Application of higher-order flux-limited methods in compositional simulation

A higher-order flux-limited finite-difference scheme has been implemented 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 criteria are imposed directly to the finite-difference equations and the bounds 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 condition.The scheme has been tested for miscible and immiscible flow problems in one and two dimensions, and the results were compared with those using a third-order method without flux limiting and some available analytical solutions.