Operator-based linearization for efficient modeling of geothermal processes

•New linearization technique proves applicability to geothermal problems.•The approach uses coarsening in physical representation.•It improves the performance of simulation.•It also helps to identify major nonlinearities driving the simulation convergence.•Errors, introduced by physics coarsening, r...

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Bibliographic Details
Published in:Geothermics 2018-07, Vol.74, p.7-18
Main Authors: Khait, Mark, Voskov, Denis
Format: Article
Language:English
Subjects:
Coarsening
Coarsening in physical representation
Computational fluid dynamics
Computer applications
Computer simulation
Energy conservation
Enthalpy
Financial management
Geothermal power
Geothermal simulation
Interpolation
Isothermal flow
Linearization
Mathematical analysis
Mathematical models
Nonlinear equations
Nonlinear systems
Nonlinearity
Operator-based linearization
Operators
Physical properties
Physics
Representations
Reservoirs
Risk analysis
Robustness (mathematics)
Simulation
Uncertainty
Uncertainty analysis
Viscosity
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Summary:•New linearization technique proves applicability to geothermal problems.•The approach uses coarsening in physical representation.•It improves the performance of simulation.•It also helps to identify major nonlinearities driving the simulation convergence.•Errors, introduced by physics coarsening, remain under control. 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 te
ISSN:0375-6505
1879-3576
DOI:10.1016/j.geothermics.2018.01.012