Abstract
We study an immiscible incompressible two-phase, such as water–oil flow through a -periodic double porosity media. The mesoscopic model consists of equations derived from the mass conservation laws of both fluids, along with a generalized Darcy law in the framework of Kondaurov’s non-equilibrium flow model. The mobility functions as well as the capillary pressure function for each component of the porous medium are the functions of the saturation and an additional non-equilibrium parameter, which satisfies a kinetic equation coming from the definition of the Helmholtz free energy. The fractured medium consists of periodically repeating homogeneous blocks and fractures, where the permeability ratio of matrix blocks to fracture planes is of order . Using the method of two-scale asymptotic expansions, we derive the macroscopic model of the flow which is written in terms of the homogenized phase pressures, saturation, and the non-equilibrium parameter. For small relaxation times, we compare our model with the global models obtained earlier by H. Salimi and J. Bruining. We show the novelty of our macroscopic double porosity flow model.
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