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# Modeling geothermal reservoirs

Geothermal reservoirs have many complexities, many of which are not common in petroleum reservoirs. This can create challenges to developing reliable models of these reservoirs via simulation or other means.

## Numerical simulation

Simulation of geothermal processes involves solution of highly nonlinear, coupled equations describing mass and energy transport in complex, heterogeneous media. The first models of geothermal simulation appeared in the 1970s.[1][2][3] However, it was not until the 1980 Code Comparison Study[4] that numerical models for reservoir management were generally accepted. In that code comparison study, a suite of six geothermal problems were made available to geothermal code developers, and results of the problem set were published. The results showed that numerical models were capable of solving these complex equations. Since that time, numerical models have been developed for more than 100 geothermal fields. O’Sullivan et al.[5]present an excellent overview of geothermal reservoir simulation.

Coupled mass and energy (heat) transport in heterogeneous media is a complex problem. The primary component of geothermal reservoirs is water, which can exist in a vapor, liquid, or adsorbed state.[6] Phase behavior is further complicated by vapor pressure lowering[7] and by the presence of noncondensible gases (e.g., CO2) and salts. Phase changes (condensation and vaporization) occur in native state heat pipes[8][9] and also because of injection/production operations. Minerals may also precipitate or dissolve in response to phase change, affecting permeability and porosity in near-well regions.

The basic equations that are solved in geothermal simulation are the same as in thermal petroleum (or hydrology) simulation: conservation of mass for each component and conservation of overall energy. These can be found in standard references[10] and are not repeated here.

## Conceptual models and the native state

Geothermal reservoirs frequently exhibit conditions not encountered in petroleum reservoirs. Convection cells arising from local differences in heat flux are encountered in the native (i.e., pre-exploited) state, and both energy and mass are in a state of dynamic equilibrium. In addition to the more conventional issues of reservoir structure, fault locations, permeability structure, etc., there exist other concerns that impact initializing a geothermal simulation model. Reservoir boundaries are typically not sealed, and conceptual reservoir models must capture heat flux from a localized or variable heat source from below, heat loss to caprock or atmosphere (e.g., via fumaroles, steaming ground, etc.), and fluid recharge and discharge locations and magnitude. Large chemical changes occur spatially, in part, because of Rayleigh condensation patterns[11] and fluid recharge.

### Effect of fractures

Reservoirs are nearly universally fractured, requiring accurate treatment of flow through primary flowpaths, storage in bulk porosity, and mass and energy transfer between the two. While many petroleum reservoirs are also fractured, a "representative" pressure diffusivity κ = k/Φ μc for geothermal reservoirs is 1 to 2 orders of magnitude lower than for petroleum reservoirs, because, in large part, of lower matrix permeability and larger effective compressibility. This invariably implies that either a Multiple Interacting Continua (MINC) or MINC-like[12][13] method or other variation of dual-porosity model[14] be used to simulate pressure and temperature transients. Some studies have included explicit representation of dominant fractures[15][16]; however, most hydrothermal reservoir models employ some type of continuum model.

### Simulation process

As already noted, a typical geothermal reservoir is in dynamic equilibrium with its surroundings, with boundaries at least partially open and large heat flux both into and out of the reservoir. For these reasons, a reservoir simulation study usually commences with a native state model, in which the initial (dynamic) state is simulated over geologic time. At steady state, temperature distributions, locations, and strength of observed discharge (e.g., hot springs), and chemistry are compared against simulated results, and the reservoir structure is adjusted accordingly. Input parameters that may be changed during this stage include the permeability structure and location and strength and chemical makeup of inflow (both heat and mass). After obtaining a good match between simulated and observed initial conditions, what production history exists is then history matched. Data used in this effort include production rates, enthalpy, and geochemistry of the produced fluids, either by an individual well or a combination of wells. Relatively recent history match exercises have included tracer test results[17] and geophysical measurements[18][19][20][21] to assist in the model-calibration exercise.

Since the mid-1990s, several new capabilities have been developed to facilitate geothermal reservoir simulation. In particular, inverse modeling and uncertainty analysis[22] are used to replace the tedious and often subjective, manual history-match exercises with automated methods. More recent work has focused on extending those concepts by adding geophysical measurements to the model calibration work, and several research groups are working towards using this combined suite of tools to estimate reservoir parameters and reduce the associated uncertainty.

