AN ADVANCED NINE-POINT SCHEME BASED ON FINITE ANALYSIS IN TWO-DIMENSIONAL NUMERICAL RESERVOIR SIMULATION

In this article, an advanced nine-point (9P) scheme is proposed for solving multiphase flow problems in 2D heterogeneous porous media. The proposed 9P scheme is an extension of the five-point (5P) scheme constructed using the finite analytical method (FAM). As the heterogeneity of porous media increases, the error of the traditional algorithms becomes uncontrollable due to their significant underestimation of nodal transmissibility. However, the transmissibility in the FAM is calculated based on the local analytical solution, and its accuracy is high and does not depend 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 the alleviate grid orientation effect (GOE) under adverse mobility ratios. In practice, 2 × 2 or 3 × 3 subdivisions for one original grid are recommended for the proposed FAM-9P method, regardless of the strength of heterogeneity.