Optimization and Engineering

, Volume 16, Issue 2, pp 409–440 | Cite as

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

  • Martin Ballerstein
  • Achim Kienle
  • Christian Kunde
  • Dennis Michaels
  • Robert Weismantel


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.


Distillation Melt-crystallization Deterministic global optimization Relaxed MINLP formulation Bound tightening 



This work is part of the Collaborative Research Centre “Integrated Chemical Processes in Liquid Multiphase Systems” funded by the German Research Foundation (DFG). Financial support by the Deutsche Forschungsgemeinschaft (DFG) is gratefully acknowledged through TRR 63. Especially, the first and the fourth authors thank the DFG for its financial support. Main parts of the submitted version has been finished while the fourth author was at the Institute for Operations Research at ETH Zurich and financially supported by DFG (TRR 63).


  1. Achterberg T (2007) Constraint integer programming. Ph.D. thesis, Technische Universität BerlinGoogle Scholar
  2. Adams WP, Forrester RJ (2007) Linear forms of nonlinear expressions: new insights on old ideas. Oper Res Lett 35(4):510–518MathSciNetCrossRefMATHGoogle Scholar
  3. 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 22:1137–1158CrossRefGoogle Scholar
  4. Al-Khayyal FA, Falk JE (1983) Jointly constrained biconvex programming. Math Oper Res 8(2):273–286MathSciNetCrossRefMATHGoogle Scholar
  5. 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 552–556CrossRefGoogle Scholar
  6. 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):447–459CrossRefGoogle Scholar
  7. 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):5298–5307CrossRefGoogle Scholar
  8. 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):3441–3457CrossRefGoogle Scholar
  9. Bausa J, Watzdorf R, Marquardt W (1998) Shortcut methods for nonideal multicomponent distillation: 1. Simple columns. AIChE J 44(10):2181–2198CrossRefGoogle Scholar
  10. Belotti P, Lee J, Liberti L, Margot F, Wächter A (2009) Branching and bounds tightening techniques for non-convex MINLP. Optim Methods Softw 24:597–634MathSciNetCrossRefMATHGoogle Scholar
  11. 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):477–493CrossRefGoogle Scholar
  12. Caprara A, Locatelli M (2010) Global optimization problems and domain reduction strategies. Math Program 125:123–137MathSciNetCrossRefMATHGoogle Scholar
  13. Domes F, Neumaier A (2010) Constraint propagation on quadratic constraints. Constraints 15(3):404–429MathSciNetCrossRefMATHGoogle Scholar
  14. 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):2925–2942CrossRefGoogle Scholar
  15. GAMS Development Corp (2009) GAMS—the solver manuals. Washington, DCGoogle Scholar
  16. 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):343–355CrossRefGoogle Scholar
  17. 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):2261–2271CrossRefGoogle Scholar
  18. Grossmann IE, Aguirre PA, Barttfeld M (2005) Optimal synthesis of complex distillation columns using rigorous models. Comput Chem Eng 29(6):1203–1215CrossRefGoogle Scholar
  19. Hansen P, Jaumard B, Lu SH (1991) An analytical approach to global optimization. Math Programm 52(1–3):227–254. doi: 10.1007/BF01582889 MathSciNetCrossRefMATHGoogle Scholar
  20. Henley EJ, Seader JD (1981) Equilibrium-stage separation operations in chemical engineering. Wiley, Wiley series in chemical engineering, New YorkGoogle Scholar
  21. Hooker JN (2002) Logic, optimization, and constraint programming. INFORMS J Comput 14:295–321MathSciNetCrossRefMATHGoogle Scholar
  22. Jach M, Michaels D, Weismantel R (2008) The convex envelope of (\(n\)\(1\))-convex functions. SIAM J Optim 19(3):1451–1466MathSciNetCrossRefMATHGoogle Scholar
  23. Kearfott RB (2006) Discussion and empirical comparisons of linear relaxations and alternate techniques in validated deterministic global optimization. Optim Methods Softw 21(5):715–731MathSciNetCrossRefMATHGoogle Scholar
