Acuifer Behavior

College Station June, 2002

Texas A&M University

Design and History Matching of Waterflood/Miscible CO2

Flood Model of a Mature Field: The Wellman Unit,

West Texas

Chair of Advisory Committee: Dr. David Schechter

Committee Members: Dr. Duane McVay and Dr. Luc Ikelle

by

Jose Rojas

Master of Science Candidate



Content

• Research Objectives

• Review of Geology

• Historical Reservoir Performance

• OOIP and Water Influx (Material Balance)

• Simulation Model

• Model Calibration – History Matching

• Results: Primary Depletion

Waterflooding

CO2 Injection

• Conclusions and Recommendations



Objectives

Revise and integrate data from the reservoir description to

develop a full field, three-dimensional black oil simulation

model to reproduce via history matching, the historical

performance of the reservoir under primary, secondary and

tertiary stages of depletion

Secondly, develop a calibrated model that can be used to

evaluate, design and plan future reservoir management

decisions.



Wellman

Field

Midland

Horseshoe

Atoll

Review Of Geology

Location

•Terry county, TX, along the

Horseshoe Atoll reef complex that

developed in North Midland during

Pennsylvanian and early Permian

time


Texas A&M University Review Of Geology

Field is considered geologically unique, because it comprises two

types of reef construction

Pennsylvanian Cisco Reef Permian Wolfcamp Reef

• Built in deep clear water

• Large mound shape structure

• Strong depositional dip

• Water bearing

• Built in shallow muddy(turbid) water

• Encroaching shales at the flank

• Smaller cone-shape structure

• Oil bearing



• Wolfcamp deposited on top of the prominent Cisco Reef

• Curved layers at the bottom, more horizontal in upper structure

Review Of Geology

Reef on Reef Depositional Model

• Structural Northeast – southwest cross section reveals the cone shaped

structure

Top of

Wolfcamp

Spraberry

Sand


Texas A&M University Review Of Geology

Structural Setting

• Oval shaped covering a

productive area of 2100 acres

• Two local highs (dual, cone-shaped

anticlinal structure)

Isopach Structure Map

Lithology

• Secondary Porosity to diagenesis

- Intercrystalline

- Vugular

- Natural Fractures

• Carbonate reservoir (skeletal

marine organisms)

NNN


Texas A&M University Historical Reservoir Performance

Primary Depletion (1950 – 1979)

1) 1950-53 oil rate peaked 6 MSTBD

2) 1954 allowable restrictions oil rate

reduced to 3, then 1.7 MSTBD

3) 1966 oil rate peaked 8 MSTBD

4) 1976-79 produced below Pb until

reached minimum 1,050 psig

Pb at 1,248 PSI

1

2

3

4

5) 1976-79 GOR did not increase

secondary gas cap formed.

H2O cut: from 10 to 25%

5

Cum. Oil: 41.8 MMSTB

RF: 34.6%



Waterflooding (1979 – 1983)

Cum. Oil: 23.9 MMSTB

Sec. RF: 19.5%

H2O Inj

CO2 Inj

OWOC

H2O Inj

CO2 Inj

OWOC

H2O Inj

OWOC

1979 - four flank H2O injectors

re-pressurize (MMP), re-dissolve

part of the gas, displace oil

upward

Waterflooding

• Pressure increased from 1,050 to

1,600 psig prior CO2 (1983)

• Oil rate increased to 9 MSTBD

• Water cut from 25 to 40%

GOR aprox. constant

• Water cut controlled by plug

downs.

Historical Reservoir Performance



H2O Inj

CO2 Inj

OWOC

H2O Inj

CO2 Inj

OWOC

H2O Inj

CO2 Inj

OWOC

1983-89 - Three crestal injectors to

displace oil downward and reduce Sor

CO2 Injection (1983 – 1995)

• 1984-89, CO2 Inj. From 5 to 15

MMCFD.

• 1985, break water cut from 40 to

85%. (ESP’s, leaks, corrosion)

• GOR peaked to 3000 SCF/STB

(mostly CO2)

• Pressure from 1600 to 2,300

peaked at 2,500 psig in 1994.

