Stochastic programming in process synthesis: A two-stage model with MINLP recourse for multiperiod heat-integrated distillation sequences

Paules, Granville; Floudas, Christodoulos A.

doi:10.1016/0098-1354(92)85006-t

Cited by 62 publications

(31 citation statements)

References 27 publications

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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.…”

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

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“…In these papers formulations of the following problems of flexibility theory were given: (a) Feasibility Test (Halemane and Grossmann, 1983), (b) Flexibility Index (Swaney and Grossmann, 1985) and (c) the two-stage optimization problem (TSOP) (Halemane and Grossmann, 1983). In the following years there was a significant effort in flexibility analysis research (see for example Pistikopoulos and Grossmann, 1989;Pistikopoulos and Ierapitritou, 1995;Ostrovsky et al, 1994Ostrovsky et al, , 1997Paules and Floudas, 1992;Bernardo et al, 1999;Raspanty et al, 1995).…”

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Process optimization under uncertainty when there is not enough process data at the operation stage

et al. 2006

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The main issues in the design and optimization of a chemical process under uncertainty are the feasibility test, flexibility index and the two-step optimization problem. The formulations of these problems are based on the implicit supposition that at the operation stage it is possible to correct all uncertain parameters in the chemical process models. However, in practice, one can improve the accuracy of only some of the uncertain parameters. As a result, we consider two groups of uncertain parameters. We postulate that one can significantly improve the accuracy of the first group of uncertain parameters using process data at the operation stage. This necessitates the formulation of a new feasibility test and the associated two-stage optimization problem. We consider the general case when both groups of uncertain parameters may or may not be statistically dependent. We propose methods of solving the problems based on the supposition that the parametric uncertainty region is small. Under this condition, the process models are well represented by linearized models whose accuracy is asymptotically equal to that of the original process models. This leads to substantial computational savings. Computational tests show that when it is not possible to improve the accuracy of some of the uncertain parameters, using standard flexibility analysis can lead to processes that are not flexible.Springer 250 I. Datskov et al.

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“…Paules and Floudas [146,147] proposed and MINLP model for heat integrated distillation sequences, and Raman and Grossmann [92] a disjunctive representation.…”

Section: Process Synthesismentioning

confidence: 99%

Review of Mixed‐Integer Nonlinear and Generalized Disjunctive Programming Methods

Trespalacios

Grossmann

2014

Chemie Ingenieur Technik

152

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This work presents a review of the applications of mixed-integer nonlinear programming (MINLP) in process systems engineering (PSE). A review on the main deterministic MINLP solution methods is presented, including an overview of the main MINLP solvers. Generalized disjunctive programming (GDP) is an alternative higher-level representation of MINLP problems. This work reviews some methods for solving GDP models, and techniques for improving MINLP methods through GDP. The paper also provides a high-level review of the applications of MINLP in PSE, particularly in process synthesis, planning and scheduling, process control and molecular computing.

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Stochastic programming in process synthesis: A two-stage model with MINLP recourse for multiperiod heat-integrated distillation sequences

Cited by 62 publications

References 27 publications

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

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

Process optimization under uncertainty when there is not enough process data at the operation stage

Review of Mixed‐Integer Nonlinear and Generalized Disjunctive Programming Methods

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