APPLICATION OF SINGULARITY THEORY TO A NON-ISOTHERMAL CSTR WITH AN AUTOCATALYTIC REACTION

Cho SM; Ko BS; Rhee HK

Korean Journal of Chemical Engineering, Vol.12, No.1, 56-60, January, 1995

The steady-state behavior is investigated for a non-isothermal, non-adiabatic CSTR in which an autocatalytic reaction takes place with kinetic scheme A+B → 2B+heat, rate = k(T) C_AC_B Singularity theory is applied to find the maximal number of steady-state solutions and to determine the regions in the parameter space corresponding to these solutions. The parameter space is divided into four regions corresponding to four types of different steady-state structure and it is shown that multiple steady-states (up to three) exist for some set of parameter values.

Keywords:Singularity Theory;Autocatalytic Reaction;Steady-State Multiplicity;Bifurcation Diagram;Non-Isotherm CSTR

[References]

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Chang HC, Calo JM, Chem. Eng. Sci., 34, 285 (1979)
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Brooks BW, Chem. Eng. Sci., 43, 1287 (1988)
Brooks BW, Chem. Eng. Sci., 43, 2795 (1988)
Sapre AV, AIChE J., 35, 655 (1989)
Chen CT, Crynes BL, Ind. Eng. Chem. Res., 26, 574 (1987)
Aris R, Gray P, Scott SK, Chem. Eng. Sci., 43, 207 (1988)
Gray P, Scott SK, Chem. Eng. Sci., 38, 29 (1983)
Scott SK, Chem. Eng. Sci., 38, 1701 (1983)
Scott SK, Chem. Eng. Sci., 42, 307 (1987)
Lin KF, Can. J. Chem. Eng., 57, 476 (1979)
Lin KF, Chem. Eng. Sci., 36, 1447 (1981)
Lynch DT, Chem. Eng. Sci., 47, 347 (1992)
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Scott SK, Farr WW, Chem. Eng. Sci., 43, 1708 (1988)
Adesina AA, Adewale KEP, Ind. Eng. Chem. Res., 30, 430 (1991)
Balakotaiah V, Proc. R. Soc. London A, 411, 193 (1987)
D'Anna A, Lignola PG, Scott SK, Proc. R. Soc. London A, 403, 341 (1986)
Hu R, Sapre AV, AIChE J., 36, 342 (1990)
Golubitsky M, Schaeffer DG, Commun. Pure Appl. Math., 32, 21 (1979)
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[1] Lijenroth FG, Chem. Met. Eng., 19, 287 (1918)

[2] VanDenBosch B, Luss D, Chem. Eng. Sci., 32, 203 (1977)

[3] Chang HC, Calo JM, Chem. Eng. Sci., 34, 285 (1979)

[4] Hlavacek V, Chem. Eng. Sci., 27, 719 (1972)

[5] Luss D, Chen GT, Chem. Eng. Sci., 30, 1483 (1975)

[6] Pikios CA, Luss D, Chem. Eng. Sci., 34, 919 (1979)

[7] Golubitsky M, Keyfitz BL, SIAM J. Math. Anal., 11, 316 (1980)

[8] Balakotaiah V, Ph.D. Thesis, University of Houston (1982)

[9] Balakotaiah V, Luss D, Chem. Eng. Sci., 37, 1611 (1982)

[10] Balakotaiah V, Luss D, Chem. Eng. Sci., 38, 1709 (1983)

[11] Balakotaiah V, Luss D, Chem. Eng. Sci., 39, 865 (1984)

[12] Horak J, Chem. Eng. Sci., 26, 1 (1971)

[13] Brooks BW, Chem. Eng. Sci., 43, 1287 (1988)

[14] Brooks BW, Chem. Eng. Sci., 43, 2795 (1988)

[15] Sapre AV, AIChE J., 35, 655 (1989)

[16] Chen CT, Crynes BL, Ind. Eng. Chem. Res., 26, 574 (1987)

[17] Aris R, Gray P, Scott SK, Chem. Eng. Sci., 43, 207 (1988)

[18] Gray P, Scott SK, Chem. Eng. Sci., 38, 29 (1983)

[19] Scott SK, Chem. Eng. Sci., 38, 1701 (1983)

[20] Scott SK, Chem. Eng. Sci., 42, 307 (1987)

[21] Lin KF, Can. J. Chem. Eng., 57, 476 (1979)

[22] Lin KF, Chem. Eng. Sci., 36, 1447 (1981)

[23] Lynch DT, Chem. Eng. Sci., 47, 347 (1992)

[24] Lynch DT, Chem. Eng. Sci., 47, 4435 (1992)

[25] Kay SR, Scott SK, Lignola PG, Proc. R. Soc. A, 409, 433 (1987)

[26] Kay SR, Scott SK, Tomlin AS, Chem. Eng. Sci., 44, 1129 (1989)

[27] Scott SK, Farr WW, Chem. Eng. Sci., 43, 1708 (1988)

[28] Adesina AA, Adewale KEP, Ind. Eng. Chem. Res., 30, 430 (1991)

[29] Balakotaiah V, Proc. R. Soc. London A, 411, 193 (1987)

[30] D'Anna A, Lignola PG, Scott SK, Proc. R. Soc. London A, 403, 341 (1986)

[31] Hu R, Sapre AV, AIChE J., 36, 342 (1990)

[32] Golubitsky M, Schaeffer DG, Commun. Pure Appl. Math., 32, 21 (1979)

[33] Golubitsky M, Schaeffer DG, "Singularities and Groups in Bifurcation Theory," Springer-Verlag, New York (1985)