An efficient and physically consistent numerical method for the Maxwell-Stefan-Darcy model of two-phase flow in porous media

Numerical modeling of two-phase flow in porous media has extensive applications in subsurface flow and petroleum industry. A comprehensive Maxwell-Stefan-Darcy (MSD) two-phase flow model has been developed recently, which takes into consideration the friction between two phases by a thermodynamically consistent way. In this paper, we for the first time propose an efficient energy stable numerical method for the MSD model, which can preserve multiple important physical properties of the model. Firstly, the proposed scheme can preserve the original energy dissipation law. This is achieved through a newly-developed energy factorization approach that leads to linear semi-implicit discrete chemical potentials. Secondly, the scheme preserves the famous Onsager's reciprocal principle and the local mass conservation law for both phases by introducing different upwind strategies for two phase saturations and applying the cell-centered finite volume method to the original formulation of the model. Thirdly, by introducing two auxiliary phase velocities, the scheme has ability to guarantee the positivity of both saturations under proper conditions. Another distinct feature of the scheme is that the resulting discrete system is totally linear, well-posed and unbiased for each phase. Numerical results are also provided to show the excellent performance of the proposed scheme.