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 $\varepsilon\delta$, and an $\varepsilon$-periodic system of disjoint matrix blocks. We derive global behavior of the fractured media by passing to the limit as $\varepsilon\rightarrow 0$ and then as the relative fracture thickness $\delta\rightarrow 0$, taking into account that the permeability of the blocks is proportional to $(\varepsilon\delta)^2$, 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.