Disjunctive optimization design models for complex liquid-liquid multistage extractors
A new method for the optimal design of multicomponent liquid–liquid extraction processes using multistage countercurrent extractor systems is proposed. The method determines the optimum number of equilibrium stages and flow rates needed to obtain a specified product separation and recovery, and acco...
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| Published in | AIChE journal Vol. 47; no. 10; pp. 2243 - 2252 |
|---|---|
| Main Authors | , |
| Format | Journal Article |
| Language | English |
| Published |
Hoboken
Wiley Subscription Services, Inc., A Wiley Company
01.10.2001
Wiley Subscription Services American Institute of Chemical Engineers |
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| Abstract | A new method for the optimal design of multicomponent liquid–liquid extraction processes using multistage countercurrent extractor systems is proposed. The method determines the optimum number of equilibrium stages and flow rates needed to obtain a specified product separation and recovery, and accounts for the possibility of side feed streams and product extractions. A superstructure is proposed that has embedded all potential configurations and interconnections. Based on this superstructure representation, the problem is formulated as an optimization problem using generalized disjunctive programming (GDP) to minimize the total cost of the process, subject to design specifications. The robustness and computational efficiency of the model is illustrated with different cases involving single and complex countercurrent cascades in a quaternary liquid–liquid system. |
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| AbstractList | A new method for the optimal design of multicomponent liquid–liquid extraction processes using multistage countercurrent extractor systems is proposed. The method determines the optimum number of equilibrium stages and flow rates needed to obtain a specified product separation and recovery, and accounts for the possibility of side feed streams and product extractions. A superstructure is proposed that has embedded all potential configurations and interconnections. Based on this superstructure representation, the problem is formulated as an optimization problem using generalized disjunctive programming (GDP) to minimize the total cost of the process, subject to design specifications. The robustness and computational efficiency of the model is illustrated with different cases involving single and complex countercurrent cascades in a quaternary liquid–liquid system. |
| Author | Reyes-Labarta, Juan A. Grossmann, Ignacio E. |
| Author_xml | – sequence: 1 givenname: Juan A. surname: Reyes-Labarta fullname: Reyes-Labarta, Juan A. organization: Dept. of Chemical Engineering, University of Alicante, Ap. Correos 99, Alicante E-03080, Spain – sequence: 2 givenname: Ignacio E. surname: Grossmann fullname: Grossmann, Ignacio E. organization: Dept. of Chemical Engineering, Carnegie Mellon University Pittsburgh, PA 15213 |
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| Cites_doi | 10.1205/026387698524785 10.1252/jcej.9.40 10.1137/0606047 10.1016/0098-1354(93)E0010-7 10.1021/ie000103q 10.1016/0098-1354(95)00219-7 10.1002/aic.690371202 10.1016/S0065-2377(08)60203-3 10.1093/oso/9780198562368.001.0001 10.1021/ie9906520 10.1021/ie9900723 10.1021/ie950687 10.1016/0098-1354(94)00123-5 10.1021/je980198r 10.1007/BF01580665 |
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| Copyright | Copyright © 2001 American Institute of Chemical Engineers (AIChE) 2002 INIST-CNRS Copyright American Institute of Chemical Engineers Oct 2001 |
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| Keywords | Water Chloroform Liquid liquid extraction Multicomponent mixture Multistage process Countercurrent flow Quaternary system Optimization Optimal design Disjunction Non linear model Superstructure Numerical simulation Acetic acid In series Computer aided design Acetone |
