THE FRACTAL RESPONSE OF ROBUST SOLUTION TECHNIQUES TO THE STATIONARY POINT PROBLEM

The mathematical nature and physical significance of the stationary po int problem, as related to the computation of phase equilibria, is rev iewed. Robust (Newton) techniques are used to compute stationary point s in composition space for three ternary systems: (1) a simple model o f excess Gibbs energy; (2) a Type I van der Waals mixture at a tempera ture and pressure which does not have any real-root multiplicity when solving the cubic equation-of-state; (3) the same Type I van der Waals mixture at a temperature and pressure which has real-root multiplicit y when solving the cubic equation-of-state. All three examples can exh ibit fractal behavior with respect to the points of initiation of the robust solution technique. The occurrence and nature of the fractal pa tterns are a function of the location of the reference point of the so lution search in the composition space.