Primary

Depletion CO2

Injection

Waterflooding

Cum. Oil: 6.3 MMSTB

Ter. RF: 5.4%

Historical Reservoir Performance



Bottom Water Drive

Original Reservoir Conditions

Sec. Gas

Cap

Prod Prod

Bottom Water Drive

Before Waterflooding (1979)

Prod Prod

WIW WIW

Bottom Water Drive

Waterflooding (Before CO 2 Flood),1983

CO2 ICO2 I

WIWWIW

Prod Prod

Waterflood and CO2 Injection (1995)

Bottom Water Drive

Bottom Water Drive


Bottom Water Drive


Sec. Gas

Cap

Prod Prod

Bottom Water Drive


Prod Prod

WIW WIW

Bottom Water Drive


CO2 ICO2 I

WIWWIW

Prod Prod


Bottom Water Drive

CO2 ICO2 I

WIWWIW

Prod Prod


Bottom Water Drive

WIWWIW

Prod Prod


Bottom Water Drive

Bottom Water Drive


Bottom Water Drive


Sec. Gas

Cap

Prod Prod

Bottom Water Drive


Prod Prod

WIW WIW

Bottom Water Drive


CO2 ICO2 I

WIWWIW

Prod Prod


Bottom Water Drive

CO2 ICO2 I

WIWWIW

Prod Prod


Bottom Water Drive

WIWWIW

Prod Prod


Bottom Water Drive

Bottom Water Drive


Bottom Water Drive


Sec. Gas

Cap

Prod Prod

Bottom Water Drive


Prod Prod

WIW WIW

Bottom Water Drive


CO2 ICO2 I

WIWWIW

Prod Prod


Bottom Water Drive

WIWWIW

Prod Prod


Bottom Water Drive

CO2 ICO2 I

WIWWIW

Prod Prod


Bottom Water Drive

WIWWIW

Prod Prod


Bottom Water Drive

Chronological Stages of Depletion



OOIP and Water Influx

Material Balance

Straight line Material Balance for Reservoir Without Gas Cap, m=0

0

10

20

30

40

50

60

0 0.05 0.1 0.15 0.2

Delta Bt, Rb/stb

Qp

, M

MS

TB

Qp Vs Delta Bt


0

10

20

30

40

50

60

0 0.05 0.1 0.15 0.2

Delta Bt, Rb/stb

Qp

, M

MS

TB

Qp Vs Delta Bt

N

Expected

Real


0

10

20

30

40

50

60

0 0.05 0.1 0.15 0.2

Delta Bt, Rb/stb

Qp

, M

MS

TB

Qp Vs Delta Bt


0

10

20

30

40

50

60

0 0.05 0.1 0.15 0.2

Delta Bt, Rb/stb

Qp

, M

MS

TB

Qp Vs Delta Bt

N

Expected

Real

• Lack of linearity

• Not Volumetric

• Most likely producing

under influence of an

aquifer

• Validate existence and influence of external energy (aquifer)

• Use performance data and fluid properties prior waterflooding

Havlena and Odeh



• Estimate and validate previous OOIP assessments

• Estimate water influx rate prior waterflooding

OOIP and Water Influx

Material Balance

Hurst and Van Everdigen

Results

• OOIP (N) aprox 125 MMSTB

• We10: approximately 8.0 MMRB

Final Aquifer Properties

H, Feet 68

K, md 25

, Fraction 0.9

Ro/Re 2

Ro, Feet 3000

Angle (f=1) 360


Texas A&M University Simulation Model

H2O Inj

CO2 Inj

OWOC

H2O Inj

CO2 Inj

OWOC

H2O Inj

CO2 Inj

OWOC

Grid System

• Use of flexible grids: corner point,

non - orthogonal geometry.

• K, direction subdivided in 23 layers

based on porosity correlations

(geological description)

• 27 x 27 gridblocks I,J direction

Full field, 3-D black oil simulation

“Imex” – CMG

• Total 16,767 gridblocks


Texas A&M University Simulation Model

3D – Structure Development



Simulation Model

Input Data

Production data

• Over 45 years of monthly cumulative oil, gas and water production from 47

wells was converted into daily rate schedules for simulation

• Model initially constrained by oil rates and water/CO2 injection rates

Pressure data

• Pressure measurements reveal good communication within the reservoir

• Use of BHP corrected and averaged to a common mid-perforation

• Static BHP seemed to be representative of the average reservoir pressure

0

500

1,000

1,500

2,000

2,500

3,000

3,500

4,000

4,500

A-49 M-53 J-57 A-61 S-65 O-69 D-73 J-78 F-82 M-86 M-90 J-94

Time, years

Bo

tto

m H

ole

Pre

ssu

re

(BH

P),

P

si

Unit 1-1 Unit 2-1 Unit 2-3 Unit 3-3 Unit 4-1 Unit 4-2

Unit 4-3 Unit 4-4 Unit 4-5 Un it 4-6 Unit 4-7 Unit 5-1

Unit 5-2 Unit 5-3 Unit 5-4 Unit 5-5 Unit 6-1 Unit 6-2

Unit 7-1 Unit 7-2 Unit 8-3 Unit 8-5 Unit 8-6 Unit 8-7A

Individual Static Bottom Hole Pressure



• Use of isopach maps resulted from geological and petrophysical study in 1994

• Geological and stratigraphic correlation (Core vs Log data)

