Tie-simplex-based nonlinear solver for massvariables compositional formulation

A new nonlinear solver based on correction of unknowns along flux function in parameterized compositional space is developed for general-purpose compositional simulation. This solver takes full advantage of the hyperbolic nature of the transport equations of compositional problem. Since compositional recovery processes evolve along a few 'key' tie-simplexes, the flux functions (fractional flow curves) parameterized along these tie-simplexes play a dominant role in the evolution of the solution. For a given nonlinear iteration, the flux functions associated with the parameterized tie-simplex are segmented into trust regions which includes appearance and disappearance of phases, changes in mobility of phases, and the inflection point of flux function. These regions are used to guide the evolution of the composition unknowns on nonlinear iteration since they delineate convex regions of the flux function, where convergence of the Newton iterations is guaranteed. Several challenging compositional problems are used to test the robustness and efficiency of this tie-simplex-based 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, the new nonlinear solver converges within a fewer number of Newton iterations.