Formulations of two phase liquid gas compositional Darcy flows with phase transitions

In this article, three formulations of two phase compositional Darcy flows taking into account phase transitions are compared. The first formulation is the so called natural variable formulation commonly used in reservoir simulation, the second has been introduced in [14] and uses the phase pressures, saturations and component fugacities as main unknowns, and the third is an extension to general compositional two phase flows of the pressure pressure formulation introduced in [2] in the case of two components. The three formulations are shown to lead to equivalent definitions of the phase transitions for our gas liquid thermodynamical model. Then, they are compared numerically in terms of solution and convergence of the Newton type non linear solver on several 1D and 3D test cases including gas appearance and liquid disappearance. The 3D discretization is based on the Vertex Approximate Gradient (VAG) scheme [10] and takes into account discontinuous capillary pressures.