Dissipation-Based Nonlinear Solver for Fully Implicit Compositional Simulation

Abstract

Summary In reservoir simulation of complex recovery processes, solving nonlinear equation system arising from the fully implicit method (FIM) poses a significant challenge. The Courant-Friedrichs-Lewy (CFL) conditions can span orders of magnitude in heterogeneous reservoir models because of large variations of permeability and porosity. The standard Newton method often fails to converge for large timestep sizes. We extend a new dissipation-based continuation (DBC) method to multiphase and compositional problems. The objective is to avoid timestep cuts and maintain efficient timestepping in FIM simulations. The method constructs a homotopy of the discrete governing equations by adding numerical dissipation. A continuation parameter is introduced to control the dissipation level and ensure that the accuracy of the converged solution is not degraded. Within the DBC framework, we develop general dissipation operators for multiphase and compositional flow models. Adaptive strategies are also proposed to determine the optimum dissipation matrix for hyperbolic systems. We evaluate the efficiency of the new nonlinear solver using several challenging cases. Results show that the standard damped Newton solver is afflicted by severe timestep restrictions and wasted computations. By comparison, the DBC solver enables superior nonlinear convergence. The dissipation operators can effectively overcome major convergence difficulties of coupled flow and transport problems.