An unstructured edge-based finite volume formulation for solving immiscible two-phase flows in porous media

摘要

Unstructured mesh based discretization techniques can offer certain advantages relative to standard finite difference approaches which are commonly used in reservoir simulation, due to their flexibility to model complex geological features and to their ability to easily incorporate mesh adaptation. Within such class of methods the most frequently used are the finite element method (FEM) and the finite volume method (FVM). The latter is particularly attractive in reservoir problems due to its local and global conservation properties. The main goal of the present paper is to describe an unstructured edge-based FVM formulation which is used to solve the partial differential equations resulting from the modelling of two-phase fluid flow of oil and water in homogeneous porous media, when an IMPES (IMplicit Pressure Explicit Saturation) approach is used. This finite volume formulation is similar to the edge-based FEM formulation when linear triangular or tetrahedral elements are employed. Some model examples are presented in order to validate the presented formulation.