Explicit Saturation Research Articles

Instability in Runge-Kutta schemes for simulation of oil recovery

Runge-Kutta timestep schemes have been used recently in an attempt to increase the maximum stable timestep for IMPES (implicit pressure, explicit saturation) simulation of oil recovery. It has been claimed that anm-stage method will increase the real stability boundary bym2. A rigorous stability analysis for a Buckley-Leverett problem shows that this claim is false, and that previous stabilized IMPES schemes are never more efficient than ordinary IMPES. Test calculations support these results.

Multigrid Solution of the Pressure Equation in Reservoir Simulation

Abstract The multigrid technique is compared with the incomplete Cholesky conjugate gradient/modified incomplete Cholesky gradient (ICCG/M1CCG) methods for solving implicit pressure, explicit saturation (IMPES)-type pressure equations. The numerical results of several test problems with widely varying transmissibilities are presented. The multigrid algorithm is enhanced by pattern relaxation and acceleration. Optimization of the ICCG/MICCG algorithms is investigated by high-order (up to tenth) decompositions and different ordering schemes. For large problems the multigrid method is superior in terms of scalar work. The multigrid scheme can also be highly vectorized, and is an O(N) algorithm even for problems with large jump discontinuities in equation coefficients. Results of the multigrid method applied to nonsymmetric problems are also presented.