Abstract
Various dynamical characters of continuous stirred tank reaclors (CSTR) are introduced with respect to the effects of reaction types, extra thermal capacitance, periodic forcing, and coupling of CSTRs. The subject includes the classical dynamics of two-dimensional model and the variety of complex dynamics in three or higher dimensional systems such as periodic bifurcations to torus or chaos, aperiodic oscillations on invariant torus, and universal dynamics of alternating periodic-chaotic sequences with k.2v-cycles for every natural number k. Particularly this review intends to bring about the problems that the engineers must be prepared to encounter in solving various physical systems including chemically reacting systems.
Article PDF
Avoid common mistakes on your manuscript.
References
Liljenroth, F.G.:Chem. Metall. Engng,19, 287 (1918).
Semenov, N.N.:Z. Phys.,48, 571 (1928).
Burton, A.C.:J. Cell. Comp. Physiol,14, 327 (1939).
Denbigh, K.G.:Trans. Faraday Soc,43, 648 (1947).
Denbigh, K.G., Hicks, M., and Page, F.M.:Trans. Faraday Soc,44, 479 (1948).
Frank-Kamenetskii, D.A.:Zh. Fiz. Khim.,14, 30 (1940).
Frank-Kamenetskii, D.A.:Usp. Khim.,10, 372 (1941).
Salikov, I.E.:Dokl. Akad Nauk.,60, 405 (1948).
Van Heerden, C.:Ind. Engng Chem.,45, 1242 (1953).
Bilous, O. and Amundson, N.R.:AlChE J.,1, 513 (1955).
Aris, R. and Amundson, N.R.:Chem. Eng. Sci.,7, 121, 132, 148(1958).
Warden, R.B., Aris, R., and Amundson, N.R.:Chem. Eng. Sci.,19, 149, 173 (1964).
Berger, J.S. and Perlmutter, D.D.:Chem. Eng. Sci.,20, 147(1965).
Gurel, O. and Lapidus, L.:CEP Symp. Ser.,61, 78 (1965).
Luus, R. and Lapidus, L:Chem. Eng. Sci.,21, 159 (1966).
Luus, R. and Lapidus, L.:AlChE J.,18, 1060 (1972).
Dorawala, T.G. and Douglas, J.M.:AlChE J.,17, 974(1971).
Heberling, P.V., Gaitonde, N.Y., and Douglas, J.M.:AlChE J.,17, 1506 (1971).
Hyun, J.C. and Aris, R.:Chem. Eng. Sci.,27, 1341, 1361 (1972).
Uppal, A., Ray, W.H., and Poore, A.B.:Chem. Eng. Sci.,29, 967 (1974).
Uppal, A., Ray, W.H., and Poore, A.B.:Chem. Eng. Sci.,31, 205 (1976).
Golubitsky, M. and Keyfitz, B.L:SIAM J. Math. Anal.,11, 316(1987).
Golubitsky, M. and Schaeffer, D.:Commun. Pure Appl. Math.,32, 21 (1979).
Golubitsky, M., Keyfitz, B.L, and Schaeffer, D.:Commun. Pure Appl. Math.,34, 433 (1981).
Balakotaiah, V. and Luss, D.:Chem. Eng. Sci.,37, 1611 (1982).
Balakotaiah, V. and Luss, D.:Chem. Eng. Commun.,19, 185 (1982).
Balakotaiah, V. and Luss, D.:Chem. Eng. Sci.,38, 1709(1983).
Farr, W.W. and Aris, R.:Chem. Eng. Sci.,41, 1385 (1986).
Kahlert, C, Rossler, O.E., and Varma, A.: “Modeling of Chemical Reaction Systems”, Edited by Ebert, K. and Jaeger, W., Springer-Verlag, Heidelberg, (1981).
Jorgensen, D.V. and Aris, R.:Chem. Eng. Sci.,38, 45 (1983).
Rossler, O.E.:Phys. Lett,57A, 397 (1976).
Hudson, J.L., Hart, M., and Marinko, D.:J. Chem. Phys.,71, 1601 (1979).
Roux, J.C. and Swinney, H.L.: “Nonlinear Phenomena in Chemical Dynamics”, Edited by Vidal, C. and Pacault, A., P81, Springer-Verlag, Berlin, (1981).
Simoyi, R.H., Wolf, A., and Swinney, H.L.:Phys. Rev. Lett.,49, 245 (1982).
Epstein, I.R.:Physica,7D, 47 (1983).
Chang, K.S. and Aris, R.:Kor. J. Chem. Eng.,4, 95 (1987).
Keller, H.B. : “Application of Bifurcation Theory”, Edited by Rabinowitz, P.H., Academic Press, (1977).
