Homogenization of two-phase flow in fractured media

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 ε 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 ε², microscopic models for two-phase, incompressible, immiscible flow in fractured media converge to a dual-porosity model as ε goes to 0. If the ratio is smaller than order ε², the microscopic models approach a single-porosity model for fracture flow. If the ratio is greater than order ε², then microscopic models tend to another type of single-porosity model. In this work, these results will be proved by a two-scale method.