Physics-preserving IMPES based multiscale methods for immiscible two-phase flow in highly heterogeneous porous media

In this paper, we propose a physics-preserving multiscale method to solve an immiscible two-phase flow problem, which is modeled as a coupling system consisting of Darcy's law and mass conservation equations. We use a new Physics-preserving IMplicit Pressure Explicit Saturation (P-IMPES) scheme in order to maintain the local conservation of mass for both phases. Besides, this scheme is unbiased and if the time step is smaller than a certain value, the saturation of both phases are bounds-preserving. When updating velocity, MGMsFEM serves as an efficient solver by computing the unknowns on a coarse grid. We follow the operation splitting techinque to deal with the two-phase flow. In particular, we use an upwind strategy to iterate the saturation explicitly and the MGMsFEM is utilized to compute velocity with a decoupled system on a coarse mesh. To show the efficiency and robustness of the proposed method, we design a set of interesting experiments. A rigorous analysis is also included to serve as a theoretical base of the method, which is well verified by the numerical results. Both simulations and analysis indicate that the method attains a good balance between accuracy and computation cost.

The research of Eric Chung is partially supported by the Hong Kong RGC General Research Fund (Project: 14304021). The research of Shuyu Sun is partially supported by King Abdullah University of Science and Technology (KAUST) through the grants BAS/1/1351-01, URF/1/4074-01, and URF/1/3769-01.



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