• Quantify major rock properties

• Lateral and areal continuity

Isopach Maps

• 60 geological contoured maps from gross thickness, porosity and NTGR were

digitized

• Interpolation between contour allows model to be populated

Gross Thickness Porosity Net to Gross Ratio

Simulation Model

Input Data



Permeability

• Use previous estimates from correlations between open-hole logs and core

measurements K = 10^(0.167 * Core porosity – 0.537)

Simulation Model

Input Data

Swc, aprox 20% for Ф = 8.5%Swc, aprox 20% for Ф = 8.5%



Simulation Model

Input Data

Fluid Properties

• Use PVT properties contained in previous lab and reservoir studies

• Bubble point: 1248 – 1300 psig

• Rs, 400-500 SCF/STB

• Oil Gravity, 43 API

• OFVF, 1.30 RB/STB

• Oil Viscosity, 0.4 cp

• Black oil fluid type

Relative Permeability

• Special core analysis for core well No. 7-6 included measurements on only

two samples with a low non-representative permeability

• Use functions derived from Honarpour’s correlation (past studies)

Initial Oil - Water Relative Permeability

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8

Water saturation (Sw),fraction

Rela

tive P

erm

eab

ilit

y, fr

acti

on

Krow

Krw

Initial Gas - Oil Relative Permeability

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8

Gas saturation (Sg) fraction

Rela

tive P

erm

eab

ilit

y, fr

acti

on Krg

Krog

Initial Oil-Water and Gas Relative Permeability



Simulation Model

Input Data

Capillary Pressure Data

• Only 4 samples, K > 1 md

(Special core analysis)

Leverett's- J Function Vs. Water Saturation

0

1,000

2,000

3,000

4,000

5,000

6,000

7,000

8,000

0 10 20 30 40 50 60 70 80 90 100

Water saturation (Sw), percentage

J-

Fu

ncti

on

CC-76 H, K=18 md CC-77 H,K=161 md

CC-79 H,K= 9.07 md CC-86 H,K= 18 md

• Shape suggests lack of

capillary transition zone

• Data normalized by

Leverett J-function

• Good vertical communication

capillary effect “not significant”


Texas A&M University Model Calibration – History Matching

Objective: Validate the model adjusting the reservoir description until

dynamic model match the historical production and pressures

• Weight and rank properties by level of uncertainty (quality,

source, amount, availability of data)

Historical Responses to be Matched

• Fieldwide average reservoir pressure

• Fieldwide production rates

• Fieldwide GOR and Water cut

• Arrival times

• Individual responses (lesser degree)

Reservoir and Aquifer Parameters Level of

Uncertainty

Aquifer Transmissibility, kh 9

Aquifer Storage, Φhct 9

Reservoir Transmissibility, kh 9

Reservoir permeability distribution, k 7

Chronological well completions 7

Oil-water and gas relative permeability, kr 6

Reservoir oil and gas properties 5

Mixing parameters 5

Capillary pressure functions, pc 4

Reservoir porosity and thickness 3

Structural definitions 3

Rock compressibility 2

Water– Oil – Contacts 2

Tuning uncertain properties

influencing the solution

Sensitivity analysis

simulation runs

Via


Texas A&M University Results: Primary Depletion

• No aquifer modeled

• Poor pressure response

First simulation runs

• Need of external energy

“recognized”


Texas A&M University Results: Primary Depletion

• Carter and Tracy “Analytic”

• MB case too strong (top)

• Aquifer size (Ф,h), trans. (K,h)

• Reference datum adjusted

• Influx 20% greater, best case

• Fetkovich, “Analytical Aquifer”

• First years not matched

• Radius ratio, K and Ф

Preliminary runs Aquifer Calibration



Results: Primary Depletion

Preliminary runs

• Water arrival time and cumulative

did not match

• Highest corresponds to MB

• Poorest corresponds “no aquifer”

• Poorest corresponds “no aquifer”

• Best pressure match “sharp gas

increase”

• Secondary gas cap formed

Need for improvement

was recognized !




