Energy inequalities in compositional simulation
Jiří Mikyška, Ondřej Polívka · 2016
We investigate the single-phase flow of a mixture composed of $n$ components in a porous medium under the influence of pressure gradients, viscosity, and gravity. For the case of the single-phase flow (i.e. assuming that under given conditions the phase splitting will not occur), we derive an energy inequality for the continuous problem. Then, we propose the fully implicit discretization of the transport problem which uses a combination of the mixed-hybrid finite element method for the velocity approximation and the finite volume method for the discretization of the transport equations. We prove that the proposed numerical scheme fulfills a discrete version of the energy inequality. A numerical experiment reveals exponential decay of the Helmholtz free energy when a system approaches the equilibrium state.