University of AucklandNew Zealand

Geothermal GroupDepartment of Engineering Science

Computer Modelling of Gas and Liquid Tracers in

Geothermal Reservoirs

Mark Trew

Colin Harvey

Michael O’Sullivan

Errol Anderson

Karsten Pruess

University of AucklandNew Zealand

Geothermal GroupDepartment of Engineering Science

Introduction

• Scope and aim of research • Gas and liquid tracers• Partitioning models

– Gas tracers: Henry’s Law and the Harvey (1996) correlation for Henry’s constants

– Liquid tracers: Wilson’s model of the molar excess Gibbs energy

• Implementation in TOUGH2• Test problem

University of AucklandNew Zealand

Geothermal GroupDepartment of Engineering Science

A partitioning model for gas tracers

)(2

TC

P

M

MX

H

g

OH

gg

ii

i

independent variable

Harvey empirical correlation of Henry’s constant

s

N

j g

gg

g

j

i

iY

1

calculated assuming ideal gasbehavior:

calculated from a standard empiricalcorrelation

a

ggg RT

PM i

ii

Liquid mass fraction (Henry’s Law):

Vapor mass fraction:

University of AucklandNew Zealand

Geothermal GroupDepartment of Engineering Science

A partitioning model for gas tracers - Harvey correlation

)()(2

TMTR

TCOH

saH

41.0*

1

*

355.0*

*

*

11lnln

T

eC

T

TB

TAPC

T

sH

Harvey (1996) empirical correlation of Henry’s constant for the entire temperature range:

Sample data from gas distribution coefficient:

regression of gasdistribution coefficient

baT log

University of AucklandNew Zealand

Geothermal GroupDepartment of Engineering Science

A partitioning model for gas tracers - application

SF6 R-12 R-123

Tracer A B C

SF6 -27.8787 0.8698 31.5000R-12 -23.5424 1.9532 25.8484

R-123 -17.5548 0.6613 20.2303

Linear least-squares fit of Harvey function to gas distribution coefficient regression data

University of AucklandNew Zealand

Geothermal GroupDepartment of Engineering Science

A partitioning model for liquid tracers

jlX independent variable

mixture

jljj

jvp

vpll

l P

Pxy

calculated from a standard empirical correlation

Liquid mass fraction:

Vapor mole fraction:

activity coefficient;calculated from the Wilson model

l

jljj

N

j vpll Px0

mass fractionmole fraction

University of AucklandNew Zealand

Geothermal GroupDepartment of Engineering Science

A partitioning model for liquid tracers - Wilson’s model

)ln()ln( lwlwwwlwll

E

xxxxxxRTg

wwll

E

xxRTg lnln

Molar excess Gibbs free energy:

Wilson’s binary mixture two-parameter model:

binary interaction parameters

University of AucklandNew Zealand

Geothermal GroupDepartment of Engineering Science

A partitioning model for liquid tracers - Wilson’s model

l

l

j

k

l

ji

N

kN

j kjl

kilN

jijll

x

xx

00

0

ln1ln

Activity coefficients for a multi-component mixture(using binary interaction parameters):

University of AucklandNew Zealand

Geothermal GroupDepartment of Engineering Science

A partitioning model for liquid tracers - application

Wilson models of the molar excess Gibbs free energy

n-propanol

methanol

Mixture lw

wl

methanol-water 0.2053 1.4510n-propanol-water 0.0154 0.7002

University of AucklandNew Zealand

Geothermal GroupDepartment of Engineering Science

Implementing partitioning models in TOUGH2

Mass fraction calculations:(1) gas tracers in liquid phase(2) gas tracers in vapor phase(3) water in liquid phase(4) water/liquid tracers in vapor

phase

ji lg XPTP ,,,Compressed liquid

ji lg XPTP ,,,Superheated vapor

ji lgvv XPSP ,,,Two-phase mixture

Determinephasestate

Calculatethermodynamicproperties ofcomponents

Sequence of calculations in the TOUGH2 equation of state (EOS):

Independent variables for each phase state:

University of AucklandNew Zealand

Geothermal GroupDepartment of Engineering Science

Qualitative results - test problem

• Isotropic reservoir: 1 km3, = 0.1, k = 10-14 m2

• Two-phase convective fluid flow

200ºC 10% vapor saturation

• 3374 computational blocks• 100 kg of each tracer

injected for 20 minutes into central region

Steady-statesolution

University of AucklandNew Zealand

Geothermal GroupDepartment of Engineering Science

Qualitative results - gas tracersSF6 R-12

Following injection

100days

R-123

University of AucklandNew Zealand

Geothermal GroupDepartment of Engineering Science

Qualitative results - liquid tracersTritiated water Methanol

Following injection

100days

n-Propanol

University of AucklandNew Zealand

Geothermal GroupDepartment of Engineering Science

Summary and conclusions

• Partitioning models have been developed for gas and liquid tracers

• The models have been implemented in a TOUGH2 equation of state

• Qualitative test results show the predictive and interpretative value of the models

• Further work:– determine mixture values for more tracers– continue to test models by matching recorded tracer

returns

University of AucklandNew Zealand

Geothermal GroupDepartment of Engineering Science

Acknowledgements

• Mike Adams (EGI Utah)• JAPEX Geoscience Institute