RI 7487 Method For Controlling Instability Of Liquid-Saturation Computations

A method is described for controlling instability in finite-difference computations of liquid saturation near the borehole of a recovery well. Differences of pressure-and saturation-dependent variables are indexed offcenter, upstream and downstream alternately, to provide a stabilizing average. It was found that size of the time step could be increased by a factor of 4 without loss of numerical stability. Finite differences of the variables occur in a variety of relative numerical sizes and combinations. Those relationships of the differences that contribute to instability may be identified by the computing program in which they occur and modified to assist convergence of the computations and execution of the partial differential equations of liquid and gas flow.