A New Preconditioner for Solving Difficult Large Scale Thermal Models

One of the best methods for solving the large sparse systems of linear equations that arise from reservoir flow equations is the flexible generalized minimum residual (FGMRES) method with a two-stage constrained pressure residual (CPR) preconditioner. A linear solver using CPR with AMG first-stage and ILUK second-stage preconditioner was shown to be scalable and very efficient for solving large-scale isothermal problems. However, this is not always the case for thermal problems. A more robust and efficient linear solver algorithm is needed for difficult thermal models. The central idea of the new solver algorithm is to exploit the sparsity within the NeqxNeq submatrices of the second-stage preconditioner and use the magnitude of the in-fill terms to adaptively modify the factorization sparsity pattern to improve accuracy. We combine matrix pre-scaling, equilibration, and reordering before applying ILUT. This new method selects the stronger terms in the matrix factorization and discards the weaker terms based on a user-defined threshold. The new solver algorithm was implemented in the reservoir simulator and applied to several large scale thermal models with up to 10 million cells. For these models it reduced linear iterations by 80% to 93% and gave run time speed-up factors of 2 to 5.5.