Effective Equations for Two-Phase Flow with Trapping on the Micro Scale

In this paper we consider water-drive for recovering oil from a strongly heterogeneous porous column. The two-phase model uses Corey relative permeabilities and Brooks–Corey capillary pressure. The heterogeneities are perpendicular to the flow and have a periodic structure. This results in one-dimensional flow and a space periodic absolute permeability, reflecting alternating coarse and fine layers. Assuming many—or thin—layers, we use homogenization techniques to derive the effective transport equations. The form of these equations depends critically on the capillary number. The analysis is confirmed by numerical experiments.