University of Auckland New Zealand Geothermal Group Department of Engineering Science Computer...

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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

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

A partitioning model for gas tracers

independent variable

Harvey empirical correlation of Henry’s constant

calculated assuming ideal gasbehavior:

calculated from a standard empiricalcorrelation

ggg RT

Liquid mass fraction (Henry’s Law):

Vapor mass fraction:

A partitioning model for gas tracers - Harvey correlation

355.0*

11lnln

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

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

A partitioning model for liquid tracers

jlX independent variable

mixture

calculated from a standard empirical correlation

Liquid mass fraction:

Vapor mole fraction:

activity coefficient;calculated from the Wilson model

j vpll Px0

mass fractionmole fraction

A partitioning model for liquid tracers - Wilson’s model

)ln()ln( lwlwwwlwll

xxxxxxRTg

xxRTg lnln

Molar excess Gibbs free energy:

Wilson’s binary mixture two-parameter model:

binary interaction parameters

A partitioning model for liquid tracers - Wilson’s model

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

A partitioning model for liquid tracers - application

Wilson models of the molar excess Gibbs free energy

n-propanol

methanol

Mixture lw

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

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

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:

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

Qualitative results - gas tracersSF6 R-12

Following injection

100days

Qualitative results - liquid tracersTritiated water Methanol

Following injection

100days

n-Propanol

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

Acknowledgements

• Mike Adams (EGI Utah)• JAPEX Geoscience Institute

University of Auckland New Zealand Geothermal Group Department of Engineering Science Computer...

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