Coupling-strength criteria for sequential implicit formulations

The Fully Implicit Method (FIM) is used widely in the reservoir simulation community, especially for the so-called black-oil model. The primary reason for resorting to FIM is its unconditional stability, but this comes at the high computational cost of solving coupled nonlinear systems of all the conservation equations simultaneously. In addition, having a scalable FIM simulator relies on specialized multi-stage linear solvers. In the last few years, the Sequential Fully Implicit (SFI) formulation has received a great deal of attention. SFI decomposes the fully coupled nonlinear problem into two nonlinear sub-problems: flow and transport. The flow problem is solved implicitly for pressure, and the transport problem is solved implicitly for the saturation(s). The splitting usually assumes that the total-velocity is fixed during the transport computations. Because the pressure has a near-elliptic behavior and the saturation(s) have near-hyperbolic behavior, the flow-transport splitting of SFI allows for the use of dedicated scalable nonlinear and linear solvers for each sub-problem.