Computer studies of heat tracer experiments in fractured rock · Tprtr Rpn t Thrtr , 2, n (Tt 8.....

Computer studies of heat tracerexperiments in fractured rock

Item Type Thesis-Reproduction (electronic); text

Authors Leo, Timothy Patrick,1961-

Publisher The University of Arizona.

Rights Copyright © is held by the author. Digital access to this materialis made possible by the University Libraries, University of Arizona.Further transmission, reproduction or presentation (such aspublic display or performance) of protected items is prohibitedexcept with permission of the author.

Download date 06/06/2021 06:17:48

Link to Item http://hdl.handle.net/10150/191982

http://hdl.handle.net/10150/191982

COMPUTER STUDIES OF HEAT TRACER EXPERIMENTS

IN FRACTURED ROCK

by

Timothy Patrick Leo

A Thesis Submitted to the Faculty of the

DEPARTMENT OF HYDROLOGY AND WATER RESOURCES

In Partial Fulfillment of the RequirementsFor the Degree of

MASTER OF SCIENCEWITH A MAJOR IN HYDROLOGY

In the Graduate College

THE UNIVERSITY OF ARIZONA

1

1988

STATEMENT BY AUTHOR

This thesis has been submitted in partial fulfillmentof the requirements for an advanced degree at The Universityof Arizona and is deposited in the University Library to bemade available to borrowers under the rules of the Library.

Brief quotations from this thesis are allowable with-out special permission, provided that accurate acknowledgmentof source is made. Requests for permission for extended quo-tation from or reproduction of this manuscript in whole or inpart may be granted by the head of the major department orthe Dean of the Graduate College when in his or her judgmentthe proposed use of the material is in the interest of schol-arship. In all other instances, however, permission must beobtained from the author.

SIGNED:

APPROVAL BY THESIS DIRECTOR

This thesis has been approved on the date shown below:

2

S. P. NEUMAN

DateProfessor of Hydrology and

Water Resources

Cindy

3

With all my love, I dedicate this thesis to you.

ACKNOWLEDGMENTS

Support for this thesis was provided by the U. S.

Nuclear Regulatory Commission under contract (NRC-04-86-123).

Without this funding this research would not have been

possible.

I extend my deepest thanks to Dr. Shlomo Neuman for

his patience and encouragement. His guidance throughout this

research was truly inspiring. I also thank Dr. Eugene Simp-

son and Dr. Jim Yeh for their time and thoughtful comments.

Many thanks to Steve Silliman, Tim Flynn, and to all

the students and staff members who participated in the field

experiments that made this research possible. I am also

grateful to Gordon Wittmeyer and Colleen Woloshun for their

cart in the many impromptu discussions that helped shape this

thesis.

My sincere appreciation goes to Augusta Davis and

Fran Jansen for their help in getting all the "little" things

done. I also thank Mike Osborn for the use of the WRRC

computer equipment and Erika Louie for her expert preparation

of the final manuscript.

Finally, and most deeply, I thank my parents. Mom

and Dad, your love and support has made this, and everything

I achieve possible.

4

5

LIST OF

LIST OF

ABSTRACT

TABLE OF CONTENTS

ILLUSTRATIONS

TABLES

Page

7

11

12

1. INTRODUCTION 13

1.1 Objective of Thesis 16

2. THEORY 18

2.1 Fluid Flow Equation 182.2 Energy Transport Equation 21

3. NUMERICAL MODEL PT 24

3.1 Numerical Formulation 243.1.1 Fluid Flow Equation 253.1.2 Energy Transport Equation 28

3.2 Solution Technique 313.3 Relevant Features of PT used to Model

Heat Tracer Experiments 323.3.1 Numerical Options 333.3.2 Time Steps 333.3.3 Input-output 34

4. CONCEPTUAL MODEL OF FLOW SYSTEM 35

4.1 Site Description 354.2 Cross-correlation of Hydraulic Tests

and Geophysical Logs 414.2.1 Heat Pulse Flowmeter Tests 414.2.2 Single-Hole Packer Tests 434.2.3 Geophysical Logs 494.2.4 Results of Cross-Correlation 53

5. DESCRIPTION OF THREE-BOREHOLE RECIRCULATIONHEAT TRACER EXPERIMENTS 56

6

TABLE OF CONTENTS--Continued

Page

5.1 Field Test Procedure 563.2 Field Results 63

5.2.1 Test 1 645.2.2 Test 2 675.2.3 Test 3 715.2.4 Test 4 755.2.5 Test 5 79

6. MODELING PROCEDURE 88

6.1 Adaptation of Conceptual Model forNumerical Simulations 88

6.2 Heat Conduction During Phase 1 906.3 Borehole Model 926.4 Quasi-Three-Dimensional Model 936.5 Phase 1 (No-Flow Heating in M-1) 96

6.5.1 Boundary Conditions at M-1 976.6 Phase 2 (Pumping from H-3 and Injec-

tion into M-1) 1026.6.1 Boundary Conditions at M-1 1026.6.2 Boundary Condition at H-3 103

7. SENSITIVITY ANALYSIS 106

8. CONCLUSIONS AND RECOMMENDATIONS 123

APPENDIX A: COEFFICIENTS IN LIQUID WATERDENSITY CALCULATIONS 128

APPENDIX B: METHOD TO DETERMINE TRANSMISSIVITYOF FAULT ZONE 131

APPENDIX C: METHOD TO ASSIGN BOREHOLE STORAGECOEFFICIENT IN PT 133

REFERENCES 136

7

LIST OF ILLUSTRATIONS

Figure Page

3.1. Typical Cell Network in IFDM 26

3.2. Typical Cell Network Used to Specify BoundaryConditions 29

4.1.Topographic Map of Northern Santa CatalinaMountains 36

4.2. Diagram of the Oracle Site 38

4.3. Vertical Flow in M-1 for Two Surveys;Injection Rate for Both Tests was 1.9 1/minin H-3 Over the Interval 74.4 m to 79.6 m 42

4.4. Vertical Flow in H-3 While Injecting 1.9 1/mininto M-1 Over the Interval 80.8 m to 86.1 mor with H-2 Filled to Overflow and Maintainedat Constant Head 44

4.5. Vertical Flow in H-2 While Injecting 1.9 1/mininto H-3 Over the Interval From 74.4 m to79.6 m 45

4.6. Comparison Between Hydraulic ConductivityProfiles from Single-hole Packer Tests andNatural State Geothermal Gradients 46

4.7. Kriged Log-Hydraulic Conductivity in ThreeDimensions 48

4.8. Gamma Logs in Boreholes M-1, H-2, and H-3 50

4.9. Interval Acoustic-Velocity Data for a Cross-Section Defined by Boreholes H-4, H-3, H-2,and M-1 51

8

LIST OF ILLUSTRATIONS—Continued

figure Page

4.10. Neutron-log Response Versus Log-hydraulicConductivity for Straddle-packer Intervalsof Boreholes M-1, H-2, H-3, and H-4 52

4.11. Schematic Diagram of Fault Zone 54

5.1. Three-hole Recirculation Heat Tracer TestConfiguration 58

5.2. Location of Thermistors in M-1 for All Tests 59

5.3. Location of Heater, Pump, and Thermistorsduring Tests 1 and 2 61

5.4. Location of Heater, Pump, and Thermistorsduring Tests 3-5 62

5.5. Temperature Response at Thermistor #2 in M-1(Test 1) 65

5.6. Temperature Response at Thermistor #9 in H-2(Test 1) 66

5.7. Depth to Water in H-3 (Test 1) 68








9

LIST OF ILLUSTRATIONS--Continued

Figure Page

5.15. Temperature Response at Thermistor 415 in H-2(Test 4) 78

5.16. Depth to Water in H-3 (Test 4 ) 80

5.17. Temperature Responses at Thermistors #1, #2,#3 in M-1 (Test 5) 81

5.13. Temperature Responses at Thermistors 14-20 inH-2 and Their Arithmetic Average (Test 5) 83


5.20. Temperature Variation with Depth in H-2(Test 5) 85


6.1. Idealized Diagram Showing Fault Zone andBoreholes 89

6.2. Axisymmetric Finite Difference Grid Used toModel Heat Conduction During Phase 1 91

6.3. Finite Difference Grid Used in Quasi-three-dimensional Model 94

6.4. Schematic Diagram Showing Cell Network AroundM-1 98

6.5. Typical Match Between Computed and MeasuredTemperature Responses in M-1 100

6.6. Idealized Diagram Showing Relative Locationof Heater and Fault Zone 101

6.7. Schematic Diagram Showing Cell Network AroundH-3 104

6.8. Typical Match Between Computed and MeasuredWater Levels in H-3 105

7.1. Computed Thermal Responses in H-2 (gw = 74 m)...108

1 0

LIST OF ILLUSTRATIONS--Continued

Figure Page

7.2. Computed Thermal Responses in H-2 (gw = 14 m) 111

7.3. Computed Thermal Responses in H-2 (gw = .7 m) 114

7.4. Effect of Changes in Porosity on ComputedThermal Response 116

7.5. Effect of Increasing K c on Computed ThermalResponse 117

7.6. Variation of b' (t) With Time 121

LIST OF TABLES

Table Page

4.1. Boreholes at Field Site 39

5.1. Instrument arrangement and flow rate for eachof the three-hole recirculation tests 57

7.1. Initiai oarameter values 107

7.2. Parameters used in grid width case A 110

7.3. Parameters used in grid width case B 113

11

12

ABSTRACT

The computer model PT is used to analyze a three-

borehole recirculation heat tracer test conducted in a

fracturea granitic rock mass near Oracle, Arizona. Results

of hydraulic tests and geophysical logs are cross-correlated

=o determine the location, orientation and thickness of a

high permeability fault zone, in which flow between the

potencies during the heat tracer test is believed to occur.

