagram (Figure 1) .

Mass transfer takes place between the C02 rich

The extraction of hydrocarbons by CO and its condensation into 2 The develop-

This representation although not quantitative demonstrates how

F I G U R ~ 1. SCHEMATIC TERNARY DlAGRAM

315

important it is to be able to predict the critical point of a mixture for a multiple contact miscible process. critical point and it is its relative position in respect of the point that represents the reservoir fluid composition that defines whether under certain conditions the mixture of the injected qas and the reservoir fluid can obtain miscibility (Figure 2). The requirement for the generation of a miscible displacement is that the reservoir fluid composition must lie either to the right of the extension of the tangent to the phase boundary curve at the critical point or above the critical point in the single phase region.

The same remarks apply more or less for a lean gas injection flooding where the vaporization of the light hydrocarbons from the reservoir fluid to the gas phase controls the whole process.

There are also some minor mechanisms to improve the enhanced oil recovery by injection of CO . These are: oil swelling, reduction of oil viscosity, increase in oil density,2high solubility of CO and therefore the overriding of the ca2-water mixture and the acidic effect on the rock which increases the permeability of the reservoir.

The theoretical studv of a miscible displacement experiment or of a miscible reservoir flooding requires accurate and reliable phase behaviour data. The phase envelope of the mixture at different conditions is required to determine the minimum miscibility pressure and the equilibrium lines (tie-lines) in order to study in detail the distribution of the different components in the two-phases.

The miscibility path passes throush the

in water which reduces the water density

TWO PHASE REGION

CRITICAL POINT A

FIGURE 2. MISCIBILITY CONDITIONS

3 16

Either an equation of state based method is used to establish phase behaviour and properties or equations are used which have been obtained by curve fitting experimentally derived data. Due to inconsistent phase properties near the critical point and the requirement for comprehensive experimental data for each oil composition of the latter, the equation of state based method is now widely preferred. to suffer from requiring a great number of iterations or do not converge at all in the critical point area, the key area for any miscible displacement.

Most of the current published equation of state based methods appear

PHASE EQUILIBRIA MODEL FOR A MISCIBLE OIL RECOVERY PROJECT

The technique being presented here for calculating vapour-liquid equilibria using an equation of state includes a system of non-linear equations and an iterative sequence to solve the equations. The system of equations consists of:

(i) An overall material balance equation

L + V = 1

(ii) Component material balance equations

Lxi + vy = zi i = l,n i

(iii) Restrictive equations on the phase compositions

n n

i = l i = l c x i = l , c y i = l

(iv) Thermodynamic phase equilibria equations

i = l,n fiL = fiv

Three different equations of state can be used to provide values for the compressibility factor of the vapour and liquid phase. These are:

(1) The Peng-Robinson equation of state

(P-Rl p=-- RT a (TI

v-b v(v+b) + b(v-b)

or in terms of the compressibility factor:

2 2 2 3 Z3 - (1-B)Z + (A-3B -2B)Z - (AB-B -B ) = 0

where:

2 a(T) = 0.45724 - i+m(l-T:) ,m = 0.37464 + 1.542261 - 026992W R2Tc2 pC J

bP RT

RT b = 0.0778 , A = - r2 , B = - (for pure components)

pC R T

317

Ci

nC4

nCIO

(2) The modified Soave-Redlich-Kwong equation of state:

(M-S-R-K) p - RT v-b v(v+b)

RB RA COATS % COATS 'A FUSS % FUSS

0.4265 0.0862 0.42617 0.086173 0.4251 0.0859

0.4198 0.0794 0.419367 0.0794 0.4154 0.0759

0.4638 0.0734 0.451875 0,070452 0.46512 0.07259

or in terms of the compressibility factor

3 2 2 Z -Z +(A-B-B )Z-AB = 0

where:

2 a(T) = 0.42727 l+m(l-.,'), m = 0.48508 + 1.551711 - 0.15613W R2T pC J

ap bP b = 0.0867 2, A = -, B = - 2 2 RT

RT (for pure components)

pC R T

(3) Modified Redlich-Kwong Equation of State

-4 v-b v(v+~) (M-R-K) RT aT p=---

or in terms of the compressibility factor

where:

2 2.5

a = R - bP aP bP 2 2, B = - t b = S & ~ h = s A = -

RT RTC

A pc C R T

Tc

(pure components).

RA,nB are supposed to be functions of temperature and of the nature of each component. The values of these parameters are calculated from generalised correlations applicable over a wide range of temperature. In Table I values of the parameters R A, RB calculated by our model are compared against those obtained bg Coats and Fussell for a ternary mixture of C - nC4 - nC at 160 F (344.3K). 10

318

For the same mixture and for composition (mole fraction) :

CH4 : 0.253

n-Butane : 0.661

n-Decane : 0.086

the K-values and the saturation pressure estimated using the Modified Redli' Kwonq Equation of State compared to the values predicted by Coats and to th, experimental ones are given in Table 11.

K-Val. COATS

3.173

0.297

0.008

4

10

nC

nC

Satur. Press. 972.7 psia

K-Val OUR MODEL K-Val. EXPER.

3.174 3 -174

0.2969 0.297

0.00806 0.013

975.1 psia 1000 psia

For multicomponent mixtures the following mixing rules proposed by Soave are used:

0.5 a 0.5 n n

i=l j=1 a = C C x x a . (1 -ki )

j i, , aij = ai

n

i=l b = C xibi , Kij = interaction parameter

The fugacity coefficients of component i in a mixture are calculated using the following equations

For the liquid phase:

Px.exp{b (2 -1)) - iL L 1 < - l S n

B~ 'i

zL

fiL - (2 -B ) {1+ -} L L

For the vapour phase:

Px . exp{b (Zv-l)

B 'i

zV

1 4 i S n - 1 iv

fiv -

(2 -B ){I+ ") v v

3 19

where: U, = AL(2aiL-biL)/BL, Wi = A (2a -b )/Bv v iv iv

The equilibrium ratios K are defined as: i

Ki = Yi/xi = (fi L /xiP)/(fiV/YiP) = $iL/$iv

DESCRIPTION OF THE PROGRAMME

The programme is written in Fortran Iv language and is implemented as a conversational time-share package. and calculation options by a question and answer sequence at the visual display unit .

The user is guided through the data input

There are four modes of calculations.

(i) Isothermal flash calculation

(ii) Bubble or dew-point calculation

(iii) K-values prediction

(iv) Binary coefficient optimization

The programme storesphysical properties for the pure components as molecular weights, critical temperatures and pressures and accentric factors.

The results printed out by the programme comprise the following items:

Liquid and vapour phase mole fractions, L and V, compressibilities and densities

Composition of each phase by mole fractions x i, yi and k-values for each component

Saturation pressure or temperature

Liquid and vapour phase enthalpies and liquid yield

Mass ratio of vapour to feed and volume ratio of vapour to feed

Homogeneous mixture density

Binary interaction coefficient (if requested)

SOLUTION TECHNIQUE

Iteration Method

A minimum variable iteration method is used to reduce the size of the Correction step by eliminating as many unknowns as possible. correction step is accomplished by dividing the unknown variables into two groups. The first group contains iteration (independent) variables which are the unknowns to be corrected. and there is an equal number of equations to define them.

The size reduction of the

The second grouv contains dependent variables

320

The iteration sequence is a four step process:

- Select the iteration variables and assume values for these variables

- Use the defining equations to calculate the dependent variables

Use the error equations to calculate the error - - Use a correction step to update the variables

Initial Estimates of the Iteration Variables

For the prediction of the saturation conditions a first estimation of the unknown phase composition has to be taken using the component K-values calculated by the empirical equation

K = exp {5.37(1+Wi)(1- -)}/Pri 1 , 1 <- i n T ri

i

For the isothermal flash calculations the corresponding saturation conditions are used as initial estimates.

Correction Step

The correction step used is a modified full Newton step and it requires the calculation of an approximation to the Jacobian obtained by numerical differentation of the function f(G) for the first iteration and the Broyden’s updating technique to improve the matrix for the rest number of iterations. This technique avoids analytical differentation of very complex functions and requires only one numerical differentation of the function f(x) per calculation The value of the iteration variable x at the K + 1 iteration is given by:

k+l -k k G = x + A ( x )

where:

The array x contains n elements (the number of components present in the systein). For a saturation calculation these n iteration variables are n-1 compositions plus the saturation pressure or temperature. calculation are n-1 compositions plus the vapour of liquid phase fraction tv or L).

Btk) is the Broyden’s approximation to the Jacobian.

For an isothermal flash

Error Equations

The Euclidean norm of the residuals of the thermodynamic phase equilibria equation

Mi - - fiL - fiv, 1 c i n

must be less than the error tolerance.

32 1

Total No. Iterations Bubble-point curve

(18 points)

No. iterations for

30% COP - 70% Oil bubble-point

No. iterations for critical point 82% C02 - 18% oil

EXTRAPOLATION TECHNIQUE TO IMPROVE INITIAL ESTIMATES

There is an option available in the programme to calculate the whole phase envelope of a certain mixture of reservoir oil and injection gas starting from the saturation conditions of the reservoir fluid and ending at the critical point of the mixture where usually the injection gas composition is relatively high and the two fluids are becoming first contact miscible. successive calculation changes as the physical properties of the two phases are approaching each other. As the overall composition approaches the critical one, the step is being reduced to a minimum because in this region of the phase diagram very small changes in composition cause very significant and radical changes in the phase properties. carry out this series of calculations. and saturation conditions of the former step are used as initial estimates of the iteration variables in the next step or these values are extrapolated using a combination of quadratic and linear extrapolation to the new composition step. than 60% the rumber of iterations required to achieve convergence. indicates the total number of iterations required for a complete bubble-point curve calculation. synthetic mixture ranging from 0% CO which corresponds to the critical composition). for bubble point calculation for two different compositions of the synthetic oil-CO mixture.

The step for each

Two different approaches have been tried to Either the estimated phase compositions

The second approach improved the method drastically by reducing more Table I11

(At 18 different compositions of an eleven cmponents up to 81% CO

2 2 It also presents the number of iterations required

2

No Extrapolation Extrapolation

100 46

5 2

5 1

TABLE I11 - NUMBER OF ITERATIONS FOR A SYNTHETIC MIXTURE

Using the extrapolation technique and the step by step approach to the critical region the final calculation forthe critical Doint itself usually requires only one or two iterations. synthetic mixture with and without extrapolation. close to the actual value, the extrapolated from the previous calculation initial estimates of the vapour phase CO compositions, are. The extrapolated values are also compared with those that would be the initial estimates if the extrapolation technique has not been applied.

Table IV gives the Euclidean norms for the same Table V demonstrates how

2

322

Synthetic oil CO mixture calculation steps

30%C02-4O%CO 2

40%C02-50%C0 2

There is also an option incorporated in the model to plot the pressure-composition data in an X - Y diagram.

An attempt was made to calculate the matrix used for the iteration sequence only once in the beginning of each series of calculations and then to update it continuously all across the saturation curve avoiding the recalculation of the approximation to the Jacobian at each composition step. this method can be applied only when the composition step is very small, sme- thirgthat seems to be time consuming and not practical at all.

It has been found that

TABLE IV - EUCLIDEAN NORMS FOR A SYNTHETIC MIXTURE

Extrap. initial estimates CO mole fraction 2

0.5358

0.6393

Euclidean

Non extrap. initial estimates CO mole

2 fraction

0.4176

0.5329

0.6356

norms for bubble point 30% COP

Actual CO mole fraction next step

2

0.5329

0.6356

0.7241

No. Iteration No Extrapolation

0.4704

0.04629

0.00697

0.000397

0.0000257

TABLE V - EXTRAPOLATED INITIAL ESTIMATES

Extrapolation

0.000502

0.0000033

50%C02-6O%CO 0.7298

I

APPLICATIONS - DISCUSSION OF RESULTS

In order to test the accuracy of our computer model various calculations have been performed for hydrocarbon/CO mixtures for which the phase behaviour data

2 has been published. These tests include binaries, ternaries, synthetic oils and mixtures of injection gases and reservoir oils.

3 2 3

Isobutane - CO, system

The phase behaviour of this mixture has been measured by Besserer and Robinson and theoretical predictions reportedbypeng and-inson. The phase envelope was calculated at 100°F and is illustrated in Figure 3 . The fitting of the predicted phase boundaries to the experimental data is almost perfect. coefficient of 0.105 was used in the modified Redlich-Kwong equation of state as the iteraction parameter for the mixture.

A binary

N-Butane-Decane-C02 system

The experimental data for this ternary mixture has been published by Metcalfe and Yarborough. pressures 1700 psia and 1500 psia at 160°F

The phase envelopes were calculated for two different (Figure 4).

Synthetic oil C02 system

This mixture has been studied by Metcalfe and Yarborough. the synthetic oil and the phase envelope were calculated at 15OoF. and Figure 6 present the experimentally obtained pressure-composition data and the predicted data derived using the M-R-K and the M-S-R-K equations of state. The M-R-K equation of state seems to fit perfectly well the dew-point curve and the critical point. The maximum deviation between the predicted and the experimental points is 3.6%. The interaction coefficient used for CO - hydrocarbons is 0.1 and for methane -C6+ is 0.04-0.05.

The composition of Figure 5

2

Rangely field oil - injection gases 1 & 2

The experimental data has been published by Graue et al. bubble point curve using the Peng-Robinson equation of state is plotted in Figure 7. experimental points is 3.5% and occurs at the critical composition.

The calculated

The maximum observed deviation between the predicted and the

Reservoir oil-C02 mixture

This oil has been studied by Simon et al. three pseudo cdmponents and the bubble point curve was calculated at 255 F using the M-R-K equation of state (Figure 7). Once again in the near the critical point region the fitting of the predicted curve is almost perfect.

The theoretical model described above, is a part of a research programme on dynamic contact CO miscible studies. The various calculations that have already been performed are for U . S . oils and reservoir conditions. stage will be the generation of experimental phase behaviour data for CO -oils for a whole range of North Sea crudes using a rig for multiple contact equilibrium experiments which has now already started to operate. The experimental results will be a test for our compositional simulator and especially for the assumptions we used. model can decrease dramatically the cost of a miscible flooding because only a few experimental results, which are very expensive and time consuming, have to be obtained in order to establish a complete view of the phase behaviour of the reservoir fluids.

The C7+ cut has been divided into 0

2 The next

2

A valid and reliable theoretical

32 4

1.10.

I."-

FIGURE

+ PRED. POINTS 0 EXPER. POINTS

Q 6) Q

.90-

.80.

.70-

.60-

.50-

.40-

.30-

.20.

c

X

.OO "@@ .OO . I 0 .20 .30 . 4 a .so .m .70 .80 .go I .0a

MOLE FRACTION CARBON DIOXIDE

3.PHASE ENVELOPE FOR C02- ISO-BUTANE MIXTURE TEMPERATURE=IBBF R-K

50-50 '02-

FIGURE 4. PHASE ENVELOPES FOR THE C O ~ - N C ~ - C ~ O TERNARY PRESSURE

1500, 1700 PSIA TEMPERATURE 160O~

EOS

50-50 COZ - Nc4

325

(0 a L!& 1.50-

1.40-

1.30-

I .20-

I . 10-

I .OO

2

a a

MOLE FRACTION.CARBON D I O X I D E

11

FIGURE 5. PHASE ENVELOPE FOR CO2-SYNTHETIC OIL MIXTURE TEMPERATURE=I50F R-K EOS

MOLE FRACTION CARBON D I O X I D E

FIGURE 6. PHASE ENVELOPE FOR'C02-SYNTHETIC OIL MIXTURE TEMPERATURE=lSBF M0D.S-R-K EOS

326

2

w I): P

: 2.00- I .50.

1.00-

.50-

.OO

0 EXPER. POINTS

4.50 GAS-2

6)

< I E 3.50r IJ 3.00

$ 2.50 w K l 2 2.001

GAS- I J

.OO . I0 .20 .30 .40 .50 .60 .70 .OO .90

MOLE FRACTION CARBON D I O X I D E

.OO

F I G W 7. BUBBLE POINT CURVE FOR RANGELY FIELD OIL-CM MIXTURES TEMPERATURE=tGBF P-R EOS

MOLE FRACTION CARBON DIOXIDE

FIGURE 8. BUBBLE POINT CURVE FOR CU2-RESERVOIR OIL MIXTURE TEMPERATURE=255F R-K EOS

3 2 1

CONCLUSIONS

A robust computer programme for isothermal flash, bubble and dew point calculations using one of the Peng-Robinson, Soave-Redlich-Kwong, Modified Redlich- Kwong equation of state has been developed applicable to the severe reservoir conditions encountered in miscible gas flooding enhanced oil recovery schemes.

The demonstrated examples show very good and rapid convergence at any point across the phase boundaries of the CO /hydrocarbon mixtures and particularly the

2 sensitive critical point region. A case has not yet been found where the proposed scheme does not converge although we have, however, found situations where the MSRK or PR equations of state converge to unrealistic solutions.

Various tests indicated that the MSRK equation appears in some cases to give closer approximation to the experimental data than the PR equation. The MRK equation appears to fit better the dew point curve than the bubble point one. The treatment of the pseudo components in the oil mixtures is under more investigation.

a, b =

f. iL

fiv

i K

L

P

pc

'r

R

T

TC

Tr

V

V

i X

Yi

'i

z

W

L

NOMENCLATURE

Temperature, pressure and composition dependent parameters

Fugacity of component i in liquid phase, psia

Fugacity of component i in vapour phase, psia

Equilibrium ratio y./x

Mole fraction of liquid phase

Pressure

Critical pressure

Reduced pressure P/P

Gas constant

Temperature

Critical temperature

Reduced temperature T/T

Vapour phase mole fraction

Molar volume

Mole fraction of component i in liquid phase

Mole fraction of component i in vapour phase

Global mole fraction of component i

Compressibility factor of vapour phase

Accentric factor

i i

328

REFERENCES

1.

2 .

3.

4.

5.

6.

7.

8.

9.

10.

11.

12.

McGLASHAN, R.S.; "A Compositional Phase Equilibrium Model Applied to Pressure Drop Prediction in North Sea Oil Wells", Ph.D Thesis, Heriot- Watt University, 1980

COATS, K.H.; "An Equation of State Compositional Model", SPEJ, October 1980, p.363

GARDNW, J.W., ORR, F.M., PATEL, P.D.; "The Effect of Phase Behaviour on CO Flood Displacement Efficiency", SPE 8367, 1979

NGHIEM, L.X., AZIZ, K.; "A Robust Iterative Method for Flash Calculations using the Soave-Redlich-Kwong or the Peng-Robinson Equation of State", SPE 8285, 1979

FUSSELL, D.D., YANOSIK, J . L . ; "An Iterative Sequence for Phase Equilibria Calculations Incorporating the Redlich=Kwong Equation of State". SPEJ, June 1978

2

PENG, D.Y., ROBINSON, D.B.; "A New %-Constant Equation of State", Ind. Eng. Chem. Fundam. Vol. No. 1, 1976

GRABOSKI, M., DAUBERT, T.; "A Modified Soave Equation of State for Phase Equilibrium Calculations", American Chemical Society Journal, 1978

BESSERER, G., ROBINSON, D.; "Equilibrium Phase Properties of i-Butane-CO System", J. Chem. Eng. Data, Vol. 3, No. 3, 1973, p. 298

OLDS, REAMER, SAGE, LACEY; "Phase Equilibria in Hydrocarbon Systems N-Butane CO System", Ind. & Eng. Chem., 1949, p. 475

SIMON, ROSMAN, ZANA; "Phase Behaviour Properties of CO - Reservoir Oil Systems", SPEJ, Feb. 1978, p. 20

GRAUE, D.J., ZANA, E.; Field, Colorado", SPE 7060, 1978

METCALFE, R.S., YARBOROUGH, L.; Displacement Mechanism, SPE 7061. 1978

2

2

2

"Study of a Possible C02 Flood in the Rangely

"Effect of Phase Equilibria on the C02

M I S C I B L E GAS DISPLACEMENT 329

PHASE EQUILIBRIUM CALCULATIONS IN THE NEAR-CRITICAL REGION

RASMUS RISNES Norsk Agip AIS

VILGEIR DALEN, JAN WAR JENSEN

Con tinen tal Shelf Institu te

ABSTRACT

The present paper addresses the problem of phase equilibrium calculations in the critical point region. The approach is based on an equation of state, and both the Soave-Redlich-Kwong and the Peng-Robinson equations are considered. An accelerated and stabilized successive substitution method is presented. A procedure for disappearing phases is included, making the method convergent also in the single phase region. The accelerated successive substitution method has been compared with Newton type methods like Powell's method. Maps of an error norm which measures the fugacity deviations, are presented to illustrate how the different solution techniques perform. The general conclusion is that the accelerated successive substitution method is faster and much more stable than the Newton type methods considered.

INTRODUCTION

During recent years, hydrocarbon phase equilibrium calculations based on cubic equations of state has received considerable attention, partly because of the demand for accurate and consistent phase predictions encountered in connection with enhanced oil recovery techniques like gas miscible flooding. Both the Soave-Redlich-Kwong (SFX) equation /1/ and the Peng-Robinson (PR) equation /2/ have been extensively used. They both perform well on hydrocarbon mixtures, the PR equation being slightly better in predicting liquid densities. The basic solution procedure for flash calculations is the successive substitution method (SSM). It has however been reported to show poor convergence, or even no convergence,'close to saturation pressures. To overcome the convergence problem, Fussel and Yanosik /3/ introduced Newton type iteration methods, and since then the trend has been towards such refined numerical solution techniques. Newton type methods are however dependent on good initial estimates. In a recent paper Nghiem and Aziz /4/ presented an algorithm using Powell's method which is a combination of a Newton method and the steepest decent method. They also presented a method to detect single-phase states. Their method was extended to three- and four-phase systems by Mehra 151. Also Mott / 6 / has presented a two-phase algorithm based on Powell's method. An important problem in equilibrium calculations is to avoid false trivial solutions where the vapor and the liquid phase are identical. This aspect has been discussed by Maddox and Erbar 111.

The present work is part of a research project concerned with the development of numerical simulation models for enhanced oil recovery processes. It was

330

directed towards the development of a thermodynamic simulator capable of predicting the phase behaviour of mixtures of hydrocarbon reservoir fluids and possible injection gases. The resulting computer program is called COPEC. The program is based on an equation of state approach, and both the SRK and the PR equations are included. Several solution options are available including Powell's method, but the basic solution method is an accelerated and stabilized successive substitution method (ASSM). The method is designed to converge also in the single-phase region, and it contains a bring-back procedure that brings the solution back to the two phase region if it reaches the single-phase region too soon. The acceleration routine employs an Aitken type formula for correcting K-values.

EQUILIBRIUM CONDITIONS

If we consider N moles of mixture or feed of composition z . which separate into L moles of liquid of composition x. and V moles of vaior of composition y., we have an overall material balanceland a component balance equation for eich component:

L + V = N (1)

Lx. + vy. = Nz.

As the compositions are given in mole fractions we have the following constraints:

z z . = L. = zy. = 1 (3)

Eqs. (l), (2) and one of the restricting equations (3 ) constitute a system of n+2 equations in the 2n+2 unknowns, L, V, xi, yi: n is the number of components. The remaining n equations needed are provided by the thermodynamic criterion stating that the fugacities in the liquid and the vapor phase must be equal:

These 2n+2 equations define the two-phase equilibrium problem.

In an equation of state approach, the fugacities can be calculated from the equation of state. The fugacity will depend on temperature, pressure, composition and the type of phase considered,

f. = f. (T, P, xi, type) 1 1

With cubic equations of state, the same equation is used both for the liquid and the vapor phase. A cubic equation may give 3 solutions in volume. The distinction between liquid and vapor phase is then made by choosing the smallest volume for the liquid phase and the greatest volume for the vapor phase.

Formulas for the Soave-Redlich-Kwong (SRK) and the Peng-Robinson (PR) equations of state are given in Table l .

BASIC SUCCESSIVE SUBSTITUTION METHOD

The successive substitution method is based on the concept of equilibrium constants K defined by:

i

K. = y./x. 1 1 1

(5 )

331

Table 1 Suormary description of the Soave-Redlich-Kwong and Peng-Robinson equations of state.

Soave-Redlich-Kwong:

p = - - a RT v-b v(v+b)

RT b = 0.08664 2

pC

R ~ T * pC

a(T) = 0.42747 U

wom5 = 1 + m(l - T:*’) m = 0.480 + i.574~, - 0 . 1 7 6 ~ ~

The cubic equation for the compressibility factor Z = Pv/RT is:

2 z3 - z2 + (A-B-B )z - AB = o aP bP where A = - and B = -

RT R ~ T ~

With mixing rules as given below, the fugacity coefficient of compo- ponent k is given by:

bk In Wk =a (Z-1) - ln(Z-B) -

A ’i aik - a) bk ln(l+Z) B B ( a

Peng-Robinson:

p = R T - a v-b v(v+b) + b(v-b)

RT b = 0.07780

PC

R ~ T ~ ~

pC

a(T) = 0.45724 - U

L Y ~ ’ ~ = 1 + m(1 - Tro”) 2 = 0.37464 + 1.54226~ - 0.26992~

The cubic equation for the compressibility factor Z = Pv/RT is:

2 2 Z3 -(l-B)Z +(A-3B -2B)Z-(AB-B2-B3) = 0 aP . bP where A = - and B = - RT R ~ T ~

With mixing rules as given below, the fugacity coefficient of component h is given by:

bk In Vh = (Z-1) - ln(Z-B) -

The mixing rules employed for both equations are:

b = 1 xi bi i

a = I I xi x

8.. = (1 - ti..) ai

8.. i j J 1J .

0.5 .0.5 j 1J 1J

where tiij are binary interaction coefficients

332

where y. and x. are mole fractions in equilibrium. If values for the equilibrium chstanti are assumed, and the fugacity equations ( 4 ) are replaced by the Ki-equations (5), the resulting set of equations can easily be solved for the unknowns L, V, x. and y.. With these compositions improved K.-values can be obtained, and the'cycle ;epeated.

Introducing the fugacity coefficients JI. the fugacities can be written 1'

In equilibrium the fugacities are equal and hence the equilibrium constants are given by

Ki = JIiL1JIiV

This is an important relation as it allows the defin outside the two-phase region.

During the iteration process when the fugacities are proved K-value estimates are obtained by

(7)

tion of K-values also

not yet equal, the im-

where j is the iteration number and R. is the fugacity ratio fiL/f.". The criterion for acceptance of a solutio; is based on the fugacity rakios. To comply with other solution methods the following error norm is used

2 p = I(Ri - 1) < E

When the equilibrium constants are given, the system of flash equations (11, (2), (3 ) and (5 ) can most conveniently be solved by introducing the g(V) function following Nghiem and Aziz 141. If we consider one mole of feed, N=l, eliminate L in Eq. (2), and then sum up all the equations we obtain

1Xi + m y i - Xi) = 1 (10)

The g(V) function is defined by

(Ki-l)zi

l+(Ki-l)V g(V) = I(Yi -'x.) = 1 ~ (11)

From Eq. (10) we see.that V is determined as the root in the equation

P(V) = 0 (12)

This equation is readily solved by Newton's method. As the g(V) function always has a negative slope, there will only be one root of interest. When the value of V is determined, the compositions can be calculated in a straightforward manner.

When the root of Eq. (12) gets outside the interval [0,1], this indicates a single-phase state. We then calculate the non-existing phase as if the system were at the saturation pressure:

3 3 3

K.x. -

Z Ki xi 1 1 If VtO, then V is set equal to 0, xi = zi, yi =

The normalization is necessary as this is not automatically assured outside the two-phase region.

A common factor in the K-values has no effect on the composition of the non- existing phase, and when the K-values are corrected according to the fugacity ratios, the compositions are corrected only to the extent that the fugacity ratios deviate from the average value. The system will converge to a definite composition, and the fugacity ratios will converge to a common constant value. This limiting value will be different from unity except if the system is at the saturation pressure.

K-VALUE ESTIMATION

The set of initial K-values is the starting point for the iteration procedure. There are 3 conditions these estimates should meet:

1. The estimates should be as close as possible in order to obtain a rapid solution.

2. The estimates should assure that the calculations start in the two-phase region in order to avoid false single-phase solutions.

The estimates should have sufficient spread to avoid false solutions where 3. all K-values become equal to one.

The often quoted empirical formula from Wilson /8/

11 1 K. = - exp [5.3727 (l+ui) (1 - - 'ri Tri

normally meets these requirements well.

An alternative to the empirical formula can be based on the equation of state. The basic idea is the following. The mixture or feed is assumed to be 1 quid at the temperature and pressure given, and the fugacities are calculate . We then assume a gas phase to be formed by evaporation from this liquid. The evaporation rate for each component is assumed to be proportional to the fugacity of that component, the proportionality constant being the same for all components. The evaporation must be stopped before we run out of any component in the liquid phase, but if possible, the evaporation should proceed until only half of the liquid remains. From the resulting compositions, the fugacity coefficients are calculated, and from these we obtain the K-value estimates.

These fugacity based K-values work very well in the near critical region. The reason is probably that in addition to start with K-values consistent with the equation of state, we start in the middle of the two-phase region with both L and V equal to one half. The method also works well along the bubble point curve and in most of the two phase region. It may however break down along the lower dew point curve. There, a restriction of the liquid 2-factor to say ZL<0.3, may be needed in order to assure that the assumed liquid behaves liquid-like.

334

THE ACCELERATION PROCEDURE

When the system is close to the critical point, the convergency may be very slow. A method similar to Aitken's accelerating formula can then be used to speed up the convergence rate.

The equilibrium constants can be regarded as long products, starting with the initial estimate Ko and then multiplied by the fugacity ratios R. which approaches unity as the number of iterations increases. This can bi written

Taking the logarithm we obtain

1 log Ki = log KY + log R. + l og R: + log R: + .... + log R: + ... (17)

In the first part of an equilibrium calculation the fugacity ratios may change from values smaller than one to values greater than one, causing alternate signs in the series above. But after say 20 to 50 iterations, the situation is characterized by a monotone and steady approach towards the solution.

The process can now be accelerated by replacing the remaining part of the series by a geometric series where k is the ratio between the terms

. l og R:

1 1-k log Ki = log Ki + l og R: (1 + k + k2 + ..) = log KJ + ~ (18)

The quotient k is calculated as the ratio between the last two consecutive terms (omitting the subscript i)

and the resulting accelerating step is

1 K. = KJ ' R; (l-k) 1 1

where l/(l-k) is exponent to the fugacity ratio.

When this acceleration step is used, it must always be tested that it leads to an improved solution in the way that it brings the fugacity ratios closer to unity. If not, it must be rejected and replaced by a single step. Between each accelerated step there must be a single step in order to determine the quotient k in the exponent in Eq. ( 2 0 ) .

A simplified approach is to assume a constant value for the exponent to the fugacity ratio. If we wait until the system is well on the right track, an exponent of 2 may normally safely be employed. We routinely apply this exponent after 10 iterations, also in conjunction with proper acceleration.

THE BRING-BACK PROCEDURE

When the system is in a single-phase state, the composition of the non-existing phase is calculated by formula (13) or (14). As a common factor in the set of equilibrium constants has no influence on the composition of the non-existing

335

phase, this gives the possibility to adjust the K-values to make the g(V)- function zero, or in other words, to keep the non-existing phase at the edge of the two-phase region while we test for its existence.

If we consider a single-phase liquid, V equals zero, and the multiplication factor y is determined from

I(yKi - 1 ) zi = 0 ( 2 1 )

which gives a new set of equilibrium constants

= yK. = Ki 1 Z Ki zi ( 2 2 )

on which we apply the normal correction factors (fiL/f ). iV

Physically this corresponds to creating a nucleus gas bubble and see if it will grow or disappear. A gas bubble will grow spontaneously if the fugacity is lower in the gas phase than in the liquid phase. This corresponds to having correction factors (f. /f. ) mostly greater than one. The K-values will then 1L be further increased and kge system will return to the two phase state. If, however, the fugacities are higher in the gas phase than in the liquid phase, the bubble will disappear spontaneously. When the correction factors (fi /f are mostly less than one, the K-factors are reduced bringing the system kacttv to the single-phase state.

If the single phase is gas, we may reason in a similar way. As V equals one, the multiplication factor is in this case determined from

Z ( 1 - - )zi=o Y Ki

NEWTON-TYPE METHODS

As a supplement to the acceleration procedure described above, we have also implemented the Newton-type method described by Powell / 9 / . This algorithm has been used by several other workers during recent times 1 4 , 5 , 6 / and is claimed to be a robust and efficient tool for the problem at hand. In summary, Powell's algorithm is based on the classical Newton method, but differs from that method in two important ways. First, the robustness is increased by combining the Newton method with the more stable steepest descent method. Secondly, inversion of matrices at each iteration step is avoided by using an approximate matrix-updating scheme directly on the inverse of the Jacobian.

Using Powell's method, the equilibrium problem is stated as a system of n non- linear equations in n independent variables by

and the solution is accepted when the residual norm p of Eq. (9) gets below a selected tolerance as before. Independent variables are selected from the following options:

=-iteration: L and x . for all but the last component. LY-iteration: V and yf for all but the last component. m-iteration: niL forla11 components. NV-iteration: niV for all components.

336

n. nii = vyi.

and niv are liquid and vapor fractions per component, i.e. niL = Lxi and

Following Nghiem and Aziz 141, the strategy adopted here is to start with successive substitutions and then switch to Powell's method if the convergence is slow. A switch after i iterations reauires all of the following conditions to be fulfilled:

E~ < pj < E~ and --& > E~

0 < VJ < 1

pJ-l

V and 1 VJ - VJ-ll < E

Default valugs of E ~ , E ~ , E ~ , cV and E of Eq. ( 0.01 and 10 , respectively.

are set to D - ~ , 0 . 5 ,

The flash equilibrium problem may also be formulated as a pure minimization problem, and some tests of this approach has been made utilizing the general- purpose minimization routines E04JAF and EO4FDF contained within the NAG library /lo/.

APPLICATIONS

The above algorithms have been implemented into a computer program COPEC, and some applications on relatively simple fluid systems are discussed in the following. All cases are run in double precision on a VAX-11/780 computer. Relevant component properties are summarized in Appendix.

Mixtures of Isobutane and Carbon Dioxide

Tests with this binary system has been made with the PR version, and all results shown here are obtained for a temperature of 311 K (100'F). The phase behaviour of this system for a wide range of CO Fig. 1 and is in good agreement with previous calculations and experimental data 1 2 , 61.

contents is depicted in 2

CALCULATED - 0 MEASURED

I--\ I \

'A !

0' " 0

I I I 1 I 0 m 40 %a '80

MOLE PERCENT CO2

Figure 1 Phase envelope for binary mixtures of isobutane and carbon dioxide at 311 K (100'F).

Y)

337

In most parts of the two-phase region of Fig. 1 , solutions are obtained easily even with pure successive substitutions, whereas the region indicated by a circle may pose more difficult problems. More detailed results in this region are given in Figs. 2 and 3 . With the refined successive substitution method presented here, we encountered no serious problems obtaining saturation points as indicated in Fig. 2. These points are obtained by repeated flash calculations and not by direct saturation point calculations, and they demonstrate thus the ability to perform flash calculations very close to a critical point. Details of the volumetric behaviour in this near-critical region are shown in Fig. 3 . A critical C02 content between 89.1 and 89.2% is predicted.

I 1 I I I 1 8 5 8 4 8 5 8 6 8 7 8 8 8 9

MOLE PERCENT CO,

Figure 2 Same system in the nearcritical region (calculated

100

80

60

40

20

0

points are indicated bydots).

---T MOLE PERCENT

&' /

m 970 980 geo loo0 1010 1020

PRESSURE (PSIA)

Figure 3 Volumetric behaviour of I-C4 - C02 at 311 K (100'F) in the near- critical region (calculated points are indicated by dots).

338

In Fig. 4, the predicted flash behaviour for a C02 content of 89 mole percent is considered in detail, and several observations can be made. First, it can be seen that a relatively high tolerance level on the8fugacity residuals ( E in E q . (9)) tends to widen the two-phase region. E = 10 also gives a smooth curve, but is obviously a too high tolerance this close to a critical point. If such a condition is suspected, the sensitivity of the solution with respect to the tolerance level should always be investigated.

A more serious matter is the observation that for pressures above 6.977 MPa, the Powell method converges to a false or, more precisely, trivial solution. Such solutions are characterized by all K-values approaching unity and may appear when the feed composition yields one and only one root in the cubic equation for the compressibility factor. The problem of avoiding such trivial solutions is probably the biggest problem encountered with flash calculations near to a critical point.

The failure of Powell's method is investigated further in Figs. 5 and 6. These are plots of the fugacity residual norm p as function of the independent variables corresponding to a W-iteration and depict in detail the performance of the different solution alternatives. Contour values refer to the logarithm of p (log p) . The vanishing norm for a I-C vapor mole fraction of 0.11 corre- spondsl?o the trivial solutions of K. = 4.0.

c

0 K Y P

W -I

t

P P 9 2

-I

0 t o 0 ss.f = l o 1 6

0 s s . € = 1 0 - 8

A Powell. E = 10.16 90

80

70

.60

50

40

ss. f = 1016

s s . € = 1 0 - 8

Powell. E = 10.16

6.99

30 6.94 6.95 6.96 6.97 6.98

PRESSURE (MPal

Figure 4 Flash behaviour of a I-C4 - CO 311 K (100'F) for different sofution alternatives.

mixture (89 mole percent C02) at

3 3 9

Fig. 5 shows the solution space at a relatively large scale and depicts the performance of the first 15 pure successive substitutions. K-value estimates both by formula (15) and the fugacity approach are included. The fugacity approach starts off somewhat better, but in this case this makes very little difference when some 15 iterations hays been performed. After 15 iterations the residual norm is approximately 10 , and Fig. 6 depicts what happens if acceleration or Powell's method is started at this point. As may be seen, the accelerated successive substitution method proceeds in rather large steps towards a true solution whereas Powell's method rather quickly finds a trivial solution. The fi ure alsogshows what happens when Powell's method is employed at a norm of lo-' and 10 . In the former case, a trivial solution is rapidly found, while after 300 iterations in the latter case, the solution is stuck at what appears to be something like a saddle point. It should be noted gqso, that it takes 172 pure successive substitutions- reach a norm of 10 whereas the accelerated version reaches a norm of 10 '' in just 31 iterations. Fig. 5 clearly shows that is not an appropriate tolerance level in the present case. A large region in the-fglution space satisfies this tolerance. Moreover, a maximum norm of only 10 separates the true solution from the trivial ones. It should be understood that the small-scale contour features in the lower left-hand parts of Fig. 6 are artifacts originating from that map (and all the other maps shown here) being contoured from a 101 by 101 network of points.

VAPOR MOLE FRACTION

Figure 5 Residual norm plot for a 11% I-C4 - 89% C02 mixture (P = 6.980 MPa, T = 311 K).

3 4 0

VAPOR MOLE FRACTION

Figure 6 Residual norm plot for a 11% I-C4 - 89% CO behaviour of different solution alternatives (P = 6.980 MPa, T = 311 K).

mixture showing 2 the

Fig. 7 shows similar fugacity residual norm plots for a decreasing pressure. P = 6.981 MPa corresponds to a single-phase liquid. The others show how the delineation between true two-phase solutions and trivial solutions is gradually improved as the pressure drops off from the bubble-point.

The independent variables selected for the norm plots are probably not the natural ones for successive substitution. If anything, successive substitution must be considered as a process taking place in a space spanned by the K-values. It would be interesting to see the performance in such a space, and it might be an idea to employ the K-values as independent variables in Newton-type methods as well.

A further illustration of the acceleration process is given in Fig. 8. Again the 89% C02 system is considered, and the iteration performance is plotted for two pressures in Fig. 4, namely P = 6.94 and 6.98 MPa. It is seen that the acceleration process improves the successive substitution method dramatically. AS we have seen, Powell's method does not give a true solution at all at 6.98 MPa. At 6.94 MPa a proper solution is obtained, but at approximately twice the no. of iterations required with acceleration. In addition, a Powell iteration generally takes more computer time than a successive substitution iteration.

341

0.10

a

f z- U

V

z - 0 V

9

0’ w

I

0.11 P = 6.940 MPa P - 6.970 MPa

VAPOR MOLE FRACTION

i

\ U

V

z -

0

a V

lL w

$ I

0.01 VAPOR MOLE FRACTION 0.61 0.10 I

I \

a p f

W

d 5

0.11 P - 6 9 7 9 MPa

0.01 VAPOR MOLE FRACTION VAPOR MOLE FRACTION . 0.51

\

a P > z-

0.11 P = 6.980 MPa P - 6 . 9 8 1 MPa

Figure 7 Residual norm plots for a 11% I-Cq - 89% COP mixture at 311 K.

342

0

10-5

10-1( z P :: 5

K

10-l!

10-n

I

I I

I I

i , x

I I

I

O S S

X SSwithur .

- _ _ __ __ p - 6.94 MPa

p - 8.98 m h

1 1 I l l l , , l , , , ,

50 loo

NO. OF ITERATIONS

0

Figure 8 Iteration performance for a 11% I-CL - 89% CO mixture at 311 K. 2

Another aspect of the refined successive substitution method presented here is illustrated in Fig. 9. It depicts the iteration performance for a step in a series of flash calculations where resulting K-values from one point is used as initial estimates for the next. A 89.3% CO mixture is considered and the pressure step in question is from 6.82 to 6.6% m a , corresponding to a decrease in liquid mole fraction from 9.01 to 0.46%. The solution escapes the two-phase region after 3 iterations, but with Eq. (14) defining a hypothetical liquid phase, the iteration phase region before the tolerance level is met. The figure also shows the favourable effect of the multiplication factor y defined by Eq. (23). The solution is much more quickly returned to the two-phase region, and the no. of iterations required to achieve convergence is significantly reduced.

is continued and brings the solution back into the two-

10-

10-

B 10- B

10-

10-

10-

\ Y

\ \ \ I \

< 10 7.0

NO. OF ITERATIONS

3 4 3

0.12

1.10

1.08

LO2

1.m

Figure 9 Effec t of bring-back procedure.

A Ternary Mixture

Figs . 10 and 11 show some r e s u l t s obtained with a ternary mixture of 40% ethane, 40% propane and 20% n-butane. The SRK equation of s t a t e and t h e accelerated successive s u b s t i t u t i o n method i s used throughout this example. This mixture has a l s o been s tudied by Gundersen i l l / . Using a stepping procedure towards t h e c r i t i c a l region and a spec ia l treatment of 2-factors , he was able t o perform f l a s h ca lcu la t ions up t o some 0.02 MPa from the c r i t i c a l point .

The predicted f l a s h behaviour a t some temperatures i n the v i c i n i t y of the c r i - t i c a l temperature i s shown i n Fig. 10. We had no d i f f i c u l t i e s obtaining convergence even more close t o t h e c r i t i c a l point then indicated i n the f igure.

3 4 4

4.8 4.8 6.0 6.1 5.2

PRESSURE (MR)

Figure 10 Flash behaviour of the ternary test mixture at different temperatures.

However, with a "normal" tolerance level of some of the isotherms were found to become irregular as the saturation pressure was approached. The previous example clearly shows that such irregularities are to be expected, and that the tolerance has to be gradually reduced to get accurate results as a critical point is approached. In most practical applications, consistency near a critical point is probably more important than to pursue solutions very close to this critical point. In Fig. 10 an attempt is made to define a critical point vicinity where a phase separation is not insisted on and the solution is interpreted as a single-phase "critical" mixture. Specifically, the calculations are terminated when 1 z.(K. - 1) gets less than O281, and this criterion is felt to be well adapted to'tht tolerance level of 10 . Nghiem and Aziz 141 indicated a similar approach.

The effect on the isotherms is to create a discontinuity from two-phase to single-phase. In Fig. 10, all isotherms between 365.6 and 366.7 K experience this discontinuity (points beyond this discontinuity are not plotted), and the corresponding effect on the P-T phase diagram is to cut a top off the two-phase region as shown in Fig. 11.

Yarborough Mixture No. 8

The algorithms considered in this paper have been extensively tested also on systems consisting of a larger numbers of components, and some results obtained for a 6-component synthetic oil mixture commonly referred to as Yarborough mixture no. 8 1121 will be presented here. These results will concentrate on the solution performance. However, to set a background, the flash behaviour obtained at several temperatures is ploited in Fig. 12. Fair agreement with experimental results is obtained at 200 F, and the critical temperature is estimated to approximately 55'F.

345

I

! I

I

I / I / I I

TEMPERATURE I K I Figure 11 Phase diagram of the ternary test mixture.

The isotherm of 75'F is sufficiently close to the critical point to yield relatively hard flash equilibrium problems, and results of some testing of different solution alternatives for this temperature is given in Tables 2-4. Seven pressures are considered, and when converging, 514 the alternatives yield essentially the same results. A tolerance of 10 present context,Resulting liquid mole fractions are included in Table 2 .

has been used in the

Table 2 No. of iterations (and CPU-time) for different versions of SSM, Yarborough mixture no. 8 .

Pressure Liquid mole Pure SSM with SSM with (psia) fraction SSM overshoot acceleration

2000 0.2621 19 ( 0 . 2 3 ) 2500 0.3188 32 ( 0 . 3 5 ) 2750 0.3537 47 ( 0 . 4 8 ) 2875 0.3740 66 (0 .67 ) 3000 0.3953 147 ( 1 . 4 1 ) 3050 0.3987 282 ( 2 . 7 1 ) 3075 0.3878 NC

13 (0 .16 ) 13 (0 .16 ) 20 (0 .23 ) 20 (0 .27 ) 28 (0 .31 ) 31 (0 .37 ) 37 ( 0 . 4 2 ) 39 (0 .41 )

224 (2 .45 ) 28 (0 .34 ) 293 (2 .98 ) 34 (0 .45 ) NC 41 (0 .48 )

NC - Not converged within 300 iterations

346

Table 2 compares different version of the successive substitution method. The pure version yield a prohibitively high no. of iterations for the higher pressure values. With overhoot the fugacity ratios are raised to the power of 2 in Eq. (8) after a fixed no. of iterations (10 in the present case). This may be seen to function well for the lower pressure values, but not so well more close to the saturation point. With the acceleration procedure, a maximum of 41 iterations is used for all the pressure values considered.

The reason why the overshoot feature in some instances fails is probably that it is too uncritically employed, and the testing step included in the acceleration procedure should therefore be emphasized. The acceleration procedure proceeds in pairs of steps. First a simple iteration is done in order to determine k and the exponent of Eq. (20), and thereafter an accelerated step is made in accordance with Eq. (20). An important detail is, however, that the

Mole fractions

c1 0.8097 c2 0.0566 c3 0.0306 N-C5 0.0457 c7 0.0330 C10 0.0244

0

PRESSURE IPSIA)

Figure 12 Volumetric behaviour of Yarborough mixture no. 8 at different temperatures.

347

Pressure SSM with SSM + Powell SSM + Powell (psis) accelerat ion W - i t e r a t i o n NL-iteration

2000 13 (0.16) 13 (0.16) 13 (0.16)

2750 31 (0.37) 23 + 28 (0.70) 23 + 17 (0.52) 2875 39 (0.41) 32 + 26 (0.72) 32 + 18 (0.59) 3000 28 (0.34) 17 + 27 (0.58) 17 + 19 (0.45) 3050 34 (0.45) 21 + 30 (0.67) 21 + 26 (0.59) 3075 41 (0.481 23 + 39 (0.83) 23 + 30 (0.69)

2500 20 (0.21) 20 (0.21) 20 (0.21)

accelerated s t e p is re jec ted i f the fugaci ty res idual norm f a i l s t o be decreased by t h i s s tep . I n t h i s case j u s t the simple s t e p i s ' t a k e n and is followed by a new p a i r of s teps . The accelerat ion performance recorded a t 3050 p s i a i l l u s t r a t e s t h i s point :

I t e r a t i o n No.

22 24 26 28 30 32

Fugacity r a t i o exponent

17.764 -2.544 ( re jec ted) 27.007 0.940 ( re jec ted)

47.860 ( re jec ted) 27.125

I n essence w e have applied the same c r i t e r i o n f o r s t a r t of accelerat ion as f o r switch t o Powell's method, see Eq. (25 ) . Table 3 compares d i f f e r e n t a l te rna- t i v e s f o r the most important parameter i n t h i s c r i t e r i o n , namely &u, and il- l u s t r a t e s t h a t some caution should be used when s e t t i n g t h i s parameter. If it is too high, too many accelerat ion s teps a r e re jected. I f it i s too low,-koo many i t e r a t i o n s a r e made before acce lera t ion i s attempted. A value of 10 has been found t o be s u i t a b l e i n most cases and y ie lds t y p i c a l l y some 15-30 i t e r a - t i o n s before acce lera t ion is attempted.

Comparisons with Powell's method a r e made i n Table 4 . Here, NL-iterations a re somewhat more e f f i c i e n t than W - i t e r a t i o n s , bu t both a l t e r n a t i v e s a r e somewhat slower than the accelerated successive s u b s t i t u t i o n method.

Table 3 No. of i t e r a t i o n s a s funct ion of s t a r t of accelerat ion, Yarborough mixture no. 8

I Residual norm a t s t a r t

348

We also did some tests with general-purpose, Newton-type minimization routines / l o / . Both the routines E04JAF and E04FDF were found to be less efficient than the other solution alternatives considered here, but one observation is worth mentioning. Working with the object function only, a more direct expression for Gibbs free energy is much better than a fugacity residual norm.

CONCLUSIONS

An accelerated and stabilized successive substitution method (ASSM) has been formulated for flash calculations of multi-component systems and has been especially designed for applications in the near-critical region. The method is made convergent also in the case of a disappearing phase,and will therefore detect single-phase solutions automatically. The acceleration procedure is based on an Aitken type formula for correcting the K-values, but acceleration steps are never taken unless they lead to improved solutions. In the examples presented, the ASSM method has been shown to be a highly stable and efficient method. As special saturation pressure calculations are not needed to delineate the two-phase region, the method is well adapted for incorporation in compositional simulators.

Compared with Powell's method and other Newton type methods, the greatest advantage of the ASSM method is its stability close to saturation pressures. Generally, it is also faster than Newton type methods.

The method presented is based on the Soave-Redlich-Kwong and the Peng-Robinson equation of state. However, it can easily be adapted to other equations of state.

k K.

n N P

T

V

L1

R, Ri

V

i ii

Zi

"i

X

Y

P E

W

NOMENCLATURE

Equation of state coefficients Equation of state coefficients Liquid and vapor phase fugacities Gibbs free energy Acceleration parameter Equilibrium constants, K. = y./x. Liquid moles or liquid mile flacgion No. of components Total no. of moles Pressure Gas constant and fugacity ratios Temperature Molar volume Vapor moles or vapor mole fractions Mole fraction of component i in liquid Mole fraction of component i in vapor Mole fraction of component i in system Compressibility factor K-value multiplication factor Tolerance Fugacity residual norm Fugacity coefficients Acentric factor

349

Subscripts

C = Critical i, j = Component no. j = Iteration no. (as superscript) L = Liquid phase r = Reduced V = Vapor phase

ACKNOWLEDGEMENT

This research is part of a joint project between Norsk Agip A/S and the Continental Shelf Institute (IKU). The project is fully financed by Norsk Agip A/S. The authors wish to thank Norsk Agip A/S for permission to publish this paper.

1.

2.

3.

4.

5.

6.

7.

8.

9.

10.

REFERENCES

SOAVE, G.: "Equilibrium Constants from a Modified Redlich-Kwong Equation of State", Chem. Eng. Sci., Vol. 27 (1972), pp. 1197-1203.

PENG, D.-Y. and ROBINSON, D.B.: "A New Two-Constant Equation of State", Ind. Eng. Chem. Fundam., Vol. 15, No. 1 (1976), pp. 59-64.

FUSSEL, D.D. and YANOSIK, J.L.: "An Iterative Sequence for Phase- Equilibrium Calculations Incorporating the Redlich-Kwong Equation of State", Sac. Pet. Eng. J., Vol. 18, (June 1978), pp. 173-182.

NGHIEM, L.X. and AZIZ, K.: "A Robust Iterative Method for Flash Calcula- tions Using the Soave-Redlich-Kwong or the Peng-Robinson Equation of State", SPE Paper 8285 presented at the 54th Annual Fall Meeting of SPE of AIME, Las Vegas (1979).

MEHRA, R.K. et el.: "Computation of Multiphase Equilibrium for CoIpposi- tional Simulation", SPE Paper 9232 presented at the 55th Annual Fall Technical Conference and Exhibition of SPE of AWE, Dallas (1980).

MOTT, R.E.: "Development and Evaluation of a Method for Calculating the Phase Behaviour of Multi-Component Hydrocarbon Mixtures Using an Equation of State", AEE Winfrith Report 1331, Dorchester (1980).

MADDOX, R.N. and ERBAR, J.H.: "Equilibrium Calculations by Equations of State". Oil and Gas Journal, (Feb. 2, 198l), pp. 74-78.

WILSON, G.: "A Modified Redlich-Kwong Equation of State, Application to General Physical Data Calculations", paper no. 15C presented at the AIChE 65th National Meeting, Cleveland, Ohio, May 4-7, 1969.

POWELL, M.J.D.: "A FORTRAN Subroutine for Solving Systems of Non-Linear Algebraic Equations", in RABINOWITZ, P. (ed.): "Numerical Methods for Non- Linear Algebraic Equations", Gordon and Breach Science Publishers, London (1970).

NAG Library Manuals, Numerical Algorithms Group Ltd., Oxford (1978).

3 50

11.

12.

13.

GUNDERSEN, T.: "Numerical Aspects of the Implementation of Cubic Equa- tions of State in Flash Calculation Routines", to appear in Comp 6r Chem. Eng . YARBOROUGH, I,.: "Vapor-Liquid Equilibrium Data for Multicomponent Mix- tures Containing Hydrocarbon and Nan-Hydrocarbon Components", J. Chem. Eng. Data, Vol. 17 (1972), pp. 129-133.

McCAIN, W.D.Jr.: "The Properties of Petroleum Fluids", Gulf Publ. Comp., Tulsa (1973).

APPENDIX - COMPONENT DATA The critical properties used in the computer program COPEC are taken from McCain /13/, and those used in the example calculations are given in Table 5.

For the binary test system considered in this paper, the PR equation with a binary interaction coefficient of 0.13 has been used.

For the tertiary test system, the SRK equation has been used with binary interaction coefficients as follows:

c2 - c3 : 0.001

c3 - N-C4 : 0.012 C2 - N-C4 : 0.009

For the six-component Yarborough mixture the PR equation is used with all binary interaction parameters equal to zero.

Table 5 Component properties

Comp. Hole weight Pc (ma) Tc (K) Acentric factor

c02 44.010 7.387 304.21 0.2250 c1 16.043 4.606 190.58 0.0104 c2 30.070 4.882 305.42 0.0986 c3 44.097 4.251 369.82 0.1524 1 4 4 58.124 3.650 408.14 0.1848 N-C4 58.124 3.799 425.18 0.2010 N-C5 72.151 3.370 469.65 0.2539 c7 100.205 2.737 540.26 0.3498 c10 142.286 2.096 617.65 0.4885


THE EFFECT OF SIMULATED COZ FLOODING ON THE PERMEABILITY OF RESERVOIR ROCKS

GRAHAM D. ROSS, ADRIAN C. TODD and J. ANDREW TWEEDIE

Department of Petroleum Engineering, Heriot- Watt University

Both formation damage and stimulation e f f ec t s have been experienced during "miscible" carbon dioxide f i e l d and laboratory tests i n the USA. the stimulation e f f ec t s have been a t t r ibu ted to dissolution of the reservoir rock by carbon dioxide enriched flood water no work has been done t o ident i fy and quantify t h i s phenomenon. Nor has any established theory for the formation damage been identified, although it seems l ike ly t h a t i n some instances formation damage may be caused by formation fines, released by dissolution and subsequently migrating i n t o pore throats.

This paper describes a laboratory investigation i n t o the e f f ec t s of rock - f lu id interaction under s imula t a reservoir conditions, and i n par t icu lar the carbonated w a t e r - carbonate mineral reaction in sandstones during a C02 enhanced recovery process. fo r flowing CO - w a t e r mixtures through l inear rock cores are described, together w i t h $he ana ly t ica l methods used to assess changes i n core characterist ics. The paper presents r e su l t s from i n i t i a l tests on four d i f fe ren t carbonate containing core materials.

While

The design and operation of experimental equipment

(1) General

Successful laboratory investigations of miscible, carbon dioxide, flooding have been w e l l documented i n the literature. Field experience, however, has only recently begun to accumulate. A l l the projects reported havebegunsince 1972 (mostly i n the United S ta tes ) , thus, only limited empirical data is currently available. Although encouraging, f i e l d r e su l t s to date have been suf f ic ien t to ident i fy several major problems and opportunities with the carbon dioxide technique.

One of the problems is tha t -of reduced in j ec t iv i ty experienced i n sane reservoirs on in jec t ing carbon dioxide. due to the depositfon of high molecular weight materials upon mixing of crude and carbon dioxide 2' occurrence of t h i s type of precipitation . Observed reductions i n

While many have reported t h i s to be

i n situ pluggiag tests have not proved the

352

injectivity can probably therefore be attributed to other mechanisms, one of which may be the disintegration of carbonate cements in the reservoir rock, and movement of particulate matter i n t o the throats of in te rs t i t i a l pores.

Conversely, increases in injestivity have also been experienced i n the course of carbon dioxide field tests . These were in t u r n attributed to dissolution of carbonate minerals i n carbon dioxide enriched floodwater (carbonated water), causing increased permeability.

In view of the lack of data and uncertainty in the published results relating to carbonate dissolution on carbon dioxide flooding, a research programme has been init iated to study the phenanenon. The objectives of the programme are to evaluate the dissolution effects of carbonated water on formation carbonates, and to determine how formation permeability characteristics are likely to be altered during a carbon dioxide flood. This paperpresentsthe first phase of the study, the developpent and operation of apparatus for flowing C02-water mixtures through linear rock cores, together w i t h the results of experiments undertaken to establish the mechanism(s) of carbonate dissolution i n porous media.

(2) Carbonate Dissolution in Reservoir Rock

Many producing formations contain carbonates i n sme form. limestone and dolomite reservoirs, carbonates constitute the bulk of the formation rock. I n sandstones, carbonates are cormnonly found as pore f i l l ing and replacement cements consolidating the sand grains, although varying, but usually minor amounts of de t r i ta l carbonate grains may also be present. Since the cementing material i n sandstone is located between sand grains adjacent to flaw channels, a relatively s m a l l change in the pore framework due to carbonate dissolution may significantly affect the total permeability.

Upon injection, carbon dioxide, mixing with either injection water or connate water, w i l l form carbonic acid. One characteristic of carbonic acid is that a t very low carbon dioxide par t ia l pressure, the pH is reduced considerably. Thus, carbonated water w i l l retain its acid nature w i t h very l i t t l e C02 i n solution.

The carbonates most conrmonly found i n reservoir rocks are those of calcium (calcite), combinations of calcium and magnesium (dolomite) and iron (siderite). pheric conditions, but become increasingly soluble w i t h increasing water carbonation (or C02 concentration) and pressure. converted to that of the soluble bicarbonate, the following equation representing the chemical reaction for calcium carbonate:

I n the case of

These minerals have a l o w solubility in pure water a t atmos-

The carbonate form is

Similar chemical reactions take place w i t h the other carbonates.

The solubility trends 6f calcium carbonate in carbonated water as a function of pressure and temperature are gresented i n Figure 1. Although no work has been carried out in the 0 to 100 C mf ra tu re range a t pressures above 100 bars, indications from other studies are that calcite solubility:

(1) increases w i t h increasing temperature a t constant total pressure and COP concentration,

353

increases with total pressure a t constant temperature and CO concentratSon, and 2

increases up to a maximum a t five weight per cent COP concentration before falling again a t higher CO concentrations a t constant temperature and tota9 pressure.

2 5 0 [ 10 3 2(

2

CO* PRESSURE (bars)

Figure 1 Solubility of calcite i n carbonated water

Carbonated water, formed upon injection of carbon dioxide i n t o a w e l l , w i l l react with the carbonate minerals i n the rock and transport the dissolved products through the reservoir. This dissolution effect w i l l be more pronounced i n the vicinity of the wellbore since the carbonated water solution w i l l approach total bicarbonate saturation as the water moves away from the well. permeability i n the reservoir by releasing particles which then migrate and plug flow channels, or an increase i n permeability, is not apparent from tests undertaken t o date.

However, whether the reaction effects a reduction i n

EXPERIMENTAL

A high pressure, high temperature penneameter was designed and constructed to permit an examination of carbonated water dissolution effects. shown i n Plate 1 , i s capable of operation i n moderately corrosive liquid environments under controlled conditionerof temperature, pressure and flow rate. Figure 2.

The apparatus,

A process flow scheme of the core flooding apparatus is presented i n

354

Pla te 1 Front view of experimental apparatus

A detailed description of the major e q u i p e n t components follows:

(a) Core Holder: The core holder cell was designed for high pressure core flooding i n corrosive l iquid environments. It consists of a thick-walled s t a in l e s s steel outer cylinder with removable l i d , f i t t e d in te rna l ly with a sleeve core holding assembly.

The sleeved core is secured between the c e l l l i d / i n l e t end p l a t e and the o u t l e t end p l a t e by three t i e rods. end p la tes serve a s d i s t r ibu tor and receptor respectively for the f l u i d flowing through the core. Both end p la tes a re scored with l i nes radiating from the centre and a l so with concentric c i r c l e s about the centre. These l i nes allow even f lu id and pressure d is t r ibu t ion across the ends of a core, The ou t l e t end p l a t e can be precisely adjusted on the t i e rods to enable short cores (down to 1.5 an long) to be f i t t e d i n the ce l l .

The cylindrical she l l has four entry por t s o r taps, one i n the side-wall fo r the core sleeve confining pressure and the others i n the l id s one each fo r the core influent, the core effluent and a thermocouple probe.

The

The c e l l l i d is secured to

Brine Preparation and vacuum System

1 Viscome ter

P Core Holder

W ul ul k==i

Figure 2 Experimental F l o w Apparatus

356

the base by twenty high t ens i l e bo l t s and sealed by an O-ring. supply the core sleeve confining pressure.

to a maximum working pressure of 6,000 psi .

(b) Viscosity Measurement System: Required da ta on carbonated brine v iscos i ty are not reported i n the l i t e r a tu re . Consequently an "in l ine" capi l la ry tube viscometer was incorporated i n the flow apparatus to enable l iqu id viscosity measurements t o be made under test conditions. The general arrangement of the v iscmeter is shown diagrauanatically i n Figure 2. The main elements ,are (1) a 20 QD length of 0.2 mm precision bore s ta in less steel tube (secured by epoxy res in inside a length of support tubing) and (2) a d i f f e ren t i a l pressure transducer.

Water from a hydraulic pump is used to

The core holder has been tested and ce r t i f i ed fo r use up

From the capi l la ry tube dimensions and measurement of the pressure drop across the tube a t known constant flow rate, the required v iscos i t ies can be calculated from the Hagen- Poiseuille Equation.

(c) Transfer B a r r i e r : The t ransfer barrier unit is a f lu id pressure transfer device, comprising an open-ended rubber bladder o r membrane enclosed i n a 5 l i t re capacity cylindrical steel pressure vessel. ated water preparation and as a f lu id separator i n which pressure and volume changes between the drive f lu id (hydraulic o i l ) and the core flooding f lu id (brine o r carbonated brine) are tzansmitted through the f lex ib le rubber membrane.

It serves as a mixing vessel during carbon-

(d) Intensified C02 Supply: Carbon dioxide pressures greater than cylinder pressure (830 ps i ) are obtained using a gas booster. Intensification is obtained by a l a rge area reciprocating piston pushing a s m a l l C02 compression piston with a r a t i o of 100 to 1 between the piston areas. A compressed a i r driven hydraulic pump drives the large area piston.

(e) Transfer Barrier Rocking Mechanism: To enable e f f i c i en t and rapid preparation of equilibrium solutions of carbon dioxide i n w a t e r , a rocking mechanism was attached t o the t ransfer bar r ie r . The drive fo r the mechanism is supplied by a Kopp variable speed motor, connected through a drive arm and couplings to a steel cradle holder bolted to the t ransfer barrier. The dr ive arm length is fixed to give a rocking angle of 30 degrees, and the rocking rate from 15 to 90 cycles per minute, is controlled manually by a remotely controlled adjuster f r aa the variable speed motor.

The f l u i d l i nes to and from the t r ans f i r barrier are sp i ra l led around the axis of rocking. the in tegr i ty of various connections, by offering resistance to the je rks caused by the rocking mechanism.

The s p i r a l s help to maintain

( f ) Displacement System: The flow rate was determined i n a l l cases by employing an Eldex Precision Pump i n conjunction with the back pressure regulator. The Eldex posit ive displacement punp

357

delivers a steady flow that can be varied from 0 to 4.5 cc per minute. The flow rate within this range is adjusted by a micrometer screw on the pump, which sets the length of stroke. The pump is capable of delivery pressures i n excess of 5000 psi.

fluid to displace the core flood liquid from the membrane i n the transfer barrier. The drive o i l was drawn fran a perspex reservoir by the Eldex pump and delivered a t constant volume to the base of the transfer barrier.

A non-corrosive fluid (hydraulic o i l ) was used as a drive

(9) Pressure Measurement System: As shown i n Figure 2, the flow apparatus is equipped with four pressure gauges and two pressure transducers. The gauges are as follows:

(1) 0 to -1.0 bar vacuum gauge, connected i n the l ine to the vacuum pump - used in i t i a l vessel and pipework evacuation.

a i r supply l ine to the gas booster - to monitor the a i r pressure to the gas booster and hence the level of gas intensification.

sleeve confining pressure l i n e - to monitor core sleeve pressure.

0 to 400 bar precision gauge with a stainless s teel measuring element, connected immediately upstream of the back pressure regulator - to monitor system back pressure.

during

(2) 0 to 10 bar gauge, connected in the compressed

(3) 0 to 600 bar gauge, connected to the core

(4)

Both pressure transducers are S.E. Labs. 21/V models:

(1) 0 to 5000 psi absolute pressure transducer, connected to the transfer barrier to measure the system "upstream" pressure. electrically connected to an Analogic digi ta l unit for visual observation.

connected across the core holder and viscosity measurement capillary tube. It is linked to a s t r ip chart recorder to provide a continuous record of the pressure differential data.

It is

(2) 0 - 50 psi differential pressure transducer,

(h) Temperature Control System: The temperature control System consists of three independent sub-systems:

(1)

(2)

(3) to maintain the viscometer temperature.

to heat khe contents of the transfer barrier,

to maintain the core and fluids entering the core a t the desired temperature level, and

Heat to the transfer barrier and core holder is supplied electricakly by close f i t t ing mesh elements and controlled in each case w i t h i n t 1 C ) by a thermostat/thermomuple controller. provided

Xnmlatfon for the vessels is by 4 cm thick layers of rock wool encased in aluminised glass

358

cloth jackets. To ensure that a l l fluid entering the core is a t tes t temperature, the f l u i d l ine immediately upstream of the core holder is coiled tightly around the core cel l lid. The capillary tube viscometer is enclosed i n a water bath where it i s maintained a t the desired temperature by hot water circulation.

A series of chromel-alumel thermocouples are used to monitor temperature throughout the flow system. digital thermometer for visual display and recording.

These are linked via a selector unit to a

(i) Effluent Collection and Measurement System: Core effluent, reduced to atmosuheric uressure on discharse from the back pressure regulator, enters the gas/liquid separator. The separator is a sealed perspex cylinder w i t h a capacity of 300 ccs. It has an in le t for the core effluent near the top and outlets i n the l i d and base for the separated gas and liquid respectively. is measured by a wet-type volumetric meter connected directly to the gas outlet fran the separator. device provided with a 150 mm dial of 100 divisions and a six digi t revolution counter form of totaliser. Liquid from the base of the separator flows via a five-way selector valve to sealed glass collection vessels for measurement and analysis.

The volume of carbon dioxide produced

The meter is a precision

(2) Experimental Procedure

In i t ia l testing consists of flowing base water (i.e. brine or dis t i l led water) through the core to establish the in i t i a l or reference (stabilised) permeability. Subsequently brine, carbonated to the desired level inside the rubber membrane of the mixing vessel, is injected into the core a t constant rate by hydraulic o i l displacement. The carbonated water and core temperatures are carefully controlled to represent o i l reservoir conditions. A back pressure above the carbonation pressure is maintained throughout the tes t to ensure that only liquid phase exists a t a l l p i n t s i n the flow system. and a l l core effluent is collected for chemical analysis.

Following a core flood experiment a series of analyses are performed on the core and effluent liquid. calcium and magnesium by EDTA t i tration, and the core is divided i n t o a series of segments. The permeability, porosity, pore size distribution and overall dissolution effect i n each of the core segments is then assessed.

The permeability of the core is measured as a function of time,

The effluent liquid is analysed for content of

(3) Porous Media

To enable study of the carbonated water-carbonate mineral reaction i n sandstone without interference from other effects such as clay or mica alteration, it was necessary to choose material w i t h a relatively simple mineralogical composition. Thus, a relatively pure quartz-carbonate sandstone, a calcareous gr i t , was chosen for the in i t i a l stage of the study. particular sandstone, fran a quarry i n the Yorkshire Jurassic, was also partly based on its high carbonate content.

However, to gain a more complete understanding of the reaction effect of carbonated water on carbonate mineral i n reservoir rock, two other sandstones and a limestone were tested i n this in i t i a l study. These materials are l isted and described i n Table 1. The analytical procedures used i n the description of these materials, both before and af ter core flooding were:

The selection of this

TABLE I Summarised descriptions of core materials

Formation Rock Type Description Mineral Content Physical Properties

Yorkshire Jurassic Calcarenaceous Sands tone

Fife Carboniferous Dololdtic Sandstone

Rotliegende Sandstone Calcitic Sandstone

Oxfordshire Jurassic Oolitic Limes tone

Composed of subrounded detrital quartz grains and detrital carbonate debris cemented by micritic calcite

Composed of angular to subrounded quartz grains partially cemented by secondary dolanite. The dolomite is evenly distributed, occurring as rho& shaped crystals and crystalline masses in the voids between sand grains

Composed of subrounded to ro*mded quartz grains with patchy calcite pore fill and clay

Composed of ooliths and shell fragments cemented by micritic calcite

Quartz 80% Ferroan Calcite 20%

Permeability 10OmD Porosity 16%

Quartz 90% Permeability 20OmD Dolomite 10% Porosity 10% Felspar and Clay less than 1%

Quartz 95% Permeability 3 0 W Calcite 2.5% Porosity 15% Felspar and Clay 2%

Permeability 6OmD Calcite 98% Quartz 2% Porosity 15%

W ul W

3 60

(1) thin section petrographic analyses,

(2) differential dye staining for carbonate identification

( 3 ) scanning electron microscope analyses,

(4) porosity, pore size distribution and permeability measurements.

For each series of experiments a number of 2.5 cm diameter X 7.5 cm length cylindrical cores were drilled and trimmed from the same block of rock, so that variation in the properties would be kept to a minimum. As a precaution against collapse on dissolution, the cores were coated on the cylindrical surface with epoxy resin.

RESULTS

(1) The initial series of experiments were carried out on the Yorkshire Jurassic calcitic sandstone. First tests with distilled water and brine (no carbonation) were aimed at establishing a stabilised or reference permeability, prior to any carbonated water flood. The results of two such tests, R7 and R9, are presented in Figure 3. Significant increases in permeability were obtained in the tests, with little apparent levelling off in the rate of permeability increase and attainment of a reference value, upon injection of up to 500 pore volumes. Chemical analysis of the core effluents for calcium showed the permeability increases to be attributable to the dissolution of calcite cement in the flood liquids.

As a comparison with the base liquid experiments, a series of tests with carbonated brine were then undertaken. As shown in Figure 4, much greater permeability increases were obtained, although again there was little indication of any fall in the rate of permeability increase. of the core effluent analysis as compared with those from a brine flood (R9) are presented in Figure 5 . As expected, the calcium concentrations in the effluent samples from the carbonated brine tests were far higher than in the brine test, although there was a significant difference between the results for carbonated brine tests R20 and R21. Examination of the flooded cores showed this was because in R20 a thin band was preferentially dissolved, whereas in R21 a more uniform dissolution took place (Plate 2). Presumably in R20, as the flood progressed, the main flow was through the thin permeability "streak", resulting in lower total dissolution than in R21.

