A New Algorithm for Computing Process Flexibility

Abstract

In the design of a chemical process (CP), certain design specifications (for example, those related to process economics, process performance, safety, and the environment) must be satisfied. During the operation of the plant, because design models have uncertainties associated with them, we need to ensure that, within the region of uncertainty, all design specifications are satisfied. In recent years, research has focused on the investigation of the process flexibility (Biegler et al. Systematic Methods of Chemical Process Design; Prentice Hall: Englewood Cliffs, NJ, 1997) based on the feasibility function (Halemane and Grossmann AIChE J. 1983, 29 (3), 425) which is a measure of the CP's ability to meet design specifications under uncertainty. Several researchers have proposed methods for calculating the process feasibility function, which involves solving a very complex multiextremal and nondifferentiable optimization problem. Current methods for calculation of the flexibility function use an enumeration procedure (explicit or implicit), which in the worst case can require a large number of iterations. To try to address this issue, in this paper, we have introduced an efficient approach, which avoids enumeration. Through examples, we have shown that the new method leads to a small number of iterations and has low CPU requirements.

Flexibility analysis and design using a parametric programming framework

“…Halemane and Grossmann 1983 Feasibility test; design for fixed degree of flexibility Ž . Ostrovsky et al 1994Ostrovsky et al , 1997Ostrovsky et al , 2000 Bounding algorithms for the problems considered by Halemane and Ž . Grossmann 1983 Ž .…”

Mathematical Tools for the Quantitative Definition of a Design Space

“…These require explicitly known constraints and may make assumptions regarding the convexity of the feasible region [65]. For instance, many of the aforementioned methods require that the feasible region be convex or 1 À d quasi-convex in the uncertain variables [64,70,78,82]. In addition, deterministic solvers sometimes experience difficulty when dealing with large or complex optimization problems.…”

“…(13) is satisfied, where is a user-defined tolerance. A branch-and-bound procedure is used to explore potential process designs to find the one corresponding to the greatest flexibility [70].…”

“…A full development of the split and bound strategy for solving flexibility index problems can be found in Ostrovsky et al [68][69][70]. In order to apply the aforementioned solution strategies, the feasibility function and constraints must satisfy certain conditions [71].…”

“…3a [62,66]. This corresponds to the feasible region being jointly convex in the control variables and the uncertain parameters [70]. The active set strategy requires that the feasibility function χ(d) be quasi-concave with respect to the uncertain parameters θ and quasi-convex with respect to control variables z for fixed values of the uncertain parameters as well as quasi-concave in the control variables and uncertain parameters [64].…”