A quasi-three-dimensional model of fluid flow and heat

transport in the fault zone is used to qualitatively re-

produce a steep rise in measured temperature within a

monitoring borehole. Computed thermal breakthroughs are

found to be sensitive to two numerical grid parameters--

Thickness and width. A grid thickness of 1.0 cm and a grid

width of 0.7 m are sufficient to qualitatively reproduce the

steep temperature increase. Further research into the impor-

tance of heat convection under static conditions during the

test is recommended.

13

CHAPTER 1

INTRODUCTION

Generally, tracer tests conducted in porous media

involve the injection, monitoring, and/or withdrawal of

labeled water. Labeling of injected water can be achieved

through the addition of chemicals, radioactive isotopes, or

dyes. Tests using these methods often require elaborate

field and analytical equipment and may require long time

periods between tests so that flushing of tracer can be

completed.

An alternative ground-water tracer is heat. A heat

tracer test may consist of injecting a volume of heated or

cooled water and monitoring the subsequent movement of this

thermal plume in response to pumping in a nearby well.

Monitoring involves measuring temperature in nearby wells,

which can be performed simultaneously with relatively simple

equipment at numerous points without disturbing the flow

system. Due to the rapid heat dissipation within the rock a

series of heat tracer tests can be conducted with relatively

short rest periods between tests.

In the past, the use of water temperature as a ground

water tracer has been done primarily in porous aquifers.

Keys and Brown (1968) traced thermal pulses resulting from

14

the artificial recharge of playa lake water into a sandy

aquifer. Hufschmied (1984) conducted a similar study in

Switzerland, where he used water temperature to evaluate the

migration of recycled geothermal water in a gravelly aquifer.

Ledoux and Clouet d'Orval (1977) and Sauty (1978b) conducted

heat tracer tests in a sand and gravel aquifer to compare the

effects of chemical and thermal dispersion. Most recently,

Barlow (1987) determined total porosity values and studied

the effect of thermal dispersion based on heat tracer tests

conducted in a shallow glacial outwash aquifer. Lapham

(1987) successfully used temperature profiles and yearly

temperature envelopes below stream beds to determine ground-

water recharge-discharge velocities and effective vertical

hydraulic conductivities of streambed sediments in New

England.

Theoretical analysis of the movement of heat and mass

(water) in porous media has been performed in conjunction

with the evaluation of the feasibility of storing thermal

energy in aquifers. Papadapulos and Larson (1978), Tsang

et al. (1981), and Sykes et al. (1982) all performed numeri-

cal simulations of aquifer thermal energy storage (ATES)

tests conducted at the Auburn University field site in

Mobile, Alabama. In similar work, Sauty et al. (1982) used

15

water temperature as a tracer in conjunction with a theoreti-

cal feasibility study of sensible energy storage in aquifers

in France.

Many investigators have conducted theoretical

studies of heat and mass movement in geothermal reservoirs.

These include Mercer et al. (1974), Sorey (1975), Witherspoon

et al. (1977), Coats (1977), Lippmann and Bodvarsson (1983),

Bodvarsson et al. (1984) and Pruess and Narismhan (1985),

among others. Bodvarsson et al. (1986) presents a summary of

recent developments in numerical modeling of geothermal

systems.

The application of water temperature as a tracer in

fractured rock has, to our knowledge, been first reported by

Flynn (1985) at the University of Arizona experimental field

site near Oracle, Arizona. The original purpose of these

tests was to delineate major flow paths between boreholes in

a qualitative manner.

The relative non-existence of reported experiments

using water temperature as a tracer in fractured rocks is

due, in part, to the lack of a well defined theoretical

framework in which such tests can be analyzed. This frame-

work must adequately account for the simultaneous movement of

heat and mass in the fractured rock system.

Early studies of heat and fluid movement in fractured

rocks were conducted by Romm (1966) and Bodvarsson (1969).

16

Gringarten et al. (1975) present a theoretical analysis of

heat extraction from fractured hot dry rocks. 0 - Niel' et al.

(1976) simulated heat transport in fractured, single phase

geothermal reserviors, and later O'Niell (1978) analyzed the

transient three-dimensional flow of heat and liquid in

fractured porous media. Pruess et al. (1984) studied the

thermal effects of reinjection in geothermal reserviors with

vertical fractures and Bodvarsson et al. (1985) considered

injection and energy recovery in fractured geothermal

reservoirs.

1.1 Objective of Thesis

The purpose of this thesis is to examine the extent

to which the heat tracer experiments of Flynn (1985) at

Oracle might be given to interpretation. The method of

interpretation utilizes a computer code, PT, developed by

Bodvarsson (1982) for mass and heat transport in porous

media.

Chapter 2 presents the governing equations of mass

and energy transport in a porous medium. Chapter 3 intro-

duces the numerical model, PT, and describes the numerical

formulation and solution technique used to solve the

governing equations. Chapter 4 correlates field data from

the Oracle site to describe the controlling flow system.

Chapter 5 describes, in detail, the field procedure and

results of the three-borehole recirculation heat tracer

17

tests. Chapter 6 presents the modeling procedure used to

simulate the heat tracer tests. Chapter 7 presents the

results of these simulations, and Chapter 8 lists the impor-

tant conclusions from this research and offers recommenda-

tions for further improvements to both the modeling and field

procedures.

18

CHAPTER 2

THEORY

In this chapter we present the equations governing

fluid flow and heat

Fluid mass

transport

2.1 Fluid

in a porous medium.

Flow Equation

conservation coupled with Darcy's law in a

volume

f [Ss) g

V of

,iLD

-9L-

porous

n.1pf (patTE

medium

,„ riuv = j

can

p

be written in integral form as

- (71) - p g) ndr + rGf dV

J V F (2.1)

where Pf is the fluid density, S s is the specific storage of

V[S s = Pf + if)], is porosity, P is pressure, k is the

intrinsic permeability tensor of the medium, a = (0,0,-g)

being the acceleration due to gravity, Gf is a fluid source

term, F is the boundary of V, and n is a unit normal to r

pointing outward.

The compressibility of the rock matrix 8r is defined

[ V

1 alr

v dP

T(2.2)

where V v is the volume of void space. Other definitions of

are possible, resulting in different forms of S. For

19

more details on the relationship between Fs, and S, see Freeze

and Cherry (1979), Bear (1979), Marsily (1986), among others.

The value of is required input for Pm. The compressibil-

ity of the fluid ief is defined

[Sf = - 1 d Pf(2.3)

P f dP

f can either be specified in the input or can be calculated

as a function of pressure and temperature.

The total thermal expansivity of the medium at is

defined by

OEt = a r + a f (2.4)

with a r and Of being the thermal expansivity

matrix and fluid, respectively. or and of

of the rock

are defined as

a =1rdV

r(2.5)V

[dT

I

o f =

r

1[p

f

dpf

P

(2.6)dT

where V r is the volume of rock matrix.

We wish to solve (2.1) subject to the initial condi-

tion

20

P(x,y,z,0) = Po (x,y,z) (2.7)

and boundary conditions specified in one of three ways:

1. Prescribed Pressure (Dirichlet)

P(t) = P r (t)

P r (t) = specified pressure on r

2. Prescribed fluid mass flux (Neumann)

-Pfg = F(x,y,z,t) (2.9)

= volumetric flux normal to I" as described by

Darcy's law

F(x,y,z,t) = known function specifying mass flux

3. Cauchy condition

Pf g = a*[P(t) - P*(t)] (2.10)

c‘ * = proportionality constant related to the

permeability along r

P (t) = pressure outside flow domain

Generally, the fluid and formation properties depend

upon the thermodynamic variables--pressure and temperature--

so that the above -oroblem is nonlinear. The relationships

between the fluid properties Pf and 1-1 and the pressure and

21

temperature are described by equations of state. The fluid

density Pf is determined by

Pf (P,T) = A(T) + C(T)B(P) (2.11)

where A(T), B(P), and C(T) are specified functions given in

Appendix A. Equation (2.11) is accurate to within 1% for

0 < T < 300 °C and 5% for 300 < T < 350 °C (Buscheck, 1980).

The viscosity of the fluid p is determined by

d

rr + 2d 3 ]P(T) = d1 10

where d1 = 2.414 x 10 -5 , d2 = 247.8, and d3 = 133.15

(Buscheck, 1980).

(2.12)

2.2 Energy Transport Equation

Energy conservation in V can be written in integral

form as

f m mTE- (p c T)dV = f(KVT) . ridr - f(p fc fuTrndrV r r

+ f GhdV

V

(2.13)

where Pmcm is the integrated heat capacity of V (i.e., pmcm =

(Ppfcf + (1-$)p r c r ), c r is the specific heat capacity of the

rock matrix, P r is the density of the rock matrix, cf is the

specific heat capacity of the fluid, K = KT 4- KTD, K T is the

22

thermal conductivity tensor of the fluid-rock system, KTD is

the kinematic (convective) dispersion tensor, T is the

temperature inside V, (ST is the difference between the

temperature on the boundary and the average temperature

inside the volume V, and Gh is a heat source term.

