Modeling of capillary and thermal nonequilibrium flows in porous media

Complex structure of a skeleton of saturated porous medium can have a great influence on the processes of heat and mass transfer. 

There are various approaches to the description of  two-phase flow: direct numerical calculation of fluid flow in the pore space, multicontinuous models with the laws of mass exchange between continua, single-continuum models of non-equilibrium flow. In the family of isothermal non-equilibrium filtration models, the relative phase permeabilities and capillary pressure are functions not of current saturation but of their change history.

In this work we generalize the relaxation model of capillary nonequilibrium to the non-isothermal case. We introduce two internal thermodynamic parameters (capillary and thermal nonequilibrium) which depend on change history of saturation and temperature. In the model relative phase permeabilities and capillary pressure are functions of saturation, temperature, and current values of these internal parameters. Based on the analysis of the dissipation inequality, thermodynamically consistent kinetic equations for the evolution of these parameters are proposed. The parameters of the single-continuum model are clarified with double-porosity model of porous media with special structure. Structure of the penetration front of fluid hot (or cold) compared to the skeleton was investigated.

This work was supported by the Russian Foundation for Basic Research: grant N19-01-00592.