The Fully Implicit Method (FIM) and the Adaptive Implicit Method (AIM) are widely used for general-purpose reservoir simulation. There has been growing interest, however, in sequential-implicit schemes. The standard sequential solution strategy is SFI (Sequential Fully Implicit). For problems with tightly coupled nonlinear interactions between the multiphase flow and the multi-component transport, the SFI approach may require many more Newton iterations, and/or smaller time steps compared with FIM or AIM. Here, we propose a modification of SFI that improves the convergence behavior substantially. The modification is based on additional coupling terms to the pressure equation. These additional terms are limited in space and time. We show across a wide parameter range that this new algorithm has convergence properties that are quite close to those of FIM and AIM and consistently better than those of SFI. Realistic compositional systems in addition to real reservoir simulation models are presented and discussed.
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