A New MPFA Formulation for Subsurface Flow Problems on Unstructured Grids: Derivation of the Discrete Problem

The accurate computation of solutions for multiphase flow problems in a geologically complex subsurface is a great scientific and environmental challenge. Some authors have developed finite-volume methods of new generation (the so-called Multi-Point Flux Approximation methods, commonly called MPFA methods)for addressing this kind of problems.This communication presents some finite-volume based flexible MPFA methods which display strong capabilities to handle flow problems in geologically complex reservoirs.It is well known that the flux continuity across grid-block interfaces combined with the local mass conservation (i.e., mass conservation at grid-block scale)make the finite volume methods a powerful computational tool for flow problems.These properties are met by the variants of MPFA methods presented in this paper. In addition, these new variants provide some added values as (1)an approximate pressure which is continuous in the whole domain, (2)sharp results are provided even on relatively coarse grids, (3)large scale flow problems governed by a symmetric and nonsymmetric full effective permeability tensor can be addressed.A Numerical implementation of these variants of MPFA methods has been done for solving a real-life problem, namely the Darcy flow in the Andra Couplex 1 test case.