Enhanced Interval Analysis for Phase Stability:  Cubic Equation of State Models

Abstract

The reliable prediction of phase stability is a challenging computational problem in chemical process simulation, optimization and design. The phase stability problem can beformulated either as a minimization problem or as an equivalent nonlinear equation solving problem. Conventional solution methods are initialization dependent, and may fail by converging to trivial or non-physical solutions or to a point that is a local but not global minimum. Thus there has been considerable recent interest in developing more reliable techniques for stability analysis. Recently we h a ve demonstrated, using cubic equation of state models, a technique that can solve the phase stability problem with complete reliability. The technique, which is based on interval analysis, is initialization independent, and if properly implemented provides a mathematical guarantee that the correct solution to the phase stability problem has been found. However, there is much r o o m for improvement in the computational e ciency of the technique. In this paper we consider two means of enhancing the e ciency of the method, both based on sharpening the range of interval function evaluations. Results indicate that by using the enhanced method, computation times can be reduced by nearly an order of magnitude in some cases.

Phase Behavior and Reliable Computation of High-Pressure Solid−Fluid Equilibrium with Cosolvents

“…Another approach for reliable determination of phase stability from cubic EOS models is that of Harding and Floudas 45 , who use a global optimization method based on branchand-bound using convex underestimating functions. However, this approach will not find all of the stationary points of the tangent plane distance (useful to initialize the phase split computations) and so is not directly comparable to the approach of Hua et al 35 …”

“…However, as noted above, knowledge of the stationary points may be useful for initializing the phase split computations, so we typically use IN/GB to find all the stationary points. These procedures are outlined in more detail by Xu et al 7 , and further details are given by Hua et al 34,35 and Schnepper and Stadtherr. 36 Properly implemented, the IN/GB technique provides the power to find, with mathematical and computational certainty, enclosures of all solutions of a system of nonlinear equations, or to determine with certainty that there are none, provided that initial upper and lower bounds are available for all variables.…”

“…In the approach used here, essentially all the CPU time is spent in the phase stability analysis stage of the problem, for which, as discussed above, the interval methodology of Hua et al 35 is used. Another approach for reliable determination of phase stability from cubic EOS models is that of Harding and Floudas 45 , who use a global optimization method based on branchand-bound using convex underestimating functions.…”

Global optimization in the 21st century: Advances and challenges

“…Hua, Brennecke, and Stadtherr (1998a) applied an interval analysis method for the phase stability computations of binary and ternary mixtures using equation of state models. Hua, Brennecke, and Stadtherr (1998b) introduced two enhancements on their interval analysis approach based on monotonicity and mole fraction weighted averages for improving the efficiency in the tangent plane stability analysis for cubic equations of state. Zhu and Xu (1999b) used simulated annealing for the tangent plane stability analysis criterion and they applied it to ternary systems.…”

Parameter estimation for VLE calculation by global minimization: the genetic algorithm

“…Use of global techniques in these problems is relatively unexplored and deserves greater investigation. Only deterministic global solvers, such as the homotopy continuation method (Sun and Seider, 1995), the interval Newton method (Hua et al, 1998a(Hua et al, , 1998b, and the Lipschitz algorithm (Zhu and Xu, 1999), have been employed; all these methods use highly complex mathematics. On the other hand, stochastic optimization techniques use simple mathematics and have often been found to be as powerful and effective as deterministic methods in many engineering applications.…”