Fully homogenized model for immiscible incompressible two-phase flow   through heterogeneous porous media with thin fractures
  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. 
Mladen Jurak, Leonid Pankratov, Anja Vrba\v{s}ki
math.AP