To gain an understanding of the variation in local permeability, the cores from the various tests were retrieved after flooding and cut into three 2.5 cm long segments. and plotted as a function of axial position in the core. The plots for R9 and R2O are presented in Figure 6. permeability at the inlet end of the cores was increased considerably more than that at the outlet end. mately the same shape, infers that the location of each profile is simply determined by the level of carbonation of the brine. Since constant flow rate was used in the experiments, this result implies that a zone of increasing permeability, which can be considered as a front, was moving through the cores. turn a function of the liquid flow rate through the core and carbonation level of the brine.

The results

The permeability of each segment was then measurod

The profiles obtained show the

Also, the fact that the profiles have approxi-

The velocity of the permeability front migration is in

361

M0

2 R7 Calcitic Sandstone /

3

R9 Calcitic Sandstone 3% Brine, 2Ooc, 1000 psi

1 : 100 200 300 400 500

PORE VOLUMES INJECTED

Figure 3 Permeability changes during runs 7 and 9

22

19

16

13

10

7

4

1 i 00 200 300

PORE VOLUMES OF CARBONATED WATER INJECTED

Figure 4 Permeability changes during runs 20 and 21,

362

0.12

0.08

0.04

R20 - thin band preferentially dissolved -

- R21 - uniform dissolution

- R9 - brine flood -

W w W w Q A

600 1200 1800

CORE FLOOD VOLUME (cc)

Figure 5 Comparison of effluent calcium concentration profiles for runs 9, 20 and 21

. ) . .

Plate 2 Comparison of Yorkshire Jurassic sandstone cores before (left) and after (right, run 21) a carbonated water flood

363

600

400

200

,

-

. INITIAL PERMEABILITY - - - - - - - - - -

I I I 1 2.5 5.0 7 . 5

AXIAL DISTANCE ALONG CORE (all)

Figure 6 Permeability profile for runs 9 and 20

The porosity and pore size distribution of each of the 2.5 an long segments from all the above tests were measured and compared to initial whole core values. Generally it was found that although large increases in the permeability had occurred, the porosity had changed little. This result illustrates that the main mechanism for the increase in permeability is probably not the uniform dissolution of carbonate cement, but rather the removal of constrictions in the larger pores. This is confirmed by the mercury porosimeter pore size distribution results, which show that it was primarily the diameters of the larger pores which were increased during the tests.

(2) To further, and more realistically, test the permeability front migration phenomenon, a series of tests were initiated on material with a much lower carbonate concentration than the Yorkshire Jurassic sandstone. Difficulty in acquiring calcite cemented sandstone led to a dolomitic material from the Fife Carboniferous being used at this stage. It was hoped that it would be possible to dissolve out all the dolomite cement from this sandstone and thus eventually achieve constant permeability. However, the low reaction rate of dolomite in carbonated water, compared to that of calcite, effectively ruled out this possibility.

The permeability profiles of two tests, R22 and R23, on the dolomitic sandstone are presented in Figure 7. under ambient temperature conditions meant virtually no dissolution effects were observed in R22, while in R23, although a fairly significant permeability increase was obtained, chemical analysis of the core effluent showed that only a small proportion of the dolomite cement was leached out.

(3) Some tests were then carried out on a calcitic Rotliegende Sandstone from a Southern North Sea gas field, but a series of core collapses, caused by weakening on wetting, meant abandonning the use of this material and continuing the search for other sources of calcitic sandstone.

The very slow reaction rate of dolomite

364

600 -

400 .

R23 Dolomitic Sandstone -

R 2 2 Dolomitic Sandstone 1000 p s i Carbonation, ZOOC

200 - - " v 0

200 400 600

PORE VGLUMES OF CARBONATED WATER INJECTED

Figure 7 Permeability changes during runs 22 and 23

R26 Oolit ic Limestone

1500 ps i Carbonation, 80°C

10 20 30 40 50

Pore Volumes of Carbonated Water Injected

Figure 8 Permeability change during R26

(4) A test w a s run on an o o l i t i c limestone from the Oxfordshire Jurassic, the permeability prof i le of which is presented in Figure 8. increase i n permeability was obtained, with the d i f fe ren t ia l pressure across the core f a l l i ng t o almost zero a t maximum flow rate, a f t e r injection of only 50 pore volumes. because two 1.5 mm diameter "wormholes" of roughly c i rcu lar cross section had formed over the length of the core.

A very rapid

Examination of the flooded core shaved t h i s was

365

Pore s i z e d i s t r i b u t i o n a n a l y s i s of the limestone ind ica ted an extremely wide pore diameter d i s t r i b u t i o n and, as expected, it w a s the s e l e c t i v e enlarge- ment of t h e l a r g e pores a t the upper extreme of t h e d i s t r i b u t i o n that contr ibuted s i g n i f i c a n t l y to t h e increase i n permeabi l i ty i n this test.

CONCLUSIONS

(1) The high pressure, high temperature carbonated water permeameter constructed to inves t iga te carbonate d isso lu t ion e f f e c t s on carbon dioxide flooding i s providing new i n s i g h t i n t o the var iab les that cont ro l t h e d isso lu t ion process.

(2 ) minerals were experienced. plugging w a s obtained i n the experiments.

(3) The d isso lu t ion of carbonate mineral from cores produces a change i n local permeabi l i ty which t r a v e l s as a f r o n t through the c y l i n d r i c a l core.

(4) w a t e r f lood i s probably due t o removal of c o n s t r i c t i o n s and s e l e c t i v e d isso lu t ion of t h e l a r g e r pores.

Only increases i n core permeabi l i ty from disso lu t ion of carbonate N o evidence f o r f i n e s migration o r p a r t i c l e

The dramatic increase i n permeabi l i ty of a core during a carbonated

REFERENCES

1. NEWTON, L. E. and McCLAY, R. A.; "Corrosion and Operation Problems, C02 Project , SACROC Unit", Paper SPE 6391, presented a t t h e SPE-AIME Permian Basin O i l and G a s Recovery Conference, Midland, TX, March 10-11, 1977

WNTIOUS, S. B. and THAM, M. J.; Review of Flood Performance and Numerical Simulation Model", Paper SPE 6390, presented a t the SPE-AIME Permian Basin O i l and G a s Recovery Conference, Midland, TX, March 10-11, 1977

3. HANSEN, P. W.; "A CO T e r t i a r y Recovery P i l o t , L i t t l e Creek Fie ld , Mississippi'!, Paper S8E 6747, presented a t the SPE-AIME 52nd Annual F a l l Technical Conference and Exhibition, Denver, O c t . 9-12, 1977

4. DOSCHER, T. M. and KUUSKRAA, V. A.; "Carbon Dioxide f o r Enhanced Recovery of Crude O i l " , paper presented a t t h e European Symposium on Enhanced O i l Recovery, Edinburgh, J u l y 5-7, 1978

2. "North Cross Unit C02 Flood -

5. CAMERON, J. T.; "SACROC Carbon Dioxide In jec t ion - A Progress R e p o r t " , paper presented a t t h e API Production Department Annual Meeting, Los Angeles, Apri l , 1976

Geological Implications", Am. Jour. Sci. , (March 7953) 250, 161-203

6. MILLER, J. P.; "A Port ion of t h e System CaC03-C0 0, with

7. ELLIS, A. J.; Am. Jour. Sci., (May 1959) 257, 354-365

"The S o l u b i l i t y of Calcite i n Carbon Dioxide SOlUtiOnS",

366

8. SEGNIT, E. R., HOLLAND, H. D. and BISCARDI, C. J.; "The Solubility of Calcite in Aqueiaus Solutions", Geochim. et Cosmochim. Act., (1962) 26, 1301-1331

S H A R P , W. E.; and Aqueous Solution", PhD Thesis, Univ. of California, 1964

9. "The System CaO-C02-H20 in the Two Phase Region Calcite

10. S W , W. E. and KENNEDY, G. C.; "The System Ca0-C02-H20 in the Two Phase Region Calcite and Aqueous Solution", Jour. of Geol. (1965) 73, 391-403 -

NUMERICAL METHODS 367

COMPUTER MODELLING OF EOR PROCESSES

KHALID AZIZ

Computer Modelling Group, 3512-33 Street, N. W.,

Calgary, Alberta T2L 2A6, Canada

ABSTRACT

This paper presents a rather personal view of recent developments, current problems and future prospects for the computer simulation of enhanced oil recovery schemes. While substantial progress has been made over the past twenty years o r so, some problems of significant practical importance remain unresolved.

INTRODUCTION

This paper is neither a comprehensive review of past work on reservoir simulation - also referred to as reservoir modelling - nor a complete catalogue of current activities in this field. Instead it presents the author's view of (a) the status of simulation technology, and (b) current and future problems. The paper is intended primarily for individuals interested in using models rather than those who are engaged in the development of models.

The contents of the paper are heavily influenced by work conducted by the author's students at the University of Calgary and his colleagues at the Computer Modelling Group (CMG). Important work underway at other institutions may not be mentioned here primarily because of the lack of up-to-date information available to the author. CMG is, however, a vehicle for cooperative research in reservoir simulation among universities, research organizations, government agencies and industry. Currently 34 such organizations are members of CMG and these organizations have a rather direct and significant influence on its work. Hopefully, because of this type of interaction, problems being investigated by CMG reflect current industry.needs.

Modelling is an iterative process consisting of the following major stepsl:

1. 2. 3. 4. 5. 6. 7. 8.

Describe Reservoir Describe Recovery Mechanism Write Mathematical Model Develop Numerical Model Develop Computer Model (Program) Validate Model Match History Predict Future Performance

Often during steps 6, 7 and 8 it becomes necessary to go back to steps 1 , 2, 3 or 4 and alter some of the assumptions made earlier. Assumptions are necessary at various stages to (a) allow simulation of processes where recovery mechanisms are

368

no t f u l l y understood, (b) make t h e problem tractable, and (c) reduce c o s t o f s imulat ion. Obviously t h e need f o r t h e assumptions is c o n s t a n t l y changing with improved understanding o f t h e phys ica l and chemical a s p e c t s o f t h e recovery processes, development of new numerical techniques, and hardware innovat ions. S t e p s 6 and 7 dea l ing with t h e v a l i d a t i o n and use o f models w i l l no t be considered i n t h i s paper.

CLASSIFICATION OF MODELS

A large v a r i e t y o f models are i n c u r r e n t u se and t h e number is c o n s t a n t l y in - creasing. New models are developed t o (a) s imula t e new processes , (b ) s imula t e behaviour of r e s e r v o i r s with s p e c i a l c h a r a c t e r i s t i c s , (c) reduce c o s t , (d) i m - prove accuracy, (el have access t o a s u i t a b l e model under accep tab le cond i t ions , or ( f ) understand r e s e r v o i r s imulat ion. Table 1 prov ides a c l a s s i f i c a t i o n based on Recovery Mechanisms, Reservoir/Well C h a r a c t e r i s t i c s , Numerical Approximations, FluidIRock P r o p e r t i e s , So lu t ion Techniques and Computer Type.

Table 1 C l a s s i f i c a t i o n o f Models

1. RECOVERY MECHANISMS

1.1 WATERFLOOD OR PRIMARY DEPLETION 1.1.1 Three component, t h r e e phase 1.1.2 Two component, two phase

1.2.1 Multicomponent, s i n g l e phase 1.2.2 Multicomponent, mult iphase

1.2 GAS OR SOLVENT INJECTION

1.3 CHDfICAL FLOOD 1.3.1 Four component, two or t h r e e phase (polymer) 1.3.2 Multicomponent, mult iphase ( s u r f a c t a n t , c a u s t i c )

1.4.1 Three component steam 1.4.2 Compositional steam 1.4.3 Steam wi th add i tkves 1.4.4 I n s i t u combustion

2. RESERVOIR/WELL CHARACTERISTICS

1.4 THERMAL MODELS

2.1 RESERVOIR WELL COUPLING

2.2 FRACTURES 2.2.1 S t a t i c f r a c t u r e 2.2.2 Dynamic f r a c t u r e 2.2.3 Uniformly d i s t r i b u t e d f r a c t u r e s

2.3 CONSOLIDATION OF RESERVOIR ROCK 2.3.1 Sand flow 2.3.2 Ground subsidance

3. NUMERICAL APPROXIMATIONS

3.1 PRIMARY VARIABLES 3.1.1 S e l e c t i o n o f v a r i a b l e s 3.1.2 S e l e c t i o n o f equa t ions 3.1.3 Alignment o f v a r i a b l e s and equa t ions

369

Table 1 (Cont'd)

3.2 LINEARIZATION 3.2.1 Newton's method 3.2.2 Other methods

3.3.1 Fully impl ic i t 3.3.2 Sequential 3.3.3 3.3.4 Dynamic Impl ic i t 3.3.5 Band reducing techniques

3.4.1 Single point upstream 3.4.2 Two point upstream 3.4.3 Harmonic average 3.4.4 Centralized upstream 3.4.5 3.4.6 Nine-point schemes

3.3 DECOUPLING

Impl ic i t Pressure Expl ic i t Saturat ion (IMF'ES)

3.4 INTERBLOCK FLOW

Other interblock mobility ca lcu la t ion methods

3.5 TRUNCATION ERROR 3.5.1 Standard f in i te -d i f fe rences 3.5.2 Higher order f in i te -d i f fe rences 3.5.3 Variat ional 3.5.4 Semi-analytical 3.5.5 3.5.6 Curvilinear g r i d 3.5.7 Local g r i d refinement 3.5.8 Moving g r i d

Location of g r i d point i n a block

4.

5.

6.

FLUID/ROCK PROPERTIES

4.1 RELATIVE PERMEABILITY CALCULATION 4.1.1 Three phase model 4.1.2 Temperature effect model 4.1.3 Composition e f f e c t model 4.1.4 Hysteresis model

4.2 FLUID PROPERTIES 4.2.1 Empirical cor re la t ions 4.2.2. Equation of state

SOLUTION TECHNIQUES

5.1 ORDERING OF EQUATIONS

5.2 GAUSSIAN ELIMINATION

5.3 ITERATIVE METHODS

COMPUTER TYPE

6.1 STANDARD

6.2 VECTOR PROCESSORS

6.3 INTERACTIVE DATA INPUT AND ANALYSIS OF RESULTS

3 70

This classification provides a suitable framework for comment on the status of some aspects of the technology.

RECOVERY MECHANISMS

The simplest models that can be used for primarily depletion and water or hydrocarbon gas injection studies are referred to as black-oil or models. Themodels of this type have been in use for over twenty years and are based on the assumption that the reservoir fluids can be assumed to consist of only three pseudo- components - oil, water and gas at standard conditions. This rather gross assumption works well for systems that remain far from the critical or the retrograde region during the recovery process and where the injected fluids consist of the same components as in the in situ fluids. Even in this relatively simple case different models can yield different results for the same problem2. Most of these differences may be attributed to the numerical aspects to be discussed later.

Compositional models allow for the representation of oil and gas by a mixture Of several m o m pseudo-components each. They can handle complex phase behaviour associated with, for example, the injection of C02. Chemical flood models are even more complicated compositional models with capabilities to handle important rock/fluid and fluid/fluid reactions. Each component or pseudo-component yields one conservation or mass balance equation to be solved for each grid point. Hence as the number of components increases, the number of equations to be solved increases in direct proportion.

Thermal models can vary in complexity from the simple three component steam model to the complex in situ combustion model. In addition to the conservation of mass we must also add the conservation of energy to our system of equations to be solved.

The problems in defining the recovery mechanism from the point-of-view of the modeller usually relate to the lack of experimental information for the selection of pseudo-components, to predict their physical and chemical properties, and to validate the assumptions of the mathematical model. Contrary to the belief held by some, reservoir simulation does not reduce or eliminate the need for experiments - it allows us to get the most out of laboratory and field experiments we can afford to run.

Examples of the phenomena that can not be handled in a satisfactory fashion at this time are (a) formation and flow of emulsions, and (b) flow of more than two liquid phases.

RESERVOIR/WELL CHARACTERISTICS

The intimate interaction between the reservoir and the flow in the wellbore (tubing or annulus) of both injection and production wells must be recognized for realistic simulation. While it is relatively easy to do single phase well flow calculations to any desired accuracy, the same is not true when two or three phases exist in the wellbore. The transient nature of the flow causes further complications. Modellers often underestimate the importance of the wellbore/ reservoir coupling and overestimate the reliability of correlations for performing wellbore calculations. Errors of the order of 20% are possible even when "best" available methods are utilized. Since there are no clear schemes for the determination of what wellbore flow calculation method may be the best in each situation, even higher than 20% errors are possible.

Simulation of the initiation, extension and closing of a fracture requires the coupling of rock and fluid mechanics. This important field has only recently started receiving attention. Much work is required before this technology can be used to improve the design of massive-hydraulic fractures now being conducted in tight formations4,5. These models are also required to predict fracture orienta-

371

tion and size in unconsolidated oil sands, where fracturing is used to provide initial communication between the injectors and the producers.

Except for single well studies in cylindrical coordinates, economic constraints demand that blocks containing wells be orders of magnitude larger than the Size of the well. The problem then is to relate the calculated conditions at the grid point in a block to the well that may be located anywhere in that block. Analy- tical solutions based on single phase flow theory are used to relate the well pressure to the block pressure6. Detailed simulation of the zone near the well through the use of small blocks and cylindrical coordinates is necessary when saturation and/or thermal effects become important. The information generated from such a local study of the well vicinity is used in the form of pseudo- functions for the simulation of the reservoir. A better solution of this problem would be to have the capability to do local grid refinement without placing small blocks where they are not needed. The multi-grid approach may offer a solution to this problem7.

Recently it has been possible to generalize the well treatment to handle vertical fractures that go through a number of grid pointsa. For single phase flow, where it is possible to compare numerical and analytical solutions, the agreement is excellent. For multiphase flow, in addition to the problems encountered for wells, we also have the unresolved problem of multiphase flow in the fracture.

Reservoir rocks that are naturally fractured behave in a significantly different fashion from conventional reservoirs. They may be simulated through the concept of double-porous-media with separate equations for each system and appropriate transfer terms for interaction between the systemsg. Some of the problems with the practical use of this concept are (a) determination of the value of the transfer terms, and (b) experimental verification, particularly for multiphase flow.

Some reservoirs are either unconsolidated or only partially consolidated. The flow of sand in such systems alters rock properties. In shallow reservoirs removal of fluids (and/or solids) may also cause ground subsidance. Little is known about these two mechanisms and their simulationlo.

NUMERICAL APPROXIMATIONS

The mathematical model of flow in a conventional reservoir consists of one partial differential equation for each pseudo-component. Furthermore, for thermal processes an additional partial differential equation for temperature is obtained from the conservation of energy. In addition several constraints and algebraic relations must also be satisfied. The equations of the mathematical model may be manipulated to obtain a set that is more amenable to numerical treatment. At this stage a set of primary variables, equal in number to the partial differential equations to be solved, is selected. Sometimes the selection is postponed until after the application of some technique to translate the partial differential equations to difference equations. For example in black oil simulation, the oil phase pressure, and gas and water saturations form a suitable set of primary variables. The selection of primary variables and the alignment of these variables with appropriate equations can have a substantial effect on the eventual performance of the model.

Numerical difficulties can result due to the appearance and disappearance of a phase during simulation. This happens, for example, in thermal and in variable bubble point black oil problem simulation. This problem may be circumvented by variable substitution or b using a technique that does not allow the phase to disappear completely6,ll 9 1z~13. The same result is obtained by both techniques, however program complexity and computer time can differ substantially. With the use of variable substitution it is possible to solve for one less equation and

372

t h u s save computer time. However, s p e c i a l care is necessary f o r a smooth t r an - s i t i o n from one set o f v a r i a b l e s t o ano the r s e t l 2 .

Most r e s e r v o i r s imula to r s u t i l i z e three-point f i n i t e - d i f f e r e n c e approximation f o r second o rde r space d e r i v a t i v e s a s s o c i a t e d w i t h t r a n s p o r t terms and two-point backward d i f f e r e n c e approximation f o r first o rde r d e r i v a t i v e s a s s o c i a t e d w i t h t h e accumulation terms. The end r e s u l t of such a n e x e r c i s e is a set o f non-l inear , coupled algebraic equa t ions of t h e form:

F(X) = 0 ( 1 )

where X is t h e v e c t o r o f unknowns ( = number o f primary v a r i a b l e s number Of

b locks) f o r a time s t ep . Such a set o f non-linear equa t ions can on ly be solved by some i t e r a t i v e technique. Applicat ion o f Newton’s method y i e l d s :

A(fi+1 - f i ) = -F(Xv) ( 2 )

where (v) is the l e v e l of i t e r a t i o n and A is t h e Jacobian with elements a f i / a x j . These elements can be evaluated either numerical ly or a n a l y t i c a l l y , depending on the problem. Each non-zero e n t r y i n t h e ma t r ix is a NEQxNEQ block element where NE4 is the number of primary va r i ab le s .

The Jacobian matr ix is s p a r s e w i t h t h e form shown i n F igu re 1.

7

x x x X x x x x X x x x x X

x x x x x X

x x X X X x x x X

x x x x x X x x x X X X x x X x x x x X x x x x X x x x X

X x x x X x x x x X x x x x X x x X X X x x x X x x x x x X x x x x x X x x x X X X x x X x x x x X x x x x X x x x - -

Figure 1 S t r u c t u r e of Matrix A f o r a 4 x 3 ~ 2 Grid

(Each X r e p r e s e n t s a NEQxNEQ block matr ix)

Each time s t e p u s u a l l y r e q u i r e s 2 t o 5 Newton i t e r a t i o n s f o r the s o l u t i o n of ( 1 ) . Hence f o r a t y p i c a l problem, equat ion ( 2 ) must be solved many hundreds of times. A s t h e number o f blocks i n c r e a s e s , t h e f r a c t i o n o f t o t a l computer time tha t is spent on ( 2 ) also inc reases . Recent research t o reduce t h i s e f f o r t w i l l be discussed i n the fol lowing sec t ion . The f u l l y i m p l i c i t method has un l imi t ed

373

stability, but Newton's method may not converge, or converge to an unreal solution if the initial guess (previous time step) is too far from the solution. Other variations of Newton's method like the semi-implicit or linearized implicit also work well for some problems. Non-linearities associated with the production/ injection terms can have a significant influence on the stability and time truncation error of the modell4. A problem of convergence to unreal solutions, which arises in the simulation of steam displacement with a non-condensable gas, has been eliminated through the addition of a "penalty source" term to the inert gas equationl2.

The size of the matrix equation to be solved can be reduced by suitable approximations that partially or fully decouple the equations (SEQUENTIAL METHOD) and reduce the number of implicit equations to one (IMPES). In the IWES method the pressure is solved for implicitly while the saturations are treated explicitly. This results in a limitation on stabilityl. The decoupling can take place at the Jacobian level of the partial differential equations, the difference equations, or the matrix. Approximations of this type do, in some cases, increase the number of iterations necessary for convergence over the time step or fail to converge. The reliability of such methods is questionable for difficult problems.

The flow into and out of a block depends upon the permeability (kp, = k kr8)values at the block boundaries. The value of absolute permeability at the boundary is computed as the harmonic average of the two adjacent blocks. The rules for the computation of relative permeability are not well defined. The most comon approach is to use the relative permeability of the upstream block. Many different methods have been investigated with a view to reducing the grid orientation and truncation errorl5. KO et al.15 expressed transmissibilities for the two phase pressure and saturation equations as

AT and

respectively. They found that the fw AT

fWIBB = 4 fWuu - fWu + 4 fwd

and harmonic total mobility (HTM):

(3)

(4) centralized upstream for f, (CUF):

(5)

worked best. Even this method failed when the shock mobility ratio, M,, exceeded 2. However their tests were for incompressible water flood problems. The behaviour of these schemes is different for compressible systems and when the saturation change is not monotonic.

Another approach to reduce the grid orientation effect is to allow flow in directions that are both parallel and diagonal to the grid. This can be accomplished through a nine-point (as opposed to five-point ) scheme for two-dimensional problemsl3, l6 and a twenty-seven (as opposed to seven-point) scheme for three- dimensional problems. Abou-Kasseml3 has observed significant reduction in grid orientation with the nine-point scheme for a steam displacement problem where five-point shows substantial effect of the orientation of the grid.

Grid orientation is a major unresolved problem that raises some serious questions about the credibility of simulation for highly unfavourable mobility ratios. Although the nine-point formulation works, its use at this time is prohibitively expensive. For some situations ourvilinear grid can be used to reduce both grid orientation and truncation error. However this approach is also not suitable for general applications.

374

Space and time t runca t ion e r r o r s can be maintained a t t o l e r a b l e l e v e l s f o r conven- t i o n a l simulation. However, t h e e f f e c t of space t runca t ion can mask t h e t r u e phenomena i n processes where block s i z e is too l a r g e t o de f ine even t s i n t h e r e se rvo i r . Examples o f t h i s s i t u a t i o n are (a) misc ib l e o r chemical s l u g s , and ( b ) combustion f ron t . I n a mul t ip l e con tac t miscible d r i v e process , t h e r e s u l t s can be e s p e c i a l l y s e n s i t i v e t o t h e s i z e o f t h e blocks i n t h e zone where m i s c i b i l i t y is being e s t ab l i shed . The accuracy of s imulat ion could be improved by (a) adap t ive g r i d refinement, (b ) using higher o rde r methods, o r ( c ) using ano the r (poss ib ly a n a l y t i c a l ) model w i th in the block t o provide t h e necessary d e t a i l . None of t hese approaches have f u l l y succeeded so far.

FLUID/ROCK PROPERTIES R e a l i s t i c p red ic t ion of f l u i d and rock p r o p e r t i e s f o r t h e changing cond i t ions during s imulat ion is of c r u c i a l importance i n r e s e r v o i r s imulat ion. However, t h i s a spec t of t h e problem is no t t o t a l l y i n t h e c o n t r o l of t h e s imulator developer. Often l ack o f good experimental data and the need f o r answers wi th in t i g h t time c o n s t r a i n t s f o r c e s one t o make assumptions t h a t may o r may no t be j u s t i f i e d . I n s i t u a t i o n s of t h i s type, it is t h e r e s p o n s i b i l i t y of t he modeller t o make t h e l i m i t a t i o n s of the r e s u l t s c l e a r t o t h e use r of t h e information der ived from t h e s imulat ion.

Most of the p r o p e r t i e s required f o r t he s imulat ion of primary dep le t ion o r water f looding i n crude o i l r e s e r v o i r s can e a s i l y be measured i n t h e l abora to ry , and are usua l ly ava i l ab le . One exception t o t h i s is data on t h r e e phase r e l a t i v e perme- a b i l i t y , and on the e f f e c t of temperature and i n t e r f a c i a l t ens ion on r e l a t i v e permeabi l i ty , and c a p i l l a r y pressure. Models are o f t e n used t o p r e d i c t t h r e e phase r e l a t i v e permeabi l i ty from two phase data, and t h e effects o f temperature, i n t e r f a c i a l tension and h y s t e r e s i s phenomenon. More data than what is c u r r e n t l y a v a i l a b l e are required t o v a l i d a t e and r e f i n e these models.

Re la t ive ly simple equat ions of state when properly tuned and used o f f e r a powerful means of computing f l u i d p r o p e r t i e s i n an accu ra t e and c o n s i s t e n t fashionl7. These equat ions can be imbeded within a compositional model. Since compvtations with t h e equation of state a r e i t e r a t i v e , t h e modeller must ensure t h a t the scheme w i l l converge i n d i f f i c u l t s i t u a t i o n s with r e l a t i v e l y few i t e r a t i o n s l 7 , 1 8 . Several groups, including CMG appear t o be making s i g n i f i c a n t advances i n t h i s area. Inves t iga t ions are a l s o underway on methods of s e l e c t i n g an optimum number of components t h a t can be used t o r ep resen t t h e r e s e r v o i r and i n j e c t e d f l u i d s l g . There is a l s o concern t h a t , a t least f o r some processes l i k e t h e i n j e c t i o n of CO2 i n heavy o i l , t h e assumption of thermodynamic equi l ibr ium between phases i n a block may not be val id .

A s t he processes become more complex t h e data requirements i nc rease while the a v a i l a b i l i t y of data decrease. An example of t h i s is t h e k i n e t i c s of low tempe ra tu re oxidat ion f o r i n s i t u combustion processes.

SOLUTION OF MATRIX EQUATIONS

The heart o f a r e s e r v o i r s imulator is a program f o r t h e s o l u t i o n o f a l a r g e set of l i n e a r equat ions t h a t may be expressed as

where A is a s p a r s e matr ix with a well def ined s t r u c t u r e , x*l is a vec to r r ep resen t ing change i n t h e primary v a r i a b l e s from v t o * l i t e r a t i o n , and r i s t h e r e s i d u a l vector . Equations of t h i s type may be solved d i r e c t l y by Gaussian e l imina t ion , o r by some i t e r a t i v e method which involves the repeated s o l u t i o n of s e v e r a l sets o f sma l l e r matr ix equat ions by Gaussian el iminat ion. The work required f o r the direct s o l u t i o n of a system l i k e t h i s is given by

375

WD f I(NEQ J K ) 3 (8) where I, J , and K are the number of grid points in the three directions. To minimize work I is chosen to be the direction with the largest number of grid points. The coefficient f=l for standard ordering may be reduced to between .l9 and .5 for D4 orderingl.

Work required for iterative methods is difficult to predict since the number of iterations required depends on the problem. Another problem with iterative methods is their reliability in difficult situations. In general iterative methods that work are cheaper than direct elimination for larger problems. The cross-over point depends upon the methods and the problem.

Some rather powerful iterative methods have been developed recently. One such method, known as COMBINATIVE, has worked even for extremely difficult thermal problems20. This method became more economical than the direct elimination if

(J*K*NEQ + NEQ-1) 2 50 (9) The combinative method involves the following steps: (a) decouple pressure equation by neglecting appropriate terms in (7), (b) solve the pressure equation by Gaussian elimination with D4 ordering and obtain initial estimate of pressure, (C) use this pressure estimate to form new residuals for (7), (d) do an LU factor- ization of the whole set and obtain an initial estimate of the remaining variables and an extra contribution to the initial pressure estimate obtained in step (a), and (e) apply ORTHOMIN20 acceleration. This procedure is repeated until convergence is achieved.

Other iterative methods based on the multi-grid21 approach now being developed show even greater promise. Iterative methods also require less storage than direct methods. In difficult problems it is necessary to treat the coupling between the well and the reservoir in a fully implicit fashion. If the well goes through more than one layer or block, additional terms are introduced. Unless properly handled, work required to solve the equations can increase substantially22.

COMPUTER HARDWARE

In addition to the computers becoming faster with larger and larger memory, there are two other developments that are beginning to have a profound influence on reservoir simulation. These are (a) the development of pipeline and parallel processors, and (b) the development of display and interactive techniques.

The pipeline and parallel processors can perform a large number of operations (up to 5 x lo8 floating point operations per second) very quickly provided the software is designed to take full advantage of the hardware. The current compilers can only go partways in achieving high efficiency with such processors. Program structure and solution algorithms are being developed for this class of computers. One disadvantage of this approach is that as efficiency on one machine increases, the program becomes less and less portable.

Interactive preparation of data and graphical display of results can make it much easier to run simulators and analyze results. This is particularly true of the new or infrequent users of a complex model. Within the next few years this is expected to become the normal procedure for conducting simulation studies.

CONCLUSIONS

The need for robust, economical, realistic and easy to use simulators is increasing as the oil recovery mechanisms being applied become more and more complex. Simulators are an essential tool for understanding and predicting reservoir performance. Their intelligent use can play a key role in optimizing oil recovery.

376

Along with the development of new numerical techniques, experimental studies must be continued to provide data and correlations for the prediction of fluid and rock properties. Model validation with carefully conducted experiments is also essential.

Significant new developments in numerical techniques, process understanding and hardware have taken place over the last few years, but much more needs to be done and will be done over the next few years.

ACKNOWLEDGEMENTS

The Department of Energy and Natural Resources of the Province of Alberta and the Department of Energy, Mines and Resources of the Government of Canada, provide partial funding for the work of CMG through the AlbertaKanada Energy Resources Research Fund. Additional support is provided by Associate'Members of CMG through the membership fees. The work at the University of Calgary has been supported over the past sixteen years by the National Science and Engineering Research Council (previously National Research Council).

The author is indebted to these organizations for financial support and to his students and colleagues for the generation of ideas and for their implementation in practical simulations.

NOMENCLATURE

A Jacobian matrix

I,J,K

k absolute permeability

kr-9.

NE4

r Residual vector

Grid nodes along the three directions

relative permeability of phase 9.

Number of equations per grid block ( = number of primary variables)

X Vector of change in primary variables over an iteration

X Vector of primary variables (unknowns)

Pa viscosity of phase 9.

SubscriDts

BB Block boundary

d 1 point downstream of block face in question

U 1 point upstream of block face in question

uu 2 points upstream of block face in question

377

Superscript

V

1.

2.

3.

4.

5.

6.

7.

8.

9.

10.

11.

12.

13.

14.

15 -

Iteration level

REFERENCES

AZIZ, K. and SETTARI, A.; "Petroleum Reservoir Simulationf1, Applied Science Publishers, London (1979).

ODEH, A.S.; "Comparison of Solutions to a Three-Dimensional Black Oil Reser- voir Simulation Problem", J. Pet. Tech. (January 1981) 3, 1, 13-25.

FOGARASI, M., GREGORY, G.A. and AZIZ, K.; "Analysis of Vertical Two Phase Flow Calculations: Crude Oil - Gas Flow in Well Tubing", Cdn. J. Pet. Tech. (1980) 3, 1, 86-92.

WADE, R. and AZIZ, K.; llStimulating the Triassic Carbonates in the Foothills Gas Trend of Northeast British Columbia", CIM 81-32-35, presented at the 32nd Annual Technical Meeting of the Petroleum Society of CIM, Calgary, Alberta (May 1981).

SETTARI, A.; "Simulation of Hydraulic Fracturing Processes", Soc. Petrol. Eng. J. (December 1980) 20, 6, 487-500.

AU, A., BEHIE, A., RUBIN, B. and VINSOME, K.; "Techniques for Fully Implicit Reservoir Simulation", SPE 9302, presented at the 55th Annual Fall Technical Conference and Exhibition of the SPE of AIME, Dallas, Texas (September 1980).

BRANDT, A.; "Multi-Level Adaptive Solution to Boundary Value Problems", Math. Comp. (April 1977) 2, 138, 333-390.

NGHIEM, L.; llModelling Infinite-Conductivity Vertical Fractures Using Source or Sink Terms", CMG.Re.02, (February 1981).

GESHELIN, B.M.; Y3tatic Fracture Model", CMG.RB.01, (January 1980).

Ertekin, T. and Farouq Ali, S.M.; "Numerical Modelling of Reservoir Compac- tion and Associated Ground Subsidence under Non-Isothermal Two-Phase Flow Conditions", presented at the SIAM Fall Meeting, Houston, Texas (November 1980).

CROOKSTON, R.B., CULHAM, W.E. and CHEN, W.H.; "A Numerical Simulation Model for Thermal Recovery Processes", Soc. Petrol. Eng. J. (February 1979) 9, 1,

FORSYTH, P.A. Jr., RUBIN, B. and VINSOME, K.; "Elimination of the Constraint Equation and Modelling of Problems with a Non-Condensable Gas in Steam Simu- lation", CIM 81-32-50, presented at the 32nd Annual Technical Meeting of the Petroleum Society of CIM, Calgary, Alberta (May 1981).

ABOU-KASSEM, J.H.; "Investigation of Grid Orientation in a Two-Dimensional, Compositional, Three-Phase Steam Model", Ph.D. Thesis, University of Calgary

FONG, D.K.S. ; llTreatment of Nonlinearities and Production Allocation in a Fully Implicit, Three-Phase Coning Model", M.Sc. Thesis, University of Calgary (1980).

KO, S.C.M., BUCHANAN, W.L. and VINSOME, K.; "A Critical Comparison of Finite- Difference Interblock Mobility Approximations in Numerical Reservoir Simu- lation", CIM 81-32-23, presented at the 32nd Annual Technical Meeting of the Petroleum Society of CIM, Calgary, Alberta (May 1981).

37-58.

(1981).

378

16. KO, S.C.M. and AU, A.; **A Weighted Nine-Point Fini te-Difference Scheme f o r Eliminating t h e Grid Or ien ta t ion Effec t i n Numerical Reservoir Simulation", SPE 8248, presented a t the 54th Annual F a l l Technical Conference and Exhib- i t i o n of t h e SPE of AIME, Las Vegas, Nevada (September 1979).

17. N G H I D l , L. and A Z I Z , K.; "A Robust I t e r a t i v e Method f o r Flash Calculat ions Using t h e Soave-Redlich-Kwong o r t h e Peng-Robinson Equation of Statell , SPE 8285, presented a t the 54th Annual F a l l Technical Conference and Exhibit ion of the SPE of AIME, Las Vegas, Nevada (September 1979).

18. MEHRA, R.K., HEIDEMA", R.A. and A Z I Z , K.; V a l c u l a t i o n of Multiphase Equil- ibrium f o r Compositional Simulationf1, SPE 9232, presented a t t h e 55th Annual F a l l Technical Conference and Exhibit ion of the SPE of AIME, Dallas, Texas (September 1980).

19. LEE, S.T., JACOBY, R.H., CHEN, W.H. and CULHAM, W.E.; Wxperimental and Theoret ical Studies on the Fluid Proper t ies Required f o r Simulation of Ther- mal Processest1, SPE 8293, presented a t the 54th Annual F a l l Technical Con- ference and Exhibit ion of t h e SPE of AIME, Las Vegas, Nevada (September 1979).

20. BEHIE, G.A. and V I N S O M E , K. ; "Block I t e r a t i v e Methods f o r Ful ly Impl ic i t Re- s e r v o i r Simulation", SPE 9303, presented a t t h e 55th Annual F a l l Technical Conference and Exhibit ion of the SPE of AIME, Dallas, Texas (September 1980).

21. BEHIE, G.A. and FORSYTH, P.A. J r . ; "Multi-Grid Solut ion of the Pressure Equation i n Reservoir Simulationf1, CMG.Rl7.01 (Ju ly 1981).

22. GEORGE, A.; "On Block Elimination f o r Sparse Linear Systems", SIAM J. Numer. Anal. (June 1974) 11, 2, 585-603.


THREE-DIMENSIONAL NUMERICAL SIMULATION OF STEAM INJECTION

P. LEMONNIER

Institut FranGais du Pktrole, Rueil Malmaison, France

ABSTRACT

k three-dimensional thermal model has been developed for simulating both cyclic steam injection and steam drive. The numerical model !IWIST describes three-phase flow (oil, water and steam) heat flow in the reservoir a& heat conduction in the surrounding formations. Wellbore heat losses between the surface and the reservoir are taken into account. The various reservoir heterogeneities and temperature dependent parameters (including relative permeabilities) are considered. the decreased residual oil saturation when steam is present. Mass conservation and energy equations are solved simultaneously to improve stability. A semi-implicit method is used for time formulation. The oil phase equstion is decoupled with a scheme of the type p-T-S /S this thermal simulator to be very efficient $n akms of coinputing time and stability .

Distillation effects are approximated through

This formulation enables

Numerical results are presented showing e steam stimulation history of five cycles and the influence of steam quality, initial reservoir pressure and steam injection rate on steamflood performance in a five-spot pattern.

INTRODUCTION

TWIST (Tool When Injecting Steam) is a three-dimensional steamflood model, which describes.three-phase flow (oil, water reservoir. Vertical heat losses to overlying and underlying strata and wellbore heat losses between the surface and the reservoir are taken into account.

The literature on the simulation of steamflooding is extensive 1-7. The efforts have been concentrated on methods of solution. The equations are solved sequentklly or simultaneously and the formulation is explicit, weakly or highly implicit.

steam) and heat flow in the

We use a formulation which requires significantly less computing time per grid block-time step than the implicit scheme, and is nevertheless highly stable, owing to the fact that the water and gas flow equation and the energy equation are solved simultaneously with implicit treatment of the gas trans- missibility. This formulation has been mentioned in the literature6 but not tested otherwise than in isothermal black-oil model.

3 8 0

iv'e encountered no difficulties in simulating field cases rith TWIST. Our experience includes steam stimulation and steam drive for pilots of various pattern shapes and various oil viscosities.

Numerical results are present,ed shoving a steam stimlation history of five cycles and the influence of steam quality arid reservoir pressure on oil recovery in steam drive.

MODEL DESCRIPTION

Simulator equations

The model consists of four equations expressing (1) conservation of mass for water and steam, ( 2 ) conservation of mass for oil phase, ( 3 ) conservatioo of energy and ( 4 ) equilibrium constraints. temperature, steam and water saturations. We have three additional equations for obtaining oil saturation, gas and water pressures : (5) saturations constraint, ( 6 ) and (7 ) capillary pressures.

The four unknowns are oil pressure,

s + s + s = 1 o w s

Po - Pw = PCW

P, - Po = Pcg

The phase velocity 7: is defined as

The condensation term is eliminated by summing the water aad steam mass conservation equations 3.

The equilibrium constraints are expressed by one of the three equations (4) for the following cases : no steam, saturated steam, superheated steam.

381

Additional assumptions

1 - The model can operate in one, two or three dimensions with Cartesian or'radial grid.

2 - Reservoir dip and gra.vity are takeo into account. 3 - Reservoir rock and fluids areampressible. 4 - The model is not compositional. Distillation effects are approxi-

mated through decreased residual oil saturation in the presence of steam.

5 - Reservoir can be anisotropic, homogeneous o r heterogeneous by layers or by cells.

6 - Temperature dependency of the physical and thermal parameters is accounted for.

7 - Three-phase relative permeabilit'es at each temperakure value are i calculated using Stone's method ,

8 - Numerical simulations include steam drive and steam stimulation. Heat loss to overburden and underburden

Heat loss by conduction to the overlying and underlying strata is calcu-

We as- lated from the numerical solution of the heat conduction equation. tion is approximated by the standard finite -difference approximation. sume negligible effects of heat conduction in the horizontal directions 3 . The heat conduction equation for the surrounding rock is not solved simultaneously with the reservoir equations. At,time step n+l the equation is solved using the reservoir boundary temperature at the previous time step.

The equa-

Well model

The wells have the following specifications :

1 - Bottom-hole pressure 2 - Water or steam injection rate 3 - Liquid production rate 4 - Oil production rate 5 - Shut in. Each well can operate successively in injection and production modes

(for huff and puff process for example).

Wellbore heat losses in the injection wells are calculated. The injection pressure and the steam quality are s ecified at surface or reservoir conditions. We use the method o f Rameyl3, SatterP4 for wellbore heat losses computations 20. The basic assumptions o f the method are as follows:

- Steam is injected at a constant rate, wellhead pressure, temperature and quality.

- Any variation in steam pressure with depth is negligible.

382

Fluid and rock properties

The steam and water properties are expressed through correlations fron the steam tables.

Oil and water enthalpies are expressed as polynomial functions of temperature. Steam enthalpy am2 all fluid densities are treated as functions of pressure and temperature.

Water and steam viscosities are expressed as functions of temperature. Oil \-iscosity is entered into the model as tabular function of temperature with exponential interpolation between adjacent entries in the table.

Residual oil and irreductible water saturations are represented as linear functions of temperature; the same assumption is made for the,relatire permeability end points. curves is described by shifting the curves wit.hout changing the curves shape5.

The rock specific heat and thermal conductivity are represented as linear

The influence of temperature on the relative permeability

functions of temperature.

User facilities

User facilities have been developed in the simulator. Arrays are dimen- sioned automatically with appropriate values at the beginning of each run. input cards are checked for validity and for inconsistencies. All errors encountered are listed at the end of the dataprocessing. Various print,ing options are allowed for input data and output rpsults. lected and printed with any orientation. Graphic plotting of input data (oil viscosity, relative permeabilities, . . .) and well behaviour versus tine (pressure, oil recovery, WOR, ...) are available, just as pressure, temperature or saturations contours or profiles,

All

Array maps can be se-

SOLUTION METHOD

Discretization

The three equations ( 1 ) ( 2 ) ( 3 ) are discretized into finite - difference form with upstream densities, mobilities and enthalpies in the flow terms.

Semi-implicit .%pproximcttions9 are used for time discretization. Interblock transmissibilities o r flow terms are treated as follows. level n) dating is considered for fluid viscosities, fluid densities and f l u i d enthalpies, on account of the weak sensitivity to implicit versus explicit dating encountered in numerical simulations. Explicit dating is used f o r water and oil relative permeabilities end semi-implicit formulation is used for steam relative permeability. Capillary terms are expressed explicitly in saturation.

Explicit (i.e. time

The accumulation terms are written with implicit dating. The resulting formulation is then linearized as follows :

(9) df df df

f (pn+', sn+l , Tn+') = f (p", Sn, Tn) + b~ bp +-6;5 b S +z 6T where bX = x"" - f with X = p, S, T.

3 8 3

With these approximations the four equations ( 1 ) ( 2 ) ( 3 ) ( 4 ) are expressed in terms of the four unknowns bp, 6T, 6Ss andbs,. The first three equations can he represented by

The explicit treatment o f oil and water relative permeabilities allows the

The"e1imination of 6 s water saturation unknown 6 s to be eliminated in equations (10) and (12) by means of equation ( 1 1 ) . coupled equations ( 1 3 ) (14) :

results in a system of two W

I A i4 A .

F21 l4 X A - Ft i l = Fil - - 2 j A24

A . . = A , . - - 1 3 13 , A24

I A . 14

A24

reduced to two equations in the two uknowns bp, 6X constraints ( 4 ) .

according to the equilibrium condition in the grid cell at time step n+1.

R . = R . - - x R 2 i = 1 et 3 , j = 1 , 3

The equations ( 4 ) (13) (14) involving the three unknowns 6p, bT,

The unknown bX is equal t o bT o r 6Ss. 6X can vary from one grid cell to an other and from one time step to an other

8 S s are by use of the equilibrium

The definition of

If no steam is present at time step n+l , 6X = 6 T and equation (4a) is used for eliminating 6 S s .

eliminating 6 T If steam is present at time step n+l, 6 X = 6 S S and equation (4b) is used for

If superheated steam is present at time step n+l, 6X =6T and equation (4c) is used f o r eliminating 6 S s .

Explicit dating of saturation-dependent production terms can give saturation oscillations in grid cells near the wellbore. production terms similar to that described by Spivak and Coatsto is used for increasing computational stability.

A semi-implicit formulation for

Resolution Procedure

The procedure of solution of the equations for the time step n+l is as follows :

1 - Solve the two equations ( 1 3 ) (14) for bp and 6 X using Gaussian direct solution with I) 4 ordering 1 1 . The substitution of the unknowns 6s or bT is made with the equilibrium conditions at time step n.

384

2 - Check the validit,y of the solution for each grid cell. If not, choose an other equilibrium condition and solve again the two equations for 6p and 6X.

3 - Solve equation (11) for 6 s using the values dp, 6T and 6 s . W s

EXAX’LES OF API‘LICATIOXS

k’e used the model for simulating a number of field cases. Numerical simulation studies of a steam drive pilot12 were made with a two-disensional grid. Simulations of the whole seven-spot pattern are now pursued with a three dimensional grid (12 x 9 X 5).

Two example cases are presented to illustrate the use of the model in the case of well stimulation and steam drive.

Well stimula.tion

The first application of the model consisted in simulating the production history of a well submitted to five successive steam stimulation cycles. The data are given in Table 1. The top of the reservoir is located at a depth of 228 m (748 ft). 4270 mPa.s (cP). Other values are given in Table 2. two-dimensional radial configuration (r, z) with a 12 x 6 grid.

Oil viscosity at initial temperature of 26OC (790F) is The run were made in a

TABU 1 - DATA FOR W L L STIMULATION PROBLEM Zone thickness Exterior radius Porosity Horizontal permeability Anisotropy kh/kv Irreductible water saturation Residual oil saturation to water Residual oil saturation to steam Rock compressibility Initial temperature Initial pressure Initial water saturation

24 m (78.74 ft) 200 m (656.16 ft) from 0.1 to 0.25 from 0.8 to 2 p 2 (800 to 2,000 nd) 10 0.2 0.43 at 26OC and 0.19 at 22OOC 0.1 5.10-5 Ha-’ (3.4 1C-4 psi-1\ 26OC (790F) 2800 kPa (406 psia) 0.2

TABLE 2 - OIL PRASE VISCOSITT Temperature Well stimulation problem Steam drive problem

200’2 ( 680F) 8924 mPa.s (cP) 5159 nif‘a.S (CP) 5OoC (1220F) 545 I’ 180

150OC (3020F) 8.3 I’ 5.5

II

II 1 oooc (2120F) 36 ’’ 19

2OOOC (3920F) 4.1 2.6 26OOC ( 5000F) 2.5 It 1.27

We specified a steam injection rate of 100 metric tomes per day (629 B/D cold water equivalent) into the six layers. face conditions and the injection temperature was 264OC (5070F). losses computed by the model give at the end of injection a quality of 90% at the bottom of the well.

The steam quality was 100% at sur- Wellbore heat

3 8 5

0.8 - .)

\ .)

P

S 0.6-

I- 3 0 - I

a

g 0.4- f

?

We simulated five cycles. One cycle involves 25 injection days, 5 soaking days and a producing period with a totai fluid production rate of 20m3/ day (126 BID). A new cycle is initiated when the oil rate has decreased to 5m3/da.y (31 BID). production cycles have been 152, 99, 136, 130 and 133 days. The variations of oil rate and water cut with time for the successive cycles are shown in Fig. 1 and Fig. 2. The well bottom-hole pressure evolution is shown in Fig.3

According to this criterion the durazions of the successive

16 I

T I M E , DAYS Fig. 1 - Oil production rate for five successive steam stimulation cycles

1.

Cycle 1

o ! I I

0 200 400 600 t T IME , DAYS

Fig. 2 - Water-cut versus time for five stimulation cycles

0

386

during the 800 days of history. The history includes 125 days of injection, 25 days o f soaking and 650 days of production. The total oil recovery was 3,570m? (24,346 STB) for a total steam injection of 12,500 tomes (78,616 STB cold water equivalent) and a total water production o f 8 ,1271113 (51,113 STB) . The values of the oil/steam ratio for each of the five cycles are the Dollo- wing: 0.64, 0.18, 0.31, 0.23 and 0.19. The criterion chosen for the end of the production phase leads to a greater length, L higher depletion and a better performance for the first cycle and to a relatively poor per%ormance forthe second cycle (Fig. 1).

60

0 a

0 240

u t 5 v)

t 3

20

0

Cycle 1 Cycle 2 Cycle 3 Cycle 4 . Cycle 5

END OF INJECTION

START OF PRODUCTION

I 1 I

200 400 600 8 T I M E , DAYS

0

Fig. 3 - Well bottom-hole pressure versus time for five stimulation cycles

An other simulation performed with predefined values for the length of the five successive production phases leads to the following values of the oil/steam ratio: 0.4 after 90 producing days o f the first cycle, 0.24 after 90 producing days of the second cycle, 0.32 after 120 producing days of the third cycle, 0.29 after 150 producing days o f the fourth cycle and 0.27 after 180 production days of the last cycle. The total oil recovery was the same.

The fair values of the oil/st,eam ratio may be essentially attributed to the relatively low porosity of the reservoir and to the high viscosity of the oil.

387

Steam-drive

Many studies have been devoted to the evaluation of the performance of steam flooding technique .l 5-18. parame-cers has not yet been clarified. servoir pressure on steamflood performance were investigated in a five-spot pattern with the simulator.

However the influence of some operating The effects of steam quality and re-

One eighth of a five-spot pattern was represented by a 6 X 3 X 5 grid (Fig.4) with A x =Ay = 14.14m (46.4 ft) and Az = 4m (13.12 ft) . Table 3 summarizes the data for this problem and Table 2 shows the oil viscosity versus temperature. The relative permeabilities were temperatwe dependent. The water-oil relative permeability curves are shorn in Fig. 5 for two temperature

3

U I 1 2 3 4 5 6

PRODUCER I N J E C T O R

Fig. 4 - Simulation grid for one--eighth of five spot pattern

Fig. 5 - Water-oil relative permecl- Fig. 6 - Gas-oil relative permeability curves bility curves

388

TABLE 3 - DATA FOR STEAM-DRIVE PROBIXM

Area (5-spot) Reservoir thickness Porosity Horizontal permeability Vertical permeability Formation compressibility Specific heat of formation Specific heat of overburden and underburden Thermal conductivity of formation Thermal conductivity of overburden and underburden Oil compressibility Thermal expansion coefficient of oil Specific heat of oil Stock-tank oil density Irreductible water saturation Residual oil saturation to water Residual cil saturation to steam Initial temperature Initial water saturation Initial pressure

Injection rate for full pattern (WE) Production bottomhole pressure

2 10,000 m (2.5 acres) 20 m (65.6 ft)

0.35 2 .5 p2 (2500 md)

1 ( 6 . 8 psi- ) 2.35 J/cm3 - OC ( 3 5 Btu/cu.ft -OF)

2.5 J/cm - O C (37 Btu/cu.ft -OF)

2.3 W/m - O C ( 3 2 Btu/ft - day - OF) 2.3 Wim - O C (32 Btu/ft - day - OF) 6.4 kPa-’ (4.4 10-6 psiA’) 6 .5 OC-’ ( 3 . 6 OF-l)

0.95 g/cm3 (60 lb/cu. ft) 0.25 at 25°C and 0.4 at 175OC 0 .4 at 25°C and 0.2 at 17joC 0.1

0.4

(580 psia)

I . p2 (1000 md) 1

3

2.1 J/e - O C (0 .5 Btu/lb - OF)

25°C (77OF)

500 kPa (72.5 psia) and 4000 lil’a

50 m3/day (314 B/D) 300 kEa (43.5 psia) and 3800 kPa

(551 psia)

values 09 25OC (77OF) and 2OO0C (3920F). The gas-oil relative permeability curves are shown in Fig. 6.

We studied the effects of varying bottom-hole steam quality from 0 to 1 for two values o f initial reservoir pressure, 500 kPa (72.5 psia) kPa (580 psia) respectively. Specified injection rate for both set of cases was 50 tonnes/day (314 B/D cold water equivalent) for the full pattern; steam is injected only into the two bottom layers. vity indices as calculated according to Peaceman l 9 were multiplied by two. Production wells produce from the five layers at deliverability against a bottom-hole pressure of 300 kPa (43.5 psia) and 3800 kF’a (551 psia), for both cases respectively.

and 4000

Well injectivity and producti-

Fig. 7 shows the effect of steam quality on injection pressure. The high

Injection pressure starts to

increase of injection pressure results from the formation of a high viscosity oil bank downstream from the condensation front. decrease when the oil bank becomes mobile.

As shown in Fig. 8 the oil recovery for a given heat input is little sen- The heat input is equal to sitive to steam quality when quality is above 6%.

the cumulative enthalpy o f steam at sand face referred to initial reservoir temperature. Fig. 9 shows earlier steam breakthrough when steam quality increases and initial pressure decreases.

389

60 -

2 -r 45-

2 w

4

Lu & 3 v, y 30- a

i=

2 15- I N I T I A L PRESSURE = 500 k P o

s 2 -

-- - -----------

O-- I 0 1 2 3

T I M E ,YEARS

4 ----- I

Fig. 7 - Effect of steam quality and initial reservoir pressure on injection pressure

0 0.2 0.4 0.6 0.8 1 STEAM O U A L I T Y

Fig. 8 - Effect of steam quality and initial reservoir pressure on oil recovery after 30 TJ heat input.

S T E A M OUALITY

Fig. 9 - Effect of steam quality and initial reservoir pressure on steam breakthrough.

390

Vertical heat losses to overlying and underlying strata are relatively independent of time after steam breakthrough. Heat losses after 6 Sears of steam injection are presented in Fig. 10; less heat losses are achieved for the lower initial pressure when quality is above 3@, due to lower steam t,emperature and faster heating of the reservoir. For a steam quality of 6% and an initiai reservoir firessure of 500 kPa (72 psia) the vertical heat loss is 31% of hea.t input. servoir and t,he reservoir thickness 50 m.. For these two values the vertical heat l o s s curves of Gomaal7 obtained with an initial pressure of 414 kPa give the same Talue of 31%. reservoir pressure dependent. For a pressure of 4000 kPa (580 psia) the heat injection rate is 505 kJ/D-m3 res. and the heat loss is 38.5% of heat input, instead of 29% in the low-pressure case considered by Gomaa.

The heat injection rate for this case is 460 kJD-m3 re-

The results in Fig. 10 show that the curves are also

Low heat, loss to overburden strata and early breakthrough result in a high amount of heat produced by the wells when operating at low initial reservoir pressure (Fig. 1 1 ) .

0 0.2 0.4 0.6 0.8 S T E A M O U A L l T Y

Fig. 10 - Effect of steam quality and initial reservoir pressure on vertical heat loss after 6 years

I I N l T l P L PRESSURE

a 6o - -- 500 k P o ( 72 p i 1 0 I - 4 0 0 0 k P o ~ 5 8 0 p 8 i s ) 2

5 0 -

z

0 0.2 0.4 0.6 0.6 1

STEAM O U A L l T r

Fig. 11 - Effect of steam quality and initial reservoir pressure on heat produced

The cumulative oil/steam ratio is plotted in Fig. 12 versus steam quality and initial reservoir pressure, after 6 years of injection. the oil/steam ratio is improved when steam quality increases and initial reservoir pressure decreases.

It appears that

The oil/steam ratio does not take into account the variation of heat input due to the variation of steam quality. meter, the energy yield EY, f o r comparing the performances of the tests. The energy yield is defined as the ratio between the calorific value of the cumulative oil produced and the heat input previously defined. equal to one when the energy content of the steam at sand face is equal to the calorific value of the produced oil (calorific valae of oil = 38 GJ/m3). shows the effect o f steam quality and initial reservoir pressure on the energy yield. An optimum steam quality value can be determined in Fig. 13, depending on initial reservoir pressure and on the duration of steam injection.

Hence we introduce an adimensional para-

The value of EY is

Fig. 13

39 1

T n e selisitilTitY t o steam qualitj- is much stronger at low pressure than 2 t high pressure. This is relared to t he higher amount of heat transported by the produced fluids in the case of lokT pressure tests (Fig. 11). The same reason may explain the shift of the optimum sream quality towards lower values when t,ime increases. As 2 matter of fact the heat produced after 6 years of injectiori is about tvice the value obtained after 3 years.

0 02 0:4 0:6 0.8 1 S T E A M OUALlTY

Fig. 12 - Effect of steam quality and initial reservoir pressure on cumulative oil/steam ratio after 6 years

Fig. 13 - Effect of steam quality and initial reservoir pressure on energy yield.

The optimum volumetric injection rate, after the project had reached a peak oil-production rate, was determined at Kern River from field results16. We made a similar study with the simulator in the case of 6% bottomhole steam quality and 500 kPa (72.5 psia) initial reservoir pressure.Fig. 14, as a result optimizes the rate of t e instantaneous oil/steam ratio. An optimum steam injection rate of 2.5 10 found (1.5 B/D -A-ft for Kern-River16). as the curve developed for Kern-River. The dispersion of the data is less than in the case of Kern-River since the simulations were carried out on a uique pattern whereas the correlation f o r Kern-River had been obtained from the field results o f several pilot tests. This optimum steam rate corresponds to the value of 50 m3/day (314 B/D ) used in the sensitivity study for the full five- spot pattern.

-5 . m3/day/m3 of reservoir volume (1.94 B/D - A-ft) was

The curve in Fig. 14 has the same shape

Model running time

The formulation described above is very efficient in terms of computing time. 0.002 seconds per grid block-time step on the CDC 7600 computer. of the steam drive pilot12 with a three-dimensional grid 9 X 12 x 5 (405 active cells) requires 0.0018 seconds per grid block-time step. here of a three-dimensional steam-drive with a 6 X 3 x 5 grid (60 active cells) requires 0.0008 seconds per grid block-time step. simulating a 9-year steam drive (582 time steps) with 4000 kPa initial pressure

A three-dimensional run with a 25 x 8 x 4 grid (800 cells) requires The simulation

The case presented

The computation time fo r

392

BOTTOM-HOLE STEAM CUALITY = 6041~

0 0.25 0.50 O j 5 1.60 1.25

Fig. 14 - Optimum injection rate PRODUCTION 1 6 4 d / L J A Y - M3 OFRESERVOIR VCUJME

and 6% downhole The ratio between computing times on a CDC 7600 and a vector computer CUP 1 has been 5.5 f o r a 12 X 12 X 4 grid (576 cells).

steam quality has been 28 seconds on the CDC 7630 computer.

CONCLUSIONS

1 - The semi-implicit formulation of the.solution method used for the three-phase three-dimensional model TWIST enables the simulator to be very efficient in terms of computing time and stability. The model may be used for simulating a wide variety of thermal problems.

2 - Five successive steam injection cycles in a low porosity reservoir have been simulated to evaluate the decline of the oil/steam ratio from cycle to cycle.

3 - The influence of steam quality and initial reservoir pressure on steamflood performance has been investigated. It appears that these parameters affect the heat loss to the surrounding formations, the heat transported by the produced fluids and the performance of the process. Better performances and higher sensitivity to steam quality are observed at lower pressures.

4 - The analysis of the steamflood performances obtained for various steam injection rates at givenquality and pressure indicates the existence of an optimum injection rate.

ACKNOWLEDGEMENTS

The author wishes to thank Institut Franqais du PCtrole for permission to publish this paper. Institut Francais du PBtrole f o r his helpful and constructive discussions.

He also expresses his appreciation to Mr. J.G. BURGER of

Partial financial support for the realfzation of the simulator used in this study was provided by Soci6t6 Nationale Elf-Aquitaine (Production).

393

NOMEXCLATURE

= enthalpy (J/g) = absolute permeability (m2) = relative permeability = thermal conductivity (W/m - OC) = pressure (kPaj = capillary pressure (pa) = mass injection or production rate (Ton/day) = enthalpy production rate (J/day) = heat loss rate (J/day) = saturation = time = temperature ("C) = temperature of saturated steam (OC) = internal energy (J/g) = phase velocity = depth, measured vertically downward (m) = specific weight (kPa/m) = time difference operator, e.g., 6~ = Xn+l - X" = viscosity (Pa.s) = porosity = density (g/cm )

Subscripts and superscripts

3

qL S t T

TS U

= steam = time level = oil = rock = steam = water

RGFERENCES

1 - Shutler, N.C.: "Numerical, Three-Phase Model of the Two-Dimensional Steam- flood Process", SOC. Pet. Eag. J., (Dec, 1970) 405-417.

2 - Weinstein, H.G., Wheeler, J.A., Woods, E.G.: "Numerical Model for Thermal Processes", SOC. Pet. Eng. J, (Feb, 1977) 65-78.

3 - Coats, K.H, George, W.D., Chu, Chieh, Marcum, B.E.: "Three-Dimensional Simulation of S';eamflooding", SOC. Pet. Eng. J. (Dec, 1974) 573-592.

4 - Ferrer, J. Farouq Ali, S.M.: "A Three-Phase, Two-Dimensional, Compositional Thermal Simulator for Steam Injection Precesses" - Paper 7613 presented at 27th Annual Technical Meeting of the Petroleum Society of CIM, Calgary, June 7-11 1936.

5 - Coats, K.H. : "Simulation of Steamflooding with Distillation and Solution Gas", SOC. Pet. Eng. J. (Oct. 1976) 235-247.

6 - Coats, K.B.: "A Highly Implicit Steamflood Model", SOC. Pet. Eng. J (Oct. 1978) 369-383.

7 - Grabowski, J.W., Vinsome, P.K., Lin, R.C., Behie, A. and Rubin, B.: "A fully Implicit General Purpose Finite-Difference Thermal Model for In-SLtu Combus- tion and Steam?, paper SPE 8396, presented at SPE 54th Annual Fall Meeting, Las Vegas, W, Sept. 23-26, 1979.

Oil Data", J. Can. Petr. Tech., V. 12, no 4, (Oct. 1973). 8 - Stone, H.L.; "Estimation of Three-Phase Relative Permeability and Residual

394

9 - Lolen, J.S, Berry, D.W. : "Tests o f the Stability an2 Time-Step Sensitivity of Semi-Implicit Reservoir Simulation Techniques", SOC. Pet,. Eng. J (June 1972) 253-266.

Production Terms", SOC. Pet. Eng. J. (Sep. 1970) 257-267.

Pet. Eng.J. (June 1974) 295-308.

Reservoir Lacq SupCrieur Field, "paper SPE 9453, presented at SPE 55th Annual Fall Meeting, Dallas, Texas, Sept. 21-24, 1980.

10 - Spivak, d . , Coats, K.H. : "Kumerical Simulation of Coning Using 1mpli.cit

11 - Price, H.S., Coats, K.H. : "Direct Methods in Reservoir Simulation", SOC.

12 - Sahuquet, E.C, Ferrier, J.J. : "Steam Drive Pilot in a Fractured Carbonated

1 3 - Ramey, H.J, JR. : "Wellbore Heat Transmission", J. Pet. Tech. (Apri1,1962)

14 - Satter, A. :"Heat Losses During Flow of Steam Down a Wellbore", J. Pet. 1 5 - Chu, C., Trimble, A.E. :"Numerical Simulation of Steam Displacement Field

16 - Bursell, C.G., Pithan, G.M. : "Performance of Steam Displacement in the

17 - Gomaa, E.E. :"Correlations for Predicting Oil Recovery by Steamflood",

18 - Nolan, J.B., Ehrlich, R., Crookston, R.B. :I1 Applicability of S t e m

427-435.

Tech. (July, 1965) 845-851.

Performance Applications", J. Pet. Tech. (June, 1975) 765-776.

Kern River Field", J. Pet. Tech. (August, 1975) 997-1004.

J. Pet. Tech. (Feb. 1980) 325-332.

flooding for Carbonate Reservoirs*!, paper SPE 8821, presented at the First Joint SPE/DOE Symposium of Enhanced Oil Recovery, Tulsa, Oklahoma, April 20-23, 1980.

Reservoir Simulationt9, SOC. Pet. Eng. J. (June, 1978) 183-194.

To be published by Editions Technip, Paris.

19 - Peaceman, D.W., : I 1 Interpretation of Yell-Block Pressures in Numerical

20 - Burger, J., Sourieau, P. :"Thermal Methods of Oil Recovery: Chapter 4.

NUMERICAL METHODS 39 5

SPECIAL TECHNIQUES FOR FULLY-IMPLICIT SIMULATORS

J. R. APPLEYARD, I. M. CHESHIRE and R. K. POLLARD

Atomic Energy Research Establishment, Hawell, Ox fordshire, England

ABSTRACT

This paper addresses some problems which arise when a fully-implicit black oil simulator is allowed to take large time steps. It is shown that, by using a new form of time averaged relative permeability, it is possible to reduce time truncation errors to a very low level. The application of this technique also reduces the non-linearities in the mass conservation equations which are solved at each time step.

The solution of the linearised equations using iterative techniques becomes more difficult as the time step is increased. A new 'nested factorisation' algorithm for solution of these equations is described. The new method is shown to be more efficient than existing techniques on a set of 2D test problems. Experience with large 3D problems arising from North Sea applications has been most encouraging.

INTRODUCTION

The use of fully-implicit numerical methods in reservoir simulators is becoming increasingly wide~pread('*~'~). methods I s motivated principally by the much greater stability and robustness of fully-implicit methods when applied to problems involving strong gravity segregation, high permeability contrasts, coning, bubble point crossing, etc. As a direct result of this improved robustness, reservoir engineers are freed from the need to consider the internal working of their simulator, and can concentrate on more important issues. The wide applicability of fully-implicit methods also reduces the need for special purpose simulators designed for particular applications (e.g. coning).

It is often thought that fully-implicit simulators are less efficient in their use of computer time than IMPES and semi-implicit alternatives. In our experiencecl), this need not be the case, as the strong stability of the method allows the simulator to take much longer time steps than would otherwise be possible. Indeed, for many problems, a fully-implicit simulator is the most efficient, as well as the most robust alternative.

However, this gain in efficiency is realised only if the special problems associated with long time steps can be overcome. Of these problems, the most obvious is the increased numerical dispersion arising from time truncation errors (as distinct from space truncation errors) resulting in additional smearing of flood fronts. The convergence of the non-linear equations which are solved at each time step can also present difficulties for long time steps, particularly if the relative permeability curves are highly non-linear. Finally,

This shift away from IMPES and semi-implicit

396

s o l u t i o n of t h e l i n e a r equa t ions us ing i t e r a t i v e techniques becomes more d i f f i c u l t as t h e t i m e s t e p is inc reased .

Th i s paper addresses each of t h e s e problems i n t u r n . is p o s s i b l e t o reduce t i m e t r u n c a t i o n errors s i g n i f i c a n t l y us ing a new technique f o r computing t i m e averaged flows. reduces t h e s e v e r i t y of non- l inea r convergence problems. F i n a l l y , w e i n t roduce a new and h igh ly e f f i c i e n t technique f o r i t e r a t i v e s o l u t i o n of t h e l i n e a r equa t ions , and p r e s e n t comparisons wi th o t h e r widely used methods.

F i r s t l y , w e show t h a t i t

The a p p l i c a t i o n of t h i s technique a l s o

TIW TRUNCATION ERRORS

The space d i s c r e t i s e d f i n i t e d i f f e r e n c e equa t ions governing t h e flow of o i l , water and gas can be summarised i n t h e form

- = dM F ............................. (1) d t

where M and F are vec to r s . Elements of Y r e p r e s e n t t h e mass of a phase i n a ce l l , and elements of F t h e sum of flows from neighbouring cel ls and w e l l s . I n t e g r a t i n g (1) over a t i m e s t e p A t g ives

t+At

t

I n the s t anda rd f u l l y - i m p l i c i t method t h e r ight-hand s i d e of equa t ion ( 2 ) is approximated by

AM = I F<t')dt' ......................... ( 2 )

FCt')dt' = F(t+At) . A t ..................... (3) rAt and t h e t i m e d i s c r e t i s e d e q u i v a l e n t of t h e d i f f e r e n t i a l equa t ion (1) is

.......................... - = t: F(t+At) (4)

Equation (4) is s t r o n g l y s t a b l e which m a k e s i t p o s s i b l e t o achieve h igh computing e f f i c i e n c y by t a k i n g l a r g e t i m e s t e p s . However, i n p r a c t i c e , i t is o f t e n necessary t o l i m i t t h e t i m e s t e p i n o r d e r t o prevent t h e growth of t i m e t runca- t i o n errors. An estimate of t h e s e errors can be ob ta ined by comparing flow and w e l l terms a t t h e beginning and end of each t i m e s t e p .

E = F(t+At) - F ( t ) ....................... ( 5 )

Using equa t ion ( 5 ) i t is p o s s i b l e t o p l o t g r i d maps of t h e t i m e t r u n c a t i o n e r r o r and, as one might expec t , t h e main t i m e t r u n c a t i o n errors occur i n those cel ls where s a t u r a t i o n s are changing r a p i d l y . Th i s sugges t s t h a t i t may be p o s s i b l e to reduce t i m e t r u n c a t i o n e r r o r s s i g n i f i c a n t l y by performing a c a r e f u l t i m e i n t e g r a t i o n i n which s p e c i a l a t t e n t i o n is given t o t h e non-l inear r e l a t i v e pe rmeab i l i t y terms.