Most Uncertain Parameters influencing Production of Fluids

Model Calibration

Vertical Transmissibility

Aquifer/reservoir

• vertical arrays

Aquifer Properties

• , h,k Relative Permeability

Functions

• end points, shape, crit. sat

Re-interpretation

Completion intervals

• Plug-downs

• GOR, water cut

cutoff

“K.H” Term

Prod / Inj Index

Uniform Mod.

Fluid PVT

Local Absolute (K)

Lesser degree




Diagnosis



Results: Primary Depletion Final Results



Case OOIP

(STB)

Thesis

OOIP

Ref. 2

OOIP

Ref. 5

R.F

(%)

Thesis

R.F

(%)

Ref.2

OWOC

Increase

(FT)

Thesis

OWOC

Increase

(FT)

Ref.2

March_19_29 122.6 126 121.5 34.6 33.2 208 220

Testeardat 122.6 126 121.5 34.6 33.2 208 220

Jose_6 122.6 126 121.5 30.8 33.2 208 220

March_19_8 121.3 126 121.5 34.6 33.2 208 220

March_19_35 122.0 126 121.5 34.6 33.2 208 220

Results: Primary Depletion Final Results


Texas A&M University Results: Waterflooding

H2O Inj

OWOC

H2O Inj

OWOC

• 4 producers converted

to water injectors (1979)

• Injection below and above OWOC @ - 6,680 ft

• Located at the flank

forming a perimeter belt

• Model primarily constrained

by historical injection rate

schedule

Injector Location



Initial runs

• Green, one of the best cases from primary depletion match

• Blue, same with water injectors

• Pressure continued declining

• Adjustment “KH” term of the

injectivity index to match constraint

• Injection rate and volumes matched

Adjustment

• In spite of injecting the

correct volume of water

reservoir pressure continued

declining

• Water and gas exceeded

historical data (H2O: 47%)

Fluid production needs

to be controlled !


Model Calibration


Aquifer/reservoir

• vertical arrays

Aquifer Properties

• , h,k Relative Permeability

Functions

• end points, shape, crit. sat

Re-interpretation


• Plug-downs

• GOR, water cut

cutoff

“K.H” Term

Prod / Inj Index

Uniform Mod.

Fluid PVT

Local Absolute (K)

Lesser degree


Texas A&M University Diagnosis

Results: Waterflooding

Model Pressure Map Voidage Replacement Ratio


Texas A&M University Model Calibration for Final Pressure Match


Numerical aquifer




Model fluid match



WOC Movement

(a)

(b)

(c)

1950

1979

1983

208 ft

210 ft


Texas A&M University Results: CO2 Injection

H2O Inj

CO2 Inj

OWOC

H2O Inj

CO2 Inj

OWOC

H2O Inj

CO2 Inj

OWOC

Miscible Displacement

• Modification of the black oil sim.

• Pseudo-miscible option with

no chase gas

• Based on the “Todd and Long-

staff” theory

Highlights

• Modifies physical properties

and flow characteristics of

the miscible fluids

• Requires definition of new param.

• CO2 PVT prop., MMP, ωo(P)


Texas A&M University Results: CO2 Injection

Initial runs

• Abnormal increase in reservoir pressure

• VRR greater than 1, correlates with sharp pressure increase

• VRR decreased (1992) correlating with decrease in pressure

What is happening ?



Results: CO2 Injection

Water Rate Solvent Rate

• Model is not able to reproduce rapid water rate increase (1986)

• In 1986, insufficient water and solvent production results in

a dramatic increase in reservoir pressure

Initial runs




Model Calibration


Aquifer/reservoir

• vertical arrays

• local refinements

• Kv / Kh > 1

Aquifer Properties

• , h,k

Relative Permeability

Functions

• end points, shape, crit. Sat

• New set for middle reef

Account for ESP’s

Re-interpretation


• Plug-downs

• Include wells high

on the struct.

“K.H” Term

Prod / Inj Index

Uniform Mod.

Fluid PVT

Local Absolute (K)

Lesser degree


Negative Skin

Stimulations - Acidizing

Kv areal distribution 2nd Relative permeability region


Texas A&M University Diagnosis / adjustments


• Identification of abnormal

individual performance

• Fluid saturation distribution

• Adjustment completion intervals




• Good pressure match “primary”. Lost

during waterflooding, poor at CO2 Inj.

