Operator-based linearization for efficient modeling of geothermal processes

Abstract

Numerical simulation is one of the most important tools required for financial and operational management of geothermal reservoirs. The modern geothermal industry is challenged to run large ensembles of numerical models for uncertainty analysis, causing simulation performance to become a critical issue. Geothermal reservoir modeling requires the solution of governing equations describing the conservation of mass and energy. The robust, accurate and computationally efficient implementation of this solution suggests an implicit time-approximation scheme, which introduces nonlinearity into the system of equations to be solved. The most commonly used approach to solving the system of nonlinear equations is based on Newton's method and involves linearization with respect to nonlinear unknowns. This stage is the most complicated for implementation and usually becomes the source of various errors. A new linearization approach – operator-based linearization – was recently proposed for non-isothermal flow and transport. The governing equations, discretized in space and time, were transformed to the operator form where each term of the equation was specified as the product of two operators. The first operator comprises physical properties of rock and fluids, such as density or viscosity, which depend only on the current state of a grid block, fully defined by the values of nonlinear unknowns. The second operator includes all terms that were not included in the first operators, and depends on both the state and spatial position of a control volume. Next, the first type of operators was parametrized over the physical space of a simulation problem. The representation of highly nonlinear physics was achieved by using multi-linear interpolation, which replaces the continuous representation of parametrized operators. The linearization of the second type of operators was applied in the conventional manner. In this work, we investigated the applicability of this approach to the geothermal processes, specifically for low-enthalpy and high-enthalpy geothermal doublet models with hydrocarbon co-production. The performance and robustness of the new method were tested against the conventional approach on a geothermal reservoir of practical interest. This approach shows significant improvement of geothermal simulation performance, while errors, introduced by coarsening in physics, remain under control. The simplicity of implementation on emerging computational architectures and nonlinearity reduction provide advanced opportunities for uncertainty quantification and risk analysis of geothermal projects.