Mathematical structure of the black-oil model for petroleum reservoir simulation
SIAM Journal on Applied Mathematics
Mathematical structure of compositional reservoir simulation
SIAM Journal on Scientific and Statistical Computing
The Unified Modeling Language user guide
The Unified Modeling Language user guide
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SIAM Journal on Applied Mathematics
Formulations and Numerical Methods of the Black Oil Model in Porous Media
SIAM Journal on Numerical Analysis
Numerical simulation of three-phase flow in heterogeneous porous media
VECPAR'06 Proceedings of the 7th international conference on High performance computing for computational science
Mathematics and Computers in Simulation
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This paper presents new results for applying the sequential solution method to the black-oil reservoir simulation with unstructured grids. The fully implicit solution method has been successfully applied to reservoir simulation with unstructured grids. However, the complexity of the fully implicit method and the irregularity of the grids result in a very complicated structure of linear equation systems (LESs) and in high computational cost to solve them. To tackle this problem, the sequential method is applied to reduce the size of the LESs. To deal with instable problems caused by the low implicit degree of this method, some practical techniques are introduced to control convergence of Newton-Raphson's iterations which are exploited in the linearization of the governing equations of the black-oil model. These techniques are tested with the benchmark problem of the ninth comparative solution project (CSP) organized by the society of petroleum engineers (SPE) and applied to field-scale models of both saturated and undersaturated reservoirs. The simulation results show that the sequential method uses as little as 20.01% of the memory for solving the LESs and 23.89% of the total computational time of the fully implicit method to reach the same precision for the undersaturated reservoirs, when the same iteration control parameters are used for both solution methods. However, for the saturated reservoirs, the sequential method must use stricter iteration control parameters to reach the same precision as the fully implicit method.