Non-equilibrium two-phase flow in porous media

The book is devoted to the study of a non-equilibrium two-phase flow through a ¿-periodic double porosity media. The mesoscopic model consists of equations derived from the mass conservation laws along with a generalized Darcy law in the framework of the non-equilibrium Kondaurov flow model. The mobility and capillary pressure functions for the matrix part are the functions of the saturation and the non-equilibrium parameter. The fractured medium consists of periodically repeating blocks and fractures. Using the method of two-scale asymptotic expansions we derive the macroscopic model which is written in terms of the homogenized phase pressures, saturation, and the non-equilibrium parameter. It is shown that the homogenized model can be represented as usual equations of two-phase immiscible incompressible flow, except for the addition of two source terms calculated by a solution to a local problem in the matrix block being a boundary value problem for a non-equilibrium imbibition equation given in terms of the real saturation and a non-equilibrium parameter. The results of numerical simulation of the incompressible non-equilibrium two-phase flow are also presented.