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Erschienen in: Optimization and Engineering 2/2015

01.06.2015

Deterministic global optimization of binary hybrid distillation/melt-crystallization processes based on relaxed MINLP formulations

verfasst von: Martin Ballerstein, Achim Kienle, Christian Kunde, Dennis Michaels, Robert Weismantel

Erschienen in: Optimization and Engineering | Ausgabe 2/2015

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Abstract

This paper deals with the deterministic global optimization of hybrid distillation/melt-crystallization processes for closely boiling mixtures. An algorithm is presented that exploits the problem specific structure of continuous, counter-current distillation to reduce the domain of the corresponding mixed-integer nonlinear program (MINLP). We apply a bound tightening technique based on the explicit computation of extreme column solution profiles, which enclose all possible solutions of the distillation column model. A relaxed MINLP model formulation is then used to exclude several non-optimal and infeasible column configurations. The numerical performance of the proposed algorithm is demonstrated on a test series of stand-alone distillation column processes and hybrid separation processes.

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Literatur
Zurück zum Zitat Achterberg T (2007) Constraint integer programming. Ph.D. thesis, Technische Universität Berlin Achterberg T (2007) Constraint integer programming. Ph.D. thesis, Technische Universität Berlin
Zurück zum Zitat Adams WP, Forrester RJ (2007) Linear forms of nonlinear expressions: new insights on old ideas. Oper Res Lett 35(4):510–518MathSciNetCrossRefMATH Adams WP, Forrester RJ (2007) Linear forms of nonlinear expressions: new insights on old ideas. Oper Res Lett 35(4):510–518MathSciNetCrossRefMATH
Zurück zum Zitat Adjiman CS, Dallwig S, Floudas CA, Neumaier A (1998) A global optimization method, \(\alpha \)BB, for general twice-differentiable constrained NLPs - I. Theoretical advances. Comput Chem Eng 22:1137–1158CrossRef Adjiman CS, Dallwig S, Floudas CA, Neumaier A (1998) A global optimization method, \(\alpha \)BB, for general twice-differentiable constrained NLPs - I. Theoretical advances. Comput Chem Eng 22:1137–1158CrossRef
Zurück zum Zitat Ballerstein M, Kienle A, Kunde C, Michaels D, Weismantel R (2011) Towards global optimization of combined distillation-crystallization processes for the separation of closely boiling mixtures. In: Pistikopoulos EN, Georgiadis MC, Kokossis AC (eds) 21th European symposium on computer aided process engineering—ESCAPE 21. Elsevier, Amsterdam, pp 552–556CrossRef Ballerstein M, Kienle A, Kunde C, Michaels D, Weismantel R (2011) Towards global optimization of combined distillation-crystallization processes for the separation of closely boiling mixtures. In: Pistikopoulos EN, Georgiadis MC, Kokossis AC (eds) 21th European symposium on computer aided process engineering—ESCAPE 21. Elsevier, Amsterdam, pp 552–556CrossRef
Zurück zum Zitat Ballerstein M, Michaels D, Seidel-Morgenstern A, Weismantel R (2010) A theoretical study of continuous counter-current chromatography for adsorption isotherms with inflection points. Comput Chem Eng 34(4):447–459CrossRef Ballerstein M, Michaels D, Seidel-Morgenstern A, Weismantel R (2010) A theoretical study of continuous counter-current chromatography for adsorption isotherms with inflection points. Comput Chem Eng 34(4):447–459CrossRef
