A New Method for Reducing Numerical Accumulation and Dispersion - Application to Enhanced Oil Recovery

The numerical dispersion of components in EOR problems generally makes forecasting pessimistic or impossible. This problem has been known for a long time, and efforts are still being made to solve it. To reduce this difficulty, some authors have used highorder numerical schemes (two-point upstream weighting, Van Leer, Leonard, etc.). By their overcorrecting, these schemes often lead to a reverse error called numerical accumulation. This paper proposes a New Flux Correcting (NEC) method based on an original correction of the mass flux in each grid-block. The corrected flux will be a weighted average between the flux at the time considered (upper approximate value) and the flux at the preceding time (lower approximate value). Bounded by these limits, the corrected flux generates neither excessive numerical dispersion nor accumulation. A theoretical study was made to determine the suitable value of the weighting factor. The stability conditions of the new process have also been determined. Several examples of applications have been performed. In particular, the injection of a surfactant slug followed by polymer injection has been considered. Each oil displacement (1D or 2D) was simulated several times to test and compare the various methods of dispersion correction. The NEC method has been revealed to be very effective. It is a robust method, easily added to existing industrial simulators.