Time Truncat ion Cor rec t ion

The s t anda rd f u l l y - i m p l i c i t f low i n t e g r a l can be w r i t t e n a s

F(t ' )dt '= X(t+At)kr(t+At)At .................. (6)

397

where kr(t+At) is the value of t h e r e l a t i v e permeability a t t h e end of t h e t i m e s tep . To obta in a more accurate approximation w e wish t o replace the r e l a t i v e permeability by i ts t i m e averaged value

t + A t - =-L kr(t ')dt ' ........................ ( 7 ) kr A t

Relat ive permeabi l i t ies a r e funct ions of s a t u r a t i o n , and it is therefore necessary t o transform the t i m e in tegra t ion i n ( 7 ) t o an equivalent sa tura t ion i n t e g r a l . An approximate transformation can be obtained by assuming t h a t (a) the flow is l o c a l l y incompressible (b) c a p i l l a r y forces a r e negl ig ib le (c) t h e flow out of a cel l depends only on the average sa tura t ion i n the c e l l

so t h a t

_ - ds - 0(6- f (s ) ) ......................... ( 8 )

where 0 is a constant , and f(s) is the f r a c t i o n a l flow curve f o r the phase under consideration. The constant , 6 , is set t o 1 f o r an invading phase and zero for a displaced phase t o ensure t h a t

d t

- - ds - 0 ............................. (9) d t

as the s a t u r a t i o n approaches its l imi t ing value. Equation ( 8 ) can now be used t o transform t h e t i m e in tegra t ion i n ( 7 ) t o an equivalent sa tura t ion i n t e g r a l giving

krds ......................... (10)

Equation (10) forms t h e b a s i s of a p r a c t i c a l technique for computing average r e l a t i v e permeabi l i t ies during la rge t i m e s teps . If t h e r e l a t i v e permeability curves a r e approximated by piecewise l i n e a r funct ions, the in tegrg ls i n

equation (10) can b e performed a n a l y t i c a l l y , so t h a t both ir and 2 can be computed exact ly a t modest o v e r a l l cos t . Because the ca lcu la t ion takes de ta i led account of t h e shape of the r e l a t i v e permeability curve, r a t h e r than focusing a t t e n t i o n a t one or two point values, i t is poss ib le t o take la rge t i m e s teps without l o s i n g accuracy.

I t may be shown t h a t t h e t i m e averaged r e l a t i v e permeability is close t o the time-centred value, &(kr(t+At) + k r ( t ) ) , if the s a t u r a t i o n change is small, but approaches the i m p l i c i t value, kr( t+At) , as t h e sa tura t ion change increased.

The d i s c r e t i s e d equivalent of (1) may now be wr i t ten as

_ - AM - P ............................. (11) A t

where values, k,. A l l o ther terms a r e evaluated a t t h e end of t h e t i m e s tep .

The coupled non-linear equations (11) are solved for pressure and sa tura t ion i n each gr id block by Newtonian i t e r a t i o n :

is obtained by replacing r e l a t i v e permeabi l i t ies by t h e i r t i m e averaged

- [---Z]AZ=E- A t az ax E .................... (12)

398

Number o f t i m e s t e p s 16 32 64 128 256

Standard r e s u l t -659 .677 .687 .692 -695

TTC r e s u l t .700 .698 .698 .698 .698

where t h e s o l u t i o n v a r i a b l e s (p re s su re and s a t u r a t i o n changes) are rep resen ted

ax , and r e s i d u a l v e c t o r , - - F , a r e by x. The Jacobian ma t r ix , (1 * - 2] eva lua ted a t t h e c u r r e n t b e s t estimate of t h e s o l u t i o n , x.

AM - A t At ax

512

.697

.698

In some c a s e s , t h i s i t e r a t i o n converges very slowly. For example, when s tudy ing t h e e f f e c t s o f water i n j e c t i o n , eng inee r s f r e q u e n t l y use r e l a t i v e pe rmeab i l i t y curves f o r t h e i n j e c t e d phase which are set t o ze ro below t h e Buckley-Leverett s a t u r a t i o n . Th i s technique h e l p s t o reduce numerical d i s p e r s i o n , b u t it a l s o in t roduces a d i s c o n t i n u i t y i n t o t h e f u l l y - i m p l i c i t equa t ion ( 4 ) , which makes t h e s o l u t i o n much more d i f f i c u l t to f i n d . These problems are much reduced if t i m e averaged r e l a t i v e p e r m e a b i l i t i e s are used. Th i s is because Er i s eva lua ted as an i n t e g r a l ove r t h e t i m e s t e p , and as such v a r i e s cont inuously i n t i m e , even if kr( t+At) does no t . A s a r e s u l t t h e r e is no d i s c o n t i n u i t y i n t h e t i m e averaged equat ion (11)

Numerical Examples of T i m e T runca t ion Cor rec t ion

The e f f e c t of t h e T i m e T runca t ion Cor rec t ion (TTC) is i l l u s t r a t e d us ing l D , 2D and 3D examples.

The f i r s t is a s t anda rd Buckley-Leverett problem wi th equa l o i l and water v i s c o s i t i e s . The f r a c t i o n a l flow of water used is

2 ......me ........ (13) kl-w = f =

km + kro s2 + (I-s)

Figure 1 shows water s a t u r a t i o n d i s t r i b u t i o n s a f t e r twelve cell po re volumes have been i n j e c t e d . A l l t h e r e s u l t s show cons ide rab le numerical d i s p e r s i o n due t o space t r u n c a t i o n errors, b u t o u r concern h e r e is s o l e l y wi th t i m e t r u n c a t i o n e r r o r s . Resu l t s are d i sp layed f o r one p o i n t upstream weight ing us ing 32 t i m e s t e p s both wi th and without t h e t i m e t r u n c a t i o n error c o r r e c t i o n . A series of runs showed t h a t t h e t i m e t r u n c a t i o n error i s halved as t h e number of t i m e s t e p s is doubled and t h a t t h e s t anda rd f u l l y - i m p l i c i t method e v e n t u a l l y converges t o the TTC r e s u l t as t h e t i m e s t e p is r e f i n e d . The convergence rate is shown .in Table 1 f o r cel l number 12.

TABLE 1

THE WATER SATURATION I N GRID BLOCK 12. RESULTS OBTAINED USING SINGLE POINT UPSTREAM WEIGHTING

Figure 1 a l s o shows r e s u l t s u s i n g t w o p o i n t upstream ~ e i g h t i n g ' ~ ) . of t h e t i m e t r u n c a t i o n e r r o r c o r r e c t i o n is similar t o t h a t observed wi th s i n g l e p o i n t upstream weight ing. The a n a l y t i c Buckley-Leverett r e s u l t i s also shown for comparison. F i n a l l y , w e no te t h a t i f t h e r e l a t i v e pe rmeab i l i t y o f water is

set to ze ro below t h e Buckley-Leverett s a t u r a t i o n (--) t hen t h e f u l l y - i m p l i c i t

two p o i n t upstream weight ing r e s u l t is v i r t u a l l y i d e n t i c a l t o t h e a n a l y t i c r e s u l t

The e f f e c t

1 Jz

399

c 0

0

.- c

L

c 3

0 ln

h ,Analytic Solution

-.-. 2PT Upstream ITTCI 2PT Upstream

......... . 1 PT Upstream ITTCI J 1 1 PT UDstream

Cell Number

FIG.l. SATURATION PROFILES FOR ONE DIMENSIONAL TEST OF TIME TRUNCATION CORRECTIONS

Problems 2 and 3 were run on PORES, a fully-implicit black oil simulator described in reference 1. Time stepping in PORES is not controlled by maximum permitted saturation and pressure changes as in most other simulators. Instead, the estimate of time truncation error (equation 5) is converted to a local material balance error by scaling with cell pore volumes and formation volume factors. The time stepping algorithm attempts to keep the root mean square of this local material balance error within specified bounds. Thus time stepping is tied directly to the best available estimate of time truncation error.

Case 2 is a 38 x 8 cross section with a water injector in column 1 and an oil producer in column 38. Both wells are completed in layers 1, 3-5 and 7-8. The second layer is inactive and the reservoir is therefore in two sections which communicate only through the wells. Further details of this problem are given in reference 1.

Figure 2 shows the water cut as a function of time for Case 2 using (a) PORES default TTE controls (z ASmax = 0.3) (b) PORES default TTE controls/lOO ( z ASmax = 0-05 ) (c) PORES default TTE controls with time averaged relative permeahilities.

The results indicate that the time averaging technique virtually eliminates time truncation errors.

Case 3 is a 3 dimensional gas/oil problem described by Odeh(5). shown in figure 3 again illustrate that time truncation errors are dramatically reduced using time averaged relative permeabilities.

The results

0.7

0.6-

0 .5 -

- 0 . 4 -

L a - P

0.3-

0.2-

.-...,....... Standard TTE Controls - Standard TTE Controls 1100 Standard TTE Controls + T T C --- -

-

I I I

:: I I I

.... . . . . . Standard TTE Contrds

- Standard.TTE Controls tTTC .” , ---- Standard TTE Contrds 1100

h Y S Years

F I G . 2 . W A T E R CUT AGAINST T I M E FOR TWO DIMENSIONAL I X SECTION 1 TEST OF T I M E TRUNCATION CORRECTION

F I G 3 .GOR AGAINST T I M E FOR T H R E E D I M E N S I O N A L T E S T OF T I M E T R U N C A T I O N CORRECTION

401

Total Number of Tota l Number of Newton I t e r a t i o n s Linear I t e r a t i o n s

Time Steps for Tot a1 Simulation

Period

12 67 366

18 55 237

23 64 226

48 116 273

LARGE TIME STEPS AND THE SOLUTION OF THE LINEAR EQUATIONS

Linear I t e r a t i o n s Per

Newton Iteration

5.46

4.31

3.53

2.35

A t each Newton i t e r a t i o n , i t i s necessary t o solve t h e l i n e a r i s e d equations (121, t o obtain an updated est imate of t h e so lu t ion t o the non-linear equations (11). For small problems, these equations may be solved by Gaussian el iminat ion. How- ever t h i s is not prac t icable f o r l a r g e 3 dimensional s t u d i e s , a s s torage and computing t i m e increase very rap id ly with t h e problem s i z e . In such cases , some form of i t e r a t i v e so lu t ion method must be used. of the r e s u l t i n g procedure depend c r i t i c a l l y on the e f fec t iveness of the s o l u t i o n method adopted.

This observation is p a r t i c u l a r l y t r u e of fu l ly- impl ic i t s imulat ions with long t i m e s t e p s , a s the mass accumulation t e r m i n t h e Jacobian matrix (equation (12)) which makes it diagonal ly dominant (and therefore non-singular) is inversely proport ional t o the t i m e s t e p length, A t . As a r e s u l t , the l i n e a r equations a r e more d i f f i c u l t t o so lve i f long time s t e p s a r e taken. This e f f e c t i s i l l u s t r a t e d i n Table 2 , which shows how t h e number of l i n e a r i t e r a t i o n s required f o r each Newton i t e r a t i o n increases with the t i m e s t e p s i z e , for a f a i r l y eventful period i n a typ ica l simulation.

The e f f ic iency and robustness

Because t h e l i n e a r equations a r e more d i f f i c u l t t o solve with la rge t i m e s teps i t is important t o devise powerful i t e r a t i v e methods t o make fu l ly- impl ic i t codes e f f i c i e n t .

Nested Fac tor i sa t ion

A l l i t e r a t i v e methods f o r the s o l u t i o n of t h e l i n e a r equations

In t h e following sec t ion w e descr ibe t h e method used i n PORES.

Ar = b ............................. (14)

depend on the exis tence of an approximation, B , t o the c o e f f i c i e n t matrix A such t h a t B-'8 is e a s i l y ca lcu la ted f o r any vector 8. The r a t e of convergence of the i t e r a t i o n depends pr imari ly on how w e l l B approximates t o A.

The bes t choice of B w i l l , i n general , depend on the s t r u c t u r e of A. Five point f i n i t e d i f fe rence methods give rise t o t h e nested block t r id iagonal s t r u c t u r e shown i n Fig. 4.

............... A = d + + U1 + E2 + U2 + E3 + U3 (15) 1

In t h i s paper, w e present a way of approximating such a matrix by nested f a c t o r i s a t i o n . Because t h e algorithm e x p l o i t s the s t r u c t u r e of the matrix t o the f u l l , it i s not e a s i l y adapted t o dea l with general sparse matrices.

4 0 2

I, .u1 Bands connect Cells in X Direction 1 2 , u2 Bands connect Cells in Y Direction

1 3 , u 3 Bonds connect Cells in Z Direction

FIG.L.THE STRUCTURE OF THE COEFFICIENT MATRIX FOR A F I V E POINT F I N I T E DIFFERENCE SIMULATION

The nested factorisat ion approximation for a 3D system may be summarised as

B = (a + E3)a-l(a + u 1

8 = (y + E1)y -1 (y + U1)

............................... (16)

............................... (17)

............................... (18)

........... (19)

3

a = (8 + E2)6-1(8 + uz)

Y d - Ely -1 u1 - colsum(E 8 -1 u + E.a-lu3) 2 2 3

Here,colsum(X) is the diagonal matrix formed by summing the elements of X i n COlUmaS.

403

By combining equations 16-19, we obtain the following expression for B

B = A + (E28-1u2 + E3a -1 u3) - colsum(.E2B -1 u2 + E a -1 u,) D o . . a (20 ) 3

For two dimensional systems, E3 = u3 = 0, and the outermost layer of the factorisation (equation (16)) may be omitted, leaving

-1 B = ( B + E,)B ( B + u,)

= A + E2B -1 U2 - colsum(!L2B -1 U2) ........... (21) The method reduces to an exact Cholesky decomposition for one dimensional problems

-1 B = (Y + (.Y ul)

= A ...................................... (22)

In PORES, this approximation is used as a preconditioning matrix for a truncated conjugate gradient algorithm of the type described by Vinsome(6). applications which give rise to a symmetric coefficient matrix, it would be more appropriate to use it as preconditioning for a symmetric conjugate gradient algorithm as described by Meijerink and Van der Vorst(').

The procedure for evaluating B-l8 is hierarchical. solve block triangular matrix equations of the form

For

At the outermost level, we

(a + E3)p = B .......................... (23)

Because the matrix a is block diagonal, these equations can be solved a plane at a time, using

-1 u = a ( 8 - P.9) ........................ (24)

This is not recursive, as E3p involves the solution from the previous plane.

Within each plane, the equations are solved a line at a time using

= B-'(B - E2p) ........................ ( 2 5 )

where once again, only known solution variables appear on the right-hand side.

Similar considerations apply to the evaluation of y, which must be done before the iteration begins. The calculation proceeds a plane at a time and, within each plane, a line at a time. At each stage,,the calculation involves elements of y from the previous cell in the current line, the previous line in the current plane, and from the previous plane. The evaluation of ~olsum(E~B-~u2 + P.3a-lu3) which is required in the calculation of y, is achieved by multiplying a column vector whose elements are all unity by the transpose of (E26-1~2 + k3a-1243). cols~m(I126-~u~ + E3a-12.43).

It will be noted from equation ( 2 0 ) that y has been set in such a way that the column sum of the error matrix, B-A,is zero. The object of this choice of y is to force the sum of the residuals, which in a reservoir simulator corresponds to a total material balance error, to zero. I f the iteration is started from the

The result vector contains the diagonal elements of

40 4

initial solution 5 = B-'b . . . . . ~. ~. . ..*. o . 9 . . . . . . a - (26)

then the initial residual ro is given by

r = b - A x

and the sum of the components of ro is zero if colsum(B - A) = 0. shown that this condition, once established, remains valid throughout the iteration('). Moreover, it may be seen that because the error matrix is block diagonal, the residuals sum to zero independently within each plane (or, for 2D systems. within each line) and that this condition also holds throughout the i terat ion ~

It is easily

It is well known that in most iterative methods for solving linear equations, it is low frequency eigenvectors which are most persistent, and which ultimately determine the rate of convergence. Indeed, it was this observation which prompted the additive correction methods of Watts(') and of Settari and Azi~'~), and which led to the recent upsurge of interest in other multi-grid methods(''). The method described above avoids the worst of these problems by eliminating the lowest frequency eigenvectors (those with a non-zero residual sum) from the out- set. Algorithms displaying similar properties have been described by Gustafsson(ll) and Cheshire et al(') although only the latter noted the importance of starting the iteration from an initial solution with zero residual sum (equation 26). The fact that residuals sum to zero within each plane may also be used as a test on the correctness of the program.

An important consideration in the implementation of this algorithm is the orientation of lines (cells connected by the &1 and u1 bands) and planes (lines connected by the 11, and u2 bands). The best strategy, deduced from a series of numerical experiments, appears to be to align the axes so that the largest off- diagonal elements are on the 111 and u1 bands, the next largest on the E2 and 7.42 bands. and the smallest on the 113 and 7.43 bands. In the PORES implementation, this choice is made automatically.

Whilst it is convenient when describing the algorithm to view it as a series of nested LDU factorisations (equations 16-18) a significantly more efficient implementation is achieved by combining the D and U factors.

B = (a + E3) (I + a-' u3) ...- D . e s D . . . . O . . . D . O (28)

-1 where a = ( B + i2) (I + f3 u,) Oe.D.O.OO.....eD.... (29)

Given this form of the algorithm, the evaluation of B-'8 for an arbitrary n- vector 8 requires about 22n floating multiplications for 3D problems (10n for 2D problems). The total for each preconditioned conjugate gradient iteration is 33n(19n) if A is symmetric, or somewhat more for a Vinsome type truncated conjugate gradient algorithm. The figure for 2D problems can be reduced to 16n by combining the calculation of B-% with that of AB-10.

An important feature of the nested factorisation algorithm is its very modest storage requirements. Evaluation of B-'8 requires storage for only one diagonal

405

matrix ( i n general y- l ) i n addi t ion t o t h e elements of A. required by the conjugate gradient algorithm.

Numerical T e s t s of the Nested Fac tor i sa t ion Algorithm

The nested f a c t o r i s a t i o n algorithm was t e s t e d on a series of s i n g l e phase 2D test problems described by S e t t a r i and Aziz('). Because these problems give rise t o symmetric coef f ic ien t matr ices , w e have used a symmetric conjugate gradient algorithm t o acce lera te convergence. The r e s u l t s a r e shown i n Table 3 , together with r e s u l t s obtained on the same problem using SlP(12), I C C d 7 ) , a var ian t of ICCGO i n which the column sum of t h e e r r o r matrix is forced t o zerocl), and ICCG3(7). In each case, w e have shown t h e computational work required t o reduce the l a r g e s t normalised res idua l t o The u n i t of work is taken a s a SIP i t e r a t i o n (about 22n f l o a t i n g point mul t ip l ica t ions) . The corresponding f igures for t h e o t h e r methods a r e 16n f o r ICCGO and ICCGO with colsum, 22n for ICCC3 and 19n f o r nested f a c t o r i s a t i o n , (it would be possible t o reduce t h i s f igure t o 16n on these problems).

Some storage is a lso

Problem Number

1

2

3

4

5

6

TABLE 3

COMPARISON OF NESTED FACTORISATION WITH OTHER ITERATIVE METHODS

COMPUTATIONAL WORK (SIP ITERATIONS)

SIP* ICCGO I CCGO ICCG3 NESTED (WITH COLSUM) FACTORISATION

28 32 19 20 13

20 26 20 29 6

38 36 22 22 13

28 31 20 20 16

> 50 34 21 21 12

50 27 17 15 11

The r e s u l t s show the nested f a c t o r i s a t i o n method t o be f a s t e s t of the methods t e s t e d on a l l t h e problems. Perhaps t h e m o s t s i g n i f i c a n t r e s u l t is t h a t on problem number 2,which is t h e only one which e x h i b i t s t h e s t rong d i r e c t i o n a l i t y c h a r a c t e r i s t i c of c ross s e c t i o n and 3D reservoi r simulations. the nested f a c t o r i s a t i o n algorithm is f a s t e s t by a f a c t o r of th ree .

The importance of forc ing the sum of t h e res idua ls t o zero by choosing B i n such a way t h a t colsum(B-A) is zero is shown by t h e r e s u l t s from ICCGO and ICCGO (with colsum). The l a t t e r converges s i g n i f i c a n t l y f a s t e r i n every case, and competes e f f e c t i v e l y with ICCG3 which i s more complex and requi res more s torage.

The 2D r e s u l t s discussed above correspond only t o a s i n g l e nes t ing (B = a ) and do not demonstrate the f u l l p o t e n t i a l of t h e technique a r i s i n g from the second nes t ing for 3D problems. The algorithm is implemented i n PORES for 1, 2 and 3 phase simultaneous problems and our experience t o date on l a r g e complex 3 D s imulat ions a r i s i n g from p r a c t i c a l North Sea s t u d i e s has been very encouraging.

On t h i s problem

CONCLUSIONS

A new technique has been developed t o cont ro l t i m e t runcat ion e r r o r s i n reservoi r simulation.

406

1.

2.

3.

4.

5 .

6 .

7 .

A

B

The method can be incorporated i n t o e x i s t i n g s imulators with r e l a t i v e ease and has been demonstrated on one, two and t h r e e dimensional t e s t problems.

I t is shown t h a t , as l a r g e r time s t e p s a r e taken, the l i n e a r i s e d equations become more d i f f i c u l t t o solve by i t e r a t i v e methods.

A new nested f a c t o r i s a t i o n method is described f o r t h e so lu t ion of the l i n e a r i s e d f i n i t e d i f fe rence equations.

Because the nested f a c t o r i s a t i o n method is highly recursive i t makes minimal addi t iona l demands on computer s torage .

By comparison with e x i s t i n g published r e s u l t s i t is shown t h a t t h e nested f a c t o r i s a t i o n method i s highly e f f i c i e n t f o r simple two dimensional problems.

The nested f a c t o r i s a t i o n method has been incorporated i n PORES and our experience t o date ind ica tes t h a t the f u l l power of the method i s most apparent on l a r g e d i f f i c u l t th ree dimensional s t u d i e s a r i s i n g i n North Sea appl icat ions

NOMENCLATURE

= Jacobian matrix a r i s i n g i n f i n i t e d i f fe rence ca lcu la t ions

= an approximation t o t h e Jacobian matr ix A

Colsum = diagonal matrix formed by summing the elements of a matrix i n columns

b

d

E

F

- F

f

f W

kr

kr

k r w

kro II

M

Ah!

n

r

= right-hand s i d e of t h e l i n e a r equatian

= diagonal elements of A , each element of d is a 3x3 matrix i n simultaneous 3 phase s imulat ions

= est imate of t i m e t runca t ion e r r o r vector

= flow vector , each element represents the sum of flows i n t o a c e l l from neighbouring c e l l s and wells

= flow vector obtained by replacing a l l r e l a t i v e permeabi l i t ies a t t h e end of a t i m e s t e p by t i m e averaged r e l a t i v e permeabi l i t ies

= f r a c t i o n a l flow of o i l , water or gas

= f r a c t i o n a l flow of water

= r e l a t i v e permeability ( o i l , water o r gas)

= average r e l a t i v e permeability over a t i m e s t e p

= r e l a t i v e permeability of water

= r e l a t i v e permeability of o i l

= lower band of t h e Jacobian matrix

= mass accumulation vector , each element of M represents t h e mass of a phase i n a c e l l

= change i n M over a timestep A t

= number of elements i n d

= res idua l vector

407

S

As

t

At

TTC

U

X

Ax

a

B

Y

6

0

x Q

U

= saturation

= change in saturation during a time step

= time

= duration of a simulation time step

= time truncation correction

= upper band of the Jacobian matrix

= solution of a linear equation, state vector

= change of state vector during a Newton iteration

= matrix for two dimensional systems

= matrix for one dimensional systems

= diagonal matrix

= 0 or 1 corresponding to an invading or displacing phase

= constant

= pressure dependent component of the flow vector

= right-hand side of a linear equation

= solution of a linear equation

ACKNOWLEDGEhlENTS

The authors wish to thank the United Kingdom Department of Energy, the British National Oil Corporation and the British Gas Corporation for permission to publish this work.

REFERENCES

1.

2.

3.

4.

5.

6.

CHESHIRE, I.M., APPLEYARD, J.R., BANKS, D., CROZIER, R.J., and HOLMES, J.A.; "An Efficient Fully Implicit Simulator", paper EUR 179 presented at the European Offshore Petroleum Conference and Exhibition, London, England, (Oct. 1980), 325-336.

BANSAL, P.P., HARPER, J.L., McDONALD, A.E., MORELAND, E.E. and ODEH, A.S.; "A Strongly Coupled, Fully Implicit, Three Dimensional, Three Phase Reservoir Simulator", paper SPE 8329 presented at the SPE-AIME 54th Annual Fall Meeting of the SPE, Las Vegas, Nev. (Sept. 1979).

AU, A.D.K., BEHIE,,A., RUBIN, B., and VINSOME, P.K.W.; "Techniques for Fully Implicit Reservoir Simulation", paper SPE 9302 presented at the SPE-AIME 55th Annual Fall Meeting of the SPE, Dallas, Texas (Sept. 1980).

TODD, M . R . , O'DELL, P.M. and HIRASAKI, G.J.; "Methods for Increasing Accuracy in Numerical Reservoir Simulators", Soc.Pet.Eng.J. (Dec. 1972), 515-530 ~

ODEH, A.S.; "Comparison of Solutions to a Three-Dimensional Black-Oil Reservoir Simulation Problem", J.Pet.Tech. (Jan. 1981) 33, 13-25.

VINSOME, P.K.W-; "Orthomin, an Iterative Method for Solving Sparse Banded Sets of Simultaneous Linear Equations", paper SPE 5729 presented at the SPE-AIME Fourth Symposium on Numerical Simulation of Reservoir Performance, Los Angeles, Ca. (Feb. 1976).

7. MEIJERINK, J.A. and VAN DER VORST, H.A.; "An Iterative Solution Method for Linear Systems of which the Coefficient Matrix is a Symmetric M- Matrix",Mathematics of Computation (Jan. 1977) 2, 148-162,

8. WATTS, J.W.; "An Iterative Matrix Solution Method Suitable for Anisotropic Problems", S0c.Pet.Eng.J. (March 1971) 11, 47-51.

9. SETTARI, A. and AZIZ, K O ; "A Generalisation of the Additive Correction Methods for the Iterative Solution of Matrix Equations", SIAM J.Numer.Ana1. (June 1973) 2, 506-521.

10. BRANDT, A.; "Multi-Level Adaptive Solutions to Boundary-Value Problems", Mathematics of Computation (April 1977) 3l, 333-390.

11. GUSTAFSSON, I.; "A Class of First Order Factorisation Methods", BIT (April 1978) 18, 142-156.

12. STONE, H.L.; "Iterative Solution of Implicit Approximations of Multidimensional Partial Differential Equations", SIAM J.Numer.Ana1. (Sept. 1968) 5, 530-558.


SOME CONSIDERATIONS CONCERNING THE EFFICIENCY OF CHEMICAL FLOOD SIMULATIONS

R. W. S. FOULSER

AEE Winfn’th, Dorchester, Dorset, DT2 8DH

ABSTMCT

This paper discusses some aspects of improving computational efficiency and accuracy in surfactant flood calculations. The use of curvilinear grids in chemical flooding simulation can reduce grid orientation effects and speed up the calculations. For the low tension, low concentration surfactant processes being considered, the work of Martin and Wagner supports the application of conformal grids. The development at Winfrith of the PASL code, which applies the results of potential theory, has enabled suitable grid patterns to be generated for use in the CFTE code. visualising flow patterns and consequent mesh requirements for studying possible pilot applications of surfactant flood under real reservoir conditions.

A further improvement in the efficiency with which the CFTE code can be applied has been achieved by incorporating a line successive overrelaxation iterative solver (LSOR) into the code, as an alternative to the direct inversion method. Initially written for a scalar machine, its application on the CRAY vector machine has led to the development of alternative LSOR codes using different grid block orderings. direct inversion on the IBM scalar machine and, when vectorised on the CRAY, they run up to 6 5 times faster than the original code on the IBM. Thus the vectorised LSOR approach has proved to be very powerful.

This mesh generation code has also proved useful in

These LSOR options run about twice as quickly as the

INTRODUCTION

The Chemical Flood Ternary Equilibrium Simulator (CFTE Ref I ) is one of several EOR codes being used at AEE Winfrith. During the period for which CFTE has been available, a number of assessments studies have been performed, one of which has been reported elsewhere by Fayers et a1 (Ref 2). assessment calculations have been undertaken, it has become necessary to develop supplementary programs to aid the generation of input for the studies. Computational time is also becoming a significant factor in the use of the CFTE code in large assessment calculations. This paper briefly presents some of the experience associated with the use of a special mesh generation code, PASL, that has been written as one of the support programs, and also the steps that have been taken to improve the efficiency of CFTE when used on the CRAY vector processor.

As more difficult

4 10

The PASL mesh generation code has been used as a tool in preliminary studies to determine broad characteristics of flow patterns within possible pilot areas of an oil field. alternative well patterns in a pilot flood and also as a means of studying pattern confinement strategies. a basis for identifying computing mesh requirements in subsequent CFTE calculations. The PASL code may also be used to generate curvilinear co-ordinate The use of curvilinear co-ordinates in surfactant flood calculations allows a considerable improvement to be obtained in calculation efficiency as well as a reduction in the errors caused by grid orientation effects. using parallel and diagonal Cartesian grids with curvilinear grids.

The CFTE code uses the IMPES formulation, and the resulting implicit pressure matrix problem was originally solved by direct methods. blocks in three-dimensional calculations, the matrix inversion time begins to dominate the total execution time. Because of this, it was decided to incorporate an iterative solver into the code. CRAY-I vector processor in association with the IBM 3033 at Harwell, where the computing for this project is undertaken, emphasised the need to choose a method which could be readily vectorised. The LSOR method was chosen, partly because of its robustness and its relatively simple form for progranrming, but also because this iterative method is more readily vectorised than some of the more complicated strategies, such as SIP. concerned with an investigation of the performance of the LSOR method in chemical flooding calculations and also with the aspects of vectorisation of this particular method.

This has been especially useful in examining

The preliminary flood pattern studies provide

systems for use in CFTE.

These improvements are quantified by comparing the results

With about 400 grid

The recent availability of a

The second part of this paper is

THE DETERMINATION AND USE OF CURVILINEAR GRIDS IN SURFACTANT FLOODING STUDIES

The generation of curvilinear grids and the study of flow fields for arbitrary arrangements of injection and production wells has been implemented in the PASL code. No-flow boundaries associated with linear fault lines have also been included in the formulation which uses the basic results of potential theory. The faults are dealt with by applying conformal transformations.to obtain a continuous line fault and the method of images is then used to provide an equivalent system of wells in an infinite domain. The solution method then uses the classical equations for representing a distribution of wells in infinite space (Ref 3). stream function are given by:

For a system of wells the velocity potential and

where mi is the strength of well i. have been computed, inverse conformal transformations are used to map the results back to the original co-ordinate system. curvilinear mesh dimensions in a format suitable for direct input to CFTE.

One of the first examples studied using a grid generated bv PASL, was Concerned with the problem of mesh orientation effects during the calculation of a simple surfactant flood in a 5spot geometry with a uniform residual oil saturation. The CFTE code was used to model a low concentration surfactant flood in a 1/8 th symmetry sector of the 5-spot pattern. Sone investigations of this type of surfactant flood for North Sea applications have been discussed in Ref 2. The basic

Once the streamlines and equipotentials

The code provides output of

411

data adopted a r e s imi la r to those described i n tha t reference. A v a r i a t i o n of r e l a t i v e permeability with capi l la ry number similar t o t h a t used by Todd and Chase (Ref 1) has been assumed where, i n t h i s case, the r e l a t i v e permeability of the o i l and water phases move progressively from t h e i r i n i t i a l o i l -water forms a t low c a p i l l a r y numbers (26 x t o t h e i r l imi t ing s t r a i g h t l i n e forms as the c a p i l l a r y number increases t o 2 x

The r e s u l t s of the ca lcu la t ions a r e shown i n Figure 1 where the +spot region has been covered by 90 gr id blocks f o r the p a r a l l e l and curv i l inear gr id systems and 91 blocks f o r the diagonal g r i d system. These diagrams show the o i l d i s t r i b u t i o n a f t e r 0.5 PV of sur fac tan t so lu t ion i n j e c t i o n which is not long a f t e r breakthrough of the o i l bank. concentrations around the i n j e c t i o n w e l l wi th a f a i r l y s teep rise i n o i l s a t u r a t i o n i n t o the o i l bank where the o i l s a t u r a t i o n reaches about 40%. A l l three ca lcu la t ions a l s o show the o i l bank pinching o f f a small region where the s a t u r a t i o n has not y e t r i s e n above t h a t l e f t a f t e r waterflooding. be expected, the p a r a l l e l g r i d shows a p r e f e r e n t i a l flow along the d i r e c t path between the wel ls , while the diagonal g r i d allows the less accessible corner region t o be swept more eas i ly . s imulat ion l ies between these two rectangular g r i d r e s u l t s . production curves, not Shawn, a l s o ind ica tes t h a t the curv i l ineaf gr id gives r e s u l t s intermediate t o the Cartesian mesh arrangements.

From a computational point of view, the c u r v i l i n e a r ca lcu la t ion was by f a r the most e f f i c i e n t , running some 5 times f a s t e r than the others . This occurred because the connections with the wells i n the curv i l inear ca lcu la t ions was v i a 5 f a i r l y l a r g e g r i d blocks,rather than v i a the s i n g l e smaller g r i d block i n the Cartesian systems. It i s these connecting gr id blocks which tend t o cont ro l the timestep s i z e t h a t can be taken i n the e x p l i c i t so lu t ion of the concentrat ion and s a t u r a t i o n equations.

I n the p a r t i c u l a r example s tudied the water + f ron of the o i l bank has a mobil i ty of 1.25 mD/cp, the t o t a l mobil i ty (4 + b) i n the o i l bank i s 1 .OS and behind the bank the mobil i ty of the sur fac tan t so lu t ion is somewhat grea te r than 5. Thus the equal ly mobile two phase mixture i n the o i l bank and the watered out zone ahead are being displaced by a much more mobile f l u i d . therefore , an example of the unfavourable mobility r a t i o e f f e c t s i n sur fac tan t flooding. Martin and Wagner (Ref 4) suggest t h a t t h i s type of problem i s amenable t o f ixed stream tube methods, thus supporting use of curv i l inear two-dimensional g r i d s i n CFTE ca lcu la t ions with t h i s type of system.

The s u i t a b i l i t y of curv i l inear g r i d methods f o r more general appl ica t ion i s a l s o being s tudied. code, when appl ied t o an inverted 5-spot operated i n i s o l a t i o n , but i n the v i c i n i t y of two i n t e r s e c t i n g impermeable f a u l t s . Note t h a t the f a u l t s a r e s t reamlines of the flow p a t t e r n and t h a t the equipoten t ia l s cross t h e steamlines perpendicularly. The i n t e r s e c t i o n of s t reamlines and equipoten t ia l s have been used i n CFTE ca lcu la t ions as the gr id block corners of a conformal curv i l inear co-ordinate system. are usual ly chosen t o produce equal volume g r i d blocks along the s h o r t e s t stream tube. t h i s way t o generate co-ordinate s y s t e m f o r the problem on which CFTE performance estimates are reported i n the second half of t h i s paper. This is an example of a f i e l d problem f o r which s e l e c t i o n of a s a t i s f a c t o r y Cartesian mesh would have been very d i f f i c u l t . A t t h i s s tage, it has only been possible t o study problems f o r spec ia l ly chosen sec tors , because of l imi ta t ions i n the connect ivi ty of mesh which can be handled by the CFTE code. General isat ion of the mesh connect ivi ty arrangements w i l l be s tud ied i n the f u t u r e i n connection with the LSOR method discussed i n the next sect ion.

A l l th ree calculat ions show low

A s would

The predict ion of the curv i l inear gr id The cumulative o i l

This is ,

Figure 2 shows flow pa t te rns generated from the PASL

For maximum ef f ic iency i n the CFTE code the equipotent ia ls

The shaded region i n the Western sec tor of t h i s f i g u r e has been used i n

4 12

PARALLEL GRID

, - -1 -- DIAMNAL GRID

FIG.I COMPARISON OF LW TENSION SURFACTANT FLOOO COMPUTED aL MSTRlBUTlONS AFTER 0.5 PV OF FLUB INJECTION.

quipatmt id

4 13

r r t n o m l i r

lnpcrmeoblc foul1

FIG.2 EXAMPLE OF APPLICATION OF POTENTIAL FLOW THEORY TO ROW FAlYDN VISUALISATION IN AN INVERTED 5-SPOT CONFINED BY INTERSECTING FWLTS.

THE PERFORMANCE OF SCALAR AND VECTOR VERSIONS OF THE LSOR METHOD IN CHEMICAL FLOOD CALCULATIONS

In view of the need to speed up the inversion process for large problems with curvilinear meshes, and the practical difficulties imposed by generalised connectivities between meshes introduced by such schemes, it was decided to investigate the application of the LSOR iterative procedures as analternative to the existing direct inversion method in the CFTE code. The robustness of the convergence behaviour of LSOR, its ease of programning, and its simplicity for vectorisation on a CRAY were further reasons for choosing this method.

Outline of LSOR

In block successiveaver relaxation the system of equations to be solved can be written in the form:

C h i y = q k - I, ..., K (3) i

where xi is an n-tuple correspodding sub-matrix of co-efficient8 and the n-tuple In line successive over relaxation, the blocks are chosen to correspond to lines of grid blocks.

of variables (the block sire) and Aki and Q are the

An iterative sequence of vectors sf: may then be defined right-hand side.

where B i s a re laxa t ion f a c t o r . This may be w r i t t e n i n matrix form:

The convergence of the i t e r a t i v e scheme describe- by equation (5) depends on the spec t ra l radius w of the i t e r a t i o n matr ix E-’F (Ref 5) . point approximation t o the three-dimensional Laplacian operator i t can be shmn tha t , provided the blocks hi are ordered cons is ten t ly , then w i s r e l a t e d t o the s p e c t r a l radius !J of the matrix (Aii)A-I by:

For a seven

Since the matrix (&d)A-I i s dependent only on the o r i g i n a l matrix and on the block s e l e c t i o n ( i e the d i r e c t i o n of the l i n e s i n LSOR), !J depends only on the block arrangement of the matrix and on the re laxa t ion f a c t o r 6. point successive re laxa t ion the optimal re laxa t ion f a c t o r B can be shown t o be given by:

As i n

By put t ing BPI i n equation (6 ) , i t may be seen t h a t p2 = w.1 so t h a t equation (7) may be rewr i t ten as:

This shows t h a t the optimum re laxa t ion fac tor can be determined by powering the i t e r a t i o n matr ix E-’F assuming B = 1 . w l i s the asymptotic r a t i o of successive i t e r a t e s of the eigenvector elements (p287 Ref 6 ) . The s p e c t r a l radius of the i t e r a t i o n matrix with the optimal re laxa t ion f a c t o r can be shown t o be w = 6-1 and t h i s gives a value f o r the asymptotic r a t e of convergence of:

IL = -log (;I

The e s s e n t i a l points of LSOR a r e thus:

( i ) To choose the d i rec t ion of the l i n e s ( i e the Akk) 80 a s t o maximke the rate of convergence given by equation (9). In reservoi r s i t u a t i o n s t h i s almost invariably means choosing the v e r t i c a l d i r e c t i o n f o r the l i n e s .

415

( i i )

( i i i )

( iv )

To choose an order f o r rev is ing the a t h a t i s cons is ten t . A necessary and s u f f i c i e n t condition f o r an order ing t o be cons is ten t i s given on page 245 of Ref 7.

To power the matr ix E-lF with f b 1 so a s t o determine w use equation (8) t o determine the optimum re laxa t ion fac tor .

To use equation (5) t o i t e r a t e on the unknown vector zn+l u n t i l convergence i s achieved.

and then

The convergence t e s t f o r the pressure d i s t r i b u t i o n t h a t has been used i n t h i s appl ica t ion is:

(10)

and E has been taken t o be 0.001. This t e s t ensures t h a t successive i t e r a t e s must be more t i g h t l y converged when the convergence is slow, ie w i s close to uni ty . Checks of the mater ia l balance i n chemical flooding calculat ions have shown t h i s t o be an adequate test.

Scalar Code

Ei ther the x, y or z di rec t ion may be chosen f o r the l i n e d i r e c t i o n i n a l l th ree var ian ts of the LSOR code discussed i n t h i s paper. However, f o r convenience it i s re fer red t o as the v e r t i c a l d i rec t ion . I n the s c a l a r version of the code, the l i n e s of gr id blocks are ordered i n a na tura l order i n the horizontal plane, s t a r t i n g i n one comer of the a rea modelled and working up t o the opposi te corner. l i n e s i s shown i n Figure 3. This ordering is cons is ten t . Although the gr id block arrangement i s displayed as a square, t h i s i n f a c t represents the curv i l inear co-ordinate system f o r the curv i l inear s t r u c t u r e shown i n Figure 2, where t h e wells a r e connected t o the gr id blocks along the l e f t andr ightedges .

I n order t o determine the i t e r a t i o n matrix eigenvalue the matrix i s powered. This involves the i d e n t i f i c a t i o n of the eigenvector corresponding t o the maximum eigenvalue of the i t e r a t i o n matrix. This s t e p i n the procedure can be q u i t e cos t ly unless a l l the eigenvector is s tored f o r use as an i n i t i a l guess a t subsequent t i m e s teps . Usually the eigenvector changes r e l a t i v e l y slowly during a displacement ca lcu la t ion and only a few addi t iona l i t e r a t i o n s are needed a t each timestep. The eigenvector a r ray represents about half the scra tch s torage requirement. The o ther half of the s c r a t c h s torage is used t o s t o r e the previous eigenvector i t e r a t e during the s p e c t r a l norm calculat ion, and a f t e r t h i s the previous i t e r a t e the pressure so lu t ion .

The pressure d i s t r i b u t i o n i s found using equations (5) and ( 8 ) and the convergence c r i t e r i o n i n equation (10).

The t o t a l sc ra tch s torage space needed by the s c a l a r LSOR code i s compared i n Figure 4 with the s torage required by the D4 d i r e c t e l iminat ion code o r i g i n a l l y i n CFTE. The advantage of i t e r a t i v e schemes i n t h i s respect is w e l l known.

An ordering of a 7 x 7 arrangement of gr id block

of the pressure d i s t r i b u t i o n is s tbred during

43 1 11 12 13 Tt;t;

7 1 2 3 4 5 6 l " " " I

M 2 3 4 5 6 7 1

DIAGONAL GRoupHt USB) FOR VBCTOR PROGRAM PRINCIPLE OF ORMRlNG SHOW ABOVE HAS VETOR LENCTH OF 7 DEVELOPMENT S E W HAS VECTOR LENGTH OF 21

2 1

1 2

NOLEN'S RED-BLAtK OROERNG USED FOR VECTOR PROGRAM

FIG.3 GRID BLOCK ORDERIN6 SCHEMES USED TO INVESTIGATE LSOR PERFORMANCE.

Words 10

1C

Oirrt lmtnion D, Ordwig / LSOR

I I 1

S lo 6 J-Dimcnrion

FIG.4 COMPARISON OF SCRATCH STORAGE REQUIREHENT FOR LsoA MATRIX INVERSKW STRATEGIES J x J x 5 PROBLEM.

A number of t e s t s have been made using t h i s version of the code. of gr id blocks varying from 7 x 7 ~ 5 (245 g r i d blocks), 10~10x5 (500 gr id blocks) and 14x14~5 (980 g r i d blocks). The same sur fac tan t system as described i n the sec t ion on curv i l inear gr ids has been used,and to introduce some a x i a l var ia t ions , the permeabi l i t ies of the 5 + e r t i c a l l ayers have been varied with values of 10,3,10,3,10 mD respect ively. Pressure constrained w e l l models were assumed i n which 15% of the t o t a l pressure drop a t the i n i t i a l conditions was l o s t i n the w e l l completion fac tor . This influences the s p e c t r a l norm of the i t e r a t i o n matrix.

The canputing time taken t o i n v e r t the pressure matrix using LSOR var ies with time according t o the d i f f i c u l t y of the problem ( i e i n i t i a l guess and the matrix s p e c t r a l radius) . Figure 5 shows the t i m e taken f o r the f i r s t 150 timesteps of the sample problem. time taken by the d i r e c t E4 matrix, inversion rout ine ava i lab le i n the CFTE

The nmber

Also shown f o r comparison purposes is the

4 18

Gaussian etiminatim with 01, ordering

0.2

.-:& .-*.- .- .- .-. -. - 7 x 7 x 5 GRIDBLOCKS . --. ...- c-

-. - .- * .. ,.r. ..# ..- .. .. - . - a:. -

I 6 . ..-

lOxlDx5 G R D W C K S

Y t r l C x S GRIDBWCKS

RG.5 EXAMPLES OF TIME SPENT IN MATRIX INVERSION USING SCALAR VERSION OF LSOR Co[E AND CURVILINEAR GRlO BUXK REPRESENTATION OF WESTERN QUADRANT OF INVERTED 5-SPOT SHOWN IN FIG.2

4 19

Mesh s i z e

I t e r a t i o n matrix spec t ra l radius

Asymptotic convergence rate (9)

Typical average convergence rate

code. seen i n the la rges t problem, i s t h a t of a decrease i n inversion t i m e from the i n i t i a l conditions, followed by an increase a t about 0.2 PV of f l u i d in jec t ion and then a gradual decrease. Over the timescales represented, LSOR i s more e f f i c i e n t than the d i r e c t method, even f o r the smallest problem (245 gr id blocks).

A t long timescales the ca lcu la t iona l time i n LSOR becomes ins igni f icant as the pressure d i s t r i b u t i o n changes very l i t t l e during the timesteps. increase i n inversion t i m e a t 0.2 PV co-incides with the breakthrough of the o i l bank a t the producer w e l l . pressure changes t h a t occurred making the eigenvector and pressure d i s t r i b u t i o n s a t the previous timestep less good as i n i t i a l guesses. micellarfpolymer floods the most pronounced peaking has been noted when a highly viscous micro-emulsion breaks through i n t o the producerwell.

It i s of i n t e r e s t t o compare the achieved convergence rates with the asymptotic rates given by equation (9). be low :

The overa l l pa t te rn of behaviour i n these calculat ions, most c l e a r l y

The

This occurs because of the r e l a t i v e l y rapid

In

This i s summarised i n Table I

TABLE 1

COMPARISON OF THEORETICAL AND CALCULATIONAL CONVERGENCE RATES

7X7X5 IOxlOx5 14X14X5

0.674 0 796 0.854

0.39 0.23 0.16

0.30 0. I8 0.12

A s may be seen, the average convergence rate achieved i s somewhat slower than the asymptotic rate, as would be expected. The increase i n i t e r a t i o n matrix s p e c t r a l radius , and thus the decrease i n convergence rates, with increasing problem s i z e i s w e l l known; however, a l s o of i n t e r e s t i s the f a c t t h a t the w e l l f a c t o r s can considerably inf luence the convergence propert ies of the i t e r a t i o n scheme. Making the w e l l f a c t o r s very large, and thus increasing the coupling between the ca lcu la t iona l mesh and the f ixed well bore pressures, speeded up convergence by 20% i n the examples discussed above.

Vector isat ion of LSOR f o r CRAY - Algorithm Performance

The s c a l a r vers ion of LSOR described i n the previous sec t ion w a s t ransferred to the CRAY without modification and some matr ix inversion timings were made t o compare the CRAY and IBM performance.

The CRAY ca lcu la t ions without vec tor i sa t ion were about twice as f a s t as the equivalent IBM calculat ions. This i s less than the f a c t o r of four expected on the b a s i s of the r e l a t i v e clock times of the machines. It i s believed t h a t t h i s r e s u l t s from the optimising capabi l i ty of the IBM compiler used, which more than halved the running t i m e r e l a t i v e t o code generated by a non-op t imi s ing compiler .

420

It should also be noted that very little of the original LSOR coding could be vectorised automatically. This was due to three causes:

(i) the use of conditional testing to eliminate inactive grid blocks.

(ii) the recursive nature of the Thomas' algorithm which is the kernel sub-program in the LSOR method.

the extensive use of indirect addressing to reference neighbouring grid blocks.

(iii)

Most of the conditional testing and indirect addressing could be removed by suppressing the elimination of inactive grid blocks. For Cartesian grid approximations to flow patterns in repeated patterns, the removal of this facility incurs a significant work penalty since unnecessary matrix solutions are undertaken for grid blocks which are isolated from the active region by imposing zero transmissibilities. However, for the preferred curvilinear co-ordinate method the inactive grid block facility would not normally be required.

Each line of grid blocks gives rise to a tridiagonal system of operations which cannot be vectorised by the CRAY due to the recursions that occur in performing the forward eliminations and back substitutions. Following Buzbee et a1 (Ref 8) the method employed to overcome this has been to solve for a number of lines simultaneously.

The choice of lines which are solved simultaneously is important for two reasons. solution strategy of the algorithm. Killough has described an attempt to vectorise the SIP algorithm (Ref 9); unfortunately the vectorisation method degraded the convergence of the algorithm so as to outweigh the gain in speed due to vectorisation. systemwhichallows the gridblocks in a line, and thegridblocks in neighbouring lines, to be easily referenced. lines for simultaneous solution can be chosen so that the asymptotic convergence behaviour is preserved. ordering must be consistent.

Firstly, the ordering of the grid blocks must not degrade the basic

Secondly, the choice must lead to a grid block referencing

The attraction of the LSOR method is that the

The required condition is that any chosen

Nolen (Ref 8) has identified one possible ordering scheme in which the lines are ordered with a chequer board arrangement, the red lines are solved first and then the black lines. reported by Nolen to allow an odd number of grid block lines to be used, as well as even. vector length for the simultaneous tridiagonal solver is NX.NY/2 for problems with an even number of grid blocks, and (NX.NY+I)/Z and (NX.NY-I)/2 for the red and black groups respectively, when there is an odd number of lines. The generalisation to an odd number of grid block lines in the plane makes the arithmetic expressions for referencing neighbouring grid blocks more complicated than in the less general situation.

The concept has been generalised slightly fromthat

An example of the line ordering is shown in Figure 3. The

An alternative to the red-black ordering scheme has also been investigated. This was prompted by the observation that the red-black scheme resembles a two-step line over relaxed Jacobi scheme for the initial iterations, and therefore the average convergence properties might be less than for other possible ordering schemes. The alternative scheme devised corresponds to

421

Mesh size

Standard ordering

Red-black ordering

Diagonal line ordering

grouping the lines in diagonals so as to obtain a number of line problems that can be solved simultaneously. the grid block eigenvector elements or pressures have been revised. The basic arrangement is illustrated in the top middle diagram of Figure 3. This scheme allows neighbouring grid blocks to be referenced by simple arithmetic expressions.

To understand the possible differences in initial convergence behaviour further, it is necessary only to consider curvilinear calculations with a symmetric arrangement of NxN grid blocks in the horizontal plane. diagonal grouping, the influence of the well connected to the left hand edge of the grid pattern is transmitted in the first iteration to the lower triangular zone of 0.5 (N2+N) mesh points, but only the line of 1.0N grid points along the right boundary are directly coupled to the well on the right in this iteration. on each side in the red sweep (for N even), and I.ONgrid points in the black sweep. across the area faster, but is asymmetric in its behaviour. introduced in the diagonal scheme by reversing the sweep order on successive iterations, but this has not been investigated.

The asymptotic convergence rates of the two schemes must be identical with the standard ordering, since all three are consistently ordered. convergent problems the schemes should behave identically.

On the CRAY the vector performance becomes awre advantageous the longer the vector length, subject to the limitation of filling the 64 element registers. The diagonal grouping leads to vector lengths of NY for the tridiagonal solver, which for small problems may not be sufficient to take full advantage of the vector machine. Thus, for small problems, the diagonals have been combined to increase the vector length. The lower diagram in Figure 3 indicates one of these combinations, and the order in which the grid block line problems are solved in this strategy. combinations. In the particular case shown each pass of the program revised each line three times, so one pass is equivalent to three iterations.

The calculations already reported for the scalar code have been repeated using code modifications employing the red-black and diagonal grouping ordering. These calculations correspond to the initial steps in a chemical flood simulation and as such represent the calculation of an almost symmetric problem. The average rates of convergence achieved by the alternative strategies are sham in Table 2:

Each diagonal is considered in turn until all

With the

In the red-black arrangement, 0.5N grid points are coupled to wells

Thus the diagonal arrangement can on average transmit boundary effects Symmetry could be

Thus for slowly

The ordering remains consistent despite these

7X7X5 1 ox 10x5 14X14X5

0.30 0.18 0.12

0.38 0.22 I). 16

0.37 0.22 0.14

TABLE 2

COMPARISON OF CONVERGENCE RATES WITH VARIOUS ORDERINGS

422

For some small problems, such as the 10x10~5 calculation, the red-black and diagonal group orderings cu-kcidedue to the combining of groups to increase the vector length, and thus the convergence rates are identical. The diagonal grouping in the 7x7~5 problem leads to a slight asymmetry in the initial revision pattern, so the convergence in this case is slightly slower. In the 14x14~5 case, four diagonals are grouped together, and the asymmetric propagation is more marked, thus the reduced convergence compared with the red-black scheme. In all cases the standard ordering leads to an initial asymmetric behaviour even more pronounced than the diagonal grouping, and this explains why this scheme has the poorest average convergence rate.

Vectorisation of LSOR for CRAY - Coding Performance

While the overall strategy in the vectorised scheme is the same as in the original code, the implementation of the two alternative ordering schemes entailed completely rewriting the routines concerned with powering of the iteration matrix, and iterating the pressure distribution. to vectorise the above algorithms involved the extensive use of additional scratch storage associated with use of the CRAY SCILIB routines GATHER and SCATTER (Ref 10). However, program refinements eliminated the need for these routines and the additional scratch storage, with the resulting storage requirements shown in Figure 4.

Conditional testing, an inefficient computing task, has also been completely eliminated from the routines, except when testing for convergence.

Most of the execution time is expended in the iterating routines. Table 3 indicates the vector lengths achieved in the major sections of these routines when applied to the 14x14~5 sample problem.

Initial attempts

TABLE 3

EXAMPLE VECTOR-LENGTHS ACHIEVED WITH DIFFERENT ORDERING SCHEMES

Operation

Updating previous iterate

Setting up right-hand sides for Thomas' algorithm

Setting up left-hand sides

Thomas' Algorithm

Updating solution (relaxation step)

Convergence test

Red-Black Ordering

980

5

490

98

490

980

Diagonal Grouping

980

70

70

56

70

980

Table 4 gives the CRAY cpu time required by the various vectorised options to perform one iteration in either the eigenvalue calculation or the calculation of the pressure distribution.

4 2 3

Mesh size

Standard ordering

Red-Black ordering

Diagonal grouping

TABLE 4

Eigenvalue calculation Pressure distribution

7x7~5 10x10~5 14x14~5 7x7~5 10x10~5 14~14x5

3 .67 - 11.04 3 .69 - 14.78

0 . 7 3 I .47 2.85 0 . 7 7 1.49 2.88

0 . 3 4 0.51 0.89 0.35 0.51 0.90

CRAY CPU TIME IN MILLI-SECONDS TO EXECUTE ONE ITERATION

As may be seen the red-black coding is 4 or 5 times faster than the original code and the diagonal grouping is 10 to 16 times faster. The difference between the last two options is almost certainly due to the slightly more complex arithmetic needed in the red-black code to identify the neighbouring grid blocks, and also the shorter vector length associated with setting up the right-hand side column vector. By reverting to the restricted case where the number of grid blocks in the plane is known to be even, it may be possible to make the two vectorised options comparable.

A small part of the gains achieved above are associated with simply reducing the generality of the inversion programming and the generation of better fortran coding. IBM machine, where enhancements by factors of 1.2 and 1.3 were observed.

This has been demonstrated by using the same inversion routines on the

CONCLUSIONS

This paper has discussed advantages which can be derived in utilising curvilinear mesh co-ordinate systems in surfactant flood calculations. allows a computational geometry to be adopted broadly consistent with the anticipated flow patterns of a problem. utilising the code PASL has been illustrated for a generalised field problem with sealing fault lines. mesh blocks adjacent to wells, which in turn gives a superior time step capability in an IMPES formulation, such as that adopted in the CFTE code for simulation of surfactant floods. The reduction in mesh orientation errors resulting fromthe use of curvilinear co-ordinates has been demonstrated for a 5-spot pattern with surfactant flooding.

Direct inversion employed in the solution of the implicit formulation of the pressure equation in the CFTE program leads to computer speed limitations for large curvilinear mesh problems. To overcome this, the LSOR method has been programed and tested using the standard ordering, as well as a red-black and a diagonal line consistent ordering. to be amenable to selection of long vector lengths on a CRAY computer so that diagonal line formulation in the revised code runs up to 19 times faster than the standard ordering in LSOR.

This

Implementation of flow stream geometry

The curvilinear geometry gives advantages in choice of

The last two arrangements have been shown

Relative to D4-direct inversion on the IBM 3033

4 2 4

machine, LSOR diagonal line inversion runs some 65 times faster on the CRAY. The total code performance is dependent on problem size and for the largest example discussed here of 980 mesh blocks, direct inversion required about 60% of the overall running time. Much larger problems are needed for real field studies where the inversion aspect becomes completely dominant. these improvements have placed field computation closer to practical realisation in terms of computer costs.

Consideration of further generalisation of the LSOR method to curvilinear meshes with a wider range of connectivities, and with consequent difficult patterns of off-diagonal non-zero elements, needs to be considered in the future .

Thus

ACKNOWLEDGEMENT

The work reported i n t h i s paper has been funded by the UK Depart- ment of Energy.

REFERENCES

1

2

5

6

7

8

9

10

TODD M.R. and CHASE C.A., "A Numerical Simulator for Predicting Chemical Flood Performance". Paper SPE 7689, presented at the Fifth Symposium on Reservoir Simulation, Denver 1979.

FArdRS P . J . , HAWES R.I. and MATTHEWS J . D . , "Some Aspects of the Potential Application of EOR Processes in North Sea Reservoirs". Paper EUR 194, presented at the European Offshore Petroleum Conference and Annual Exhibition, 1980.

MUSKAT M., "Flow of Homogeneous Fluids Through Porous Media", McGraw Hill, 1937.

W T I N J.C. and WAGNER R.E., "Numerical Solution of Multiphase Two- Dimensional Incompressible Flow Using Stream Tube Relationships". SOC. Pet. Eng. J. (October 1979) pp313-323.

PEACEMAN D.W., "Fundamentals of Numerical Reservoir Simulation", Elsevier, 1977.

VARGA R . S . , "Matrix Iterative Analysis", Prentice Hall, 1962.

FORSYTHE G.E. and IiASOW W . R . , "Finite Difference Methods for Partial Differential Equations". John Wiley, 1960.

BUZBEE B.L., BOLEY D. and PARTERS.V., "Applications of Block Relaxation" Paper SPE 7672, presented a& the Fifth Symposium on Reservoir Simulation, Denver 1979.

KILLOUGH J.E., "The Use of Vector Processors in Reservoir Simulation". Paper SPE 7673, presented at the Fifth Symposium on Reservoir Simulation, Denver 1979.

CRAY-I Library Reference Manual. SR-0014.


CONTROL OF NUMERICAL DISPERSION IN COMPOSITIONAL SIMULATION

D. C. WILSON, T. C. TAN, P. C. CASINADER

Deparmzent of Mineral Resources Engineering, Imperial allege, London S W 7 2BP

ABSTRACT

T h i s p a p e r p r e s e n t s a technique, s u i t a b l e f o r multidimensional app l i ca t ion , f o r reducing numerical d i spe r s ion on f u l l y i m p l i c i t compositional simulators. S imple g e o m e t r i c a l a n a l y s i s of curve prof i les and r e e x a m i n a t i o n of var ious weighting schemes lead t o t h e development of a dynamic w e i g h t i n g t e c h n i q u e t h a t e x p l o i t s t h e optimum f e a t u r e s of 1 - p o i n t , 2 -po in t and mid-point weighting schemes. Th i s weighting scheme l a gene ra l i n i t s a p p l i c a t i o n i n f i n i t e d i f f e r e n c e models f o r r e d u c i n g d i spe r s ion i n convective parameters s u c h as s a t u r a t i o n and c o n c e n t r a t i o n . We show how t h i s scheme c a n b e i m p l e m e n t e d on a n i m p l i c i t , e q u a t i o n of s t a t e , c o m p o s i t i o n a l model. Numerical examples including mul t ip l e con tac t (MCM) and n e a r m i s c i b l e (NM) prob lem are used t o compare i t s performance with two published compositional s i m u l a t o r s which u t i l i s e f u l l ups t r eam w e i g h t i n g . Our r e s u l t s show a s i g n i f i c a n t r e d u c t i o n i n t h e number of g r i d blocks required t o achieve t h e same numerical accuracy.

1.0 INTRODUCTION

The f i r s t compositional s imula to r s appeared i n t h e la te 1960's. Since then, tremendous progress has been achieved i n the t reatment of f l u i d p r o p e r t i e s , s o l u t i o n techniques and model gene ra l i t y . In common with B-simulators, numerical d i s p e r s i o n r ema ins a ma jo r problem. The most dominant a s p e c t of n u m e r i c a l e r r o r s o c c u r i n t h e composltfonal f i e l d . As i n B-models, a l b e i t i n a l e s s o b v i o u s m a n n e r , s a t u r a t i o n d i spe r s ion and e r r o r s i n t h e pressure f i e l d remain. Various techniques have been reviewed and are discussed below. McFarlane e t a1 (1) used smaller cells i n t h e r eg ion of m a x i m u m compositional change, with l a r g e r c e l l s e l s e w h e r e . T h i s t e c h n i q u e i s n o t even r o b u s t enough f o r 1-D problems. P r i c e e t a1 (2) proposed t h e use of time and space d i s c r e t i s a t i o n i n 1-D, such t h a t t h e n u m e r i c a l d i f f u e i v i t y i s of t h e same o r d e r a s t h e p h y s i c a l d i f f u s i v i t y . T h i s i s t o o e x p e n s i v e f o r p r a c t i c a l a p p l i c a t i o n . The works of Peaceman (3 ) and L a n t z (4) on s t a b i l i t y and t r u n c a t i o n e r r o r a n a l y s i s l a i d down t h e foundation f o r many subsequent works, i n c l u d i n g t h e p r e s e n t one. It i s t h u s p o s s i b l e t o u s e a n a r t i f i c i a l d i f f u s i o n term t o c a n c e l out t h e numerical d i f f u s i v i t y i n e x p l i c i t backward (Chaudhari (S) ) , and i m p l i c i t backward (Van Quy ( 6 ) ) d i f f e r e n c e e q u a t i o n s . They r e q u i r e s e v e r e t i m e s t e p , g r i d s i z e l i m i t a t i o n s and are p r i m a r i l y

4 2 6

L - l

s u i t a b l e f o r miscible d i s p l a c e m e n t . Laumbach ( 7 ) deve loped a t r u n c a t i o n c a n c e l l a t i o n procedure which removed t h e time s t e p and g r i d s i z e l i m i t a t i o n s by cance l l i ng a po r t ion of t h e e r r o r i n t h e convection term with t h a t i n t h e a c c u m u l a t i o n term. It is a p p l i c a b l e f o r miscible , incompressible systems, where c o m p o s i t i o n s a r e t h e o n l y v a r i a b l e s s o l v e d . F i e l d a p p l i c a t i o n , however, r e q u i r e s both pressure and concen t r a t ionso lu t ions . It appears t h a t t h e e a r l y work of Gardner e t a1 ( 8 ) using the method of c h a r a c t e r i s t i c s is of g r e a t e r u t i l i t y i n m i s c i b l e flooding. However, t h e compositional f i e l d is decoupled from the conservat ion equat ion used f o r so lv ing t h e p r e s s u r e , and so does n o t s t r i c t l y o b s e r v e t h e c o n s e r v a t i o n p r i n c i p l e . The e x p l i c i t 2-point ups t r eam w e i g h t i n g scheme is t h e most w i d e l y quo ted d i s p e r s i o n c o n t r o l t e c h n i q u e (Todd e t a 1 ( 9 ) ) . It has r e c e n t l y been improved (Banks e t a1 ( L O ) ) , and extended f o r i m p l i c i t t reatment (Wheatley (11)). Nghtem e t a 1 ( 1 2 ) , r e p o r t e d t h e u s e o f 2-point upstream weighting scheme f o r a n IMPES compositional s imulator . T h i s p a p e r g i v e s some simple a n a l y s i s of var ious r ep resen ta t ive p r o f i l e s of convective parameters i n t h e l i g h t of e x i s t i n g s t a b i l i t y and t runca t ion e r r o r a n a l y s i s . T h i s l e a d s t o t h e i d e n t i f i c a t i o n of s e v e r a l weaknesses i n t h e 2 -po in t ups t r eam w e i g h t i n g scheme, and t h e b e s t me thod of e x p l o i t i n g mid-point we igh t ing . A v a r i a b l e time l e v e l , v a r i a b l e d i s t ance weighting scheme has been developed which opt imises t h e bes t f e a t u r e s of t h e 1 - p o i n t , 2 -po in t and t h e h i t h e r t o unused mid-point schemes. The development is empir ical , i n nature , but is within t h e c o n s t r a i n t s of n u m e r i c a l S t a b i l i t y , and is gu ided by t h e a v a i l a b l e knowledge on t runca t ion e r r o r s . We r e p o r t success fu l app l i ca t ions on d i f f i c u l t numerical problems.

i .4 i+ I

2.0 THEORETICAL DEVELOPMENT

The following s e c t i o n s d i scuss t h e t h e o r e t i c a l b a s i s f o r our model.

2.1 I n t e r p o l a t i o n Methods Cons ide r a c o n v e c t i v e pa ramte r C, which is assumed t o be cont inuous and l i n e a r i n space and t i m e (Fig. 1).

I n+ I

For i n t e r b l o c k f low a t i+3, t h e parameter C f o r t h e f i n i t e d i f f e r e n c e e q u a t i o n must be e v a l u a t e d a t I+&. An o b s e r v e r a t I+* would n o t i c e a continuous change in the value of C from Cn I+$ a t the start of a t i m e s t e p , t o Cyit a t the end of t h e time s tep. The i n t e g r a l average of C i+Q over t h e time s t e p is the arittnoetic mean of CM1 T h i s a n a l y s i s a g r e e s w i t h t h e l i n e a r i s e d t r u n c a t i o n e r r o r a n a l y s i s f o r t h e convection equation in which mid-point weightings in space and t i m e are found t o be t h e most accurate (Appendix A l ) . In prac t ice , however, C v a r i e s non-lineazly, and may become d i s c o n t i n u o u s . Consequent ly , t h e i n t e r - b l o c k v a l u e Ci+k is n o t a simple a r i thmet ic mean between tn and tn*'; ins tead, i t must be found by a time-integration over t h i s range.

I+% and Chr I+& .

427

S i n c e t h e parameter C p r o p a g a t e s w i t h time, i t f o l l o w s t h a t t h e a b o v e i n t e g r a l must be equal t o a dis tance i n t e g r a l between x I+$ and some upstream point X Thus:- - X

C ( % t 7 dx] /(x- "'+&I , (2 1 c;+r = [,, - and. by t h e Mean Value Theorem, Ci++ must correspond t o some point i n t h e ~- i n t e r v a l (xi++, X ) . T h i s shows t h a t n e i t h e r s i n g l e p o i n t upstream nor midstream weight ing i s t o t a l l y cor rec t for t h e non-linear problem, and that some intermediate weighting f a c t o r must be determined. A descr ip t ion of our proposed theory now follows. Consider the general l i n e a r in te rpola t ion formula:- * rr+l * tn4t b t

(3 ) cx = e [ ~ c ~ + ~ + ~ ~ - w ~ c ~ ~ ' ~ + ~ ~ - e ~ [ w c ~ + ~ ~ - w ~ c ~ ~ ~ X i & X " X i + , >

where 8 and W are t h e t i m e and d is tance weighting factors ,with values between 0 and 1. W o condi t ions must be s a t i s f i e d f o r l i n e a r i n t e r p o l a t i o n t o be val id . (1) A continuous l i n e a r (or near l i n e a r ) curve between the pivotal points. ( 2 ) The p i v o t a l p o i n t s must be "mobile". By t h i s we mean t h a t C should be i n t h e mobile range bounded by t h e maximum and minimum possible values . For example, t h e mobile range of water s a t u r a t i o n i s between Swc and (1-Sor),but does not include these ac tua l values. Our a im i s t o u s e e q u a t i o n ( 3 ) t o p r e d i c t t h e v a l u e of an i n t e r b l o c k c o n v e c t i v e parameter such t h a t i t l ies c l o g e t o t h e t r u e t i m e - i n t e g r a l average v a l u e of C on t h e h i s t o r y curve a t L*. Before doing t h i s , i t i s necessary t o examine the representa t ive curves which a r e t o be interpolated.

2.2 Curve Anal sis C o n s i d e r 4 arYbitrary p r o f i l e s a t a f i x e d t i m e l e v e l (F ig . 2 ) . I n t h e following descr ip t ion , equal gr id spacing is assumed.

- c PROFILE Figure2a 1 I 1FigureZb

I I I

igure 2d r 1 I I J

Figure (2a) Curve 1 : increasing gradient , concave (2b) Curve 2 : increasing gradient , convex ( 2 c ) Curve 3 : decreasing gradient , convex (2d) Curve 4 : decreasing gradient , concave

We are i n t e r e s t e d i n approximating t h e value of C at I*. Both upstream e x t r a p o l a t i o n from 1-1 and 1, and i n t e r p o l a t i o n b e t w e e n i and i + l , a r e p o s s i b l e . On Curves 1 and 2 , t h e ex t rapola ted values can be found on t h e upstream p o r t i o n of t h e c u r v e s , w h i l e t h e i n t e r p o l a t e d v a l u e s l i e on t h e downstream par t of t h e curves with reference t o I+$. This implies that t h e use of upstream ext rapola t ion is e f f e c t i v e l y upstream weighted ( f c w < l ) , a n d

4 2 8

hence s t ab le . W < i ) , and hence u n s t a b l e . T h i s s i t u a t i o n occurs j u s t behind an immiscible displacement,where a shock i s p resen t ,o r i s b u i l d i n g up. Thus Curve 1 c a n r e p r e s e n t t h e o i l s a tu ra t ion , and Curve 2 can represent t he water Sa tu ra t ion . It is w e l l known that the use of mid-point weighting c r e a t e s overshoot unde r such circumstances,while full upstream weighting r e s u l t s i n an undershoot of t h e d i sp lac ing phase ( s a t u r a t i o n dispers ion) . On C u r v e s 3 and 4, t h e r e v e r s e c o n d i t i o n s occur . The u s e of u p s t r e a m ex t r apo la t ion is e f f e c t i v e l y downstream weighted. Thus on Curve 3, ups t r eam e x t r a p o l a t i o n c r e a t e s u n d e r s h o o t , a n d on Curve 4, i t creates o v e r s h o o t . Further a n a l y s i s of upstream e x t r a p o l a t i o n and mid-point I n t e r p o l a t i o n i s given i n t h e Appendix A2. Suf f i ce i t t o say he re t h a t both ex t r apo la t ion and i n t e r p o l a t i o n have t h e i r advantages and l i m i t a t i o n s . They are camplementary i n t h e i r funct ions. When ex t r apo la t ion i s unstable , i n t e r p o l a t i o n i s s t a b l e , and v i c e v e r s a . Under c e r t a i n c o n d i t i o n s t h e y a r e b o t h m i s t a b l e . T h i s o c c u r s when t h e p i o v o t ( s ) become "immobile". In such s i t u a t i o n s upstream weighting i s t h e bes t s t a b l e approximation. The same a n a l y s i s can be extended t o t h e h i s t o r y curves a t a f i xed point. We are i n t e r e s t e d i n t h e h i s t o r y curve a t 1% over t h e time s t e p . Due t o t h e c o n v e c t i v e na tu re of C, a h i s t o r y curve a t a f ixed point over a t i m e s t e p i s r e l a t e d t o t h e po r t ion of t h e d i s t a n c e p r o f i l e immedia t e ly ups t r eam of t h e f ixed point a t t h e beginning of t h e t i m e s t ep .

The use of i n t e r p o l a t i o n i s e f f e c t i v e l y downstream weighted (o<

2.3 A Dynamic Weighting Scheme The pu rpose of t h i s development i s t o f ind a method of eva lua t ing e x p l i c i t l o c a l weighting f ac to r s , such t h a t t h e l i n e a r i n t e r p o l a t i o n formula, e q u a t i o n ( 3 ) . c a n b e i n c o r p o r a t e d i n t o a n i m p l i c i t s i m u l a t o r t o s u b s t i t u t e f o r i n t e rb lock convective parameters o r t h e i r dependent funct ions. The 4 b a s i c c u r v e t y p e s ( F i g 2.) can be subdivided i n t o 2 groups. Group 1 (curves 1 and 2 ) has inc reas ing g r a d i e n t s i n t h e flow d i r e c t i o n , a n d Group 2 ( c u r v e s 3 and 4) h a s d e c r e a s i n g g r a d i e n t s . E i t h e r Group 1 or Group 2 are present l o c a l l y a t a f ixed t i m e . I d e n t i f i c a t i o n is poss ib l e through g rad ien t t e s t i n g .

