An Improved Numerical Technique for Solving Multi-Dimensional Miscible Displacement Equations

Analog difference equations of high order accuracy describing stable miscible displacement are presented. The high order difference scheme eliminates almost all the numerical smearing, which is the result of the normally used approximations, and leaves only the effect of the physical dispersion in the solution. In a one-dimensional system, the technique involves an addition of a negative dispersion term to the continuity equation. The negative dispersion term which is called the numerical dispersion coefficient, depends upon the flow velocity, the time-step size, and the block size. The procedure is extended to multi-dimensional systems. As a check, comparisons of the computed results with analytical solutions in one and 2- dimensional systems are made. The error function solution in a one-dimensional miscible system and a 5-spot fractional flow curve computed from the potentiometric model are considered as the analytical solutions in the 2 cases.