We wish to solve (2.13) subject to the initial

condition

T(x,y,z,0)=T0 (x,y,z) (2.14)

and boundary conditions specified in one of three ways:

1. Prescribed Temperature (Dirichlet)

T(t) Tr(t) (2.15)

Tf(t) = specified temperature on r

2. Prescribed heat flux (Neumann)

-J = QH(t)r

(2.16)

J = heat flux as described by Fourier's law

QH(t) = specified heat flux across r

3. Cauchy condition

= e[T(t) - T * (t)] (2.17)

f3,* = proportionality constant referred to as

the heat transfer coefficient

T * = temperature outside flow domain

23

In equation 2.13, K includes the combined effects of

conduction and thermal dispersion. Thermal dispersion is a

direct consequence of the kinematic dispersion, due to the

heterogeneities of the matrix on the small scale (Sauty,

1977; Sauty et al., 1978). These small scale heterogeneities

cause fluctuations in the microscopic pore velocity, result-

ing in the dispersion of heat. This dispersion of heat

enhances heat conduction in the presence of fluid movement.

For a complete theoretical development of the form of the

thermal dispersion tensor see Sauty (1977) and Sauty et al.

(1978). 1arsily (1986) gives an overview of the relationship

between thermal dispersion and chemical dispersion.

For more complete derivations of the fluid flow and

energy transport equations, see Mercer et al. (1974),

Pritchett et al., (1975) Witherspoon et al. (1975), among

others.

Equations (2.1) and (2.13) are coupled through the

relationships between the fluid properties (pf, T1) and the

thermodynamic variables P and T. In the program PT, the

resulting set of governing equations are solved simulta-

neously for the unknowns P and T.

24

CHAPTER 3

NUMERICAL MODEL PT

The numerical code PT (Pressure-Temperature) was

developed by G. S. Bodvarsson at Lawrence Berkeley Labor-

atory. It is a modification of an earlier code CCC (Conduc-

tion Convection-Consolidation) developed by Lippmann et al.

(1977).

In this chapter, the numerical formulation and solu-

tion technique employed in the program PT are described. In

addition, the relevant features of the program used to model

heat tracer experiments are discussed.

3.1 Numerical Formulation

PT solves numerically the fluid mass flow and energy

transport equations given in chapter 2 due to the flow of a

single phase fluid in a heterogeneous anisotropic porous med-

ium, subject to spatially varying initial and boundary condi-

tions. The program employs the Integral Finite Difference

Method (IFDM) to discretize the governing equations in space

and time. The IFDM is related to the familiar Finite

Difference Method. Except for the procedure used to evaluate

the gradients, the IFDM and the modified Galerkin Finite

25

Element Method (with diagonal capacity matrix) are conceptu-

ally very similar (Narasimhan and Witherspoon, 1976).

Detailed descriptions of the IFDM are given by Edwards

(1972), Sorey (1975), and Narasimhan and Witherspoon (1976).

In practice, :he entire flow domain is subdivided

into finite-size cells such as in Figure 3.1. Mass and

energy balance equations are written for each cell. For

maximum accuracy and to insure consistency, interfaces

between elements should be perpendicular to and bisect the

lines joining the nodal points.

The following presentation of the governing equations

in numerical form and the method used to solve these equa-

tions is based on Bodvarsson (1982).

3.1.1 Fluid Flow Equation

The mass conservation equation combined with Darcy's

law written in numerical form is

(WP ) ''11 -.a--1-A =[

LAt

rpfri•f n L. Lt Pm n,m

m

P

n

)IDn,m

p n g + (G fV) n+D g g

(3.1)

where Dn, m and Dm , n represent the distances from nodal points

n and m to the common element interface, respectively. The

quantity n g is the direction cosine of the angle between the

vertical and the outward normal of elements n and m.

26

Figure 3.1. Typical Cell Network in IFDM.

27

The permeability is evaluated using the harmonic mean

to insure continuity of flux at the interface, for example

D +Dn,m m,n km,n

= k km n kDmn,m

+ knDm,n

(3.2)

where k m and k n are the permeabilities in elements m and n,

respectively. For anisotropic conditions, the values of k in

the coordinate directions x and y are determined by specify-

ing k x , the element and the ratio k /k.y x. The working

coordinates x and y are fixed parallel to the principal axes

of hydraulic anisotropy.

The density at the interface Pf n,11 is calculated

based on a simple weighted average:

p Dn,m

+pf Dm,n

f Dn,m

+Dn,m m,n

(3.3)

However, in the gravity term, the fluid density Pg is calcu-

lated assuming linear variations in pressure and temperature

between elements:

1-2 (P f + 0 )' f

m(3.4)

The remaining terms in 3.1 are the same as defined in Chap-

ter 2.

The initial condition for equation 3.1 is the same

as given for equation 2.1. The program PT utilizes external

auxiliary cells, e, to facilitate specification of boundary

28

conditions (Figure 3.2). The general form of the conditions

prevailing on the boundary is

Qt a(p8 _ (3.5)

where Qt is the mass flux, P and Pt designate the pressure

inside the internal and external elements, respectively, and

t represents the time level. For prescribed pressure

(Dirichlet) conditions, a is set very large and Pe is assign-

ed the desired pressure; for prescribed flux (Neumann)

conditions, assign g >> P a = Qt/II; and for mixed

(Cauchy) conditions, pressure dependent sources are assicjned

along the appropriate boundary.

3.1.2. Energy Transport Equation

The energy transport equation written in numerical

form is

AT n(pmcm)V At = / D[ n

umm,n

n,rn iT

m n,m + D ' m T

n) + [

m,n nfcfrl

11 n,m(T - T).

[D

Prn - Pn n,m

+ Dm,npgng] + (GhV) n

(3.6)

where the temperature T m , n at the interface between elements

m and n is evaluated using an upstream weighting criterion

Tm , n = dTm + (1 - d)T n (3.7)

external I i nternalcell cell

gridboundary

1 L

1

Figure 3.2. Typical Cell Network Used to Specify BoundaryConditions.

29

30

where in is the upstream element and d, the weighting factor,

is restricted to the range 0.5 to 1.0 for unconditional

stability. The remaining terms in 3.6 are the same as

defined in Chapter 2.

The value of Km , n is evaluated using the harmonic

mean in the same manner as for the permeability. For

anisotropic conditions, the values of K in the coordinate

directions x and y are determined by specifying K x in the

element and the ratio K /Ky x-

The initial condition for equation 3.6 is the same as

given for equation 2.9. The temperature boundary conditions

are specified in the same manner as the pressure boundary

conditions (Figure 3.2). The general form of the boundary

conditions is

QH = b(Te - Ti)

(3.8)

where Q /L_-1 is the heat flux and T1 and Ti are the temperatures

inside the external and internal elements, respectively. For

prescribed temperature (Dirichlet) conditions, b is set very

large and T is assigned the desired temperature; for pre-

scribed heat flux (Neumann) conditions, 4 >> q_ and b =

QH / T8; and for mixed (Cauchy) conditions, temperature

dependent heat sources are assigned along the appropriate

boundary.

31

3.2 Solution Technique

In PT, equations 3.1 and 3.6 are solved implicitly.

The implicit formulation is incorporated by means of the

following expressions:

Tn = TE + QTAT n (3.9a)

Tm = T2 + 761,AT a (3.9h)

Pn = PR

(3.9c)

Pm = P2 + QpAPm (3.9d)

where TE, T2, PE, and P2 are the computed temperatures from

the previous time step. LP and AT represent the changes in

pressure and temperature during the previous time step. The

weighting factor 2 is generally allowed to vary automatically

between 0.57 and 1.0 so as to obtain unconditionally stable

solutions, but may also be specified as a constant. If Q is

0.5, the Crank-Nicholson (central differencing) scheme

results; if is 1.0, a fully implicit (backward differ-

encing) scheme is employed.

Equations 3.1 and 3.6 are combined for simultaneous

solution into a single matrix equation

A(P,T) x = b (3.10)

The coefficients in the matrix A are in general a

function of the temperature and pressure and therefore the

32

equations are nonlinear. The vector x contains the unknowns

LP and P..T and the vector b contains the source terms and

boundary values as well as terms written at the previous time

level.

The set of nonlinear equations are solved using an

efficient direct solver (Duff, 1977). The nonlinear coeffi-

cients are evaluated using linear approximation over suffi-

ciently small time steps.

The matrix of coefficients A is pre-ordered such that

the resultant matrix is in block-diagonal form. LU decom-

position is then performed to obtain factorization into

the lower triangular Lk and upper triangular Uk parts.

Finally, forward and back substitution is used to solve the

matrix equations. In this solution package (Duff, 1977), no

restriction is placed on the characteristics of the matrix of

coefficients, i.e., it need not be symmetric or possess a

specified degree of sparsity.

3.3 Relevant Features of PT used toModel Heat Tracer Experiments

The computer program PT is a powerful numerical

simulator. This made it easy to adapt PT for modeling of

heat tracer experiments. The code is very well suited for

modeling three-hole recirculating heat tracer experiments.

33

3.3.1 Numerical Options

The program offers the option of solving both the

mass and energy equations, or only one of the two. If only

one equation is solved, a smaller matrix is needed and the

calculation becomes more efficient (Bodvarsson, 1982). This

feature of PT is useful in modeling phase 1 of the Oracle

heat tracer experiments which consists of heating without

forced flow.

3.3.2 Time Steps

PT contains several options for selecting the time

steps to be taken during simulation. The initial time step

is specified in the input. The maximum and minimum time

steps may be specified, or the time steps may be automat-

ically determined based on the desired maximum pressure

and/or temperature change during the time step (Bodvarsson,

1982). This option proved useful in preparing the model

output for graphical analysis, since the model output times

and the field data times could be easily matched.

The problem can be ended when any one of several

criteria is met. These include attainment of steady state,

reaching a specified upper or lower limit for temperature

and/or pressure, completing the required number of time

steps, and reaching the specified maximum simulation time.

34

3.3.3 Input-Output

The input-output of the model was slightly modified

so that micro-computer graphics could be used. In general,

these modifications entailed reading and writing to magnetic

tapes rather than using computer cards. These changes,

combined with the built-in restart procedure, enabled easy

modeling of the two phase nature of the heat tracer experi-

ments.

