Enhanced Constrained Pressure Residual ECPR Preconditioning for Solving Difficult Large Scale Thermal Models
Gary Z. Li, J. R. Wallis · SPE Reservoir Simulation Conference · 2017
Abstract The Constrained Pressure Residual (CPR1,2) preconditioning method with FGMRES3 acceleration, although very efficient for iterative solution of isothermal fully implicit linear systems, may encounter significant convergence difficulties for large scale thermal cases. This is in part due to the fact that for these problems pressures are not the only strong variables. For such cases this paper describes an enhanced version of CPR (ECPR) preconditioning which is simple to implement and can significantly decrease iterations by 50% −80% or more depending on problem difficulty, converge where CPR fails, and substantially reduce work. The two-stage ECPR preconditioning uses an expanded variable set for the first stage. The key step involves a fast strong variable selection algorithm which can substantially increase the robustness of CPR. For the approximate solution of this enhanced first stage we used FGMRES with equilibrated ILUC as the preconditioning. The improved strength of this step allows the use of a less expensive second stage preconditioning such as block ILU(0) rather than block ILU (1)2. The block ILU(0) /ECPR method showed significant improvement in convergence rate for these difficult thermal cases over the original block ILU(1)/CPR method. We observed over 50% reduction in the number of iterations for our moderately difficult test cases over entire runs and reduction in run times. For individual linear systems requiring many CPR iterations test cases show iterations can be reduced by 80% or more using ECPR. In one particular test case CPR failed to converge after 100 iterations but ECPR converged in 7 iterations.