Multi-point flux approximations (MPFAs) have been developed in recent years to improve the accuracy of the flux computation for reservoir simulation when the reservoir grids are not K-orthogonal. Recent studies, however, have shown that commonly used MPFA approaches could pose severe limitations. Specifically, it has been observed that MPFA can cause severe nonphysical oscillations in numerical solutions for the single-phase pressure equation if the permeability field is strongly anisotropic. Some researchers have linked those numerical oscillations to the lack of monotonicity in the solution matrix for the discretization problem and efforts have been made to improve MPFA so that matrix monotonicity can be restored.
This paper will present new techniques, collectively called enriched multi-point flux approximations (EMPFAs), to reduce or eliminate numerical oscillations in the solutions. The key to improving the consistency and accuracy of the local flux calculations is the introduction of new temporary unknowns and the application of better pressure interpolation techniques. EMPFA can be used for modeling general multiphase flows in 2-dimensional or 3-dimensional reservoir models, and the grid can be Cartesian, Voronoi, or even arbitrary. Simulation results will demonstrate the differences among EMPFA, MPFA, and the original two-point flux approximation (TPFA).