35

CHAPTER 4

CONCEPTUAL MODEL OF FLOW SYSTEM

Flow between the boreholes at the Oracle site occurs

primarily through a subhorizontal high permeability fault

zone which is bounded on top and bottom by a low permeability

rock mass. The depth below land surface (BLS) of this fault

zone is approximately 76 to 82 meters. In this chapter, we

correlate the results of selected geophysical logs, hydraulic

tests, and natural state geothermal gradient surveys to

define more clearly the location, thickness, and hydraulic

properties of this fault zone. In addition, we cite quali-

tatively the results of chemical tracer tests which further

illustrate the highly conductive nature of the fault zone.

Only field results pertaining to the fault zone are discussed

in this thesis.

4.1 Site Description

The Oracle field site, now inactive, is approximately

8 km southeast of the community of Oracle, located approxi-

mately 60 km north of Tucson, Arizona. The site lies on a

pediment surface flanking the northwest end of the Santa

Catalina Mountains (Figure 4.1). The major lithologic unit

underlying the site is known informally as the Oracle

CONTOUR INTERVAL600 FEET

DATum IS SEA LEVEL

0 MILE

36

Figure 4.1. Topographic Map of Northern Santa CatalinaMountains. (After Jones et al., 1985)

37

granite. The geology of the Oracle granite was studied in

detail by Banerjee (1957), and its geologic history was eval-

uated by Davis (1981). Figure 4.2 shows the configuration of

boreholes at the site, and Table 4.1 contains data pertinent

to borehole construction. Only boreholes M-1, H-2, and H-3

are considered in this thesis.

Borehole geophysical surveys were performed by W.

Scott Keys of the U. S. Geological Survey, Denver, Colorado.

The geophysical measurements include: neutron, caliper,

single-point resistivity, natural gamma, interval acoustic

velocity (at 0.3 m spacing) and acoustic televiewer. Results

of these logs were given by Keys (1981) and summarized by

Jones et al. (1985). In addition, geotomography was per-

formed by Ramirez (1986) of Lawrence Livermore National

Laboratory.

Heat pulse flowmeter tests were performed by Messer

(1986). These tests indicate hydraulic connections between

boreholes by injecting water in one borehole and monitoring

the changes in flow pattern in a neighboring borehole.

Generally, the heat pulse flowmeter tests concentrated on the

high-permeability fault zone connecting boreholes M-1, H-2,

and H-3.

Single-hole and cross-hole packer tests were con-

ducted by Hsieh (1983). Hsieh et al. (1983) presented the

theory behind and gave complete results of these tests.

38

KEY

WELL *•

DEPTH

meters

H8•

76.2H5•

76.2

ANALYTICALEQUIPMENTSHED

H7 H6• •

76.2 76.2

H4 H3 H2 MI• • •87.8 91,4 91.4 91.4

1 4- 6.1m -4-14- 9.1m

Figure 4.2. Diagram of the Oracle Site. (After Aikens,1986)

39

Table 4.1. Boreholes at Field Site (after Jones et al.,1985).

BoreholeNo.

TotalDepth

(meters)

CasingDepth

(meters)

NominalCasing

Diameter

NominalBoreholeDiameter(meters)

DrillingMethod**(meters)

M1 91.5 17.7 0.20 0.17 0-17.7 MR17.7-32.3 C32.3-91.5 AH

H2 91.5 18.0 0.13 0.11 0-18.0 MR18.0-91.5 AH

H3 91.5 17.7 0.18 0.17 0-17.7 MR17.7-91.5 AH

H4 87.8 13.1 0.13 0.11 0-13.1 MR13.1-87.8 C

H5 76.2 18.6 0.13 0.11 0-76.2 AH/F

116 76.2 19.2 0.13 0.11 0-767.2 AH/F

H7 76.2 20.1 0.13 0.10 0-20.1 AH/F10.2-76.2 C

H8 76.2 18.0 0.13 0.10 0-18.0 AH/F18.0-76.2 C

** AH/F = air hammer/foamAH = air hammerMR = mud rotaryC = cored

40

Single-hole packer tests conducted over 3.8 m intervals in

the boreholes reveal information about the hydraulic conduc-

tivity in the vicinity of the packed-off interval. Cross-

hole packer tests conducted at a given depth between two

boreholes provided information about hydraulic diffusivity

(K/S s ) in the direction of the line joining the injection and

monitoring intervals. Cross-hole packer tests were not

performed in the fault zone; therefore, they are not included

in this analysis.

Natural state geothermal gradient surveys were

conducted by Flynn (1985). Deviations in the geothermal

gradient indicate zones of inflow to the borehole. Flynn

(1985) reported identifying such zones in borehole H-2. In

this thesis, geothermal gradients in boreholes M-1 and H-3

are also presented.

Convergent and divergent flow chemical tracer tests

were performed by Grisak et al. (1982), Cullen et al. (1985),

and Barackman (1986). In general, these tests provided

qualitative insight into the hydraulic conductivity of flow

zones between the boreholes. Aikens (1986) presented a

preliminary analysis of a diverging flow chemical tracer test

conducted in the high permeability fault zone. Zhang

(personal communication) presented a similar analysis of the

two borehole convergent chemical tracer tests. The rapid

chemical breakthrough observed in tests conducted in the

41

fault zone further support the impression that this zone is

highly conductive.

4.2 Cross-correlation of Hydraulic Tests and Geophysical Logs

The results of the above field tests are cross-

correlated among boreholes M-1, H-2, and H-3. Whenever

oossible, the results of different field methods are compared

simultaneously to show correlation or the lack of it. First,

we present the results of the heat pulse flowmeter tests,

which provide direct information about the location of the

fault zone based on actual flow into and out of the bore-

holes. We then correlate this information with the results

of the remaining field tests. Finally, all pertinent

evidence is superimposed on a schematic diagram of the bore-

holes, providing a best estimate of the location, orientation

and thickness of the fault zone.

4.2.1 Heat Pulse Flowmeter Tests

Two heat pulse flowmeter tests were conducted in M-1

(HPFM #1). In both tests, water was injected in H-3 over the

interval 77.4-79.6 m at a rate of 1.9 1/min. In both cases,

flow measurements throughout the borehole indicated one major

hydraulic connection with H-3 intersecting M-1 between 84 and

85 m (BLS) (Figure 4.3). A second set of flowmeter tests was

conducted using boreholes H-2 and H-3 (HPFM #2). In the

first test, H-2 was filled and the water level was maintained

FLCW ntrnin)

0.0 0.1 0.2 0.3 0.4 05 0.6 0.7 0.8

Figure 4.3. Vertical Flow in M-1 for Two Surveys; InjectionRate for Both Tests was 1.9 1/min in H-3 overthe Interval 74.4 m to 79.6 m. (After Messer,1986)

42

20

D

H

(m)

70

43

at ground surface. Results from the flowmeter survey (Figure

4.4) indicate that most of the water entering H-3 was

Produced above a highly conductive zone between the depths 75

and 78 m BLS. With the test configuration reversed and

injecting water in H-3 between the depths 74.4 and 79.6 m,

one major inflow zone was located in H-2 between the depths

79 and 81 m (Figure 4.5). The locations of these high K

zones are shown later, superimposed on a schematic diagram of

the boreholes.

4.2.2 Single-hole Packer Tests

The bar graphs in Figure 4.6 represent the results of

the single-hole packer tests (SHPT) in boreholes M-1, H-2 and

H-3. In each profile, the relatively large K values between

the depths of 75 and 85 m BLS indicate the fault zone.

Strong evidence of the fault zone is clearly seen in the pro-

files for H-2 and H-3. The computed K values for the fault

zone, however, are not reliable, as most of the injected

water has entered neighboring boreholes through the fault

zone (Hsieh et al., 1983). In addition, leakage of injected

water around the packers results in overestimation of K.

Depner (1985) presented similar profiles where he corrected

the hydraulic conductivity data based on estimation of

leakage around the packers. Therefore, the hydraulic

conductivity profiles serve primarily as a qualitative

indication of the location of the fault zone.

1

H-3, NJ. NTO r1-1

-4- H-3, KJ. INTO H-2

44

FLOG (1/m4tt)

0.0 0.2 0.4 0.6

0.8

1.0

1.2

20

30

0 40

50

H

(m)

70

80

90

Figure 4.4. Vertical Flow in H-3 While Injecting 1.9 1/mininto M-1 Over the Interval 80.8 m to 86.1 m orwith H-2 Filled to Overflow and Maintained atConstant Head. (After Messer, 1986)

43

FUN (lhnin)

0.0 0.1 0.2 03

0.4

0.510 -

20

30

40

50

60

70

90

D

H

(m)

Figure 4.5. Vertical Flow in H-2 While Injecting 1.9 1/mininto H-3 Over the Interval From 74.4 in to79.6 m. (After Messer, 1986)

oo0(-4

• 1-

I .,

o o o o o

6 ci 6 6 6 6

c. .. o o oI I I 1 -1

1o

ee* 1 o...

.-— T

re

-F

oo

w *ylciaa

.1J oo

46

E Noo

oO

4'7

Superimposed on these results (Figure 4.6) are the

natural state geothermal gradients. In borehole M-1, the

deviation in geothermal gradient at about 70 m BLS indicates

a source of cooler water intersecting the borehole. This

deviation, however, does not correlate with the location of

the fault zone as inferred from the single-hole packer tests.

In all three geothermal gradient profiles a major deviation

occurs between the depths of 81 and 86 m BLS. This form of

deviation near the base of the borehole has been observed by

Silliman (unpublished manuscript) in several other boreholes

located in significantly different media including shales and

alluvial deposits. An investigation is currently underway by

Silliman to determine the cause of these deviations.

