### Reliable Prediction of Phase Stability Using an Interval-Newton
Method

by

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

#### ABSTRACT

A key step in phase equilibrium calculations is determining if, in fact,
multiple phases are present. Reliably solving the phase stability and,
ultimately the phase equilibrium problem, is a significant challenge for
high pressure vapor/liquid, liquid/liquid and vapor/liquid/liquid equilibrium.
We present the first general-purpose computational method, applicable to
any arbitrary equation of state or activity coefficient model, that can
mathematically guarantee a correct solution to the phase stability problem.
In this paper, we demonstrate the use of this new method, which uses techniques
from interval mathematics, for the van der Waals equation of state to determine
liquid/liquid and liquid/vapor phase stability for a variety of representative
systems. Specifically, we describe and test interval methods for phase
stability computations for binary mixtures that exhibit Type I and Type
II behavior, as well as for a relatively simple ternary mixture. This shows
that interval techniques can find with absolute certainty all stationary
points, and thus solve the phase stability problem with complete reliability.

Fluid Phase Equilib., 116, 52-59 (1996)