A multi-scale finite-volume (MSFV) method for solving multiphase flow problem in highly heterogeneous media was recently developed. In contrast with classical upscaling techniques, the goal of multiscale methods is not simply to capture the large-scale effects of the fine-scale heterogeneity, but to provide an efficient tool for solving large flow problems with fine-scale resolution. The MSFV is based on a fractional flow formulation of the problem: first an equation for the total velocity is solved,...