Title:

Numerical Modeling of Geothermal Systems

Authors:

Cedrick COPOL, Jacques LAMINIE, Simon LOPEZ

Key Words:

modeling of geothermal systems, porous media

Conference:

Stanford Geothermal Workshop

Year:

2014

Session:

Modeling

Language:

English

Paper Number:

Copol

File Size:

1409 KB

View File:

Abstract:

The purpose of our study is to model a geothermal reservoir. When geothermal reservoirs are assumed to be composed of pure water, the transfer of mass and energy is classically described by two balance equations: mass balance equation and energy balance equation. In addition to those equations, fluid velocity is classically given by the Darcy law while thermodynamic properties, inferred from theoretical or empirical equations of state, are used to close the mathematical system. Once this system is closed, there exist different solutions. The first one is to solve for pressure and temperature with a variable switch to saturation in the two-phase region (e.g. TOUGH2). The second one is to solve for pressure and enthalpy to increase stability of phase transition between single and two-phase states (e.g. Hydrotherm). We adopted the second option and chose to use a splitting method to get rid of the complexity of coupling equations and a finite volume method for the spatial discretization. Selecting object-oriented languages, we developed a multi-language framework, combining Python, Fortran and a C++ implementation of IAPWS (from the freesteam project) including the supercritical region. We offer some freedom to users thanks to the implementation of several methods like explicit or implicit Euler, Runge-Kutta or BDF2 for time integration and GMRES or BICGSTAB for the linear solver. We can handle several boundary conditions such as no-flow --- describing a boundary which cannot exchange matter with the exterior --- or a mixed-therm condition --- with a Dirichlet condition on the pressure and a Dirichlet or an outflow condition on the temperature. The latter can be used to describe a recharge or a discharge zone. As a first test case we have used our code to model heat mining by a doublet exploitation with single-phase fluid and temperatures below 70°C (parameters corresponding to the Dogger aquifer of the Paris basin). We successfully compared our results with those obtained with the TOUGH2 code. We then considered higher-energy test cases, with possibly supercritical conditions and benchmarked our code against results from the CSMP++ platform (Coumou, 2008) with satisfactory agreement (even showing improvement near some boundary conditions). Finally we can also successfully represent actively convecting hydrothermal systems in a 2D vertical fault. The next step will be to model the geothermal field of Bouillante (Guadeloupe, Caribbean). It's the only high energy geothermal reservoir in France producing electricity with the earth power. Since 1995 the Bouillante power plant has given 30 GWh of electricity a year to Guadeloupean people. Reservoir temperatures are around 250 °C and the geothermal brine is composed of sea-water (60 %) and meteoric water (40 %). Yet our goal is to model the full hydrothermal system from the deep magmatic heat source, which is believed to reach up to 1000 °C and a pressure range of a few hundred MPa to outflow surface zones where fumaroles and hot sources are present.


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