Finite analytical method on corner‐point grid for fluid flow in heterogeneous porous media

Abstract

AbstractThe three‐dimensional (3D) corner‐point grid system, as an industrial standard, has been widely used in oil reservoir geological modeling and numerical simulation due to its versatility compared to traditional orthogonal grids. The finite analytical method (FAM) is proposed for corner‐point grid systems in this article, which can greatly improve the simulation accuracy, especially for strongly heterogeneous porous media. Based on the approximate analytical solution around the edge of the corner‐point cells, the internodal transmissibility of two adjacent cells is recalculated to replace the traditional one. The traditional internodal transmissibility is calculated based on the harmonic mean of the permeabilities of the two adjacent cells, which will greatly underestimate the transmissibility and lead to an uncontrollable error as the strength of heterogeneity increases. The proposed FAM can calculate the internodal transmissibility rather accurately, and its accuracy is irrelevant to the strength of the heterogeneity, which is the main advantage of FAM. Numerical tests show that the simulation results of the proposed FAM converge much faster than the traditional method as the cells are refined. The proposed FAM can be easily extended to the simulation of multiphase flow and be easily embedded in commercial reservoir numerical simulation software.