Geothermal reservoir fluids are geochemically complex, typically not neutral pH, and exhibit a large degree of rock-fluid interaction. Until recently, geothermal simulators treated the fluids as pure water. That has changed within the last decade, with equations of state available to treat mixtures of water, CO2, and dissolved solids.[23][24][25] More sophisticated multicomponent chemical models have been developed for geothermal application but are largely restricted to phase behavior routines that neglect flow.[26][27][28] More recent attempts have been made to develop fully coupled transport and chemical interaction models.[29][30] While not fully developed as yet, these models have been used to evaluate minerals extraction from geothermal brines.[31]

While not normally considered for hydrothermal reservoir simulation, coupled thermal, hydrologic, and mechanical (T-H-M) models are being developed for studying enhanced geothermal systems (EGS) reservoirs.[32] Other groups are extending the thermodynamic limits of fluid properties to super-critical conditions to study deep-seated geothermal zones.[33][34][35]

## References

1. Mercer, J.W. Jr. and Pinder, G.F. 1973. Galerkin Finite-Element Simulation of a Geothermal Reservoir. Geothermics 2 (3–4): 81.
2. Coats, K.H. 1977. Geothermal Reservoir Modelling. Presented at the SPE Annual Fall Technical Conference and Exhibition, Denver, Colorado, 9-12 October 1977. SPE-6892-MS. http://dx.doi.org/10.2118/6892-MS.
3. Donaldson, I.G. and Sorey, M.L. 1979. The Best Uses of Numerical Simulators. Proc., Fifth Workshop on Geothermal Reservoir Engineering, Stanford University, Stanford, California, 241.
4. Stanford Special Panel. 1980. Proc., Special Panel on Geothermal Model Intercomparison Study, Stanford University, Stanford, California, 120.
5. O’Sullivan, M.J., Pruess, K., and Lippmann, M.J. 2001. State of the Art of Geothermal Reservoir Simulation. Geothermics 30 (4): 395.
6. Pruess, K. and O’Sullivan, M.J. 1992. Effects of Capillary and Vapor Adsorption in the Depletion of Vapor-Dominated Geothermal Reservoirs. Proc., Seventeenth Workshop on Geothermal Reservoir Engineering, Stanford University, Stanford, California, 165.
7. Edlefsen, N.E. and Anderson, A.B.C. 1943. Thermodynamics of Soil Moisture. Hilgardia 15 (2): 31.
8. White, D.E., Muffler, L.J.P., and Truesdell, A.H. 1971. Vapor-Dominated Hydrothermal Systems Compared with Hot-Water Systems. Economic Geology 66 (1): 478.
9. Pruess, K. 1985. A Quantitative Model of Vapor-Dominated Geothermal Reservoirs as Heat Pipes in Fractured Porous Rock. Geothermal Resources Council Trans. 9: 353.
10. Lake, L.W. 1989. Basic Equations for Fluid Flow in Permeable Media. Enhanced Oil Recovery, Ch. 2. Englewood Cliffs, New Jersey: Prentice Hall Inc.
11. D’Amore, F. and Truesdell, A.H. 1979. Models for Steam Chemistry at Larderello and The Geysers. Proc., Fifth Workshop on Geothermal Reservoir Engineering, Stanford U., Stanford, California, 283.
12. Pruess, K. and Narasimhan, T.N. 1985. A Practical Method for Modeling Fluid and Heat Flow in Fractured Porous Media. SPE J. 25 (1): 14–26. SPE-10509-PA. http://dx.doi.org/10.2118/10509-PA.
13. Pritchett, J.W. 1997. Efficient Numerical Simulation of Nonequilibrium Mass and Heat Transfer in Fractured Geothermal Reservoirs. Proc., Twenty-Second Workshop on Geothermal Reservoir Engineering, Stanford University, Stanford, California, 287.
14. Warren, J.E. and Root, P.J. 1963. The Behavior of Naturally Fractured Reservoirs. SPE J. 3 (3): 245–255. SPE-426-PA. http://dx.doi.org/10.2118/426-PA.
15. Suarez Arriaga, M.C., Samaniego, V.F., and Rodriquez, F. 1996. Some Mismatches Occurred When Simulating Fractured Reservoirs as Homogeneous Porous Media. Proc., Twenty-First Workshop on Geothermal Reservoir Engineering, Stanford University, Stanford, California, 179.
