Compositional nonlinear solver based on trust regions of the flux function along key tie-lines

A new nonlinear solver that combines tie-line and fractional-flow information is developed for general-purpose compositional simulation. The solver, which takes advantage of the hyperbolic nature of the transport equations, is demonstrated for a compositional formulation that employs molar (or mass) variables. Since compositional recovery processes evolve along a few 'key' tie-lines, the flux functions (fractional flow curves) associated with these key tie-lines play a dominant role in the evolution of the solution. A two-stage nonlinear solver is proposed, and its applicability and efficiency for general-purpose compositional simulation is demonstrated. In the first stage, given the pressure and overall composition of the current nonlinear iteration, the key tie-lines are computed using a negative-flash procedure, and the nonlinear unknowns are updated accordingly. In the second stage, the flux functions associated with the computed tie-lines are segmented into trust regions (i.e., appearance and disappearance of a phase, and the inflection point of the S-shaped two-phase region), which are then used to guide the consistent evolution of the compositions. These trust regions delineate convex parts of the flux function, where convergence of the Newton iterations is guaranteed. Several challenging, multi-contact, miscible compositional problems, including the SPE 10 permeability field with the 6-component SPE 5 fluid, are used to test the robustness and efficiency of this new nonlinear solver. The convergence rate of the new nonlinear solver is always better than our standard safeguarded Newton method, which employs heuristics on maximum changes in the variables. We demonstrate that for aggressive time stepping (i.e., maximum throughput - so called CFL numbers - is hundreds to thousands of times larger than the IMPES limit), the new nonlinear solver converges within a few Newton iterations for the wide range of problems we studied.