  The Sequential Fully Implicit (SFI) method was proposed to simulate coupled
immiscible multiphase fluid flow in porous media. Later, it was extended to the
black-oil model, whereby the gas component is allowed to dissolve in the oil
phase. Most recently, the SFI approach was extended to fully compositional
isothermal displacements. SFI schemes solve the fully coupled system in two
steps: (1) Construct and solve the pressure equation (flow problem). (2) Solve
the coupled species transport equations for the phase saturations and phase
compositions. Experience indicates that complex interphase mass transfer
behaviors often lead to large numbers of SFI outer iterations compared with the
Fully Implicit (FI) method. Here, we demonstrate that the convergence
difficulties are directly related to the treatment of the coupling between the
flow and transport problems, and we propose a new SFI variant based on a
nonlinear overall-volume balance equation. The first step consists of forming
and solving a nonlinear pressure equation, which is a weighted sum of all the
component mass conservation equations. The second step of the new SFI scheme
entails introducing the overall-mass density as a degree-of-freedom, and
solving the full set of component conservation equations cast in the
natural-variables form. During the second step, the pressure and the
total-velocity fields are fixed. We analyze the `splitting errors' associated
with the compositional SFI scheme, and we show how to control these errors in
order to converge to the same solution as the Fully Implicit (FI) method. This
robust sequential-implicit solution scheme allows for designing numerical
methods and linear solvers that are optimized for the sub-problems of flow and
transport.
