A Higher-Resolution Flow-Oriented Scheme With an Adaptive Correction Strategy for Distorted Meshes Coupled With a Robust MPFA-D Method for the Numerical Simulation of Two-Phase Flow in Heterogeneous and Anisotropic Petroleum Reservoirs

Abstract

Summary In this paper, we propose a full-cell-centered finite-volume approach to simulate two-phase flow in heterogeneous and anisotropic petroleum reservoirs. We adopt a segregated formulation where the pressure equation is discretized by a multipoint flux approximation with a diamond-type support (MPFA-D). To solve the saturation equation, we propose a higher-order modified flow-oriented scheme (M-FOS). In this scheme, adaptive weights tune the formulation multidimensionality according to the grid distortion. Also, we adopt a multidimensional limiting process (MLP) and an efficient entropy fix to produce convergent solutions. We evaluate the performance of our numerical schemes by solving some relevant benchmark problems.