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| References_xml | – reference: Tsuboka, T., and T. Katayama, "General Design Algorithm Based on Pseudoequilibrium Concept for Multistage Multicomponent Liquid-Liquid Separation Processes," J. Chem. Eng. Jpn., 9, 40 (1976). – reference: Turkay, M., and I. E. Grossmann, "Logic-Based MINLP Algorithms for the Optimal Synthesis of Process Networks," Comput. Chem. Eng., 20, 959 (1996). – reference: Marcilla, A., A. Gómez, and J. Reyes, "New Method for Designing Distillation Columns of Multicomponent Mixtures," Lat. Amer. Appl. Res., 27 (1-2), 51 (1997). – reference: Brooke, A., D. Kendrick, A. Meerhaus, and R. Raman, GAMS Release 2.25 Language Guide, Version 92, Gams Development Corporation, Washington, DC (1997). – reference: Raman, R., and I. E. Grossmann, "Modeling and Computational Techniques for Logic Based Integer Programming," Comput. Chem. Eng., 18, 563 (1994). – reference: Minotti, M., M. F. Doherty, and M. F. Malone, "Economic Trade offs for Extraction Systems," Trans. Inst. Chem. IChem. Eng., 76, 361 (1998). – reference: Barnes, N. G., M. B. Gramajo de Doz, and H. N. Solimo, "Liquid-Liquid Extraction of trans-Aconitic Acid from Aqueous Solutions with Tributyl Phosphate and a Mixed Solvent at 303.15 K," Ind. Eng. Chem. Res., 39, 3364 (2000). – reference: Quesada, I., and I. E. Grossmann, "Global Optimization of Bilinear Process Networks with Multicomponent Flows," Comp. Chem. Eng., 12, 1219 (1995). – reference: Thornton, J. D., Science and Practice of Liquid-Liquid Extraction, Oxford Univ. Press, New York (1992). – reference: Grossmann, I. E., "Mixed-Integer Optimization Techniques for Algorithmic Process Synthesis," Adv. Chem. Eng. Process Synth., 23, 171 (1996). – reference: Marcilla, A., A. Gómez, J. A. Reyes, and M. M. Olaya, "New Method for Quaternary Systems Liquid-Liquid Extraction Tray to Tray Design," Ind. Eng. Chem. Res., 38, 3083 (1999). – reference: Wankat, P. C., Equilibrium Stage Separation, Elsevier, New York (1988). – reference: Balas, E., "Disjunctive Programming and a Hierarchy of Relaxations for Discrete Optimization Problems," SIAM J. Algebraic Discrete Methods, 6, 466 (1985). – reference: Seader, J. D., and E. J. Henley, Separation Process Principles, Wiley, New York (1998). – reference: Barnes, N. G., M. B. Gramajo de Doz, and H. N. Solimo, "Liquid-Liquid Extraction of Oxalic Acid from Aqueous Solutions with Tributyl Phosphate and a Mixed Solvent at 303.15 K," J. Chem. Eng. Data, 44, 430 (1999). – reference: Fidkowski, Z. T., M. F. Malone, and M. F. Doherty, "Nonideal Multicomponent Distillation: Use of Bifurcation Theory for Design," AIChE J., 37, 1761 (1991). – reference: Minottim, M., M. F. Doherty, and M. F. Malone, "A Geometric Method for the Design of Liquid Extractors," Ind. Eng. Chem. Res., 35, 2672 (1996). – reference: Treybal, R. E., Liquid Extraction, McGraw-Hill, New York (1963). – reference: Yeomans, H., and I. E. Grossmann, "Disjunctive Programming Models for the Optimal Design of Distillation Columns and Separation Sequences," Ind. Eng. Chem. Res., 39, 1637 (2000). – reference: McCormick, G. P., "Computability of Global Solutions to Factorable Nonconvex Programs, Part I. Convex Underestimating Problems," Math. Prog., 10, 146 (1976). – volume: 38 start-page: 3083 year: 1999 article-title: New Method for Quaternary Systems Liquid‐Liquid Extraction Tray to Tray Design publication-title: Ind. Eng. Chem. Res. – volume: 10 start-page: 146 year: 1976 article-title: Computability of Global Solutions to Factorable Nonconvex Programs, Part I. Convex Underestimating Problems publication-title: Math. Prog. – year: 1963 – volume: 27 start-page: 51 issue: 1–2 year: 1997 article-title: New Method for Designing Distillation Columns of Multicomponent Mixtures publication-title: Lat. Amer. Appl. Res. – volume: 44 start-page: 430 year: 1999 article-title: Liquid‐Liquid Extraction of Oxalic Acid from Aqueous Solutions with Tributyl Phosphate and a Mixed Solvent at 303.15 K publication-title: J. Chem. Eng. Data – volume: 12 start-page: 1219 year: 1995 