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