An Advanced Nine-Point Scheme based on Finite Analysis in Two-Dimensional Numerical Reservoir Simulation

This article proposes an advanced nine-point (9P) scheme for solving multiphase flow in heterogeneous porous media, which is an extension of the 5P scheme constructed by the finite analytical method (FAM). As media heterogeneity increases, the error of traditional algorithms become uncontrollable due to their significant underestimation of nodal transmissibility. However, the transmissibility calculated in FAM is based on a local analytical solution and its accuracy is not dependent on the strength of heterogeneity. The proposed FAM-9P scheme offers two distinct advantages. Compared to the traditional 9P scheme, it provides much more accurate simulation results, especially for strongly heterogeneous porous media. Additionally, compared to the FAM-5P scheme, it can alleviate grid orientation effect (GOE) under adverse mobility ratios.