G i = q+l- c;

(4) [\Gi\ -~GIL- , \ ] > 0 .=$ crouP '

X k , - xi

xi - xi- I - ci - ci-l

< 0 4 Group 2}, = 0 S) &-car [ The b,ssic assumptions are:-

(1) Group 1 curves do no t evolve i n t o Group 2 curves over a time s tep. The same d i s t a n c e weighting f a c t o r s can be used a t two f ixed t i m e l e v e l s , n and n+l, i n t h e l i n e a r i n t e r p o l a t i o n equation. (2 ) The h i s t o r y curve a t t h e block i n t e r f a c e ie over t h e t i m e s t e p i s i n t h e same c u r v e g roup as t h e immediate upstream p r o f i l e a t t i m e l e v e l n (see next s ec t ion ) . Therefore, t h e i n t e r p o l a t i o n f a c t o r on t h e h i s t o r y p r o f i l e , 8 , is assumed t o be equal t o t h e d i s t ance i n t e r p o l a t i o n f a c t o r , W. Based on t h e previous curve a n a l y s i s , t h e following s t r a t e g y i s adopted. When a Group 1 c u r v e i s d e t e c t e d , an upstream ex t r apo la t ion i s required t o provide low numerical dispers ion,while maintaining numerical s t a b i l i t y . Th i s c a n be invoked on t h e l i n e a r i n t e r p o l a t i o n fo rmula by choosing weighting f a c t o r s between 0 .5 and 1.0 ( e q u a l g r i d s p a c i n g ) . Simple g e o m e t r i c a l cons t ruc t ions show how t h i s can be done. (Pigs. 3a, b).

F i q r e 3.3

2 - p i n t upstream e x t r a p l a t i o n . D can be foundon t h e chord BF.

Firmre 3b /lE t

429

A B is an upstream chord. BF is a downstream chord. It is required t o f i n d t h e e x t r a p o l a t e d point D on BF. This point is D’. The necessary weighting f a c t o r f o r the in te rpola t ion formula, W, is derived below.

= ai + (I- aL)(x-x,) /x. (54)

s u b s t i t u t i n g equation (5c) i n t o equation (5b) gives

When a Group 2 curve is detected, i n t e r p o l a t i o n is super ior . f a c t o r s are ca lcu la ted by s e t t i n g R i l l . g ives Wi-ai-0.5.

S c r e e n i n g must be a p p l i e d t o exc lude t h e use of t h e in te rpola t ion formula under 2 inva l id conditions:- (1) Gradient r e v e r s a l (R i is negat ive) ( 2 ) E i t h e r , o r both,of t h e pivots (%, c ) are ”immobile” Once t h e s e condi t ions are detected, f u l f upstream weighting a f fords the best s t a b l e a l t e r n a t i v e avai lable . The i n t e r p o l a t i o n scheme proposed is therefore dynamic i n nature. Ef fec t ive f u l l upstream, 2-point upstream e x t r a p o l a t i o n , o r mid-stream i n t e r p o l a t i o n w i t h v a r y i n g d e g r e e of i m p l i c i t n e s s can be invoked l o c a l l y via the same l i n e a r in te rpola t ion formula.

w b = I + (ai-i)/Q (54 The weight ing

I f t h e gr id spacing is miform, t h i s

2.4 Relat ionship Between Time Weighting and Distance Weighting

Figure 4a Figure 4b Figure 4c

F i g u r e 4a shows t h e p r o f i l e of a typ ica l parameter C a t t i m c t“ , CI being i t s value a t the i n t e r f a c e between b l o c k s i and i+l. F i g u r e 4b shows t h e same p r o f i l e w i t h r e s p e c t t o X , t h e d i s t a n c e measured upstream from t h e in te r face . Assuming that the p r o f i l e X(C) and t h e v e l o c i t y of propagat ion V ( C ) are known, i t is required t o determine t h e shape of the h i s t o r y curve, t ( c ) (Figure 4c) , a t t h e in te r face , which is given by:-

Case 1 V(C) - constant - v T h i s assumption is approximately va l id i f t h e t i m e s t e p is smal1,so that t h e band of values ( c l , c2),which crosses the i n t e r f a c e o v e r t h e t i m e - s t e p , i s narrow. For such a case,

x(4 , t ( c ) = - V

and hence t ”(C) - X “(C)/V. S i n c e V is p o s i t i v e , t ” has t h e same sign as X”, and hence t (C) belongs t o t h e same group of curves as X (C).

4 30

Case 2 V(C) i s v a r i a b l e . D i f f e r e n t i a t i n g (6) w. r . t . C, we obtain:

t J = (vx'- x v ' ) / v 2 , a n d , d i f f e r e n t i a t i n g y e t again, we have

tJ'= [v(vx"- xv'/) - ~ V / ( V X ' - X V ' ) ] / V 3

Now, s i n c e X ' and V' have opposi te s i g n s , i t follows t h a t t h e second term of t h e above expression [ - 2 v - (VX' - XV' ) ] i s always pos i t i ve . Furthermore, i f X '*7 0, then V Y 0, and t h e e n t i r e expression w i l l be p o s i t i v e , and so X" and t" w i l l have t h e same s i g n , and t h e c u r v e s w i l l belong t o t h e same g r o u p (1.e . Group 1). I f , however, X Z O (1.e. Group 2) , then, due t o t h e second term being p o s i t i v e , we cannot be c e r t a i n whe the r or n o t t" w i l l change s i g n . N e v e r t h e l e s s , f o r p r a c t i c a l purposes, we s h a l l assume that, f o r a l l cases , X and t belong t o t h e same group.

3.0 OVERALL APPLICATION TO AN IMPLICIT COMPOSITIONAL SIMULATOR

There is a unique dependence of t h e o v e r a l l component f r a c t i o n a l flows on t h e o v e r a l l composition. For propagat ional s t a b i l i t y , c o n c e n t r a t i o n v e l o c i t i e s a t a f i x e d p o i n t i n s p a c e and t i m e are e q u a l ( H e l f f e r i c h (13)). It i s t h e r e f o r e appropr i a t e t o f i n d t h e dynamic w e i g h t i n g f a c t o r s based on t h e l o c a l o v e r a l c o n c e n t r a t i o n p r o f i l e s . We f u r t h e r assume t h e l o c a l ex i s t ence of e i t h e r t h e Group 1 c u r v e s , o r t h e Group 2 c u r v e s . The c o n c e n t r a t i o n p r o f i l e o f t h e most " s e n s i t i v e " component i s u t i l i s e d t o e v a l u a t e t h e weighting f ac to r s . They a r e used f o r a l l components i n b o t h hydroca rbon p h a s e s , i f 2 phases e x i s t . S e l e c t i o n of t h e most " sens i t i ve" component i s important t o a v o i d t h e need t o choose t h e most s t a b l e w e i g h t i n g f a c t o r s evaluated f r a n a l l t h e concentrat ion p r o f i l e s . The "immobile" condi t ions f o r t he se l ec t ed canponents must a l s o be def ined. These ideas are i l l u s t r a t e d i n t h e n u m e r i c a l examples . To account f o r phase d i scon t inu i ty , f u l l upstream weighting i s used i f t h e upstream and downstream blocks do not have t h e same number of hydrocarbon phases.

Figure 5

3.1 Construct ion of t h e Model The compos i t iona l model used i n t h i s s tudy i s based on an equat ion of state, and f o l l o w s t h e i m p l i c i t f o r m u l a t i o n p r e s e n t e d by C o a t s (14). We w i l l , t h e r e f o r e , o n l y d i s c u s s t h e model where i t h a s been modified t o take i n t o account t he preceding discussion.

3.1.1 Temporal and S p a t i a l Weightin

A t any point i n t h e system, t h e value of a v a r i a b l e u, a t t i m e t*(where tnS t% tn+' 1, can be r e l a t e d t o i t s va lues a t tn and tn+' by:-

* n+ I

(10%)

00 4)

u = e K + ( I - e ) Z = kn+ eSu""

2'- U" = SU* = e Sun+'- O f ,

431

so, f o r each i t e r a t i o n , t h i s implies:-

The symbols %'IA (=cC - K ) and SK (=V u. ) denote the change i n u over t h e i t e r a t i o n 1, and the cumulative change, respect ively. I f , however, i n addi t ion t o t h i s intermediate time-level, u i s also evaluated a t a point o ther than t h e block-centres , t h e n i t h a s t o be r e l a t e d t o t h e block-centre values by means of t h e dis tance weighting formula.

st$ - 8 sLn+l U (4 - C+l 4 c+: %

Thus:- * * u" = wu; +(l-w)uL+l ;

s u b s t i t u t i o n then leads to: 4 n+l -! n+( S'? = ewsKL; + e( i -w)Sai+, .

3.1.2 Expansion of t h e "Flow" term The f low between two ne ighbour ing b l o c k s i a n d i + i can be expressed i n t h e form:-

T+(C,- P:) . Increments i n the t ransmiss ib i l i ty term T are ca lcu la ted by means of partial d e r i v a t i v e s w . r . t . the complete set of var iab les (U, , ..... Un).

and, f i n a l l y , using equations ( ~ O C ) , ( l l b ) and (12a), we obta in t h e expansion of t h e flaw term, as follows:-

4.0 DISCUSSION OF RESULTS

Three d i f f e r e n t d i sp lacement problem were chosen, i n order t o demonstrate the appl ica t ion of t h e above theory i n a var ie ty of s i tua t ions . The da ta f o r t h e s e r u n s were taken from Coats (14). Leach and Yel l ig ( 1 5 ) , and Smith and Yarborough (16 ) , respect ively.

4.1 Displacement 1 (Coats (14)). T h i s i s a n MCM problem, involving components: C1,n-C4 and n-C 10. The system e x i s t s i n i t i a l l y as an undersaturated l iqu id , and i s displaced by a r i c h gas.

In the s imulat ion, three zones can be ident i f ied : a downstream zone containing undersaturated o i l , a middle zone comprising two phases whose c o a p o s i t i o n s converge i n t h e upstream d i r e c t i o n , and f i n a l l y an upstream miscible zone containing a s ingle dense f l u i d whose composition changes from t h e c r i t i c a l composition t o t h a t of the i n j e c t i o n gas. The boundary between the f i r s t two zones w i l l be re fer red t o as t h e gas f ront , while t h a t between the latter two w i l l be c a l l e d t h e miscible f ront . In MCM problems, t h e use of s i n g l e point upstream weighting l e a d s t o s e v e r e composi t iona l dispers ion which causes s u b s t a n t i a l delay i n the attainment of m i s c i b i l i t y . T h i s r e t a r d a t i o n of t h e m i s c i b l e f r o n t i s conspicuous in C o a t s ' r e s u l t s , where t h e u s e of 20, 4Omd 80 b l o c k s show a p r o g r e s s i v e

432 8.2- , , , , , , , .

COAT S I - D M C M PROBLEM 1.0 ' TIME=210 DAYS 20 BLKS D lMAX=7.5 DAYS

U

0 0.5

a

COAT S I -D M C M PROBLEM

- NO courm z 0

L 200 DINAMC WEICI I IWC

COAT S I - D M C M PROBLEM . 6 1 . 0 -

COAT S I - D MCM PROBLEM TlMEn2lO D A Y S 20 BLKS OlMAX=T.S DAYS

+ U - "0 CO"TI10L

TIME.DAYS

4 I- 3 m 0 . 1

_I

U W

0

. @z 0 . 2 .

F i g u r e 6 - Displacement 1 (MCH) : 1-D c o m p a r i s o n o f dynamic weighting with f u l l upstream weighting.

( a ) Sg p r o f i l e . ( b ) Advance of m i s c i b l e f r o n t . ( c ) C4 concentrat ion p r o f i l e (d) o i l recovery and GOR vs t ime.

i n c r e a s e i n i t s speed of p r o p a g a t i o n . I n t h e absence of a n a n a l y t i c ' a l s o l u t i o n , i t is j u s t i f i a b l e t o assume t h a t t h e 80-block s o l u t i o n is t h e nearest t o r e a l i t y . The i n t r o d u c t i o n of t h e dynamic weight ing scheme described i n t h i s paper produces a marked improvement, and has enabled us t o obtain, with 20 b l o c k s , a n s w e r s which are of comparable accuracy t o C o a t s ' 40-block s o l u t i o n . Figures 6a, b, c , d show a comparison between the use of t h i s technique and s i n g l e - p o i n t upstream weighting. The use of the proposed technique c l e a r l y results In a f a s t e r advance of the miscible f ront , which is confirmed by t h e e a r l y and s teep rise i n GOR, following i ts breakthrough t o the producer. The scheme has a l s o been tes ted i n 2D, using a Cartesian gr id of 9x9 blocks , w i t h t h e i n j e c t i o n and product ion w e l l s located i n two diagonally-opposite corner blocks. (Figures 7a, b, c, d) . Once a g a i n , a n improvement i n t h e s i z e of t h e miscible zone can be observed, using our technique.

4.2 Displacement 2 (Smith and Yarborough (16)). The system used i n t h i s displacement was a binary mixture of C 1 and nC5,being displaced by dry gas (Cl). In t h i s case, evaluat ion of weighting f a c t o r s can be c a r r i e d out on e i t h e r component. Thus C 1 was a r b i t r a r i l y chosen f o r t h i s purpose. Tbo runs were perfomed on t h i s system, t h e f d r s t of t h e s e be ing des igned t o s i m u l a t e FCN disp lacement . T h i s was achieved by assuming a n i n i t i a l composition of 50% C 1 and 50% n-CS,and simulating t h e displacement i n the s u p e r c r i t i c a l region ( a t 3000 psi). Since t h i s is a perfect piston-type d i s p l a c e m e n t , t h e a n a l y t i c a l s o l u t i o n c o n s i s t s o f a s t e p c h a n g e i n composi t ion from t h e i n j e c t i o n composi t ion t o t h e i n i t i a l composi t ion .

4 3 3 - v .

?\

0 T I VF I 0 1.240 '''' PV INJ ~0.637 OIL R E C ~ 0 . 5 6 4

\

0 c 7 d ) T I V E I o 1-240 PV INJ -0.637

= O .564

A \ \ I \

Figure 7 - Displacement 1 (MCM) : 2-D comparisons.

( a ) Gas s a t u r a t i o n map, dynamic weighting. (b) C4 concentrat ion map, dynamic weighting. ( c ) Gas s a t u r a t i o n map, f u l l upstream weighting. (d) C4 concentrat ion map, f u l l upstream weighting.

Figures 8a and 8 b show t h e C 1 p r o f i l e a t 210 days, and the n-C5 concentration i n t h e e f f l u e n t as a funct ion of time. The weighting technique shove better r e s u l t s than the "full upstream" case, a l t h o u g h b o t h show a n a p p r e c i a b l e compositional dispers ion r e l a t i v e t o t h e a n a l y t i c a l solut ion. I n the second run, an i n i t i a l composi t ion of 87.5% C 1 and 12.5% n-C5 was chosen , so as t o y ie ld an i n i t i a l condensate l i q u i d of 7% sa tura t ion a t 1525 p s i , which was a l s o t h e p r e s s u r e a t which t h e s i m u l a t i o n was conducted. Agein, C 1 was in jec ted , and t h e problem was run i n t h e 2-phase mode, with t h e l i q u i d assumed t o be immobile. The purpose of t h i s run was t o demonst ra te t h a t , f o r some problems ( s u c h as of t h i s type) t h e amount of compositional d i spers ion i s negl igible . T h i s p o s t u l a t e d absence of c o m p o s i t i o n a l d i s p e r s i o n i s v e r i f i e d by t h e numerical results shown i n Figures 8c and Ed, i n both of which the results of u s i n g s i n g l e p o i n t upstream weight ing are v i r t u a l l y i d e n t i c a l t o t h o s e obtained with t h e present technique.

4 3 4

DRY GAS DISPLACING RICH GAS 1 . 1

.385 PV INJECTED 210 DAYS ( 3 4 STEPS).

= i4 ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ': 0

l =W=DYN ,

50 100 150 200 250

DISTANCE ,FEET

CONOENSATE REVAPORIZATION

DRY GAS DISPLACING RlCH G A S

PV CH4 INJECTED

CONDENSATE REVAPORIZATION I Q+IO-

0.08--

0.06--

0.04.-

0.02--

DISTANCE ,FEET PV METHANE INJECTED Figure 8 - Displacement 2 : 1-D comparison of dynamic weight ing with f u l l upstream weighting.

( a ) C1 c o n c e n t r a t i o n p r o f i l e (FCN). ( b ) C5 c o n c e n t r a t i o n i n e f f l u e n t v s t i m e (FCN). ( c ) C1 and o i l s a t u r a t i o n p r o f i l e s (re-vaporieation). (d) C5 concentrat ion i n e f f l u e n t , and advance of "dry front" vs t i m e (re-vaporization).

4.3 Displacement 3 (Leach and Yel l ig (15)) . This m e a study of t h e mechanisms involved i n t h e displacement, by CO2, of a synthe t ic crude o i l . Leach e t a1 (15) presented laboratory results cover ing t h e various displacement types (PCM, MCM and NM), and aleo simulated these on t h e i r compositional model, using 100 blocks. To tes t our technique, two rune were chosen: an MCM d r i v e (Run 61, and an NM d r i v e (Run 7). The component which we s e l e c t e d f o r " g r a d i e n t t e s t i n g " was t h e one which had t h e least i n i t i a l concentrat ion - namely C6. The rJeighting technique has enabled us t o match t h e laboratory results t o a good a c c u r a c y , w i t h m e r e l y 2 0 b l o c k s . Cons ider ing t h e MCM r e s u l t s f i r s t , F i g u r e 9 a demonstrates t h e f a s t e r advance of t h e misc ib le f r o n t , and t h e s t e e p e r C02 p r o f i l e r e s u l t i n g f ran the use of t h i s technique. Figures 9b and 9c f u r t h e r support our dispers ion cont ro l method, by showing the delayed breakthrough of C02, and t h e s teep change i n t h e GOR and t h e e f f l u e n t composition. The above f e a t u r e s have a l s o been v e r i f i e d i n t h e NM r u n , perhaps t o a g r e a t e r e x t e n t , a s c a n be seen , f o r example, i n t h e s i g n i f i c a n t sharpening

435

LEACH ETAL DATA RUN 6

20 BLK DT=.I D A Y

.-- , A. . I . . . 1 . 1

0 . 2 0 . 4 0.6 0 . 8 1.0 1.2 0 .

(b) HCPV COZ INJECTED

LEACH ETAL DATA (RUN 6 )

DINAMC wuGnnNG

NO CONfRCX I '

' O . O 0

TIME ( D A Y S )

1

I . ? . . - . , . . . . , . . . . , , - . - . . . , . . . . , . . . . LEACH ETAL DATA RUN 7 . 4 HCPV C02 INJECTED 20 ELKS

- OVNAHC wmcnn"

. I - u

.(I

. L

J

. a

[L 0 . 6 - 3 ' I - , a

(d) DISTANCE FROM INJECTION END (FEET )

l ! o ' '' b j 2 : b i 4 ' O ~ l i O ' 'I ' ,!. ( C ) HCPV C02 INJECTCD Fig.9 (a)-(d). Capuon overleaf.

436

Q I . 4 20 ELK D T = . I D

"8.0 0.2 0 . 4 0.6 0 . 8 1 . 0 1.2 1 . 4

HCPV C02 INJECTED (el

15.-

1 3 . 5 -

1 2 . - 0

c z m

W \ L u 9. u

LI W

m

- 7.5 - 0 > c II a 6 . w (I >

0 =' V 0 4 . 5 W \ II L n ; a =I 0 3 . o - - 0

CL - - p 1 0 . 5

= a

I .5

'O.Q0

Figure 9 - Dirplacement 3 : 1-D comparison of dynamic VOightlng vlth full uprtrerm Wlghting. (a) Sg and COZ concentration profller (MCM). (b) Normalized concentration of 032, rod CZ-C6 in effluent vr HCPV injected (MCW). ( c ) COR and o i l recovery vs HCPV injected (ncn). (d) Sg and COZ concentration profilea (Nn). (e) Norullred concentrrtlon of CO2 and C 1 i n effluent v. HCPV injected (Nn). (f) COR and 011 recovery va HCPV injected (NH).

which occurs i n the Sg and C02 p r o f i l e s , due t o t h e weighting scheme ( F i g u r e 9d). The p r o d u c t i o n h i s t o r y ( F i g u r e 9 e ) and t h e e f f l u e n t C 1 - and C02 - concentrat ions (Figure 9 f ) confirm the delayed a r r i v a l of t h e 2-phase zone, and t h e consequent higher recovery r e s u l t i n g from t h e use of t h i s technique. It needs t o be mentioned, however, t h a t a cr i t ical gas s a t u r a t i o n of 1 5 % had t o be i n t r o d u c e d t o t h e r e l a t i v e permeabi l i ty t a b l e , before t h e r e s u l t s of Leach e t a1 (15) could be success fu l ly reproduced.

5.0 CONCLUSIONS

T h e w o r k d e s c r i b e d i n t h i s p a p e r l e a d s u s t o t h e f o l l o w i n g m a i n conclusions : - (1) The use of single-point upstream weighting causes seve re composi t ional d i spe r s ion , p a r t i c u l a r l y when s imulat ing FCM, MCM and NM displacements. ( 2 ) A dynamic w e i g h t i n g scheme h a s been d e v e l o p e d , which u t i l i s e s t h e p r o f i l e of t h e v a r i a b l e concerned, t o determine the optimum weighting f a c t o r s i n t i m e a n d s p a c e . It e x p l o i t s t h e c lass ica l f e a t u r e s of mid-stream, two-point ups t r eam, and s i n g l e - p o i n t u p s t r e a m s c h e m e s , b a s e d on t h e p rope r t i e s of t h e p r o f i l e . ( 3 ) The t e c h n i q u e h a s been s u c c e s s f u l l y t e s t e d o n M C M , FCM a n d NM d i s p l a c e m e n t s , a n d y i e l d s r e s u l t s which, i f t h e i r a c c u r a c y i s t o be reproduced on a " f u l l y upstream" model, would r e q u i r e s e v e r a l times a s many g r i d blocks. (4) The method i s supported by geometr ical arguments, and can beimplemented e a s i l y i n multi-dimensional s imulators .

437

ACKNOWLEDGEMENTS

The a u t h o r s would l i k e t o t h a n k t h e UK Department of Energy and Imperial College of Science and Technology f o r s u p p o r t i n g t h i s r e s e a r c h , P r o f e s s o r C.G. Wall, D r . R.A. Dam f o r t h e i r cont inuing i n t e r e s t , a n d Hiss M. Green of ERC f o r he r pa t i ence i n typing the var ious d r a f t s of t h i s paper.

REFERENCES

1. MCFARWE, R.C., MUELLER, T.D., MILLER, F.G.; "Uns teady-S ta t e D i s t r i b u t i o n s of F l u i d C o m p o s i t i o n s i n Two-Phase O i l R e s e r v o i r s Undergoing Gas I n j e c t i o n " , S o c i e t y of Petroleum Engineers J. (March, 1967), 1, 61-74. 2. PRICJ3,H.S. and DONOHUE, D.A.T., "Isothermal Displacement Processes wi th In t e rphase Mass Transfer", Society of PetroleumEngineers J. (June 1967) 1, 115-130.

"Fundamentals of Numerical Reservoir Simulation", E l s e v i e t , Amsterdam, (1977) 65-82 4. LANTZ, R.B. " Q u a n t i t a t i v e Evaluation of Numerical Diffusion (Truncation Error)", s o c i e t y of PetroleumEngineers J. (1971), 11, 315-320; Trans. AIME, 251

"An Improved Numerical Techn ique f o r S o l v i n g Mult i -Dimensional M i s c i b l e Di sp lacemen t E q u a t i o n s " , S o c i e t y of P e t r o l e u m E n g i n e e r s J. (1977) , 2, 277-284; Trans., AIME, 251 6. VAN QUY, N., SIMANWUX, P. and CORTEVILLE, J. ; "A Numerical Study of Diphasic Multicomponent Flow", S o c i e t y of Pe t ro l eum Engineers J. (Apr i l 1972), 12, 171-184; Trans., AIME 253 7. LAUMBACH, D.D.; "A H i g h A c c u r a c y , F i n i t e D i f f e r e n c e T e c h n i q u e f o r T r e a t i n g t h e Convection-Diffusion Equation", S o c i e t y of P e t r o l e u m E n g i n e e r s J . , (1975) -, 15 517-531 8. GARDNER, A.O. and P E A C W , D.W. and POZZI, A.I.; "Numerical C a l c u l a t i o n of M u l t i d i m e n s i o n a l M i s c i b l e Displacement by t h e Method of C h a r a c t e r i s t i c s " , S o c i e t y of P e t r o l e u m E n g i n e e r s J. (19641, A, 26-36 9. TODD, M.R., ODELL, P.M., and HIRASAKI, G.J. ; "Methods f o r I n c r e a s e d Accuracy i n Numerical Reservoir Simulators", Society of Petroleum Engineers J. (1972), l.2, 515-530 10. BANKS, D., 'CHESHIRE, I.M., and POLLARD, R.K.; "A Technique f o r Control l ing Numerical D i s p e r s i o n i n F i n i t e - D i f f e r e n c e O i l R e s e r v o i r S i m u l a t i o n " , P roceed ings of BAIL Conference, Dublin (June 1980). 99-203

"A Version of Tvo Poin t Upstream Weigh t ing For Use i n I m p l i c i t Numerical R e s e r v o i r Simulators", paper presented a t Soc ie ty of Petroleum Engineers 5 t h Symp. On Reservoir Simulation, Denver, 1979; SPE Paper No. 7677 12. NGHIEM, L.X., FONG, D.K., and AZIZ, K.; "Compositional Modelling w i t h An E q u a t i o n of S t a t e " , SPE Pape r 9306, SPE Annual F a l l Meeting, Dallas, Texas (September 1980) 13. HELFFERICH, F.G.; "Genera l Theory of Multicomponent, Multiphase Displacement I n Porous Media", Society of Petroleum Engineers J. (February 1981), z, Trans., AIME, 261 14. COATS, K.H.; "An Equation of S t a t e Compositional Model", Society of Petroleum Engineere J. (October 1980). 20, 363-377

3. P E A C W , D.W.

5 . CHAUDHARI, N.M.

11. WHEATLEY, M.J . ;

438

15. LEACH, M.P. and YELLIG, W.F.; "Compositional Model Studies: Co2 - O i l Displacement Mechanisms", SPE Pape r 8368, SPE Annual F a l l Meeting, Las Vagas, Nevada (September 1979) 16. SMITH, L.R. and YARBOROUGH, L.; " E q u i l i b r i u m Revapor i za t ion of Retrograde Condensate by Dry Gas I n j e c t i o n , " Trans. AIM, (1968), 243 87-94

"A Nonlinear S t a b i l i t y Analysis fo r Difference Equations Using Semi - Impl i c i t Mobili ty", Society of P e t r o l e u m E n g i n e e r s J. ( F e b r u a r y 1977) . 17, 79-91; Trans., AIME 259

17. P E A C W , D.W.;

APPENDICES

A l . S t a b i l i t y , Truncat ion Errors and Numerical Dispersion

The nonl inear convect ion equat ion is:

a x 2 . ( A \ . \ ) Truncat ion e r r o r a n a l y s i s on t h e f i n i t e d i f f e r e n c e a p p r o x i m a t i o n of t h e l i n e a r i s e d equat ion

(A I . 2 ) shows a leading t runca t ion e r r o r term of t h e form:

(A I .3) ank*a+ 2% 1

DalLm = V / A ~ [w-+) + vd+g(e--:)]. W and 8 a r e t h e d i s t a n c e and time weightinn f a c t o r s f o r C i n t h e d i f f e r e n c e - - equation. By solving t h e d i f f e r e n c e equat ion of e q u a t i o n A1.2, w e are, i n e f f e c t , solving a d i f f u s i o n - convection equat ion of t h e form:

a%- "f';: - ac. (A 1 . 4 ) . %&* ax+ at This c r e a t e s a r t i f i c i a l d i f f u s i o n of C,and is terned numerical dispers ion. Linear ised s t a b i l i t y a n a l y s i s shove that t h e numerical s o l u t i o n s are s t a b l e i f t h e w e i g h t i n g f a c t o r s l i e i n t h e r a n g e 0.5 t o 1 (Equal g r i d spacing) . Peaceman (17 ) showed t h a t a n o n l i n e a r s t a b i l i t y a n a l y s i s gave t h e same p r a c t i c a l c r i t e r i a for a f u l l upstream d i f f e rence scheme (W-1). The r e s u l t s of t h e l i n e a r i z e d s t a b i l i t y a n a l y s i s a r e summarised i n t h e diagram shown below. The approx ima te s t a b i l i t y subdomain i n which t h e dynamic weighting scheme is opera t ing is more r e s t r i c t i v e than t h a t permitted by t h e l i n e a r i z e d S t a b i l i t y ana lys i s .

A Schematic I l l u s t r a t i o n of The Numerical S t a b i l i t y Domains

S t a b i l i t y

Domain i n weighting

Domain

whichdynamic schemeoperates

Condit ional S t a b i l i t y Domain

Inc reas ing Numerical S t a b i l i t y and Trunc- a t i o n E r r o r s

la 0

0 w - I

439

A.2 Schemes

The p r e v i o u s c u r v e a n a l y s i s shows t h a t 2-point upstream weighting cannot be app l i ed on Group 2 curves. Todd e t a 1 (9) showed 2 cases which,according t o our present ana lys i s ,be long t o t h e Group 2 curves category.

Case 1: Todd e t a 1 showed an example of u n i t mobil i ty , miscible d i sp l acemen t of o i l by s o l v e n t . It i s p o s s i b l e t o c a l c u l a t e o i l r e l a t i v e permeabi l i ty which is g r e a t e r than 1 by 2-point upstream eXtraFQlatiOn,aS shown. Todde t a1 recommended s e t t i n g the spurious ex t r apo la t ed value t o t h e maximum of t h e 2 bounding v a l u e s . Our c u r v e a n a l y s i s i n d i c a t e s t h a t t h i s i s e f f e c t i v e l y downstream weighting and could create an undershoot of t h e o i l phase i f i t i s a p p r o a c h i n g z e r o s a t u r a t i o n . A m i d s t r e a m i n t e r p o l a t i o n is t h e b e s t a l t e r n a t i v e . I t i s e f f e c t i v e l y upstream,but not f u l l y upstream weighted on t h e a c t u a l curve p ro f i l e .

Case 2: Todd showed t h a t a spurious e x t r a p o l a t i o n e r r o r would occur n e a r a s h a r p WOC or GOC. T h i s i s a Group 2 curve s i t u a t i o n c rea t ed by the use of r e l a t i v e p e r m e a b i l i t y (Kr) e x t r a p o l a t i o n , w h i c h i s less c o n s i s t e n t t h a n s a t u r a t i o n ex t r apo la t ion on t h e following grounds:- (1) S a t u r a t i o n s a t t h e b l o c k i n t e r f a c e d i c t a t e t h e i n t e r b l o c k f low. However, t h e e x t r a p o l a t e d r e l a t i v e pe rmeab i l i t i e s w i l l not correspond t o a t o t a l s a t u r a t i o n of 1. ( 2 ) It c r e a t e s , o r accentuates t h e c r e a t i o n of ,a Group 2 p r o f i l e (which i s no t amenable t o l i n e a r ex t r apo la t ion ) . I n t h i s example, a Group 1 s a t u r a t i o n p r o f i l e exists. Had s a t u r a t i o n ex t r apo la t ion been used, Krw a t 1124 would be 0.7 in s t ead of t h e spurious negat ive value. ( 3 ) T y p i c a l l y , f o r a water f looding problem, Group 2 s a t u r a t i o n p r o f i l e s e x i s t above t h e shock f r o n t s a t u r a t i o n value. The corresponding K r w p r o f i l e s

Addit ional Notes on 2-Point Upstream Weighting and Mid-Point W e i g h t i n g

1.1 . . . , . . . . . LANGSRUD DA TA

Figure LO - Comparison of w a t e r s a t u r a t i o n p r o f i l e s f o r v a r i o u s mobil i ty evaluat ion schemes (black o i l model). (a) Spivak d a t a (SPEJ, February 1977). (b) Langsrud d a t a (Nolen and Berry, SPEJ June 1972).

4 4 0

have s t r o n g e r Group 2 c h a r a c t e r i s t i c s . The f a c t that e x p l i c i t 2-point Kr e x t r a p o l a t i o n d o e s n o t c a u s e i n s t a b i l i t y is p r o b a b l y d u e t o t h e non-sharpening n a t u r e of t h i s s a t u r a t i o n range. On the o ther hand, Group 1 curves (which are not amenable t o in te rpola t ion) a r e present around the flood f r o n t . The s a t u r a t i o n r a n g e b e l o w t h e s h o c k f r o n t s a t u r a t i o n i s self-sharpening, thereby a g g r a v a t i n g t h e weakness of i n t e r p o l a t i o n . T h i s supports the evidence that mid-point weighting i s unstable.

Figure 1Oa i l l u s t r a t e s some ueaknesees of using Kr e x t r a p o l a t i o n , normal ly n o t observable without imposing f r o n t a l control . An e x p l i c i t vers ion of t h e dynamic weighting scheme, using 2-point s a t u r a t i o n e x t r a p o l a t i o n a t t h e c o n t r o l l e d f r o n t and midstream weighting everywhere else, i s i l l u s t r a t e d i n Figure lob.

NUMERICAL METHODS 4 4 1

INTERPHASE MASS TRANSFER EFFECTS IN IMPLICIT BLACK OIL SIMULATORS

D. BANKS and D. K. PONTING

Atomic Energy Research Establishment, Hanuell, Oxfordshire, Enghnd

ABSTRACT

Mass t r a n s f e r may be described i n black o i l s imula tors by allowing o i l and gas t o e x i s t i n both l i q u i d and vapour phases. A n q f f i c i e n t f u l l y implicit method of simultaneously modelling bubble and dew poin t is described. A subtracted total gaa formulation is found to combine the advantages of the free and total gas approaches. A partial re-solution algorithm opt ion is descr ibed which I n t e r p o l a t e s bettween total- and nore-solution logic. The d l s p r e i o n o f di88olved gaa and vapourlsed o i l is discussed.

B l a c k o i l s imulators , charac te r i sed by the treatment of j u s t two hydrocarbon components, have t r a d i t i o n a l l y been more concerned w i t h d i8placemnt mechanisms tha t the PVT dominated processes of EOR 8tudies . C-slt ional effects are modelled simply by mass t r a n a f e r between l i q u i d and vapour phases. I n th i s paper we discuss a n u m b e r o f v p e c t s ofma8stransferinblackoilsimulator8, mainly f romthe s tandpoint of a f u l l y implicit formulation.

Black o i l models genera l ly descr ibe the concentrat ion of dissolved gaa i n the reservoir l i q u i d by t h e bubble poin t pressure, Pb, or the rrolution gaa-o i l ratio, R . The q u a n t i t y of o i l i n t h e vapour is described by t h e dew poin t pressure , Pa, or t t e vapour oil-gaa ratio r or R , [1,23. The vapour oil-gru ratio is general ly preferable, aa it enabfes thx vapour t o be described i n reglons o f low pressure and re, for which no dew p o i n t exists. The ‘ o i l ’ and ‘gaa’ M y be any two groups of hydrocarbon components, or t r u e stock tank o i l and gaa.

I n a genera l black o i l model t h e r e are therefore f i v e independent var iab les per cell: P , Pb or Re, P or re, Sw, S . The equation6 determining P and r8 involve df f fus ion , convection and &EI transfer rates. A t p resent , t h e extra c a p l t a t i o n a l effort required t o so lve the four th and f i f t h equat ions is prohib i t ive . The three equation p i c t u r e may be res tored by employing bubble and dew p o i n t models, d i n g two o f t h e var iab les dependent on t h e primary ones. A v a r i a b l e s u b s t i t u t i o n method for simultaneouslymodellingofp and rs v a r i a t i o n s i n an implicit black s imulator is descr ibed i n Sect ion 2. mil% thi8 cannot y i e l d the d e t a i l e d d a c r i p t l o n obtrined from a t r u e multi-coaponent compositional s imulator , the greater computational

would d

4 4 2

ef f ic iency enables detailed f u l l f ield s t u d i e s t o be performed. F a c i l i t i e s such as f a u l t connections and d i r e c t i o n a l r e l a t i v e permeabilities are then a v a i l a b l e for s t u d i e s involving mildly v o l a t i l e o i l s or dew poin t t r a n s i t i o n s , and numerical dispers ion may be limited by the use of amall g r i d blocks. I n our experience var iab le s u b s t i t u t i o n is the only method of modelling mass t r a n s f e r which does not l i m i t the a b i l i t y of the s imulator t o t a k e l a r g e time steps, although other methodg are possible i f the time step length is restricted.

The quant i ty of gas e x i s t i n g i n s o l u t i o n may be t y p i c a l l y 50-1000 times g r e a t e r than tha t e x i s t i n g i n the vapour phaae. The quest ion arises aa to whether t h e maas conservation equation for gas should involve a l l t h e g a s , or j u s t the f r e e component. Or ig ina l ly a free gas formulation waa used i n PORES [lo]. I n solving t h e material conaervat ionequat ions, however, aco lumnsumcondi t ion is imposedwhichat temptsto zero the sum of errors on diagonal planes of cells within the reservoir model. This is p a r t i c u l a r l y important i n the sequent ia l method of so lv ing t h e l i n e a r matrix equations. For a free gas formulation, the column sum condit ion represents an attempt t o c o n s e n e free gas, a conservation condi t ion v io la ted when in te rphase maas t r a n s f e r occurs. A total gaa formulation avoids t h i s , bu t , due t o the l a r g e dissolved gas cont r ibu t ion , leaas t o poorly conditioned equat ions which t h e sequent ia l method frequent ly fails t o solve. A subtracted to ta l gaa method which overcomes t h i s is described i n Sect ion 3. Such methods may be important f o r compositional s imulators aa the increasing number of equat ions renders f u l l y simultaneous s o l u t i o n methods imprac t ica l ly expensive.

Gas must come out of s o l u t i o n when the o i l pressure crosses the bubble poin t , bu t the re-solutionof gasdepends on t h e p r e s e n c e o f gas i n c o n t a c t w i t h l i q u i d o i l , and the rate at which so lu t ion occurs . Experiment [7] i n d i c a t e s that, where an in t imate gas-oil contact e x i s t s , equi l ibr ium is established on a timescale short compared t o those t y p i c a l l y involved i n reservoir engineering. The determining factor i n gas so lu t ion is the rate a t which gas d i f f u s e s through l i q u i d o i l . I n PORES, and other black o i l s imulators , t w o a l t e r n a t i v e s are a v a i l a b l e f o r the t reatment o f gas so lu t ion . No- re- so lu t ion assumes that dissolved gaa does not d i f f u s e through o i l , so that a layer of sa tura ted o i l w i l l immediately b u i l d up at a gas-oil i n t e r f a c e and prevent f u r t h e r so lu t ion . While t h i s opt ion is l o g i c a l l y cons is ten t , it is u n r e a l i s t i c f o r res idua l o i l droplets, and w i l l overest imate gas cap sizes. Using typical d i f fus ion c o e f f i c i e n t s , it can e a s i l y be shown t h a t a Inm d r o p l e t w i l l reach 991 of its u l t i m a t e dissolved gas concentrat ion i n less than 24 hours.

Total re-solution l o g i c assumes that interphase equi l ibr ium always exists i n each cell, so that free gas may only exist w i t h s a t u r a t e d o i l . This aSSumptiOn of instantaneous equi l ibr ium is usua l ly also made i n compositional s imulators . and e s s e n t i a l l y implies instantaneous flow of dissolved gaa through o i l . I n practice, however, vapour invading o i l is l i k e l y to f inger or channel, r e s u l t i n g i n the gas bypassing some of the o i l . Free gas may then pass through a cell without Coqpletely s a t u r a t i n g the o i l . I n Sect ion 4 we descr ibe a partial re-solution opt ion which enables the engineer t o set a re-solut ion or equi l ibr ium f r a c t i o n for each cell, the f r a c t i o n o f the l i q u i d hydrocarbon i n a cell i n contac t w i t h the vapour. This can still be f u l l y expanded i n a three v a r i a b l e formulation, and is similar t o the trapping f r a c t i o n approach.

Simulators which permit gas s o l u t i o n have d i f f i c u l t i e s w i t h the d ispers ion of dissolved gas and cell size dependence. These problem8 are, i f anything, more severe for vapourised o i l . This is due to the non-specification of the d e t e d n i n g d i f f u s i o n rates, so that changes i n R and r are M i a t e l y p r o m a t e d across cells. I n a sense, t h e artificial'cell k u n d a r i e s introduced by t h e s imulator prevent d i spers ion f r o m b e i n g t o t a l , rather than causing it. NO re-solut ion logic has an equivalent problem i n t h a t gas is evolved from undersaturated o i l when flow

Those are the nore-solut ion and total- re-solut ion opt ions.

4 4 3

occurs across an R gradien t . It is possible t o c o n t r o l th i s d ispers ion for t h e simple case of fret gas invading o i l by only allowing R to rise due t o contac t w i t h f r e e vapour. However, such methods run i n t o t rouble &en a d r y vapour or dissolved gas s l u g is propogated, as t h e y modify the s l u g shape by sharpening t h e lead ing edge.

MODELLING BUBBLE AND DEW POINT VARIATIONS

Two main approaches e x i s t t o modelling mass t r a n s f e r i n black o i l s imulators : the v a r i a b l e s u b s t i t u t i o n method [4 ,5] , and one cell methods i n which cell properties are modified t o be c o n s i s t e n t w i t h t h e s o l u t i o n i n terms of a f ixed set of v a r i a b l e s [3]. These correspond t o s a t u r a t i o n pressure and flash technique8 i n compositional s imulat ion [ 5 , 6 ] . Both methods have been used i n PORES, and v a r i a b l e s u b s t i t u t i o n has proved super ior , al though it involves organisa t iona l d i f f i c u l t i e s i n keeping trackof whether t h e t h i r d s o l u t i o n v a r i a b l e is S P orr The cell by cell technique r e t a i n s Po, Sw and S as s o l u t i o n varia%;es, and a d j u s t s R (Pb) to s a t i s f y phase equi l ibr ium. If gas i a e c t i o n occurs i n t o undersaturated 011. for example, R;I is increased, as i n the pseudo s o l u t i o n gas method. Unless th i s is done exact ly , a negat ive gas s a t u r a t i o n is obtained on t h e subsequent i t e r a t i o n and general ly causes m a t e r i a l balance errors. This can be overcome by using a one cell Newtonian i t e r a t i o n toexact m a t e r i a l b a l a n c e t o f ixthe Rs change p r e c i s e l y . This y i e l d s a working scheme, b u t runs i n t o convergence problem on long t i m e steps, as the pressure changes which occur when free gas goes i n t o s o l u t i o n d i s t u r b the in te rb lock flows i n a manner not incorporated i n t o the Jacobian of the newtonian i t e r a t i o n . I n the undersaturated o i l case the gas equat ion is being converged t o a known so lu t ion , S - 0; more p r e c i s e l y , the bubble poin t is implicit, but no t f u l l y expanded.

V a r i a b l e s u b s t i t u t i o n does not attempt t o r e t a i n gas Satura t ion as the third v a r i a b l e a t a l l times. Depending on the condi t ions i n a cell, gas 8atura t ion , bubble p o i n t or vapour oil-gas ratio, r , may be the primary s o l u t i o n var iab le . I n each case it is c r u c i a l that the func t fona l dependence of the secondary variables, (such as Pb and r i n a cell i n which S is the primary v a r i a b l e ) , and of funct ions of t h e s e secondary bariables, is knoun 8nd included i n the Jacobian. The omission of apparent ly minor terme from the Jacobian can l i m i t convergence of t h e non l i n e a r equat ions unacceptably. However, the exact c a l c u l a t i o n of in te rb lock and w e l l f lows a t the advanced time level, which is obtained w i t h increas ing accuracy as the Newtonian i t e r a t i o n converges, prevents i n s t a b i l i t i e s which can occur using first order approximations t o the implicit flows [ll].

b 8'

9

Assuminginterphase equi l ibr ium, there areonlythreepossibilities f o r t h e state of a cell:-

(i) Vapouronly. Po, Swandr a r e s o l u t i o n v a r i a b l e s , w i t h S -1-S andPb-Po s o w

are Solut ion g

( ii ) Liquid and vapour hydrocarbon A t e s e n t . P S and S variables, w i t h Pb-Po, rs-rs ( Po+Pcq?kg fi

s and P are s o l u t i o n var iab les , w i t h (iii) Liquid only. Po, b

( 0 ) ) ......................... (1) s a t S -0 and rS-r (Po+Pcog g s

r sat( P ) is the curve descr ib ing the oil-gas ratio for vagour in equi l ibr ium w i t h l f q u i d 811.

4 4 4

The maas conservation equations take the form

T+AT I ( 2 )

1 TAT TAT R - -[m. - mT] - qJ - & f n j ............

j n j AT J

j-l,..,N , N the number of cel ls .

Elements of the residual, R, mass terms, w e l l term and flows have a three vector formr-

R j - q j W + R s q O 1 j w

............... ( 3 )

where fo are the free o i l , water and free gaa flows given by Darcy's Law i n t%' us& way, "Ad g,w are the corresponding w e l l terms.

The equatioagiven by R ( X w A T a are solved by Newtonian iteration, derivatives being taken w i t h respect t o the primary solution variables for each cel l . Transitions may occur between the three states of (l), on the -is of the cur ren t approximation t o the advanced time step solution, as follows:-

fw and fg

s a t s a t From s t a t e (i), if rs)rs (Po+P (1-5 ) ) . Set rs-r ,S -6,

Prom s t a t e (ii), i f So<O. Se t rg-rs (Po+P (S ))-c,Sg-l-Sw,

From s t a t e

cog w 0 9 . change t o (ii)

s a t

cog g change t o (i)

(ii), i f S < O . Se t S -O,Pb-Po-c, change t o ( i i l ) 9 g

From s t a t e (iii), i f Pb)Po. Set Pb-PO,Sg-~, change t o ( l i )

...................... ( 4 )

This is essentially a combination of the methods proposed by Cook et a1 [ 2 ] and Spivak and Dixon [l],

The extra cost of aodelling r variation is s m a l l , aa cel ls i n which r is the Solution variable would o t h e h s e be repeatedly solved for a constane gas saturation of zero. When re is not the prirary variable, the effeck is merely t o add extra terme t o the Jacobian. This enable. effects such as the vapourisation of residual o i l into re-injected gas, an EOR type process expected t o some extent i n most reservoirs with gaa injection, t o be followed, aa w e l l as gaa solution and a primary recovery waterflood.

4 4 5

TBE SUBTRACTED 'IDTAL GAS PO-TION

The r e s i d u a l i n (3) i n c l u d e s t e for to ta l o i l , water and total gaa. The corresponding free gaa r e s i d u a l is?'-R "-R R '. A free gaa f o m l a t i o n was o r i g i n a l l y used i n PORES. Both thd it.&$ l l n e a r solver and s e q u e n t i a l method u s e column sum methods to preserve zero r e s i d u a l s u r - s f f e c t i v e l y material balance on d i a g o n a l planes of cells. This c o n s t r a i n t , which g e n e r a l l y speeds convergence, haa l i t t l e v a l u e i f a free gas fo rmula t ion is used, as free gaa r e s i d u a l s w does not correspond t o material b a l a n c e i f s a t u r a t e d o i l is p r e s e n t .

It is possible no t t o d i f f e r e n t i a t e t h e R t e rm i n the r e s i d u a l , l e a d i n g t o a eet of equa t ions , which, i f so lved exactly, a r e e t q u i v a l e n t to those ob ta ined from a total gaa r e s i d u a l . The Jacob ian is t h e n n o t the derivative of the r e s i d u a l , and acme of the convergence properties of the f u l l Newton method are lost.

The a l t e r n a t i v e is t o u s e a s t r a i g h t f o r w a r d total gas formulat ion. This is posn ib le for s imultaneous s o l u t i o n methods, b u t the s e q u e n t i a l method fails completely. The dissolved gaa c o n t r i b u t i o n swampa the free component i n t h e equa t ion determining t h e gaa s a t u r a t i o n .

The S e q u e n t i a l method of s o l v i n g the l inear eqUatiOM, i n the simple case of a non- condensate gaa o i l system, invo lves the matrix d e c o l p o s i t i o n r -

........... ( 5 ) O I I J g r p Jg,gl - I O llJg,p 919

J 0,p J 019 1 JolP-DJglp

J

The elements of Re are g iven by ( R ) Ix3

- S R and D is a d iagona l ma t r ix , such that The change i n ASg ov&iaN&Anfat; i t e r a t i o n i 8 X -6( As ), dofinad by

9.9-Jo.g. 9 9

J X - R - R t g ................................. (6) 9,g 9 9 x

where

Rtg X is approximate, given by R: - J ( Jo , p-DJg, p)-bo-D(Rf<RsXe

I f a free gas fo rmula t ion is used, X is g iven b~ 9

Zr or8 arise i n the e v a l u a t i o n of the right-hand aide of (b). I n the free gaa cam R f g c o n s i s t s f a n approxisate m a t r i x a c t i n g o n R -D R , whi le i n a total g u &-lation R " is g iven by a approrirate m a t r i x %tini%n Ro-D( Rf +R R ) . If2 the ersors i n the l i q u i d and vapour flaw are camQarab1e. Rxg I R8R , ktR 8 .Y O( 10 - 10 ). The right-hand s i d e of the equa t ion d e f i n i n g gaa s a t u r a 6 o M cowk8, i n the total gaa caae, of two large c a n c e l l i n g term, one of which i 8 agproriute, and the r e s u l t i n g v a l u e s of As are less a c c u r a t e than i n the f n e QM C a m

9

4 4 6

Errors i n S are fed back i n t o the o i l r e s i d u a l v i a So- 1-s -S

The advantages of both formulat ions may be combined i n a subtracted total gas formulation, i n which the gas equat ion r e s i d u a l is

and the i t e r a t i o n of ten diveqges. w g'

( 8 ) R - R - R'"~R ..*.....................*....... s t g g s 0

The choice of R sub is rather critical, and s e v e r a l a l t e r n a t i v e s have been tr ied. The best eema 80 be$, updated by the predictor a t the start of each tim step. The USC d R rather t h a n z s can increase run times by 50%. The continuous updating of R~ a d seem e s s e n t i a l .

Anadvantage o f t h i s m e t h o d i s t h a t i s o l a t e d d i s s o l v e d gaa changes, s u c h a s those due t o gaa i n j e c t i o n , s tand o u t over the R subt rac t ion , causing r e s i d u a l s which the s imulator converges o u t accura te ly . all that is remved is the bulk of the i n i t i a l dissolved gas which otherwise causes the gaa equat ion t o be a near m u l t i p l e of the o i l equation. The s e q u e n t i a l method can still fa i l when a l a r g e i n i t i a l R gradien t exists across t h e reeerpoir, i n which case a f u l l y simultaneous s o l u t i o n k t h o d must be used.

A n sub

THE S O u l T I O N OF GAS I N O I L

Black o i l s imulator s h a v e tended not t o p r o v i d e the e n g i n e e r w i t h v e r y comprehensive facilities for i n v e s t i g a t i n g gaa Solut ion effects. P a r t l y , th i s is due t o a lack of knowledge concerning the processes involved. It seem clear that r e s i d u a l o i l droplets w i l l e q u i l i b r a t e quickly, butal metre diameter area of o i l w i l l take over a Y e a r to s a t u r a t e i f f r e e gaa channels past it. Providing no- and total- re-solut ion opt ions enables the s e n s i t i v i t y of the problem t o gas s o l u t i o n effects t o be es tab l i shed . If t h i s is a major effect, however, as i n the Odeh test problem [9], there are no facilities for h i s t o r y matching. I n p a r t i c u l a r , the degree of equi l ibr ium between phases w i l l be d i f f e r e n t for r e s i d u a l o i l i n a gas cap from that a t t a i n e d i n t h e case of gas i n j e c t i o n i n t o undersaturated o i l , and these processes may occur i n the same study.

The PORES partial re-solut ion opt ion al lows the user t o d e f i n e a re-solut ion or equi l ibr ium f r a c t i o n , f , o f the o i l i n a cell which is i n close contac t w i t h vapour. For a time step from T to *AT, t h e partial re-solut ion opt ion r a y be sunmurised as;-

Undersaturated o i l , Pb is s o l u t i o n v a r i a b l e

If

I f

T+AT T+AT then sT+ATIOl pT+AT_pT PT < Pb <Po

bmin g bmin bmin

T+ATIO T+ATlpT+AT

9 bmin b then S I P

Saturated o i l , S is so lu t ion v a r i a b l e g

T+AT T+AT T+ATIMin T I f S >O then Pb -P ,P 9 0

4 4 7

B u b b l e po in t t r a n s i t i o n , gas appearing

T+AT TtAT T+AT_Min T 0 bmin

set t o E,P -P ,P 9 b I f Pb

................. ( 9 )

Pban is t h e minimum bubble p o i n t a t t a i n e d by the cel l during the s imulat ion. The q u a n t i t y of dissolved gas i n t he cell and in te rb lock flows is obtained as a weighted average using

a c t i n g as bubble poin t for the 'trapped' or non-equilibrium o i l f r a c t i o n . This model y i e l d s to ta l and no-resolution as the limits of f-1 and 0 respec t ive ly . The r value can be followedfir t he vapour as described i n Sect ion 2. A l l function& d e r i v a t i v e s can be expanded i n the JaCobianInlkrms of the pr- var iab les .

There are s e v e r a l respects i n which t h i s partial re-solut ion scheme is less than ideal I -

( i ) If pressure drops through the bubble p o i n t of the by-passed o i l , and gas comes out of s o l u t i o n a t less thanmobile s a t u r a t i o n , then it w i l l not re-dissolve i n the non-equilibrium f r a c t i o n or re-preseurisat ion. This could be allowed, bu t it seem u n r e a l i s t i c t o ascribe d i f f e r e n t behaviours t o gas at j u s t under and over critical s a t u r a t i o n . I n addi t ion , discont inuous changes i n the func t iona l form of the r e s i d u a l can s l o w convergence.

(ii) When f inger ing or channel l ing occurs, it would be expected that t ransverse s a t u r a t i o n would occur behind the f r o n t . This does not occur i n th i s model.

Other possibilities exist for partial re-solut ion opt ions, such as re-solution i n r e s i d u a l o i l . However. when gaa displacement is stable, due t o g r a v i t y seg- rega t ion , t h i s is equiva len t t o total re-solut ion. For gas i n j e c t i o n , r e s i d u a l o i l s a t u r a t i o n is r a r e l y a t t a i n e d . There is also the d i f f i c u l t y of i d e n t i f y i n g t h e r e s i d u a l o i l i f the cell is subsequently f lushed w i t h mobile o i l .

It would be possible t o have a similar opt ion f o r o i l vapourisat ion. I n most condensate s t u d i e s , however, o i l s a t u r a t i o n s remain less than critical, so t h a t equi l ibr ium is a reasonable assumption. The equivalent of g u i n j e c t i o n r a r e l y arises.

DISPERSION PROBLElls I N MASS TRANSPER

Varia t ions i n Rs and Is, due t o convection and maas t r a n s f e r usua l ly show dispers ion effects. When, for example, the bubble p o i n t rises i n a cell due t o gas s o l u t i o n t h i s rise is assumed t o occur evenly throughout the e n t i r e cell, and is comunicated t o its neighbours by o i l flows. The r e s u l t i n g rise i n R for the neighbouring cell s is then passed, i n the same time step, to t h e next cell. I n cases of high throughput ratio, a considerable f r a c t i o n of t h e reservoir r a y need to be s a t u r a t e d before free gas appears i n the i n j e c t i o n cell. This problem might be expected t o be r a t h e r less severe i n IHPES type simulators , which e f f e c t i v e l y impose an upper l i m i t of AX/AT on t h e speed a t which dissolved gas or vapourised o i l may propopate, as d i f f u s i o n is limited to one block per time etep. However, such a simulator i e l i k e l y t o t a k e more steps than a f u l l y implicit one t o so lve a given problem, o f f - s e t t i n g the advantage of lover dispers ion per time step.

4 4 8

For simple gas i n j e c t i o n i n t o undersaturated o i l , it is f a i r l y easy t o prevent th i s d i s pers ion by assuming that gas passing i n t o a cell s a t u r a t e o i l only as it overr ides it, so t h a t an increased R value w i l l not appear a t the downstream i n t e r f a c e u n t i l the cell is s a t u r a t a . The result. of such a technique on the cam 2 odeh problem are shown i n f i g . 1. However, t h i s method of d ispers ion c o n t r o l runs i n t o problems when the convection of s l u g s is considered. P a r t i c u l a r l y i n the came of condensate reservoirs, where gas i n j e c t i o n may be cont ro l led by production rates and s a l e a c o n t r a c t s , the r e s u l t i n g r d i s t r i b u t i o n s may not have simple shapes. Front sharpening methods w i l l tend to d i s t o r t such s l u g s by sharpening the leading edge. Interblock flow schemes other than upstreamlng w i l l y i e l d unphysical r e s u l t s i f f lowoccurs fromacellof zero re t o o n e o f f i n i t e r b u t upatreaming causes unacceptable artificial diffu8ion. 8'

CASE 2, GOR VS T I M E

cy 0 U

0 1 2 3 4 5 6 7 8 9 10 0

T I M E I N YEARS

Figure 1.

449

W e can present no simple s o l u t i o n t o the d ispers ion problem, and it may be that it is inherent i n the concept of using a dew or bubble poin t model r a t h e r than a separate equat ion. The b a s i c a l l y convect ive na ture of r and R transport suggests a point following algorithm, although those s u g g e s t e d t o date are not f u l l y implicit. It may be cheaper, however, to add an extra t ransport- type equat ion t o t h e t r a d i t i o n a l black o i l p i c t u r e than t o go t o the number of cells required t o reduce dispers ion t o an acceptable l e v e l .

CONCLUSIONS

(i) It is possible t o model gas condensate and bubble poin t e f f e c t s simultaneously i n an e f f i c i e n t genera l purpose black o i l s imulator . Minor o i l vapouri- s a t i o n and condensate effects w i l l occur i n many s t u d i e s , and these can be included a t l i t t l e extra cost.

( ii) There is a need t o provide engineers w i t h a more flexible method of matching gas s o l u t i o n e f f e c t s . A re-solut ion f r a c t i o n approach enables o i l bypass and channel l ing e f f e c t s t o be included, and has a simple funct iona l form which is p a r t i c u l a r l y s u i t a b l e for i m p l i c i t s imulators . No- and total- re-solut ion opt ions are obtained as l i m i t i n g caees.

(iii) For s e q u e n t i a l methods, a cont inuously modified subtracted total gas formulation is preferable to either total or f r e e gas formulationn.

( i v ) A l l bubble and dew poin t models are a poor excuse f o r so lv ing a dissolved gas or vapourised o i l equat ion. I n p a r t i c u l a r , numerical d i spers ion of vaporised o i l and d isso lved gas can be s i g n i f i c a n t . This can be c o n t r o l l e d i n Simple cases, such as dry gaa invading undersaturated o i l , b u t d i spers ion c o n t r o l methods may dis tor t t h e shape of convected s lugs . This may be p a r t i c u l a r l y important for gas i n j e c t i o n i n t o condensate reservoirs.

b I r ~ a ~ e ~ ~ ~ r f O ~ u ~ ~ ~ e V o l u m e factor for phase p, def ined aa , where p is f l u i d dens i ty

P /P P p P

I b xb. p rock

b Pr

f ' I The flow rate, measured i n terms of sur face volume, of phase p, from cell n n j t o cell j

N : The numbsr of a c t i v e cells i n the reservoir

P I The bubble poin t pressure of cell j

P : The dew p o i n t p r e s r u r e of cell j

P I The pressure of phase p i n cell j

S : The s a t u r a t i o n of phase p i n cell j

b j

d j

P j

P j P

q jw

R j P

: The rate of flow, measured i n term of sur face volume, from w e l l w t o cell j

: The r e s i d u a l of the maas convervation equat ion for cell j , phase p

4 50

J 'j : The element of the Jacobian, a < i a S j

x : The pth primary solution v a r i a b l e for cell j P,V

Pj

:The minimum Re va lue i n the reservoir model

: The mean Rs value i n the reservoir model

s

Rs

REFERENCES

1. SPIVAII. A. and DIXON, T.N.; "simulation of gas condensate reseervoirs", SPE4271, Proc. 3rd symp. on Numerical Simulation o f Reservoir Performance, Houston, 1973.

2. COOIC, R.E., JACOBI, R.H. and RAWZSH, A.B. J "A beta-type reservoir Simulator for approximating compositional e f f e c t s during gas in jec t ion" , Soc.Pet.Eng.J., (06. 1974), 471-481

3. AU, A.D.K., EERIE, A, RUBIN, 8. and VINSOM!, K. ; Techniques for f u l l y -licit resemoir simulation", Proc. 55th Ann. P a l l Conf. and Exhibi t ion of SPE, milas, 1980.

4. BANSAL, P.P. et al; "A s t r o n g l y coupled, f u l l y implicit, t h r e e dimensional, t h r e e phase reservoir s imulator , SPE8329, Proc. 54th Ann. F a l l Conf. and Exhibi t ion o f sPE, Las Vegas, 1974.

1980 ), 363-376 5. COATS, K.H.; "An equat ion of state compositional Podel", Soc.Pet.Eng.J., (Oct.

6. NGEEIU, L.X., PONG, D.K. and AZIZ, K.; "Compositional modelling w i t h an equat ion of state", SPE9306, Proc. 55th Ann. P a l l Conf. and Exhib i t ion o f SPE, milas, 1980. NO=, J.S.; "Numerical s imulat ion of compositional phenomena i n petroleum reservoirs", SPE Reprint Ser ies , No. 11, (1973). 269.

7. RAIIIOM)I, P. and mRCAS0, U.A.; "naes transfer between phases i n a porous medium: A study of equilibrium", Soc.Pet.Eng.J. (March 1965), 51-59, Trans. AIM! 234

8 , SAWDRu, R. and NIELSEN, R.; " ~ y n d c s of petroleum reservoir. under gas in j ec t ion" , Gulf Pub.Co., 1974

ODEE, A; "Comparison of solutions t o a three dimensional black-oil reservoir simulat ion problem", J.Pet.Tech., (Jan. 198l ) , 13-25

9.

10. CBESHIRC, 1.14. et al; " ~ n efficient f u l l y implicit simulator", -79. Proc. European Offshore Conference and Exhibi t ion, London, 1980, 325

11. COATS, K.H.; "Reservoir simulation: A genera l model formulation and associated physical/numsrical sources of i n s t a b i l i t y " , Proc. BAILl Conf., Dublin, June 1980. 62-76, ed. Uiller, J.J.H., Bode Press .

EXPERIMENTAL TECHNIQUES 451

A NOVEL DEVICE FOR CO, CORE FLOODING

VOLKER MEYN

Institut f i r Tiefbohrkunde und Erdolgewinnung der TU clmrsthal

ABSTRACT

A newly d e v e l o p e d core f l o o d i n g a p p a r a t u s is described. The appa-

r a t u s p e r m i t s t h e c o n d u c t i n g of f l o o d e x p e r i m e n t s w i t h l i v i n g o i l

w i t h i n a p r e s s u r e r a n g e be tween 1 and 600 bar a t f l o o d i n g rates

from 1 t o 50 cm3.h-l. During t h e e x p e r i m e n t , t h e mass f l o w of C02

a t t h e i n p u t is h e l d c o n s t a n t . The f o l l o w i n g d a t a a r e t h e r e b y mea-

s u r ed :

o i l p r o d u c t i o n , water c u t produced , number of moles of g a s pro-

d u c e d , g a s c h r o m a t o g r a p h i c a l g a s a n a l y s i s u p to . C7, a n a l y s i s of

s t o c k t a n k o i l up t o C 2 6 , p r e s s u r e d i f f e r e n c e .

Because t h e per fomance of core f l o o d i n g e x p e r i m e n t s i s f e a s i b l e on-

l y w i t h i n a c e r t a i n l e n g t h l i m i t , whe reas t h e deve lopment of t h e

t r a n s i t i o n zone n e a r t h e minimal miscibil i ty p r e s s u r e r e q u i r e s a

f l o o d d i s t a n c e of a t l e a s t 1 m , a new e x p e r i m e n t a l s e t - u p h a s been

tested.

The f l o o d i n g e x p e r i m e n t s are t o be c o n d u c t e d w i t h t h e t r a n s i t i o n zo-

n e s p r e v i o u s l y e s t a b l i s h e d . T h i s design is based on a p u b l i c a t i o n

by WATKINS. The e s t a b l i s h m e n t of t h e t r a n s i t i o n zone d u r i n g the f l o o d

p r o c e s s is s i m u l a t e d i n a t h r e e - s t a g e mixing d e v i c e , which con-

sists of i n c l i n e d p i p e s w i t h a t o t a l l e n g t h o f abou t 6 m . The mixer

was tested w i t h o i l from German o i l r e s e r v o i r . The c o n c e n t r a t i o n s of

t h e components C 0 2 , a s w e l l a s C1 t o CZ6, were recorded gas-chroma-

t o g r a p h i c a l l y a t t h e o u t p u t of t h e mixing d e v i c e . With t h e h e l p of

t h e s e e x p e r i m e n t s , i t c a n be d e m o n s t r a t e d t h a t s u c h a mixer is ca-

p a b l e of p r e p a r i n g a p h a s e whose c o m p o s i t i o n s i m u l a t e s t h a t i n t h e

r e a l t r a n s i t i o n zone , even i n t h e v i c i n i t y of t h e minimal misci-

b i l i t y p r e s s u r e .

4 5 2

INTRODUCTION

L a b o r a t o r y i n v e s t i g a t i o n s are b e i n g per formed i n t h e c o u r s e of

a p r o j e c t /1/ c o n c e r n i n g t h e p o s s i b i l i t i e s of C 0 2 f l o o d i n g i n

West Germany. For t h e f l o o d e x p e r i m e n t s , a d e v i c e which s h o u l d

be s u i t e d f o r b o t h s l i m t u b e tests and c o r e f l o o d e x p e r i m e n t s

h a s been d e v e l o p e d . A main o b j e c t i v e is t o p r o v i d e e x p e r i m e n t a l

d a t a f o r a s i m u l a t i o n s t u d y .

A r e q u i r e m e n t f o r t h e u s e of black o i l s i m u l a t o r s is t h a t t h e t r a n -

s i t i o n zone is r e s t r i c t e d t o a s i n g l e c e l l . For t h i s r e a s o n t h e

t r a n s i t i o n zone must be s h o r t . Such a r e q u i r e m e n t c a n n o t be s a t i s -

f i e d i n t h e c a s e of c o r e f l o o d e x p e r i m e n t s w i t h p u r e C 0 2 , s i n c e

t h e c o n s t r u c t i o n of t h e t r a n s i t i o n zone r e q u i r e s . a length of a t least

1 m /2/.

WATKINS / 3 / h a s d e m o n s t r a t e d t h a t t h e r e s i d u a l o i l s a t u r a t i o n

c a n be s u b s t a n t i a l l y r e d u c e d , even i n " s h o r t " r e s e r v o i r models,

by t h e u s e of a p remix ing v e s s e l . C o n s e q u e n t l y , o n l y a s h o r t

l e n g t h is n e c e s s a r y f o r c o n s t r u c t i n g t h e t r a n s i t i o n zone i n t h i s

c a s e . Fo l lowing t h i s c o n c e p t , t h e u s e of a p remixe r s h o u l d p e r -

m i t d i s p l a c e m e n t by a medium whose c o m p o s i t i o n is s i m i l a r t o t h a t

of t h e t r a n s i t i o n zone . I n order t o d e m o n s t r a t e s u c h a p o s s i -

b i l i t y , mixer tests and comparab le s l i m t u b e e x p e r i m e n t s have

been conduc ted .

I n order t o a l low a measurement of t h e u n i t d i s p l a c e m e n t e f f i -

c i e n c y , s l i m cores a r e b e i n g employed d u r i n g an i n i t i a l phase .

However, t h e embedding, e s p e c i a l l y of s l i m c o r e s , imposes d i f f i -

c u l t i e s b e c a u s e of t h e h i g h - p r e s s u r e C 0 2 and t h e t e m p e r a t u r e s u p

t o 12OoC. I n g e n e r a l , o r g a n i c s e a l i n g m a t e r i a l s t e n d t o s w e l l

and b l i s te r unde r t h e s e c o n d i t i o n s .

A f u r t h e r d i f f i c u l t y ar ises from t h e i n v a s i o n of t h e core by t h e

a d h e s i v e . For t h i s r e a s o n a c e l l of t h e Hassler t y p e c o n s i s t i n g

o n l y of T e f l o n (PTFE) and s t a i n l e s s s t ee l h a s been d e v e l o p e d .

EXPERIMENTAL SET-UP

The s e t - u p is d e s i g n e d f o r a p r e s s u r e u p t o 6 0 0 bar and a t e m -

p e r a t u r e u p t o 150OC. It c o m p r i s e s a pumping u n i t f o r i n j e c t i n g

t h e C 0 2 , t h e f l o o d t u b e , and t h e a n a l y t i c a l equipment .

453

mesitylene 8

Fig. 1: Set up of t h e f lood device:

1 , 2 back pressure r egu la to r ; 3 m i x e r tank; 4 f lood tube;

5 C02-sto.rage vessel ; 6 displacement pumps

The se t -up ( f i g . 1) is designed such t h a t t h e C 0 2 mass flow a t

t he i n l e t is maintained cons tan t . For t h i s purpose, C 0 2 is d i s -

placed by mercury a t a cons tan t f low r a t e from a s t o r a g e vessel

( 5 ) , i n which t h e p re s su re and temperature a r e maintained con-

s t a n t .

The s t o r a g e v e s s e l is thermostated a t a temperature below t h e

c r i t i c a l va lue , i n o rder t o keep t h e compress ib i l i t y low.

The pressure i n t h e s to rage vessel is held cons tan t by means of

the .back-pressure r egu la to r (1). The pumping r a t e can be varied

wi th in a range from 0.4 t o 50 cm /h.

I n the case of t h e s l i m tube tes ts , t h e f lood tube ( 4 ) c o n s i s t s

of s t r a i g h t tube s e c t i o n s 2 m i n length connected by elbows. For

a n a l y t i c a l reasons a comparatively l a r g e diameter of 0.875 c m

was chosen f o r t he tubing. The f lood tube is immersed i n a t he r -

mos ta t ic o i l bath which can accomodate a t o t a l l ength of 30 m .

In order t o f a c i l i t a t e t he packing of t h e f l ood tube , tee f i t -

t i n g s were i n s t a l l e d a f t e r every 4 m of length . The tube bundles

can be e a s i l y emptied and t h e r e f o r e reused o f t en .

For t h e c o r e f lood experiments of t h e f i r s t phase, a diameter

of about 11 mm was se l ec t ed . The aim is t o achieve a t o t a l

l eng th of 2 m . According t o previous experience, co res up t o

3

454

200 m m i n l e n g t h and w i t h a d i a m e t e r of 11 mm c a n be d r i l l e d

w i t h o u t d i f f i c u l t y . The d r i l l i n g of l o n g e r c o r e s p r e s e n t s d i f -

f i c u l t i e s w i t h t h e s a n d s t o n e u s e d h e r e . The c o r e s e c t i o n s a r e

i n s e r t e d i n t o a T e f l o n s l e e v e . T h i s s l e e v e is i n s t a l l e d i n t h e

s t a i n l e s s s tee l body by means of p a c k e r s ( f i g . 2). S i n c e a s i n g -

l e packe r seals a t two p o s i t i o n s , i t is p o s s i b l e t o d r i l l a h o l e

th rough t h e p a c k e r down t o t h e core a f t e r t h e a s sembly , i n order

t o a t t a c h a p r e s s u r e t r a n s d u c e r .

