A fully mass-conservative iterative IMPEC method for multicomponent compressible flow in porous media

Abstract

In this paper we consider efficient and fully mass-conservative numerical methods for the multicomponent compressible single-phase Darcy flow in porous media. Compared with the classical IMplicit Pressure Explicit Concentration (IMPEC) scheme by which one of the components may be not mass-conservative, the new scheme enjoys an appealing feature that the conservation of mass is retained for each of the components. The pressure–velocity system is obtained by the summation of the discrete conservation equation for each component multiplying an unknown parameter which is nonlinearly dependent of the molar concentrations. This approach is quite different from the conventional method which is used in the classical IMPEC scheme. We utilize a fully mass-conservative iterative IMPEC method to solve the nonlinear system for molar concentration, pressure and velocity fields. The upwind mixed finite element methods are used to solve the pressure–velocity system. Although the Peng–Robinson equation of state (EOS) is utilized to describe the pressure as a function of the molar concentrations, our method is suitable for any type of EOS. Under some reasonable conditions, the iterative scheme can be proved to be convergent, and the molar concentration of each component is positivity-preserving. Several interesting examples of multicomponent compressible flow in porous media are presented to demonstrate the robustness of the new algorithm.