ABSTRACT
The phenomenon of numerical dispersion is due to the finite grid size in simulators. This effect can severely influence the results of simulations of displacement of oil by carbon dioxide. Mathematical techniques for controlling such spurious dispersion are described. The resulting scheme is compared to the industry standard upstream weighted finite difference method for gas drives which are: (a) immiscible, (b) have limited miscibility by a vaporizing gas drive mechanism, (c) exhibit developed miscibility, and (d) are fully miscible.
The results presented are of value for the following reasons. First, we discuss modifications that we have made to implement methods developed for mathematical model problems in a compositional simulator. Second, we have shown that such techniques represent an improvement from the state-of-the-art. Our particular contribution is the method by which we modify a central difference approximation to insure monotonie behavior. Third, we provide direct comparisons between the standard scheme and our modified scheme. Fourth, we show that, to obtain a specified level of numerical dispersion, at minimum a threefold reduction in computer costs is realized by our scheme with respect to the industry standard method. Last, we show that this estimate of benefit is conservative, as we can obtain up to a fiftyfold improvement in some cases.