Treating highly anisotropic subsurface flow with the multiscale finite-volume method

The multiscale finite-volume (MSFV) method has been designed to solve flow problems on large domains efficiently. First, a set of basis functions, which are local numerical solutions, is employed to construct a fine-scale pressure approximation; then a conservative fine-scale velocity approximation is constructed by solving local problems with boundary conditions obtained from the pressure approximation; finally, transport is solved at the. ne scale. The method proved very robust and accurate for multiphase flow simulations in highly heterogeneous isotropic reservoirs with complex correlation structures. However, it has recently been pointed out that the fine-scale details of the MSFV solutions may be lost in the case of high anisotropy or large grid aspect ratios. This shortcoming is analyzed in this paper, and it is demonstrated that it is caused by the appearance of unphysical "circulation cells." We show that damped-shear boundary conditions for the conservative-velocity problems or linear boundary conditions for the basis-function problems can significantly improve the MSFV solution for highly anisotropic permeability fields without sensitively affecting the solution in the isotropic case.