Implementation of higher-order methods for robust and efficient compositional simulation

Numerical simulation of two-phase multicomponent flow in permeable media with species transfer between the phases often requires use of higher-order methods. Unlike first-order methods, higher-order methods may be very sensitive to problem formulation. The sensitivity to problem formulation and lack of recognition have hindered the widespread use of higher-order methods in various problems including improved oil recovery and sequestration from CO 2 injection. In this work, we offer proper formulation of species balance equations and boundary conditions which overcome problems of formulations used previously that were detrimental to the efficiency of higher-order methods. We also present proper approximation of phase fluxes in the mixed finite element method. Our proposals remove major deficiencies in using higher-order methods in two-phase multicomponent flow. Numerical examples are presented to demonstrate robustness and efficiency of our approach.