ABSTRACT
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 , where
is the relative fracture thickness and an
-periodic system of disjoint cubic matrix blocks. We derive the global behavior of the model by passing to the limit as
, assuming that the block permeability is proportional to
, while the fracture permeability is of order one, and obtain the global
–model. In the
-model we linearize the cell problem in the matrix block and letting
, 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
sufficiently small, the exact global
-model can be replaced by the fully homogenized one without significant loss of accuracy.
Disclosure statement
No potential conflict of interest was reported by the authors.