Analytical decoupling techniques for fully implicit reservoir simulation

This paper examines linear algebraic solvers for a given general purpose compositional simulator. In particular, the decoupling stage of the constraint pressure residual (CPR) preconditioner for linear systems arising from the fully implicit scheme is evaluated. An asymptotic analysis of the convergence behavior is given when Δt approaches zero. Based on this analysis, we propose an analytical decoupling technique, from which the pressure equation is directly related to an elliptic equation and can be solved efficiently. We show that this method ensures good convergence behavior of the algebraic solvers in a two-stage CPR-type preconditioner. We also propose a semi-analytical decoupling strategy that combines the analytical method and alternate block factorization method. Numerical experiments demonstrate the superior performance of the analytical and semi-analytical decoupling methods compared to existing methods.