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Deterministic global optimization in isothermal reactor network synthesis

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Abstract

The reactor network synthesis problem involves the simultaneous determination of the structure and operating conditions of a reactor system to optimize a given performance measure. This performance measure may be the yield of a given product, the selectivity between products, or the overall profitability of the process. The problem is formulated as a nonlinear program (NLP) using a superstructure based method in which plug flow reactors (PFRs) in the structure are modeled using differential-algebraic equations (DAEs). This formulation exhibits multiple local minima. To overcome this, a novel deterministic global optimization method tailored to the special structure and characteristics of this problem will be presented. Examples of isothermal networks will be discussed to show the nature of the local minima and illustrate various components of the proposed approach.

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References

  • Achenie, L.K.E. and Biegler, L.T. (1986), Algorithmic Synthesis of Chemical Reactor Networks Using Mathematical Programming. Ind. Eng. Chem. Fund. 25, 621.

    Google Scholar 

  • Achenie, L.K.E. and Biegler, L.T. (1988), Developing Targets for the Performance Index of a Chemical Reactor Network. Ind. Eng. Chem. Res. 27, 1811.

    Google Scholar 

  • Achenie, L.K.E. and Biegler, L.T. (1990), A Superstructure Based Approach to Chemical Reactor Network Synthesis. Comput. Chem. Eng. 14(1), 23.

    Google Scholar 

  • Adjiman, C.S., Androulakis, I.P. and Floudas, C.A. (1998a), A Global Optimization Method, αBB, for General Twice-Differentiable NLPs - II. Implementation and Computational Results. Comp. Chem. Eng. 22(9), 1159–1178.

    Google Scholar 

  • Adjiman, C.S., Androulakis, I.P., Floudas, C.A. and Neumaier, A. (1998b), A Global Optimization Method, αBB, for General Twice-Differentiable NLPs - I. Theoretical Advances. Comp. Chem. Eng. 22(9), 1137–1158.

    Google Scholar 

  • Adjiman, C.S., Androulakis, I.P., Maranas, C.D. and Floudas, C.A. (1996), A Global Optimization Method, αBB, for Process Design. Computers Chem. Eng., Suppl. 20, S419–S424.

    Google Scholar 

  • Adjiman, C.S. and Floudas, C.A. (1996), Rigorous Convex Underestimators for General Twice- Differentiable Problems. Journal of Global Optimization 9, 23–40.

    Google Scholar 

  • Al-Khayyal, F.A. (1990), Jointly Constrained Bilinear Programs and Related Problems: An Overview. Computers Math. Appl. 19(11), 53–62.

    Google Scholar 

  • Al-Khayyal, F.A. and Falk, J.E. (1983), Jointly Constrained Biconvex Programming. Maths Ops Res. 8, 273–286.

    Google Scholar 

  • Androulakis, I., Maranas, C.D. and Floudas, C.A. (1995), αBB: A Global Optimization Method for General Constrained Nonconvex Problems. Journal of Global Optimization 7, 337–363.

    Google Scholar 

  • Balakrishna, S. and Biegler, L.T. (1992a), A Constructive Targeting Approach for for the Synthesis of Isothermal Reactor Networks. Ind. Eng. Chem. Res. 31(9), 300.

    Google Scholar 

  • Balakrishna, S. and Biegler, L.T. (1992b), Targeting Strategies for Synthesis and Energy Integration of Nonisothermal Reactor Networks. Ind. Eng. Chem. Res. 31(9), 2152.

    Google Scholar 

  • Balakrishna, S. and Biegler, L.T. (1996), Chemical Reactor Network Targeting and Integration: An Optimization Approach. In: J.L. Anderson (ed.), Advances in Chemical Engineering, Vol. 23. Academic Press, pp. 247–300.

  • Chitra, S.P. and Govind, R. (1981), Yield Optimization for Complex Reactor Systems. Chem. Eng. Sci. 36, 1219–1225.

    Google Scholar 

  • Chitra, S.P. and Govind, R. (1985), Synthesis of Optimal Serial Reactor Structures for Homogeneous Reactions. AIChE J. 31, 177–193.

    Google Scholar 

  • Cordero, J., Davin, A., Floquet, P., Pibouleau, L. and Domenech, S. (1997), Synthesis of optimal reactor networks using mathematical programming and simulated annealing. Comp. Chem. Engng. 21, S46–S53.

    Google Scholar 

  • Dyson, D.C. and Horn, F.J.M. (1967), Optimum Adiabatic Cascade Reactor with Direct Intercooling. J. Opt. Theory Appl. 1(1), 40–52.

    Google Scholar 

  • Esposito, W.R. and Floudas, C.A. (2000a), Deterministic Global Optimization in Nonlinear Optimal Control Problems. Journal of Global Optimization 17, 97–126.

    Google Scholar 

  • Esposito, W.R. and Floudas, C.A. (2000b), Global Optimization for the Parameter Estimation of Differential-Algebraic Systems. I&EC Res. 37(5), 1841–1858.

    Google Scholar 

  • Feinberg, M. (1999), Recent results in optimal reactor synthesis via attainable region theory. Chem. Eng. Science 54, 2535–2543.

    Google Scholar 

  • Feinberg, M. (2000a), Optimal reactor design from a geometric viewpoint - III. Critical CFSTRs. Chem. Eng. Sci. 55, 3553–3565.

    Google Scholar 

  • Feinberg, M. (2000b), Optimal reactor design from a geometric viewpoint. Part II. Critical sidestream reactors. Chem. Eng. Sci. 55, 2455–2479.