A geostatistical interpolation procedure called

"kriging" was performed on the log-hydraulic conductivity

data (LogloK) from the single-hole packer tests. This

procedure provides an estimate of the three-dimensional

distribution of log-hydraulic conductivity between the

boreholes (Figure 4.7) (Jones et al., 1985). In addition, a

geophysical tomography image was obtained for a vertical

cross-section at the Oracle site by Lawrence Livermore

National Laboratory. Ramirez (1986) demonstrated that the

kriged estimates of log-hydraulic conductivity correlate

favorably with the geotomographic image. Both indicate the

H 8H S

LEGEND

11E113Do abo..6.5 Velue of Log-Hydraulic Conductivity

Nogat i vo of Logo.- i Ova,Exomplo 10.E-8.S

SCALE meters

0 15 30

Nor t I,- Soo t F1 emoggor at i on & 1(6

Figure 4.7. Kriged Log-Hydraulic Conductivity in ThreeDimensions. (After Jones et al., 1985)

4 8

49

presence of the highly conductive fault zone beneath 76

meters BLS.

4.2.3 Geophysical Logs

Gamma logs (GL) for boreholes M-1, H-2, and H-3 are

given in Figure 4.8. Jones et al. (1985) inferred the loca-

tion of the fault zone (76.8-83 m BLS) based on the leftward

deflections in the logs, which represent a decrease in the

total emitted gamma radiation from naturally occurring

isotopes. This decreased gamma intensity in the fault zone

is believed to be the result of solution and migration of

radioisotopes in circulating meteoric groundwater (Jones

et al. 1985).

Interval acoustic-velocity logs (IAVL) for boreholes

M-1, H-2 and H-3 are shown in Figure 4.9. Jones et al.

(1985) inferred the location of the fault zone (76.8-83 m

BLS) based on the leftward deflections in the logs, which

represent a decrease in the compressional-wave velocity in

the surrounding rock parallel to the borehole. This decrease

in compressional-wave velocity generally results from a

decrease in lithostatic pressure. The location of the fault

zone based on gamma and interval acoustic-velocity logs shows

good correlation with the results of the single-hole packer

tests.

Figure 4.10 points to the existence of a linear

relationship between inverted-integral, neutron log response

K36€57 H4 MI EAST

J Jo309 4416

2 , 1 I. ......14c411

C foe

444

15

75

90

45

50

Figure 4.8. Gamma Logs in Boreholes M-1, H-2, and H-3.(After Jones et al., 1985)

- 15

-30

45

- 60

75

ti It2 hi 1wEsr Eks-To

14 IC If 7S Z.? 14 If

IV J I 21 22

ZS 22

14 le IV 21

21 Air ...nt•I t

51

Figure 4.9. Interval Acoustic-Velocity Data for a Cross-Section Defined by Boreholes H-4, E-3, E-2, andM-1. -- Log scales are in kilofeet per second.contours relate to acoustic velocity of unfrac-tured rock only. Cycle skips are not shown.(After Jones et al., 1985)

Ma»

I-4

3800 . . . ,-18.8 20.8 -8.8 -7.8

LOG—HYDRAULIC CONDUCTIVITY(METERS PER SECOND)

Figure 4.10. Neutron-log Response Versus Log-hydraulicConductivity for Straddle-packer Intervals ofBoreholes M-1, H-2, H-3, and H-4. (After Joneset al., 1985)

52

53

and log-hydraulic conductivity over at least two orders of

magnitude of hydraulic conductivity variation. The simi-

larity in slopes of all three straight lines suggests that a

correlation between total porosity of the rock and hydraulic

conductivity exists because the neutron log responds to total

porosity (a large part of which is fracture porosity) and to

hydrous minerals, because of alteration along fractures.

Acoustic televiewer logs were also performed in the

boreholes. However, these logs were difficult to analyze in

the vicinity of the fault (due to poor photo-copy repro-

duction) and therefore are not included in the cross-

correlation. In addition, coring was performed in selected

boreholes--however, never at the depth of the fault zone in

boreholes M-1, H-2, H-3.

4.2.4 Results of Cross-correlation

The inferred results of the heat pulse flowmeter

tests, geophysical logs, and single-hole packer tests are

superimposed on a schematic diagram of the boreholes (Figure

4.11). The diagram suggests that the fault zone may be

dipping from H-3 towards M-1. Thickness based on these data

alone may range between 73-83 m in H-3 to 76-85 m in M-1, but

could be as little as 5 m in H-3 and 1 m in M-1. A porosity

value of .10 was reported by Cullen (1985) based on the

analysis of chemical tracer tests conducted in the high

permeability fault zone. Aikens (1986) reported a porosity-

54

H-3 H-2 M-1

65 m —

HPFM- GL SHPT

70 m —

75

FALL80 m —

----------------------------

T zONE

85 m —

-1

Figure 4.11. Schematic Diagram of Fault Zone.

55

thickness product of .009 based on a numerical modeling study

of the divergent flow chemical tracer test. With our extreme

values of thickness (1 and 10 m) and this relationship, poro-

sity ranges from .009 to .0009. In addition, Zhang (personal

communication) determined a porosity-thickness product of

about .03 m based on a later numerical modeling study of the

two-well convergent flow chemical tracer tests. Repeating

the above process gives porosities of .03 and .003.

56

CHAPTER 5

DESCRIPTION OF THREE-BOREHOLE RECIRCULATIONHEAT TRACER EXPERIMENTS

This chapter describes the three-borehole recircu-

lation heat tracer experiments conducted at the Oracle field

site by Flynn (1985) during the dates 7/14/84 and 12/12/84.

The results of these tests are also discussed.

5.1 Field Test Procedure

Six tests using water temperature as a tracer were

conducted at the Oracle site. Table 5.1 contains a summary

of these tests (Flynn, 1985). The final test on 12 December

1984 used cold water as a tracer. This test is not consid-

ered in this thesis. The remaining five tests used heated

water as a groundwater tracer.

Each of the five tests using heated water was

conducted in boreholes M-1, H-2, and H-3 (Figure 4.2). The

test configuration is shown in Figure 5.1. In all tests, a

submersible 1.2 m modified Calrod tubular heater (6 kilowatt)

was placed in borehole M-1 at approximately 76 m below land

surface (BLS). Three thermistors (temperature measuring

devices), one above, one adjacent to, and one below the

heater were also placed in M-1 (Figure 5.2). The heater was

placed just above the estimated fault zone location.

rv) cs,I tO

M

C,^)I CO

X CV

Cf1CDCOCN

LC>

COLi

"0

Wcl0 wac WMCO o o o

O- cs) o

▪

:7) o O H o 0-1a _a a 4-) _a a -Li 4_1

-H I - C.) I C.) C.)O c-) 4-I C 4-) C.) W J.--) CD a) >,

rcs -(-1 rt - I—I 3 a 1--) )--)• W Ca) oa)a ova ow a COQ 0 a) ..a ..c -H 0

57

14-1

0

0.4 04 04 04 04c)-1

tN

c

CD Hi

0

0 HIIn I Lc-) In I

Ln

Ill IcN X (NZ

CN

C

- - - - - _0 0 0 0 CD C>C-1 Cr) r"--- r- r-- r--(N (N\I Cn1 CV (N (N (N (N CV CV CV

58

PERRECORDINGEQUIPMENT

INJECTIONWATER

PUM P

•••

PACKER-

MULTIPLE THERMISTORSTRING (MOVABLE)

INJECTIONLINE

1i 7-111E RM *TOR

4-.--•SU9MERSI8LEPUMP

..

PUMPEDWELL

H-3

.11n•nnn

THERM ISTORS

SAMPLINGWELL

H-2

INJECTIONWELL

M- 1

NERATOR

TUBULAR, HEATER

Figure 5.1. Three-hole Recirculation Heat Tracer TestConfiguration. (After Flynn, 1985)

M-1

59

74.7—

.--...E

76.2—=--4-1

o_ia)-o

77.7—

#1 *

,

# 3 *

heater

* denotesthermistor

Figure 5.2. Location of Thermistors in M-1 for All Tests.

60

In H-2 a multiple thermistor string was approbriateiv

positioned to monitor temperature changes in an interval of

interest. Figure 5.3 shows the location of the thermistor

string in tests 1 and 2, and Figure 5.4 shows the same for

tests 3 through 5. In tests 1 and 2, thermistors 7 through

14 were located in or near the fault zone. The same was true

for thermistors 14 through 20 in tests 3 through 5. This

multiple thermistor string, operated from the surface by a

data-logger control system, enabled rapid point temperature

measurements over a 19 in interval without disturbing the

surrounding flow system. Flynn (1985) gave a complete

description of the multiple thermistor string and data-logger

control system. An inflatable packer was positioned in the

cased portion of H-2 (= 9 in BLS) above the thermistors. The

packer dampened hydraulic effects caused by pumping.

A pump was positioned in borehole H-3 at a depth of

85 in BLS. The discharge pipe connected to the pump allowed

water to be recirculated back to M-1. A thermistor was

placed above the pump (= 82.3 m BLS) to monitor temperature

in the pumped borehole.

Inflatable packers were placed in the cased portions

(= 9 in BLS) of all nearby boreholes to minimize their hy-

draulic influence.

The following description of the field test is from

Flynn (1985). In general, the three-borehole recirculation

72.5

4 73.55 74.16 74 .7

97&.5---------

7 5.3 8 75.9

10!77.1

1 78.0

13? 799

;

16 83.2

7

H-2 M-

61

65 m —

70 m —

HPFM— — CL SHPT

thermistor

75 m —

80 m

85 m — 1

pump

—heater

Figure 5.3. Location of Heater, Pump, and Thermistors durincjTests 1 and 2.

