Mathematical and Numerical modeling of liquid filtration Processes in a porous Medium

In this paper one mathematical model of filtration theory with phase transitions is investigated. When using surface-active substances (surfactants) for the development of oil and gas fields in the reservoir occur sorption processes at the interfaces of individual phases (surfactants and oil, or surfactants and soil). In real processes a finite time is required for achievement equilibrium. Therefore considering the mathematical model was called the mathematical model with phase relaxation. The solvability of the mathematical model, the limiting transition in relaxation time are investigated. It is proved that in the limiting case, the original problem is a problem of Stefan type.