The Discontinuous Solutions of the Transport Equations for Compositional Flow in Porous Media

In the present paper we consider a multicomponent multiphase isothermal flow in porous media with mass exchange between phases. The system of equations of multiphase multicomponent flow has discontinuous solutions, but is not hyperbolic, except some particular cases. For this general, non-hyperbolic system, we propose a free energy condition to select unique physically admissible discontinuous solutions. We also develop a geometrical procedure which provides a tool to analyze the free energy condition. For a two-component mixture, analytical formulae are obtained for the allowed discontinuities.