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

by

J. Z. Hua, J. F. Brennecke, and M. A. Stadtherr

#### ABSTRACT

The reliable prediction of phase stability is a challenging computational
problem in chemical process simulation, optimization and design. The phase
stability problem can be formulated 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 have 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 room for improvement
in the computational efficiency of the technique. In this paper we consider
two means of enhancing the efficiency 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.

Comput. Chem. Eng., 22, 107-1214 (1998).