university of auckland new zealand geothermal group department of engineering science computer...
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![Page 1: University of Auckland New Zealand Geothermal Group Department of Engineering Science Computer Modelling of Gas and Liquid Tracers in Geothermal Reservoirs](https://reader036.vdocuments.mx/reader036/viewer/2022070400/56649f115503460f94c23c60/html5/thumbnails/1.jpg)
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
![Page 2: University of Auckland New Zealand Geothermal Group Department of Engineering Science Computer Modelling of Gas and Liquid Tracers in Geothermal Reservoirs](https://reader036.vdocuments.mx/reader036/viewer/2022070400/56649f115503460f94c23c60/html5/thumbnails/2.jpg)
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
![Page 3: University of Auckland New Zealand Geothermal Group Department of Engineering Science Computer Modelling of Gas and Liquid Tracers in Geothermal Reservoirs](https://reader036.vdocuments.mx/reader036/viewer/2022070400/56649f115503460f94c23c60/html5/thumbnails/3.jpg)
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:
![Page 4: University of Auckland New Zealand Geothermal Group Department of Engineering Science Computer Modelling of Gas and Liquid Tracers in Geothermal Reservoirs](https://reader036.vdocuments.mx/reader036/viewer/2022070400/56649f115503460f94c23c60/html5/thumbnails/4.jpg)
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
![Page 5: University of Auckland New Zealand Geothermal Group Department of Engineering Science Computer Modelling of Gas and Liquid Tracers in Geothermal Reservoirs](https://reader036.vdocuments.mx/reader036/viewer/2022070400/56649f115503460f94c23c60/html5/thumbnails/5.jpg)
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
![Page 6: University of Auckland New Zealand Geothermal Group Department of Engineering Science Computer Modelling of Gas and Liquid Tracers in Geothermal Reservoirs](https://reader036.vdocuments.mx/reader036/viewer/2022070400/56649f115503460f94c23c60/html5/thumbnails/6.jpg)
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
![Page 7: University of Auckland New Zealand Geothermal Group Department of Engineering Science Computer Modelling of Gas and Liquid Tracers in Geothermal Reservoirs](https://reader036.vdocuments.mx/reader036/viewer/2022070400/56649f115503460f94c23c60/html5/thumbnails/7.jpg)
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
![Page 8: University of Auckland New Zealand Geothermal Group Department of Engineering Science Computer Modelling of Gas and Liquid Tracers in Geothermal Reservoirs](https://reader036.vdocuments.mx/reader036/viewer/2022070400/56649f115503460f94c23c60/html5/thumbnails/8.jpg)
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):
![Page 9: University of Auckland New Zealand Geothermal Group Department of Engineering Science Computer Modelling of Gas and Liquid Tracers in Geothermal Reservoirs](https://reader036.vdocuments.mx/reader036/viewer/2022070400/56649f115503460f94c23c60/html5/thumbnails/9.jpg)
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
![Page 10: University of Auckland New Zealand Geothermal Group Department of Engineering Science Computer Modelling of Gas and Liquid Tracers in Geothermal Reservoirs](https://reader036.vdocuments.mx/reader036/viewer/2022070400/56649f115503460f94c23c60/html5/thumbnails/10.jpg)
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:
![Page 11: University of Auckland New Zealand Geothermal Group Department of Engineering Science Computer Modelling of Gas and Liquid Tracers in Geothermal Reservoirs](https://reader036.vdocuments.mx/reader036/viewer/2022070400/56649f115503460f94c23c60/html5/thumbnails/11.jpg)
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
![Page 12: University of Auckland New Zealand Geothermal Group Department of Engineering Science Computer Modelling of Gas and Liquid Tracers in Geothermal Reservoirs](https://reader036.vdocuments.mx/reader036/viewer/2022070400/56649f115503460f94c23c60/html5/thumbnails/12.jpg)
University of AucklandNew Zealand
Geothermal GroupDepartment of Engineering Science
Qualitative results - gas tracersSF6 R-12
Following injection
100days
R-123
![Page 13: University of Auckland New Zealand Geothermal Group Department of Engineering Science Computer Modelling of Gas and Liquid Tracers in Geothermal Reservoirs](https://reader036.vdocuments.mx/reader036/viewer/2022070400/56649f115503460f94c23c60/html5/thumbnails/13.jpg)
University of AucklandNew Zealand
Geothermal GroupDepartment of Engineering Science
Qualitative results - liquid tracersTritiated water Methanol
Following injection
100days
n-Propanol
![Page 14: University of Auckland New Zealand Geothermal Group Department of Engineering Science Computer Modelling of Gas and Liquid Tracers in Geothermal Reservoirs](https://reader036.vdocuments.mx/reader036/viewer/2022070400/56649f115503460f94c23c60/html5/thumbnails/14.jpg)
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
![Page 15: University of Auckland New Zealand Geothermal Group Department of Engineering Science Computer Modelling of Gas and Liquid Tracers in Geothermal Reservoirs](https://reader036.vdocuments.mx/reader036/viewer/2022070400/56649f115503460f94c23c60/html5/thumbnails/15.jpg)
University of AucklandNew Zealand
Geothermal GroupDepartment of Engineering Science
Acknowledgements
• Mike Adams (EGI Utah)• JAPEX Geoscience Institute