Zurück zum Zitat Barttfeld M, Aguirre PA (2002) Optimal synthesis of multicomponent zeotropic distillation processes. 1. Preprocessing phase and rigorous optimization for a single unit. Ind Eng Chem Res 41(21):5298–5307CrossRef Barttfeld M, Aguirre PA (2002) Optimal synthesis of multicomponent zeotropic distillation processes. 1. Preprocessing phase and rigorous optimization for a single unit. Ind Eng Chem Res 41(21):5298–5307CrossRef
Zurück zum Zitat Barttfeld M, Aguirre PA (2003) Optimal synthesis of multicomponent zeotropic distillation processes. 2. Preprocessing phase and rigorous optimization of efficient sequences. Ind Eng Chem Res 42(14):3441–3457CrossRef Barttfeld M, Aguirre PA (2003) Optimal synthesis of multicomponent zeotropic distillation processes. 2. Preprocessing phase and rigorous optimization of efficient sequences. Ind Eng Chem Res 42(14):3441–3457CrossRef
Zurück zum Zitat Bausa J, Watzdorf R, Marquardt W (1998) Shortcut methods for nonideal multicomponent distillation: 1. Simple columns. AIChE J 44(10):2181–2198CrossRef Bausa J, Watzdorf R, Marquardt W (1998) Shortcut methods for nonideal multicomponent distillation: 1. Simple columns. AIChE J 44(10):2181–2198CrossRef
Zurück zum Zitat Belotti P, Lee J, Liberti L, Margot F, Wächter A (2009) Branching and bounds tightening techniques for non-convex MINLP. Optim Methods Softw 24:597–634MathSciNetCrossRefMATH Belotti P, Lee J, Liberti L, Margot F, Wächter A (2009) Branching and bounds tightening techniques for non-convex MINLP. Optim Methods Softw 24:597–634MathSciNetCrossRefMATH
Zurück zum Zitat Bergamini ML, Grossmann I, Scenna N, Aguirre P (2008) An improved piecewise outer-approximation algorithm for the global optimization of MINLP models involving concave and bilinear terms. Comput Chem Eng 32(3):477–493CrossRef Bergamini ML, Grossmann I, Scenna N, Aguirre P (2008) An improved piecewise outer-approximation algorithm for the global optimization of MINLP models involving concave and bilinear terms. Comput Chem Eng 32(3):477–493CrossRef
Zurück zum Zitat Franke MB, Nowotny N, Ndocko EN, Gorak A, Strube J (2008) Design and optimization of a hybrid distillation/melt crystallization process. AIChE J 54(11):2925–2942CrossRef Franke MB, Nowotny N, Ndocko EN, Gorak A, Strube J (2008) Design and optimization of a hybrid distillation/melt crystallization process. AIChE J 54(11):2925–2942CrossRef
Zurück zum Zitat GAMS Development Corp (2009) GAMS—the solver manuals. Washington, DC GAMS Development Corp (2009) GAMS—the solver manuals. Washington, DC
Zurück zum Zitat Gangadwala J, Haus UU, Jach M, Kienle A, Michaels D, Weismantel R (2008) Global analysis of combined reaction distillation processes. Comput Chem Eng 32(1–2):343–355CrossRef Gangadwala J, Haus UU, Jach M, Kienle A, Michaels D, Weismantel R (2008) Global analysis of combined reaction distillation processes. Comput Chem Eng 32(1–2):343–355CrossRef
Zurück zum Zitat Gangadwala J, Kienle A, Haus UU, Michaels D, Weismantel R (2006) Global bounds on optimal solutions for the production of 2,3-dimethylbutene-1. Ind Eng Chem Res 45(7):2261–2271CrossRef Gangadwala J, Kienle A, Haus UU, Michaels D, Weismantel R (2006) Global bounds on optimal solutions for the production of 2,3-dimethylbutene-1. Ind Eng Chem Res 45(7):2261–2271CrossRef
Zurück zum Zitat Grossmann IE, Aguirre PA, Barttfeld M (2005) Optimal synthesis of complex distillation columns using rigorous models. Comput Chem Eng 29(6):1203–1215CrossRef Grossmann IE, Aguirre PA, Barttfeld M (2005) Optimal synthesis of complex distillation columns using rigorous models. Comput Chem Eng 29(6):1203–1215CrossRef