16. Yamaguchi, S. et al. 2000. The Numerical Modeling Study of the Hijiori HDR Test Site. Proc., World Geothermal Congress, Kyushu-Tohuku, Japan, 3975.
17. Parini, M., Acuna, J.A., and Laudiano, M. 1996. Re-injected Water Return at Mirovalles Geothermal Reservoir, Costa Rica: Numerical Model and Observations. Proc., Twenty-First Workshop on Geothermal Reservoir Engineering, Stanford University, Stanford, California, 127.
18. Strobel, C.J. 1991. Bulalo Field, Philippines: Reservoir Modeling for Prediction of Limits to Sustainable Generation. Proc., Seventeenth Workshop on Geothermal Reservoir Engineering, Stanford University, Stanford, California, 5.
19. Ishido, T. et al. 1995. Feasibility Study of Reservoir Monitoring Using Repeat Precision Gravity Measurements at the Sumikawa Geothermal Field. Proc., World Geothermal Congress, 853–858.
20. Ishido, T. and Pritchett, J.W. 1996. Numerical Simulation of Electrokinetic Potentials Associated with Natural and Production-Induced Hydrothermal Fluid Flows. Geothermal Resources Council Trans. 20: 323.
21. Ishido, T. and Tosha, T. 1998. Feasibility Study of Reservoir Monitoring Using Repeat Self-Potential Measurements. Geothermal Resources Council Trans. 22: 171.
22. Finsterle, S. and Pruess, K. 1995. Automatic History Matching of Geothermal Field Performance. Proc., Seventeenth New Zealand Geothermal Workshop, Auckland, New Zealand, 193.
23. Anderson, G. et al. 1992. An Accurate Model for Geothermal as Represented by H2O-CO2-NaCl Mixtures. Proc., Twelfth Workshop on Geothermal Reservoir Engineering, Stanford University, Stanford, California, 239.
24. Battistelli, A., Calore, C., and Pruess, K. 1997. The Simulator Tough2/EWASG for Modeling Geothermal Reservoirs with Brines and Noncondensible Gas. Geothermics 26 (4): 437.
25. Pritchett, J.W. 1995. Star: A Geothermal Reservoir Simulation System. Proc., World Geothermal Congress, Florence, Italy, 2959–2963.
26. Weare, J.H. 1987. Models of Mineral Solubility in Concentrated Brines with Application to Field Observations. Reviews in Mineralogy, 17, 143.
27. Wolery, T. 1992. EQ3/6, A Software Package for Geochemical Modeling of Aqueous Systems: Package Overview and Installation Guide (Version 7.0). Report UCRL-MA-110662 PT1, Lawrence Livermore Natl. Laboratory, Livermore, California.
28. Moller, N., Greenberg, J.P., and Weare, J.H. Computer Modeling for Geothermal Systems: Predicting Carbonate and Silica Scale Formation, CO2 Breakout and H2S Exchange. Transport in Porous Media 33 (1–2): 173.
29. Xu, T. and Pruess, K. 1998. Coupled Modeling on Nonisothermal Multiphase Flow, Solute Transport and Reactive Chemistry in Porous and Fractured Media: 1. Model Development and Validation. Report LBNL-42050, Lawrence Berkeley Natl. Laboratory, Berkeley, California.
30. Xu, T. and Pruess, K. 2000. Hydrothermal Fluid Flow and Mineral Alteration in a Fractured Rock under Multiphase H2O-CO2 Mixture Conditions. Proc., World Geothermal Congress, Kyushu-Tohuku, Japan, 2983.
31. Xu, T. et al. 2001. Reactive Chemical Transport Simulation to Study Geothermal Production with Mineral Recovery and Silica Scaling. Geothermal Resources Council Trans. 25: 513.
32. Swenson, D. et al. 1991. A Coupled Model of Fluid Flow in Jointed Rock. Proc., Sixteenth Workshop on Geothermal Reservoir Engineering, Stanford University, Stanford, California, 21.
33. Hayba, D.O. and Ingebritsen, S.E. 1994. Flow Near the Critical Point: Examination of Some Pressure- Enthalpy Paths. Proc., Nineteenth Workshop on Geothermal Reservoir Engineering, Stanford University, Stanford, California, 83.
34. Brikowski, T.H. 2001. Modeling Supercritical Systems with TOUGH2: Preliminary Results Using the EOS1SC Equation of State Module. Proc., Twenty-Sixth Workshop on Geothermal Reservoir Engineering, Stanford University, Stanford, California, 208.
35. Wisian, K.W. 2000. Insights into Extensional Geothermal Systems from Numerical Modeling. Geothermal Resources Council Trans. 24: 281.