Homogenization of two-phase flow in fractured media

Abstract

In a fractured medium, there is an interconnected system of fracture planes dividing the porous rock into a collection of matrix blocks. The fracture planes, while very thin, form paths of high permeability. Most of the fluids reside in matrix blocks, where they move very slow. Let epsilon denote the size ratio of the matrix blocks to the whole medium and let the width of the fracture planes and the porous block diameter be in the same order. If permeability ratio of matrix blocks to fracture planes is of order epsilon(2), microscopic models for two-phase, incompressible, immiscible flow in fractured media converge to a dual-porosity model as epsilon goes to 0. If the ratio is smaller than order epsilon(2), the microscopic models approach a single-porosity model for fracture flow. If the ratio is greater than order epsilon(2), then microscopic models tend to another type of single-porosity model. In this work, these results will be proved by a two-scale method.