Finite Analytic Numerical Method for Two-Phase Incompressible Flow in 2D Heterogeneous Porous Media

A finite analytic numerical scheme is constructed for two-dimensional two-phase flow in heterogeneous porous media. Compared with traditional numerical methods, FAM makes convergence faster as refinement parameter increases, and accuracy is independent with heterogeneity. In contrast, as using traditional numerical schemes to simulate flow through a strong heterogeneous porous medium, refinement ratio for grid cell needs to increase dramatically to get an accurate result. Compared with the proposed scheme, traditional numerical scheme underestimates greatly breakthrough time under coarse grids. However, to get a saturation distribution with high resolution even employing the proposed scheme, relative fine grids are still needed. This is different from FAM for solving a single phase flow, where coarse grids provide rather accurate results.