MODELING OF CAPILLARY PRESSURE HYSTERESIS AND OF HYSTERESIS OF RELATIVE PHASE PERMEABILITIES IN POROUS MATERIALS ON THE BASIS OF THE PORE ENSEMBLE CONCEPT

We propose a class of models of porous media based on the pore ensemble concept with a certain distribution of the main geometric parameters (e.g., pore size). The case of the saturation of the pore space with a two-phase liquid mixture has been considered. The transfer laws are deduced from the free energy dissipation condition. The hydrodynamic connection of pores is described by two kinds of kernels: one kernel describes the connection of pores in the space, and the other kernel describes the connection of pores in an elementary macrovolume. A simple model of capillary pressure hysteresis associated with the monotonicity of the function of the area-to-volume ratio of the pore is proposed. The results of numerical calculations of the capillary pressure hysteresis and relative phase permeabilities are presented.