Tests of the Stability and Time-Step Sensitivity of Semi-Implicit Reservoir Stimulation Techniques

A reservoir simulation technique that employs semi- implicit approximations to relative permeabilities exhibits excellent stability and convergence characteristics when applied to water- or gas-coning problems. Recent workers in this area have made a simplifying assumption in order to linearize the flow terms of the semi-implicit finite- difference equations. A method is described of solving efficiently the nonlinear form of the equations and demonstrates that time-step sensitivity is reduced by iterating on the nonlinear terms. In addition, it addresses the problem of allocating a well's production among multiple grid blocks. Example problems include both water-coning and gas-percolation applications.