Determination of the Effective Permeabilities in Partially Saturated Porous Media, Using the Periodic Homogenization Technique

Abstract In this study, we address determination of the effective permeabilities in rigid, partially saturated porous media for an immiscible two-phase Newtonian fluid flow. The periodic homogenization technique is applied to derive macroscopic flow laws for two-phase systems from the pore-scale Navier–Stokes equations governing immiscible fluids. Two distinguished cases are considered: two incompressible fluids (case 1) and an incompressible fluid with a compressible one (case 2). In both cases, the homogenized result shows the independence of the macroscopic laws and the closure problems on the fluid compressibility, except for the macroscopic mass conservation equation. Finally, numerical simulations are performed by solving the closure problems for a given interface position determined from the phase-field simulations, in order to analyze the role of each effective permeability in the generalized Darcy’s law for several fluid mixtures and different porosity. The numerical results offer insights into the influence of microstructure, fluid properties, and capillary bridge distribution on the effective permeabilities.