Doedel, E.J. and Heinemann, R.F.:Chem. Eng. Sci.,38, 1493 (1983).
Zeeman, E.C.: “Catastrophe Theory”, Addison-Wesley, Reading, Mass., 1977.
Kalman, R.E. and Bertram, J.E.:J. Basic Engng,82D, 371 (1960).
Marsden, J.E. and McCracken, M: “The Hopf Bifurcation and its Applications”, Springer-Verlag, New-York, Heidelberg, Berlin, (1976). ’
Grebogi, C. and Ott, E.:Physica,7D, 181 (1983).
Feigenbaum, M.J.:J. Stat. Phys.,21, 667 (1979).
Planeaux, J.B. and Jensen, K.F.:Chem. Eng. Sci.,41, 1497 (1986).
Guckenheimer, J. and Holmes, P.: “Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields”, Springer-Verlag, New York (1983).
Silikov, L.P.:Soviet Math. Dokl,8, 54 (1986).
Bailey, J.E.:Chem. Eng. Commun.,1, 111 (1973).
Bailey, J.E.: “Chemical Reactor Theory”, Edited by Lapidus, L. and Amundson, N.R., Prentice-Hall, Englewood. Cliffs, N.J., (1977).
Sincic, D. and Bailey, J.E.:Chem. Eng. Sci.,32, 281 (1977).
Mankin, J.C. and Hudson, J.L.:Chem. Eng. Sci.,39, 1807 (1984).
Kevrekidis, I.G., Aris, R., and Schmidt, L.D.:Chem. Eng. Sci.,41, 1549 (1986).
Kevrekidis, I.G., Aris, R., and Schmidt, L.D.:Chem. Eng. Sci.,41, 905 (1986).
Kevrekidis, IG., Schmidt, L.D. and Aris, R.:Chem. Eng. Sci.,41, 1263 (1986).
Varma, A.:Ind. Eng. Chem. Fundam.,19, 316 (1980).
Kubicek, M, Hoffmann, H., Hlavacek, V., and Sinkule, J.:Chem. Eng. Sci.,35, 987 (1980).
Svoronos, S., Aris, R., and Stephanopolous, G.:Chem. Eng. Sci.,37, 357 (1982).
Mankin, J.C. and Hudson, J.L.:Chem. Eng. Sci.,41, 2651 (1986).
Chang, K.S. and Aris, R.:Lat. Am. Appl. Res.,18(1), (1988).
Li, T.Y. and Yorke, J.A.:Am. Math. Monthly,82, 985 (1975).
May, R.M.:Nature,262, 459 (1976).
Hudson, J.L. and Rossler, O.E.: “Dynamics of Nonlinear Systems”, Edited by Hlavacek, V., Gordon & Breach, (1984).
Penlidis, A., MacGregor, J.F., and Hamielec, A.E.:AIChE J.,31, 881 (1985).
Kirillov, V.A. and Ray, W.H.:Chem. Eng. Sci.,33, 1499 (1978).
Schmidt, A.D. and Ray, W.H.:Chem. Eng. Sci.,36, 1401 (1981).
Hamer, J.W., Akramov, T.A., and Ray, W.H.:Chem. Eng. Sci.,36, 1897 (1981).
Schmidt, A.D., Clinch, A.B., and Ray, W.H.:Chem. Eng. Sci.,39, 419 (1984).
Fredrickson, A.G.:ACS Symp. Ser.,207, 201 (1983).
Fredrickson, A.G. and Stephanopolous, G.:Science,213, 972 (1981).
Razon, L.F. and Schmitz, R.A.:Chem. Eng. Sci.,42, 1005(1987).
Hudson, J.L. and Mankin, J.C.:J. Chem. Phy.,74, 6171 (1981).
Hudson, J.L, Mankin, J.C, McCullough, J., and Lamba, P.: “Nonlinear Phenomena in Chemical Dynamics”, Edited by Vidal, C. and Pacault, A., Springer-Verlag, Heidelberg, (1981).
Hudson, J.L, Mankin, J.C, and Lamba, P.:ACS Symp. Ser.,196, 145 (1982).
Hudson, J.L, Mankin, J.C, and Rossler, C.E.: “Stochastic Phenomena, Chaotic Behavior in Complex Systems”, Edited by Schuster, P., Springer-Verlag, Heidelberg, (1984).
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Chang, K.S., Kim, J.Y. & Rhee, HK. Intricate CSTR dynamics. Korean J. Chem. Eng. 6, 69–80 (1989). https://doi.org/10.1007/BF02697482
Received:
Accepted:
Issue Date:
DOI: https://doi.org/10.1007/BF02697482