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

Abstract

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.