Homogenization of Kondaurov’s non-equilibrium two-phase flow in double porosity media
Anton Voloshin, Leonid Pankratov, A. V. Konyukhov · Applicable Analysis · 2018
We consider a two-phase incompressible non-equilibrium flow in fractured porous media in the framework of Kondaurov’s model, wherein the mobilities and capillary pressure depend both on the real saturation and a non-equilibrium parameter satisfying a kinetic equation. The medium is made of two superimposed continua, a connected fracture system, which is assumed to be thin of order εδ, where δ is the relative fracture thickness and an ε-periodic system of disjoint cubic matrix blocks. We derive the global behavior of the model by passing to the limit as ε→0, assuming that the block permeability is proportional to (εδ)2, while the fracture permeability is of order one, and obtain the global δ–model. In the δ-model we linearize the cell problem in the matrix block and letting δ→0, obtain a macroscopic non-equilibrium fully homogenized model, i.e. the model which does not depend on the additional coupling. The numerical tests show that for δ sufficiently small, the exact global δ-model can be replaced by the fully homogenized one without significant loss of accuracy.