Multipoint Flux Approximations via Upscaling

Control-volume discretizations for fluid flow in anisotropic porous media are investigated. The method uses numerical solutions of the simplest model equation, –div[K(x) grad p(x)] = f(x). The permeability tensor, K(x), is allowed to have discontinuities. Multipoint Flux Approximations (MPFA) are used, and transmissibility coefficients are obtained, in the usual way, from local numerical flow experiments (transmissibility upscaling) for each cell face. For regular K-orthogonal grids, with a uniform permeability tensor, the scheme reduces to the standard two-point flux approximation. Monotonicity of the solution matrix is discussed and a version of the method that provides an M-matrix is described. This discretization scheme is applied to reservoir simulation on 3D structured grids with distorted geometry, highly anisotropic media, and discontinuities in the permeability tensor. Simulation results are presented and compared with results from other two-point and multipoint flux approximations.