  24. Khajavirad A, Sahidinidis NV (2011) Convex envelopes generated from finitely many compact convex sets. Math Programm A. doi: 10.1007/s10107-011-0496-5
  25. Khajavirad A, Sahidinidis NV (2012) Convex envelopes of products of convex and component-wise concave functions. J Glob Optim 52:391–409CrossRefMATHGoogle Scholar
  26. Krämer K, Kossack S, Marquardt W (2009) Efficient optimization-based design of distillation processes for homogenous azeotropic mixtures. Ind Eng Chem Res 48(14):6749–6764CrossRefGoogle Scholar
  27. Lebbah Y, Michel C, Rueher M (2005) A rigorous global filtering algorithm for quadratic constraints. Constraints 10:47–65MathSciNetCrossRefMATHGoogle Scholar
  28. 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):463–474CrossRefGoogle Scholar
  29. Linderoth J (2005) A simplicial branch-and-bound algorithm for solving quadratically constrained quadratic programs. Math Program 103(2, Ser. B):251–282MathSciNetCrossRefMATHGoogle Scholar
  30. Lucia A, Amale A, Taylor R (2008) Distillation pinch points and more. Comput Chem Eng 32:1350–1372CrossRefGoogle Scholar
  31. McCormick GP (1976) Computability of global solutions to factorable nonconvex programs. I: convex underestimating problems. Math Program 10:147–175MathSciNetCrossRefMATHGoogle Scholar
  32. Mersmann A, Kind M, Stichlmair J (2011) Therm Sep Technol. Springer, HeidelbergCrossRefGoogle Scholar
  33. Meyer CA, Floudas CA (2005) Convex envelopes for edge-concave functions. Math Program 103:207–224MathSciNetCrossRefMATHGoogle Scholar
  34. 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, GermanyGoogle Scholar
  35. Misener R, Floudas C (2013) Glomiqo: global mixed-integer quadratic optimizer. J Glob Optim 57(1):3–50. doi: 10.1007/s10898-012-9874-7 MathSciNetCrossRefMATHGoogle Scholar
  36. 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 29:226–230CrossRefGoogle Scholar
  37. Ryoo HS, Sahinidis NV (1996) A branch-and-reduce approach to global optimization. J Glob Optim 8:107–138MathSciNetCrossRefMATHGoogle Scholar
  38. 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):10,296–10,306CrossRefGoogle Scholar
  39. Skiborowski M, Harwardt A, Marquardt W (2013) Conceptual design of distillation-based hybrid separation processes. Annu Rev Chem Biomol Eng. doi: 10.1146/annurev-chembioeng-061010-114129
  40. Tawarmalani M, Sahinidis NV (2001) Semidefinite relaxations of fractional programs via novel convexification techniques. J Glob Optim 20:137–158MathSciNetCrossRefMATHGoogle Scholar
  41. Tawarmalani M, Sahinidis NV (2004) Global optimization of mixed-integer nonlinear programs: a theoretical and computational study. Math Program A 99(3):563–591MathSciNetCrossRefMATHGoogle Scholar
  42. Tawarmalani M, Sahinidis NV (2005) A polyhedral branch-and-cut approach to global optimization. Math Program 103:225–249MathSciNetCrossRefMATHGoogle Scholar
  43. Viswanathan J, Grossmann IE (1990) A combined penalty function and outer-approximation method for MINLP optimization. Comput Chem Eng 14(7):769–782CrossRefGoogle Scholar
  44. Viswanathan J, Grossmann IE (1993) Optimal feed locations and number of trays for distillation columns with multiple feeds. Ind Eng Chem Res 32(11):2942–2949CrossRefGoogle Scholar
  45. Yeomans H, Grossmann IE (2000) Disjunctive programming models for the optimal design of distillation columns and separation sequences. Ind Eng Chem Res 39(6):1637–1648CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2014

Authors and Affiliations

  • Martin Ballerstein
    • 4
  • Achim Kienle
    • 1
    • 2
  • Christian Kunde
    • 1
  • Dennis Michaels
    • 3
  • Robert Weismantel
    • 4
  1. 1.Otto-von-Guericke-Universität MagdeburgMagdeburgGermany
  2. 2.Max-Planck-Institut für Dynamik komplexer technischer SystemeMagdeburgGermany
  3. 3.Technische Universität DortmundDortmundGermany
  4. 4.Institut für Operations ResearchEidgenössische Technische Hochschule ZürichZurichSwitzerland

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