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Optimal residence time policy for product yield maximization in chemical reactors

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This paper analyzes the problem of optimal reactor-type selection for the maximization of product yield in continuous, segregated flow, isothemal or adiabatic chemical reactors of given volume. The mathematical treatment is valid for any type of chemical reaction network with arbitrary kinetics. For fixed mean residence time, it is shown that maximum or minimum yield of a product can always be obtained exactly or within arbitrary approximation by a combination of two plug-flow reactors. The analysis assumes strictly segregated flow, but some of the conclusions reached do not depend on the extent of micromixing.

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  1. 1.

    Carberry, J. J.,Chemical and Catalytic Reaction Engineering, McGraw-Hill, New York, New York, 1976.

  2. 2.

    Levenspiel, O.,Chemical Reaction Engineering, John Wiley and Sons, New York, New York, 1972.

  3. 3.

    Kemperman, J. H. B.,The General Moment Problem, A Geometric Approach, Annals of Mathematical Statistics, Vol. 39, pp. 93–122, 1968.

  4. 4.

    Richter, H., Parameterfrei Abschätzung und Realisierung von Erwartungswerten, Blätter der Deutchen Gesellschaft für Versicherungmathematik, Vol. 3, pp. 147–161, 1957.

  5. 5.

    Rogosinsky, W. W.,Moments of Nonnegative Mass, Proceedings of the Royal Society of London, Series A, Vol. 245, pp. 1–27, 1958.

  6. 6.

    Riesz, F., Sur Certaines Systémes Singuliers d'Equations Integrales, Annales Scientifiques de l'Ecole Normale Superieure, Vol. 28, pp. 33–62, 1911.

  7. 7.

    Mulholland, H. P., andRogers, C. A.,Representations Theorems for Distribution Functions, Proceedings of the London Mathematical Society, Vol. 8, pp. 177–223, 1958.

  8. 8.

    Tizs, S. H., andBorwein, J. M.,Some Generalizations of Caratheodory's Theorem via Barycenters, with Application to Mathematical Programming, Canadian Mathematical Bulletin, Vol. 23, pp. 339–346, 1980.

  9. 9.

    Lotka, A.,Undamped Oscillations Derived from the Law of Mass Action, Journal of the American Chemical Society, Vol. 42, pp. 1595–1604, 1920.

  10. 10.

    Feinberg, M.,Mathematical Aspects of Mass Action Kinetics, Chemical Reactor Theory, Edited by L. Lapidus and N. R. Amundson, Prentice-Hall, Englewood Cliffs, New Jersey, pp. 1–78, 1977.

  11. 11.

    Modell, M., andReid, R. C.,Thermodynamics and Its Applications, Prentice-Hall, Englewood Cliffs, New Jersey, pp. 14–16, 1974.

  12. 12.

    Rockafellar, R. T.,Convex Analysis, Princeton University Press, Princeton, New Jersey, 1970.

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This work was partly supported by the Hellenic Refineries of Aspropyrgos, Athens, through a fellowship to I. Andreou. The first author acknowledges helpful discussions with J. H. B. Kemperman, T. G. Hallam, and S. Papadopoulou.

Communicated by J. E. Bailey

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Nestoridis, V., Andreou, I. & Vayenas, C.G. Optimal residence time policy for product yield maximization in chemical reactors. J Optim Theory Appl 49, 271–287 (1986).

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Key Words

  • Chemical yield optimization
  • convex analysis
  • residence time distribution