On an efficient time scheme based on a new mathematical representation of thermodynamic equilibrium for multiphase compositional Darcy flows in porous media

Abstract

This paper presents a new mathematical representation of multiphase thermodynamic equilibrium using so-called repartition coefficients. Combined with a global mass formulation of multiphase Darcy flow in porous media, it allows the derivation of a computationally efficient family of time schemes. The model accounts for the mass conservation of an arbitrary number of components flowing through an arbitrary number of phases, coupled with thermodynamic equilibrium and pore volume conservation. By separating the thermodynamic equilibrium part from the flow part through the repartition coefficients, the formulation removes the need for any specific handling of phase appearance and disappearance within the flow solver. Any “black box” thermodynamic equilibrium solver can then be used to compute the repartition coefficients, from EOS based solvers to tabulated representation of the thermodynamic equilibrium, each specific choice of thermodynamic solver leading to a new scheme. Three numerical experiments, from a simple beam to a real case, illustrate the good behavior of the approach.