Compositional modeling in three-phase flow for CO₂ and other fluid injections using higher-order finite element methods

CO₂ injection is one of the most attractive options for water-flooded reservoirs. The numerical simulation of the process is computationally challenging; it requires accurate compositional modeling of three-phase flow in porous media. In this work, we simulate for the first time, three-phase compositional flow using higher-order finite element methods. Our numerical model is based on an iterative IMPEC coupling of the pressure equation and species transport equations, which are solved by mixed finite element (MFE) and discontinuous Galerkin (DG) methods, respectively. A number of numerical examples in one and two dimensions are presented to illustrate the modeling capability of the proposed algorithm. We take into account various phase behavior effects including swelling, viscosity reduction and vaporization from CO₂ injection in water-flooded reservoirs. The model captures the spike in concentration. Numerical comparison of our combined MFE-DG approach with the conventional upstream weighted finite difference method indicates that MFE-DG has low numerical diffusion. The proposed MFE-DG method can capture the solution discontinuities and yield accurate prediction of shock locations arising in computational three-phase flow. The work sets the stage for broad extension of the higher-order methods for numerical simulation of three-phase flow for complex geometries and complex processes.