A General Multiscale Finite-Volume Method for Compressible Multiphase Flow in Porous Media

The Multiscale Finite-Volume (MSFV) method was originally proposed to solve elliptic problems arising from incompressible multiphase flow in highly heterogeneous porous media at reduced computational cost. However, when phases are compressible, especially when the reservoir contains gas, mathematical formulations lead to a parabolic equation to be solved for pressure. In this paper we introduce a general MSFV method to deal with such parabolic problems. In this scheme, the basis and correction functions are numerical solutions of the full parabolic problems in localized domains. Hence compressibility effects are represented by a stencil in the coarse-system matrix, i.e. not only by a diagonal entry. Furthermore, to enhance the computational efficiency of the scheme, the basis functions are kept independent of the pressure field. As a result, only the correction functions (1 per dual-coarse cell) have to be updated during the iterative procedure. It is an important property of this approach that it requires no additional simplifications. Finally, its good efficiency is demonstrated for a number of challenging test cases.