A fixed point multi-scale finite volume method: Application to two-phase incompressible fluid flow through highly heterogeneous porous media

Abstract

An enhanced Multi-scale Finite Volume (MsFV) method is proposed to efficiently simulate two phase flow through highly heterogeneous porous media. Here, the accuracy of the MsFV method is significantly improved by enhancing its so-called basis functions, while its computational cost remains in the same order of the basic MsFV method. First, a fixed point is defined along each edge of local problems producing the basis functions and a proper basis function value at this point is estimated based on the local absolute permeability data. Then, the variable boundary condition is independently calculated for both sides of each fixed point. The proposed numerical method is validated by using the analytic solution of a heterogeneous problem. In addition, the convergence of the MsFV method is discussed. Considering highly heterogeneous permeability domains derived from 35 top layers of the tenth SPE comparative study problem, the accuracy of different localization schemes is compared for a set of imbibition problems with different global boundary conditions and mobility ratios. Numerical results have indicated that the overall accuracy of multi-scale velocity solutions is increased noticeably (up to 45%) by using the proposed localization scheme in the MsFV method. © 2022 Elsevier Inc.