F i g . 2 : Packer assembly:

1 c o r e ; 2 PTFE s l e e v e ; 3 packe r

I n order t o p r e v e n t l e a k a g e d u e t o t h e f l o w of t h e T e f l o n a t

e l e v a t e d t e m p e r a t u r e s , t h e p a c k e r is d e s i g n e d as an a u t o m a t i c

g a s k e t . To s i m p l i f y t h e a s sembly , t h e t u b e c o n s i s t s of f o u r

p a r t s . Each f l a n g e i n c l u d e s a p o r t f o r c o n n e c t i n g a p r e s s u r e

t r a n s d u c e r .

A n a l y t i c a l equipment

The a n a l y t i c a l equipment ( f i g . 3 ) is i n t e n d e d t o c o l l e c t s u c h

d a t a as o i l p r o d u c t i o n , b r i n e p r o d u c t i o n and g a s p r o d u c t i o n ,

a s w e l l as c o m p o s i t i o n of t h e g a s u p t o C, and of s t o c k t a n k

o i l u p t o C 2 6 .

O i l / b r i n e is s e p a r a t e d from t h e gas i n a small packed column

(1): t h e gas is s u b s e q u e n t l y wi thdrawn i n t o e v a c u a t e d v e s s e l s .

The number of moles of g a s is d e t e r m i n e d by means of a p r e s s u r e

455

F i g . 3: A n a l y t i c a l equipment :

1 g a s / o i l s e p a r a t o r ; 2 b r i n e l o i l s e p a r a t o r ; 3 sample

v a l v e ; 4 e v a c u a t e d v e s s e l s

measurement. I n order t o m a i n t a i n t h e p r e s s u r e i n t h e s e p a r a t o r

c o n s t a n t , a b a c k - p r e s s u r e r e g u l a t o r h a s been i n s t a l l e d . The

a d v a n t a g e o f s u c h a s e t - u p is t h e f a c t t h a t t h e measurement is

l a r g e l y i n d e p e n d e n t of t h e p r o d u c t i o n r a t e and t h a t t h e method

o f measurement is c u m u l a t i v e .

A b y p a s s w i t h a sample v a l v e ( 3 ) t o a g a s chromatograph ( P e r k i n

E l m e r Sigma 1) is i n c l u d e d .

I n p r e l i m i n a r y tests i t became e v i d e n t t h a t e m u l s i o n s c a n be pro-

duced w i t h t h e o i l employed. An e l e c t r o s t a t i c o i l / b r i n e s e p a r a -

to r w a s t h e r e f o r e i n s t a l l e d ( f i g . 4 ) . T h i s s e p a r a t o r h a s been

milled from P l e x i g l a s . The c h a n n e l s are p redominan t ly 5 x 5 mm

i n s i z e . The v o l t a g e of 60 V o v e r t h e p l a t e s is s u f f i c i e n t for

s e p a r a t i o n . The water c o n t e n t i n t h e s t o c k t ank o i l produced w a s

less t h a n 0 . 1 p e r c e n t a f t e r t h e s e p a r a t i o n .

Gor - .GOS

F i g . 4 : S k e t c h of t h e o i l / b r i n e s e p a r a t o r

0 o i l / w e i r ; B b r i n e / w e i r , A l o c a t i o n of t h e b r i n e /

water c o n t a c t

456

The q u a n t i t i e s of o i l and b r i n e i n t h e s e p a r a t o r are gove rned

by t h e d i f f e r e n c e i n h e i g h t s o f t h e w e i r s 0 and B , r e s p e c t i v e l y .

I n order t o a c h i e v e s u f f i c i e n t a c c u r a c y , t h e q u a n t i t i e s of b r i n e

and o i l i n t h e s e p a r a t o r must be k e p t c o n s t a n t w i t h i n L 0 .1 cm . T h a t is , t h e h e i g h t of t h e o i l / b r i n e c o n t a c t a t A must be h e l d

c o n s t a n t w i t h i n 5 0.2 cm. T h i s is n o t f e a s i b l e f o r a c o n s t a n t

s e t t i n g of t h e weirs, s i n c e t h e bond stress be tween t h e media

and t h e w a l l m a t e r i a l c a n change , f o r example . T h e r e f o r e t h e

s e p a r a t o r is a u t o m a t i c a l l y t i l t e d when t h e o i l b r i n e c o n t a c t a t

A d e v i a t e s from t h e s e t p o i n t . The p o s i t i o n is d e t e r m i n e d by

means of t h e change i n c o n d u c t i v i t y when t h e o i l / b r i n e c o n t a c t

p a s s e s an electrode. I n order t o c i r c u m v e n t t h e r e m a i n i n g p ro -

blems w i t h t h e bond stress ( c r e e p i n g of o i l , fo rming of a hemis-

p h e r e a t t h e water w e i r ) a Vi ton i n s e r t was used a s o i l weir,

and t h e edge of t h e b r i n e w e i r was p r o v i d e d w i t h a c e l l u l o s e

r ider.

The s e p a r a t o r s are t h e r m o s t a t e d a t a t e m p e r a t u r e of 2OoC. The

o i l and b r i n e which emerge from t h e s e p a r a t o r are weighed i n

c o l l e c t i n g bo t t les .

I n order t o d e t e r m i n e t h e o v e r a l l c o n c e n t r a t i o n of t h e i n d i v i -

d u a l o i l components , e s p e c i a l l y i n t h e t r a n s i t i o n zone , g a s c h r o -

m a t o g r a p h i c a l a n a l y s e s a r e per formed on b o t h t h e g a s and t h e o i l .

The samples of s t o c k - t a n k o i l are wi thdrawn from t h e bottom of

t h e g a s - o i l s e p a r a t o r by means of a s y r i n g e . Sampl ing beh ind t h e

o i l - b r i n e s e p a r a t o r is n o t f e a s i b l e b e c a u s e of t h e l a r g e dead

volume and o f t h e r e s u l t i n g r emix ing . G a s and o i l a n a l y s e s are

c a r r i e d o u t s i m u l t a n e o u s l y i n t h e gas ch romatograph . For t h e g a s

p h a s e , a Porapack Q/S-packed 1 / 8 " column 6 m i n l e n g t h is e m -

p l o y e d ; t h e o i l is a n a l y s e d i n a s i l i c o n e r u b b e r c a p i l l a r y column

40 m i n l e n g t h . T h i s p r o c e d u r e i m p l i e s t h a t a compromise must be

r e a c h e d be tween t h e a n a l y t i c a l r e q u i r e m e n t s imposed by t h e c a p i l -

l a r y column and t h e packed column. The s i m u l t a n e o u s e x e c u t i o n of

b o t h a n a l y s e s is n e c e s s i t a t e d by t h e l o n g d u r a t i o n o f 2 h. The

sample s t o r a g e r e q u i r e d f o r a v o i d i n g s u c h a p r o c e d u r e a p p e a r s

i m p r a c t i c a l .

3

ANALYTICAL PROCEDURE

A c a l c u l a t i o n of t h e l oca l c o n c e n t r a t i o n unde r r e s e r v o i r con-

d i t i o n s from t h e measured d a t a is p o s s i b l e o n l y i f t h e o i l ana-

l y s i s is c o m p l e t e . However, t h e a n a l y s i s e x t e n d s o n l y u p t o C26.

457

F u r t h e r m o r e , t h e a c c u r a c y of i n j e c t i o n does n o t s u f f i c e f o r cal-

c u l a t i n g t h e molar f l u x of t h e components. Hence, a t a g g i n g com-

pound, i n t h i s c a s e m e s i t y l e n e , is added t o t h e o u t f l o w a t con-

s t a n t r a t e b e f o r e t h e p r e s s u r e r e d u c t i o n . Thus it is p o s s i b l e

t o c a l c u l a t e t h e molar f l u x of a l l detected components from t h e

g a s chromatograms.

From t h e known f l o w r a t e i n t h e r e s e r v o i r model, t h e c o n c e n t r a t i o n

i s o b t a i n e d d i r e c t l y from t h e molar f l u x . Accord ing t o t h e f o l l o -

wing e q u a t i o n , t h e f l o w r a t e c a n be c a l c u l a t e d from t h e known

C02-mass

d V d t -

The main

- -

f l u x and t h e measured p r e s s u r e v a l u e s :

p u r p o s e of t h i s p r o c e d u r e is t o correct f o r i n t e r f e -

r e n c e d u e t o i n s u f f i c i e n c i e s i n t h e pe r fo rmance of t h e back-pres-

s u r e r e g u l a t o r a t t h e o u t l e t .

SLIM TUBE EXPERIMENTS

The s l i m t u b e e x p e r i m e n t s were per formed p r i m a r i l y f o r o b t a i n i n g

an estimate of t h e minimal m i s c i b i l i t y p r e s s u r e . I n order t o de-

t e r m i n e t h e r e s i d u a l o i l , t h e f l o o d t u b e w a s f l u s h e d w i t h a so l -

v e n t , f o r example t o l u e n e . The f l u s h i n g p r o c e s s w a s checked f o r

t h o r o u g h n e s s by means of p r e l i m i n a r y tests. For t h i s pu rpose sand

from t h e i n l e t and o u t l e t was a n a l y s e d f o r t o t a l c a r b o n . For t h e

o i l s u s e d h e r e , a mass c o n t e n t of c a r b o n less t h a n 0 , l p e r c e n t

was o b t a i n e d a f t e r f l u s h i n g , and d r y i n g by low p r e s s u r e C 0 2 .

I n order t o d e t e r m i n e t h e amount of r e s i d u a l o i l i n t h e e f f l u e n t ,

t h e major p a r t o f t h e s o l v e n t was d i s t i l l e d o f f , and t h e d i s t i l -

l a t e w a s a n a l y s e d g a s - c h r o m a t o g r a p h i c a l l y . Of c o u r s e , o n l y a small

q u a n t i t y o f o i l is p r e s e n t i n t h e d i s t i l l a t e . S i n c e t h e major

s h a r e of t h e r e s i d u a l o i l l i e s beyond C Z 6 and t h e r e f o r e c a n n o t be

a n a l y s e d g a s - c h r o m a t o g r a p h i c a l l y , n-hexane is added t o t h e resi-

d u e a t a r a t i o o f 1 : .1. From t h e g a s chromatogram, t h e mass r a -

t i o of n-hexane t o s o l v e n t is d e t e r m i n e d , and t h u s t h e r e s i d u a l

o i l mass c a n be c a l c u l a t e d w i t h good a c c u r a c y .

MIXER TANK

WATKINS / 3 / h a s u s e d premixed media f o r d i s p l a c e m e n t expe r imen t s .

H e allowed C 0 2 t o b u b b l e th rough t h e o i l from below i n an au to -

458

c l a v e . With t h e u s e of s u c h a p r o c e d u r e , a good mixing per forman-

ce c a n n o t be e x p e c t e d , b e c a u s e o f t h e u n f a v o u r a b l e d i a m e t e r - t o -

l e n g t h r a t i o . Hence a d i f f e r e n t method was u s e d . C 0 2 is i n j e c t e d

i n t o an o i l - f i l l e d m i x e r t a n k c o n s i s t i n g of s l i g h t l y i n c l i n e d

t u b e s ( f i g . 5 ) .

filter p l a t e 1

F i g . 5 : S k e t c h of t h e mixer t a n k

The t u b e s have an i n n e r diameter o f 0.9 cm and a l e n g t h of 2 m .

The v e r t i c a l t u b e s e c t i o n s , i n which t h e d e n s e r l i q u i d p h a s e is

d i s p l a c e d by a g a s p h a s e , s u b d i v i d e t h e m i x e r i n t o t h r e e s tages .

With in t h e i n d i v i d u a l s tages , t h e d e n s i t y d i f f e r e n c e be tween C 0 2 -

r i c h and C02-poor o i l p r o v i d e s f o r a d e q u a t e c i r c u l a t i o n , whereby

t h e d i f f u s i o n p a t h s a r e s h o r t b e c a u s e o f t h e small diameter-to-

l e n g t h r a t i o .

The f l o o d i n g of t h e t a n k ( f i g . 1 0 ) shows t h a t o n l y p u r e o i l f l o w s

o u t a t f i r s t . I f t h e amount of o i l d i s p l a c e d p u r e l y by s w e l l i n g

is c a l c u l a t e d from t h e PVT d a t a f o r C 0 2 - o i l m i x t u r e s , a v a l u e

of 170 c m 3 is o b t a i n e d . The q u a n t i t y which was produced p r i o r

t o t h e C02 b reak - th rough was 1 3 7 cm . A f t e r 1 6 1 cm3 had been p ro -

d u c e d , t h e s t o c k - t a n k o i l was o n l y s l i g h t l y c o l o u r e d . From t h e s e

two f i n d i n g s i t c a n be conc luded t h a t t h e e q u i l i b r a t i o n is r a t h e r

good i n t h e i n d i v i d u a l s t a g e s .

3

RESULTS AND DISCUSSION

E x c l u s i v e l y recombined o i l s were u s e d f o r t h e i n v e s t i g a t i o n .

For b o t h s l i m - t u b e e x p e r i m e n t s described h e r e , o i l w i t h a v i s -

c o s i t y of 6 mPa.s ( u n d e r r e s e r v o i r c o n d i t i o n s ) was employed.

For t h e f i r s t s l i m t u b e t es t shown i n f i g . 6 a s a n d pack w i t h a

p e r m e a b i l i t y of 3.08 D was used .

For p r e p a r i n g t h e s a n d pack f o r t h e second tes t ( f i g . 8 and 9 )

a 1 : 1 m i x t u r e of s a n d and silca p d e r was used (permeability: 3.03 D ) .

The f i r s t e x p e r i m e n t ( f i g . 6 and 7 ) was per formed a t a mean p r e s -

s u r e of 219 b a r and a C 0 2 - m a s s f l u x of 4.77 g / h , w i t h f l o o d

l e n g t h of 6 .3 m , r e s u l t i n g i n a v e l o c i t y of 5 .3 m / d .

459

Curve I shows t h e measured p r e s s u r e d i f f e r e n c e o v e r t h e e n t i r e

l e n g t h , c u r v e I1 shows t h e amount of s t o c k - t a n k o i l p roduced ,

and c u r v e I11 shows t h e q u a n t i t y of g a s produced ( f i g . 6 ) .

0

I .

lrngth C02-moss flux mean prrssurc

6.3 m L.11 g/h 219 bar

1

A F n bar

2.1

1.'

. I m m a '

I m .

PV F i g . 6 : Sl im t u b e experimeh't a t 219 bar:

111

n s o l "9

0.

1.3

1.2

31

D e a d o i l mass mo produced , p r e s s u r e d i f f e r e n c e Ap,

moles& g a s produced n p l o t t e d v e r s u s p o r e volumes

i n j e c t e d PV 9

dmO From t h e produced mass and t h e f l o w r a t e , t h e '$ens i t$ ' of t h e oil-

u n d e r r e s e r v o i r c o n d i t i o n s c a n be c a l c u l a t e d . The c a l c u l a t e d va-

l u e s a re shown by c u r v e I ( f ig . 7 ) . The m e a n 8 e n s i t y " b e f o r e C02

b reak - th rough amounts t o 0 . 1 7 5 g/cm3. The e x p e c t e d v a l u e is 0.805.

T h i s d e v i a t i o n c o r r e s p o n d s t o a volume e f f e c t d u e t o t h e d i s s o -

l u t i o n of C 0 2 i n t h e o i l . If i t is assumed t h a t t h e volume e f f e c t

d u e t o d i s s o l u t i o n d u r i n g t h e f l o o d p r o c e s s is comparable w i t h t h e

effect o b s e r v e d i n s i n g l e - c o n t a c t PVT measurements , and i f t h e to-

t a l volume s h r i n k a g e is e s t i m a t e d from t h e l e n g t h of t h e t r a n s i -

t i o n zone , t h e f o l l o w i n g v a i u e is o b t a i n e d f o r t h e " d e n s i t y " :

dm 0 3 - = 0.78 g/cm d V

The d e c l i n e of d m o / d V ( f i g . 7 and 8 ) a f t e r t h e C02 breakthrough

r e m a i n s l i n e a r o v e r a c e r t a i n r a n g e . Hence i t a p p e a r s p l a u s i b l e

4 60

II dm0

dV m 9/cm3

-

I \

length 6.3 m COjmass flux L.77 g/h mean pressure 219 bar

I b P

I

-.-.--.-.a--. . . . . . . -.-.-.-.--. 111 --_._.-.-. 23 k& .--.-.-. 0,l 0.2 0.3 0.1 0.5 0.6 0.7 08 0.9 1.0

PV

in !!!!lx x)2

n mi c i 3

d V

1.0

0.5

3.1

dn F i g . 7: S l i m t u b e xpe r imen t a t 219 bar:

LO '' Dens i t y 'I - dV , g a s concen t r a t ion + , f l o w r e s i s t a n c e 3 p l o t t e d v e r s u s pore volumes i n j e c t e d P\ -

at

to d e f i n e t h e l e n g t h of t h e t r a n s i t i o n zone by means of t h e i n t e r -

c e p t s of t h e s t r a i g h t l i n e w i t h t h e a b s c i s s a and w i t h t h e h o r i z o n -

t a l p o r t i o n of t h e c u r v e .

F i g u r e s 8 and 9 show a selected i n t e r v a l of an e x p e r i m e n t a t

189 bar and a C 0 2 mass f l u x of 1 .98 g / h . I n f i g u r e 9 t h e o v e r a l l

c o n c e n t r a t i o n dni /dv of C1, C 2 , i - C 4 and n-C4 unde r r e s e r v o i r

c o n d i t i o n s are p l o t t e d . These v a l u e s have been c a l c u l a t e d from

t h e gas p r o d u c t i o n d n / a t , t h e f l o w r a t e dV/dt, and t h e gas-chro-

m a t o g r a p h i c a l l y measured c o n c e n t r a t i o n .

It c a n be s e e n t h a t v e r y pronounced c o n c e n t r a t i o n maxima o c c u r

f o r t h e lower a l k a n e s . Moreover, t h e maxima are a l l s i t u a t e d a t

t h e same p o s i t i o n . The maximum of t h e n o r m a l i z e d C1-gas-concentra-

t i o n - cc The p r g s s u r e is a p p r o x i m a t e l y e q u a l to t h e MMP. Accord ing to t h e

l i t e r a t u r e /2,4,5,6/ t h e b e h a v i o u r of methane s h o u l d d i f f e r from

t h a t o f t h e o t h e r l i g h t a l k a n e s . N o s u c h d i f f e r e n c e is r e c o g n i -

z a b l e h e r e . Methane d o e s n o t show a lead, and t h e i n c r e a s e i n m e -

g

i n t h e e f f l u e n t amounts to 1.06 o n l y .

461

om0 1 Iength 10.8 m dV COZ-moss flux 1.98 g/h

in gcm3 mean pressure 189 bar

-

P

. . F i g . 8 : P a r t of a s l i m t u b e expe r imen t a t 189 bar:

d n dmo , g a s c o n c e n t r a t i o n 9 p l o t t e d v e r s u s p o r e dV d V

D e n s i t y

volumes i n j e c t e d PV

t h a n e c o n c e n t r a t i o n is of t h e same order of magni tude as t h a t f o r

t h e o t h e r components shown.

F i g . 1 0 shows t h e c a l c u l a t e d C02 and C1 c o n c e n t r a t i o n under re-

s e r v o i r - c . o n d i t i o n s . I t c a n be s e e n t h a t t h e s t a r t of c o n c e n t r a -

t i o n i n c r e a s e is a t t h e same p o s i t i o n f o r methane and ca rbon

d i o x i d e .

To d e m o n s t r a t e t h e s i m i l a r i t y be tween t h e f l o o d i n g r e s u l t s ob-

t a i n e d w i t h t h e mixer and w i t h t h e s l i m t u b e , t h e c o n c e n t r a t i o n

c a l c u l a t e d i n t h e same manner from t h e mixer o u t f l o w is p l o t t e d

ag a i n s t i n j e c t e d PV i n f i g u r e 11. T h i s e x p e r i m e n t was con-

d u c t e d a t a C 0 2 mass f l u x of 9 .91 g / h and a p r e s s u r e of 202 bar.

The scale is so chosen t h a t 1 PV c o r r e s p o n d s t o t h e mixer volume

of 424 cm . The o b s e r v a t i o n t h a t t h e c o n c e n t r a t i o n maxima f o r C1, C 2 , i - C 4

and n-C4 o c c u r a t t h e same time for t h e mixe r test too is espe -

c i a l l y s t r i k i n g .

3

462

Fig. 9:Part of a slim tube experiment at 189 bar: dn i Concentration -- d V of C1, C2, i-C4, n-C4 under reser-

voir- conditions plotted versus pore volumes PV injected

The maximal concentrations for the slim tube and mixer tests are

presented in the following table.

Table: Maximal concentrations in mol/cm 3

c1 c2 i-C4 n-C4

Slim tube 1.03 . 2.60 . 1.14 . 3.28 . Mixer 1.38 - 3.42 . 1.61 . 5.13 .

In view of the fact that the maximal value of the concentration

is given only by one gas chromatogram, the agreement between the

values is remarkably good. Furthermore, it must be taken into

consideration that the relative change in flow rate due to dis-

solution of C02 in the oil is certainly different for the slim

tube and mixer tests. For both tests it should be emphasized that

increase in concentration by a factor of about 5 occurs for the

lower alkanes considered here.

463

c1

5 , 1 0 3 dV in md mi3

1.0.

,

0.5

0.7

length 10.8 m CO2-mass flux 1.98 g/h mean pressure 189 bar

10

-./-a\./-

W 1 .o

C1

0.8 0.9

5 , 1 0 3 dV in md mi3

1.0.

,

0.5

0.7

i r

length 10.8 m CO2-mass flux 1.98 g/h mean pressure 189 bar

10

-./-a\./-

W 1 .o

C1

0.8 0.9

con-

1 1 Mixer- test 1 0 C02- 1110)s flux 9,91 g/h . . . . . . . . . - * . . ' In 9 mean pressure 202 bar . . . * .

I .:*

m.

100.

11 . '

50

.... . . . . . .* 1.2 02 0.b 0.6 0.8 1 .o

11

' i n m d n9

4 5

.3.0

.l.S

n Fig . 10: Part of a s l i m tube experiment a t 189 bar:

dn. Concentration ditions p l o t t e d versus pore volumes PV i n j e c t e d

of C1 and C 0 2 under reservoir con-

-- PV ' Fig. 11: Mixer test

Dead o i l mass produced mo, moles of gas produced n Versus pore volumes PV i n j e c t e d

plot ted 9'

1.0

0.5

Mixer- test C O y m s r flux 9.91 g/h mean pressure 202 bar

1.5 W

0.5 1.0

Fig. 12: Mixer test d n . 1 Concentration of C1, C2, i-C4, n-C4 under reservoir

conditions plotted v ersus pore volumes injected

Conclusions

On the basis of the results obtained so far, the apparatus deve-

loped appears to be suited for C02 core flooding experiments. In

particular, it allows conclusions concerning the composition un-

der reservoir conditions. The use of the three-stage mixer tank

for core flooding experiments appears promising. By means of this

device, cores can be flooded with media corresponding to a tran-

sition zone.

Nomenclature

P = inlet pressure P(p) = C02-density k = C02-mass flux

V = volume under reservoir conditions

465

v2

vO

-y 0

X 1 m

n

t

C

0

g

= volume filled by C02

= volume filled by oil

= compressibility of oil

= compressibility of C02

= mass of stock tank oil

= moles of gas

= time

= gas-concentration of methane in the effluent

Acknowledgements

The autor is grateful to the Federal Ministry of Research and Tech-

nology (BMFT) for financial support of the project as well as to

Prof. G . Pusch, the project leader, for his advice and support.

References

1. V. Meyn

G. Pusch

2. J.J. Rathmell

F. J. Stalkup

R. C. Hassing

3. R. W. Watkins

4. R.S. Metcalfe

L. Yarborough

5. L.X. Nghiem

D.h Fong

K. Aziz

6. M.P. Leach

W.F. Yelling

Laboruntersuchungen zum Kohlendioxid-

Fluten (PVT-Verhalten und Flutversuche)

ET 3048 A

A Laboratory Investigation of Mis-

cible Displacement by Carbon Dioxide

SPE 3483 (1971)

A Technique for the Laboratory Measure-

ment of Carbondioxide Unit Displace-

ment Efficiency in Reservoir Rock

SPE 7474 (1978)

The Effect of Phase Equilibria on

the C02 Displacement Mechanism

SOC. Pet. Eng. J. (1979) p. 242

Compositional Modelling with a

Equation of State

SPE 9306 (1980)

Compositional Model Studies - C02 Oil- Displacement

SOC. Pet. Eng. J. (Feb. 19811,~. 89



THE USE OF SLIM TUBE DISPLACEMENT EXPERIMENTS IN THE ASSESSMENT OF MISCIBLE GAS PROJECTS

BERNARD J. SKILLERNE DE BRISTOWE

British Petroleum Company Limited

ABSTRACT

Slim tube displacemeht experiments can be employed t o optimise dynamic miscible displacement pro jec ts with respec t t o both pressure and composition. By analogy with the minimum dynamic m i s c i b i l i t y pressure concept a minimum dynamic m i s c i b i l i t y composition may be defined which may be used t o assess the s u i t a b i l i t y of a l t e r n a t i v e i n j e c t i o n gasses .

D e t a i l s are given of the way i n which the s l i m tube displacement experiments are performed and are operated with automated data acquis i t ion . Examples are provided of the phenomena observed during the course of the experiments which may be used t o assess the nature of the displacement process. s u p e r c r i t i c a l e x t r a c t i o n phenomena which provides an explanat ion f o r the r e s i d u a l o i l phase l e f t behind i n the s l i m tube a t the end of the experiment.

The r e s u l t s are discussed i n r e l a t i o n t o

INTRODUCTION

During the las t decade a profusion of d a t a has been generated i l l u s t r a t i n g the phenomena assoc ia ted with dynamic miscible displacement A s h o r t perusal of the l i t e r a t u r e quickly shows t h a t the displacement gas used i s almost always carbon dioxide and t h a t most o f t e n the o i l i s a West Texas, Permian Basin Crude. Despite t h i s r e s t r i c t i o n i n com- p o s i t i o n l i t t l e consensus of opinion has been reached as t o what s u i t e of labora tory experiments must be performed i n order t o evaluate a given f i e l d p r o j e c t (1) except t h a t they w i l l be extensive, time consuming and consequently extremely expensive t o perform. For an operator whose i n t e r e s t s l i e f a r from West Texas and who needs t o evaluate many p o t e n t i a l prospects i t i s imperative t h a t the maximum amount of information is generated i n the most economical way possible . To do t h i s , the experiments performed should be designed i n such a way t h a t they w i l l form a r a t i o n a l b a s i s f o r investment decis ions.

Of the many experiments proposed, the s l i m tube displacement experiment o f f e r s the c l o s e s t analogue t o the processes t h a t occur wi th in ' the r e s e r v o i r while a t the same t i m e i t can be performed s u f f i c i e n t l y rap id ly for repeated experiments t o be performed under varying opera t ing condi t ions. In using the method the assumption is made t h a t the processes which r e s u l t i n dynamic miscible displacements a r e independent of the nature of the hos t porous matr ix and depend exc lus ive ly on the composition and physical p roper t ies of the f l u i d s involved and on the temperature and pressure a t which the displacement takes place. The displacement i s confined within the wal l s of a

468

narrow tube so t h a t the flow i s e s s e n t i a l l y one dimensional. I t can thus provide no information regarding the gross f l u i d movements within a reservoi r which a r e subjec t t o hydrodynamic i n s t a b i l i t i e s such as viscous f inger ing and gravi ty segregat ion. I t s major use therefore i s i n the i n i t i a l assessment of a given p r o j e c t where the compatability of the i n j e c t e d gas with the r e s e r v o i r o i l is sought. Nevertbeless , s ince a var ie ty of evidence now e x i s t s t o suggest t h a t the petrophysical p roper t ies of the rock a r e of secondary importance i n determining the displacement e f f i c i e n c y (2) i t may be used t o provide valuable q u a l i t a t i v e information about the elementary displacement mechanism. The key t o t h i s is i n ident i fy ing when the dynamic miscible displacement process is operat ing. The purpose of t h i s paper is t o show t h a t once t h i s can be done the process can be optimised with respec t to e i t h e r the pressure o r the composition of the i n j e c t e d gas.

THE SLIM TUBE DISPLACEMENT EXPERIMENT

In order t o improve the e f f i c i e n c y with which the s l i m tube experiments can be performed while making the b e s t use of the information ava i lab le the d a t a gather ing p a r t of the experiment has been automated. schematically i n Figure 1 and a block diagram of the computer cont ro l led d a t a acquis i t ion system i n Figure 2.

The general experimental arrangement i s shown

? VENT

I ,-* I L __---- --- -- -

K L Y 1. YOTORISED MERCURY P U M P

1. C O ~ I C , R E F I L L CYLINDER

L KLROSINP CYLINDCR

1. O I L CYL!NOEI

% C O 1 I C ~ C Y L I N D C R

& PRESSURE 1RANSOUCCI

7, SLIY- IUOE

L VISUAL CELL

1 01611AL OENSllY Y E I E I

I0 DACK - P l E S S U I 1 E I L G U L A I O I

1l.LIDUIO SAY?LE VALVE

11.SCPARAlOR A N 0 BALANCE

1 l . C A S S A Y P L e VALVE

IL .hA5 P L O W u t i m I S . V A L V E I ~ . V A L V C

+VENT

Figure 1. Schematic Diagram of the Slim Tube Apparatus.

469

TRANSDUCERS

Figure 2. Microcomputer Control of Slim Tube Experiments.

Many d i f f e r e n t designs f o r s l i m tube apparatus have been reported i n the l i t e r a t u r e . These have been recent ly reviewed by O r r e t a1 (1) . The present apparatus cons is t s of a motorised Ruska pump which can d isp lace mercury i n t o one o r o ther of two sample veerel's (4) and ( 5 ) . The s i n g l e phase f l u i d s contained i n these vesse ls then pass sequen- t i a l l y through t h e s l i m tube (7 ) . the windowed viewing cell (8) and the d i g i t a l dens i ty meter (9) t o a back pressure regula tor (10). The r e g u l a t o r maintains t h e o u t l e t pressure a t a predetermined value set by a gas r e s e r v o i r vesse l containing ni t rogen. As the e f f l u e n t f l u i d s pass through the back pressure regula tor , they are separated i n t o a gas and l i q u i d phase. The l i q u i d i s co l lec ted i n a perspex vesse l placed on the pan of a d i g i t a l e l e c t r o n i c balance (12). The volume of l i q u i d i n t h i s separa tor can be determined independently by observing the he ight of o i l i n the separa tor using a cathetometer. Although the dens i ty of the o i l changes a f t e r gas breakthrough the l i q u i d production f a l l s o f f rapidly so t h a t the assumption t h a t the dens i ty remains constant only introduces a small e r r o r i n t o t h e volume of o i l recovered. The gas phase passes out of the separa tor , through a gas sample valve (13) and a d i g i t a l w e t gas meter (14) and i s vented t o atmosphere.

The s l i m tube i s constructed from API Schedule 40 stainless steel tubing and a f t e r packing was co i led t o form a square' s e c t i o n h e l i x and i s mounted hor izonta l ly . are summarized i n Table 1. s teel s i n t e r s pressed i n t o the ends of the tube. s h u t off valves which a r e shown i n Figure 3 are f i t t e d t o each end of the tube. These are equipped with bleed valves which f a c i l i t a t e c leaning and allow the pore volume of the tube to be determined by weighing the column before and a f t e r i t had been f i l l e d with d i s t i l l e d water a t the temperature and pressure a t which the experiments a r e t o be c a r r i e d out . Thus

The p r o p e r t i e s of the s l i m tube The packing is he ld i n p lace by s t a i n l e s s

Spec ia l ly designed

4 70

where

i s the equation of s t a t e f o r water of K e l l and Whalley (3 and 4). In t h i s way allowance can be made f o r the d i l a t a t i o n of the tube and the compression of the packing.

Table 1. Proper t ies of the Slim Tube

I n t e r n a l Diameter 9 . 2 5 m Length 12.19m Pore Volume (25OC. O.1MPa) 290.4cm3 Absolute Permeability 9.6 (urn) Packing Lead Glass spheres Porosi ty 36% Diameter range of packing e a 80% pass 0.115mm t o 0.18Omm

The pressure drop across the s l i m tube was measured by measuring the. i n l e t and e x i t pressures using Bel l and H o w e l l sca led reference s t r a i n gauge pressure transducers. These were connected using the s p e c i a l f i t t i n g s shown i n Figure 4,

TRANSDUCER

IN -

-SMALL SWEPT DEAD VOLUME

-our

Figure 3. Spec ia l Valves Figure 4. Transducer f i t t i n g s

4 7 1

which minimise the dead volume while allowing i t t o be swept by the flowing stream. This'arrangement was adopted because the d i f f e r e n t i a l pressure transducers ava i lab le on the market have la rge unswept dead volumes which may vary with pressure. Furthermore, d i f f u s i o n of the i n j e c t i o n gas i n t o the transducer can lead t o spurious mixing and mobil isat ion of dead volume o i l which cannot be accounted f o r and complicates subsequent i n t e r - p r e t a t i o n . expense of s e n s i v i t y and the t ransducers must be very carefu l ly c a l i b r a t e d with respec t t o the e x c i t a t i o n vol tage and temperature as w e l l as the response of the diaphragm.

Prevention of t h i s can only be achieved a t the

The pressure a t which the displacement is performed, t h a t i s the pressure a t the displacement f r o n t , i s b e s t approximated by the i n l e t pressure t o the tube. The pressure i s control led, however, a t the o u t l e t by the back pressure regula tor . The flow r a t e must therefore be kept low i f a s u b s t a n t i a l pressure change a t the displacement f r o n t i s not to take p lace during the d i s - placement. This change may be regarded as an uncertainty i n the displacement pressure. The cont ro l of the gas dome-loaded back pressure regula tor depends upon the pressure i n the ni t rogen vesse l . Since 9 thermostat ing the pressure reference

e f f e c t i v e l y e l imina tes d r i f t s . I n t h i s way the o u t l e t pressure i n the tube can readi ly be kept wi th in f50kPa of the s e t point .

P T

On e x i t from the s l i m tube the f l u i d s flow through a windowed c e l l which is depicted i n Figure 5. windows he ld wi th in a s t a i n l e s s steel body. The windows a r e he ld ca 0.lm a p a r t by two PTFE "D" shaped i n s e r t s which reduce the swept volume. This arrangement produces a l a r g e area f l a t f i e l d which is photographed by a pulsed cine camera munted outs ide the oven. Time lapse photographs are taken a t ca 0.001 i n j e c t e d pore volume i n t e r v a l s so t h a t a complete record is k e p t of the phases flowing during the experiment. The u t i l i t y of t h i s when the da ta is analysed a f t e r the experiment is over cannot be exaggerated.

It c o n s i s t s of two sapphire

1 OUT

Figure 5. Windowed Cel l .

4 7 2

From the windowed c e l l the f l u i d s pass t o an Anton Paar high pressure d i g i t a l densi ty meter which i s housed i n an a u x i l l a r y a i r thermostat bath. This instrument allows a continuous record t o be kept of the dens i ty of the f l u i d s flowing through it. a very s e n s i t i v e i n d i c a t o r of changes i n composition and of the appearance of a low densi ty '*gas** phase within the o i l and can thus be used t o d e t e c t breakthrough.

I t is thus

The most important of the experimental parameters a r e the volume of gas i n j e c t e d and the volume of o i l recovered. These a r e both normalised with respec t t o the pore volume of the s l i m tube. So t h a t the displacement may be used as an ind ica t ion of the process taking p lace within the r e s e r v o i r , both of these measurements are re fer red t o the i n l e t and e x i t faces of the s l i m tube under r e s e r v o i r condi t ions. s l i m tube i s obtained, i f the flaw rate from the pump i s assumed to be constant , by

The volume of f l u i d e n t e r i n g the

c qHg (Pin, Tamb) pkg (Pin, Tamb) At

@Ig (Pin, TOV) - 6Vin

V i ( t ) = vp (Pin, TOV)

where GVin is the dead volume on the i n l e t s i d e between valve (15) and the s l i m tube. This is arranged t o be as small as possible . The s u m a t i o n i s taken from the time t=O a t which the flow is changed from crude o i l t o d i sp lac ing gas.

The s l i m tube

V,(t) =

volume of o i l recovered a t t i m e t a t the o u t l e t from the is given by

The f i n a l term i n the dividend makes allowance f o r the dead volume between the o u t l e t of the s l i m tube and the separa tor . Up t o the time of gas breakthrough t h i s s e c t i o n of tubing i s completely f i l l e d with o i l before and a f t e r a time incrementin the flow and consequently does not a f f e c t the measured recovery. From the time of gas breakthrough onwards the o i l o r i g i n a l l y i n the o u t l e t dead volume i s progressively drained and replaced by gas. This progressive drainage can be allowed f o r i f the f r a c t i o n a l flow of gas is known.

Before breakthrough Fg(t) = 0 and a t the end of the run when no l i q u i d is being recovered Fg(t) = 1. A t in termediate times Fg(t) i s experimentally inaccess ib le . In p r i n c i p l e i t could be obtained from a f lash ca lcu la t ion i f the composition and d e n s i t i e s of the flowing stream were adequately known. However, i f only ul t imate recoveries a r e required t h i s complicatibn i s unnecessary.

The procedure f o r performing the displacement experiments i s as O i l i n the sample vesse l i s made s i n g l e phase and the follows.

apparatus i s heated t o the displacement temperature. O i l is pumped through the s l i m tube a t a high r a t e , ca ZOo~rn~h-~ t o miscibly displace the keros ine l e f t i n the tube a f t e r cleaning. Af te r about

473

one pore volume has been i n j e c t e d the r a t e i s reduced t o t h a t a t which the displacement is t o be performed and i n j e c t i o n i s continued u n t i l the pressure drop and the GOR a r e both constant . During t h i s per iod the base of the gas cyl inder i s connected to t h a t of the o i l cyl inder so t h a t they come t o the same pressure. When a l l i s steady, the o i l cy l inder i s closed and the gas cyl inder is opened t o the tube. A s i g n a l is fed t o the microcomputer t h a t the displacement has commenced. A l l of the transducers a r e fed v i a s u i t a b l e i n t e r - faces t o the microcomputer which scans a l l of the input channels a t pre-arranged t i m e i n t e r v a l s . Simple ca lcu la t ions such as converting the m i l l i v o l t t ransducer inputs t o pressures and temperatures and time averaging noisy s i g n a l s a r e performed i n r e a l t i m e . 'Ihis is most r e a d i l y performed i f a 280 microprocessor i s used which has a programmable i n t e r r u p t . floppy d i s c and a l l of the sequences of the measurement and cont ro l aresynchronised by a real-time clock. A summary r e p o r t showing the v a r i a t i o n i n the major var iab les as a funct ion of the i n j e c t e d pore volume is l i s t e d on the l i n e p r i n t e r as the experiment progresses. A t the end of the experiment any f u r t h e r computations a re performed. and the r e s u l t s a r e tabulated and output t o a d i g i t a l X-Y p l o t t e r . tube i s then cleaned by f lush ing with so lvents and f i n a l l y with kerosine i n prepara t ion f o r the next experiment.

A l l of the computed d a t a i s s tored on a

The

PHENOMENA OBSERVED DURING SLIM TUBE DISPLACEMENTS

Displacement experiments may be perfonued with e i t h e r composition o r pressure as t h e independant var iab le depending upon which parameter may most readi ly be optimised within a given pro jec t . 'Ihese two approaches a r e i l l u s t r a t e d with reference to the two.o i l s whose proper t ies are l i s t e d i n Table 2. O i l A is from the Egmanton

Table 2. Proper t ies of the o i l s s tud ied .

O i l A O i l B

0.0001 0.0000

a 2 0.0012 0.0305 Composi t i on N2 (massfract ions)

c1 c2

0.0061

0.0028

0.0535

0.0080

c3 0.0079 0.0079

nC4 0.0100 0.0066

i C4 0.0033 0.0022

"C5 0.0094 0.0055

i C5 0.0067 0.0040

c6 0.0187 0.0107

c7 0.0342 0.0217

C8 0.0466 0.0294

cg 0.0355 0.0308

cg+ 0.8180 0.7892

Bubble p o i n t pressure 3.27MPa at 43.3OC 23.54MPa a t 93.3OC 0.377 ml kg-'

<M>

4 7 4

reservoi r and was s tudied i n the e a r l y p a r t of BP's East Midlands Additional O i l P ro jec t where a number of small , h ighly depleted reservoi rs were evaluated as EOR candidates (5). This reservoi r was over-pressured by water i n j e c t i o n and i t was of i n t e r e s t t o know the e x t e n t to which i t could be depressured while allowing the process t o operate . The only source of gas ava i lab le was pure COq formed as a biproduct of annnonia production. O i l B i s from a p a r t i a l l y depleted reservoi r c lose t o a source of associated gas containing a s u b s t a n t i a l quant i ty of C02. enrichment of the C02 by the intermediate hydrocarbons might be required f o r a dynamic misc ib le displacement process t o operate .

a t d i f f e r e n t displacement pressures . performed with and without formation water being present a t connate s a t u r a t i o n wi th in the s l i m tube. The r e s u l t s f o r these a r e shown i n Figs. 6 and 7 where curve (a) i s the r e s u l t obtained when connate water was present i n each case.

It was therefore of i n t e r e s t t o determine what

For o i l A a s e r i e s of displacement experiments were car r ied out Two sets of experiments were

In Figure 6 the ul t imate recovery, approximated by the recovery when 1.2 pure volumes had been i n j e c t e d i s p l o t t e d , whereas i n Figure 7 the recovery is t h a t obtained a t gas breakthrough. Ihe curves a r e

AT=!=. 1 0 0

b -0- --.

---- --7 -- 1-- ~- 5 6 7 8 0 10 11 12

P M P4 -

Figure 6. Ultimate recovery as a funct ion of pressure f o r o i l A.

0 S 6 7 8 B II 'I2

lo P - UP0

Figure 7. Recovery a t breakthrough f o r o i l A

475

t y p i c a l l y sigmoid and there i s seen t o be a s l i g h t l y b e t t e r recovery when connate water i s present than i n i t s absence. This i s thought to be due t o the o i l being a non-wetting phase when water i s present b u t the wet t ing phase when i t i s absent. 'Ihe pressure a t which the sudden increase i n recovery i s observed is independent of the point on the recovery curve a t which measurements a r e made. However, i t i s general ly more convenient to use the value a t ca V i = 1.2 s ince

0 dVr : dVi -

The poin t of gas breakthrough was determined i n these experiments by observing the change i n the GOR and by monitoring the pH of a small f l a s k containing d i s t i l l e d water through which the e f f l u e n t gas was passed. i n pH i s observed as Cog f i r s t emerges from the tube as shown i n Fig. 8.

As the associated gas contains no GO2 o r H2S a sudden decrease

0 . 5 0 .

0 0 2 O& 0.6 0.8 1.0 11

V.

Figure 8. Recovery and pH v a r i a t i o n during a s l i m tube displacement of o i l A.

The sequence of events observed i n the v i s u a l c e l l was s i m i l a r t o t h a t described by Henry and Metcalf ( 6 ) with the exception t h a t a heavy phase was never observed. was accompanied by the appearance of a colourless CO2 r i c h phase as bubbles wi th in the o i l r i c h phase. of l igh ten ing i n the colour of the o i l r ich phase w a s observed but with the presence of a colourless C02 r i c h phase. Bubbles o f t h i s co lour less phase were seen t o accompany the o i l up t o ca 10.5 ma.

A t pressures below 8MPa breakthrough

A t 8.5 MPa a progressive sequence

on a t

No

I n order t o determine t h e e f f e c t of the operat ional var iab les the recoveries observed a series of measurements were perfonned 12MPa, where dVr is small, i n which t h e displacement rate was varied.

d i f fe rence w a s observed wi th in experimental e r r o r as shown i n Fig. 9. dP

Recently, we have been ab le t o compare the recoveries with those obtained using a v e r t i c a l 2m longcolumn 2.5cm i n diameter used by IFP who are now p a r t i c i p a t i n g i n the Egmanton CO2 projec t . p ressures above ca 9MPa very good agreement exis ts between the r e s u l t s obtained from the two pieces of apparatus. The break i n s lope and minimum dynamic m i s c i b i l i t y pressures are l ikewise i n good agreement. However, a t pressures below 8MPa where an immiscible gas displacement is taking p lace the v e r t i c a l column cons is tan t ly gives higher

A t

476

lQ0

'c

0 .50

0

0 0 Q

P; 12 cpo

50 100

oco 2

Figure 9 . Dependance of Recovery on Flow Rate a t 12MPa.

recoveries than thoseobtained from the hor izonta l ly coi led tube. As the displacement i n the v e r t i c a l column is gravi ty s t a b i l i s e d t h i s i s taken t o ind ica te t h a t hydrodynamic i n s t a b i l i t i e s may be present i n the flow i n the s l i m tube even though i t i s of small diameter.

For o i l B, the e f f e c t of progressively increas ing the mole f r a c t i o n of propane i n the displacement gas (mixtures of CO2 with propane) i s shown i n Fig. 10.

0 0 2 5 0.5

Figure 10. Recovery as a funct ion of gas composition f o r O i l B

1.2

With Xc3 0 . 2 the displacements show a l l of the c h a r a c t e r i s t i c s re fer red t o previously which are observed when a dynamic miscible process is taking place. inmiscible i n character . Xc3 0 .2 which is similar t o t h a t seen on the Vr(p) diagrams. po in t i s re fer red t o as the minimum dynamic m i s c i b i l i t y composition by analogy with the minimum dynamic m i s c i b i l i t y pressure.

With Xc3 < 0 .2 the displacements are typica l ly The diagram shows a break i n s lope a t

This

477

It has been observed t h a t when the dynamic miscible process i s opera t ing ul t imate recovery is reached by V i = 1.2 . t h i s dVr is p l o t t e d as a funct ion of X3 i n Figure 11.

To i l l u s t r a t e

dVi

3 XC

Figure 11. The v a r i a t i o n of % w i t h composition dVi

Since O i l B contains an appreciable amount of C02, gas breakthrough could not be detected by monitoring the pH as with O i l A. Figures 12 and 13 show the v a r i a t i o n observed i n the t o t a l stream dens i ty and the gas-oil r a t i o during an experiment. I t w a s found t h a t the densi ty measurement gave a much more s e n s i t i v e ind ica t ion of the f i r s t change i n compq8ition than did the COR. Furthermore i f gas bubbles of low densi ty a r e en t ra ined wi th in the o i l t h e recorded dens i ty becomes very erratic. process is operat ing the densi ty v a r i e s f a i r l y smoothly a s shown i n Figure 12 . This a l s o serves t o show t h a t the composition of the t r a n s i t i o n zone may be more complex than i s usual ly depicted.

When a dynamic miscible

1.0 -

"I-

0 .5 '

0 0 0 ' 5 I .o 12

V.

Figure 12. Recovery and densi ty as funct ions of V i a t Xc3 - 0.5

478

1000

- P &Om-'

5 00

1.0

vr

0 ' 5

0

- 4.0 , L

* *

l o D"P

-2 .0

PO k 2 0 0 5 V.

Figure 13. Recovery and GOR as funct ions of V i a t Xc3 = 0 .5

DISCUSSION

The break i n s lope of the Vr(p) and Vr(x) funct ions i s now known t o be a funct ion of the composition of the d isp lac ing f l u i d , the composition of the o i l and the displacement temperature ( 7 ) . Johnson and P o l l i n (8) have shown t h a t the minimum dynamic m i s c i b i l i t y pressure f o r C02 disp lac ing a s e r i e s of pure n-alkanes i s almost exact ly given by the c r i t i c a l pressure of the binary mixture a t the temperature a t which the displacement is c a r r i e d out. e x i s t s wi th in the displacement tube the sudden increase i n recovery which i s observed m u s t be la rge ly a r e s u l t df the increased solvent powers of the displacement gas wi th in the c r i t i c a l region. increased s o l u b i l i t y is a r e s u l t of the l a r g e deviat ions from i d e a l i t y which occur wi th in t h e c r i t i c a l region. A s c r i t i c a l i t y i s reached l a r g e changes a r e observed t o occur i n many physical p roper t ies as shown i n Figure 14 f o r pure C02. superimposed upon t h i s .

Recently,

I f equi l ibr ium

The

The Vr(p) curve f o r O i l A has been A t the same t i m e as the s o l u b i l i t y increases

0 1 0

1.00

vI-

0 5 0

0

Figure 14. The v a r i a t i o n i n the physical p roper t ies of C02 i n the c r i t i c a l region.

479

within the c r i t i c a l region o ther physical p roper t ies change i n such a way a s t o favour the displacement. Thus the densi ty and v iscos i ty both increase while the product of the densi ty and se l f -d i f fus ion c o e f f i c i e n t decreases i n agreement with k i n e t i c theory. Although the s e l f d i f fus ion c o e f f i c i e n t decreases i t s value s t i l l remains considerably higher than t h a t found i n normal l i q u i d s enabling trapped o i l t o be more readi ly contacted. It i s not known a t the present time whether these changes i n physical p roper t ies w i l l e f f e c t convective d ispers ion o t h e r than through the mutual d i f fus ion c o e f f i c i e n t which appears t o follow the behaviour of the s e l f d i f fus ion c o e f f i c i e n t i n the c r i t i c a l region.

The s o l u b i l i t y of a given compound depends upon the nature of the intermolecular i n t e r a c t i o n s between i t and the solvent as is r e f l e c t e d i n the phase diagram. A t the present time phase diagrams have been determined f o r mixtures of C02 with a range of n-alkanes and a few simple cycloalkane and aromatic hydrocarbons (9 ) . p(T) sec t ions f o r the n-alkanes are shown i n Figure 15. I t can be seen from t h i s diagram t h a t f o r the lower homologues the c r i t i c a l l i n e is separated i n t o two branches, one of V-L c r i t i c a l point connecting the c r i t i c a l po in ts of the pure end members and the o ther of L-L c r i t i c a l po in ts which terminates a t a c r i t i c a l end point . For the

L O J

vapov' p-csrure c u r v e of co 2 t /'c

Figure 15. C r i t i c a l Lines f o r CO2 + n-alkane mixtures.

higher homologues the c r i t i c a l l i n e is continuous but may f o l d back upon i t s e l f r e s u l t i n g i n gas-gas immiscibi l i ty of the f i r s t kind. The c r i t i c a l pressure increases with the carbon number a t a given temperature. Thus f o r e x t r a c t i o n a t a given temperature and pressure some of the homologues w i l l have t h e i r cr i t ical regions within the range of pressures considered, while o thers w i l l r equi re a much higher pressure and y e t others , i f the temperature i s s u f f i c i e n t l y low,can never be brought i n t o the c r i t i c a l region by increase i n pressure alone. This w i l l account a t least i n p a r t f o r a res idua l 'heavy" o i l being l e f t behind a f t e r the displacement and f o r the small bu t p e r s i s t a n t increase i n recovery t h a t is observed a f t e r the minimum dynamic m i s c i b i l i t y pressure has been reached. A

4 80

s i m i l a r s u i t e of curves e x i s t f o r the aromatic and naphthenic compounds. "he displacement of these curves from one another suggests a degree of s e l e c t i v i t y i n the e x t r a c t i o n process and i t is i n t e r e s t i n g t o speculate t h a t the p a r a f f i n , naphthene, aromatic d i s t r i b u t i o n wi th in the o i l s recovered may change as the pressure changes.

Although the minimum dynamic m i s c i b i l i t y pressure appears t o be la rge ly governed by the .equi l ibr ium thermodynamic proper t ies of the f l u i d s the absolute recovery w i l l depend both on the proportion of unextractable components i n the o i l and on the hydrodynamics of the displacement. I t does not seem reasonable therefore t o quote a f ixed recovery which must be reached before i t can be coficluded t h a t the mul t ip le contact mass t r a n s f e r mechanism is operat ing. Deduction of the process mechanism m u s t thus be made on t h e b a s i s of many d i f f e r e n t observations r a t h e r than a s i n g l e one. An attempt t o summarise the more general characteristics of the d i f f e r e n t process types i s given i n t a b l e 3.

TABLE 3 KEY TO PROCESS IDENTIFICATION

PROPERTY

Recovery a t V i = 1.2

- dVf a t v i = 1.2 dVi

Rate Dependance

Breakthrough

Density Change a t breakthrough

Sight Glass Observations a t breakthrough

[ m i s c i b l e

l O W

high

l a r g e

e a r l y

Becomes very errat ic

co loot ies ! bubbles i n dark o i 1

Process 5 p e

Low IFT

intermediate

small

intermediate

errat ic a t t i m e s

Colourless bubbles i n l i g h t e r coloured o i l

Mu1 t i p l e Contact

high

zero

none

la te

smooth

Dark t o l i g h t colour change i n o i l with occasional colourless bubbles

F i r s t Contact

high

zero

none

l a t e

smooth

Progressive l igh ten ing i n colour of the o i l without gas bubbles

I f a series of displacements are c a r r i e d out a t d i f f e r i n g compositions o r pressures as i n the example given above severa l of these mechanisms w i l l be observed t o operate . required p a r t i c u l a r l y i n r e l a t i o n t o the d i f f e r e n t types of displacement which may take p lace i n the L-L and L-V regions.

Considerable refinement of t h i s scheme i s

481

CONCLUSIONS

I t has been s h a m above t h a t s l i m tube displacement experiments may be used to optimise ind iv idua l p r o j e c t s with respect t o both pressure and composition. the course of the s t u d i e s upon which the dominent mechanism which operates i n a given pressure o r composition may be deduced.

A considerable amount of information may be gathered i n

ACKNOlrTLEDGEMENT - The author wishes t o thank G . J . J . Williams. A.G. Steven,

A. Booth, C .G. Osborne, D . J . Thomas, S . Takhar. S . Bahal and C. Liang from whose work the contents of t h i s paper have been drawn.

Bo

Fg

COR

i , j, k

m l

m2

<o P

P e

qng. cop V i

VP

V r

6Vin

6Vout

xc3

T

6T

A t

a i j

NOMENCLATURE

Flash formation volume f a c t o r of o i l

Volume f r a c t i o n of gas phase

Gas o i l r a t i o

Indices i n equation of s ta te

Mass of evacuated s l i m tube

Mass of water f i l l e d s l i m tube

Number average molar mass

Pressure

Standard pressure (101.325 kPa)

Volumetric flow r a t e of mercury o r CO2

In jec ted pore volume

Pore volume of s l i m tube

Recovered pore volume

I n l e t dead volume

Out le t dead volume

Mole f r a c t i o n of propane i n mixtures

Temper a tu re

Temperature movement

T i m e movement

c o e f f i c i e n t i n equation of s t a t e

1.

2.

3.

4.

5.

6.

7.

8.

9.

p re s su re movement

dens i ty of o i l

dens i ty o f water

d e n s i t y of mercury

REFERENCES

Orr, F.M., J n r . and Taber, J.J. "Displacement of - O i l by Carbon Dioxide" F i n a l Report WE/ET/12082-9, 1980.

Y e l l i g , W.F. "Carbon Dioxide Displacement of a West Texas Reservoir O i l " SPE/DOE9785, 1981.

Ke l l , G.S. "Precise Representat ion of t he Volume Prope r t i e s of Water a t One Atmosphere" J . Chem. Eng. Data 12, 1, 66-69

K e l l , G.S. and Whalley, E. "The pVT p r o p e r t i e s of Water" P h i l Trans Roy SOC (Lond) 565 (1965)

Gair, D . J . , Grist, D.M., and Mi tche l l , R.W. "The East Midlands Addit ional O i l P ro j ec t " SPE 195 Presented a t t he 1980 European Offshore Petroleum Conference and Exhibi t ion.

Henry, R.L., and Metcalfe , R.S. "Multiple Phase Generation During COP Flooding" SPE 8812, presented a t t he F i r s t J o i n t SPE/DOE Symposium i n Enhanced O i l Recovery, Tulsa, Apr i l 20-23 (1980).

Holm, L.W., and Josendal , V.A. "Effect of O i l Composition on Miscible-Type Displacement by Carbon Dioxide". SPE 8814, presented a t t he f i r s t j o i n t SPE/DOE Symposium i n Enhanced O i l Recovery a t Tulsa , Apr i l 20-23, 1980.

Johnson, J.P., and P o l l i n , J .S. "Measurement and C o r r e l l a t i o n of C02 M i s c i b i l i t y Pressures" SPE/DOE 9790, p re sen ted a t t h e 1981 SPE/DOE j o i n t Symposium i n Enhanced O i l Recovery, Tulsa , A p r i l 5-8.'.

Schneider , G.M. "Physicochemical P r i n c i p l e s of Ex t rac t ion wi th Supercr i t i c a l Gases". Angew. Chem. I n t . Ed. Engl. 11 716-727 (1978)


NUCLEAR MEASUREMENTS OF FLUID SATURATION IN EOR FLOOD EXPERIMENTS

N. A. BAILEY, P. R. ROWLAND, D. P. ROBINSON

AEE Winfrith. Dorchester, Dorset DT2 8BH

ABSTRACT

This paper describes the nuclear measurement methods which have been selected for the determination of fluid saturation distributions within the cores of high pressure flood experiments to be carried out at Winfrith in a study of enhanced oil recovery processes. the accurate measurements of saturations, including their spatial and temporal variations, which are required to obtain a better understanding of the EOR process occurring within cores. It is intended that such measurements will provide a wider range of information for the validation of computer programs. These EOR codes are to be used for the assessment of the feasibility of EOR processes in North Sea Fields. A range of possible measurement techniques has been studied and the basis of the selection of the preferred nucleonic methods is described. The methods selected are based on the use of deuterium to determine water saturations or hydrocarbon gas componentsutilising a gama- neutron reaction, and the introduction of radioactive ferrocene as an additive to oil to measure oil saturation from gaama emission. The development work carried out to establish these nucleonic techniques is discussed in some detail, showing their clear potential, and the methods of application to high pressure core fluids are discussed. going flood experiments.

Such methods should be capable of producing

These techniques are currently being used in on-

INTRODUCTION

A programme of EOR studies is being carried out at AEE Winfrith under contract to the UK Department of Energy and an important element of this programme is the experimental programne. the testing of EOR processes under relevant conditions and the validation of codes, is centred around a number of high pressure flood rigs, the first of which is currently being constructed. experiments to be carried out at reservoir pressure, temperature and flow rate using reconstituted reservoir oils, correct salinity brines and a variety of EOR fluids including Cog and surfactants. The displacement process itself will take place in sandstone cores up to 5m long. required of such a rig are the analysis of the fluids produced from the outlet end of the core and the determination of fluid saturations within the core as a function of axial position along the core and time.

The selection, development and application of methods for such measurements of fluid saturation is the subject of this paper. used in the past for such measurements, and these are discussed below, but most

The experimental programme, whose objectives are

These rigs have been designed to allow

Key measurements which are

A number of techniques have been

are not applicable to high pressure core floods where the core has to be surrounded by a thick-walled steel pressure vessel. techniques have, therefore, been considered as they are less influenced by the presence of the pressure vessel and considerable experience with them already existed at Winfrith.

It has been concluded that at least two phases need to be marked within an EOR displacement test in which three phases can occur. Two preferred techniques have, therefore, been selected for the measurement of oil and water phases which have been subjected to detailed development, supported by theoretical assessments, to determine their performance under representative conditions. These tests have shown that very satisfactory measurements can be made of fluid saturations within sandstone cores, and work has continued to consider in detail the application of these techniques to the High Pressure Flood Rigs. One of the problems considered is the need to avoid any partition of the radioactive tracer from the phase which is being marked.

In parallel with these high pressure flood experiments, some low pressure studies have started at Winfrith, including a prograrane of waterflood displacement of oil, and these nuclear techniques are being used in these experiments where some comparisons are possible with other measurement methods.

Various nuclear measurement

SELECTION OF MEASUREMENT TECHNIQUES FOR FLUID SATURATIONS WITHIN CORES

The measurement of fluid saturation within cores is a difficult task and a review of the published literature suggests that it has only been attempted infrequently. Such measurements can, however, contribute substantially to the development of the understanding of EOR processes and their quantitative evaluation. for such measurements and these have been cbnsidered for use in high pressure floods. attractions, but capillary effects lead to the extraction of samples which are unrepresentative of local saturations. in the sample lines if the core were operated at reservoir velocities would present flushing problems leading to incorrect fluid analysis.

Some measurements have been attempted previously using non-intrusive techniques such as nuclear magnetic resonance (NMR) and microwaves. been used successfully for downhole applications by Brown and Gamson(1) and Nikias and Eyraud(2) who were able to distinguish between brine and high viscosity oils. if the high frequency alternating magnetic fields are to penetrate the core and this is not readily achieved in high pressure laboratory floods. techniques have been very successfully used by Parsons(3) to determine brine saturations but once again a nonmetallic containmect is required to avoid reflection of the microwave radiation and this reduces its applicability to high pressure experiments. techniques as they are non-intrusive and are far less sensitive to the effects of pressure containment around the core.

Nuclear Techniques

A number of nuclear techniques are potentially of use in the measurement of fluid saturnations within cores. The first technique considered is labelling particular fluids with y-emitting tracers. fluid can then be inferred from measurements of radiation as shown in Figure I. The water phase can be labelled by using radioactive forms of its dissolved salts, but the oil phase needs to have a material added to it which is of a hydrocarbon type containing a radioactive element.

Various techniques have been proposed for the present programme

Physical sampling of fluids along the length of a core has some

The low flow rates which would occur

NMR has

NMR does, however, r'equire a totally non-magnetic containment

Microwave

Preference is being given, therefore, to nuclear

The concentration of a particular

The main problem with such

485

a technique is that of handling significant volumes of continuously radiating fluids. simple, direct and well understood.

The method is, however, viable for fluid saturation measurement and is

W L T l CHANNIL ANALYSIR

F G I GAMMA TRACER METHOD

The alternative techniques rely on the response of fluids within the core to bombardment of y-rays or neutrons from an external source which can be turned off when not required. One method of this type which is being investigated is neutron activation. The core is bombarded with neutrons and the resultant y-radiation is detected and analysed using gamma spectroscopy to give a measurement of the relative abundance of the elements within the core.

A further alternative centres around the use of deuterium which emits a neutron when bombarded with high energy y-rays. of a neutron from deuterium in such a reaction is 2.23MeV. Deuterium concentration could then be determined from neutron flux. be labelled by substituting hydrogen atoms by deuterium. Supplies of heavy water, for example, are readily available at Winfrith and this can be added to B20 for marking the brine phase. A range of deutero-carbons can also be synthesised from D20. deutero-methane from the reaction of heavy water with aluminium carbide.

This avoids the problem of handling radioactive fluids.

The energy threshold for the emission

Many fluid components could

The simplest substitute hydrocarbon to produce would be

Preliminary Screening

Preliminary tests with the radioactive tracer and y-neutron techniques showed both of these methods to be fundamentally feasible, although each has its own difficulties.. obtained from reasonable activity levels for each method suggesting thaL further development of these techniques was worthwhile.

The absorption of neutrons was examined at an early stage as this was equivalent to the neutron decay logging techniques which have been used for a number of years with pulsed neutron sources downhole to measure local brine saturation ( 4 - 6 ) , or variations of salinity during waterf looding(7). Neutron absorption in a laboratory arrangement was investigated using a 1.5pg.californium source placed close to a sandpack with a porosity of 40% within a 5Omn bore glass cylinder. flux entering the sandpack was predominantly thermal and cadmium foil was used around the polythene to provide collimation. with brine over the lower half and oil in the upper half. separated by a thin polythene interface to maintain a sharp front in saturation and the transmitted neutrons were detected on a glass scintillator. measurement is based on the neutron absorption cross section in chlorine as a measure of brine saturation as this is the dominant cross section as shown in

Acceptable count rates, proportional to concentration, could be

The source was surrounded by polythene to ensure that the neutron

The sandpack was saturated The sections were

The

486

Element H D C 0 N a S i Fe

Cross Sect ion 0.173 2.6~10'4 1.8~10-3 10-4 0.289 0.083 1.32

Table 1 . On t r ave r s ing pas t t he i n t e r f a c e , however, t h e measured count r a t e f e l l by only 7% which was inadequate f o r d e t a i l e d s a t u r a t i o n measurements. was concluded the re fo re t h a t t h i s technique was no t v i a b l e un le s s f l u i d s have t h e i r c ros s s e c t i o n s increased by t h e add i t ion of a neutron absorber . The d i f f i c u l t y i n t h i s ca se could then be the sepa ra t ion of t he add i t ive from t h e phase it was marking and t h i s method has no t been explored f u r t h e r .

Tests were then c a r r i e d out i n v e s t i g a t i n g whether t he d i f f e r i n g absorpt ion c ros s s e c t i o n t o thermal energy neutrons of hydrogen and deuterium l i s t e d i n Table 1 could be employed, as t h e o r e t i c a l c a l c u l a t i o n s suggested a modest d i f f e rence i n absorpt ion behaviour could be obtained. such d i f f e rences could be de t ec t ed but no t on t ha t imescale o r r e s o l u t i o n required t o ob ta in a sharp p i c t u r e of t he movement of a f r o n t .

It

Prel iminary measurements showed t h a t

C 1

16.69

Table I Absorption Cross Sect ions (barns) t o 0.09eV Neutrons

I

10'1

10-1

I . loo0 I

CHANNEL N m x )

FIG. 2 TYPICAL NEUTRON CAPTURE GAMMA SPECTRUM WITHOUT PRESSURE VESSEL

4 8 1

A further technique which was investigated was the spectral analysis of gamma rays following activation by neutron irradiation. inelastic scattering and capture of neutrons, has been used by Hertzog(8) for downhole applications to determine the relative quantities of carbon, oxygen, silicon, calcium, iron, chlorine and hydrogen. Our experiments ccncentrated on the neutron capture process as the high energy neutrons needed for inelastic scattering led to shielding problems. on a sandpack cofitained within a 50nm bore aluminium tube with a 1 pg californium source as a neutron generator. The initial test results (Figure 2) produced a spectrum showing quite clearly the peaks associated with chlorine. Chlorine concentrations could not, however be obtained to the required accuracy within an acceptable timescale. When the sandpack was placed inside an 18nm thick steel tube to simulate the high pressure rig situation, the spectrum was dominated by iron peaks, with hydrogen and chlorine peaks being reduced to an unacceptably low level compared withthe background level produced by Compton scattering.

Because of these major difficulties encountered with neutron absorption and activation techniques it was decidad that reliance should be placed on y-tracer and y-neutron techniques which were then subjected to further development.

Such a method, covering both

The laboratory studies were carried out

ISOTOPE Na-22 cs-I37

GAMMA TRACER TECHNIQUES

Radio tracer techniques have to be restricted to y-emitting isotopes as Band y emissions will not penetrate the pressure vessel. As a gamna tracer technique depends on adding a radioactive material to a fluid, it is best achieved when the fluid normally contains materials which can be made radioactive. possible choice of radioactive material is further restricted by the need for a sufficiently long half life (preferably greater than 1 month) and sufficiently high energy gamna rays (greater than 0.5MeV) to avoid excessive absorption in the pressure vessel around the core.

Labelling the brine phase is relatively straightforward, as the naturally occurring chlorides of sodium and caesium are both readily available in radioactive form and their characteristics are sumnarised in Table 2. The oil phase is more difficult as hydrogen and carbon do not have gamma emitting isotopes. molecule which will behave as an oil component. It should also have tightly bound electron orbitals and not be strongly electro-positive. This reduced the list of candidate isotopes toSc-46, V-48,Fe-59 and Co-60. further reduced to Fe-59 and Co-60 due to the vast range of organo-metallic chemistry associated with these elements, with a preference for Fe-59 as the very long half life of Co-60 (5.26 years) leads to decontaminatidn and disposal problems. material, as it contains iron which can be made radioactive, and is one of the simplest organo-metallic molecules, containing only carbon and hydrogen in addition to the iron. as a heavy liquid oil fraction. in Table 2.

The

A suitable isotope must therefore be wrapped in a hydrocarbon type

This list was

Ferrocene (Figure 3) was therefore selected as the most suitable

Its molecular StruChure suggksts. that it should behave The characteristics of Fe-59 are also included

Table 2 - Candidate Isotopes for Labelling Fluids

Fe-59

HALF LIFE 2.6 years 30 years 45 days

0.51, 1.28 0.66 1.10, 1.29

488

nc,-&~cn wc- CH

FIG. 3 FERROCENE MOLECULE.

Prel iminary Tes t s

The f i r s t s e r i e s of t e s t s were c a r r i e d ou t on a I c m diameter pure s i l i c a sandpack, set up i n s p e c i a l g l a s s apparatus a s shown i n Figure 4 which allowed v i s u a l examination of the displacements a t the same t i m e a s ope ra t ing a t temperatures of around 90°C. tests were c a r r i e d ou t with 3% br ine , l a b e l l e d with Cs-137 a t an a c t i v i t y l e v e l of ZOpCi/ml, and medicinal pa ra f f in . could be marked with sodium f lou rosce in r and the o i l phase by Sudan Red dye. A col l imated sodium iodide d e t e c t o r was used t o measure the r a d i a t i o n using lOcm thickness of lead and a slit width of 3 m . Ca l ib ra t ion was c a r r i e d out i n s i t u both i n the empty tube and i n the sandpack a t 100% b r i n e satuEationo. The lat ter gave count r a t e s of 3000 per minute. I minute t h i s g ives a s tandard e r r o r l e v e l of ?1.8%.

The sandpack was 25cm long and the displacement

For v i s u a l purposes the a c t i v e b r ine

Using a count per iod of

FIG4 APPARATUS FOR GAMMA TRACER DEVELOPMENT TESTS.

489

The experimental prograrrme on this apparatus included:-

i downward displacement of inactive brine with active brine (miscible)

ii downward imniscible displacement of active brine by oil (paraffin)

During the first test a record was kept of the brine level above the sandpack so that the sandpack porosity could be determined both from the velocities of the front, determined by radiation measurement and visual observation of the measured brine level as well as the activity levels in and above the sandpack.

A typical scan of the sandpack for the first experiment is shown in Figure 5 where the characteristic dispersion of the front in miscible displacement can be seen. The porosities calculated (38%) agreed closely, the agreement lying within the experimental uncertainty (22%). When the active brine was displaced with oil (Figure 6) similar measurementsweremade and these indicated a frontal oil saturation of 85%. measurement of the paraffin injected into the core.

The results were considered promising as it was clear that accurate measurements were being obtained and development of the technique was transferred t o sandstone cores. was adsorption of the tracer within the sandstone.

This was confirmed by direct

At this point the first difficulty with this technique appeared which

0 5000

FIG5 DOWNWARO DISPLACEMENT OF UNLABELLEO BRINE BY LABELLED BRINE

COUNT )LII MlNUtK

0 5000

HG.6 DOWNWARD DISPLACEMENT OF LAMLLED BPlM BY OIL.

490

Adsorption

When radioactive salt tracers are dissolved in brine they form ions and the metallic components adsorb onto the surface of the rock and particularly onto clay structures within sandstones. This is very noticeable when a low concentration radioactive brine is added to dry sandstone with a substautial fraction of the measured activity eventually coming from the surface of the rock. A series of adsorption tests was, therefore, set up to investigate this behaviour using the sandstones to be used in the high pressure flood experiments. These sandstones, Clashach (20Omd permeability, 13% porosity)and Rosebrae (125Omd permeability, 24% porosity), are Triassic quarry material and have only modest clay contents.

In these experiments a rock sample was mounted in a Table Tube (Figure 7) where knowing how much solution should exist within the porous material, the amount of adsorbed isotope could be determined. systematically varied and the results for the Clashach and Rosebrae are shown in Table 3.

