Abstract
The goal of the paper is to derive a homogenized model of the incompressible two-phase flow in multiscale porous media made of disjoint non-homogeneous porous blocks surrounded by highly permeable connected porous subspace which is regarded as a fracture system. The nonhomogeneity of the porous blocks means that they contain the inclusions with contrast properties. The upscaling process is done in two steps. At the first step a Kondaurov type non-equilibrium flow model on the mesoscale level is derived. This model takes into account the capillary non-equilibrium phenomena of the flow in the blocks and fractures. Upscaling the mesoscale model, we obtain the desired macroscopic (homogenized) Kondaurovs type model. The upscaling process at the second step is justified by the numerical simulation.
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