Modeling of Two-phase Filtration Processes and Homogenization

Abstract

Unsteady processes of two-phase flow filtrations for immiscible liquids in porous media with a periodic structure are considered. The Masket-Leveret model is adopted as a mathematical model for describing such processes for media formed by a large number of blocks with low permeability and separated by a connected system of faults with high permeability. This model is typical for modeling the processes of gas production, oil production and diffusion of pollutants (for example, oil products) in groundwater. The assumption of medium periodicity is a model as simply described, since it is not known how to describe real porous media. However, sometimes the results for periodic media can be generalized to stochastic media. In addition, complex media can sometimes be approximated by periodic or quasi-periodic, which are also reduced to periodic.