62

FHPFNi— GL SHPT

* thermistor

65 m -

depth,m

1 631

24 64.9

43 66:L. 67::

5'N- 68.06k- 68.67!* 69.28 69.891)e 70.4

10i, 71.0

11 71.9

12 72.8

131 73.8

75.0

70 m -

74,7

76.2—heater

—

77.7

80 m -

85 m

pump

Figure 5.4. Location of Heater, Pump, and Thermistors during

Tests 3-5.

63

heat tracer experiments involved two phases. (1) Borehole

water was heated in M-1 under static flow conditions at a

depth of about 76 T BLS. When the difference between the

temperature at the heater and ambient groundwater temperature

(temperature measured in M-1 just prior to heating) was at

least 25 °C, the heater was turned off and the pump turned on

in H-3. Recirculation of the pumped water was started immeo-

lately and supplemented by an additional surface supply to

rapidly achieve constant head in the injection borehole M-1.

Flowrate from the pumped borehole H-3 was monitored on the

surface. (2) When the temperature at thermistor #2 (76.2

BLS) in M-1 approached the initial ambient value, heated

water (stored in a trough on the surface) was injected at a

controlled rate at the same depth as the heater. A

gasoline-powered pump with a flow regulator was used to

inject the heated water.

Temperature measurements were taken in H-2 until the

tail of the second heat pulse became evident. Measurements

of depth to water were taken periodically in all boreholes

throughout the test.

5.2 Field Results

In this section the pertinent results of each of the

five heat tracer experiments are discussed. These results

include the temperature responses in boreholes M-1 and H-2

and the depth to water measurements taken in borehole H-3.

64

Results from tests 1 through 4 are included for combler ,, -

ness. Test 5 is used in the computer studies; hence, the

results are discussed in greater detail.

5.2.1 Test 1

Test I consisted only of phase 1 (see section 4.2).

Figure 5.5 shows the temperature response in M-1 resulting

from heating under static conditions. In tests 1 through 4,

temperature responses reported in M-1 were taken at ther-

mistor #2 (76.2 in BLS). Unless otherwise indicated, the time

represented by zero on all figures refers to the time when

the heater was first turned on. No record of background

temperature measurements prior to heating is available for

test 1. In general, the temperature increased until the

heater was turned off and the pump was turned on in H-3.

This corresponds in Figure 5.5 to the first temperature

peak. During test 1 the heater was turned on a second time,

after recirculation of borehole water had commenced. This

caused the second temperature peak to develop.

The temperature response in H-2 at thermistor #9

(76.5 in BLS) is graphed in Figure 5.6. This thermistor was

located at about the same depth as the heater, both of which

were near the top of the fault zone. This plot shows that

the temperature in H-2 decreased after the pump was turned on

in H-3. This is contrary to the results of later tests, and

to this date is unexplained. The temperature in H-2

50.0

65

40.0

d

_30.0

/

ci)o_

20.0 •— n

CDH- 10.0

0.0 0.0

heater offpump on heater on

111,1,111mill

100.0 200.0 300.0 400.0 500.0

Time, minutes

Figure 5.5. Temperature Response at Thermistor #2 in M-1(Test 1).

21.50

CD21.30

HI/

ia)

-t-j) 21.10 —

20.90

66


20 .70 1111111111111!IIIIII0.0 200.0

400.0 600.0

Time, minutes

„ f 1800.0

Figure 5.6. Temperature Response at Thermistor #9 in H-2(Test 1).

67

increased later in the test, possibly due to the re-activa-

tion of the heater.

Figure 5.7 shows the water level response in H-3

during pumping.

5.2.2 Test 2

Test 2 also consisted only of phase 1. The temper-

ature response in M-1 due to no-flow heating is shown in

Figure 5.8. A single temperature measurement of 21.5 oc at

thermistor #2 was taken prior to heating and was assumed to

be ambient. Similar to test 1, the heater was re-activated

during recirculation. However, during test 2, no second

temperature peak was recorded, a phenomenon that remains

unexplained (problems with the recording equipment are

suspected).

Figure 5.9 shows the temperature response at

thermistor #9 (76.2 m BLS) in H-2. In contrast to test 1,

the temperature increased in H-2 in response to pumping in

H-3. However, the increase appears to have started just

prior or immediately upon the start of pumping, which is

inconsistent with results of later more controlled heat

tracer experiments. The same is true about the oscillations

that follow. We again suspect the possibility of noise in

the electronic system.

heater offpump on

, I 11111 11111

80.0

68

L_40.0

0

20.0 ---11

0-Q.)

0.0 I0.0 100.0 200.0

Time, minutes300.0 400.0

Figure 5.7. Depth to Water in H-3 (Test 1).

40.0

7

_ 30.0CD

o20.0

cu

Q)I— 10.0

1

•=1

50.0

69

-_- heater offH pump on heater on1 r0 .0 i 1 11111,141,,,,,1 1 [1111111[ 1 1,11,7—m7

0.0 100.0 200.0 300.0 400.0Time, minutes


21.60

121.50

CD21.40

1

D21.30 1L_

1L_00_21.20

(1.)

21.10 1

70


2 1.00 1 ill(111I111 I I I IIIIIIIIIIT11 I11 -10.0 100.0 300.0 400.0

Time, minutes


71

The depth to water measurements from H-3 are shown in

Figure 5.10. As seen, recovery was monitored for a short

period of time.

5.2.3 Test 3

Test 3 was the first to consist of both phases 1

and 2. Figure 5.11 shows the temperature response recorded

in M-1. An ambient temperature of 21 °C was listed in the

field notes. The first temperature peak was the result of

heating under static conditions (phase 1). The second

temperature peak was created during phase 2 due to injection

of heated water from the surface.

The temperature response at thermistor #15 (76.2 m

BLS) in H-2 is plotted in Figure 5.12. Background temper-

atures in H-2 prior to thermal breakthrough as well as later

appear to decrease linearly, as shown by the dotted line.

This decrease, noticed also in later tests, has been attrib-

uted by Silliman (unpublished manuscript) to a systematic

error in the electronic output. Superimposed on this drift

is a distinct peak immediately after the heater is turned off

and the pump turned on. This virtual step increase in

temperature reappears later in tests 4 and 5, and we consider

it to be the most prominent and interesting feature of the

entire test sequence. Much of our attention will therefore

focus on attempts to reproduce this rapid temperature in-

crease by means of a theoretical model.

72

60.0 —

boreholerecovery

o

20.0 —o

heater offpump on pump off

0.0 It ii t I I t tit, ii j till ti0.0 100.0 200.0 300.0 400.0

Time, minutes

Fic:ure 5.10. Depth to Water in H-3 (Test 2).

Il45.0 -

Q 35.0 -

o_E 25.0 -Q-)

73

heater off inject

pump on start stop

15.0 11111i1j111111111[11111111I I IIIIIII lui0.0

100.0

200.0 300.0

400.0Time, minutes

Figure 5.11. Temperature Response at Thermistor #2 in E-1(Test 3).

heater off inject

pump on start stop

100.0 200.0 300.0Time, minutes

II I !' ill I I I I I I ....1400.0

21.10 -

21.05 =

CD21.00 =

74

D 20.95 =

(i)0_20.90

F-20.85 =

20.80 -0.0


75

In Figure 5.12, the peak recedes toward the downward-

drifting background temperature as time progresses. We shall

refer to it as the "early breakthrough."

Figure 5.12 does not show a thermal breakthrough in

response to the second thermal pulse, a phenomenon that

remains unexplained (possibly due to low injected water

temperature).

The water level response in H-3 is shown in Figure

5.13. As in tests 1 and 2, the water level continued to drop

throughout the entire pumping period.

5.2.4 Test 4

Test 4 consisted of both phases 1 and 2. Figure 5.14

indicates the temperature response in M-1 during the entire

test. No record of background temperature measurements is

available for this test.

During test 4 problems were encountered with the pump

tubing, causing a 2-1/2 hour down-time. The exact effect of

this down-time on the thermal conditions can only be surmised

as temperature was not recorded in M-1 (see dotted line in

Figure 5.14). Once pumping was re-established for about 30

minutes, injection of heated surface water commenced (phase

2), resulting in the second temperature peak in Figure 5.14.

The temperature response at thermistor #15 (76.2 m

BLS) in H-2 is shown in Figure 5.15. The rising limb of the

first thermal breakthrough was recorded immediately upon

^

80.00-4

-1

,

]

,

60.00...i

,

-

40.00 --,

1

ii

20.00-

-

-

-

-

0.00 ,

heater offpump on

76

, , i , , , i n ,,,,,,,,,,,,,.,.,0.00 100.00 200.00 300.00

Time, minutes


77

60.0 -17

50.0 ,

40.0Q.)L._.

__ k \_ ---_ PP\

\-1

0 1 \30.0

L) _.10_ -E

_4-

Q)I--- 20.0 _ heater offpump on inject

1 f start stop

--1 , pump off pump on.i Iill111 I l 11!llti[1 111111IIITI - 1111 1111111f1 HITIfillIfilfIfilll,10.0 I

0.0 00.0 200.0 300.0 400.0 500.0 600.0Time, minutes


21.20

78

CD-

D 21.00N\svL_

Q.)o-

20.901--- heater off inject

pump on on off

pump off pump

20.80 ;

0.0 200.0 400.0

Time, minutes600.0


79

down-time and the commencement of pumping. Furthermore,

after the pump was shut off, the temperature in H-2 continued

to decrease at about the same rate as during pumping. After

pumping resumed, a second step increase in temperature was

observed.

Figure 5.16 shows the water level response in H-3.

