USE OF HIGHER ORDER FINITE DIFFERENCE METHODS IN RESERVOIR SIMULATION.

A nine point finite difference scheme is proposed which extends previous work and allows for the use of an irregular grid and nonisotropic permeabilities. Comparison of results with that achieved by conventional simulators illustrate the degree of improvement that can be achieved. It is shown, however, that while the higher order scheme considerably reduces grid orientation effects it cannot, on its own, eliminate the problem of numerical dispersion. Various devices are combined with the nine point scheme to cotrol numerical dispersion and a simple technique is demonstrated to be highly effective. The techniques described thus allow the engineer to concentrate on reservoir descriptions as the effects of grid orientation and numerical dispersion on the simulator have been significantly reduced.