article-title: Global Optimization of Bilinear Process Networks with Multicomponent Flows publication-title: Comp. Chem. Eng. – year: 1988 – volume: 39 start-page: 1637 year: 2000 article-title: Disjunctive Programming Models for the Optimal Design of Distillation Columns and Separation Sequences publication-title: Ind. Eng. Chem. Res. – volume: 20 start-page: 959 year: 1996 article-title: Logic‐Based MINLP Algorithms for the Optimal Synthesis of Process Networks publication-title: Comput. Chem. Eng. – volume: 23 start-page: 171 year: 1996 article-title: Mixed‐Integer Optimization Techniques for Algorithmic Process Synthesis publication-title: Adv. Chem. Eng. Process Synth. – volume: 9 start-page: 40 year: 1976 article-title: General Design Algorithm Based on Pseudoequilibrium Concept for Multistage Multicomponent Liquid‐Liquid Separation Processes publication-title: J. Chem. Eng. Jpn. – year: 1997 – volume: 76 start-page: 361 year: 1998 article-title: Economic Trade offs for Extraction Systems publication-title: Trans. Inst. Chem. IChem. Eng. – volume: 35 start-page: 2672 year: 1996 article-title: A Geometric Method for the Design of Liquid Extractors publication-title: Ind. Eng. Chem. Res. – volume: 39 start-page: 3364 year: 2000 article-title: Liquid‐Liquid Extraction of trans‐Aconitic Acid from Aqueous Solutions with Tributyl Phosphate and a Mixed Solvent at 303.15 K publication-title: Ind. Eng. Chem. Res. – volume: 6 start-page: 466 year: 1985 article-title: Disjunctive Programming and a Hierarchy of Relaxations for Discrete Optimization Problems publication-title: SIAM J. Algebraic Discrete Methods – volume: 37 start-page: 1761 year: 1991 article-title: Nonideal Multicomponent Distillation: Use of Bifurcation Theory for Design publication-title: AIChE J. – year: 1992 – year: 1998 – volume: 18 start-page: 563 year: 1994 article-title: Modeling and Computational Techniques for Logic Based Integer Programming publication-title: Comput. Chem. Eng. – year: 1999 – ident: e_1_2_1_12_1 doi: 10.1205/026387698524785 – ident: e_1_2_1_20_1 doi: 10.1252/jcej.9.40 – volume: 6 start-page: 466 year: 1985 ident: e_1_2_1_2_1 article-title: Disjunctive Programming and a Hierarchy of Relaxations for Discrete Optimization Problems publication-title: SIAM J. Algebraic Discrete Methods doi: 10.1137/0606047 – volume: 27 start-page: 51 issue: 1 year: 1997 ident: e_1_2_1_8_1 article-title: New Method for Designing Distillation Columns of Multicomponent Mixtures publication-title: Lat. Amer. Appl. Res. – volume-title: Liquid Extraction year: 1963 ident: e_1_2_1_19_1 – ident: e_1_2_1_14_1 doi: 10.1016/0098-1354(93)E0010-7 – ident: e_1_2_1_3_1 doi: 10.1021/ie000103q – ident: e_1_2_1_21_1 doi: 10.1016/0098-1354(95)00219-7 – volume-title: Equilibrium Stage Separation year: 1988 ident: e_1_2_1_22_1 – ident: e_1_2_1_16_1 – ident: e_1_2_1_6_1 doi: 10.1002/aic.690371202 – ident: e_1_2_1_7_1 doi: 10.1016/S0065-2377(08)60203-3 – volume-title: Science and Practice of Liquid‐Liquid Extraction year: 1992 ident: e_1_2_1_18_1 doi: 10.1093/oso/9780198562368.001.0001 – volume-title: GAMS Release 2.25 Language Guide year: 1997 ident: e_1_2_1_5_1 – ident: e_1_2_1_23_1 doi: 10.1021/ie9906520 – ident: e_1_2_1_9_1 doi: 10.1021/ie9900723 – ident: e_1_2_1_11_1 doi: 10.1021/ie950687 – volume: 12 start-page: 1219 year: 1995 ident: e_1_2_1_13_1 article-title: Global Optimization of Bilinear Process Networks with Multicomponent Flows publication-title: Comp. Chem. Eng. doi: 10.1016/0098-1354(94)00123-5 – ident: e_1_2_1_4_1 doi: 10.1021/je980198r – volume-title: Separation Process Principles year: 1998 ident: e_1_2_1_17_1 – ident: e_1_2_1_10_1 doi: 10.1007/BF01580665 – ident: e_1_2_1_15_1 |
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| SubjectTerms | Applied sciences Chemical engineering Exact sciences and technology Liquid-liquid extraction |
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| Title | Disjunctive optimization design models for complex liquid-liquid multistage extractors |
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