Water levels during pump shut down were not recorded and are

therefore shown by a dotted line.

5.2.5 Test 5

Test 5 again consisted of both phases 1 and 2. The

field notes from this test are more clear and complete than

those of previous tests. In addition, test 5 progressed

without apparent problems and was considered the most

straightforward to simulate. For these reasons, the computer

studies conducted in this thesis focus on test 5. In

preparation for these computer studies, the results of test 5

are discussed here in somewhat more detail than those of

tests 1-4.

The test configuration is shown in Figure 5.4 rela-

tive to the location of the fault zone. Figure 5.17 shows

the temperature response in M-1 at all three thermistors for

the entire test. An ambient temperature of approximately 21

°C was measured at each thermistor just prior to heating.

The temperature responses at thermistors #2 and #3, or some

combination of the two, may indicate the intake temperatures

-

04-) 20.00

0-

80.00 7

-11

80

60.00

(1)

heater offpump on

ci)pump off pump on

0.00 ITT (111111.11111j I 1 11111111111 I0.0 100.0 200.0 300.0 400.0 500.0 600.0

Time, minutes


81

60.0—, G-4-0-0-0-0 thermistor 1 r4.7 m BLSA-0-0,4-0-4 thermistor 2 76.2 m BLSae4aia.e0 thermistor 3 77.7 m BLS

-

]

10.0 li III IIII li IIIII1 IIIIIIIIIITi1-111II III II Ili0.0 100.0 200.0 300.0 400.0

Time, minutes

Figure 5.17. Temperature Responses at Thermistors #1, #2, #3in M-1 (Test 5).

heater off inject

pump on start stop

82

to the fault zone.In this thesis, the response at #2 is

used; however, based on the results herein it appears that

the response at #3 may better represent the intake tempera-

tures. The two temperature peaks on each curve are the

result of these two successive phases.

The measured temperature responses at thermistors 14

through 20 in H-2 and their arithmetic average are plotted in

Figure 5.18. The dotted line through the data illustrates

possible drift in the electronic output. The steep temper-

ature increase during early breakthrough is now seen to occur

not only at thermistor #15 but also above and below at #14

and #16. The breakthrough is not seen at thermistors #18-20,

which suggests that heated water may be exiting into H-2 only

through the upper portion of the fault zone during early

breakthrough. However, the second breakthrough occurs at all

thermistors, which may suggest that the injection of heated

water in M-1 causes hot water to propagate through a thicker

portion of the fault zone. Note that temperature measure-

ments in H-2 started about 45 minutes after the heater was

turned on in M-1. Figure 5.19 shows the thermal breakthrough

at thermistor #15 (76.2 m BLS).

Figure 5.20 shows temperature change in H-2 with

depth, Tb being the temperature just Prior to early break-

through. The early rise in temperature in thermistors above

the top of the fault zone, and the oscillatory nature of the

21.60

21.20

_20.80

15)L. 20.40

I— 20.00

100.0 200.0 .300.0 400.0 500.0Time, minutes

19.600.0

83

#20, 82.3 m

#17, 78.3 m

#18, 79.6 rn

#15, 76.2 m

average

#16, 77.1

#14, 75.0

#19, 81.1

rn

m

m

Figure 5.18. Temperature Responses at Thermistors 14-20 inH-2 and Their Arithmetic Average (Test 5).

21.15

84

heater off inject

pump on start stop

21.10

Cp 21.05

L_21.00

-4E5)

0_20.95

20.90

20.85 0.0 100.0 200.0 300.0 400.0 500.0

Time, minutes


time after pumping started25 minutes

0 0 0 0 0 295 minutes0-e-e49-e 365 minutes

jI iii ï ï ii III I I 11111 I ï II

-60.0

--65.0

--70.0

--75.0

(1)c]

--80.0 =

—85.0

—90.0 I

85

—0.05 —0.00 0.05 0.10 0.15 0.20 0.25T — Tb, C

Figure 5.20. Temperature Variation with Depth in H-2(Test 5).

86

temperature there at later times (both observed also in

previous tests) are attributed by us to the rise in hot water

due to buoyancy in H-2.

The water level response in H-3 is shown in Figure

5.21. As in previous tests, the water level continued to

fall during the entire test.

40.00 —

-

U)

LQ5 30.00-4--,ci)

E-1

..n

87

-

-

-

-

-

heater offpump on

0 .00 , , II (I IlIffi1I11111111 I10.0 100.0 200.0 .3061.0 406.0

Time, minutes


88

CHAPTER 6

MODELING PROCEDURE

In Chapter 4, we presented information about the

fault zone in which the heat tracer tests were conducted,

based on geophysical logs and hydraulic tests. We visualize

1- he Tovement of water and the convection of heat between the

boreholes to occur primarily through this subhorizontal fault

zone, which is embedded in a less permeable rock continuum.

Chapter 5 described the heat tracer test field procedure and

presented the results of each test. These results pointed to

the consistent appearance of a steep temperature increase

near and above the top of the fault zone in borehole H-2

immediately upon the onset of pumping in H-3. In this chap-

ter, we present the modeling approach used to numerically

simulate this thermal response.

6.1 Adaptation of Conceptual Model for Numerical Simulations

For simplicity, we model the fault zone as a hori-

zontal porous medium ("aquifer") of uniform thickness (Figure

6.1). Based on past tracer experiments we start by assigning

to this aquifer a kinematic porosity of .10. The permea-

bility of this aquifer is estimated using the procedure in

Appendix B and on K values from single-hole packer tests in

(not to scale)

Figure 6.1. Idealized Diagram Showing Fault Zone and Bore-holes.

89

90

the fault zone (Hsieh, 1983), which range in value from 10 -13

to 10 -14 m 2 . The fault zone is bounded on top and bottom by

fractured granites that we model as low permeability rock

continua within which fluid flow is negligible. Early simu-

lations, conducted to evaluate heat movement by conduction

under static flow conditions during phase 1, are fully three-

dimensional. Later simulations allow only horizontal flow

and heat movement in the fault zone with vertical conduction

(leakage) of heat into the confining rock.

6.2 Heat Conduction during Phase 1

The first stage of the analysis consisted of three-

dimensional simulation of heat conduction from the heated

area in M-1 during the no-flow conditions of phase 1. For

this, an axisymmetric three-dimensional model was designed of

which a vertical section is shown in Figure 6.2. Based on

the geophysical and hydraulic data presented in Chapter 4,

the fault zone is assigned a uniform thickness of approxi-

mately 7 m and is located just below the heater. A simula-

tion was conducted by keeping the temperature at the heater

(auxiliary element in Figure 6.2) at the peak temperature

recorded in thermistor #2 (T = 52 °C, Figure 5.17). After 90

minutes of heating, the isotherm representing a .005 °C

temperature increase (approximately equal to the resolution

limit of the thermistor) in the surrounding rock formation is

91

exgwal

FAULTZONE

Figure 6.2. Axisymmetric Finite Difference Grid Used toModel Heat Conduction During Phase 1.

92

located less than 1.5 meters from M-1. This demonstrates

that heat travels only a short distance by conduction during

phase 1, and no measureable temperature increase is to be

expected in the rock near H-2 prior to pumping from H-3.

That PT correctly simulates heat conduction under similar

conditions has recenity been verified by Woloshun (personal

communication). She is currently investigating the possi-

bility that convection might play a role during phase 1, but

this will not be considered in the present thesis.

6.3 Borehole Model

The temperature responses at the three thermistors in

M-1 (Figure 5.17) suggest some ideas about the flow pattern

in the borehole during phases 1 and 2. The much greater re-

sponses at thermsitors #1 and #2 than at the deeper thermis-

tor #3 suggest that hot water migrates upward in M-1 during

phase 1. This situation is clearly reversed during phase 2,

as evidenced by the rapid temperature decrease at thermistors

#1 and #2 together with the virtual step increase and ensuing

decrease at thermistor #3. This supports the notion

reflected in Figure 5.4 that the heater is located at the

top, or above, the water intake area of the fault zone. An

attempt was made to reproduce these responses by simulating

static heating (phase 1) and the subsequent downward flow in

the borehole (phase 2), but the results were not satisfactory

and hence are not reported. Some of the difficulties are

93

attributed to non-uniform flow in the borehole and the

virtual certainty that the thermistors were in contact with

the borehole walls.

6.4 Quasi-Three-Dimensional Model

To save computer time and storage we simulate phases

1 and 2 by allowing convection and conduction to take place

in the horizontal plane of the fault zone but only vertical

heat conduction in the low permeability rock above and below.

Horizontal processes are simulated using the finite differ-

ence grid shown in Figure 6.3. Vertical heat conduction in

PT is handled using a semi-analytical method presented by

Vinsome and Westerveld (1980). In general, this method

enables heat leakage to be accounted for by solving a series

of algebraic equations, which is easily done on a computer.

Boundaries are placed sufficiently far away so as to minimize

their impact on computed thermal breakthroughs. Boreholes M-

1 and H-3 are enlarged to show the discretization. Borehole

H-2 is not physically represented but is located in the

blackened cell.

Inclinometer data indicate that the boreholes devi-

ated from the vertical. The distances between the boreholes

in Figure 6.3 are corrected for such deviations.

A porosity (D) of .10 is used in all simulations. A

brief sensitivity analysis on the effect of changing (D , is

performed in the final set of simulations.

94

Arvagri. 411WA-n*Iglbstsaitt64111 Viii1111.111• _4"4.112.-nn

Figure 6.3. Finite Difference Grid Used in Quasi-three-dimensional Model.

