Skip to main content

Chaos in a Continuous Stirred Tank Reactor with Two Consecutive First-Order Reactions, One Exo-, One Endothermic

  • Conference paper
Modelling of Chemical Reaction Systems

Part of the book series: Springer Series in Chemical Physics ((CHEMICAL,volume 18))

Abstract

A CSTR with two irreversible consecutive reactions -the first exothermic, the second endothermic -shows under numerical simulation a sequence of period- doubling bifurcations of a limit cycle: an ordinary limit cycle gives way to one of period 2; the latter then is replaced by one of period 4; etc., with chaos arising in the limit. The parameter values chosen for the numerical experiment turn out to be relatively close to chemically realistic values.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 84.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. K.D. Willamowski, O.E. Rossler: Irregular oscillations in a realistic abstract quadratic mass actioVi system. Z. Naturforsch. 35a, 317–318 (1980)

    Google Scholar 

  2. C.A. Pikios, D. Luss: Steady state multiplicity of lumped parameter systems in which two consecutive or two parallel irreversible first- order reactions occur. Chem. Eng. Sci. 34, 919–927 (1979)

    Article  CAS  Google Scholar 

  3. D.S. Cohen, J.P. Keener: Multiplicity and stability of oscillatory states in a CSTR with exothermic consecutive reactions A B C. Cem. Eng. Sci. 32, 115–122 (1975)

    Google Scholar 

  4. M. Henon: A two-dimensional mapping with a strange attractor. Commun. Math. Phys. 50, 69–78 (1976)

    Article  Google Scholar 

  5. O.E. Rössler: Chaotic behavior in simple reaction systems. Z. Naturforsch. 31a, 259–264 (1976)

    Google Scholar 

  6. O.E. Rössler: “Chaos”, in Structural Stability in Physios, ed. by W. Güttinger, H. Eikemeyer ( Springer, Berlin, Heidelberg, New York 1979 ) pp. 290–309

    Google Scholar 

  7. O.E. Rössler: “Continuous Chaos”, in Synergetics A Workshop, ed. by

    Google Scholar 

  8. H. Haken (Springer, Berlin, Heidelberg, New York 1977 ) pp. 184–197

    Google Scholar 

  9. P. Coullet, C. Tresser, A. Arneodo: Transition to stochasticity for a class of forced oscillators. Phys. Lett. 72k, 268–270 (1979)

    Article  Google Scholar 

  10. R. Abraham, J. Marsden: Foundations of Mechanics (Benjamin, Reading, Mass., 1978 )

    Google Scholar 

  11. J. Herschel: Consideration of various points of analysis. Phil. Transact. London 2, 440–468 (1814). Quoted after

    Google Scholar 

  12. I. Gumowski, C. Mira: “Recurrences and Discrete Dynamical Systems”, in Lecture Notes in Mathematics, Vol.809 (Springer, Berlin, Heidelberg, New York 1980)

    Google Scholar 

  13. P.J. Myrberg: Iteration of the real polynomials of second degree, II (in German). Ann. Acad. Sei. Fenn. Ser. A 336/3, 1–18 (1963)

    Google Scholar 

  14. A.N. Sharkovsky: Coexistence of the cycles of a continuous mapping of the line into itself. Ukr. Mat. Zh. 16, 61–71 (1964)

    Google Scholar 

  15. M.J. Feigenbaum: The onset spectrum of turbulence. Phys. Lett. 74k, 375–378 (1979)

    Google Scholar 

  16. V. Hlavacek, H. Hofmann: Modelling of chemical reactors. 16. Steady state axial heat and mass transfer in tubular reactors, an analysis of uniqueness of solutions. Chem. Eng. Sci. 25, 173–199 (1970)

    Article  CAS  Google Scholar 

Download references

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 1981 Springer-Verlag Heidelberg

About this paper

Cite this paper

Kahlert, C., Rössler, O.E., Varma, A. (1981). Chaos in a Continuous Stirred Tank Reactor with Two Consecutive First-Order Reactions, One Exo-, One Endothermic. In: Ebert, K.H., Deuflhard, P., Jäger, W. (eds) Modelling of Chemical Reaction Systems. Springer Series in Chemical Physics, vol 18. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-68220-9_26

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-68220-9_26

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-68222-3

  • Online ISBN: 978-3-642-68220-9

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics