Fast and Robust Algorithm for Compositional Modeling: Part II - Two-Phase Flash Computations

In Part I of our study, stability analysis testing in the reduced space was formulated, and its robustness and efficiency in comparison to the conventional approach was explored. In this paper, we present formulations including, first, direct solution of the nonlinear equations, and second, minimization of Gibbs free energy for two-phase flash computations in the reduced space. We use various algorithms including the successive substitution (SS), Newton's method, globally convergent modifications of Newton's method (line searches and trust region), and the dominant eigenvalue method (DEM) for direct solution of the nonlinear equations defining two-phase flash and the minimization of Gibbs free energy. We also suggest a criterion based on the tangent-plane-distance (TPD) for the initialization from the equilibrium ratios. The proposed criterion has a significant effect on reducing the number of iterations. The results from various algorithms reveal that the direct solution of the nonlinear equations in the reduced space, combined with the use of the TPD criterion for initialization in the combined SS and Newton's method, can make flash computations extremely efficient. The efficiency and robustness of flash computations in the critical region are especially remarkable.