engleski

A fully homogenized model for incompressible two-phase flow in double porosity media

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 εδ, where δ being the relative fracture thickness, and an ε–periodic system of disjoint matrix blocks. We derive the global behavior of the fractured medium by passing to the limit as ε → 0, taking into account that the permeability of the blocks is proportional to (εδ)2 , while the permeability of the fractures is of order one and obtain the corresponding global δ–model, i.e., the homogenized model with the coefficients depending on the small parameter δ. In the δ–model we linearize the cell problem in the matrix block and then by letting δ → 0 we obtain the macroscopic model which does not depend on ε and δ 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.

homogenization ; incompressible ; two-phase flow ; double porosity media ; thin fractures

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