The salt concentrations were

Table 3 - Adsorption of Tracer on Sandstone

Condition

C las hac h a Solution of 6% NaCl + 1% CsCl + Cs-I37 tracer b Solution of 6% NaCl + 6% CsCl + Cs-137 tracer. c NaOH added to (b) to pH - 1 1 d Solution of 6% NaCl + Na-22 tracer e Sollition of 6% NaCl + 5% MgC12 + 5% CaC12 + Na-22 trace1

Rosebrae f Solution of 10% NaCl + 10% CsCl + Cs-137 tracer t- g Solution of 10% NaCl + 10% CsCl + Na-22 tracer

Adsorbed Activity DissQlved Activit!

in Pores

I . 3 0.53 0.47 0.20 0.12

0.10 0.05

FIG. 7 APPARATUS FOP ADSORPTION MEASUREMENT AND TYPICAL GAMMA SCAN

491

In all cases a return to inactive k i n e resulted in the activity in the sample falling to zero. decreased with increasing tracer salt concentrations, that adsorption was reversible, that the addition of divalent salts or increased pH had little effect on adsorption, and that caesium was adsorbed in preference to sodium. The tests were carried out with radiotracer concentrations of IOuCi/ml.

The most representative conditions were with brine made of 6% NaCl using a sodium-22 tracer. Under these conditions the radiation from adsorbed isotope was only 20% of that from the isotope dissoloved in the brine. It might be possible to overcome the adsorption problem by pre-saturating the core with active brine before saturating it with oil. If this quantity of tracer then remained adsorbed in the core during a flood experiment, it could be treated as an additional radiation background and measurements could still be made of water saturation albeit at a reduced accuracy. This would require that the rock remained totally water wet throughout and it is more likely that some of the adsorbed material will be displaced during a flood experiment making the interpretation of radiation measurements extremely difficult. were made in which the sandstone was preflushed with inactive brine in an attempt to saturate adsorption sites. the inactive and active ions exchange during the subsequent active displacement.

Adsorption of water-borne tracers does, therefore, severcl; limit the power of this technique to measure water saturations, so consideration was switched to the labelling of the oil phase wirh a non-polar, non-ionising material, which should not adsorb and which would allow measurement of the oil phase saturation.

Labelling the Oil Phase

Ferrocene has been selected as a suitable organo-metallic material for use as an oil tracer as it satisfies the various criteria discussed above and it is readily available in inactive form. requires either irradiation in a reactom or synthesis of ferrocene from radioactive iron via the reaction using potassium hydroxide as a condensing agent. have shown that synthesis is possible, but the main emphasis in the development has been associated with irradiation which is expected to be more econamic. Trial irradiations have been carried out on the PLUTO and DIDO reactors at Harwell for periods of up to 23 days to give a specific activity of about 0.4 mCi/pm. is in ferrocene with the remainder in a material which is insoluble in hydrocarbons. Chalmers reaction(9) which results in the iron being ejected from the molecule under irradiation, allowing the iron to oxidise in the surrounding atmosphere. The two radioactive components can readily be separated by dissolution, filtration and recrystalisation. would be about 3gm of radioactive ferrocene containing about 1.25mCi of activity. 25OuCi/litre, the statistical uncertainty in the saturation measurement on a representative core geometry will be less than +3% on a 100% saturation. accuracy is based on a 9mm slit width, a JO minute counting time, and is derived from preliminary measurements in a representative geometry.

Such a concentration is far below the solubility limit of ferrocene in oil, which was found to be about 2.5% at 2OoC and appreciably higher at higher temperature. behaviour of ferrocene between oil and brine by dissolving it at a concentration of about 0.1% in oil and then contacting the mixture with brine at 100°C for several days. determined colorimetrically or by radiation measurement.

It can be concluded, therefore, that the adsorbed fraction

Some tests

Some improvement resulted from this but

To convert it to its radioactive form

of ferrous chloride with cyclopentadiene Investigations of the latter

At the end of such an irradiation about 30% of the activity

It is believed that this breakdown is induced by the Szilard-

A typical yield from a standard irradiation

When dissolved in 5 litres of oil to give a specific activity of

This

Several tests have been carried out to examine the partition

The amount of ferrocene transferred to the water phase was then Both methods,gave

492

similar results with a partition coefficient less than 10-5 for neutral or alkaline brine but with an increased value of 10-3 for a strongly acid brine (pH-2). travel with and mark the oil. the oil, it appears to provide a very suitable method for saturation measurements.

As the solubility of ferrocene in brine is so low, this compound will As quite modest quantities are required to mark

GAMMA-NEUTRON INTERACTION

If ferrocene is to be used for labelling the oil phase, and y-emitters are of limited use for labelling the water phase, then an alternative method is required for the measurement of water phase saturations. The gamna-neutron reaction with heavy water has been selected to provide such a method. reaction can occur in any element if it is bombarded by gamnqs with energies exceeding the binding energy, but the second lowest binding energy occurs in deuterium (2.23 MeV). Thus measurement of water saturations can be achieved by using heavy water and bombarding the core with gamna rays with an energy in excess of 2.23MeV. The neutron flux produced is proportional to water saturation. The only element with a lower binding energy is Beryllium-9, which will not be present in the flood experiments. The only convenient g a m a source with a suitable energy level is sodium-24, but this unfortunately has a short half life (15 hrs) which means that special arrangements have to be made for the delivery of sources. but existing collrmercial devices would be too powerful for this application.

This technique has been considered here as a means of marking the water phase, as D20 will also have a negligible effect on the physical and chemical characteristics of the water phase. Deuterium could also be used to determine the local saturation of a particular hydrocarbon as deutero-carbons can be synthesised. The simplest would be the production of deutero-methane from the reaction between D20 and aluminium carbide, but other methods such as the Fischer Tropsch synthesis are available to synthesise higher deuterocarbons.

Development Te 8 t s

Development tests on the gamma-neutron method have been carried out on the '

apparatus shown in Figure 8. sandpack contained inside an aluminium tube with a heavy water saturation at one end separated from a light water saturation by a thin polythene film to maintain a sharp saturation front. thick steel vessel representing the pressure vessel surrounding the core in a High Pressure Flood experiment. surrounded by a polythene block containing BF3 or He3 neutron detectors. The polythene is required to thermalise and reflect neutrons before entering the neutron detectors. Optimisation studies showed that 1 6 ~ of polythene was required between core and counters to achieve optimum thermalisation and 50mn beyond the counters for reflection. up by the source and its collimator. activity of about 100 mCi and was mounted inside a lead collimator system with an adjustable slit allowing a gamma ray beam the full width of the sandpack. slit design limited the beam to a few millimetres along the length of the sandpack, so that axial variations in saturations can be adequately resolved. In the y-tracer techniques described earlier the detector was collimated, as it is not possible to collimate a source in the fluid.

The neutrons detectors were connected to a multi channel analyser initially which allowed the spectra to be investigated in detail and compared with those from pure neutron sources, but later tests have used more traditional Harwell 6000 apparatus counting all pulses above a particular threshold level which was set to reject noise.

Such a

An alternative would be to use a y-beam generator

This apparatus consisted of a 2" diameter

The sandpack was set up on its own or within a 181m

Most of the circumference of the sandpack was

The remainder of the circumference is taken The sealed source utilised had an

The

493

‘OLWHENE BLOCK

FIG. 8 APPARATUS FOR GAMMA -NEUTRON INTERACTION DEVELOPMENT TESTS.

The development experiments were concentrated on saturation measurements through a saturation discontinuity and have allowed the systematic investigation of shielding thickness in the collimator and slit width. out using 5Omm thick lead for the collimator, but it became clear that this was insufficient as a significant flux was occurring away f r w the slit position. It was found necessary to increase the lead thickness to 1 2 h to reduce this background gamma flux to an acceptable level. The weight of the collimator system at about 500kg is one of the factors to be taken into account in the design of traversing equipment.

The results of scanning through an interface with a thick walled collimator are shown in Figure 9-11. These figures show quite clearly that the step front in saturation has been smeared into a measured S-shape curve where saturations in the range 10%-90% appear over a length of about I a n . Theoretical calculations have been carried out to determine the uncollided gamma flux distribution along the centre line of the sandpack using the relationship

Initial tests were carried

where (ih is the uncollided flux,dOthe source flux, and Mi the total linear attentuation coefficient for the different materials each of thickness ti in the path of the flux, which is a function of X.

to predict the measured piofile with,e.n equation of the form From such calculations it is possihle

(2) I-

P,(x) = la f(xrl)Pt(xl)dxl

where Pi,, and Pt are the measured and true profiles respectively and f is a function of the collimator and test section geometry which can be derived analytically or from calibration experiments. Any measured profile can, therefore be deconvoluted to give the true profile by means of the relationship

where the Fourier transform of g is thereciprocal of the Fourier transform of f.

4 9 4

1.0

0 8

O b

0 4 .

0.2

1.c

0 1

0.6

0.4

0.1

C

INTERFACE

- COUNT U T E NOIIWALISED 10 1 0 0 Ye 020

-

PROFILES

-

- WIYSICAL

I 1 1 1

- 4 0 -30 -lo - 10 0 + 10 tm + 3 0 4

ACTUAL DISlRIBUtlO

COUNTCUTE

1 H t O l t t l C ~ ~ DISIRIOUIION WllHoUI VESSil PNSSURE VESSEL

MEASWD MSV WRH aESSURE

0 +I +2 +4

0

FIG. 9 MEASURED PROFILES FOP 0 -100 O/o D 2 0 STEP IN SATURATION. COLLIMATOR SLIT WIDTH - 4 mm

FIC.10 MEASURED SATURATION PPOFILES FOR VARIOUS D20 SATURATIONS KIT WIDTH = 4 mm

495

A profile derived from equation (21 for a sandpack without a pressure vessel has been included in Figure 9. the profile. probably induced by uncertainties in background level and the fact that some collided gamma rays are scattered with energy levels in excess of 2.23MeV and can produce neutrons from deuterium. 10% and 90% saturation levels is 0.8cm which compares satisfactorily with the measured values of about lcm.

The signal is also shown in these results to be directly proportional to deuterium concentration. Increasing the slit width in the collimator increases the count rate and, hence, improves the counting statistics, but at the cost of increasing the smearing of the saturation profile.

Close agreement can be observed for most of The discrepancies at the left hand side of the profile are

The predicted width of the front between

cnmns WED ON IS MINUTE COUNT

0 2 4 6 FIC.11 EFFECT OF SLIT WIDTH ON COUNT RATE I00 OIC, D2 0

PRESSURE VESSEL. WITH

Tests have also been carried out on a sandpack with only a short length of light water saturation preceded and followed by heavy water. Figure 12 confirm the ability of this technique to determine the length of such a short slug of fluid. out a pressure vessel simulation. to some attenuation of the neutron flux and further smearing of the saturation profile.

These results confirm that the y-n interrogation of deuterium provides a method which gives a good quantitative measurement of the saturation level of deuterium bearing species as a function of axial position and time. proposed to use this method for such measurements on high pressure flood experiments.

A further merit of this measurement technique is that it can be used to determine the dispersion coefficient for the core. is flooded with normal brine prior to oil flooding to set up the starting conditions for a displacement experiment. water brine. This idealised first contact miscible displacement with negligible density or viscosity differences, results in the development of a classical dispersion front and by measuring this profile using the gamma-neutron technique the dispersion coefficient for the core can be derived.

The results shown in

In Figures 9 to 12 data are included both with and with- It is observed that the pressure vessel leads

It is

At the start of an experiment the core

The brine is then displaced by heavy

496

I : 1

1

0 4 -

\ \-f f 0.1 -

f MEASURED PROFILE

ACTUAL MOFILL

I CMS ,

l- FIG.12 PROFILE ALONG D 2 0 SATURATED SANDPACK WITH 4 C M LENGTH

SATURATED WITH H20 . WITH PRESSURE VESSEL. SLIT WIDTH 8 m m

APPLICATION TO HIGH PRESSURE FLOOD TESTS

As a result of the development tests described above it has been decided to use radioactive ferrocene to label the oil phase in the High Pressure Flood Tests and heavy water to label the brine phase using a y-n reaction interrogation method. measuring saturations over the complete length of cores up to 5 metres long, traversing along cores to obtain the axial saturation distribution at intervals which can be as small as Icm. counting will be carried out for approximately 10 minutes to give sufficiently large counts to ensure reasonable accuracy. satisfactory for most conditions including a shock front travelling at 0.3mlday which might be typical of North Sea conditions. In the measurement period such a front will have moved only 2mn, which is small in relation to the slit width Although higher rates may have some experimental interest, the errors involved would be mitigated by front smearing induced by capillary forces in inmiscible processes or dispersion in miscible processes. If necessary the counting time could be reduced by increasing the ferrocene concentration and using a higher activity sodium 24 source.

It should be noted that these two methods cannot be used simultaneously as the high level of gamma radiation occurring when the sodium 24 source is in use would swamp the radiation coming from the ferrocene. measurement at a time leads, however, to simplification of the apparatus to be used on the flood rigs as only one collimator is required. The apparatus will be similar to that used for development tests (Figure 8) with He3 neutron detectors mounted in the polythene blocks for the y-n method.

It is intended that the measurement system should be capable of

At each position where measurements are required,

Such a period is generally

This restriction to one

497

Detectors are not placed directly helow the core so that the measuring apparatus can be removed readily from the core. radiation from the ferrocene, the sodium source will be removed and replaced, within the same collimator, by a sodium iodide crystal detector. was selected in preference to a Ge(Li) detector to eliminate the need for cooling the crystal to cryogenic temperatures. and becuase of its higher sensitivity.

The detectors, fed from separate Em supplies for neutron and sodium iodide detectors, will have their outputs taken to a colllllon multi channel analyser together with the outputs from separate detectors which will be used to measure background radiation levels dimultaneously. h this way the background level can be automatically removed from the measured signal. will be integrated into a minicomputer system which will control the flood rigs and carry out data processing. calibrated on a representative geometry at 100% saturations of brine and oil.

The first high pressure flood rig is currently being constructed but these measurement techniques are now in use in low pressure studies of oil displacement by waterflooding. These experiments are being carried out using brine and tetradecane in the same sandstone materials which are to be used for the high pressure experiments, and encompass both displacement tests and steady state relative permeability measurements.

When measurement is required of y-

Sodium iodide

The multichannel analyser

The detector and analyser system has to be

Conclusions

It can be concluded that two viable measurement techniques have been established for the measurement of fluid saturations within the cores of high pressure flood experiments. prcduced synthetically from active iron or from reactor irradiation. allows the oil phase saturation to be measured. A convenient method for marking the water phase with heavy water and interrogating it via a gamna-neutron interaction to measure the water phase saturation has been evaluated. prmise for measuring the concentration of a particular component in a hydrpcarbon gas or liquid system by synthesising deutero-carbon additives.

Reasonable levels of source activity and conventional counting techniques allow these saturations to be measured within about 10 minutes with a statistical uncertainty of less than k3.Z at the 100% saturation level and at the 25% saturation level the result would typically be 0.25 k0.02. These techniques allow axial and temporal variationc in fluid saturations to be determined as only about Icm of the core length is viewed at any one time snd the detectors aan be traversed along the core. can be accurately determined and although the measurement introduces some smoothing of sharp fronts, it is possible to convert the measured profile back into a more acclirate saturation profile by a deconvolution process.

The new tachniques are to be used on the high pressure flood experiments to be carried out at Uinfrith and thcy are already in use there on low pressure experiments.

Labelling the oil 'phase with radioactive ferrocene, which can be

This method also has

The location of any sharp front in saturation

Acknowledgement - This work has been supported by a contract from the UK Department of Energy.

498

1

3 -

3

4

5

6

7

8

9

REFERENCES

BROWN, I( J S and W O N , B W: "Nuclear Magnetism Logging", Petroleum Trans. (1960) 219, 199-207.

NIKIAS, P A and EYRAUD, L E: "Some Examples of Nuclear Magnetism Logging in Three San Joaquin Valley Oil Fields" JPT (Jan 1963) 23-27.

PARSONS, R W: in Laboratory Flooding Experiments. SPEJ (Aug 1975) 302-309

CLAVIER, C. HOYLE W. and MEUNIER, D: "Quantitative Interpretation of Thermal NeiitronDecay Time Logs: Part 1 . Fundamentals and Techniques". JPT (June 1971) 3 743-755.

WAHL, J S et al: "The Thermal Neutron Decay Time Log". SPEJ (Dec 1970) 365-,375.

RICHARDSON. J E et al: "Methods for Determining Residual Oil with Pulsed Neutron Capture Logs". JPT (May 1973) 593-603.

YOUNGBLGOD W E: "The Application of Pulsed Neutron Decay Time Logs to Monitor Waterfloods with Changing Salinity". JPT (June 1980) 987-963.

HERTZOG, R C: "Laboratory and Field Evaluation of an Inelastic Neutron Scattering and Capture Gamma Ray Spectrometry Tool". 327-340 OVERMAN, T and CLARK, H M: "Radioisotope Techniques". New York (1960) 378.

Microwave Attenuation - A Neu Tool for Monitoring Saturation

SPEJ (October 1980).

McGraw-Hi11


CHARACTERIZATION OF EOR POLYMERS AS TO SIZE IN SOLUTION

ROY DIETZ

Division of Materials Applications, National Physical Laboratory, Teddington, Middlesex, TW1 I OL W UK

A~STRACT

The potential is explored of extending to the characterization of EOR polymers the conventional electrical Sensing zone (ESZ) technique. Theoretical expectations and experimental factors are discussed. tested with well-characterized fractions of polyacrylamide and some biopolymer samples for which characteristics relevant to EOR use are known. largest solution species can be detected, but those species are significant in detedning technological properties. For polyacrylamides the ESZ response correlated with hydrodynamic volume. For biopolymers there were correlations with screen factor and with viscosity at concentrations of relevance in EOR. The method offers promise for monitoring solutions rapidly for microgel.

The method is

Only the

INTRODUCTION

The size of solution species is relevant to the possible use of polymers in EOR in two main respects. Solution species must be large enough to give a high viscosity at low concentrations for mobility control, but not so large that they block pores in the substrate and give rise to poor injectivity. A simple means of characterizing polymers as to size in solution would aid the production of improved polymers for mobility control, and could also serve as a means of monitoring solutions for adequate injectivity. largest solution species present control injectivity; the size distribution gives rise to great difficulties for such conventional techniques as gel permeation chromatography, ultracentrifugation and fractionation followed by independent characterization by light-scattering photometry or viscome try.

The number and size of the estimation of that part of

It is clear from experiments with filters of controlled pore size (1) (2), from determinations of radii of gyration by light-scattering photometry (3) and from estimates of hydrodynamic volume from viecometry (4) that the size range of relevance is some 0.5-1.0 pm. of particles of that size can be characterized by the electrical sensing zone (ESZ) technique. This paper describes an exploratory investigation into the applicability of that technique to dissolved polymer. samples are used to relate the ESZ response to molecular characteristics for polyacrylamide fractions and to rheological characteristics for biopolymers

In conventional particulate metrology suspensions

Well-characterized

500

DISSOLVED POLYMER IN AN ELECTRICAL SENSING ZONE

Principle and range of the ESZ method

In the electrical sensing zone method (Figure 1) a dilute suspension in a salt solution is made to flow through a small orifice (diameter - 100 um). Coulostatic circuitry is used to maintain a constant current between electrodes placed on opposite sides of the aperture. through the aperture, the electrolytic resistance is increased by the equivalent of the volume of electrolyte displaced.

When a suspended particle passes

M&MOMEl CONTACT

TO VACWM T

U

AMPLIFER

CIRCUIT

OSClLLOSCOPE

COUNTER START I STOP

C WNTER 9 Figure 1. Schematic of the ESZ method

The constant current is maintained by a voltage pulse of magnitude proportional, to a good approximation, to the size of the suspended particle. instruments have discriminator circuits capable of counting and sizing the voltage pulses. suspensions of particles of known size. particles greater than some 1 urn in diameter; operation with insulating particles of diameter 0.4 um is feasible.

Polymer structure in solution

Comnercial

The voltage scale can be calibrated in experiments with Routine operation is possible with

with precautions to reduce noise,

Application of the ESZ method to the sizing of dissolved polymer molecules introduces some special features connected with the nature of the solution species. Candidate polymers for EOR use fall into two classes of molecular

501

structure (Figure 2). The synthetic polymers (polyacrylamide, poly(viny1- pyrrolidone)) can be modelled as flexible chains. structures approximating more closely to rigid rods, at least near ambient temperature; temperatures above 60 O C .

Most biopolymers have

for xanthan there is evidence (5) of a structural transition at

Polymer -polymer <-> Polymer -solvent interact ion interact ion

Helical rod

1 Figure 2. Polymer structure in solution.

Flexible chain polymer molecules pervade m c h larger volumes in solution than the volume of the polymer molecule itself. Within that pervaded volume, most of the solvent molecules are close to several polymer chain se@ments. turns out that most of the solvent within that pervaded volume is incapable of independent hydrodynamic flow. of flexible chain molecules can be treated (6) as those of suspensions of spheres, consisting largely of bound solvent. spheres, for a monodisperse polymer of molar mass M in solution of concentration c and with an effective volume fraction 4 is

It

The hydrodynamic properties of dilute solutions

The effective volume of those

W

N c Vh = -

where No is Avogadro's constant. fraction is related to viscosity by

For a suspension of spheres, the volume

n = no(l + 2.5++ higher terms)

where n [n] can%e related to V

is the solvent viscosity. The measurable limiting viscosity number

h

502

so that for the low concentrations used in ESZ determinations, the volume of the equivalent sphere can be taken as

1

Real polymer samples are heterogeneous in molar mass and therefore in hydrodynamic volume. For a typical anionic polyacrylamide (molar mass 4000 kg/mol; 20% hydrolysed) the average hydrodynamic radius calculated from Vh is some 80 nm in 0 . 5 M NaC1. molecular aggregates may be present. fugation, the hydrodynamic properties are consistent (8) with rigid rod molecules, of length some 0.6 pm and diameter some 2 nm. Again there is evidence of much larger solution species (9), particularly in unpurified comnercial material (10).

Polymer 'particles' in the ESZ

There is evidence (7) that much larger For a xanthan sample purified by centri-

Passage of a solution of a flexible chain polymer through the ESZ aperture corresponds to the passage of spheres of solvent of much reduced mobility. Such a 'particle' will be electrolytically conducting, but the resistance should be higher than that of the same volume of solvent. The salt-containing polymer gels used in electrochemistry to provide electrolytic conduction with minimal ion transport are a relevant analogy. dissolved flexible chain polymer molecule will be smaller than that of an insulating particle, such as a polymer in latex suspension, of the same size. Biopolymer molecules in rigid rod conformation include smaller quantities of solvent, so that the discrepancy may be smallegbut in general dissolved polymer is to some extent 'transparent' in an ESZ.

It follows that the ESZ signal of a

There is also the question of molecular dynamics. Brownian motion causes the segment density, molecular shape and effective size of a flexible chain molecule to change continuously. Polymer properties are described in terms of average molecular dimensions, where the averaging is both over time for a given molecule and over the population of molecules of given chain length. fluctuations will be reflected in dispersion of the ESZ signals; polymer sample containing only onemolecular species should give signals over a discrete range of apparent size, with a peak at the pulse height corresponding to the most probable size.

Those an ideal

EXPERIMENTAL Materials

Polyacrylamide fractions were produced by the controlled addition of ethanol to dilute (0.007 g ~ m - ~ ) solutions of comaercial polymers, non-ionic and anionic, in water. Fractions were characterized by capillary viscometry (FICA Autoviscometer) and by light-scattering photometry (chrometix larangle photometer) in the solvent (0.01g/cm3 NaCl) used for the ESZ experiments. polymers were gifts from Dr I G Meldrum (BP Research, Sunbury) and Dr I W Sutherland (University of Edinburgh).

Bio-

Polymer solutions were prepared in 'Isoton' a proprietary (Coulter Electronics) saline solution, (ca 0.01g/cm3) supplied for haemacytometry. The effect of electrolyte concentration was studied by using more concentrated saline solution (0.04 g/cm3) filtered through Millipore membranes of pore size 0.1 pm.

503

ESZ measurement requires that only single particles traverse the aperture. The maximum counting rate of the instrument used limits the suspension concentration to 107-108 particles/cm3. tration corresponds to a mass concentration of 10-10-10’9g/cm3. in that concentration range were prepared by successive volumetric dilution of parent solutions of polymers of concentration ca 10-3g/cm3; those parent solutions were prepared gravimetrically and with gentle magnetic stirring overnight.

For a molar mass of lo4 kglmol, that number concen- Solutions with-

ESZ technique

The size range of insulating particles to which the ESZ method is conven- tionally applied extends down to only 1 Um; smaller signals become obscured by background noise. In order to extend the useful range, detailed attention was given to earthing and shielding. Faraday cage, and the mains supply was routed through an isolating transformer. With these precautions the background count was acceptably low at a pulse height corresponding to an insulating particle of diameter ca 0.4 Irm. A polymer latex suspension of that diameter was used to calibrate the size scale. The aperture was of nominal diameter 30 pm and the volume of liquid passed through was constant at approximately 0.05 cm3.

The instrument [Coulter ZB] was housed in a

Polymer solutions were analysed in the manual mode in order to avoid possible artifacts of automatic subdivision of the size range. was preceded by a background count. made by reducing the size threshold stepwise throughout the range for which the polymer count exceeded the background by a factor of ten or more. determinations were made in all cases; few per cent except at the extremes of the range.

Each analysis With the polymer solutions counts were

Duplicate counts were reproducible to within a

RESULTS AND DISCUSSION

ESZ analyses of the polymer solutions are presented as integral distributions of the number of particles per gram of polymer of apparent size greater than the abscissa values, which relate to the calibration with insulating particles. Smooth curves were drawn through 20 points representing counts throughout the size range. polymer-solvent interaction, and therefore of the chemical structure of the polymer, comparisons are made only between results for polymers of similar s tructure.

ESZ response versus molecular properties;

Since ESZ transparency is presumably a function of

polyacrylamide

The conjecture that the ESZ response of polymer samples of similar chemical structure should correlate with hydrodynamic volume as defined by equation 1 was tested in experiments with seven polyacrylamide fractions. fractions of nonionic polymer and three of anionic polymer were characterized by viscometry and light-scattering photometry; ranged from 3400 to 18200 kg/mol. loo00 kg/mol contains 6 x 10l6 particles/gram. [Figures 3 and 41 the number of particles per gram sensed before the signal to background ratio fell below 10 never exceeded percent of the particles present were sensed, even allowing for the poly- dispersity of the fractions. adsorption of polymer on the glass surfaces. butions gave further evidence that only a fraction of the solution species present were detectable; lowest accessible size.

Four

the mass-average molar masses A monodisperse sample of molar mass

In the ESZ experiments

It follows that only a few

In this estimate no account was taken of possible The shape of the measured distri-

thus most of the curves were rising steeply at the

5 0 4

The hydrodynamic volumes of the fractions calculated from viscometry and light-scattering photometry are average values and refer approximately to the most abundant species present, which are clearly not detected by the ESZ method, even for the fraction of largest molecular size. not provide, therefore, a critical test of the supposed correlation with hydrodynamic volume. distribution measurable only if the complete size distributions of the fractions chanced to be of similar shape. Figure 3 shows that larger particles were detectable for the nonionic fraction of largest average hydrodynamic volume throughout the ESZ size range.

The experimental results do

There would be a correlation with the small part of the

Non- ionic polyocrylomides . - Mm - "h

kglmol pm3

_ _ _ - - - _ 18200 0.031

16700 0.027

-.- 17200 0.028

- 8380 0.0081

-

----

I 1 I 1 1 I 1 I 0.4 0.6 0 .8 1.0 1.2 1.4 1.6 1.8

Apparent diometer I pm

Figure 3. ESZ response of nonionic polyacrylamide fractions

For the anionic fractions (Figure 4) the relation is less clear, but in the ESZ size range below 0.6 pm the recorded distributions follow the order of average hydrodynamic volume. The effect of added electrolyte is also consistent with a relation between the ESZ response and hydrodynamic volume. In more concentrated electrolyte (0.04 g/cm3) results for non-ionic polyacrylamides were little changed, but the number of particles sensed for an anionic polymer fell sharply. It is well known (11) that the radius of gyration and hydrodynamic radius of anionic polyacrylamides fall with increasing electrolyte concentration because the effect of repulsion between carboxyl groups along the chain is reduced.

505

-,--- -- - . I -

!

\,

\..

T. - 1- -.-r - - 7'

Anionic polyacrylomides - Mm "h

kglmol pm3 - -

- 3400 0.0011

---- 17700 0.0072

11600 O.OOL2 -. - -. . -

Apparent diameter1 pm

Figure 4. ESZ response of anionic polyacrylamide fractions

In summary, the results for well-characterized polyacrylamides are not inconsistent with hydrodynamic volume as the molecular characteristic determining the ESZ response. of particles sensed is small, even for fractions of large molar mass. technique in the conventional form employed here is sensitive only to the largest particles present, which may well be molecular aggregates. that such aggregates are thought (12) (13) to be important in determining properties of water-soluble polymers.

ESZ response versus rheological properties;

investigate with biopolymers since fractions of different molecular size but similar chemical structure are not readily accessible, at least at high molar mass. Attempts were made to fractionate xanthan by controlled orecipitation above bi) "C aud by prcparnt ivt. c i a I Iwrilwnticrn c:lii-(iiii.itc,gr;ilIhy h u t without success. cal properties relevant to use in EOR. series of experimental biopolymers prepared under contract (OT/F/443) to the Department of Energy at the University of Edinburgh; (Keltrol) was included for comparison. scleroglucans possible candidates a separate comparison was made between three samples.

Only qualitative evidence can be offered since the fraction The ESZ

It is worth noting

biopolymers

The relation between ESZ response and molecular size is more difficult to

Inscead the ESZ response of whole biopolymers was related to rheologi- Such information was available for a

a commercial xanthan Since their thermal stability (14) makes

for use under North Sea reservoir conditions,

506

Table 1. Rheological properties of biopolymers at 3 x g/cm3 in salt water

sample

Keltrol

7824

1.15

9.4

Screen factor Size of filter/vm at IS-' 1 volume 10 volumes that retains

2630 26.5 20 3

2290 9.64 11.28 0.3

<790 1.5 1.8 0.22

1096 7.38 9.36 0.45-0.3 I ESZ results for biopolymers (Figure 5) were consistent with those of poly-

acrylamides in that only a small fraction of the particles present were sensed, assuming a plausible molar mass (5000 kg/mol). Similarly the integral distribution of apparent size did not reach a limiting lower plateau. limitations, however, there were clear correlations with properties of significance for EOR use; those pro erties were measured at the University of Edinburgh

Within those

at a concentration (0.003g/cm ! ) much higher than that used in ESZ analysis.

More large particles were detected (Figure 5) in solutions of the commercial xanthan, Keltrol, than for the remaining polymers; Keltrol fails to pass in solution through a 1 vm filter.

of the samples tested only The viscosity of

I I I I 1

r Biopol ymerr

neltrol Research wrmplc 7824. uncentriluged (upprr) and

Research rompl. 1.15

bscarch romplc 9.4

- t:. \ a * , ...._.

' *

\ .*a, c.ntri1ug.d (lower)

-. --.

Figure 5 . ESZ response of biopolymers

5 0 7

solutions at a shear rate of Is-' follaws the order of the number of particles of apparent size L 1 um, but does not follow that of the number of apparent size 2 0.4 um. The screen factor, after 1 and 10 volumes, follows the former order. Figure 5 also includes the effect of centrifugation (40 krpm) upon the ESZ response of one sample (7824); sizes below 0.7 pm, but a clear decrease in count above that size. Since centrifugation selectively removes larger particles, the result links directly the ESZ signal to size in solution.

there was no significant change at apparent

Three scleroglucans were available for test (Figure 6); Actigum CSll and L21 were comnercial materials and research sample E was from the University of Edinburgh. correlations established above (Figure 5) one might predict that the screen factor and viscosity at 1s-l would be higher for L21 than both CSll and sclero- glucan E, and that the last two would have similar properties.

We have no rheological data for the set, but on the basis of the

As with the synthetic polymers studied, the ESZ response of biopolymers reflects the few largest solution species present. tions those species are deformable molecular aggregates termed microgel. correlation between the ESZ response at a concentration such that interparticle interactions can be neglected and rheological properties of the semi-dilute regime in which interparticle interaction is strong suggests that molecular aggregates can affect significantly rheological properties under EOR conditions.

In many biopolymer solu- The

Scleroglucanr L21

-.- CSll .----- Rmearch sample

-

\

0 ApporerM dmrn.1ulpm

Figure 6. ESZ response of scleroglucans

508

Microgel is also significant (10) (11) in determining injectivity of polymer solutions in porous media. Microgel is sufficiently deformable to pass through small pores at the high shear rate near the injection point, but can block pores at lower shear rates further into the substrate. method for estimating microgel is based upon filtration at a very low shear rate. The ESZ approach has promise as a more rapid and convenient technique.

Future developments

A recently suggested (15)

With some modifications of the very conventional apparatus used, the ESZ

the shear technique could well yield more information of relevance to polymer use in EOR. Controlled variation of flow rate through the orifice is desirable; rate in the conventional apparatus is high (- 103s-') and polymer solution species must be deformed in the orifice. The effect of shear rate upon pulse size would help to characterize polymer deformation in a shear field. solution species are below the accessible size range in the present work, it is superficially attractive to reduce the aperture rize in order to enhance the signal. The true sizes are larger than the size scale calibrated with insulating particles, however, and there may be advantage in working at slow flow rates in wide apertures and with different electrolyte concentrations. effect of using 'hydrodynamic focussing' to ensure passage through the centre of the orifice where the electrical field is synrmetrical needs to be investigated.

Since most of the

Again the

S m Y

When used in the mode conventional for particle sizing, but with improved earthing and shielding, the ESZ technique can sense the largest solution species of water-soluble polymers. polacrylamides, and to rheological properties of biopolymers. The method has promise in monitoring solutions of candidate EOR polymers for microgel and, with some instrumental modification, in more fundamental studies of polymer solutions.

The response is related to the hydrodynamic volume of

NOMENCLATURE

C concentration (mass/volume) of polymer

M molar mass

"lm

NO

Vh I) viscosity of solution

- mass-average molar mass

Avogadro's constant

equivalent hydrodynamic volume of a polymer molecule

viscosity of solvent 10

[I)] limiting viscosity number

4 volume fraction of polymer in solution

ACKNOWLEDGEMENTS

Dr I.W. Sutherland (University of Edinburgh) kindly provided research samples and rheological data. Dr 1.GMeldrum (BP Research) presented some coamercial samples. Molar mass characterization and fractionation was the work of M.A.Francis, and Mrs C.M.LAtkinson carried out the ESZ determinations. The work was carried out under contract (OT/F/524) to the Department of Energy.

509

REFERENCES

SMITH, F.W.; Solutions in Porous Media" J. Pet. Tech. (Feb 1970), 148-156

SZABO, M.T.; Hydrolyzed Polyacrylamide Solution Through Porous Media" SPE 4028, presented at SPE 47th Fall Conference, San Antonio (1972)

KLEIN, J and CONRAD, K-D. ; "Characterization of Poly(acry1amide) in Solution". Makromol. Chem. (1980), 181, 227-240 UNSAL, E., DUDA, J.L. and KLAUS, E.; "Comparison of Solution Properties of Mobility Control Polymers" in JOHANSEN, R.L. and BERG, R. (Eds) "Chemistry of Oil Recovery" ACS Washington (19781, 141-170

HOLZWARTH, G.; "Conformation of the Extracellular Polysaccharide of Xanthanomae campestrid'. Biochemistry (1976) 4333-4339

TANFORD, C.; "Physical Chemistry of Macromolecules". Wiley (1961) 333-344

BOYADJIAN, R., SEYTRE, G., BERTICAT, P. and VALLET, G. 'Caracterisation physico-chimique de Polyacrylamides utilises c m e Agents Floculants'. Euro. Polym. J. (1975) 11 401-407 RINAUW, M. and MILAS, M. "Polyelectrolyte Behaviour of a Polysaccharide from Xanthanomas canpestris" Biopolymers (1978) 17 2663-2678 SOUTHWICK, J.G., LEE, H., JAMIESON, A.M. and BLACKWELL, J. "Self-association of Xanthan in Aqueous Solvent Systems" Carbohydrate Res. (1980) 2 287-295

KOHLER, N. and CHAWETEAU, G.; "Polysaccharide Plugging Behaviour in Porous Media: Preferential Use of Fermentation Broth". SPE 7425. Paper presented at SPE 53rd Fall Conference, Houston (1978)

MACWILLIAMS, D.C., ROGERS,'J.H. and WEST, T.J.; Petroleum Recovery" in BIKALES, N.M. (Ed). "Water-soluble Polymers" Plenum (1973) 106-124

DUNLOP, E.H. and COX, L.R.; Reduction".

WOLFF, C. Molecular Weight in Water".

DAVISON, P. and MENTZER, E.; SPE 9030.

CHAWETEAU, G and KOHLER, N.; Polysaccharide Solutions on their Flow through Porous Media". Paper presented at SPE 55th Fall Conference, Dallas (1980)

"The Behaviour of Partially Hydrolysed Polyacrylamide

"Molecular and Microscopic Interpretation of the Flow of

'Water-soluble Polymers in

"Influence of Molecular Aggregates on Drag

"On the Real Molecular Weight of Polyethylene Oxide of High

Phys. Fluids (1977) 20 S203-S213

Canad. J. Chem. Eng. (1980) 2 634-636 "Polymer Flooding in North Sea Oil Reservoirs"

Paper presented at SPE 55th Fall Conference Dallas (1980)

"Influence of Microgels in Xanthan SPE 9295

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VISUALISATION OF THE BEHAVIOUR OF EOR REAGENTS IN DISPLACEMENTS IN POROUS MEDIA

ERIC G. MAHERS, ROBERT J. WRIGHT, RICHARD A. DAWE

Department of Mineral Resources Engineering, Imperial College, London SW7 2BP

ABSTRACT

Micromodels have been successfully employed to observe directly displacement processes, and have assisted in understanding the physics of the complex fluid phenomena involved in Enhanced Oil Recovery. Both miscible and surfactant displacement sequences are reported here.

The models have been produced by etching the pores into nylon, from which replicas in epoxy resin have been made. Computer graphics and microfilm facilities have been used to produce accurately drafted network photomasks.

INTRODUCTION

The mathematical description and prediction of fluid flow behaviour has been much assisted by direct observation. Although this is not possible in real porous media, models can be made in transparent materials which permit direct observations within the pores of fluid interactions, displacements and entrapments. These models may be monolayer packs of glass beads, as used by Chatenever (1) and Egbogah (2 ) , or two dimensional etched networks.

Mattax and Kyte ( 3 ) , Michaels et a1 (4), Davis et a1 (5) and Wardlaw (6) have used etched glass models. Mattax's network comprised of a rectangular array of straight channels of similar width but varying length. He used this model to study the mechanism of water flooding, with regard to relative permeabilities and wettability. He described the distribution of the fluids and the effect of wettability on areal sweep efficiency, but did not extend this work to cover EOR mechanisms. Michaels et a1 used the same micromodel to analyse how changes in surface wetting, by the injection of aqueous hexylamine, might mobilise entrapped oil. They concluded that the observed stimulation of oil production was the result of transient changes in wettability. et a1 made use of a commercial overlay shading medium to produce an irregular, random design. They used this model to qualitatively demonstrate the displacement of oil and water by the microemulsions used in the various Maraflood processes. A film is available from Marathon Oil Company showing the displacements of oil and water by micellar solutions specially formulated for selected U.S. crude?.

Wardlaw employed a heterogeneous, rectangular network with varying pore width. He describes the effect of pore throat size ratio on displacement efficiency, and drainage-imbibition cycles. Although he recognised the importance of pore connectivity and throat sizes on displacement mechanisms, he had not fully explored these factors in his networks.

Davis

512

The pores produced by etching into glass have been V-shaped in cross section, larger in width than those found in common reservoir rocks, usually very shallow, and with high surface roughness. This type of channel topology does not correctly scale capillary pressure effects. Special network patterns of realistic pore sizes have not, as far as we know, been incorporated into any model designs to study experimentally their effects on displacement phenomena.

The of this work is to understand the microscopic mechanics of low interfacial tension and miscible enhanced oil recovery processes by using micromodels.

objective

In our experiments we are exploring:

Pore network geometry and its effect on capillary pressure, displacement and entrapment, by varying pore shapes and throat sizes, and the connectivity of the pores, which, with the size distribution, defines the degree of freedom of route.

The scale and type of network heterogeneity, and the mechanisms by which areas of bypassed oil can be contacted and mobilised through diffusion or reduced interfacial tension.

Diffusion and mass transfer phenomena and the phase behaviour of ternary systems. Various alcohols can be used to simulate the different types of miscibility; 1.e. preferentially oil or water soluble, and first or multiple contact.

CONCEPT OF THE MICROMODEL

The micromodel networks to be described are two-dimensional and it is therefore pertinent to discuss first the validity of results from these experiments. Any two pores within a feal porous medium may be connected through a number of routes in three-dimensional space. If these pathways were rotated about a line between these two pores such that they lay wholly within a plane, a high porosity, two dimensional network would evolve. Although two-dimensional networks cannot allow bicontinua in the manner that three-dimensional models can, where the pathways can intertwine ( e.g. in the manner of a double helix), simultaneous parallel flow is still permitted. This concept of high porosity, high coordination number networks lies at the heart of our micromodel designs.

NETWORK DESIGN

Ae already indicated, most networks previously employed have been of random or simple design. In our early work a photoreduced ‘Letratone’ texture was used to obtain networks which were homogeneous overall, but had variable pore structures on the microscopic scale. The pore ‘necks’ were of 10-30 microns in width with the pore ‘bodies’ being 50 to 100 microns. Figure 1 shows the etched network used. In an attempt to simulate more closely the heterogeneous microstructure of natural media, we have developed models with layered structures, figures 2 through 4, and some with additional serial variations, such as shown in figure 5. The latter type, with their high degrees of freedom, were designed to yield fairly realistic, and approximately predictable, relative permeability and capillary pressure functions.

A doublet network, similar to figure 6, was designed to demonstrate the effects of two pore sizes in parallel. Initially, it was drafted by hand and then photographed to create the photomask for etching.

513

Accurately drafted networks have now been produced using computer graphics and microfilm facilities; this method also enables the pore parameters to be easily varied. A unit cell is composed which is repeated to build up the model. Figures 6 through 9 have been produced in this manner; where the pores are in white.

The doublet network of figure 7 has abrupt changes in pore width, which contrast with the 45 degree divergence in the earlier design ( figure 6). Figure 8 illustrates the ability to vary the pore parameters.

Although figure 9 is a regular array, an attempt has been made to create a smooth variation in channel width, with the walls comprised of arcs of circles. The pore throat to body ratio is 1:5. Development of this type of network is under way to investigate the effects of channel angularity.

Figure 1 Letratone etched network

Figure 2 Parallel channel design

514

Figure 3 Parallel channel model with obstructions

Figure 4 Network with high permeability central streak

Figure 5a Parallel design with additional serial variations

515

Figure 5b Serial model showing inlet ports

6a 6b

Figure 6 Pore doublet networks (computer drawn)

Figure 7 Doublet network with abrupt pore necks (computer dram)

516

Figure 8 Variation of pore parameters

Figure 9 Regular network of curved channels (computer drawn)

CONSTRUCTION OF THE MICROMODEL

The This is a process commonly used for making printing plates, e.g. using BASF Nyloprint, and has also been used by Bonnet and Lenormand (7). Such photoetching methods enable greater control over pore geometry than chemical etching, and can easily be done in the laboratory, without involving the hazards of hydrofluoric acid.

micromodels are produced by etching the pores into nylon film.

517

Detailed procedure

The procedure is illustrated in figure 10. The photographic negative of the network is placed over the nylon and placed under an ultra violet light source. An exposure time of about one hour was found to be adequate when the source (Philips HPW 125W F/70/2) was 200 mm from the negative, with a 10 mm diameter aperture placed midway in between. For deep pores it appears to be necessary to have a small air gap between the negative and the nylon, but the reason for this is not yet fully understood. The unexposed regions are then etched away by washing in a mixture of 90% (by volume) methylated spirits and 10% water at 35OC, for about 30 minutes. A turbulent stream of liquid 1s maintained across the surface of the nylon by circulation through a centrifugal pump. When etching is complete, the model is dried with warm air and exposed to ultra violet radiation for a further five to ten minutes to set the pore surfaces.

Ultra Violet Light

, Negative

Air Gap (a) R q Photosensitive Nylon ' Rigid Backing Plate

(b ) 1-1 Unexposcd regions etched away.

( ( 1 1-1 and then re-exposed to ultra violet.

-Perspex Plate

Resin . -. I

Figure 10 Etching procedure

In our early work we performed flow experiments directly with the nylon etchings, however these were found to suffer from significant sorption of dyes and solvents. Consequently we used the etchings as bases for preparing silicone'rubber moulds (Hopkin and William Sllastic 3110 RTV and Dow Corning Catalyst l), from which rigid, non-absorbent epoxy resin replicas are cast, which accurately reproduce the microstructure of' the nylon model. Araldite MY753, MY951 hardener, is a suitable resin for this purpose. We now have a relief structure on which a top needs to be secured, to form a two-dimensional pore network. To preserve uniform wettability, epoxy resin film has been produced in the laboratory, which can be sealed onto the epoxy cast by one of several methods:

518

1.

2.

The pores are filled with wax and then resin poured on top. The wax was removed by heating the model and injecting hot fluid, e.g. kerosene. This is a delicate operation with which we have had only limited success, however a similar method was reported by Bonnet and Lenormand (7).

The resin film is sealed on by external pressure, using screw clamps as shown in figure 11. This allows the model to be dismantled and cleaned easily. However, the seal is not always perfect and the film tends to depress into the pores, resulting in an unknown, and variable pore depth. The seal can be improved by placing the assembled model in an oven at 65OC for one or two hours. This creates a weak adhesive seal at resin-resin contacts through increased surface interaction and plastic deformation.

/ 6 mm Perspex

Plates \

Resin Costing

Resin Film

Cushion

Figure 11 Micromodel seal by external pressure

3. The best method discovered to date is to coat the perimeter of the model with epoxy, and gently press the resin film on top. This is to prevent leakage while a solution of resin in methylated spirits is injected into the pores. After two to three hours a thin, wetting resin film will have been deposited. Injection of pure methylated spirits removes any excess resin leaving a bonding film in the tiny crevices; especially between the top of the pore walls and the sealing film. This method maintains constant pore geometry over a series of experiments, and allows short working distance microscope objectives to be used. film or block.

Surface flatness is improved by using a thick resin

TOPOLOGY OF THE MICROMODEL PORES

Interfacial curvature, and therefore capillary pressure, is governed by the pore shape (the angle of divergence), contact angle and pore dimensions. In order to ensure that the capillary pressure and viscous resistance are controlled by the dimensions within the plane of the network, it is necessary for the depth of the pores to be constant and of the same order as the width. For widths greater than 50 microns, the depth tends to be constant at about 50 microns. Controlled pore widths at least as small as 20 microns are possible. Figure 12 shows the square shape of the pores in contrast to the V-shape of glass etchings.

5 19

Figure 12 Shape of the pores of a resin cast of the early doublet model

DISPLACEMENT STUDIES

Displacements within the micromodels were observed through a microscope and recorded in colour on videotape or still photographs. The floods were carried out at low flow rates of less than 50 mm/hr (four ft/day) by means of a variable rate syringe pump. The fluids were introduced into the models through the valve arrangement shown in figure 13. This eliminated dispersion in the entry tube, thereby ensuring injection of uncontaminated fluid.

Inlet 1

Inlet 2 Bypass

I

Figure 13 Valve arrangement for the injection of fluids into the micromodels

5 20

Use of dyes

Dyes were used to aid the visualisation of the fluids. Alternate injection of dyed and undyed, but otherwise identical, fluids highlighted the flow pathways, clearly showing the stagnant regions (figure 18). The distribution of this stagnant fluid is an important factor influencing the efficiency of an EOR flood.

The water-soluble dyes used in these experiments were Methylene Blue, Nigrosine Black and ICI Lissamines. The oils were dyed with ICI Waxolines. These dyes are, however, surface-active and their effect on wettability and interfacial phenomena should be taken into account when analysing results.

Mobilisation of oil

The mechanics of oil ganglia mobilisation in straight capillaries of varying cross sectional area have been described by Arriola et a1 (8.9). Under these conditions an EOR chemical can contact the downstream interface only through a wetting film surrounding the ganglion, 1.e. a contact angle of 180 degrees measured through the globule. In a two-dimensional network this contact can be achieved through neighbouring pores. These parallel routes also affect the viscous pressure drop across the ganglion, thereby determining the reduction in interfacial tension required to mobilise the drop immiscibly. This discrepancy between single pore and network studies has been discussed by Stegemeier ( l o ) , and is effectively demonstrated by the pore doublet models.

Simulation of miscible processes

Alcohols were employed to simulate miscible displacements. The wide variety of alcohols available permits a spectrum of single and multiple contact miscible systems to be studied. For instance, low molecular weight alcohols can be used to model carbon dioxide injection. The partitioning of carbon dioxide between the aqueous and oleic phases is a function of pressure, and is reflected in the choice of ternary systems. This has been discussed by Stegemeier (lo), Totonji and Farouq All (111, and Orr and Taber (12).

Examples of displacement processes

Figures 14 through 18 illustrate fluid displacement and distribution in the Letratone and doublet (hand drafted) models. Red and blue dyes were used in these experiments which, although clearly distinguishable in the original colour slides, appear as only slightly differing tones in these photographs. The interfaces are, however, well defined through light scattering at refractive index discontinuities.

We are also investigating techniques to quantitatively study fluid concentrations as functions of both position and time. Absorption of light by the dyes can be exploited to show dispersion and diffusion. It shocld be noted that because the diffusion and mass transfer of the dyes may be different to those of the fluids, and that the dyes may suffer dispersion through adsorption within the system, corrections need to be made to any measurements. It is therefore more desirable to utilise methods which exploit the refractive index properties of the liquids, e.g. interferometry.

Dynamic recordings of displacement sequences have been made on Sony U-matic videotape, and are held by the Professor of Petroleum Engineering, Imperial College.

In the following photographs flow is from left to right.

5 2 1

Figure 14 High tension, immiscible displacement of non-wetting fluid (dark tone) by a wetting phase of equal vicosity, in the Letratone model.

100 pm

Figure 15 Residual non-wetting phase (dark areas) behind the flood front of figure 14.

522

Figure 16 Displacement of water by Carnation oil, of viscosity 0.019 Pa.8, in the doublet network. The oil clearly preferred the large pores and entrapped the water within the smaller channels.

Figure 17 Illustration of a Haine's jump as the oil entered a large pore. The fluid interface moved during the exposure time.

523

1-i 1 m m

/ Water

\ Figure 18a \ I

Oil Water

I\ I - 1 m m

011 Water Oil

Figure 18b

Figure 18 Doublet model, initially fully saturated with Carnation o i l , which was partially displaced by water, followed by a dyed oil flood. Subsequent injection of undyed oil highlighted the stagnant regions.

5 2 4

I O 0 0

0

-

Quantitative results

The Letratone micromodels were used to study low tension displacements. As well as purely visual results, quantitative measurements were obtained from photographs in conjunction with flow rate data; viscosity and interfacial tension parameters were determined separately. Figure 19 shows the observed residual oil (as a percentage of the total pore volume) as a function of Capillary Number, for both high and low tension (petroleum sulphonate / kerosene) displacements. The Capillary Number was increased in steps by adjustment of the flow rate, and the remaining volume of oil measured. Some lower residuals were produced by Capillary Number 'shock' (sudden reduction in interfacial tension) at a surfactant displacement front, where microemulsions were often formed.

4 0

%

30

20

10

0

High tenvm 0

Low tension 0

0 0

0 0

O D 0

- 5 - 6 - 3 - 2

Figure 19 Residual oil saturation as a function of Capillary Number, in the Letratone model

Figure 20 illustrates the measured residual ganglion length distributions (taken in the mean flow direction). Clearly, blobs of oil longer than 500 microns are mobilised by increasing the Capillary Number within this range, while the atable globules at high Capillary Number are of the same order of size as the individual pores.

525

Fraction o f

Total NO 0.6

0 5

0.-

0.3

0.2

0.1

- 5 ........ 1 x 1 0

----- I x10-L (9 - 6 1 1 0 - 3

..... . . . . . . . 1

J . . . . . . . . . . . .

. . . . . . . . . . . . . . . . . . . . . . .

0 530 1933 1500 2330 Ganglion Length ipml

Figure 20 Size distributions of residual oil ganglia for three different values of Capillary Number.

CONCLUSIONS

Micromodelling techniques have been developed to gain insight into the physics of reservoir miscible and surfactant displacement processes by observations of alcohol and low interfacial tension systems at ambient temperature and pressure.

FUTURE WORK

We intend to develop the design of networks to relate micromodel displacement results to real reservoir rocks through pore size distribution and connectivity . Holographic interferometry is currently being employed to investigate the role that diffusion can play in the recovery of oil entrapped by small scale heterogeneities.

Techniques for producing castings in glass of the nylon etchings are being examined to create more strongly water-wet models.

ACKNOWLEDGEMENT

The would like to thank the Department of Energy and the Science and Engineering Research Council for their support of this research, Professor Colin Wall for his encouragement, and Mr Martin Hughes for technical advice.

authors

NOMENCLATURE

v = superficial (average interstitial) velocity, mls y = interfacial tension, N/m

= viscosity, Pa.s S, - residual oil saturation

The Capillary Number is defined by: Nc= p V 1 y

526

REFERENCES

CHATENEVER, A., and CALHOUN, J.C.; "Visual Examinations of Fluid Behaviour in Porous Media - Part 1". Trans., AIME (1952) 195, 149-156

EGBOGAH, E.O., and DAWE, R.A.; "Microvisual Studies of Size Distribution of Oil Droplets in Porous Media", Bull. Can. Pet. Geol. (June 1980) 2. 200-210

MATTAX, C.C., and KYTE, J.R.; "Ever See a Water Flood?", Oil and Gas Journal (Oct 1961) 2, 115-128

MICHAELS, A.S., STANCELL, A., and PORTER, M.C.; "Effect of Chromatographic Transpart in Hexylamine on Displacement of Oil by Water in Porous Media", SOC. Pet. Eng. J. (Sept 1964) - 4, 231-239; Trans., AIME, 231

DAVIS, J.A., and JONES, S.C.; "Displacement Mechanisms of Micellar Solutions", J. Pet. Tech. (Dec 1968) 3, 1415-1428; Trans., AIME, 243

WARDLAW, N.C.; "The Effects of Pore Stucture on Displacement Efficiency in Reservoir Rocks and in Glass Micromodels", SPE/DOE 1st Joint Symp. on EOR, Tulsa, Olklahoma (April 1980) 346-352; SPE paper 8843

BONNET, J., and LENORMAND, R.; "Constructing Micromodels for the Study of Multiphase Flow in Porous Media", Revue de L'Inst. Franc. du Pet. (1977) 42, 477-480

ARRIOLA, A., WILLHITE, G.P., and GREEN, D.W.; "Trapping of Oil Drops in a Noncircular Pore Throat", SPE paper 9404, SPE Annual Fall Meeting, Dallas (Sept 1980)

ARRIOLA, A., WILLHITE, G.P.. and GREEN, D.W.; "Mobilization of an Oil Drop Trapped in a Noncircular Pore Throat upon Contact with Surfactants", SPE paper 9405, SPE Annual Fall Meeting, Dallas (Sept 1980) #

STEGEMEIER, G.L.; "Mechanisms of Entrapment and Mobilization of Oil in Porous media", Improved Oil Recovery by Surfactant and Polymer Flooding, ed. Shah, D.O., and Schechter, R.S., Academic Press, Inc., New York (1977) 55-91; 81st Nat. Meeting AICHE, Kansas City (April 1976)

TOTONJI, A.H.M., and PAROUQ ALI, S.M.; "Solvent Flooding Displacement Efficiency in Relation to Ternary Phase Behaviour", SOC. Pet. Eng.J. (April 1972) 12, 89-95

ORR, F.M., and TABER, J.J.; "Displacements of Oil by Carbon Dioxide", Annual Report, U.S. DOE/MC/03260-4 (1980)

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THERMAL RECOVERY METHODS 527

THE INTERPLAY BETWEEN RESEARCH AND FIELD OPERATIONS IN THE DEVELOPMENT OF THERMAL RECOVERY METHODS

J. OFFERINCA, R. BARTHEL and J . WEIJDEMA

Konin Wijke Shell Explomtive en Produktie Labomtorium, Rijswijk, The Netherlands (Shell Research B. V.)

ABSTRACT

The role of research in the development of thermal recovery processes is discussed, viz: steam drive, steam soak, hot-water drive and in-situ combustion. The importance of feedback from field experience to research is pointed out.

Five periods are distinguished: 1. Early and mid-fifties when mainly laboratory work was carried out. 2. Late fifties and early sixties when the processes were tested in field pilot projects. 3. Mid-sixties to early seventies when large steam-soak projects were started and research experiments were carried out in large physical models. 4. Mid-seventies to early eighties when the number of steam projects has been increasing fast. The design of these projects is being carried out with the aid of nmerical simulators. 5. The present, when new techniques and applications for thermal methods are under investigation.

between research and the field is stimulating for new developments. It appears from this historical survey that in particular the interplay

INTRODUCTION

Present worldwide recovery of oil by EOR methods is estimated to amount to some 600 000 bbl/d. Nore than 80 per cent of this production is by thermal methods of which steam drive and steam soak take the major part. Usually thermal methods have been applied so far in reservoirs containing medium to heavy oil or tar.

during the past thirty years, partly in the laboratory and partly in the field.

have stimulated each other in developing these processes or where, occasionally, one or the other came to a dead end. The paper is therefore presented in the form of a historical review. It is unavoidable that some of the material of older reviews such as, for instance, by RAMEY(1) (1967) and RARMSEN(2) (1971) on steam and hot-water injection and by DIETZ(3) (1970) on in-situ combustion will be repeated. However, we believe it fulfils a useful purpose. Firstly, because these reviews are now 10-14 years old and thus only cover half of the period of interest and, secondly, because we tend much more to discuss in retrospect the role of research.

Thermal methods are the oldest EOR methods. They have been developed

The object of this paper is to show where research and field operations

528

If we sometimes seem to overemphasise Shell's role in the history of thermal recovery, this is not done intentionally but is mainly due to easier accessibility to reports and to the people who made part of this history. We are aware of the fact that similar developments to those within Shell research have also taken place in other companies. If this explanation is not fully satisfactory, it may even stimulate some petroleum engineer with a vocation for historian to write an "objective" history on the development of thermal processes.

processes. For those who are not familiar with these ample literature references are given in this paper.

In the following we do not present descriptions of the basic thermal

EARLY AND MID-FIFTIES

In an internal Shell Report of 1951 entitled "Higher ultimate recovery by heating the reservoir", it is stated that: "The idea of heating an oil reservoir in order to decrease viscosity and consequently increase recovery is not new. Already in 1917 . . .I1 Then follows a long list of papers and patents containing suggestions for heating methods. A considerable number of these ideas date from before the second world war(1). Even some early field applications are mentioned. 'In retrospect, however, these tests should be considered to be isolated events having no followup. The actual rise of the thermal recovery methods did not occur before the early fifties. Prom then on, a continuous flow of papers on research investigations and field experiences has been maintained, which has not yet stopped.

above (part of which was later published (4)) some exotic heating methods were suggested which also nowadays regularly appear in the literature, such as application of sonic waves, electromagnetic radiation, electric conduction between electrodes in wells, injection of oxygen (instead of air) and even letting down an atomic bomb into a well. Although these methods were rejected (mainly on economic grounds) it still seems recommendable to re-evaluate these techniques regularly vith changing economic conditions, new technical developments or even for deviant oil formations.

It is, furthermore, surprising to realise that in this early period attention was mainly directed to in-situ combustion. The reasons for this are that air injection was considered to be easier than, for instance, steam injection and that it requires less fuel at the surface.

It is interesting to note that in the internal Shell report mentioned

- In,s;tz cebysii_on-

Research and by Magnolia Petroleum Corporation in the U.S. Sinclair (5) experimented with injection of air/fuel gas mixtures in a shallow oil sand. Ignition was achieved by means of a gas burner. They demonstrated the propagation of a combustion wave which left a clear burnt sand. Supporting laboratory experiments demonstrated that the oil in the formation could be moved by the front edge of the heat wave. Magnolia first tried out ignition of underground combustion in a three-well test using an electric heater (6) and then carried out a successful in-situ combustion drive in a 30 acre inverted five spot (7).

These early field trials stimulated research in various companies. In laboratory tube experimentation process variables were determined, such as minimum air flux for self-sustained combustion, fuel availability dependent on oil type, and frontal advance rate in relation to air rate (8).

The first field trials on in-situ combustion were carried out by Sfnclair

529

An extensive study of combustion processes in oil sands led to a description of the drive mechanism of the process (9). In experiments in glass tubes oil-bank formation was made visible. Thermal analysis, using a pack of oil sand fluxed with air, showed that the reaction between oxygen and oil proceeds in two major steps; in a lower temperature regime (below 3000C) the oil molecules lose comparatively more hydrogen than carbon in reaction with the oxygen, leaving a carbon-rich coke-like residue which is subsequently burnt off in a temperature range of 300 to SOOOC.

Rot-yatez inlectzoz

The method that was, at least at Shell in that period, considered as second best is hot-water injection. Therefore a feasibility study was carried out on the applicability of this process in the Schoonebeek field in the' Netherlands. This field, which had once been called a play-ground for petroleum engineers specialised in thermal recovery, contains oil of 25OAPI with an initial viscosity of 180 cP. It consists of two parts: the high- pressure (70 bar) waterdrive area and the low-pressure (10 bar) solution gas drive area. The total SMIIP is l.Zx109 bbl. Hot water was intended to be injected into the waterdrive area.

the oil zone are the determining parameters of the process, an analytical model was developed to determine these temperature distributions. This model, still known as the lauwerier model (lo), mainly consists of a procedure for calculating heat losses in the formations over- and underlying the hot-water zone. It enables the average water and the average oil temperature to be calculated at a certain time and thus the average viscosities and the mobility ratio. The recovery as a function of time can then be approximated from this varying mobility ratio.

Furthermore, scaled laboratory experiments were carried out to confirm the model for an actual situation with a hot-water tongue underrunning the oil. From economical calculations it appeared that the process could be profitable provided cheap fuel is available (4).

- Steam injectlo! steam-drive process (11). It appeared in these one-dimensional experiments that a steam zone with a stable front develops, in front of which the temperature decreases gradually to the initial temperature. Further important observations were the low residual oil saturation in the steam zone, the relative independence of the process to oil viscosity and sand permeability and again the dominating effect of heat losses to over- and underlying f ormatione.

As it was realised that the temperature distributions in the water and

In the meantime also, a start had been made with tube experiments on the

LATE FIFTIES AND EARLY SIXTIES

After the preceding period of (mainly) laboratory investigations, a period had now come of active field testing of the studied processes. All three processes were tested by Shell in the Schoonebeek field: Rot-water drive in the high-pressure water-drive area and in-situ combustion and steam drive in the low pressure solution gas-drive area. In the heavy-oil fields of the Bolivar Coast in Venezuela ( 10-1SoAPI), steam drive and in-situ combustion were tested in the PIene Grande field and the Tia Juana field.

530

- 1nZsit-U combysJion-

considered a matter of particular concern. Ignition procedures using powerful well heaters to heat the formation round the injector to combustion wave temperatures (some 300°C or more) (5,6), or by use of reactive chemicals (12.13) all had their specific drawbacks, often necessitating well repairs and repeated trials (3). At Schoonebeek, for instance, ignition was achieved in the three injectors of the triple seven-spot by squeezing-in concentrated nitric acid as a strong oxidiser. In one of the injectors, however, an explosion occurred, tearing up a tubular section.

Aa in the South Belridge field test spontaneous ignition had quite unexpectedly occurred after prolonged air injection (4), interest in this manner of starting in-situ combustion led to the development of a predictive method for spontaneous ignition, based on low-temperature oxidation rates of oil sands (15). Predictions for the Tia Juana test site in Venezuela led to the decision to rely on spontaneous ignition, which actually occurred some five weeks after air injection.

Later, on basis of the predictive model, it was formulated that by heating the formation round the well bore gently and gradually to only some 100% with a low-powered well heater or by steaming the injector, a smooth well-controlled ignition could be achieved after one or two days' air injection (16.17). By steaming the injector a smooth ignition was obtained in the Tia Juana wet in-situ combustion test in 1965, discussed below.

pilots at Schoonebeek and Tia Juana, they were considered economically unsuccessful. Oil returns were low, mainly due to rapid up-dip channelling of the air.

on the tolerance of a dry combustion wave to weer injected simultaneously with the air (18). The water evaporates to steam in the hot burnt-out zone and the steam carries the heat downstream through the combustion zone. The effect of such heat recuperation is two-fold: the steam stabilises the propagation of combustion by preheating the oil and, most important, the growing steam zone effectively sweeps the mobile oil far ahead of the combustion wave. As a result, less air is needed for the combustion-drive process, so that compressor capacity can be reduced, thus economising on investment and running costs. The optimum tolerable water-injection rate relative to the air- injection rate was found to be the one at which the evaporation front moves steadily and closely behind the combustion wave.

temperature range found in combustion kinetic studies (19,20,21) a series of laboratory tube experiments was carried out at 40 bar, in which the water- injection rate was deliberately increased to far above the quoted tolerance limit (22). It appeared that as the water under these conditions enters the combustion zone and evaporates, it suppresses the combustion temperature to near-saturated steam temperatures, with the result that the less reactive coke (final oxidation step) remains unburnt. It was shown that, in spite of partial quenching of the combustion, a steady progress of the heat wave is ensured, while achieving a further important economisation on the air requirements.

partially quenched combustion the speed of the combustion wave is no longer governed by the air-injection rate (as in dry and "normal" wet combustion) but by the water-injection rate and that the air requirement per unit formation volume decreases with increasing water-injection rate. Later, more refined theories on "superwet" combustion were developed (23,24) which were reviewed in Ref. (3). Seemingly different experimental observations by others (25) appeared to fit in with these theories (26).

In designing an in-situ combustion test at that time, ignition was

Although much experience had been gained with both in-situ combustion

In the meantime a theoretical one-dimensional model study had been made

Baaed on the relatively high oxidation rates of oil in the low-

The experimental results fitted a simple theory which showed that in

531

On the basis of their experience with wet and superwet combustion in one- dimensional models, Shell decided at an early stage to try out wet combustion in the field.

In 1962, the triple seven-spot dry combustion test at Schoonebeek was converted into a wet combustion project (3). The test was terminated in 1965 after a severe production decline had set in, presumably caused by an overall formation plugging, while in addition several injectors and producers suffered from corrosion. Although the test was not considered an economic succese, it had shown that while injecting water simultaneously with the air, more than three times as much tertiary oil could be produced per unit volume of air than during the dry combustion phase.

In Venezuela, a wet combustion drive test was carried out in a seven-spot in the Tia Juana field, in the period 1965 to 1968 (3) . Compared to Schoonebeek, where conditions were rather in the range of 'normal' wet combustion, water/air injection ratios were chosen to be twice as large, to reach the range of partially quenched combustion of the laboratory experiments. Temperature profiles determined in observation wells and in producers remained below 20OoC. Though speculative, this might be taken as an indication that the combustion has'perhaps indeed proceeded in the partially quenched mode.

The test made a mall net profit. Although much uncertainty arose concerning how much oil should be attributed to the effect of the wet combustion drive (3, probably at least twice as much tertiary oil had been produced per unit volume of air as compared with the Schoonebeek test.

- Steam @JectAoz

steam-soak process in 1959 in the Mene Grande field (27). The process was discovered rather accidentally when, during the planned,steam drive, steam eruptions around an injector made it necessary to relieve the reservoir pressure by backflowing the injector. It appeared then that the well continued to flow at a rate of more than 100 bbl/d oil at a relatively low watercut, whereas surrounding producers had been pumped before steam injection at oil rates varying from 3 to 10 bbl/d.

Further testing was carried out in the Tia Juana field, the favourable r.esults of which prompted a large scale project. In the meantime also, Shell Oil tested the process successfully in its Yorba Linda field in California (28) which was the start of the large-scale applications of the process in the Californian heavy oil fields.

In retrospect, this accidental discovery has been mentioned as being more or less inevitable (29). Others consider "the observation of a phenomenon, the reallsation of its value and the initiative to apply it" to be less obvious (30). An interesting question in this respect is: Why has this process been discovered in the field and not been proposed by research? Afterwards, the idea to reduce the pressure drop around a production well by heating seems rather obvious. Same simple calculations could have demonstrated that this effect would last a reasonable time. A possible answer to the question why this idea has never been proposed is that, even if anybody had the idea, he probably would have rejected it himself because he would expect to produce mainly water. Even in recent literature different explanations (31,321 are given for the low water cut during the production phase.

The most important event of this period is probably the discovery of the

The steam-drive projects in Schoonebeek (33) (4 injectors and 8 producers) and in Tia Juana ( 3 4 ) (7 injectors and 24 producers) both proved to be a technical success. Additional oil recoveries from the test areas were estimated to be 38% and 21% STOIIP for Schoonebeek and Tia Juana respectively. In both projects it appeared that owing to gravity the steam flows only

532

through the upper part of the formation. The lateral flow patterns in both projects were far from symmetric. This phenomenon can partly be accredited to the dips of the reservoirs ( 6 . 5 O in Schoonebeek and 3O in Tia Juana) but is also due to heterogeneous sand developments.

volumetric development of the steam zone. At that time only theories describing the developnent of a one-dimensional steam zone were available. The thickness of the steam zone which determines the vertical sweep efficiency, had to be derived from field observations. These thicknesses were estimated to be between 7 and 11 m.

It followed from the analyses that oil was not only displaced by free steam but also by condensation water, in Tia Juana even in equal amounts.

The Schoonebeek project was extended to adjacent areas. In the meantime it had become apparent from the steam-soak tests in the Tia Juana field that a combination of reservoir compaction and steam soak could maintain primary recovery for a considerable period. It was therefore decided for the near future to discontinue steam-drive activities in the Bolivar Coast fields.

For correct interpretation of such projects it is important to know the

HoL-Earei &nJeEt&oz

Although the hot water injection test in the Schoonebeek field (2 injectors and 7 producers) proved to be reasonably successful, it appeared that the process is much more complicated than was initially envisaged (35). Water breakthrough occurred much earlier than expected. Later studies based on model experiments showed that the process is intrinsically subject to lateral instability and that the hot water tends to concentrate in a few tongues. Nevertheless, the performance in the Schoonebeek field was attractive enough to extend the project over a considerable part of the high pressure waterdrive area. In some parts of the reservoir hot-water injection is still being carried out. This is a quite exceptional situation since most early pilot projects were discontinued because of poor areal sweep efficiency. An explanation for the acceptable performance of Schoonebeek could be its relatively low initial oil viscosity of 180 CP (180 mPa.6).

MID-SIXTIES TO EARLY SEVENTIES

This period shows a spectacular increase in the number of steam-soak projects at the cost of the other thermal processes. Within a period of ten years the production of heavy oil due to this process increased in California to about 130 000 b/d and in Venezuela to an even higher level. Although by its nature only a stimulation procese, it enables at relatively low costs production from undepleted reservoirs which would otherwise only produce at very low rates.

Theoretical (36,37) and experimental (38) studies were carried out to investigate the performance of the process and to define optimal injection and production schemes. The effect of a number of parametere had to be investigated, among which slug size, cycle length, number of cycles, soaking time, etc. Although at that time the complete set of flow- and heat transport equatione could not yet be solved, the simplified equations were already being solved numerically with the aid of the computer. The most advanced models did not predict the performance purely based on physical input parameters but had to be matched to actual well performance.

Answers to important questions concerning whether a particular reservoir at its particular stage of depletion was suitable for steam soaking still very often had to be found by field trials.

So far we have only mentioned the Californian and Venezuelan Bolivar Coast heavy oil fields as targets for thermal recovery but not the even more important heavy oil sands of Canada and the Orinoco belt in Venezuela.

533

In this period attention in Venezuela was mainly directed to the Bolivar Coast rather than to the Orinoco belt. In Canada, however, the first pilots were started as early as 1957 (39).

tested. Also, reversed combustion was tried out. To obtain injectivity, fracturing of the formation appeared to be necessary. As a follow-up to many years of testing, a relatively large in-situ combustion test is currently being carried out in co-operation with the AOSTRA.

the oil zone is underlain by a zone with a high water saturation which is more permeable than the oil sand. No fracturing is required to inject steam in this zone. From the field-testing programme which started in 1963, a cyclic steam- injection recovery scheme has been developed which is at present being tested in a seven-7-spot pattern. Physical model experiments with vacum models were carried out to investigate the performance of this project ( 4 0 ) .