Zurück zum Zitat Henley EJ, Seader JD (1981) Equilibrium-stage separation operations in chemical engineering. Wiley, Wiley series in chemical engineering, New York Henley EJ, Seader JD (1981) Equilibrium-stage separation operations in chemical engineering. Wiley, Wiley series in chemical engineering, New York
Zurück zum Zitat Jach M, Michaels D, Weismantel R (2008) The convex envelope of (\(n\)−\(1\))-convex functions. SIAM J Optim 19(3):1451–1466MathSciNetCrossRefMATH Jach M, Michaels D, Weismantel R (2008) The convex envelope of (\(n\)\(1\))-convex functions. SIAM J Optim 19(3):1451–1466MathSciNetCrossRefMATH
Zurück zum Zitat Kearfott RB (2006) Discussion and empirical comparisons of linear relaxations and alternate techniques in validated deterministic global optimization. Optim Methods Softw 21(5):715–731MathSciNetCrossRefMATH Kearfott RB (2006) Discussion and empirical comparisons of linear relaxations and alternate techniques in validated deterministic global optimization. Optim Methods Softw 21(5):715–731MathSciNetCrossRefMATH
Zurück zum Zitat Khajavirad A, Sahidinidis NV (2012) Convex envelopes of products of convex and component-wise concave functions. J Glob Optim 52:391–409CrossRefMATH Khajavirad A, Sahidinidis NV (2012) Convex envelopes of products of convex and component-wise concave functions. J Glob Optim 52:391–409CrossRefMATH
Zurück zum Zitat Krämer K, Kossack S, Marquardt W (2009) Efficient optimization-based design of distillation processes for homogenous azeotropic mixtures. Ind Eng Chem Res 48(14):6749–6764CrossRef Krämer K, Kossack S, Marquardt W (2009) Efficient optimization-based design of distillation processes for homogenous azeotropic mixtures. Ind Eng Chem Res 48(14):6749–6764CrossRef
Zurück zum Zitat Levy SG, Van Dongen DB, Doherty MF (1985) Design and synthesis of homogeneous azeotropic distillations. 2. Minimum reflux calculations for nonideal and azeotropic columns. Ind Eng Chem Fundam 24(4):463–474CrossRef Levy SG, Van Dongen DB, Doherty MF (1985) Design and synthesis of homogeneous azeotropic distillations. 2. Minimum reflux calculations for nonideal and azeotropic columns. Ind Eng Chem Fundam 24(4):463–474CrossRef
Zurück zum Zitat Linderoth J (2005) A simplicial branch-and-bound algorithm for solving quadratically constrained quadratic programs. Math Program 103(2, Ser. B):251–282MathSciNetCrossRefMATH Linderoth J (2005) A simplicial branch-and-bound algorithm for solving quadratically constrained quadratic programs. Math Program 103(2, Ser. B):251–282MathSciNetCrossRefMATH
Zurück zum Zitat Lucia A, Amale A, Taylor R (2008) Distillation pinch points and more. Comput Chem Eng 32:1350–1372CrossRef Lucia A, Amale A, Taylor R (2008) Distillation pinch points and more. Comput Chem Eng 32:1350–1372CrossRef
Zurück zum Zitat McCormick GP (1976) Computability of global solutions to factorable nonconvex programs. I: convex underestimating problems. Math Program 10:147–175MathSciNetCrossRefMATH McCormick GP (1976) Computability of global solutions to factorable nonconvex programs. I: convex underestimating problems. Math Program 10:147–175MathSciNetCrossRefMATH
Zurück zum Zitat Mersmann A, Kind M, Stichlmair J (2011) Therm Sep Technol. Springer, HeidelbergCrossRef Mersmann A, Kind M, Stichlmair J (2011) Therm Sep Technol. Springer, HeidelbergCrossRef