• Excess of H20 (waterflooding)

• Overall insufficient water and solvent

production (tertiary), causing over-

pressurization.

• Unsuccessful match after

extensive model calibration

• Matching fluid production

more accurately is required!

Sensitivity runs



Results: CO2 Injection Final match

• Daily oil rate primary constraint

expanded to daily total liquid rate

(oil + water)

• Match is preserved (primary, H2O Inj.)

• Water and H2O breakthrough matched

• Oil match sacrificed to match pressure



Results: CO2 Injection Final match



Bottom Water Drive


Sec. Gas

Cap

Prod Prod

Bottom Water Drive


Prod Prod

WIW WIW

Bottom Water Drive


CO2 ICO2 I

WIWWIW

Prod Prod


Bottom Water Drive

Bottom Water Drive


Bottom Water Drive


Sec. Gas

Cap

Prod Prod

Bottom Water Drive


Prod Prod

WIW WIW

Bottom Water Drive


CO2 ICO2 I

WIWWIW

Prod Prod


Bottom Water Drive

CO2 ICO2 I

WIWWIW

Prod Prod


Bottom Water Drive

WIWWIW

Prod Prod


Bottom Water Drive

Bottom Water Drive


Bottom Water Drive


Sec. Gas

Cap

Prod Prod

Bottom Water Drive


Prod Prod

WIW WIW

Bottom Water Drive


CO2 ICO2 I

WIWWIW

Prod Prod


Bottom Water Drive

CO2 ICO2 I

WIWWIW

Prod Prod


Bottom Water Drive

WIWWIW

Prod Prod


Bottom Water Drive

Bottom Water Drive


Bottom Water Drive


Sec. Gas

Cap

Prod Prod

Bottom Water Drive


Prod Prod

WIW WIW

Bottom Water Drive


CO2 ICO2 I

WIWWIW

Prod Prod


Bottom Water Drive

WIWWIW

Prod Prod


Bottom Water Drive

CO2 ICO2 I

WIWWIW

Prod Prod


Bottom Water Drive

WIWWIW

Prod Prod


Bottom Water Drive

Chronological Stages of Depletion




Texas A&M University Conclusions

1. Original fluids in place (according to simulation):

Oil: 127.1 MMSTB

Water: 139.0 MMSTB

Gas: 54.3 BSCF

Model OOIP, proved to be in close agreement not only with past estimations

but also with the analytical solution of the material balance technique

previously presented.

2. Cumulative water influx (8 MSTB) was estimated from application

of the material balance theory and correlates quite well with water

influx obtained in the “best case” being 8.5 MMSTB (first 10 years).

3. The natural aquifer greatly influenced production of fluids and

consequentially, the predicted average reservoir pressure.

4. The initial set of aquifer parameters was derived analytically by the

Hurst and Van Everdigen theory and finally tuned by sensitivity

analysis



5. The Carter and Tracy (analytic) method resulted as the best alternative

to model the Cisco aquifer over the Fetkovich (analytic) and the

numerical aquifer method.

Conclusions Cont….

6. The Cisco aquifer provided energy and supplied water that encroached

uniformly advancing the WOC 208 ft (prior to waterflooding) and an

additional 210 feet (prior to CO2 injection) being in excellent agreement

with field observations.

7. The use of a flexible grid system, honored the characteristic structure

of the cone-shaped double anticline. The distorted grid blocks

allowed a good representation of Wellman Unit geological features.

8. Historical water production and breakthrough times were identified as

one of the most difficult parameters to match and one that greatly

influenced the behavior of the predicted reservoir pressure response.


Texas A&M University Conclusions Cont….

• A complete pressure match was achieved through primary depletion,

waterflooding and CO2 injection, however the match on liquid production

was compromised in order to tune the final pressure match.

• The results of this work provide the foundation for future research into

this hydraulically complicated reservoir


Texas A&M University Recommendations for Future Work….

• More research is recommended on the geology of the field with the aim

of simplifying the total number of gridblocks, specifically the number of

layers (23) by the use of some of the upscaling methods in the literature.

• Consider the use of pseudo-functions during simplification of the

existing model to increase the accuracy when modeling the production of

fluids.

• Place additional effort to update the current model by incorporating

production and injection data from 1995 to the present time, thereby it

can be used to assist future reservoir management decisions.



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Acuifer Behavior

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