Modeling compositional compressible two-phase flow in porous media by the concept of the global pressure

We derive a new formulation for the compositional compressible two-phase flow in porous media. We consider a liquid-gas system with two components: water and hydrogen. The formulation considers gravity, capillary effects, and diffusivity of each component. The main feature of this formulation is the introduction of the global pressure variable that partially decouples the system equations. To formulate the final system, and in order to avoid primary unknowns changing between one-phase and two-phase zones, a second persistent variable is introduced: the total hydrogen mass density. The derived system is written in terms of the global pressure and the total hydrogen mass density. The system is capable of modeling the flows in both one and two-phase zones with no changes of the primary unknowns. The mathematical structure is well defined: the system consists of two nonlinear parabolic equations, the global pressure equation, and the total hydrogen mass density equation. The derived formulation is fully equivalent to the original one. Numerical simulations show ability of this new formulation to model efficiently the phase appearance and disappearance.