Zurück zum Zitat Micovic J, Beierling T, Ruether F, Kreis P, Górak A (2011) Hybrid separation processes for purification of close boiling mixtures in hydroformylation of long chain olefins. In: 8th European congress of chemical engineering (ECCE-8), September 25–29, ICC Berlin, Germany Micovic J, Beierling T, Ruether F, Kreis P, Górak A (2011) Hybrid separation processes for purification of close boiling mixtures in hydroformylation of long chain olefins. In: 8th European congress of chemical engineering (ECCE-8), September 25–29, ICC Berlin, Germany
Zurück zum Zitat Müller M, Merchan V, Arellano-Garcia H, Schomäcker R, Wozny G (2011) A novel process design for the hydroformylation of higher alkenes. Comput Aided Chem Eng 29:226–230CrossRef Müller M, Merchan V, Arellano-Garcia H, Schomäcker R, Wozny G (2011) A novel process design for the hydroformylation of higher alkenes. Comput Aided Chem Eng 29:226–230CrossRef
Zurück zum Zitat Schäfer E, Brunsch Y, Sadowski G, Behr A (2012) Hydroformylation of 1-dodecene in the thermomorphic solvent system dimethylformamide/decane. Phase behavior-reaction performance-catalyst recycling. Ind Eng Chem Res 51(31):10,296–10,306CrossRef Schäfer E, Brunsch Y, Sadowski G, Behr A (2012) Hydroformylation of 1-dodecene in the thermomorphic solvent system dimethylformamide/decane. Phase behavior-reaction performance-catalyst recycling. Ind Eng Chem Res 51(31):10,296–10,306CrossRef
Zurück zum Zitat Tawarmalani M, Sahinidis NV (2001) Semidefinite relaxations of fractional programs via novel convexification techniques. J Glob Optim 20:137–158MathSciNetCrossRefMATH Tawarmalani M, Sahinidis NV (2001) Semidefinite relaxations of fractional programs via novel convexification techniques. J Glob Optim 20:137–158MathSciNetCrossRefMATH
Zurück zum Zitat Tawarmalani M, Sahinidis NV (2004) Global optimization of mixed-integer nonlinear programs: a theoretical and computational study. Math Program A 99(3):563–591MathSciNetCrossRefMATH Tawarmalani M, Sahinidis NV (2004) Global optimization of mixed-integer nonlinear programs: a theoretical and computational study. Math Program A 99(3):563–591MathSciNetCrossRefMATH
Zurück zum Zitat Viswanathan J, Grossmann IE (1990) A combined penalty function and outer-approximation method for MINLP optimization. Comput Chem Eng 14(7):769–782CrossRef Viswanathan J, Grossmann IE (1990) A combined penalty function and outer-approximation method for MINLP optimization. Comput Chem Eng 14(7):769–782CrossRef
Zurück zum Zitat Viswanathan J, Grossmann IE (1993) Optimal feed locations and number of trays for distillation columns with multiple feeds. Ind Eng Chem Res 32(11):2942–2949CrossRef Viswanathan J, Grossmann IE (1993) Optimal feed locations and number of trays for distillation columns with multiple feeds. Ind Eng Chem Res 32(11):2942–2949CrossRef
Zurück zum Zitat Yeomans H, Grossmann IE (2000) Disjunctive programming models for the optimal design of distillation columns and separation sequences. Ind Eng Chem Res 39(6):1637–1648CrossRef Yeomans H, Grossmann IE (2000) Disjunctive programming models for the optimal design of distillation columns and separation sequences. Ind Eng Chem Res 39(6):1637–1648CrossRef
Metadaten
Titel
Deterministic global optimization of binary hybrid distillation/melt-crystallization processes based on relaxed MINLP formulations
verfasst von
Martin Ballerstein
Achim Kienle
Christian Kunde
Dennis Michaels
Robert Weismantel
Publikationsdatum
01.06.2015
Verlag
Springer US
Erschienen in
Optimization and Engineering / Ausgabe 2/2015
Print ISSN: 1389-4420
Elektronische ISSN: 1573-2924
DOI
https://doi.org/10.1007/s11081-014-9267-5

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