### Robust Process Simulation Using Interval Methods

by

Carol A. Schnepper and Mark A. Stadtherr

#### ABSTRACT

Ideally, for the needs of robust process simulation, one would like
a nonlinear equation solving technique that can find any and all roots
to a problem, and do so with mathematical certainty. In general, currently
used techniques do not provide such rigorous guarantees. One approach to
providing such assurances can be found in the use of interval analysis,
in particular the use of interval Newton methods combined with generalized
bisection. However, these methods have generally been regarded as extremely
inefficient. Motivated by recent progress in interval analysis, as well
as continuing advances in computer speed and the availability of parallel
computing, we consider here the feasibility of using an interval Newton/generalized
bisection algorithm on process simulation problems. An algorithm designed
for parallel computing on an MIMD machine is described, and results of
tests on several problems are reported. Experiments indicate that the interval
Newton/generalized bisection method works quite well on relatively small
problems, providing a powerful method for finding all solutions to a problem.
For larger problems, the method performs inconsistently with regard to
efficiency, at least when reasonable initial bounds are not provided.

Comput. Chem. Eng., 20, 187-199 (1996)