High-order upwind schemes for two-phase, multicomponent flow

In this paper, we investigate high-order finite-difference schemes for compositional simulation. Results presented for one-dimensional (1D) gas-injection problems suggest that a third-order, essentially nonoscillatory scheme achieves accurate results more efficiently than first-order methods; leads to an improved treatment of phase behavior; and is more robust than traditional total variation diminishing schemes. We use phase diagrams as well as solution profiles to analyze discretization errors. Discretization errors can strongly affect the prediction of local displacement efficiency because of the nonlinear coupling introduced by the phase behavior in the system of governing equations. The study explains the ability of the numerical schemes to predict local displacement efficiency. In all of our tests, we compare numerical results to analytical and semianalytical solutions found through the method of characteristics. Our 1D results can be extended to 3D through conventional finite-difference approaches, but we plan to apply them in a streamline-based compositional simulator.