A fully homogenized model for incompressible two-phase flow in double porosity media
Mladen Jurak, Leonid Pankratov, Anja Vrbaški · Applicable Analysis · 2015
In this paper, we discuss a model describing the global behavior of the two-phase incompressible flow in fractured porous media. The fractured medium is regarded as a porous medium consisting of two superimposed continua, a connected fracture system, which is assumed to be thin of order , where being the relative fracture thickness, and an –periodic system of disjoint matrix blocks. We derive the global behavior of the fractured medium by passing to the limit as , taking into account that the permeability of the blocks is proportional to , while the permeability of the fractures is of order one and obtain the corresponding global –model, i.e. the homogenized model with the coefficients depending on the small parameter . In the –model, we linearize the cell problem in the matrix block and then by letting , we obtain the macroscopic model which does not depend on and , and is fully homogenized in the sense that all the coefficients are calculated in terms of given data and do not depend on the additional coupling or cell problems.