In the literature, the general formulation of the MsMFE method for incompressible two-phase and compressible three-phase flow has mainly addressed problems with idealized flow physics. In this paper, we present a new formulation that accounts for
compressibility, gravity, and spatially-dependent capillary and relative-permeability effects.
We evaluate the computational efficiency and accuracy of the method by reporting the result of series of representative benchmark tests that have a high degree of realism with respect to flow physics, heterogeneity in petrophysical model, and
geometry/topology of the corner-point grids. In particular, the MsMFE method is validated and compared against Shell's in-house simulator MoReS. The fine-scale flux, pressure, and saturation fields computed by the multiscale simulation show a noteworthy improvement in resolution and accuracy compared with coarse-scale models.