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 CO2CO2 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.