Mathematical analysis of the two-phase two-component fluid flow in porous media by an artificial persistent variables approach

This paper deals with the existence of weak solutions of the system that describes the two-phase two-component fluid flow in porous media. Both two-phase and possible one-phase flow regions are taken into account. Our research is based on a global pressure, an artificial variable that allows us to partially decouple the original equations. As a second primary unknown for the system, we choose the gas pseudo-pressure, a persistent variable which coincides with the gas pressure in the two-phase regions while it does not have physical meaning in one-phase flow regions, when only the liquid phase is present. This allows us to introduce an another persistent variable that is an artificial variable in one-phase flow regions and a physical variable in two-phase flow regions—the capillary pseudopressure. We rewrite the system's equations in a fully equivalent form in terms of the global pressure and the gas-pseudo pressure. In order to prove the existence of weak solutions of obtained system, we also use the capillary pseudo-pressure. By using it, we can decouple obtained equations on the discrete level. This allows us to derive the existence result for weak solutions in more tractable way.