95

Two geometric grid parameters are varied in the simu-

lations. The thickness (b) is varied between 1 m, 10 cm,

1 cm, and 1 mm. The grid width (gw), defined as the maximum

distance from the center line to the arced grid line, is also

varied. Initially, it corresponds to the entire grid in

Figure 6.3. Later, it reduces to coincide with the darkened

arced grid lines A (grid width = 14 m) and B (grid width =

.7 m) in the same figure. This is done by assigning very low

permeabilities (around 10 -25 m 2 ) to cells outside the dark-

ened arcs. The permeability of the flow region beneath the

arced grid line is assigned using the method in Appendix B.

The parameters thickness and permeability (k) are varied in

such a way to keep the transmissivity constant in each grid

width case. The values of T vary from 6 x 10 -6 m 2/s for the

the entire grid to 9 x 10 -5 m 2 /s for the smallest width

value. The corresponding hydraulic conductivity values

correlate well with corrected values (Depner, 1985), deter-

mined in the fault zone by the single-hole packer tests. The

thermal conductivity (K c ) of the confining rock is also var-

ied to approximate the effect of thermal dispersion.

In our current model of the fault zone, the effects

of thermal dispersion are neglected. Marsily (1986) defines

the thermal Peclet number as

qlP e thermal = (6.1)

KT/pc

where

q =

1 =

KT =

96

Darcy velocity

mean grain diameter

isotropic thermal conductivity

so that at large P e the effect of heat convection dominates

heat conduction. Sauty (1978) observed on a field scale that

macrodispersivity (due to large scale heterogeneities)

dominates conduction. We will show later that increased

vertical heat leakage from the fault, which acts in a manner

similar to thermal dispersion, does not aid in reproducing

the observed results.

A detailed discussion of the sensitivity analysis

performed involving the parameters b, gw, k, and K c is

given in Chapter 7. The remainder of this chapter discusses

the methods employed to prescribe the time varying pressure

and temperatures at M-1 and H-3.

6.5 phase 1 (No-Flow Heating in M-1)

Phase 1 consists of ninety minutes of heating in

borehole M-1 under static conditions. The following section

describes how the pressure and temperature conditions at M-1

are approximated.

97

6.5.1 Boundary Conditions at M-1

Accurate approximation of the prevailing boundary

conditions is crucial to the success of a numerical modeling

study. Much effort in this study focuses on developing an

appropriate method to simultaneously prescribe the tempera-

ture and pressure boundary conditions at borehole M-1.

During phase 1 the pressure head in M-1 remains con-

stant at its static value. Therefore, a constant pressure

head boundary condition is prescribed along the interface

between the borehole M-1 and the fault zone (Figure 6.4).

This is accomplished by introducing an element external to

the flow system, in which the pressure head is kept at the

specified constant value. This external element is connected

to internal elements along the appropriate boundary. A large

storage capacity is assigned to this external element to

prevent changes in pressure head due to mass outflow. In

addition, a large permeability value (10 20 m 2 ) is assigned to

effect immediate equilibration in pressure head between the

external element and the connected elements within the flow

domain.

Recall the temperature response at thermistor #2 in

M-1 during no-flow heating in test 5 (Figure 5.17). For the

purpose of modeling, the measured temperature is imposed on

the rock immediately surrounding the borehole. The inclined

internal heat source cellsaround 1V---1

externalceH

(constant head)

dotted line represents interface betweenborehole and fauit zone

Figure 6.4. Schematic Diagram Showing Cell Network AroundM-1.

98

99

nature of M-1 suggests that the heater was probably resting

against the borehole, which supports this approach.

To match the measured temperature response, heat is

generated in elements located adjacent to the borehole

(Figure 6.4). This is done by specifying a constant specific

enthalpy Tfcf (Tf and Cf being the temperature and specific

heat of the injected fluid, respectively) as required by PT,

and a time varying mass injection rate Gf(t) within each

element. The heat produced in an element per unit time is

then

Q ( ) = G f(c)• Tf Cf . (6.2)

The mass injection rate is kept small (around 10 -20 kg/sec)

so as not to affect the prescribed pressure boundary condi-

tion. Gf(t) is assigned on the basis of trial-and-error runs

until the computed temperature is within +0.25 ct of the

observed temperature. Figure 6.5 shows an example of a

typical match between computed and measured temperature

responses.

By imposing the temperature response at thermistor #2

on the rock surrounding to the borehole, we implicitly assume

that the fault zone is located directly adjacent to the heat-

er (Figure 6.6) Since there are no temperature measurements

at the apparent depth of the fault zone, the above method is

60.0 --

_

50.0 --

-

U

-

-

-

_ 40.0 -

L_L)

-

^_-o 30.0 :L)Q-

E0.)

H- 20.0-

phase 2

fi eld resultsgeeee4D numerical results

100

phase 1

heater off injectpump on start stop

10.0 I m, n ., ,,,,,,,,,,,111, 11,, I i! flifl- i r, [ r I 0.0 1 00.0 200.0 300.0 400.0

Time, minutes

Figure 6.5. Typical Match Between Computed and MeasuredTemperature Responses in M-1.

boreholeM-1

101

(not to scale)

FAULT ZONE

heater

Figure 6.6. Idealized Diagram Showing Relative Location ofHeater and Fault Zone.

102

adopted as the first approximation. We realize this may

overestimate the amount of heat that enters the fault zone.

6.6 Phase 2 (Pumping from H-3 and Injection into M-1)

Phase 2 of the heat tracer experiment consists of

pumping from borehole H-3 at a rate of 2 gpm. The water

removed by this pumping is recirculated back to M-1 to

rapidly fill the borehole. In addition, heated water is

injected at approximately 76.2 m BLS in M-1. The methods

employed to prescribe the boundary conditions in both M-1 and

H-3 are now discussed.

6.6.1 Boundary Conditions at M-1

During phase 1, a constant head boundary with heat

generation prevails in M-1. During phase 2, recirculation of

pumped water causes the water level in M-1 to rise rapidly to

the surface (=7 minutes) and eventually overflow. This over-

flow continues for the duration of the experiment. There-

fore, during phase 2, a constant head boundary is again

assigned to M-1. The pressure head assigned is that which

results from the column of water extending from the surface

down to the depth at which the heater is placed. This is

accomplished in exactly the same manner as described

earlier.

The temperature response in M-1 during phase 2 due to

the injection of heated water is shown in Figure 5.17. Once

103

again, this temperature response is prescribed in the rock

formation just adjacent to the borehole. This is accomp-

lished using precisely the same method described earlier.

6.6.2 Boundary Condition at H-3

As mentioned, water is pumped from borehole H-3

during phase 2 at an approximate rate of 2 gpm. Figure 5.21

shows the time variation in water level in H-3 during

test 5.

To simulate pumping from H-3, an external element is

connected to the elements surrounding H-3 (Figure 6.7), in

which a time-varying mass extraction rate is assigned (=2 gpm

= .13 kg/sec) by trial-and-error (until the computed and

measured water levels are within + 0.20 meters of each

other). A large permeability value is also assigned, allow-

ing the prescribed pressure decline in the external element

to propagate immediately into the internal elements. In

addition, an appropriate borehole storage coefficient is

assigned to the external element to preserve mass balance in

the borehole. The method used to determine the parameters

required to define the borehole storage coefficient is given

in Appendix C. Figure 6.8 shows a typical match between the

computed and measured water levels.

externalcell

(moss sink)

internal cellsaround H-3

dotted line represents interface betweenborehole and fault zone

Figure 6.7. Schematic Diagram Showing Cell Network AroundH-3.

104

4-0-4-4-4-* field results0 e.0„9.0.,9 numerical results

0

-4-j 10.00

_E

heater off(1) pump ono

100.0 200.0 300.0Time, minutes

0.000.0 400.0

Figure 6.8. Typical Match Between computed and MeasuredWater Levels in H-3.

105

106

CHAPTER 7

SENSITIVITY ANALYSIS

The sensitivity analysis focuses primarily on the

effect of changes in fault zone thickness and grid width.

During the final set of simulations, the porosity of the

fault zone and thermal conductivity of the confining rock are

also varied.

Table 7.1 gives the initial value of each parameter

varied in the analysis. The first simulation assumes the

fault zone is fully open to flow. A fault zone thickness of

1 m corresponds approximately to that which is suggested by

the heat pulse flowmeter test results in M-1. The value of

the thermal conductivity of the confining rock is represen-

tative of granite (Carslaw and Jaeger, 1959). The program PT

was run using the parameters given in Table 7.1. Under these

conditions, the computed temperature response in H-2 shows no

significant temperature increase throughout the heat tracer

test (Figure 7.1). This suggests the need to shorten the

travel time of the thermal plume between M-1 and H-2 to

diminish the amount of heat that dissipates. This is done by

reducing the fault zone thickness.

Two additional simulations are performed with thick-

ness values of 1 cm and 1 mm. The fault zone remains fully

Table 7.1. Initial parameter values.

Parameter Value

1.0 m

c:v7 74 m

(1) .10

6.5 ): 10 -13 m 2

K c 2.9 J/m.sec.°C

107

thickness of fault zone1.00 meter0.01 meter

-J 46-4-4.4 0.001 meter

-2,

22.50

22.00o

108

20.50 10.0

heater offpump on

IIIIIIIII 1111111,11[1111[111111

100.0 200.0 300.0Time, minutes

400.0

Figure 7.1. Computed Thermal Responses in H-2 (gw = 74 m).

109

open to flow and the values of'0 and K c remain the same as

before. However, to keep the transmissivity constant, the

permeability values are incr

Date post:	27-Jan-2021
Category:	Documents
Upload:	others
View:	2 times
Download:	0 times

Computer studies of heat tracer experiments in fractured rock · Tprtr Rpn t Thrtr , 2, n (Tt 8.....

Documents