Amoco started a field programme in which dry and wet combustion were

A special condition exists in the site of AOSTRA and Shell Canada where

In all field trials on the various thermal processes it had appeared that, however well the process might be understood in a onedimensional tube experiment, this understanding did not guarantee reliable predictions for an actual field performance. Areal distribution of the injected fluid and fluid segregation due to density difference play a major role. To study these phenomena, three-dimensional model experiments were carried out which were scaled to actual reservoir conditions.

vacuum models. Not only was it necessary to develop all kinds of new laboratory techniques field symmetry elements were simulated consisting of a few injection and production wells.

equal to (which is essential for ISC experiments) or approaching those in the field. Typical dimensions for these sand-filled models were 3 m x 1.5 m x 0.15 m. To enable maintenance of the high pressures, the models were contained in bulky pressure vessels. To simulate dip effects, the vessels could be placed in a tilted position.

In hfgh-pressure model experiments on wet in-situ combustion, using a medium viscosity (Schoonebeek type) oil, surprising observations were made (3). As expected, the injected air rapidly moved to the top of the formation, driving a combustion spearhead to the production wells, finally resulting in a tilted coke deposit (41). Temperature observations showed, however, that at several spots and at several moments combustion in the burnt-out zone revived. This was an indication that oil was being driven upwards by the growing underlying water tongue. Also, it was observed that the combustion heat made itself felt to near the bottom of the sand pack. Thus, an effective recovery mechanimn was recognised by which a considerable amount of the oil is driven upwards by the invading water tongue into the hot regime near the top of the formation where the oil becomes much more mobile and is easily driven toward the producers. A similar effective flow regime has been discovered earlier (42) for a water drive in a reservoir having a high mobility streak along the top.

Occurrence of this specific flow regime would explain why model experiments, run at a given water-injection rate but with air-injection rates differing by a factor of 4, showed practically identical recovery curves ending at an ultimate recovery of more than 1.5 higher than that obtained in a comparable plain water drive.

It would be interesting to experiment with modem computer simulators and assess how far the air injection rate can be reduced without affecting these favourable recovery results. Furthermore, it might be investigated to what

Two different types of models were applied: high-pressure models and

but also to derive scaling rules. In the tests usually

In the earlier high-pressure models, temperatures and pressures were

534

extent the sketched recovery mechanism would remain operative in reservoirs containing heavier oil, e.g. as in Tia Juana, with greater mobility contrasts to water and air.

In retrospect, it is noted that the concept of partially quenched combustion, being a marked step forward in combustion control, has been developed on basis of the frontal drive laboratory experiments and corresponding theories. These research activities have led, however, to an effective recovery process in which a mechanism other than partially quenched combustion also plays a role.

In steam-drive model experiments particular attention was paid to the development of the steam zone. Also, the utilisation of the heat injected was studied. From these experiments an analytical theory ( 4 3 ) could be derived which predicts the shape and the growth of the steam zone by making use of the concept of a pseudo-mobility ratio between oil and steam.

observed that steam followed the downdip draining hot condensate and thus broke through in a downdip well. This phenomenon had also been observed in the field. Agreement between field- and model observations was satisfactory.

Vacuum models to predict reservoir performance under steam drive were in particular applied by Shell Dev. Co. ( 4 4 ) . In vacuum models a rigid structure is obtained by imposing a vacuum on a packed bed of glass beads confined between two plastic sheats. Although these models were initially developed for low temperatures, they could also be applied for low temperature steam at the sacrifice of correct matching of the ratio between latent and sensible heat. The advantages are that they are much simpler to use and safer.

field projects such as for example Mt. Poso ( 4 4 ) , Midway Sunset, Yorba Linda and Peace River (40).

In experiments directed to the Schoonebeek field trials ( 3 3 ) it was

Information from model experiments was thus obtained for complicated

MID-SEVENTIES TO EARLY EIGHTIES

In the last ten years it has become more and more clear that the competition between the three thermal processes has been won by steam. After the oil crisis of 1973, the demand for heavy oil has increased and in particular in the U.S. many existing steam projects have been extended and new projects started. Many reservoire which have already been producing for 10 to 15 years under steam soak are now being converted to steam drive combined with steam soak.

To give an order of magnitude of these projects ( 4 5 ) : Many of them are producing in the range of 1000 to 5000 b/d. Large projects are Getty's Kern River Project with a production due to steam injection of 52,000 b/d, Shell's Hount POSO project with 20,000 b/d and Texaco's San Ardo project with 22,000 b/d.

Another important large steam drive project is being carried out by Maraven in Venezuela in a nearly depleted part of the Tia Juana field ( 4 6 ) . Although a large project on a commercial scale with a production rate of about 20,000 b/d, It is still considered to be of an exploratory nature for the wider application of steam drive in the Bolivar Coast heavy-oil fields.

For comparison, we mention some of the largest ongoing in-situ combustion projects: The Rumanian project I n the Suplacu de Barcau field ( 4 7 ) with an oil production of about 6500 b/d, Getty's project in the Bellevue field in Louisiana with about 2800 b/d and Mobll's project in the South Belridge field with 1900 b/d. Most of these projects are technically considered to be successful and profitable. This means that although steam is by far the most successful thermal method, in-situ combustion should certainly not be considered obsolete.

535

The main reservoir-engineering problem in designing new projects is the lack of simple and reliable performance prediction methods. Until the early seventies, a selection had to be made from extrapolation of pilot projects or more or less similar other projects, time-consuming scaled model experiments in the laboratory and a few simplified analytical models.

In the field of steam drive, a number of analytical methods for computing the volume and the shape of the steam zone have been derived over the years. The common basis of these various models is a procedure to account for the heat losses from the steam zone to over- and underlying formations. Furthermore, an attempt is made to disconnect the coupled heat transport equations (conduction and convection) and those for fluid flow (water, oil and steam). In one case this is done by neglecting fluid flow completely (Marx and Langenheim ( 4 8 ) ) , in another case by taking fluid flow partially into account to arrive at a better analysis of the heat distribution in front of the steam zone (Mandl and Volek ( 4 9 ) ) . A severe limitation of both approaches is that they describe only the development of a one-dimensional steam zone and do not predict its thickness. The method of Neuman (50) predicts areal and vertical development, assuming this is only determined by heat conduction and convection. Van Lookeren (43) assumes that the shape of the steam zone is determined by gravity and viscous forces but has to simplify the heat distribution. Nevertheless, some of his predictions check quite well within a defined range of applicability with observations from laboratory experiments.

With the aid of these analytical models it is possible to approximate the volune of oil displaced by steam. No straightforward methods existed to predict the volume of oil displaced by the hot condensate; neither did methods to take areal effects into account. This could only be done with the scaled model experiments and since the mid-seventies with a numerical simulator.

A lot has already been said in literature on the advantages and disadvantages of physical and numerical models (51). The consensus nowadays is, more or less, that physical experiments should provide the physical insight, and that the quantitative effect of any physical parameter could be investigated with the aid of the numerical simulator. This means that geometrically scaled model experiments as carried out in the late sixties and early seventies, will no longer be carried out in the future, since geometrical effects can much more easily be studied with a numerical simulator than with a physical model.

Simulators that can handle hot water and steam is connected with the increasing capacity of the computers: increasing speed and memory space. These factors enable the study of more details by means of the application of more grid blocks and acceptable runtimes made possible by replacing the older explicit methods by implicit methods.

Numerical simulators for the in-situ combustion process are not new either: One of the first mentioned in the literature dates from ae early as 1965 (52). However, owing to the complexity of the process, their development is far less advanced than in the case of steam models. One of the major problems in simulating field performance is the fact that the essential phenomena occurring in the combustion zone of a few metres thick have to be represented for practical reasons in grid blocks with sizes in the range of 10 m and more.

The main development in thermal simulators, or in particular those

PRESENT DEVELOPMENTS

The developments which are at present taking place in the field of thermal recovery can be grouped in the following way:

a. follow-up methods for ongoing steam projects. b. new thermal methods for the recovery of heavy oil. C. search for new targets for thermal methods. d. improvement of existing and development of new equipment.

536

Each of these groups is discussed briefly:

a. The need for follow-up processes is felt in particular in steam-drive projects which have been in progress for a couple of years, in which steam breakthrough has already taken place and where the oil-steam ratio is declining.

In reservoirs with medium viscosity oil (e.g. Schoonebeek) water injection or (if present) a strong aquifer may cause collapsing of the steam zone when steam injection is discontinued. In this way, relatively cold oil may be pushed into the hot formation. As the heat stored in the reservoir is utilised very efficiently, in this way, high oil/steam ratios may be obtained. It is clear that this process is not suitable for heavy- oil reservoirs. Nevertheless, water injection, with or without caustics, needs further consideration.

to be the application of blocking agents ( 5 3 , 5 4 ) , such as foams to divert steam into unswept areas. This method is under active study at various companies and institutes, both in the field and in the laboratory.

b. As already mentioned above, re-evaluation of heating heavy oil reservoirs by electromagnetic radiation or electric conduction regularly occurs. The major economic drawback of these methods is the low thermal efficiency inherent in the generation of electricity.

Also, the interest in the injection of oxygen (instead of air) for in- situ combustion has been revived ( 5 5 , 5 6 ) . The potential advantage of oxygen would lie in suppression of early breakthrough of large quantities of hot combustion gases in the production wells.

Methods which may become of interest with increasing oil prices are combinations of mining techniques and thermal methods (57) to increase recovery and reduce heat losses.

A promising method to improve the sweep efficiency of steam drive seems

C. With a very few exceptions, all thermal projects have been carried out in reservoirs containing heavy oil. Light-oil reservoirs were not considered because water is generally considered to be a cheaper driving fluid. If the residual oil remaining after water drive is considered to be a target, thermal methods should also be taken into account. Although not all proven to the same degree, injection of steam and hot water as well as in-situ combustion may be considered. Steam distillation,(or strip) drive in light- oil reservoirs is a process which has been technically proven both in the field (58) and in the laboratory (59). Residual oil saturations in the steamed-out zone are in the range of 3 to 8%. The economic weak points of the process are its high initial investment and high operation costs (fuel). Further study on the economic viability of the process seems necessary.

oil reservoir has already been demonstrated in the mid-sixties by Amoco in the Sloss field in Nebraska (60).

A potential process for high-pressure reservoirs might be derived from the property of hydrocarbons to dissolve in water at near-critical conditions. In practice, this means that the pressure should be above 200 bar and the temperature above 300°C. This means that this process is, anyhow, limited to deep reservoirs. Russian investigators (61) claim to have obtained high recoveries in tube experiments. Which crudes are suitable candidates for this process needs further investigation, as well as the economic viability of the process. Technical limitations can also be caused by the design of the deep injection wells.

promising are fissured limestone reservoirs. These reservoirs often consist

The technical feasibility of in-situ combustion in a watered-out light

A completely different type of target where thermal methods seem

537

of very low permeable matrix blocks containing nearly all the oil and a highly permeable fissure (or fracture) system (62). Drive processes have a very low recovery because the oil in the matrix blocks is bypassed by the drive fluid (either water or gas). Water imbibition does not occur or is very weak because the rock is oil-wet or neutral-wet. Gravity drainage is often hampered by capillary forces, the low permeability of the matrix rock and sometimes by the high viscosity of the oil.

The effect of heat can be manifold (63,64): expulsion of oil from the matrix blocks due to swelling and gas development within the matrix blocks (oil vapours and steam), improvement of gravity drainage and countercurrent imbibition due to viscosity reduction and reduction of the capillary retention. Both heavy and light oils come into consideration.

situ combustion. An important requirement for these processes to be effective is that the average fissure spacing should not be too wide to enable sufficient heat penetration into the matrix blocks.

Heat can be supplied by either injection of steam or hot water or by in-

d. Although in the field it is very often an area of serious problems, engineering of thermal projects has not been discussed so far in this paper. We will briefly touch on some of the major problem areas encountered with steam injection and some of the developments taking place in this field. These major problem areas are: water treatment, boiler design (efficiency, H2S emission, resistivity to feedwater and fuel), thermal well completions, production of sour gas due to thermal cracking and production of oil-water emulsions.

These problems cannot be considered separately: water treatment and boiler design are fully interwoven and are furthermore determined by the properties of the available water.

With the generation of steam downhole which is, at present, being actively investigated (65,66), a number of these problems is circumvented, such as boiler efficiency, H S emission and well completion.

Mechanical problems in hoz wells which increase with the depth of the wells are tackled by testing various insulations and high-temperature packers (67). The problems do not seem to be solved easily.

CONCLUDING REMARKS

In the early period much was expected of the in-situ combustion process with hot-water drive in second and steam drive in third place. At present, much more oil is produced by steam than by the two other processes. Steam soak, although not a drive process, has produced most of the "thermal" oil in the world. This process was discovered in the field and not proposed by research.

Looking at the way the three processes were developed, it appears that hot-water drive fallowed the sequence: desk study - laboratory experiments - pilot test. In the case of steam drive, laboratory experiments preceded the detailed desk study. In-situ combustion research was prompted by very early pilot tests.

From the above observations, one tends to conclude that all three phases (desk study, laboratory experiments and pilot test) are essential in the development of the process, while the sequence seems to be of less importance. On the other hand, it is very important really that all phases have been passed through. Research without field testing may lead to sterile hobbyiem and field testing without detailed preceding and following interpretation studies does not produce more than an abundance of poorly understood data.

538

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40. PRATS, M,;

42. VAN DAALEN, F., VAN DOMSELAAR, H.R. and HOOYRAAS, H.;

43. VAN LOOKEREN, J.;

SPE 6788. 44. STEGEMEIER, G.L., LAUMBACH, D.D. and VOLEK, C.L.;

"Representing steam processes with vacuum models. SPE 6787.

45. MATHENY, S.L.; %OR methods help ultimate recovery", Oil and Gas Journ. (March 31, 1980) , pp. 79-124.

"M-6 steam drive process. Preliminary results of a large scale field test",

46. VAN DER KNAAP, W.;

SPE 9452. 47. PETCOVICI, V.;

The experience of the Rumanian petrolem engineers with thermal recovery", Congreso Panamericano de Ingenieria del Petroleo, Mexico 1979.

"Reservoir heating by hot fluid injection", Trans. AIME ( 1 9 5 9 ) pp. 312-315.

"Heat and mass transport in steam drive processes", SOC. Pet. Eng. J. (March 1969) , pp. 59-79.

"A mathematical model of the steam drive process - Applications", SPE 4757.

"Physical modelling of in-situ recovery methods for oil sands", Proc. of the Canada-Venezuela Oil Sands Symposium 1977, pp. 319-326.

"A mathematical model of thermal oil recovery in linear systems", J. Pet. Tech. (Sept. 1965) , 196-210.

"Field demonstration of steam drive with ancillary materials", SPE/DOE 9777.

40. MARX, J.W. and LANGENHEIM, R.N.;

49. MANDL, G. and VOLEK, C.W.;

50. N", C.H.;

51. PAROUQ, AL1,S.M. and REDFORD, D.A.;

52. GOTTPRIED, B.S.;

53. DOSCHER, T.M. and IIAMMERSHAIMB, E .C.;

5 4 1

54. ESON, R.L. and FITCH, J.P.; "North Kern front field steam drive with ancillary materials", SPEf DOE 9778.

"ARC0 wants to test oxygen for in-situ", Enhanc. Recov. Week, November 10, 1980.

"Tertiarolgewinnungsverfahren - Die Untertageverbrennung mit Sauerstoff kombiniert mit Wasserinjektion (ISCOWI)", Erdbl und Kohle-Erdgas-Petrochemie (Jan. 1977) 2, 13-25.

"Technical constraints limiting application of enhanced oil recovery techniques to petroleum production in the United States",

58. KONOPNICKI, E.F., TRAVERSE, E.F., BROWN, A. and DEIBERT, A.D.;

55. ANON.;

56. PUSCH,.. !:;

57. BETC-STAFF;

DOE/ BETCf RI-80f 4, May 1900.

"Design and evaluation of the Shiells Canyon field steam distillation drive project", SPE 7086.

59. HAGOORT, J., LEIJNSE, A. and VAN POELGEEST, F. ; "Steam-strip drive: A potential tertiary recovery process", SPE 5570.

"A tertiary COFCAW pilot test in the Sloes Field, Nebraska", J. Pet. Tech. (June 1974), pp. 667-675.

"Method of recovering oil from an oil bearing bed", British Patent Appl. No. 15256/71.

"The reservoir engineering aspecte of fractured formations", IFP, Editions TECHNIP, Paris 1980.

"Steam drive pilot in a fractured carbonated reservoir Lacq Superieur field" , SPE 9453.

"Aspects of enhanced recovery in densely fissured carbonate reservoirs

Congreso Panamericano de Ingenieria del Petroleo, Mexico 1977.

"Feasibility evaluation of a downhole steam generator", SPEfWE 9775.

"Development of technology for downhole steam production", SPEfDOE 9776.

"Examination of techniques for thermally efficient delivery of ateam to deep reservoirs", SPE 8820.

60. PARRISH, D.R., POLLOCK, C.B., NESS, N.L. and CRAIG, F.F.;

61. CHEKALJUR, E.B. et al.;

62. REISS, L.H.;

63. SAHUQUET, B.C. and FERRIER, J.J.;

64. DE VRIES, A.S.;

. containing heavy oil",

65. WRIGHT, D.D. and BINSLEY, R.L.;

66. FOX, R.L., DONALDSON, A.B. and MULAC, A.J.;

67. JOHNSON, D.R. and FOX, R.L.;


THERMAL RECOVERY METHODS 5 4 3

US. DEPARTMENT OF ENERGY R&D ON DOWNHOLE STEAM GENERATOR FOR THE RECOVERY OF HEAVY OIL

RONALD L. FOX

Sandia National Laboratories

J. J . STOSUR

US. Department of Energy

ABSTRACT

The energy loss associated with delivering steam from surface generators to the reservoir is one of the factors that has limited most commercial steaming operations to relatively shallow oil bearing formations (about 1000 feet). The Sandia National Laboratories under contract to the U. S. Department of Energy has initiated an ambitious program for the developnent and field testing of a downhole steam generator. The advantages are impressive: exceptionally high overall thermal efficiency; good potential for alleviating air pollution from generating steam at the surface, andj significant economic benefits from accelerated oil recovery due to the introduction of combustion products along with steam.

Wo designs are being developed: a low pressure and a high pressure steam generator. through a heat exchanger, thus enabling the combustion process to be conducted at a pressure less than the injection pressure; a high pressure combustion design mixes the combustion gases directly with water, resulting in the injection of steam and combustion gases into the reservoir.

Field testing of a high pressure combustion generator was carried out in a shallow reservoir (275 meters) to determine if the system was conpatable with field conditions, if recovery with this device resulted in modifications to the reservoir or produced crude, and to assess the injection of combustion gases into the formation as a method of reducing air pollution associated with steam injection. for downhole operations in reservoirs below 700 meters.

The low pressure combustion design transfers energy to water

Follow on field tests have examined the performance of the device

INTRODWTION

THE U. S. Department of Energy initiated developnent of tools for production of steam at the oil producing formation in 1978. The technical implementation of the developnent and testing program is being carried out by the Sandia National Laboratories as part of the Department of Energy's Project DEEP STEAM. DEEP STEAM project incompasses development of methods for application of conventional steam drive to deep reservoirs as well as the downhole steam generator program. The project provides for the conception, feasibility analysis, laboratory testing, and field testing of methods for downhole production of steam.

Wo concepts for downhole production of steam for drive operations have been selected for comparative development.

The

The two designs differ in method of

5 4 4

t r a n s f e r r i n g hea t from hot combustion gases t o produce steam. combustion design t r a n s f e r s energy t o water through a hea t exchanger thus enabl ing t h e combustion process t o be conducted a t a pressure less than t h e in jec t ion pressuret a high pressure cornhuetion design mixes t h e combtistion gases d i r e c t l y with w a t e r , r e s u l t i n g i n t h e i n j e c t i o n of steam and combustion gases i n t o t h e reservoir.

The high pressure comhst ion design has been u t i l i z e d i n a series of f i e l d experiments, and t h i s paper presents t h e s t a t u s of downhole steam generator technology a s revealed i n these experiments.

A low pressure

DOWNHOLE STEAM GENERATOR PROGRAM

The developaent of technology f o r downhole steam production has been c a r r i e d out a t t h e Sandia Nat ional Laboratories and under cont rac t 'with Rockwell In te rna t iona l , Rocket%ne Division, and with Foster-Miller Associates. The design and t e s t i n g of a low pressure combustion generator has been pursued a t Rocketdyne. A high pressure combustion downhole steam generator is under development a t Poster-Miller. The Sandia National Laboratory is inves t iga t ing a high pressure generator which d i f f e r s from t h e Foster-Miller design i n t h e method f o r obtaining clean combustion a t pressures required f o r steam i n j e c t i o n operations. Sandia Systems. The f i e l d t e s t i n g has included these experiments:

T e s t A:

Test 8:

Test C: Intermediate term tes t of equipment i n downhole operat ions i n a

The f i e l d tests which have occurred t o d a t e have u t i l i z e d t h e

Intermediate term test of e q u i p e n t on sur face with i n j e c t i o n i n t o shallow reservoir. I n s t a l l a t i o n and recovery of t h e generator from a deep w e l l .

deep reservoir .

The condi t ions f o r Tes t A were f o r 3 t o 4 months of continuous operat ion u t i l i z i n g o i l f i e l d water and u t i l i t i e s with i n j e c t i o n of t h e generator e f f l u e n t i n t o a 270 m deep reservoir. Field of Cal i forn ia i n cooperation with Chevron, USA during January-May, 1980. The condi t ions f o r Tes t B were t o i n s t a l l and r e t r i e v e a downhole generatbr below 700 m i n a s tandard o i l f i e l d casing with a mechanically set packer be low t h e device. T e s t R w a s performed near Lovington, New MBxico, i n cooperation with ARC0 O i l and Gas during September 1980. The condi t ions f o r T e s t C were for 3 t o 4 months of continuous downhole operat ion i n a r e s e r v o i r a t a depth greater than 700 m. t h i s paper.

Tes t A w a s performed i n t h e Kern River

The r e s u l t s of these tests a r e given i n t h e r e m i n d e r of

SHALulw WELL OPERATIONS

A. Steam Generator. The d i r e c t contact steam/generation concept was chosen f o r t h e preliminary f i e l d test. w a s sought t o minimize t h e d e v e l o p e n t time required t o perform a test. Energy Co. of Grand P r a i r i e , Texas, produced a d i r e c t contact generator of slender c y l i n d r i c a l geometry. These u n i t s had been previously operated a t pressures up t o 100 psig. dimensions f o r damhole operation w a s procured f o r 5 x 10' btu/hr a t 3000 p s i with an outs ide dicrmeter of 6.5 inches. The design is i l l u s t r a t e d i n Figure 1 and is designated "before." I n t h i s design propane vapor is brought i n t o t h e a i r stream i n e i t h e r one or both i n l e t s ind ica ted i n t h e f igure. The propane and a i r are mixed as they t rave l d a m t h e channel. I g n i t i o n is by spark plug and occurs a t t h e area expansion. combustion region and is entrained i n t o t h e combustion gases. passes d w t h e ina ide of t h e steam generator, vaporizat ion of t h e water occurs r e s u l t i n g i n a mixture of Steam and cornbustion products (mainly COz and Nz).

A comwrcial ly a v a i l a b l e steam generator u n i t V a p o r

A s p e c i a l l y designed un i t whic could approxfmate

Water is passed up an annulus outs ide t h e As t h i s mixture

A I R I IK)DIFICATIONS

3 WATER

Propane Delivery/Mi nixture velocity Wall Propagation Water Paaaages Water Entrainment Ignition

.Xing

545

PROPANE AIR

BEFORE - WATER

A R E R - Figure 1. Direct contact Stoam Generator eefore an3

After Modification

This design was tested a t Sandia a t pressures of 100 p s i g or lower. The pressure l e v e l w a s l imi ted by t h e vapor pressure of propane a t t h e e x i s t i n g ambient temperature. t i o n w e r e noted.

1. propane is f i r s t pumped t o pressure. vaporized by h e a t t r a n s f e r from two sources: 1) propane is c i r c u l a t e d through t h e f lange which a t t a c h e s t h e mixer sec t ion to t h e combustor s e c t i o n ( t h e f lange is heated by conduction from t h e flame zone)# and 2 ) propane i a then c i rcu la ted through a jacke t around t h e a i r l i n e ( t h e a i r is warm because of compression heat) . These two zones are s u f f i c i e n t to cause partial vaporizat ion of t h e propane. i n j e c t e d i n t o t h e air stream through four holes which are 0.030" dia. ho les are normal t o t h e air flaw t o achieve penet ra t ion and improved mixing of t h e t w o streamer. s tagnat ion regime ( f law, holdern). ing temperatures i n t h e boundary layer which eliminate. flame propagation up t h e w a l l s .

2. inches. This has t h e e f f e c t of increas ing t h e flow ve loc i ty by 40% which decreased t h e p o s s i b i l i t y of burn-back.

3. The water paenage w a s modified to include a s leeve which separates t h e water and comhst ion zone t o a poin t a t which combustion is e s s e n t i a l l y cow pla te . Two benef ic ia l e f f e c t s arise from t h i s modiCication: 1) greater ease of ign i t ion , and 2 ) better combustion eff ic iency. An intermediate step i n t h i s modification w a s f o r t h e o r i g i n a l f a b r i c a t o r (Vapor Energy) to i n s t a l l a s leeve f o r t h i s purpose, with Sandia's concurrance. However, a f t e r approximately 20 h r s operat ion with t h i s modification, t h e s leeve was aeverely damaged. This w a s apparently due t o t h e s leeve not being f u l l y wetted by water. Hence, t h e f i n a l modification included a l i p on t h e end of t h e deem t o restrict water flaw and insure t h a t t h e annulua remained f u l l y wetted.

Several s h o r t c d n g e of t h i s system f o r t h e f i e l d test applica- These problems w e r e resolved by t h e following modifications:

In order to provide propane v a k r a t pressures above 400 peia, l i q u i d Then t h e propane l i q u i d is p a r t i a l l y

The r e s u l t i n g flaw then passes down a tube and i s The

A l l sur faces i n t h e mixing sec t ion are m t h t o el iminate The w a l l cool ing has t h e e f f e c t of r e d u c

The diameter of t h e mixing sec t ion was decreased from 1.5 inches t o 1.27

546

Approximately 30 s l o t s w e r e machined through t h i s l i p t o allow water passage, even a f t e r thermal expansion during operation. Additionally, t h e water passage gap a t t h e t o p of t h e combustor was increased from 0.040" t o 0.100" so t h a t it would not close upon thermal expansion. contact between water and t h e top cap w a s increased by extending t h e area expansion f u r t h e r i n t o t h e combustor.

4. t ion. without use of an e x o t i c pover source.

The above modifications a r e t h e hasis of a pa ten t appl ica t ion f i l e d by DOE.

B. Kern River F ie ld Tes t Results. The DEEP STEAM test s t a r t e d with t h e injec- t i o n of steam and combustion products i n t o t h e reservoir on February 6 , 1980, a f t e r one week of operat ions t o c a l i b r a t e equipnent and t o i n s t r u c t personnel i n t h e operat ion of t h e system. The test w a s scheduled f o r and w a s conducted on a 24-hour, 7-days a week basis.'

A f t e r t h e start up on February 6 t h e test w a s run f o r 109 days t o May 15. During t h a t per iod t h e test was in te r rupted 51 times: 8 f o t power and water f a i l u r e s which were suppl ied by others , 12 w e r e d e l i v e r a t e shutdowns, and t h e remaining 31 were represented by problems with t h e f u e l supply, computer, instruments and people. through March 20 and was caused a detonat ion being propaqated upstream through t h e a i r l i n e due t o o i l i n t h e l ine . The run t i m e excluding t h i s p a r t i c u l a r problem w a s 80% of t h e t o t a l test time.

The shallow reservoi r f i e l d test a t Kern River demonstrated t h e f i e l d performance of t h e generator system and t h a t neglectable material corrosion w a s encountered with t h e low s u l f u r LPG fue l . The combustion gases moved rapidly through t h e reservoi r , reaching production wells i n t h e 2 ~ 5 acre 5-spot p a t t e r n within 18 hrs . The o i l produced d i d not e x h i b i t any special emulsions due t o presence of t h e combustion gases. The e f f e c t of i n j e c t i n g t h e combustion gases i n t o t h e reservoi r reduced t h e environmental inpact due t o atmospheric exhaust of NOx and SOx.

Further, t h e area of

Instead of spark ign i t ion , t h e f i n a l design u t i l i z e d a flow plug f o r igni- This modification f a c i l i t a t e d ease of s t a r t i n g a t high pressure l e v e l s

The only major down period was from March 7

TEST OF GENERATOR INSTALLATION AND RETRIEVAL

The downhole generator requi res suppl ies of f u e l , water, and oxid izer t o produce steam a t t h e sand face. with these f lu ids . A tes t t o determine proceedure f o r i n s t a l l a t i o n of t h e device below 700 meters w a s performed i n la te September 1980.2 u t i l i z e d i n t h i s test w a s 15 meters long and designed f o r i n s e r t i o n with a 18 cm diameter casing. The mul t i - s t r ing supply consis ted of two jo in ted tubulars , t w o small diameter continuous tubulars , and an electrical cont ro l cable.

Multiple s t r i n g s must be run to supply t h e generator

The generator

A mechanically set Baker AB-1 packer w a s loca ted below t h e generator. w a s set a f t e r t h e generator w a s i n place. The mul t i s t r ing de l ivery system w a s pressure t e s t e d before s e t t i n g of t h e packer, a f t e r s e t t i n g , and a f t e r release of t h e packer. w a s maintained a t a l l s t a g e s of i n s e r t i o n and r e t r i e v a l .

The packer

The tes t demonstrated t h a t t h e i n t e g r i t y of t h e system

DEEP DOWNHOLE OPERATION

The generator design which w a s t e s t e d i n t h e shallow tes t i n t h e Kern River Fie ld has been replaced by a design which operated on l i q u i d f u e l s ( d i e s e l No. 21. t i o n by using more abundant fuels .

The l i q u i d f u e l design w a s developed i n order t o have wider applica-

5 4 1

A site for testing of the generator in a reservoir below 700 m was selected in the Wilmington Field in California. The test was carried out in cooperation with the City of Long Beach, California, and the Long Beach Oil Developnent Co. A new injection well was drilled for the test while existing production wells were utilized to form a five-spot 5-acre pattern. The injection well was directionally drilled at a 36 degree angle, the total length of the well is 830 meters.

The generator was inserted on June 19, 1981. The continuity of supply lines was tested and the responces of the reservoir to gas injection were studied after insertion of the device. The generator was ignited on June 22, 1981. The computerized ignition was achieved without incident, and continuous operation of the generator has proceeded ignition. gases at production wells was observed on June 26. is scheduled for completion during September 1981. A longer term follow on test may be performed in the same location for a total operation time of one year.

The arrival of combustion The intermediate term test

CONCLUSIONS

The DOE program for development of a downhole steam generator for recovery of heavy oil from deep reservoirs has proceeded through a series of successful field tests. The ability of the device to eliminate heat losses and reduce environmental impact of steam drive has been demonstrated. The operational characteristics of the device in deep downhole operations are being evaluated in current field testing.

REFERENCES

Mulac, A. J., et al, Project DEEP STEAM PrelMnary'Field Test, Sandia National Laboratories Report SANDBO-2843, April 1981

1.

2. Hulac, A. J., et al, Multiple String Demonstration Test for Project DEEP STEAM, Sandia National Laboratories Report SANDBO-2872, April 1981



STEAM DRIVE - THE SUCCESSFUL ENHANCED OIL RECOVERYTECHNOLOGY

TODD M. DOSCHER and FARHAD CHASSEMI

Department of Petroleum Engineering, Universiw of Southern calfomirr, Los Angeles, Gzlvornia 90007

I. ABSTRACT

Continued work with physical ly scaled models of t h e steam dr ive process has confirmed earlier conclusions t h a t t h e process should be viewed as being compr ised of two d i s t i n c t componenta: t h e h e a t i n g of t h e o i l a t t h e i n t e r f a c e b e t v e e n t h e o i l column and t h e o v e r r i d i n g s team, and t h e n t h e displacement of the heated oil by an except ional ly high ve loc i ty gas (steam vapor) drive.

The s t u d i e s d e s c r i b e d h e r e i n were conducted t o v a l i d a t e c e r t a i n hypotheses t h a t r e s u l t from t h e appreciat ion of the foregoing mechanism by which the eteam dr ive operatea. In general, a l l these hypotheses have been proven .

The o i l steam r a t i o , when communication between i n j e c t i o n and producing w e l l s is es tab l i shed ear ly , is not dependent upon reservoi r thickness when r e c o v e r i n g modera te ly v i s c o u s c r u d e o i l s . The o i l steam r a t i o s i n a wide range of f i e l d o p e r a t i o n s , i n keeping w i t h t h i s conclus ion , are shown t o f a l l within a very MKKOW band of values.

Perhaps the most novel conclusion a r i s i n g from t h i s study, int imated by t h e work of o t h e r s i n t h e p a s t , is t h a t t h e steam d r i v e is a powerfu l p r o c e s s f o r r e c o v e r i n g h i g h g r a v i t y c rudes , even w a t e r f l o o d r e s i d u a l s i f high i n j e c t i o n r a t e s of high q u a l i t y steam can be achieved. The s u b s t i t u t i o n of i n e r t gas f o r some of the steam i n a mature steam dr ive can s ignf icant ly i n c r e a s e t h e t h e r m a l e f f i c i e n c y b u t i t is not c e r t a i n , a t t h i s t i m e , t h a t t h e economic ef f lc iency would thereby be increased. Final ly , t h e observed e f f e c t of t h e v iscos i ty of the crude a t steam temperature on t h e e f f ic iency of t h e p r o c e s s . t h r e a t e n s t h e p o s s i b i l i t y of u s i n g t h e steam d r i v e f o r unassis ted recovery of t r u l y viscous crudes and bitumens.

11. INTRODUCTION

The s team d r i v e was f i r s t a t t e m p t e d i n t h e Hene Grande f i e l d I n Venezuela i n t h e l a t e W e where its f a i l u r e gave rise t o the use of cyc l ic ateam s t imula t ion f o r acce lera t ing the recovery of crude o i l from reservoirs conta in ig viscous Crude.. Eowever, during the subsequent decade experiments w i t h t h e steam d r i v e i n t h e San J o a q u i n Val ley of C a l i f o r n i a and i n t h e Athabasca bitumfoou8 8ands of Canada proved t h a t i t w a s a v iab le scheme f o r recovering viscous crud- and c e r t a i n bitumens.

Today, p r o d u c t i o n i n C a l i f o r n i a as a r e s u l t of b o t h c y c l i c s team i n j e c t i o n and steam dr ive OperatiOM is approximately 400,000 b a r r e l s of o i l a day, or 40% of t h e 8tate.8 total . Recovery e f f i c i e n c y in aome mature o p e r a t i o n e is d r e 8 d y well over 50% of t h e o r i g i n a l oil i n p l a c e and is

5 50

projected t o approach 70%. a value t h a t is achieved i n only a few reservoi rs t h a t a r e e x p l o i t e d by c o n v e n t i o n a l technology. Cumulat ive recovery from reservoi rs subjected t o steam i n j e c t i o n i n Cal i forn ia is now approaching 1.5 b i l l i o n b a r r e l s of o i l .

The s team d r i v e h a s been i n t e n s i v e l y s t u d i e d i n t h e Department of Pe t ro leum Engineer ing of t h e U n i v e r s i t y of Southern C a l i f o r n i a u s i n g p h y s i c a l l y s c a l e d models. The r e s u l t s of t h e s t u d i e s have c o r r o b o r a t e d a number of conclusions t h a t had been empir ical ly reached by s t u d i e s of f i e l d operations and i n addi t ion have provided f u r t h e r i n s i g h t i n t o t h e mechanism by which t h e ateam d r i v e f u n ~ t i o n s ~ , ~ , 3 , ~ . One of t h e most i m p o r t a n t conclusions from these s t u d i e s is t h a t the e f f ic iency of the steam drive is a function of the v iscos i ty of the crude o i l a t steam temperature. This i n t u r n l e a d s t o t h e f u r t h e r c o n c l u s i o n s t h a t t h e s team d r i v e may not be a s e f f i c i e n t as may have been surmised f o r the recovery of extremely viscous bitumens and may be t h e u l t i m a t e recovery scheme f o r the recovery of high gravi ty crude o i l s .

I n the c l a s s i c a n a l y t i c a l der iva t ion of the way i n which a steam dr ive functions, a t t e n t i o n is focussed on the development of a steam zone, which o c c u p i e s t h e e n t i r e c r o s s s e c t i o n of t h e r e s e r v o i r , and from which o i l i s assumed t o be depleted t o some na tura l ly determined res idua l o i l saturat ion. The f a c t is , however, t h a t t h e p r e s s u r e r e q u i r e d t o f r o n t a l l y d i s p l a c e a Viscous o i l bank a t an appreciable (economic) r a t e can r a r e l y be applied i n a r e a l reservoir.

Reported f i e l d r e s u l t s have demonstrated t h a t steam does not f r o n t a l l y d i s p l a c e heavy o i l i n a s team d r i v e o p e r a t i o n . I n j e c t e d s team i n i t i a l l y en ters the formation through a depleted or w e t in te rva l , a f rac ture , or, i n unconsolidated formations, a f lu id ized interval . I n a successful steam dr ive i n r e s e r v o i r s c o n t a i n i n g v i s c o u s c rude , t h e s team p e n e t r a t e s t o t h e producing w e l l q u i t e e a r l y i n the l i f e of the operation. Without t h i s , t h e i n f l u x of o i l i n t o t h e producing w e l l would s t i l l be l i m i t e d by t h e h igh v i s c o s i t y of t h e r e s e r v o i r crude. Even i f t h e i n i t i a l s team e n t r y i s not th rough a d e p l e t e d zone a t t h e t o p of t h e o i l s e c t i o n , t h e n t h e s team soon m i g r a t e s t o t h e t o p i f t h e r e l a any s i g n i f i c a n t v e r t i c a l p e r m e a b i l i t y a t a l l . D e p l e t i o n of t h e o i l t o a v e r y low s a t u r a t i o n o c c u r s i n t h e i n t e r v a l through which t h e steam f l o w s , and w i t h t i m e t h e d e p l e t i o n e x t e n d s d ~ w n w a r d s ~ , ~ . In the scaled physical model s tudies , t h i s v e r t i c a l extension of t h e s team zone can be f o l l o w e d i n some d e t a i l . The h e a t e d c rude a t t h e i n t e r f a c e b e t w e e n t h e steam and t h e o i l column i s s t r i p p e d o f f o r dragged along by the flowing steam. This s t r a t i f i e d flow of steam is of course not unexpected i n v i e w of its very low densi ty i n comparison t o the densi ty of t h e r e s e r v o i r f l u i d s . However, t h e unexpected r e s u l t i s t h a t t h e f l o w i n g steam is capable of dr iv ing the o i l s a t u r a t i o n down t o such low levels.

The i n t e r f a c i a l t e n s i o n of o i l a g a i n s t s a t u r a t e d s team h a s been v e r i f i e d i n our l a b o r a t o r i e s t o b e l i t t l e d i f f e r e n t f rom t h a t o i l a g a i n s t vater, and t h e r e f o r e i t a p p e a r s t h a t t h e o n l y p a r a m e t e r t o which t h e low res idua l can be a t t r i b u t e d is t h e high ve loc i ty of the gas (steam vapor). I t might be noted t h a t t h e i n j e c t i o n of 500 b a r r e l s of s team p e r day i n t o a r e s e r v o i r a t an a v e r g e p r e s s u r e of 200 ps i . i s e q u i v a l e n t ( n e g l e c t i n g condensation) t o t h e i n j e c t i o n of 6 MM SCFD of an i d e a l gas. The r e s u l t i n g v e l o c i t i e s on 2.5 t o 6 a c r e spacing ( the usual spacings f o r steam dr ive with I n j e c t i o n rates of 500 b a r r e l s p e r day) when c o u r s i n g through a 25 f o o t depleted zone are very high; of t h e order of 100 f e e t per day. Of course, a s i g n i f i c a n t f r a c t i o n of the in jec ted steam condensea, but o f f s e t t i n g t h i s somewhat is t h e f a c t t h a t t h e production pressure is less than t h e i n j e c t i o n p r e s s u r e and t h e r e f o r e t h e uncondensed steam w i l l expand and f u r t h e r increase its ve loc i ty through t h e reservoir.

551

111. THE OIL STEAM RATIO - THE MEASURE OF SUCCESS

The amount of o i l produced per u n i t quant i ty of steam injected is the most i m p o r t a n t c r i t e r i a f o r j u d g i n g t h e s u c c e s s of a s team i n j e c t i o n project. This is so because the amount of energy used t o generate the steam i n even t h e most s u c c e s s f u l p r o j e c t s i s a s u b s t a n t i a l f r a c t i o n of t h e produced o i l . The v a l u e of t h e f u e l i s overwhelmingly t h e l a r g e s t s i n g l e component of the cost of producing o i l by steam inject ion.

During t h e 60's Marx and Langenheim7 p u b l i s h e d a procedure f o r c a l c u l a t i n g t h e growth of a s team zone a s a f u n c t i o n of steam i n j e c t i o n r a t e , t i m e of Inject ion, reservoi r dimensions, and the thermal propert ies of the reservoi r and the cap and base rocks. Mandl and Volek8 l a t e r undertook a somewhat more d e t a i l e d a n a l y s i s of t h e mass and t h e r m a l b a l a n c e s a t t h e condensation f r o n t and developed a somewhat improved a n a l y t i c a l technique f o r e s t i m a t i n g t h e growth of t h e s team zone. Subsequent ly Myhi l l and Stegemeier9 codif ied Mandl and Volek's ana lys i s t o permit ready calculat ion of t h e o i l s team r a t i o a s a f u n c t i o n of a v a r i e t y of o p e r a t i n g c o n d i t i o n s and w e l l spacings.

I t 1s important t o note t h a t the o i l steam r a t i o s calculated by these methods a r e f o r un i form sands (a l though a l l o w a n c e can be made f o r unproductive but permeable layers disseminated through the reservoir sand). Also, it is assumed at the outse t of these ca lcu la t ions t h a t the in jec t ion r a t e of steam is e s t a b l i s h e d o r assumed s i n c e t h e a n a l y s i s i s s t r i c t l y a t h e r m a l one and does n o t t r e a t t h e q u e s t i o n s r e l a t e d t o f l u i d flow. Eventually, numerical methodslO were developed f o r pred ic t ing t h e performance of a s team dr ive . I t soon became obvious t h a t f o r t h e presumed r e s e r v o i r c o n d i t i o n s i n most heavy o i l r e s e r v o i r s d i d not p e r m i t t h e i n j e c t i o n of steam a t the r a t e s observed i n f i e l d operationa. I n order t o overcome t h i s d e f i c i e n c y , a n e x t r a o r d i n a r y h i g b c o m p r e e s i b i l i t y was a s s i g n e d t o t h e r e s e r v o i r . The i m p o r t a n t advantage of t h e n u m e r i c a l a n a l y s i s over t h e a n a l y t i c a l one is t h e a b i l i t y of t h e former t o include more than one layer and t h u s p e r m i t t h e development of t h e obvious g r a v i t y o v e r r i d e of t h e steam. By making s u i t a b l e adjustments i n t h e input parameters t o get a match of t h e per formance of p a r t i c u l a r o p e r a t i o n s , t h e r e s u l t i n g numer ica l a n a l y s i s can be presumed t o be a generalized s imulat ion of the steam drive process.

Both t h e a n a l y t i c a l and n u m e r i c a l models of t h e steam d r i v e p r o c e s s pred ic t a s i g n i f i c a n t e f f e c t of reservoi r thickness on the o i l steam r a t i o , a c e F i g u r e s 1 and 2. T h i s comes about f rom t h e f a c t t h a t when f r o n t a l displacement occurs, t h e heat l o s s a t the cap and base rock ie independent of t h e r e s e r v o i r t h i c k n e s s . Hence, t h e t h i c k e r t h e r e s e r v o i r , t h e g r e a t e r the f r a c t i o n of t h e in jec ted heat t h a t is captured within the reservoir.

Recent reviews of the performance of steam dr ive operations ind ica te t h a t a much lower range of o i l steam r a t i o s occur i n f i e l d operations than would be expected from the r e s u l t s of these calculat ions. The average of 7 curren t and completed steam dr ive operat ions i n th ick sands, In excess of 70 f e e t and approaching 200 f e e t , r e p o r t e d i n a r e c e n t s t u d y l l is only 0.22 with a standard deviat ion of only 0.06. On t h e o ther hand, the aver e fe;rlqfeam d r i v e s i n t h i n n e r sands , ranging from 18 f e e t t o 50 f e e t

i s s t i l l 0.20, ranging from 0.15 t o 0.25. F u r t h e r , t h e recovery e f f i c i e n c y from two of t h e s e r e l a t i v e l y t h i n r e s e r v o i r s , viz., Slocum and San Joaquin have been reported t o have approached 80%.

tt4, €9;

This anomalous behavlor of t h e o i l steam r a t i o combined with the observed o v e r r i d e of s team s u g g e s t e d t h a t t h e per formance of steam d r i v e s , a t

552

Fig.1. Effect of O i l Sat.,Reservoir Thickness and NetIGross Rat io on O/S Ratio

Fig.2. Effect of Res. Thickness on O i l / Steam Rat io

l e a s t when d e a l i n g w i t h v i s c o u s c r u d e s , is not c o r r e c t l y e s t i m a t e d by a n ana lys i s t h a t assumes f r o n t a l displacement. The ear ly work on t h e physical model experiments1*16 i n d i c a t e d t h a t t h e p r o d u c t i o n of o i l o c c u r s a t a (ver t ica l ly) moving boundary between the overr iding steam zone and the o i l column. Corre la t ive with t h i s performance is the exis tence of the fol lowing occurrences :

1. There is an optimum ateam i n j e c t i o n rate f o r a given spacing between Thin phenomenon had been observed i n Kern i n j e c t i o n and production wells.

River operat ions sometime earlied’.

2- The o i l s t e a m r a t i o i n v i r t u a l l y l i n e a r l y r e l a t e d t o t h e qua l i ty of the Injected steam. This r e s u l t i s i m p l i c i t i n t h e Mandl Volek analysis. Rot va te r i s v i r t u a l l y i n e f f e c t i v e i n r e c o v e r i n g any s i g n f i c a n t q u a n t i t y of viscoua crudes.

3. The o i l steam r a t i o i n a f u n c t i o n of t h e v i s c o s i t y of t h e v i s c o u s c r u d u at ( the average) steam temperature . For l o d e r a t e l y v i s c o u s c r u d e s t h e ra t io a p p e a r s t o b e a f u n c t i o n of t h e h a l f power of t h e i n v e r s e of t h e s t e a m temperature vi8cosi ty . Figure 3.

This observation has s e r i o u s impl ica t ions f o r t h e a p p l i c a b i l i t y of the steam dr ive proceas to highly viscous bitumens f o r which a very high steam temperature vould be required. It vould appear t h a t t h e r e s u l t i n g o i l steam r a t i o vould f a l l t o uneconomic valuea (below 0.12’1) when t h e produced crude is used as f u e l f o r generat ing steam. The f a l l i n t h e o i l steam r a t i o would be f u r t h e r e x a c e r b a t e d by t h e l o w e r f r a c t i o n of t h e l a t e n t h e a t and t h e lower s p e c i f i c volume of t h e steam a t high temperatures (pressures).

4. The p e r m e a b i l i t y of t h e f o r m a t i o n , above a darcy , h a s v i r t u a l l y no e f f e c t on t h e o i l steam r a t i o . D e t a i l e d i n v e s t i g a t i o n s have not been conducted a t lower permeabi l i t ies , but there is a suggestion t h a t very low permeabi l i t i es have a depressing e f f e c t on t h e o i l ateam rat io .

553

2 -

2

0 w - t 4 - V 3'

a t

I I I I I 1 1 1 1 I I I I I l l 1

o EARLIER STUDIES'

0 THIS STUDY

2 -

2

0 w - t 4 - V 3'

I I I I I 1 1 1 1 I I I I I l l 1

VISCOSITY OF OK AT STEAM TEMPERATURE (CD)

Fig. 3. OilfSteam Rat io as a Function of Reservoir Fluid Viscosity

5. Diurnal i n j e c t i o n of steam, as would occur i f steam was generated by 80kr devices, does not se r ious ly a f f e c t t h e o i l steam r a t i o as long as the t o t a l d a i l y rate is t h e same as in continuous inject ion3-

The current study was therefore designed t o inves t iga te j u s t why the a i l rteam r a t i o a p p e a r s t o be 80 less in a c t u s l o p e r a t i o n s t h a n would be predicted by a n a l y t i c a l and numerical models, and in addi t ion, vhy the o i l rteam r a t i o 8 a p p e a r t o f a l l w i t h i n a narrow band of v a l u e s f o r r e s e r v o i r s having a wide range of t h i c k n e s r e s . F u r t h e r , because of t h e i n c r e a s i n g v a l u e of t h e o i l #team r a t i o w i t h a d e c r e a 8 e in o i l v i s c o r i t y , i t W a s decided t o i w e 8 t i g a t e j u a t how high an o i l ateam r a t i o could be achieved in t h e d i r p l a c e m e n t of h i g h g r a v i t y c r u d e s , p a r t i c u l a r l y a t r e r i d u a l O i l ( t o water flood) maturations.

Final ly , becaume t h e steam dr ive procers appearr t o be comprised of two rcchanism8: f i r s t l y , t h e heat ing of t h e o i l a t t h e steam o i l in te r face , and 8econdly the displacement of t h e o i l from t h a t i n t e r f a c e by t h e f l w of the at-m vapor; t h e s u b s t i t u t i o n of ni t rogen f o r some of t h e ateam - t h a t p a r t used f o r displacement alone and not f o r heat ing - was invertigated.

I V . THE EFFECT OF RESERVOIR TH1CB;NESS

The e x p e r i m e n t a l p r o c e d u r e s and t e c h n i q u e s u8ed in c a r r y i n g o u t t h e physical y scaled model experimenta have been thoroughly de ta i led in earlier 8 t u d I e ~ ~ ' * ~ ~ ~ ~ . Tables 1 rummrires the prototype and model parameters f o r the experiment8 conducted with viscous o i l 8 in t h i s study.

554

TABLE 1

PROTOIYPE AND CORRESPONDING MODEL PAWTERS

Prototype

Reservoir Parameter Lloydainster Mdel

I n i t i a l Res. Temp., "F 75 3s

Pressure, psi. In j eet ion 500

Production 50

8.S

5 . 0

Sand T h i c h e s s . f t 2; 0.354

Permeability. Darcy 1 550

Porosity, I 53 55

Steam In jec t ion Temp., "F

I n i t i a l Gas Saturat ion, z 186

2

O i l Gravity, "API 14 11.8

Steam Quality, I 7s 27 .l

Scaling Factor 1 76.9

Flow Rate, (P-B/D, ?(-cc/min) 1000 186

Time (P-year, M-minute) 1 85 .7

Pattern Area (P-acre. M-ft') 5 4.6

Distance of I n j e c t o r t o R o d u c n . f t so 4.29

a) overburdon 1.09 1.15 b) uaderhrrdm 1.1 1 .o

TheriPrl conductivity, BN/hr . f t .*F

O i l Viscosity. cp a) reservoi r tamp. 100,000 ' 1000

b) stem temp. 28 5.8

Figure 4 shows t h e r e s u l t s obtained f o r a 26 foot th ick prototype on 5 a c r e r p a c i n g ( o r f o r a 1 3 f o o t t h i c k r e s e r o i r on 2.5 a c r e apac ing a t h a l f t h e indicated I n j e c t i o n rate. o r f o r a 52 foot reservoi r on 10 acre spacing a t double the indicated i n j e c t i o n rate). A conpariron of t h i s d a t a with the

555

r e s u l t s obtained earlier f o r t h e 70 foot prototype, Figure 5, ind ica tes t h a t t h e optimum stem i n j e c t i o n rate is i n t h e same range f o r both models; it is n o t dependent on t h e t h i c k n e s s of t h e format ion . F i g u r e 6 compare8 t h e per formance of t h e optimum steam i n j e c t i o n r a t e i n t h e two models. (The I n i t i a l , q u i t e pronounced d i f fe rence i n t h e two runs is due t o the f a c t t h a t i n t h e later work with t h e thinner reservoi r t h e i n i t i a l few hundreths of a pore volume of o i l t h a t was produced was not a t t r i b u t e d t o the steam drive.) Earlier c o n c l u s i o n s based on f i e l d o b s e r v a t i o n t o t h e e f f e c t t h a t t h e optimum rate is afunct ion of t h e a c r e f e e t i n the p a t t e r n area was probably due to the f a c t t h a t a l l t h e pa t te rns had t h e same thicknes.

J 0.15 6 " W

F 0.H)

2 0.05

0

Prololype Permeobilily. dorcy Oil roturolion. Y.

1.0 90

Sand Ihichner;. I 1 26 I

L 0.5 1.0 1.5

irao. ocre . Oil vixosily 01 s l a m lemo Averow rleom awlily. Y. 65 I Stcorn- pressure, Psib 190-270 , Po$osity. ,% , 33

2.0 2.5 3.0 3.5 4 0 4.5 STEAM INJECTED. EQUIVALENT WATER. P.V.'r

Pig. 4. Effec t of In jec t ion Rate on Oil/Steam Rat io

a (196.4 B/o 0.25-

L I- 0.90-

2393

V I l t l a r l l r l r L

0 1.0 2.0 3.0 4x STEAM INJECTED, EOUIVALENT WATER, P.V.' r

Pig. 5. Effec t of I n j e c t i o n Rate on Oil/Steam Rat io

556

n Thiarludy

Eorlicr studies' 0.30

f

744 B/a

657.5 B/O

1.0 2.0 3.0 4.c STEAM INJECTED, EOUIVALENT WATER, P.V.'s

Fig. 6. Comparison of OilfSteam Ratio f o r Thick and Thin Sand

The s team q u a l i t y uaed i n t h e 70 f o o t p r o t o t y p e r u n s averaged 4 5 % whereas t h e steam qual i ty f o r t h e 26 foot NN) averaged 65%. Calculat ions based on f r o n t a l dr ive theory i n d i c a t e the o i l steam r a t i o i n t h e f i r s t f i v e years should be somewhat higher f o r the th ick reservoi r than t h a t observed i n t h i s work. and j u s t s l i g h t l y higher f o r t h e t h i n reservoir. Discounting t h e e f f e c t of s team q u a l i t y , t h e results f o r t h e two r e s e r v o i r s would b e v i r t u a1 l y ident ical .

Given t h a t the descr ip t ion of t h e steam dr ive presented e a r l i e r , viz., t h a t t h e s team o v e r r i d e s t h e o i l column and g r a d u a l l y s t r i p s t h e h o t o i l f rom t h e i n t e r f a c e between t h e l a t t e r and I t s e l f , t h e r e i s no r e a s o n t o a n t i c i p a t e a s i g n i f i c a n t e f f e c t of r e s e r v o i r t h i c k n e s s on t h e process . Indeed, t h i s i s what t h e f i e l d r e s u l t s i n d i c a t e . T h e a l m o s t c o n s t a n t o i l steam r a t i o observed i n t h e wide range of steam driven reservoi rs reported above i s i n agreement w i t h t h e range of o i l steam r a t i o , 0.15 t o 0.20 observed i n t h e physical ly scaled model runs with viscous crudes. A simple mathematical formulat ion of the displacement of o i l a t the moving boundary has been developed which l e a d s t o t h e p r e d i c t i o n of j u s t such a range of values f o r t h e o i l steam ratio16.

V. EFPECT OF FLUID VISCOSITY

Figure 7 shows the r e s u l t s f o r t h e 26 foot prototype reservoi r when the prototype reservoi r f l u i d has a v iscos i ty a t steam temperature of only 0.4 cent ipoisc , s l i g h t l y g r e a t e r than water would have a t t h e same temperature- A compar ison of t h i s p r o d u c t i o n h i s t o r y w i t h t h a t of t h e more v i s c o u s reservoi r f l u i d s quickly shows t h a t displacement of t h e l o w v iscos i ty f l u i d by 8te.m r e s u l t s i n a u c h higher o i l steam r a t i o .

F i g u r e 3 shows t h e o i l a team r a t i o as a f u n c t i o n of v i s c o s i t y of t h e o i l a t steam tempera ture . The d a t a p o i n t f o r t h e t h r e e h i g h e s t v iScos i tY f l u i d s were obtained i n the earlier s t u d i e s i n a 70 foot prototype, and the d a t a p o i n t f o r t h e l o w e s t v i s c o s i t y f l u i d i s t h e one d e s c r i b e d i n t h i s study adjuated downwards because of t h e higher qua l i ty of t h e steam t h a t was used. It i8 apparent t h a t f o r the same o i l sa tura t ion , the o i l steam r a t i o COOtiruw t o Increase as t h e v iscos i ty of t h e reservoi r f l u i d decreases.

557

t . I ' 9 ' fi 1 ' 1 a ' ' ' ' ' I a ' ' I ;

0 a5 1.0 1.5 STEAM INJECTED, EOUIVALENT WAER. P.V.'s

0

Fig. 7. Oil/Steam Ratio History for Low Viscosity Fluid

A comparison of the steam (and therefore temperature) distribution i n the reservoir for the displacement of a viscous fluid and one with a low viscosity Is quite informative. Figures 8 .and 9 show the temperature distribution for the displacement of the heavy oll'and the mobile oil, respectively, after the Injection of an amount of steam generated from 0.5 pore volume of liquid water. Figures 10 and 11 portray the temperature distribution after the injection of 1.5 pore volumes.

c- FLOW DIRECIIOI

Fig. 8 . Temperature Dirtribution for the Heavy Oil After 0.51 P.V.'r of Steam Injected

558

FLOW DIRECTION

Fig. 9. Temperature D i s t r i b u t i o n f o r t h e Light O i l A f t e r 0.5 P.V.'s of Steam I n j e c t e d

c- FLOW DIRECTION

Fig. 10. Temperature D i s t r i b u t i o n f o r t h e Heavy O i l A f t e r 1.5 P.V.'s of Steam I n j e c t e d

It should be noted t h a t w i th a decrease i n v i s c o s i t y of t he r e s e r v o i r f l u i d t h e t e m p e r a t u r e d i s t r i b u t i o n i n d i c a t e a t h e mechanism is g r a d u a l l y t a k i n g on t h e a s p e c t s of a f r o n t a l d i s p l a c e m e n t . T h i s a g a i n s h o u l d be a n t i c i p a t e d s i n c e wi th decreasing v e l o c i t y t h e a v a i l a b l e p re s su re can indeed d i s p l a c e t h e bank of r e s e r v o i r f l u i d . The o i l s t e a m r a t i o s h o u l d now be e x p e c t e d t o approach t h e v a l u e s p r e d i c t e d by t h e f r o n t a l d i s p l a c e m e n t analyses, and indeed i t does. An e a r l i e r numerical s tudy a l s o ind ica t ed t h a t t h e ove r r ide of steam decreased s i g n i f i c a n t l y when i n j e c t i n g a t e i n t o a r e s e r v o i r t h a t had been water flooded t o a r e s d i u a l o i l saturat ionff .

559

C- FLOW DIRECTION

Fig. 11. Temperature Dis t r ibu t ion f o r t h e Light 011 After 1.5 P.V.'s of Steam In jec ted

V I . STEAM DRIVE OF A RESIDUAL. O I L SATURATION

The r e l a t i o n s h i p of t h e o i l s team r a t i o t o oil v i s c o s i t y , F i g u r e 3, ind ica tes t h a t a steam dr ive i n a reservoi r having a 33 percent porosity and s a t u r a t e d w i t h water w i l l produce t h e l a t t e r a t a r e s e r v o i r w a t e r l s t e a m in jec ted r a t i o of 0.7 a f t e r the i n j e c t i o n of 1.0 pore volume of steam. Even h i g h e r . i f t h e q u a l i t y of t h e i n j e c t e d steam a t t h e sand f a c e Is above 65% and t h e pressure is less than the prototype value of approximately 250 p s i used i n our s tudies .

If t h e r e s e r v o i r is n o t 100% s a t u r a t e d w i t h water, b u t c o n t a i n s a res idua l s a t u r a t i o n of a low v i s c o s i t y crude o i l which i r displaced more or less I n p r o p o r t i o n t o i ts s a t u r a t i o n i n t h e r e s e r v o i r ; t h e n t h e r e s u l t i n g o i l steam ratio would be ant ic ipa ted to be ( 0 . 7 ~ ~ ~ ) .

For a r e s i d u a l s a t u r a t i o n of 0.25, or grea ter , t h e r e s u l t i n g o i l steam r a t i o would be 0.18, or greater ; as high or higher than t h e o i l rteam r a t i o s exper ienced I n t h e steam d r i v e of heavy oi ls . The r e s u l t s of a model experiment With a res idua l s a t u r a t i o n of 22% of a prototype crude o i l having a v i s c o s i t y of 0.15 cent ipoise at a steam temperature of 401% are shown I n F i g u r e 12. The o i l a tcam r a t i o is 0.21 a f t e r t h e recovery of 32% of t h e r e s i d u a l o i l , and t h e o i l steam r a t i o i n m t i l l 0.14 a f t e r t h e recovery of 50% of t h e oil i n place.

It is I m p o r t a n t t o n o t e t h a t r e a c h i n g such h i g h o i l steam r a t i o s is dependent b o t h on a s u i t a b l y h i g h steam i n j e c t i o n ra te and a s u f f i c i e n t l y h i g h p o r o s i t y . However, t h e r e s u l t s do n o t a p p e a r t o be dependent on d i s t i l l a t i o n e f f e c t s , as had been Suggest by previous workers studying the recovery of r e s i d u a l o i l by a steam driveTib. Further, t h e mere f a c t t h a t a h i g h oil s team r a t i o is r e a l i z e d is n o t a u f f i c i e n t t o i n d i c a t e t h a t an economic steam dr ive operat ion is feasible . Certainly, an economic operation would be a t hand i f no a d d i t i o n a l w e l l d r i l l i n g c o s t a are encountered i n implement ing t h e d r i v e ; however, If many new w e l l s had t o be d r i l l e d in r e l a t i v e l y t h i n sands ( resu l t ing i n a high c a p i t a l investment per recovered bar re l ) , t h e advantages of high o i l steam r a t i o s might be overcome-

5 60

0.b 1 I I I 1 I I FROTCkYPE

401 pc-d .cP 0.15

LzQ- 7o

P X B P 774

I

mldIhal a1 22%

R O S W P W - 26 -. M Y . x 33

sfm-0, m - Rk

I I I I I I I I 1

0 20 40 60 80 100 OIL REcwup(, x O.O.I.P.

a0

Fig. 12. Cum. Oil/Steam Rat io h ia tory f o r Waterflood Residal O i l

VII. EFFECT OF CO-INJECTION OF NITROGEN AND STEAM

Figure 13 compares t h e performance of t h e steam d r i v e of a viscous 011 with with t h a t i n v i r t u a l l y t v o i d e n t i c a l reservoi r s i t u a t i o m i n which the i n j e c t i o n of steam and ni t rogen was s u b s t i t u t e d f o r t h e In jec t ion of steam alone af ter one p o r e volume of s team had a l r e d y been i n j e c t e d . I n Run 36 s team and n i t r o g e n were ~ i m u l t a n e o u a l y i n j e c t e d , and in Run 37 s l u g s Of n i t rogen vere a l t e r n a t e d with t h e steam.

0 * rb ab io

Fig. 13. Nitrogen as a Steam Additive

Compring t h e r e a u l t a of Run 36 and 37 w i t h t h e c o n t r o l . Run 38. i t is a p p a r e n t t h a t oil p r o d u c t i o n l a b e i n g m a i n t a i n e d even though ateam i n j e c t i o n is c u r t a i l e d aa a r e a u l t of t h e a n c i l l i a r y e f f e c t of t h e in jec ted i n e r t gas. There r e a u l t a c l e a r l y show t h a t i n a ateam d r i v e o p e r a t i o n t h e a t e m l a playing t h e u l t i p l e role already described.

A t t h i s t i r e , i t is n o t c lear t h a t t h e r e would be a marked economic g a i n i n t h e a u b a t i t u t i o n of an i n e r t gaa f o r mome of t h e ateam i n a mture steam dr ive because of t h e u n i t coat of compreaaed, i n e r t gaaaea. Bovever. t h i s l a n o t l i k e l y t o be t r u e i n l a r g e i n a t l l a t i o n s a t t h i n time. and may

561

n o t be t r u e a t a l l i n t h e f u t u r e as t h e c o s t of energy c o n t i n u e s t o e s c a l a t e . There is a f a r l a r g e r component of energy c o s t s i n t h e u n i t c o s t of steam than t h e r e i r t h e u n i t c o s t of i n e r t gas.

VII. CONCLUSIONS

The continued study of t h e steam dr ive i n physical ly scaled models, and c o r r e l a t i v e o b s e r v a t i o n s made on r e p o r t e d steam d r i v e o p e r a t i o n s i n t h e f i e l d lead t o t h e fol lowing conclusions:

1. The o i l steam r a t i o i n reservoi rs vhich contain a moderately viscous crude oi l , and i n which rteam overr ides the oil column w i l l aubs tan t ia l ly be t h e same regard less of reservoi r thickness. The most probable range f o r the oil steam r a t i o v i l l be 0.15 to 0.20. This conclusion presumes t h a t adequate i n j e c t i v i t y and communicat ion between i n j e c t i o n and production wells has been recured. The recovery e f f ic iency i t r e l f w i l l decrease as the reservoi r thickness increases much beyond 50 or 60 feet.

2. Because of t h e h i g h e r steam t e m p e r a t u r e s r e q u i r e d t o a c h i e v e r u f f i c i e n t mobil i ty of reservoi r crude, t h e oil steam r a t i o i n reservoirs vhich contain very viscous crudes are not l i k e l y t o permit economic recovery u n l e s s a f u e l cheaper t h a n t h e c r u d e oil i t s e l f is used f o r g e n e r a t i n g rteam.

3. The oil steam r a t i o i n c r e a s e s markedly as t h e v i s c o s i t y of t h e reservoi r crude decreares. Thin is due t o the more e f f i c i e n t s t r ipp ing of t h e h e a t e d f l u i d a t t h e oil steam i n t e r f a c e . An t h e v i s c o s i t y of t h e r e r e r v o i r f l u i d s d e c r e a s e t o t h a t of vater, t h e d i r p l a c e m e n t g r a d u a l l y c o n e r t s t o a f r o n t a l advance and t h e e f f i c i e n c y of d i s p l a c e m e n t of t h e r e s e r v o i r f l u i d a i n c r e a s e s s t i l l f u r t h e r . The i n c r e a s e i n t h e oil rteam r a t i o is s u f f i c i e n t t o i n d i c a t e t h a t 10 numerous s i t u a t i o n s v a t e r f l o o d r e r i d u a l oil aa tura t ioru can be economically recovered by a rteam drive. (An extension of t h e rame argument MY i n d i c a t e t h a t UUY resewoirr containing high gravi ty c r u d u may be more e f f i c i e n t l y exploi ted by a steam dr ive than by a vater flood.

4. An i n e r t g a r such as n i t r o g e n c a n b e r u b s t i t u t e d f o r a s i g n f i c a n t f r a c t i o n of t h e ateam, t h a t would otherwire be in jec ted i n t o a mature steam f l o o d , r t o m a i n t a i n t h e p r o d u c t i o n of oil and a c h i e v e a h i g h e r o i l f s t e a m ratio. The economic advantage of ouch a r u b r t i t u t i o n v i l l become more s i g n f i c a n t M t h e value of t h e crude oil i t r e l f increases.

5. A nimple c o n c e p t u a l model f o r t h e steam d r i v e v h i c h compr ises t h e o v e r l a y of t h e rteam, t h e h e a t i n g of t h e oil a t t h e r e s u l t i n g oil ateam in te r face , and t h e displacement of t h e heated o i l by the gas dr ive accounts f o r v i r t u a l l y a11 of t h e observatione made on rteam dr ive operat ions i n the f i e l d and i n t h e laboratory phyaical ly scaled models.

9111. REFERENCES

1. Dorcher , T. M., at. al.; "Scaled P h y s i c a l Models of t h e Steam D r i v e Process", Annual Report , C o n t r a c t EP-76-S-03-0113 36 PA, Uni ted S t a t e s Department of Energy, Oakland, Cal i forn ia

2. Doacher, T. M., and Baung, V.; "Steam Drive Per formance Judged from Use of Physical Modelr", O i l and Gas J. ( O c t 1979) 52

562

3. Doscher, T. U., Ghassemi, F., and Omoregie, 0. S.; "The A n t i c i p a t e d Effect of D i u r n a l I n j e c t i o n on Steam D r i v e Eff ic iency" , Paper SPE 8885 preaeated a t SPE 50th Cal i forn ia Regional Meeting, Lo8 AngeleS, Apri l 9-11, 1980

4 0 Ree, S. W., and Doscher, T. U.; "A Uethod, f o r p r e d i c t i n g O i l Recovery by Steamflooding Including t h e Effec t of D i s t i l l a t i o n and G r a v i t y Override", SOC. Pet. Eng. J. (AUg 1980) 249-266

5. Blevins , T. R ., and B i l l i n g s l e y , R. R.; "The Ten P a t t e r n Steam Flood, Kern River Field", J. Pet. Tech. (Dec 1975) 1505-1514

6. Neuman, C. 8.; "A W a t h e m a t i c a l Model of S t e a m Dr ive P r o c e s s Applications", Paper SPE 4757 Presented a t SPE 45th Annual Ueeting , Held i n Ventura, Apr i l 2-4, 1975

7. Uarx, J. W., and tangenheim, K. H.; "Reservoi r H e a t i n g by Rot F l u i d Injection", Trans., AIIIE, 216, 312-315

8. Process", SOC. Pet. Eng. J. (Uar 1969) 59-79

9. Myhi l l , 1. A*, and S t e g e m e i e r , G. L.; "Steam-Drive C o r r e l a t i o n and Prediction", J. Pet. Tech. (Fib 1978) 173-182

Uandel, G., and Volek, C. W.; "Reat and Mass T r a n s p o r t i n Steam D r i v e

10. Comma, E. a; "Correlat ions f o r Predic t ing O i l Recovery by Steamflood", J. Pet. Tech. (Feb 1980) 325-332

11. Farouq A l i , S. X., and Ueldau, R. F.; "Current Steamf lood Technology", J. Pet. Tech. (Oct 1979) 1332-1342

12. B a l l , A. Lo, and Bowman, R. W.; "(Tperation and Performance of t h e Slocum Thermal Recovery Project", J. Pet. Tech. (Apt 1973) 402-408

13. Blevins , T. B., A B e l t i o e , B. J., and Kirk , R. S.; "Analys is of a Steam Drive Project , Inglewood Field, California", J. Pet. Tech. (Sept 1969) 1141- 1150

14. Wooten. R. W.; "Case H i e t o r y of a S u c c e s s f u l 1 Steamf lood Project-Loco Field", Paper SPE 7548 Presented a t 53rd SPE Annual Meeting, Houston, O c t 1- 3, 1978

15. Greaser, G. R., and Shore, R. A.; "Steamflood Per formance in t h e Kern River Field", Paper SPE 8834 , Presented a t F i r s t J o i n t SPE/DOE Symposium, Tulsa, Apri l 20-23, 1980 16. Doscher, T. M., and Ghassemi, F.; "The E f f e c t of R e s e r v o i r Thickness and low V i s c o s i t y F l u i d on The Steam Drag Process" , Paper SPE 9897, Pre6ented a t The Cal i forn ia Regional Meeting, Bakersfield, March 25-26, 1981

17. B r u s e l l , C. G., and P i t t m a n , G. U.; "Performance of Steam Disp lacement in the Kern River Field", J. Pet. Tech. (Aug 1975) 997-1004

18. Stegemeir , G. L., Laumbach, D. D., and Volek, C. W.; ' a e p r e s e n t i n g Steam P r o c e s s w i t h Vacuum Uodels", P a p e r SPE 6787, P r e s e n t e d a t 52nd SPE Annual F a l l n e t t i n g , Denver, Oct 9-12, 1977

1% A y d e l o t t e , S. R., and Ramesh, A. B.; "Economic F e a s i b i l i t y of Steam D r i v e i n L i g h t O i l Reservoirs" , P r e s e n t e d a t 5 t h Annual DOE Symposium, T u h a , Auguat 22-24, 1979

20. P o t e n t i a l Ter t ia ry Recovery", J. Pet. Tech. (Dec 1976) 1409-1419

Bagoot, J. L e i j n s e , A., and Van P o e l g e e s t , F.; "Steam S t r i p Drive: A


DOWNHOLE STEAM GENERATION USING A PULSED BURNER

D. A. CHESTERS, C. J . CLARK and F. A. RIDDIFORD

BP Research Centre, Chertsey Road, Sunbury

ABSTRACT

The recovery of viscous crude oils using downhole steam generation provides a significant It is also 1 kely to be an economically viable solution for oil recovery at depths greater than 30%. the formation, the technique is virtually pollution free and provides a source of C02 to assist viscosity reduction. The operation of a continuously fired, high intensity burner within the confines of an oil well, hwever, presents a number of technical problems, the most intractable of which relates to the selection of materials to operate at high burner temperatures.

