Evolution of concepts and models for quantifying resiliency and flexibility of chemical processes

Abstract

This paper provides a historical perspective and an overview of the pioneering work that Manfred Morari developed in the area of resiliency for chemical processes. Motivated by unique counter-intuitive examples, we present a review of the early mathematical formulations and solution methods developed by Grossmann and co-workers for quantifying Static Resiliency (Flexibility). We also give a brief overview of some of the seminal ideas by Manfred Morari and co-workers in the area of Dynamic Resiliency. Finally, we provide a review of some of the recent developments that have taken place since that early work.1

Mathematical Tools for the Quantitative Definition of a Design Space

“…They describe the ability of a process to generate acceptable product across a range of process design and operating conditions in the presence of potential variability. In other words, they are concerned with feasible operation of a process, given uncertainty in its inputs, design and operating conditions [57]. Sources of variability include variation in input material quality, disturbances in operating conditions, or plant-model mismatch [58].…”

“…The value of θ that corresponds to the solution of the flexibility index problem is referred to as the critical parameter point θ C . This is the parameter value that limits the flexibility of the design, and the corresponding constraint(s) along which θ C occurs are the critical constraints that limit flexibility [57]. Relaxing these constraints would thus increase the size of the feasible region for the process.…”

“…In problem (4), the region T(δ) describes a variable range for the uncertain parameters. δ is a non-negative scalar value such that if δ < 1, the corresponding feasible region is T δ ð Þ & T , if δ > 1 the corresponding feasible region is T δ ð Þ ' T and if δ ¼ 1 the corresponding feasible region is T(δ) ¼ T. The quantities Δθ À and Δθ + represent deviations from the nominal values of the uncertain parameters in the negative and positive directions, respectively [57,61,62,65].…”

“…(2). This problem can be solved using standard linear (LP) or nonlinear (NLP) programming solvers, depending on the nature of the constraints [57,65]. …”

On the relation between flexibility analysis and robust optimization for linear systems

“…In a recent review paper, 2 Grossmann et al give a historical perspective on the evolution of the concepts and mathematical models used for flexibility analysis. Some of the earlier works in this area include the work of Friedman and Reklaitis 3,4 from the mid 1970s, who proposed techniques for solving linear programming (LP) problems with some of the parameters subject to uncertainty; subsequently from the 1980s the resiliency concepts proposed by Saboo et al 5 and applied to heat exchanger networks (HENs); and the development of optimization models to quantify process flexibility by solving the flexibility test and flexibility index problems.…”