APPLICATION OF HIGHER-ORDER FLUX-LIMITED METHODS IN COMPOSITIONAL SIMULATION

A higher-order flux-limited finite-difference scheme has been implemen ted into a compositional simulator to discretize the convection terms of the component conservation equations and the relative permeability terms of the phase fluxes. Harten's total variation diminishing criter ia are imposed directly to the finite-difference equations and the bou nds of the flux limiters which are suitable for larger Courant numbers and nonuniform grid systems are obtained. A time-correction technique is applied to increase the time accuracy and improve the stability co ndition. The scheme has been tested for miscible and immiscible flow p roblems in one and two dimensions, and the results were compared with those using a third-order method without flux limiting and some availa ble analytical solutions. It has been shown that the scheme effectivel y reduces numerical dispersion and results in superior resolution of c oncentration and saturation fronts compared to conventional schemes. T he stability conditions are also improved by using a time-correction t echnique. The results of the scheme are in good agreement with the ana lytical solutions. These improvements were achieved with negligible in crease in computational effort. The scheme can also be applied to simu lation problems with nonuniform gridblock sizes.