In order to obviate these difficulties BP has been developing a eystem based upon a pulsed burner. achieves the overall required combustion intensity as a series of high intensity, short duration pulses. velocity combustion products, the quantity of steam being governed by ignition frequency and mixture flow rate. demonstrated on a 75 m test wen.

A high pressure test rig, designed to simulate oil well conditions at greater depths, has been built to test pulsed burners operating on both gaseous and liquid fuels. only on gaseous fuels. Under pulsating conditions, the temperatures on the combustion chamber walls are close to that of saturated eteam at the operating pressure.

Current developments are being directed towards liquid f'uel operation, with the ultimate objective of proving a system on residual fuel.

rnprovement in t h e m 1 efficiency over surface steam generation.

In addition, by discharging combustion products into

The unit operates in a "quasi" detonation m d e and

Steam is produced by atomi8ing water into the high

The feasibility of this eystem has been

To date, operating experience on this scale has been obtained

INTRODUCTION

Dohnhole steam generation for the recovery of viscous crude oils offers a number of potential advantages over conventional surface methods. In particular, it is predicted from numerical simulation of the downhole steam generation process that the combined injection of steam and combustion derived C02, which assists in viscosity reduction, will significantly increase recovery rates compared to conventional steam drive (1). As a result of this interaction, it is also predicted that the operating cost per barrel of recovered crude oil is independent of depth up to-1500 m (1). are eliminated, the technique is also more thermally efficient, an advantage that becomes progressively more significant as deeper reservoirs are prcbed and higher pressures encountered. an attractive solution to thermal recovery in deep reservoirs.

Since surface and well thermal losses

Downhole steam generation therefore appears to be

564

The advantages of downhole steam generation were recognised a number of years ago when the US Department of Energy set up the research programme "Project Deep Steam". combustion ( 2 ) ) and direct (high pressure combustion (3)). methods of downhole steam generation. exchanger and the combustion gases are ducted back up the well casing. are, therefore, only those required to maintain the flow of reactants and products within the system. directly to steam by the combustion gases and the mixture injected into the formation. Combustion therefore takes place at reservoir pressure. Both systems have reached an advanced state of development and have been tested downwell (4.5). The operation of high output continuous burners within the confines of MA o i l well, however, presents a number of technical problems. high heat fluxes encountered within the canbustion chamber coupled with the degree of mixing required to achieve high combustion intensities necessitate careful attention to cooling and fuel/air mixing. in high pressure applications where the technology literally enters the space age; advanced rocket engines using exotic f'uels rarely exceed pressures of 70 bar. therefore complex and requires the use of highly specialised materials. experience gained to date has already highlighted the importance of these pnrticular areas (6).

In order to overcome the potential problems of a continuously fired downhole burner, Bp have developed a downhole steam generator that operates in a pulsed combustion mode. This paper deals with the current state of the development and discusses:-

This project has resulted in the development of indirect (low pressure

In the indirect method, steam is generated within a downhole heat Pressures

In the direct method, however, water is flashed

In particular, the very

The problems are accentuated

The design of a continuous burner and associated downhole hardware is Field

(a)

(b)

(c)

the principles of operation and general construction of a pulsed downhole stem generator; operational experience of a methane fired downhole steam generator;

current progress in the development of a liquid fuel fired burner.

MIXING M A D

SURFACE ROUGHNESS

.--&

01 INOUCtlOLl bj IWllDN d PRop4G41DN dj EIHAVS1

Figure 1. Schematic Diagram of the Individual Phases in the Firing Cycle of a Pulsed Burner.

565

I 1.3 m

4.0 m

DESCRIPTION OF A PULSED DOWNHOLE STEAM GENERATOR

The essential difference between the BP downhole generator and those being developed elsewhere i s that it operates i n a pulsed mode rather than i n a continuous mode.

Within t h e pulsed burner, combustion occurs by the repet i t ive f i r i ng of discrete volumes of f'uel/air mixture. schematically i n Figure 1.

A t the s t a r t of the f i r i ng cycle (Figure l a ) , fuel and a i r are introduced from separate supply l i nes a t one end of a tube roughened over part of i t s length. The tube i s f i l l e d over i t s ent i re length with fuel /a i r mixture. On ignit ion (Figure l b ) flames propagate both upstream and downstream. The pressure r i s e within the combustion tube modulates the reactant flow and the upstream propagating flame is extinguished at the mixing head (Figure l c ) . AB a resul t of turbulence induced acceleration, the flame within the roughened tube reaches a velocity that i s about 25% of the detonation velocity of the fuel /a i r mixture (-500 m s - 1 ) . This corresponds t o a pressure r a t io across the flame front of 2.5. coupled system or "quasi" detonation, the velocity of which is determined primarily by the roughness of the tube walls. A detailed description of the propagation mechanism i s given in Ref 7. In the final phase of the cycle (Figure l a ) combustion gases are exhausted from the burner a t high velocity. Since the i r residence t i m e v i thin the burner i s short, l i t t l e heat i s transferred t o the canbustion tube wal ls ; for the greater part of the cycle the tube i s f i l l e d with relat ively low temperature gares.

The power output, and hence potential steam output of a pulsed burner, i s determined by the frequency with which each discrete volume of reactants, that is the volume of the combustion tube, i s ignited. Power output is simply adjusted by varying fue l / a i r f low r a t e and ignition frequency. The upper l i m i t t o power output i s theoretically determined by the maximum propagation velocity tha t can be achieved i n a roughened tube. In practice, however, power output i s limited by a r e a l i s t i c frequency aad fuellair f l o w rate. For burners presently being designedran output of 10 Mw ( - 2000 bbl steam/day*) a t a depth of fib m i r believed t o be achievable. An operating pressure of 70 bar has been selected M a target for the i n i t i a l phase of burner development. A specifioation for such a burner i s given i n Table 1.

The individual phases i n the f i r i ng cycle are sham

The flame and associated shock structure propagate as a

Table 1 Typical Specification for a 10 MW Pulsed Burner Operating at 70 bar

Principal Burner Charac t e r i s t i c s I

Diameter of canbustion tube Overall diameter of generator

Length of combustion tube Overall length of generator

89 nun

127 nun

Heat output range I 0 - 1 o M w

Ignition Frequency I 0 - 5 HZ a This is defined as the number of barrels of water converted t o steam.

566

A comparison of the combustion intensities that can be achieved in continuously fired high intensity combustion systems is given in Table 11. these data shows that the combustion in a pulsed burner is only exceeded by the most exotic systems.

Examination of

Table I1 Comparison of Typical Combustion Intensities Achieved in High Intensity Combustion Systems.

Combustion System

Steam boiler

Gas turbine

Ram jet

Rocket engine

Pulsed burner

Operating Pressure (bar)

4

5

35

70

Combustion Intensity m / m 3

1 - 3

370

750

105

1.3 103

Although high combustion intensities may be achieved using a pulsed burner, the fact that flame stabilisation is not required and that the entire combustion tube is available to mix fuel and air prior to combustion, permits significant simplification in the design of the mixing head and combustion tube. In addition, because of the low wall temperatures that result from a pulsed mode of operation, the burner requires only simple cooling and may be constructed from conventional materials. That low w a l l temperatures are indeed measured during normal operation is demonstrated in Figure 2a. from thermocouples set in the wall of a burner operating at a pressure of 7 bar. and that it drops to well below the saturation steam temperature some distance downstream. If, however, the burner changes to a continuous mode Of operation, the change in wall temperature is dramatic. Figure 2b. The short duration plateau, followed by a rapid temperature rise, indicates a change to film boiling within the water jacket. operation under these conditions would result, after a few minutes operation, in total failure of the unit. included to sense such an event and initiate shut down.

The overall design of the entire downhole steam generator is shown schematically in Figure 3. system, with the ignition and instrumentation lines strapped to the air line. The upper part of the assembly comprises instrumentation and ignition packages which provide, respectively, a continuous monitor of combustion performance and ignition control. the ignition cycle is initiated, as already discussed. directly into the combustion chamber via an annular water jacket. flashed directly to steam and the resulting mixture of steam and combustion products is injected into the formation. escape of steam up the annulus.

Small scale experimental burners of this general design have been successhiLly operated on gaseous fuel (methane and hydrogen) in a high pressure test rig. Limited field work has also demonstrated that the system represents a practical means of downhole steam generation.

These data were obtained

It is seen that the wall temperature is highest nearest the mixing head

The effect is shown in

Continuous

In the prototype burner, instrumentation is

Fuel and air are supplied to the burner through a dual string

Fuel and air are injected into the combustion tube and Water is sprayed

The water is

A high pressure packer prevents the

Burners are currently being developed to use

567

uo-

;;no- t W a D

4 a W P

I Y c -I a

c

s 110

1od

liquid fuels (ranging from middle distillate to residual fuels) to meet a variety of operational requirements. is now separately discussed.

Each of these aspects of the deve1opner.f

-

1 0 100 1oD Po 40 yx) a0 lm 8ca

1E~PERATURERANCERECORDEDON ”’ INSIDE AND WTSIOE OF COMEWTION Tuea-wAu

SHUl DOWN OF BURNER

a 5 la E 20 a TIME (SECONOS)

Figure 2b temperature with time following a change to continuous operation at 2 bar.

Variation of combustion tube well

Figure 2a combustion tube of a prototype 0.25 MW pulsed burner during operation a t 7 bar.

Temperature p r o f i l e along the

568

FUEL!

.. . '

. . PUSED BURNER

N E L AND AIR PASSED DOWN WELL USING INDIVIDUAL WATER SUPPLY IN JECTK: . PIPES NOZZLES .c\s

\ WATER . r;..

F - 9::

PASSED DOWN ANNULUS CONNECTING

WlOP .. .

Figure 3 - Schematic diagram of a prototype Pulsed Downhole Steam Generator

. 5

69

P 5 B ti

y\

0

u

k

0

d

.PI a Figure 4 General arrangement diagram of the 0.5 MW burner used i n f i e l d trials

570

OPERATIONAL EXPERIENCE OF A DOWNHOLE GAS FIRED GENERATOR

A ser ies of experiments w a s carried out i n a water well d r i l l ed in to Bunter Sandstone and located i n the Midlan&' gas f ie ld . prove t h e operation of a pulsed burner i n a downhole environment. was designed t o operate on local ly available methane a t depths of up t o 75m. The t e s t burner had a maximum diameter of 0.13m, a length of 1.0 m and a combustion tube volume of 0.007 m3. heat output i n the range 0.125 - 0.5 MU. t e s t burner is given i n Figure 4 . through a h i energy (10 J ? aeroengine ign i t e r si tuated a short distance downstream of the mixing head; i n t h i s design the mixing head is located under the packer.

During the early stages of the t r ia l , d i f f i cu l t i e s were experienced with the ignit ion system; short c i r c u i t s within the high tension uni ts and leads resulted i n the t e s t being discontinued a f t e r a few hours' operation. Tests were resumed w i t h an improved igni t ion system which enabled continuous operation fo r 24 hour periods a t a depth of 75 m. period, the work did demonstrate t h a t downhole operation of a pulsed burner i s technically possible. In addition, it highlighted a number of deficiencies i n the system tha t required further development. the design of a r e l i ab le ignit ion system i s of c r i t i c a l importance t o the successful operation of the burner. packer assembly was a l so recognised as being an important requirement for downhole burners.

The aim of the work w a s t o The burner

The f i r i n g frequency was 0.5 - 2 Hz, giving A general arrangement drawing of the

Water, fuel and air were fed i n separate l ines pressure bellows aeal. Ignition was achieved by means of a h1sh

Although the burners operated fo r only a limited

In particular, it was c lear that

A closer integration of the burner and

CURRENT PROGRESS I N THE DEVELOPMENT OF A LIQUID FUEL BURNER

I n i t i a l development work on the pulsed downhole burner was carried out using hydrogen or methane as fuel . supplies may not always be available fo r downhole stem generation. considered essent ia l , therefore, that a downhole burner should be capable .of operating on a range of fuels. extended t o l iquid fuels with the ultimate aim of operating on residual fuel or produced crude.

The operation on a l iquid fue l presents a number of d i f f i cu l t i e s fo r both pulsed and continuous burners. associated with the i n i t i a t i o n of a "quasi" detonation.

It i s generally agreed ( 8 ) t h a t , i n two phase detonations, fue l droplets are broken up by secondary a t d s a t i o n t o produce a combustible mixture of fue l micromist (micron s i ze droplets) and hot oxidiser i n the wake of each parent droplet. The l a rge surface area between micromist and oxidiser enables chemical reaction t o occur a t a r a t e t h a t i s suff ic ient ly rapid t o support the incident shock front. A similar mechanism generates the "quasi" detnnation. In order tQ i n i t i a t e a d i r ec t detonation i n a fuel/air mixture, a f igh energy ignition source is required, the precise energy requirement being dictated by the overall induction period of the reaction. governed solely by chemical processes, whilst i n a heterogeneous system both physical and chemical processes play a role. As a re su l t , the induction period and hence the energy requirement fo r direct igni t iex is greater fo r heterogeneous systems. i n i t i a t ion and propagation of a detonation (9).

Owing t o e c o n d c / p o l i t i c a l constraints, gas It is

For t h i s reason, the developent has been

For the pulsed burner, the greatest diff icul ty i s

In a gaseous system the induction period is

O f t h e physical parmetkrs, droplet s i ze plays a key ro l e i n the

The operation of a pulsed burner on liquid fuels has therefore necessitated the development of two key areas of burner operation, namely:

(a) Fuel atomisation and mixing.

(b) High energy ignition systems.

To date, a burner has been successfully fired at atmospheric pressure on liquid kerosene. atomising nozzles using combustion air as the atmising medium. initiated by a high energy source generating approximately 250 J ignition event. triggered by a plasma plug. reliability, discussed previously. and operates in a surface discharge fashion, the main discharge taking place within the confines of a small cavity.

In this mode of operation the breakdown voltage is lower than that required for a conventional air gap and, furthermore, exhibits a smaller pressure dependence. Trigger voltages are maintained at an acceptable level even at pressures of 70 bar. enclosed electrode assembly and a self-cleaning action. These features have enabled plasma plugs to be operated reliably in laboratory test rigs at high pressure.

Future work e l l be directed towards developing burners to operate on fuels of laver volatility.

Within the burner, atomization is effected by a ring of twin fluid Detonation is at each

This system operates on an energy awentation principle The latter has overcome the problem of igniter

The plasma plug is a recent developnent (lo)

The plasma plug has the additional advantages of a variable output, an

1. offers a number of advantages for downhole steam generation.

A burner that operates in a pulsed mode, rather than in a continuous mode, These include:-

(a) low burner temperature;

(b)

(c) high combustion intensities;

(d) high turndown ratio

A steq generator incorporating the principle of pulsed combustion has been

A reliable ignition system is an essential requirement for a burner operating

relatively simple construction from conventional materials;

2. successfully demonstrated downhole.

3. in a pulsed continuous mode.

4. using a high energy ignition source.

A n atmospheric pulsed burner has been successflilly operated on liquia kerosine

ACKNOWLEDGEMENT

Permission to publish this paper b s been granted by the British Petroleum Company Limited.

The authors acknowledge the support given by the European Economic Community.

572

1.

2.

3.

4.

5.

6.

7.

8.

9.

10.

BADER, B.E. and FOX, R.L.; "The Potential of Downhole Steam Generation t o the Recovery of Heavy O i l s " , UNITAR 1 Fi r s t International Conference on the Future of Heavy Crude and Tar Sands, Edmonton, Alberta 4 - 12 June 1980.

WRIGHT, D.E. and BINSLEX, R.L.; "Feasibility Evaluation of a Downhole Steam Generator"; SPE/DOE 9776, Paper presented t o the Second Joint Symposim on Enhanced O i l Recovery of the Society of Petroleum Engineers, Tulsa, Oklahoma, 5 - 8 April 1981.

MULAC, A.J., e t al ; "Roject Deep Steam - Pre1hrinax-y Field Test Bakersfield, California, SAHD 80 - 2843.

"Downhole un i t said t o be ready for sale"; Enhanced Recovery Week, May 11, 1981.

30. 1981. "Test s la ted f o r damhole steam generator"; O i l and Gas Journal, March

JOHNSON, D.R., e t al; Project Deep Steam Quarterly Report, July 1 - September 30, 1980.

LEE, J.H.S. and MOEN, 1.0.; "The Mechanism of Transition fram Deflagration t o Detonation i n Vapour Cloud Explosions", Prog. Energy Combust. Sci., (1980) 6, 359 - 389.

DABORA, E.K. and WEINBE3GER, L.P.; "Present Status of Detonations i n Two-phase Systems"; Acta Astronautica (19741, 1, 361 - 372.

LU, P.L., SLAGG, N. and FISHBURN; B.D.; "Relation of Chemical and Physical Processes i n Tvo-phase Detonations", Acta Astronautica (19791, 6, 815 - 826.

ASIK, J.R., PIATKOLSKI, P., FOUCHER, M.J. and RADO, W.G.; "Design of a Plasma Jet Ignition System fo r Autanotive Application "(No 7703551, Society of Automotive Engineers, International Automotive Engineering Congress and Exposition Cob0 H a l l , 28th February 1978.


HOT CAUSTIC FLOODING

R. JANSSEN-VAN ROSMALEN and F. Th. HESSELINK

Koninklijke Shell Explorative en Roduktie Luboratorium, Rijswijk, The Netherlands (Shell Reseurch B. V.)

SUMHARY

A chemical recovery method used as a follow-up to or in combination with thermal methods is restricted to processes that are not too sensitive to elevated temperatures and temperature gradients. Caustic flooding is one of the few processes which can meet these requirements. Three different recovery mechanisms can be created by varying the salt content and/or adding extra chemicals to the caustic slug. The caustic process at high salinities is regarded to offer the best prospects for "hot caustic", since the process does not require extra chemicals (e.g. polymer) for mobility control.

an increase in temperature can be favourable for in-situ emulsification and, once an emulsion is formed, can drastically influence the flow properties of the emulsion. For a caustic flood following a hot water drive, a minimum shear rate was found to be necessary for emulsification.

In the caustic flooding experiments where a mobile emulsion was formed, oil recoveries superior to those of a comparable hot-water flood have been obtained. In one-dimensional packs of reservoir sand a hot caustic flood recovered 16-18% PV additional oil after a hot water drive. The sweep- improving effects of a sufficiently mobile caustic emulsion are expected to give a substantially higher additional recovery in a real three-dimensional flood .

In our studies on caustic floods, laboratory experiments have shown that

1. INTRODUCTION

Caustic flooding is an enhanced oil recovery method which is based on the principle that organic acids, naturally occurring in some crude oils, can react with the alkali of the caustic injected. This chemical reaction leads to the formation of surfactants at the oil-water interface, resulting in a decrease in interfacial tension between the oil and the water phase and in in- situ emulsification when a caustic solution of suitable alkalinity is injected into an oil-bearing formation.

A basic requirement for the caustic recovery method is that the oil contains a sufficient amount of natural acids. In this connection an acid nmber of about 1 mg or higher is desirable (+> (2> but active caustic systems have also been reported at lover acid nmbere (2). This activity is, among other things, related to the percentage of natural acids having a sufficiently high molecular weight to be effective in reducing the oil-water interfacial tens ion.

5 7 4

Several mechanisms have been proposed to describe the effect of caustic injection on the recovery of oil. Johnson (2) has given an overview of the different mechanisms involved in caustic flooding, such as emulsification and entrapment (L), wettability reversal (L) (5) (i) and emulsification and entrainment (2). Recently Meyer et a1 (z) have summarised data on field tests, and related the results to caustic concentrations and salt contents of the floods. Their status report shows that different recovery mechanisms are dominating in the various caustic flooding field trials.

In the present paper the effect of an increase in temperature on the caustic flooding process will be discussed. A method of this kind is indicated in Ref. 8. The application of "hot caustic" may be considered for the following reasons. In some cases a hot caustic injection may yield increased oil recoveries, while at reservoir temperature the injection would not lead to a better performance in comparison with a plain water drive. It should be noted that injection of hot caustic into an ambient temperature reservoir may require preheating of the reservoir, since the thermal front will move through the reservoir at a much slower rate than the caustic front. In other cases the reservoir may already have been preheated by a steam drive or a hot water drive. A chemical recovery method to follow up these thermal methods is restricted to processes that are not too sensitive to high temperatures and temperature gradients as occur in preheated zones. Such conditions adversely affect a surfactant or polymer flood. The prospects offered by a foam or caustic process are more promising under conditions as described above.

The scope of the present study is to provide an indication of: - which caustic recovery mechanism can best be chosen at elevated

temperatures. - how the parameters that are important for a caustic process are

influenced by an increase in temperature. - the oil recovery when applying hot caustic flooding.

The investigation of caustic flooding In conjunction with a thermal project is especially relevant, since the high-acid-number crudes suitable for caustic flooding are usually low-gravity crudes (1> for which thermal EOR processes are often considered. The preceding steam flood may even have increased the acid number of the crude.

2. THE CAUSTIC PROCESS

2.1. Principal recovery mechanisms

the type of emulsion formed during caustic flooding have been found to be dependent on the salinity of the caustic injected (2) (L). This means that the recovery mechanism is likewise affected by salinity. Reisberg and Doscher (2) have reported that caustic solutions used in conjunction with surfactants were effective in increasing oil displacement. The combination of an alkaline solution with a co-surfactant was also mentioned for the formation of a microemulsion to be injected into a reservoir (10). Research on the application of polymers in caustic flooding to provide mobility control is in progress (2)

The interfacial tension between the oil and the water phase as well as

(11) (12).

In order to catalogue the variety of alternatives for the caustic process, we would propose to classify the caustic recovery mechanisms (see Fig. 1) in parallel with the various mechanisms identified in surfactant floodinn. as follows: -. - The under-optimum system. -----------------I------

At low salinity of the caustic injected a non-viscous oil-in-water emulsion is formed. This system is often formed at sodium ion

575

I I OPTIMUM

I OIL +CAUSTIC 1

OVER-OPTIMUM

SALINE WATER WIO EMULSION

CONTINUOUS PHASE! OIL -

I UNDERQPTIMUM I FRESH WATER O/W EMULSION

CONTINUOUS PHASE:

LOW VlscOSlry

+ MOBILITY CONTROL 0 7 OILBANK G= ,-,

FIG.! :CAUSTIC RECOVERY MECHANISMS

concentrations lower t an 0.5 mol/l. Oil/water interfacial tensions (IFT) can be very low (< lo-’ mN/m). Oil recovery can be increased either by entrament of emulsified oil drops in the pore throats, reducing water mobility (A), or by very low interfacial tension, leading to reduced residual oil saturation through a favourable capillary number (13). In the first case an improvement in sweep efficiency is achieved. In general, however, the latter mechanism is more common; it may lead to oil bank formation in cases where interfacial tensions are sufficiently low. Mobility control (polymer, foam) is required for stable displacement 0’:

such an oilbank. The oEtimum system. iiS;~pt~~sa~ion~r’the amount of salt and/or the addition of surfactants (z), interfacial tensions may become ultra-low, so that capillary-trapped oil is mobilised and an oilbank is formed. This system also requires mobility control.

At high salinities a viscous water-in-oil emulsion is formed (2). Interfacial tensions are reduced somewhat. Once an emulsion bank has formed, caustic fingers through the emulsion bank are converted into emulsion, sealing off the finger. Extra oil recovery is obtained by improved mobility, leading to a better areal and vertical sweep efficiency in the reservoir. In addition, the increased viscosity of the viscous emulsion drive, combined with the reduced IPT, may (at least in the laboratory) cause such an increase in the capillary number that residual oil becomes mobilised, leading to oilbank formation ahead of the emulsion drive.

2!rover:sptL!E!?-syelem,

576

An application of the over-optimum caustic system, not shown in Fig. 1, is the possible permeability reduction of a water-flooded zone by emulsion formation. This would divert the main flow direction and consequently improve the sweep efficiency.

The over-optimum system seems to be most suitable in the case of a hot caustic process, since this system provides its own mobility control by the formation of a viscous emulsion. The other two systems would generally require the addition of extra chemicals, which would make the process more sensitive to temperature, and also more complicated and costly.

2.2. Parameters for the over-optimum system

schematically given in Pig. 2. When a caustic solution is injected into a The parameters that are of importance for caustic flooding are

ACID OIL

- SALINITY

REDUCED INTERFACIAL

TENSION

COALESCENCE

FIG. 2 : INTERACTION-DIAGRAM FOR CAUSTIC FLOWING

reservoir, part of the caustic is used to form surfactants, and part of it is depleted by interaction with rock and reservoir water. This interaction is highly dependent on type of rock, pH and composition of the caustic solution, reservoir salinity and temperature (14). If depletion is excessive, it may accordingly retard or even prevent the onset of increased oil production (12).

The surfactants formed in situ, will reduce oil-water interfacial tension. Since the water phase is saline, this reduction is not drastic. Divalent ions (Ca*,Mg*) may be detrimental to the process, leading to the formation of less interfacially active soaps (see Fig. 3). Calciun is much more detrimental than magnesium in this respect. The calcium concentration in the water should therefore be controlled by the addition of chemicals to the flood water. For instance, addition of soda ash (Na Cog) to the allcaline water causes most of the calcim ions originally present $0 precipitate as calcim carbonate.

As a result of reduced interfacial tensions, emulsification is promoted under the action of interfacial tension gradients (Marangoni effects which may result in turbulence at the oil/water interface) and/or by an extra mixing effect (see Fig. 2) generated by external shear forces. In general, no extra mixing energy is required to form an oil-in-water emulsion, since in that case interfacial tensions are much lower. Wettability reversal of the rock to oil- wet (2) may play a role in the formation of a stable water-in-oil emulsion. Flow behaviour of the emulsion, in relation to droplet size is an important aspect for the overall flooding behaviour.

10.0

t E \ 2 E z

1 3.0 a 9 E 1.0 W

H d m \

0.3

v- 'v,

1.67 mor/i NOCI

Q + 25ppmCo**

o + 5 0 p p r n ~ a + +

x + ~ p p m ~ o * + v +XK)ppm CO++

t \ \

\ 5 \ \ \ \ \

1 i I 9.0 10.0 11.0 12.0 13.0 14.0

-pH OF ausncsOulTloN

FIG.3: ILLUSTRATION OF INTERFACIAL TENSIONS AS A FUNCTION OF pH AT DIFFERENT CALCIUM CON- CENTRATIONS (Acid number of crude uwd : 3.0)

578

Besides the emulsification phenomena, coalescence of the emulsion also contributes to the performance of a caustic flood. Since an emulsion is a thermodynamically unstable system, phase separation occurs through coalescence of the droplets. The rate of coalescence is dependent on temperature, flaw rate, interfacial properties and viscosity. In an effective caustic process the coalescence rate is balanced by the emulsification rate.

Extra oil recovery by improved sweep efficiency and oil bank formation in relation to the caustic required for an effective process will determine the economic feasibility of a caustic flooding process.

2.3. The effect of an increase in temperature

emulsification (the interaction of Wrangoni effects and external shear forces), the coalescence rate, the flow behaviour of the emulsion and the total caustic losses (see Fig. 2).

Emulsificati_on_aid_c_oalescence_

of organic acids to the oilfwater interface. Thus the acid-caustic reaction is accelerated and the mixing process due to Marangoni effects is promoted. Aa a result, water droplets become more readily dispersed in the oil. In some cases, hawever, as will be shown in section 3, extra mixing energy is needed to further break up the water droplets to achieve a better emulsion stability. This energy is to some extent provided by the flow in the porous medim. If velocity gradients and ensuing shear forces are large enough, interfacial forces are no longer able to keep fluid particles intact, and they are broken up into smaller droplets. The theory of deformation and break-up of a droplet in a flaw field was first formulated by Taylor (16) and modified by e.g. Karam et al. (17).

An Increase in temperature will have a considerable impact.on the ease of

The reduced oil viscosity at higher temperatures promotes the diffusion

001 01 0.1 1 0 10

VISCOSITY R A T I O . v;p

FIG.4:BREAK-UP OF DROPLETS IN A SIMPLE SHEAR FIELD

579

Taylor showed that the drop behaviour only depends on the two dimensionless parameters u’ /p and Gru/y, where p ’ is Khe viscosity of the discontinuous phase, u of the continuous phase, G the shear rate, r the diameter of the droplet and y the interfacial tension. In accordance with this, Karam et al. have plotted their results of droplet break-up of different fluids as a function of these two dimensionless parameters (see Fig. 4). Irrespective of the system studied, a single curve should be obtained by such 8 dimensionless plot. Droplet break-up occurs above this curve.

be drawn from this plot. If the interfacial tension is increased, for example by divalent ions present in the reservoir water, the shear rate in the porous medium needs to be increased by the same factor to cause similar droplet break-up (see Fig. 4). It is therefore very important that most of the divalent ions are precipitated using a suitable buffer solution. Secondly, the break-up of a liquid droplet occurs readily when the viscosity ratio between the water and oil phase ( p ’ / p ) is of the order of 0.2 to 1 (see Fig. 4). ’his implies that not only the acid number, but also the viscosity of the oil under consideration is an important criterion for the caustic process. By the application of heat the difference in viscosity between the oil and the water phase becomes less pronounced, resulting in easier emulsification.

In a good caustic process a balance exists between emulsification and coalescence. Since an increase in temperature will enhance the coalescence rate, the temperature can affect the performance of a caustic flood in this way.

El~w-b$h~v~our-of the -m-l~i~n-

In connection with the caustic process the following main conclusions can

The temperature effect on the flow behaviour of the emulsion is important in the following respect. The apparent viscosity of the emulsion should preferably be somewhat higher than that of the oil phase in order to provide mobility control, and it can be much higher in the case of diversion of the main flow from a water-flooded area (see also section 2.1). The strong dependence of apparent viscosity on temperature will be shown in section 3.

Caustic in the form of sodim hydroxide has been shown to strongly interact with the rock at elevated temperatures (14). On the positive side, the dissolution interaction generates in situ water-soluble silicates which may have a beneficial effect on oil recovery (15). In contrast to these high losses resulting from sodium hydroxide, we found considerably lower consumptions when using carbonate buffer solutions. ‘Ihis is probably due to the lower initial pH values required when a buffer solution is applied instead of sodium hydroxide.

3. EXPERIMENTAL RESULTS AND DISCUSSION

The crude used for the caustic flooding and emulsification experiments was characterised by an acid number of 3.6 and a viscosity of 170 mPa.s(-cP) at reservoir t e m p e r a w (42OC). The reservoir brine contained 76115 ppm TDS, of which 3200 ppm Ca

Optimum emulsion stability was found at a pH of 9.5 of the caustic solution. The caustic solution was a carbonate/bicarbonate buffer with sodium chloride added (total Na+ content: 1.25 mol/l). The effectiveness of such a caustic solution in recoversng the oil has been studied in Bentheim sandstone cores (permeabslity: 1.5 urn ) and in sandpacks of reservoir sand (permeability: 3-9 pm ). In the case of sand packs more divalent ion exchange can be expected, by which emulsification could be hampered.

and 960 ppm Mg*.

5 80

Exp. No.

The caustic flooding experiments were carried out at high initial oil Saturation at initiation of the caustic injection and at low oil saturations, 1.e. after a water drive. The effect of temperature, shear rate and permeability on the emulsification process and the corresponding oil recovery has been studied. Shear rates have been calculated from (18):

G - 4u/J (8M) (1)

where u is the flooding rate, k the permeability and 0 the porosity of the porous medium.

Since the flooding experiments in the porous media used represented one- dimensional floods, the oil recoveries observed only accounted for possible extra oil recovery because of slightly reduced residual oil saturation and/or oil bank formation (see Fig. 1) on account of the steep pressure gradients in the emulsion zone. A possible improvement in sweep efficiency for a real three-dimensional caustic flood can be expected when emulsion formation in combination with pressure build-up across the porous pack was observed.

h u s t l d w a t e r Tenp. Shear r a t e Enulslon l n l t l a l 011 011 recovered d r l v e [%I a t all formed s a t v a t l o n , per cent of Sol

After 1 PV Flnal so I

3.1. Caustic flooding experiments at high initial oil Saturations Caustic flooding experiments were carried out at elevated temperature,

------ 1 caustlc dr. 42 27.4 YES 0.95 2 a t e r dr. 42 27.4 - 0.95 3 caustlc dr. 80 27.4 YES a 78 4 a t e r dr. 80 27.4 - 0.78

2

5 caustlc dr. 42 7.8 NO 0.79 6 a t e r dr. 42 7.8 - 0.79

court I c dr. 80 4.2 YES 0.87

xperlnwnts I n sand padts (poror1ty:O.l and pemsablllty:9.5 urn ,except

7al caustlc dr. 80 7.8 YES 0.84

3 water dr. 80 27.4 - 0.78

80°C, and for comparisonat a reservoir temperature of 42OC. Caustic was injected after saturating the porous medium with synthetic reservoir brine and subsequent flooding with tank oil to irreducible water saturation.

flooding rate of 1.06 x lo-! m/s ( 0 3 ft/day). At a temperature of 42OC (exp.1) a considerable pressure build-up over the core length was registered during the caustic flood, indicating the formation of a viscous emulsion. The low mobility of this emulsion may explain why the oil recovery in this caustic drive was not significantly improved over that of a plain water drive (compare exp. 1 and 2). In a caustic drive experiment at 8OoC (exp. 3) the pressure initially increased, pointing to in-eitu emulsification, and afterwards decreased when most of the oil, followed by some emulsion, had been produced, indicating that the emulsion in this case did not have too low a mobility. The

The experiments in Ben helm sandstone (see Table I) were performed at a

TABLE 1 - 0 I SPLACMENT EXPERIMENTS I N POROUS PAO(S

f loodlng rate: 1.06 lo-' m/s (= 5 ft/day). except ow. 7b: 0.55 m/s

45 48 59 45 82 83 42 47

ew&and 8; Iengtk22 cm.

40 48 48 56 64 75 63 75 40 41

581

Exp. Rrnsaq l l l ty Tenp. Floodln rate" Shear ra te Enulslon 01 I satwatton k lp f f%f x lo-' n/s a t wall formed after water drlve.

O l P S

emulsion obviously acted as a viscous phase, forcing the o i l out of t h e porous pack. The o i l recovery ( 8 3 % ) was f a r super ior t o t h a t of the comparable water- dr ive experiment (47%, see exp. 4 ) . This la rge d i f fe rence i n recovery and pressure behaviour between a c a u s t i c d r i v e and a water d r i v e a t 80°C was confirmed i n dupl ica te experiments.

In reservoi r sand a t 42OC the c a u s t i c dr ive showed no pressure build-up, and the o i l recovery w a s even lower than i n t h e corresponding water dr ive (see exp. 5 and 6 i n Table I) . flooding rates: 0.35 * resp.). Although shear r a t e s ( s e e eq. 1 ) were d i f f e r e n t (cf . exp. 7a with exp. 7b, Table I), both cases showed some pressure b u i l d u p , point ing t o t h e in- s i t u formation of an emulsion bank. The o i l recoveries were i n both cases equal ly high. The corresponding hot water dr ive (see exp. 8 ) yielded a 20% (of OIP) lower o i l recovery. A t h igher permeabi l i t ies , however, less d i f fe rence i n recovery was found between t h e c a u s t i c and hot water dr ives , probably because of t h e e f fec t iveness of the v i s c o s i t y reduction of the o i l (from 170 mPa.s (9

cP) a t 42OC t o 27 mPa.s a t 8OoC) i n porous media of high permeability. These experiments i n sandpacks i n d i c a t e t h a t a t higher temperatures

(8OoC) mixing induced by Plarangoni e f f e c t s and a l s o d i f fus ion processes may be s u f f i c i e n t f o r t h e formation of a small emulsion bank, probably because of a l a r g e contact area a t t h e i n t e r f a c e between t h e o i l and the c a u s t i c s lug jus t a f t e r in jec t ion . So t h i s process a t high i n i t i a l o i l sa tura t ions was found not t o be dominated by ex terna l shear forces .

t 80% the d r i v s were conducted a t two d i f f e r e n t and 1.06 * lo-' m / s ( 1 f t /day and 3 f t /day ,

011 recowei af ter 1 PV fractlon of

3.2. Caustic f loodin e eriments a f t e r a (hot ) water dr ive The flooding e z e r z e n t s were performed a t reservoi r temperature (42OC)

1 1.5 88 3 x 0.35 2 1.5 80 3 x 0.35 3 1.5 80 a 3 5 4 1.5 60 3 x 0.35 27.4 5 1.5 42 3 x 0.35 27.4 YES

and a t e levated temperatures. Crude and br ine were in jec ted i n order t o bring t h e porous system at connate water sa tura t ion and subsequently reduce it t o a low o i l sa tura t ion . The water dr ives p r i o r t o t h e c a u s t i c i n j e c t i o n were performed a t t h e same temperatures as the c a u s t i c flood.

The r e s u l t s of these tests a* given i n Table XI. They show t h a t in-s i tu emulsif icat ion can indeed occur a t low o i l s a t u r a t i o n s , and t h a t t h i s process i s c r i t i c a l l y dependent on shear rate, i n cont ras t t o t h e process a t high i n i t i a l o i l sa tura t ions . Both t h e flooding rate using one p a r t i c u l a r type of porous material, and t h e permeability times porosi ty of the core are important

0.40 0.50 0.38 0.40 a 39

TABLE I t - CAUSTIC FLOOOING EXPERIMENTS AFTER A HOT WATER DRIVE

6 9.1 80 3 x 0.35 7.6 NO 0.36 7 3.2 80 8 x 0.35 3 x 4 YES a 4 1 8 3.0 80 6 x 0.35 27.1 YES 0.37 9 3.2 60 5 x 0.35 2 2 4 YES o. 50

10 3.2 60 8 x 0.35 35.8 YES 0.40

7 41 42 10 12

64 51 20 44 1 1

582

parameters for emulsification (cf. exp. 2 and 3, and exp. 2 and 6). In the experiments where no emulsion is formed, the additional oil recovery is not higher than obtained by a prolonged water drive. Also in experiments at sufficiently high shear rates where an emulsion is formed, but which were run at lower temperatures, the additional oil recovery is poor (see exp. 5, 9 and 10). This is for the same reason as given for the experiments at high initial oil saturations, which were carried out at relatively low temperatures, i.e. the emulsion mobility is too low. The result is that at low temperatures most of the emulsion formed remains in the core, and that the caustic solution breaks through the emulsion bank.

where an emulsion bank of higher mobility is formed; see Table 11. 'Ihis is supported by viscosity measurements. At 80°C the viscosity of the emulsion produced in the effluents during the caustic flood was found to be 200 mPa.s, in contrast with an emulsion viscosity of 2200 mPa.6 at 60°C.

As a second effect of temperature, the amount of emulsion formed during flooding at one particular shear rate was found to decrease with increasing temperature. 'Ihis phenomenon may be caused by enhanced coalescence, which is common for emulsions at higher temperatures.

Under optimal conditions for the formation of a stable and at the same time mobile emulsion bank, a sharp increase in oil saturation in front of the emulsion bank could be observed in both Bentheim sandstone and reservoir sand. This resulted in general in a decrease in water cut from about 100% to 60%, as is illustrated in Fig. 5 (exp. 1). After the emulsion bank had been produced, the o i l production stopped completely. In Bentheim sandstone the oil recovery was far superior to that of a comparable hot water drive (- 25% of OIP extra oil recovery at 8OoC). In reservoir sand the caustic flood performance at 80°C was similar to that in Bentheim sandstone in terms of pressure behaviour and oil bank formation, yielding an extra oil recovery after a waterflood of about 20% of OIP (- 18% PV), as illustrated in Fig. 6 (exp. 8 ) . For comparison, the production curve of a caustic flood at 42OC is given in the same figure.

Improved caustic flood recoveries are obtained at higher temperatures,

1.0

0.9

0.8

0.7

o.6

0.5 5 s

0.4 ' 0.3

0.2

0. I

0

FIG.5 :CAUSTIC FLOODINO EXPERIMENT IN A BENTHEIM SANDSTONE CORE FOLLOWING A WATERDRIVE.

583

0.8 - HOT CAUSTIC(80"C)

START CAUSTIC INJECTION

4. COMPARISON OF THE EMULSIFICATION IN A COUETTE APPARATUS AND IN A POROUS MEDIUM

Since the emulsification process at low initial oil saturations was found to be dependent on shear rate, we decided to study emulsion formation at different shear rates in more detail, using a thermostatted Couette apparatus. This apparatus (Pig. 7) consists of two concentric cylinders, the inner one of which can rotate. The Couette apparatus is particularly suitable for this investigation, since the shear rate is almost constant throughout the small gap between the inner and outer cylinder. The emulsification behaviour of a caustic solution in contact with crude in the Couette apparatus (see Table 111) has been compared with that in a porous medium at relatively low oil saturations (Table 11).

EMULSION Dl EMULSION

NO EMULSIFICATION PARTIAL EMULSIFICATION COMPLETE EMULSIFICATION

FIG.7:EMULSION FORMATION IN A COUETTE APPARATUS

The emulsions formed in the porous medium and in the Couette apparatus were characterised by droplet size analysis (using a HIAC 520 particle-size analyser) and by microphotography. In general, a fairly good similarity between the emulsions was observed. In both cases peaks were found at a droplet size of 2.8 and 4 . 3 vm (see Fig. 8).

FIG.6:FLOODlNG EXPERIMENTS IN SANDPACKS.

TABLE I I I - EMJLSlFlCATlON I N COUElTE APPARATUS

: l o '

b 5 -

a?

I- 0 t

Shear r a t e 1s-1 I

2 8

38

4 6

68

113

brmtlon of W/O w l r l o n 40°C 6 8 C 80%

YES YES No (16% free a t e r ) OOS free a t e r )

(5s free a t e r ) YES YES No

K S YES KS

YES YES YES

KS YES TEES

Number distribution - porous medium I- C O U e t h r p p 8 d U S

b I' a?

2 2 5 3 L 5 6 1 8 9 1 0 I! 20 2 5 3 0 40 50

DROPLET SIZE (pm)

Volume dislribullon - porous medium --- couette 8pprretur

I : . . . . . . . . 2 2.5 3 A 5 6 7 8 9 10 I5 20 I S 30 LO 50

DROPLET SIZE (pm)

FIG.8: DROPLET SIZE DISTRIBUTIONS OF EMULSIONS FORMED AT 60.C IN A POROUS MEDIUM (Exp.9,TablrE) AT A SHEAR RATE OF 22SII.AND IN A COUETTE APPARATUS AT A SHEAR RATE OF 4 6 9 (ToblrXU)

At the oneet of the emuleification proceee in the Couette apparatue, the development of inetabilitiee at the interface between the cauetic eolution and the oil wae observed, resulting in the formation of relatively large droplets. 'Iheee droplete only broke up further and f o m d a stable emuleion when the shear rate exceeded a critical value (eee Fig. 4, eection 2.3). Dependent on the shear rate applied, three eituatione could be dietinguiehed (see Fig. 7): (I) the two phaeee remained completely separated, (11) only part of the two phaeee wae emuleifled, (ill) complete emuleification.

585

The r e s u l t s of the Couette experiments performed a t d i f f e r e n t temperatures and shear rates (see Table 111) i n d i c a t e t h a t the higher t h e temperatures, the higher are the shear rates needed f o r emulsif icat ion. P a r a l l e l t o t h i s , i t w a s found t h a t i n t h e core f loods an increase i n temperature a t a f ixed shear rate resu l ted i n a decrease i n t h e amount of emulsion produced (see sec t ion 3.2). This phenomenon can be a t t r i b u t e d t o reduced s t a b i l i t y , which is in general observed with emulsions a t higher temperatures, probably due t o enhanced coalescence.

shear r a t e s exceeded about 20 s-', whereas in the Cou t t e apparatus t h i s threshold value was somewhat higher, i.e. about 40 s-'. The lower threshold value in porous media may a r i s e from t h e f a c t t h a t , apar t from simple shear flow, e x t r a ve loc i ty changes involved in the flow through cons t r ic t ions and d i l a t a t i o n s a l s o cont r ibu te t o t h e emulsif icat ion process.

In the core flood tests (Ta l e 11) s t a b l e emulsions were formed when the

5. CONCLUSIONS

1. The c a u s t i c process a t high s a l i n i t i e s is considered t o be most s u i t a b l e i n t h e case of a hot c a u s t i c dr ive, s ince t h i s process provides i t s own mobil i ty cont ro l by t h e formation of a viscous water-in-oil emulsion.

2. High temperatures can be favourable for t h e onset of in-s i tu emulsif icat ion.

3. Apparent v i s c o s i t i e s of water-in-oil emulsions were found t o be very temperature-dependent (in our s p e c i f i c case .I 200 mPa.6 (- cP) a t 80°C, .I 2200 mPa.s a t 6OoC).

4. In laboratory experiments on c a u s t i c flooding where an emulsion bank was formed, but where the emulsions were too viscous, genera l ly no e x t r a o i l recovery was observed. This system may, however, be f e a s i b l e i n a waterflooded area t o decrease t h e permeability and consequently d i v e r t the main f l o v d i r e c t i o n t o areas of higher o i l saturat ion. This would imply i n j e c t i n g a small s lug of c a u s t i c , followed by (hot) water o r steam.

the emulsif icat ion process w a s found t o be c r i t i c a l l y dependent on shear rate (a flooding r a t e , permeability, porosi ty) . The shear rate probably becomes less important i f an oilbank has b u i l t up i n f r o n t of t h e emulsion bank, s ince from t h a t moment on a s i t u a t i o n resembling c a u s t i c flooding a t high i n i t i a l o i l s a t u r a t i o n is reached.

6. An emulsion bank of s u f f i c i e n t mobil i ty was e f f e c t i v e i n displacing t h e o i l , and resu l ted a t low i n i t i a l o i l s a t u r a t i o n i n the formation of an oilbank. In one-dimensional packs of r e s e r v o i r sand e x t r a o i l recoveries of about 18% PV have been achieved as compared t o water floods of t h e same temperatures.

7. Apart from a reduction i n Sor, i n a three-dimensional flood a s u f f i c i e n t l y mobile c a u s t i c emulsion is expected t o y i e l d addi t iona l recovery because of improved sweep ef f ic iency over t h a t of a water drive.

5. A t low o i l sa tura t ion , which implies a c a u s t i c flood a f t e r a water drive,

REFERENCES

1. JENNINGS, R.Y., Jr.; "A study of c a u s t i c solution-crude o i l i n t e r f a c i a l tensions", SOC. Pet. Eng. J. (June 19751, 197.

" O i l recovery by a l k a l i n e waterflooding", J.Pet. Tech. (Dec. 1974) 26 (12), 1365.

"Status of c a u s t i c and emulsion methods", J.Pet. Tech. (Jan. 1970), 85.

2. COOKE, C.E., Jr., WILLIAMS, R.E. and KOLODZIE, P.A.;

3. JOHNSON, C.E., Jr.;

586

4. JENNINGS, H.Y., Jr., JOHNSON, C.E., Jr., and McAULIFFE, C.D.; "A c a u s t i c waterf looding process f o r heavy o i l s " .

5.

6.

7.

8.

9.

10.

J.Pet. Tech. (Dec. 1974); 1344. WAGNER, O.R. and LEACH, R.O.; "Improving o i l displacement by w e t t a b i l i t y adjustment", Petr . Trans. AIME (1959) 216, 65. EHRLICH, R., HASIBA, H.H. and RAIMONDI, P.; "Alkaline waterflooding f o r w e t t a b i l i t y a l t e r a t i o n - Evaluation a p o t e n t i a l f i e l d appl icat ion", J.Pet. Tech. (Dec. 1974) 1335. MAYER, E.H., BERG, R.L., CARMICHAEL, J.D. and WEINBRANDT, R.M.; "Alkaline i n j e c t i o n f o r EOR - A s t a t u s report" , SPE 8848, (Apr i l 1980). SCHULZ, W.; "Verfahren zur FMrderung von ErdMl", Deutsches Patentamt, Auslegeschrif t 26.02.450, Bekanntmachungstag (1.6.1978). REISBERG, J. and WSCHER, T.M.; " I n t e r f a c i a l phenomena i n crude o i l - w a t e r systems", Producers Monthly (Nov. 1956) 2, no. 2, 43.

" O i l recovery by micro-emulsion inject ion", US pa ten t 4.008.769 (Feb. 22. 1977).

CHANG, H.L.;

. . 11. SZABO, M.T.;

I I A n eva lua t ion of water-soluble polymers f o r secondary o i l recovery - Par t I", J.Pet. Tech. (May 1979) 553.

"A chemical theory f o r l i n e a r a l k a l i n e flooding", SPE 8997 (May 1980).

"Role of c a p i l l a r y f o r c e s i n determining microscopic displacement e f f i c i e n c y f o r o i l recovery by waterflooding", J.Can. Petr . Techn. ( O c t . 1974) 1.

"Elevated temperature c a u s t i c sandstone i n t e r a c t i o n - imp l i ca t ions f o r improving o i l recovery", SPE-DOE 9810 (Apr i l 1981) 517.

15. CAMPBELL, T.C.; "A comparison of sodium o r t h o s i l i c a t e and s o d i m hydroxide f o r a l k a l i n e waterflooding", SPE 6514, 47th Annual Ca l i f . Reg. Meeting, Bakersf ie ld CA. April 13-15, 1977.

"The information on emulsions i n de f inab le f i e l d s of flow", Proc. Roy. Soc. London (1934) 146A, 501.

"Deformation and break-up of l i q u i d d r o p l e t s i n a simple shea r f ie ld" , I E C Fundamentals (1968) 3 no. 4, 577.

"Uber k a p i l l a r e Leitung des Wassers in Boden", Berichte Wien Akad., 136-U (1927) 271.

12. DE ZABALA, E.F., VISLOCKY, J.M., RUBIN, E. and RADKE, C.J.;

13. MELROSE, J.C. and BRANDNER, C.F.;

14. SYDANSK, R.D.;

16. TAYLOR, G.1.;

17. KARAM, H.J. and BELLINGER, J.C.;

18. KOZENY, J.;

The au tho r s would l i k e t o express t h e i r thanks t o t h e i r col leagues i n KSEPL. Special thanks are due t o Mr. J.C.Stekelenburg, who c a r r i e d ou t t h e experimental work.

UNITED STATES RESEARCH PROGRAMME 587

ENHANCED OIL RECOVERY R&D IN THE UNITED STATES AND IN THE U.S. DEPARTMENT OF ENERGY

J. J . GEORGE STOSUR

Office of Oil, Gas and Shale Technology, U.S. Lkparfment of Energy

ABSTRACT

The paper provides a general o u t l i n e of t h e s t a t u s of t h e enhanced o i l recovery technology i n the United S t a t e s with emphasis on t echn ica l problem and the sea rch f o r so lu t ions . Upon t h i s background, t he U.S. Department of Energy's e f f o r t and the research p r i o r i t i e s i n enhanced o i l recovery a r e descr ibed including t h e new comprehensive d a t a c o l l e c t i o n system and analysis on s e v e r a l hundred f i e l d p r o j e c t s .

INTRODUCTION

There is un ive r sa l agreement t h a t enhanced o i l recovery (EOR) p resen t s one of t h e b e s t opt ions f o r l i q u i d f u e l s production i n t h e next two decades.

The U.S. resource t a r g e t f o r EOR is very l a r g e ; of t he 450 b i l l i o n b a r r e l s of o i l t h a t have been discovered to-date, only one-third, o r 150 b i l l i o n ba r re l s W i l l be produced through primary and secondary methods, that is through d v l e t i o n and waterflooding. of 011, t h e loca t ion of which is known and i n r e s e r v o i r s which, though depleted a r e usua l ly reasonably w e l l def ined and ou t l ined .

Of t he 450 b i l l i o n b a r r e l s found to-date i n U.S., 350 b i l l i o n b a r r e l s a r e considered as l i g h t o i l (general ly wi th g r a v i t i e s above 250 APT o r 0.91 g/cc). Even a f t e r waterflooding, 230 b i l l i o n b a r r e l s of t h i s l i g h t o i l remain i n the ground await ing enhanced recovery technologies , and even l a r g e r percentage f r a c t i o n of heavy oils remains unrecovered. While t h e r e is uncertainty a s t o exac t ly how much of t h i s o i l can be recovered by EOR processes , a range of from 18 t o 52 b i l l i o n b a r r e l s is reasonable , depending on technological successes and energy p r i c e s i n t h e f u t u r e . Here l i g h t o i l accounts f o r between 12 and 33 b i l l i o n b a r r e l s and heavy o i l f o r 6 t o 19 b i l l i o n b a r r e l s . comparison, 52 b i l l i o n b a r r e l s is nea r ly twice U.S. proved reserves and equals t h e t o t a l output from 7 1 synfuel p l a n t s , each producing 100.000 b a r r e l s Per day over a 20-year p l an t l i f e .

While o i l production through EOR can be brought on l i n e f a r more quickly than synfue l s , t h e r e are a number of c o n s t r a i n t s t h a t must be resolved before t h i s can happen. Some of t he more prominent are t echn ica l c o n s t r a i n t s . of t h i s paper is re sea rch and development conducted a t U.S. Department of Energy t o m i t i g a t e t h e t echn ica l Cons t r a in t s i n t h e a p p l i c a t i o n of EOR technologies.

The views expressed i n t h i s paper are those o f t h e author , and they do not n e c e s s a r i l y r ep resen t those of t h e U.S. Department of Energy.

That l eaves a t a r g e t of over 300 b i l l i o n ba r re l s

By way of

The subject

588

EOR TECHNIQUES - AN HISTORICAL OVERVIEW There are three generic groups of EDR processes: immiscible) and thermal. are most widely applied are:

Chemical

chemical, gas (miscible and Each has several variants, but the processes which

- Polymer-augmented waterflooding. It relies on the addition of "thicken- ing" agents to water in order to increase displacement efficiency by reducing mobility of the displacing fluid.

It is based on the addition of strong caustic sub- - Alkaline flooding. stances to injection water in order to affect reduced surface tension between reservoir fluids, thus permitting easier fluid movement.

- Surfactant polymer flooding. Surface active agents are injected to displace oil by reduced surface tension which allows building an oil bank that is subsequently pushed by polymers and water.

- Gas (miscible and immiscible)

- Hydrocarbon miscible. Miscibility is obtained by the injection of hydrocarbon gases which dissolve in oil, reduce viscosity the creation of an oil bank which can then be pushed to producing wells by water. Now that the cost of natural gas and LPG is high, the method is not much used.

and help

- Carbon dioxide flooding. It is based on injection of C02 t o strip the lighter components, swell the oil, partially mix with it and create an Oil bank which can then be displaced by additional gas or water.

- Nonhydrocarbon gas drive. Inert gases can be used such as nitrogen or flue gas, primarily to add pressure to reservoir but also to attain miscibility (depending on pressure) and displace the oil in much the same way as Cop or natural gas.

Thermal processes

Thermal processes apply largely to the recovery of heavy oils which are too viscous in their natural state to flow freely. exponential decline of oil viscosity as temperature rises when reservoir is heated with steam injected from the surface or generated in the reservoir by in situ combustion.

Here, advantage is taken of the

- Steam soak. The steam soak variety is typically used for stimulation to either accelerate or establish primary production in an otherwise unproductive heavy oil reservoir. quite efficient under favorable conditions, but efficiency quickly

oil is reduced until it becomes mobile and can be displaced Or Produced by gravity drainage in surrounding wells.

Multi-cycle steam applications can be

- Stem drive. Steam is injected COntinOUSly in one well, viscosity Of

- Pireflooding. It uses energy derived from burning part of the oil in a reservoir to assist in the recovery o f the remaining unburnt oil. combustion is supported by injected air and often water to increase efficiency of the process.

The

589

Potent ia l EOR technologies

- Microbial EOR. Microorganisms can be used t o generate surfactants , to produce C02 i n the reservoi r and t o otherwise change the composition of the o i l f o r improved recovery. This method is l a rge ly i n research stage, though a few f i e l d tests were performed.

- Combination mining. Several approaches have been proposed f o r the d i rec t ex t rac t ion of crude o i l , including la rge diameter s h a f t s from which horizontal o r upwardly s lanted w e l l s are d r i l l e d f o r drainage.

- Steam dr ive i n l i g h t o i l . There is evidence that steam d r i v e could hold promise i n shallow l i g h t o i l reservoi rs where o ther methods fa i led .

- RF heating. It is based on beaming radio frequency energy i n t o a heavy The method is curren t ly being f i e l d tes ted t o determine o i l reservoir .

i ts poten t ia l .

An h i s t o r i c a l summary of EOR projec ts in t h e U.S. based on biennial O i l and Gas Journal surveys (1) is shown i n Table 1.

Table 1. United S ta tes EOR projec ts i n perspective

1979 - Method 1970 1975 1977 1973 - - Chemical

Polymer Flood 14 9 14 2 1 22 Caustic Flood 0 2 1 3 6 Mice1 lar /Polymer 5 7 1 3 22 14

Miscible Gas

Hydrocarbon Miscible 2 1 12 15 15 9 Carbon Dioxide 1 6 9 14 17 Other Gases 0 1 1 6 8

Thermal

Steam Drive 22 22 31 43 79 Cyclic Steam 31 42 54 56 54 I n S i t u Combustion - 17 21

132 120 159 196 226

- 16 - - 19 - 38

Closer examination of the ten-year h i s t o r y of chemical EOR projec ts i n U.S. shows: steady increase i n the number of polymer pro jec ts s ince 1973; carefu l experimentation with caustic floods, though s t e a d i l y increasing over t i m e , and; steady increase i n new starts of the micellar/polymer pro jec ts u n t i l 1977 and then a sharp dec l ine i n response t o discouraging r e s u l t s .

The miscible gas pro jec ts show a gradual phasing out of hydrocarbon miscible pro jec ts due t o rapidly increasing value of na tura l gas; steady increase i n the number of carbon dioxide pro jec ts , which apparently replaced the increasingly c o s t l y na tura l gas, and; a recent surge of i n t e r e s t i n nonhydrocarbon gases, even though most of the tests are very small.

590

The thermal recovery projects are most numerous, reflecting the relative maturity of the technology and show steady increase in the number of steam drive projects with a sharp increase in 1979 (even sharper increase is expected for 1981); gradual increase, then leveling off and slight decline in 1979 of steam soak projects in favor of the more efficient steam drive projects, and; a sharp decline of in situ combustion projects after 1970 when euphoria over the new technology gave way to the somber reflection that the technology I s a lot more difficult to apply than it appeared.

These observations underline the tendency by the private sector to prefer the lower-risk, proven technologies such as cyclic steam and steam drive and to avoid the less certain and the less predictable but advanced approaches such as micellar/polymer floods, due to the high degree of risk and poor performance predictability.

Equally interesting is the operators' own evaluations of their projects which was compiled from the Oil and Gas Journal survey (l), Table 2. Again, most of the projects judged technically and economically successful or promising are those in the more or less established and less risky processes which include thermal recovery and polymer flooding.

Table 2. Operators' own evaluation of project performance-March 1981

Tech. Tech. but Terminated Tco Total and Econ. not Econ. or Early

METHOD Success Success Promising Discouraging to Tell Eval.

Steam 57 In Situ Comb. 7 Polymer 10 Caus t ic - Micellar/Polymer - Carbon Dioxide 2

2 Other Gases

Total 77

-

6 2

2 1 1

-

- - 11

26 1 4 1 2 5 3

42

-

~

5 1 3

3 2

-

14

~

19 3 5 3 8 7 3

48

-

113 14 22 6 14 .17 8

194

-

The year 1981 will prove to be the year of a sharp increase of new EOR projects in the United States. program was set forth by the Economic Regulatory Administration. program an operator of a qualifying EOR project was permitted to realize b-orld oil price for controlled oil, provided that the difference was invested In the project. 75% of qualifying costs with a limit of $20 million per project. was to ameliorate the high front-end costs associated with EOR. was overwhelming, with as many as 4 2 3 FAIR projects by the time the program was concluded in March 1981, following total decontrol of crude oil prices.

The incentive program for EOR was designed t o begin many.EOR projects that would lead to rapid oil production and, as expected, most of the projects proposed by industry involved the use of current technology, those processes that are less risky, better understood and requiring smaller capital investment. Table 3 shows the types and number of projects in various categories.

To stimulate industry activity in U)R, a special incentive Under this

There were several limits: a project could recover no more than The purpose The response

591

Table 3. New Enhanced Oil Recovery projects due to Energy Regulatory Administration's special incentive program

Oil Recovery Technique

Miscible Fluid Displacement (Less C02) CO2 Miscible Fluid Displacement Conventional Steam Drive Injection Unconventional Steam Drive Injection Microemulsion Flooding In Situ Combustion Polymer Augmented Waterflooding Cyclic Steam Injection Alkaline (Caustic) Flooding Immiscible Nan-hydrocarbon Gas Displacement Enhanced Heavy Oil Recovery (Other Than Thermal) Other Tertiary Enhanced Recovery Techniques

Number of Projects

13 95 93 34 37 35 48 16 32 11 3 6 -

Total 423

The new EOR projects represent over $15 billion of private investment and are expected to recover nearly 3 billion barrels of crude oil, but as much as 80% of the total number use proven, less risky technology. The major promise of EOR is, however, with the newer, high risk "advanced" processes that have shown great promise in theory and in the laboratory, but .have not fared well in the transition to the field.

The large number of new EOR field tests provide a unique opportunity for gather- ing and analyzing actual field data in a compressed period of time. The 423 incentive projects include a sufficient number of advanced technology applications that, when measurement and analyses are linked with oil production data, an excellent opportunity will present itself for scientific observation of their performance. selected from among the cost-shared and incentive field tests for extensive pre- and post-test observation, diagnostics and analysis. It is hoped that these data coupled with the results from laboratory experiments and small nonproducing mini-tests, will be used to greatly improve the fundamental understanding of how and why the advanced EOR techniques behave as they do. contribute towards more effective prediction of various processes under different reservoir conditions (2).

Accordingly, a few of the more advanced field tests will be

The results should

TECHNICAL CONSTRAINTS AND SEARCH FOR SOLUTIONS

The high risks that deter operators from the advanced technologies are the principal focus of the goals of the DOE Enhanced Oil Recovery R&D program. R&D priorities among the processes directly reflect the degree of risk associated with each technology and the size of the potential of the respective processes. Research priorities have been developed to reduce or eliminate certain constraints. processes are reflected in the current R&D program, as follows:

These priorities for the chemical, miscible gas and thermal EOR

592

Chemical

- Basic studies on mechanism of displacement of bypassed oil. - Effect of surface and physical chemistry of microemulsions on displace- - Chemical degradation at high temperature, high connate water salinity

- More effective formulations of microemulsions and additives for mobility - Fundamental R6D on rock/fluid interactions, which includes adsorption, - Quantitative determination of the effects of dispersion, relative

ment efficiency.

and high clay content.

control,

wettability, ion exchange and formation damage.

permeability, apparent viscosity and inaccessible pore volume on mobility control under one-, two- and three-phase flow for the development of equations to be used for improving the precision of predictive reservoir simulators.

Gas Miscible Displacement (C02 Flooding)

A number of technical constraints to a wider application of gas miscible displacement are similar to those of chemical and even thermal recovery methods. One such generic problem is lack of adequate mobility control and the resultant low areal and vertical sweep efficiencies. Even when the displacing phase 1s fully miscible with crude oil under all conceivable reservoir conditions, an unfavorable mobility ratio leads to fingering which causes premature breakthrough and poor sweep efficiency. mobility control the R&D effort in miscible displacement processes includes:

Other than the ever present problem of

- Fundamental studies on miscibility with reservoir oil, criteria for - Formation damage in carbonate reservoirs due to Cog flooding. - The effect of N2 and other gases on phase behavior and displacement

- Static and dynamic laboratory investigations of phase behavior of C02- - Studies of the effect of foams, polymers, graded-viscosity slugs and - Supply of natural C02 and its cost.

miscibility (single contact and multiple-contact miscibility).

efficiency.

crude oil systems.

emulsifiers on the mobility ratio and displacement efficiency.

Thermal Recovery

- Development of downhole steam generation capability at depths exceeding 2500 feet with the triple objective of substantially reducing transmission heat losses, overcoming flue gas emission probleme and increasing recovery efficiency due to the action of 0 2 with steam.

displacement and sweep efficiencies. - Fundamental research on the effect of ancillary materials with steam on

- Improved insulation of steam injection wells and the development of a metal-extrudable packer for high temperature wells.

- Development of techniques for tracing the position of the high temperature front in steam flooding and in situ combustion methods (surface mapping of thermal fronts).

from tar sands using steam flooding, reverse in situ combustion and tk.e combination of both methods.

- Field experimentation to determine the feasibility of bitumen recovery

593

One of the more interesting EOR related projects sponsored by the Department of Energy is the development of a downhole steam generator at Sandia National Laboratories. wide publicity in trade journals and some independent work by private interests. The downhole steam generator has indeed unique potential: ally high overall thermal efficiency (not only due to the elimination of heat lost in the transmission of steam from the surface to the bottom of the bed, but also due to the elimination of heat rejected and lost up the stack of a conventional steam generator); it can help overcome air pollution by injecting combustion products with steam into oil reservoirs, and; its economic benefits may be superior to the currently used steam generators. A prototype has already been tested under simulated conditions at the surface and a real downhole test of the high pressure system will be conducted in Long Beach, California, in the summer and fall of 1981.

Another example of advanced technology brought to fruition and transferred to the private sector is in the area of faster, more efficient drilling. National Laboratory has developed a special bonding technique which permitted a new bit design with polycrystalline diamond cutters. One source quotes oil companies' reports that three synthetic-diamond bits can drill one 5000 ft.- deep well section in 112 hours, while in the past, such a section would use up as many as 13 conventional bits (3). Far more important that the difference in hardware cost is the saving in time; synthetic-diamond bits can cut drilling time by several days for a saving of up to $1 million in the more expensive offshore wells. Worldwide, 13 companies now fabricate the synthetic diamond bits, with total capacity of the U.S . companies in the range of 2,800 bits per year and several of them have order backlogs extending for a year or more.

A good example of the kind of long-term R6D pursued by the Department of Energy is microbial EOR (4). to determine whether microbial cells can be used to selectively plug high- permeability layers and thus improve sweep efficiency; to .examine the potential of using microorganisms for EOR by mechanisms other than selective plugging, such as in situ production of biosurfactants and biopolymers; to ecreen qualitatively and quantitatively for microbial organisms' ability to produce gases such as carbon dioxide, hydrogen and methane and; to determine the feasibility of bacteria to produce acids such as acetic acid, solvents such as alcohols and acetone as well as small molecules possessing surfactant properties. By most accounts microbial EOR is avant-garde, insufficiently pursued by private interests and yet, according to many scientists, offers exciting possibilities for brand new concepts in EOR.

The project was started 3 years ago and has recently attracted

it offers exception-

Sandia

There are currently five contracts with universities

CONCLUSIONS

Enhanced oil recovery has the highest probability of new-term impact on the production of liquid fuels, with lowest cost premium. program of field experiments and supporting R6D is required to accelerate both the development of technology and early commercial implementation. end, the U.S. Department of Energy has established a highly organized effort through its Energy Technology Centers, National Laboratories and nearly 30 universities to systematically attack the complex technical problems that have inhibited industry application of the potentially efficient but expensive and risky technologies.

The U.S. Department of Energy R6D priorities reflect the new emphasis on high- risk, long-range, high potential EOR technologies. It is presumed that the industry will respond to the recent oil price decontrol with stepped-up development activities, including the economically marginal petroleum resources and increasing recovery efficiency. In all cases, the EOR program is closely coordinated with industry to avoid duplication of effort.

However, a coordinated

TO this

594

REFERENCES

1. SHANNON, L. Matheny, Jr.; "EOR Methods Help Ultimate Recovery", Oil and Gas Journal (Mar 31, 1981) 79-124.

"The DOE Light Oil Research-and-Development Program," Draft publication dated May 21, 1981.

"Synthetic Diamonds Shake-up The Drill-Bit Market", Business Week, December 1, 1980, 98-99.

"Contracts for Field Projects and Supporting Research on Enhanced Oil Recovery and Improved Drilling Technology", 26, WE/BETC-80/ 4, Sept 30, 1980.

2.

3.

4.

595

ACS, G. , 299 AKSTINAT, M. H . , 43

ANDREWS, C . , 63

APPLEYARD, J. R. , 395

AZIZ, K . , 367

BAILEY, N . A., 483

B A L ~ N T , v. , 299 BANKS, D. , 441 BARTHEL , R. , 527 BiRO, 2 . , 299 BLACKWELL, R. J . , 237 BREIT, V. S., 223

BROWN, C. E . , 81

CARMICHAEL, J. D., 223

CASINADER, P. C. , 425

CHAUVETEAU, G., 197

CHESHIRE, I. M . , 395

CHESTERS,, D. A., 563

CLARK, C. J. , 563

CLINT, J. H. , 135

COLLEY , N . , 63

DALEN, V., 329

DAWE, R.A., 161, 511

DIETZ, R., 499

DOLESCHALL, S . I 299

DOSCHER, T . X., 267, 549

AUTHOR INDEX

EL ARABI, M., 267

FARKAS, E . , 299

FOULSER, R. W. S., 409

FOX, R. L . , 543

GHARIB, S. , 267 GHASSEMI, F . , 549

HANDY, L. L . , 149

HESSELINK, F. TH., 573

HUGHES, D. S. , 247

JANSSEN-van ROSMALEN, R., 573

JENSEN, J. I., 329

JONES, T . J. , 135

LABASTIE, A., 213

LANGLEY, G. 0. , 81 LEMONNIER, P., 379

LOREW, P . B. , 123

McCAFFERY , F. G. , 285 MAHERS, E. G., 511

MATTHEWS, J. D., 2 4 1

596

MAYER, E. R., 223

MEYN, V., 451

M I N KWAN THAM, 123

MOTT, R. E . , 247

NEUSTADTER, E. L . , 135

NOVOSAD, J. , 101

OFFERINGA, J., 527

OYEKAN, R., 267

P A , T . , 299

POLLARD, R. K . , 395

PONTING, D. K . , 441

PUSCH, G., 179

RIDDIFORD, F. A., 563

RISNES, R., 329

ROBINSON, D. P . , 483

ROSS, G. D., 351

ROWLAND, P . R., 483

SAYEGH, S. G., 285

SHAH, D. O., 1

SKILLERNE DE BRISTOWE, B. J . , 467

STEWART, G., 313

STOSUR, J. J. G., 543, 587

TAN, T. C. , 425

THAVER, R., 63

TODD, A. C., 313, 351

TOROK, J., 299

TWEEDY, J. A. , 351

VAROTSIS, N . , 313

V I O , L . , 213

VOGEL, P., 179

WEIJDEMA, J. , 527

WILSON, D. C . , 425

WRIGHT, R. J., 161, 511

ZAITOUN, A., 197

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13. Enhanced Oil Recovery - Fayers

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