Modeling and simulation of partially miscible two-phase flow with kinetics mass transfer

Multiphase flow equations for two components (for instance water and hydrogen) and two phases (liquid and gas), with equilibrium phase exchange, have been used to simulate the process of miscible displacement in porous media. Laboratory and field studies have shown that this assumption fails under certain circumstances especially for accurate description of the pollution and a finite transfer velocity, called here the kinetics. We propose a numerical scheme based on a two-step convection/diffusion-relaxation strategy to simulate the non-equilibrium model. In the first step we solve the intra-phase transfer (convection/diffusion) working with liquid saturation, liquid pressure and dissolved hydrogen concentration as primary variables. In the second step, we address the interphase transfer using the solubility relation that is solved by projection on the equilibrium state. This technique also ensures the positivity for the liquid saturation and produces energy estimates. One important advantage of this approach is the fact that the simulation can be easily adapted to different linear and non-linear equilibrium laws between phases. Another advantage is that our proposed method includes the kinetics in a projection step and keeps the displacement of the components. We implemented this new model in in-house simulation code and present numerical results comparing the model with equilibrium and non-equilibrium one.