Macroscopic Model of Two-phase Flow of Compressible Fluidsin Double-porosity Media
For a two-phase flow of compressible liquids in a compressible porous medium with double porosity, a macroscopic model is obtained, on the basis of which a qualitative analysis of the mechanisms of occurrence of various types of memory (delay) is performed. The two main mechanisms are non-instantaneous capillary phase redistribution and non-instantaneous pressure relaxation. In addition to them, cross effects of memory arise, caused by asymmetric squeezing of liquids from pores due to phase expansion and pore compaction, as well as nonlinear overlap of compressibility and capillarity (nonlinear squeezing). To construct the model, the asymptotic method of two-scale homogenization in the variational formulation is applied. Complete homogenization has been realized thanks to the separation of nonlocality and nonlinearity into different levels of asymptotic expansion. All characteristic delay times are explicitly defined as functions of saturation and pressure.