Fully homogenized model for immiscible incompressible two-phase flow through heterogeneous porous media with thin fractures

Abstract

In this paper we discuss a model describing global behavior of the two phase incompressible flow in fractured porous media. The fractured media is regarded as a porous medium consisting of two superimposed continua, a connected fracture system, which is assumed to be thin of order $\epsilon \delta$, and an $\epsilon$-periodic system of disjoint matrix blocks. We derive global behavior of the fractured media by passing to the limit as $\epsilon \to 0$ and then as the relative fracture thickness $\delta \to 0$, taking into account that the permeability of the blocks is proportional to $(\epsilon \delta {)}^2$, while permeability of the fractures is of order one. The macroscopic model obtained is then a fully homogenized model, i.e., where all the coefficients are calculated in terms of given data and do not depend on the additional coupling or cell problems.

22 pages, 1 figure