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

摘要

In this paper we discuss a model describing global behavior of the two phaseincompressible flow in fractured porous media. The fractured media is regardedas a porous medium consisting of two superimposed continua, a connectedfracture system, which is assumed to be thin of order $\varepsilon\delta$, andan $\varepsilon$-periodic system of disjoint matrix blocks. We derive globalbehavior 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 blocksis proportional to $(\varepsilon\delta)^2$, while permeability of the fracturesis of order one. The macroscopic model obtained is then a fully homogenizedmodel, i.e., where all the coefficients are calculated in terms of given dataand do not depend on the additional coupling or cell problems.