Flexibility analysis and optimization of chemical plants with uncertain parameters

Ostrovsky, G. M.; Volin, Yu. M.; Barit, E.I.; Senyavin, M.M.

doi:10.1016/0098-1354(93)e0013-y

Cited by 49 publications

(35 citation statements)

References 11 publications

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“…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 .…”

Section: Preliminary Definitionsmentioning

confidence: 99%

Flexibility analysis and design using a parametric programming framework

2002

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Section: Preliminary Definitionsmentioning

confidence: 99%

Flexibility analysis and design using a parametric programming framework

2002

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“…Grossmann, 1989 . Ž A number of flexibility analysis methods Pistikopoulos and Ierapetritiou, 1995;Ostrovsky et al, 1994 Ostrovsky et al, , 1997Paules and Floudas, 1992; Bernardo et al, 1999;Raspanti, 2000; Straub and Grossman, 1995;Ahmad et al, 2000;Biegler et al, 1997; were since developed. These approaches took into account uncertainty at the design stage, but not at the operation stage, since they used the implicit assumption that at the operation stage, uncertain parameter values could be determined exactly.…”

mentioning

confidence: 99%

Process uncertainty: Case of insufficient process data at the operation stage

et al. 2003

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Flexibility analysis is of prime importance in chemical process systems, since it permits the creation of chemical processes, which can satisfy all design specifications in spite of changes in internal and external factors during the operation stage. The modern foundations of flexibility analysis were de®eloped in the 1980s by Grossman and coworkers. They formulated solution approaches for the main problems of flexibility ( ) analysis feasibility test , flexibility index, and the two-stage optimization problem. All the formulations are based on the supposition that during the operation stage there are enough experimental data to accurately determine uncertain parameter ®alues, but in practice, these assumptions are not likely to be met. This article discusses extensions of ( ) the feasibility test and the two-stage optimization problem TSOP , which take into account the possibility of accurately estimating some of the uncertain parameters while estimating with less accuracy the remaining uncertain parameters. To sol®e the TSOP, the split and bound approach was de®eloped based on a partitioning of the uncertainty region and estimation of bounds on the performance objecti®e function. Three computa-( tional experiments show the importance of taking into account the possibility or lack) thereof of obtaining ®alues of greater accuracy for uncertain parameters at the operation stage. IntroductionDesign specifications usually have to be met during the Ž . design and synthesis of chemical processes CP . However, the satisfaction of such design specifications is complicated by the presence of uncertainty in the process model parameters. The issue then is how could one guarantee satisfaction of all design specifications at the operation stage? Flexibility analysis addresses this problem. The first articles in flexibility Ž analysis appeared in the 1970s Takamatsu et al., 1973; . Grossmann and Sargent, 1978;Johns et al., 1978 . However, foundations of the modern theory of flexibility analysis were Ž laid in the 1980s Halemane and Grossmann, 1983; Swaney . and Grossmann; 1985;Grossmann and Floudas, 1987 . For-Ž mulations of the feasibility test and the flexibility index all . subproblems of flexibility analysis , and the two-step optimization problem were given in these articles. In addition, some solution approaches were suggested.Correspondence concerning this article should be addressed to L. E. K. Achenie. where x is a vector of state variables, z is a vector of control variables, and is a vector of uncertain variables. Equation 5 Ž describes the state of the CP i.e., material and energy bal-. ances , while the inequalities in Eq. 6 are design specifications. Here, dim hsdim x and x can be obtained from Eq. 5, either analytically or numerically using fixed values of the variables d, z, . Thus With the preceding definitions, the two-stage optimization Ž . Ž problem designated here as TSOP1 is given as Halemane . and Grossmann, 1983Ž . Ž . 1Ä 4 where E . . . is the mathematical expectation over the re-T Ž .U Ž . gion ...

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“…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].…”

Section: Mathematical Formulationmentioning

confidence: 99%

“…These can be solved using commercially available MIP or MINLP solvers. Ostrovsky et al [68,69] have proposed an alternate strategy that involves determining upper and lower bounds to the flexibility index by solving a series of simpler problems. This so-called split and bound strategy includes partitioning the uncertain region (T) into N k sub regions (T 1 ,T 2 ,.…”

Section: Mathematical Formulationmentioning

confidence: 99%

Mathematical Tools for the Quantitative Definition of a Design Space

Rogers

Ierapetritou

2016

Methods in Pharmacology and Toxicology

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This chapter focuses on the application of process modeling to determination of design space for pharmaceutical manufacturing processes. The first two sections define design space and related terms from a regulatory perspective and discuss how these apply in practice during pharmaceutical process development. In Sect. 3, a variety of mathematical techniques that can be used to guide design space development are introduced. An emphasis is placed on the use of feasibility analysis and the relationship between process feasibility and design space. Statistical techniques, including latent variable and Bayesian methods, are also discussed in detail. For methods that have been reported in the literature for pharmaceutical manufacturing applications, an overview of the relevant case studies is provided. If methods have not yet been applied to pharmaceutical processes, potential applications for these techniques are indicated. To illustrate the applicability of these concepts to pharmaceutical manufacturing processes, a brief case study is presented in Sect. 4. A discussion of design space verification and issues related to scale-up is provided in Sect. 5. Finally a brief summary of the concepts presented and their potential role in design space development for pharmaceutical processes is given in Sect. 6. This chapter is intended to provide readers with an understanding of mathematical techniques that can be used during process development to assist in the determination of process design space. An overview of the problem formulation and solution approaches for each method are presented. More detailed mathematical developments for each technique are available in the references provided. Table 1 provides a list of symbols that are used throughout this chapter, while Table 2 describes acronyms used within this chapter.

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Flexibility analysis and optimization of chemical plants with uncertain parameters

Cited by 49 publications

References 11 publications

Flexibility analysis and design using a parametric programming framework

Flexibility analysis and design using a parametric programming framework

Process uncertainty: Case of insufficient process data at the operation stage

Mathematical Tools for the Quantitative Definition of a Design Space

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