New Sequential Scheme for Mixed-implicit Compositional Flow Simulation

The Fully Implicit (FI) and the Adaptive Implicit (AI) methods are widely used for general-purpose reservoir simulation. There has been growing interest, however, in sequential-implicit schemes. The common sequential solution strategies are: IMplicit Pressure Explicit Saturations (IMPES) and Sequential Fully Implicit (SFI) methods. In highly heterogeneous domains with tight coupling between the multiphase flow and the multi-component transport, IMPES suffers from severe restrictions on the size of the stable timestep, and SFI suffers from slow convergence of the sequential updating between the flow and transport problems. Here, we describe a modified SFI (m-SFI) scheme that improves the convergence behavior substantially. The modification entails additional coupling terms to the pressure equation that are limited in both space and time. Specifically, the pressure equation is complemented with a local approximation of the pressure-saturation/composition coupling terms that are brought about by the appearance of the gas-phase during iterations. This modification is also applied to the modified Sequential Adaptive Implicit (m-SAI) scheme. We consider several very challenging compositional processes whereby the SFI method suffers from severe nonlinear convergence behaviors, and we demonstrate using numerical experiments and analysis that the modified algorithms have convergence properties that are quite close to those of the FI and AI methods.