Rapid and robust phase behaviour stability analysis using global optimization

Reliable phase behaviour prediction is of great importance in chemical and petroleum engineering applications. It is difficult to predict correct behaviours, particularly for multiphase cases, or near critical points (K-points (L1 = V + L2), L-points (L1 = L2 + V), ordinary (L = V)) where local and global Gibbs free energy minima are numerically similar. False convergence or convergence to trivial roots or saddle points frequently occurs. Commercial process simulators as well as research tools are both prone to false convergence. Computational difficulties are due to the non-linear and potentially non-convex form of the objective functions employed. Correct identification of the composition associated with the global minimum in the tangent plane distance function normally leads to successful phase behaviour and phase composition calculations. However, convergence to correct solutions is not guaranteed. Phase equilibrium solutions should be subjected to a second stability test to validate them. Robust computational methods used for stability analysis are normally associated with significant computational loads that prohibit their use in practice, e.g., for oil and gas reservoir simulation and distillation column design, where equilibrium calculations are performed repetitively. In this contribution, a global optimization computational method called Dividing RECTangles (DIRECT), introduced by Jones et al. [D.R. Jones, C.D. Perttunen, B.E. Stockman, Journal of Optimization Theory and Applications 79 (1993) 157-181] is used to solve six benchmark phase equilibrium examples drawn from the literature. This method converged to the global minimum in the tangent plane distance function for all examples evaluated. One to three orders of magnitude fewer function evaluations were typically required compared with other successful methods. This robust and rapid computational approach has the potential for use in a broad range of practical phase equilibrium calculation applications where currently less reliable but rapid approaches are employed. (c) 2007 Elsevier B.V. All rights reserved.