    Google Scholar 

  • Feinberg, M. and Hildebrandt, D. (1997), Optimal Reactor Design from a Geometric Viewpoint-I. Universal Properties of the Attainable Region. Chem. Eng. Sci. 52(10), 1637–1665.

    Google Scholar 

  • Gill, P.E., Murray, W., Saunders, M. and Wright, M.H. (1986), User's Guide for NPSOL (Version 4.0). Systems Optimization Laboratory, Department of Operations Research, Stanford University. Technical Report SOL 86–2.

  • Glasser, D., Crowe, C. and Hildebrandt, D. (1987), The Attainable Region and Optimization in Concentration Spaces. Ind. Eng. Chem. Res 26(9), 1803–1810.

    Google Scholar 

  • Hildebrandt, D. and Biegler, L.T. (1995), Synthesis of Reactor Networks. In: L.T. Biegler and M.F. Doherty (eds.), Foundations of Computer Aided Process Design, Vol. 91 of AIChE Symposium Series. New York, p. 52.

  • Hildebrandt, D. and Glasser, D. (1990), The Attainable Region and Optimal Reactor Structures. Chem. Eng. Sci. 45, 2161–2168.

    Google Scholar 

  • Hildebrandt, D., Glasser, D. and Crowe, C.M. (1990), Geometry of the Attainable Region Generated by Reaction and Mixing: with and without Constraints. Ind. End. Chem. Res. 29, 49–58.

    Google Scholar 

  • Horn, F. (1964), Attainable Regions in Chemical Reaction Technique. In: The Third European Symposium on Chemical Reaction Engineering. Pergamon, Oxford, pp. 1–10.

    Google Scholar 

  • Horn, F.J.M. and Tsai, M.J. (1967), The Use of Adjoint Variables in the Development of Improvement Criteria for Chemical Reactors. J. Opt. Theory Appl. 1(2), 131–145.

    Google Scholar 

  • Kokossis, A.C. and Floudas, C.A. (1990), Optimization of Complex Reactor Networks-I. Isothermal Operation. Chem. Eng. Sci. 45(3), 595–614.

    Google Scholar 

  • Kokossis, A.C. and Floudas, C.A. (1991), Synthesis of Isothermal Reactor-Separator-Recycle Systems. Chem. Eng. Sci. 46(5/6), 1361–1383.

    Google Scholar 

  • Kokossis, A.C. and Floudas, C.A. (1994a), Optimization of Complex Reactor Networks-II. Nonisothermal Operation. Chem. Eng. Sci. 49(7), 1037–1051.

    Google Scholar 

  • Kokossis, A.C. and Floudas, C.A. (1994b), Stability in Optimal Design: Synthesis of Complex Reactor Networks. AIChE J. 40(5), 849–861.

    Google Scholar 

  • Lakshmanan, A. and Biegler, L.T. (1996), Synthesis of Optimal Chemical Reactor Networks. Ind. Eng. Chem. Res. 35(4), 1344.

    Google Scholar 

  • Levenspiel, O. (1973), Chemical Reaction Engineering. Wiley, New York.

    Google Scholar 

  • Levenspiel, O. (1993), The Chemical Reactor Omnibook. OSU Book Stores, Inc.

  • Maranas, C.D. and Floudas, C. (1994), Global Minimum Potential Energy Conformations of Small Molecules. Journal of Global Optimization 4, 135.

    Google Scholar 

  • Marcoulaki, E.C. and Kokossis, A.C. (1999), Scoping and Screening Complex Reaction Networks using Stochastic Optimization. AIChE Journal 45(9), 1977–1991.

    Google Scholar 

  • McCormick, G.P. (1976), Computability of Global Solutions to Factorable Nonconvex Programs: Part I-Convex Underestimations Problems. Mathematical Programming 10, 147–175.

    Google Scholar 

  • Ong, S.L. (1986), Optimization of CSTRs in Series by Dynamic Programming. Biotechnology and Bioengineering 28, 818–823.

    Google Scholar 

  • Pontryagin, L.S. (1962), Ordinary Differential Equations. Addison-Wesley Publishing Co. (Translated from Russian by L. Kacinskas and W. B. Counts).

  • Quesada, I. and Grossmann, I. (1995), Global Optimization of Bilinear Process Networks with Multicomponent Flows. Comp. Chem. Eng. 19(12), 1219–1242.

    Google Scholar 

  • Schweiger, C. and Floudas, C. (1999), Optimization Framework for the Synthesis of Chemical Reactor Networks. I&EC Res. 38(3), 744–766.

    Google Scholar 

  • Schweiger, C.A. and Floudas C.A. (1998), MINOPT: A Modeling Language and Algorithmic Framework for Linear, Mixed-Integer, Nonlinear, Dynamic, and Mixed-Integer Nonlinear Optimization. Princeton University, 3rd edition.

  • Trambouze, P.J. and Piret E.L. (1959), Continuous stirred tank reactors: Designs for maximum conversions of raw material to desired product - Homogeneous reactions. AIChE J. 5, 384–390.

    Google Scholar 

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Author notes

  1. W. R. Esposito

    Present address: Praxair, Inc., 175 East Park Drive, Tonawanda, NY, 14150, USA

Authors and Affiliations

  1. Department of Chemical Engineering, Princeton University, Princeton, NJ, 08544-5263, USA

    W. R. Esposito & C. A. Floudas

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  1. W. R. Esposito
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  2. C. A. Floudas
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Correspondence to C. A. Floudas.

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Esposito, W.R., Floudas, C.A. Deterministic global optimization in isothermal reactor network synthesis. Journal of Global Optimization 22, 59–95 (2002). https://doi.org/10.1023/A:1013842726210

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