| Abstract: | A class of models of porous media based on the concept of an ensemble of pores with a certain distribution of the main geometric parameters (for example, the pore size) is considered. The cases of pores saturated with single-and two-phase multicomponent liquid mixtures are investigated. The properties of equilibrium states of the mixture are derived from the minimum free energy condition and the transfer laws from the decreasing free energy condition. The hydrodynamic connectivity of the pores is described by two types of kernels: one describes the spatial connectivity and the other the connectivity in an elementary macrovolume. Analytically and numerically, the one-dimensional problems of establishment of a steady-state regime, propagation of a passive admixture, and two-phase flow (an analog of the Buckley-Leverett problem) are investigated. A relationship between the models in question and relaxational filtration models is demonstrated. A simple model of capillary hysteresis related with the non-monotonicity of the pore area to volume ratio function is proposed. |
