An analysis of the unified formulation for the equilibrium problem of compositional multiphase mixtures

In this paper , we conduct a thorough mathematical analysis of the unified formulation advocated by Lauser et al . [ Adv Water Res 34 (2011), 957-966] for compositional multiphase flows in porous media The interest lies its potential to automatically handle appearance and disappearance phases. However practical implementation turned out be not always robust realistic fugacity laws associated with cubic equations state as shown Ben Gharbia Flauraud Oil & Gas Sci Technol 74 (2019), 43]. By focusing on subproblem phase equilibrium derive sufficient conditions existence corresponding system equations. We trace back difficulty deficiency Gibbs functions that comes into play due `` unifying '' feature new formulation. propose partial remedy problem extending domain definition these natural way Besides highlight crucial but seemingly unknown fact encapsulates all properties known physicists such tangent plane criterion minimization energy mixture.