Homogenized model with memory for two-phase compressible flow in double-porosity media

A completely averaged model of two-phase flow of compressible fluids in a medium with double porosity is developed. The variational asymptotic two-scale averaging method with splitting the nonlocality and nonlinearity is presented. Several mechanisms of delay are detected, as the nonequilibrium capillary redistribution of phases, pressure field relaxation caused by the compressibility, and the cross effects of fluid extrusion from pores due to rock compaction and fluid expansion. A generalized nonequilibrium capillary equation is obtained. All characteristic times of delay are explicitly defined as functions of saturation.