Hostname: page-component-586b7cd67f-2plfb Total loading time: 0 Render date: 2024-11-27T00:32:56.867Z Has data issue: false hasContentIssue false
  • English
  • Français

Stochastic analysis of the Transient Behavior of an msmpr Crystallizer

Effects of the Seed Size Distribution and Size- Dependent Growth Rate

Published online by Cambridge University Press:  27 July 2009

S. T. Chou  and
J. P. Hsu
S. T. Chou
Affiliation:
Department of Chemical Engineering Kansas State University Manhattan, Kansas 66506
J. P. Hsu
Affiliation:
Department of Chemical Engineering National Taiwan University Taipei, Taiwan
Get access Rights & Permissions [Opens in a new window]

Abstract

The transient crystal size distribution (CSD) in a continuous mixed suspension, mixed product removal crystallizer has been modeled through a stochastic approach. Effects of the seed size distribution and size-dependent growth rate on both the transient and steady-state CSD have been investigated. It has been found that the seed size distribution causes a maximum in the steady-state CSD and the size-dependent growth rate results in an upward curvature at the lower end in a semilogarithmic plot of steady-state CSD against crystal size. Under appropriate conditions, the mean CSD of the present stochastic model reduces to the results predicted by the corresponding deterministic population balance model.

Type
Articles
Information
Probability in the Engineering and Informational Sciences , Volume 1 , Issue 4 , October 1987 , pp. 383 - 404
Copyright
Copyright © Cambridge University Press 1987

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Abegg, C.F., Stevens, J. D., & Larson, M.A. (1968). Crystal size distributions in continuous crystallizers when growth rate is size-dependent. AIChE J. 14: 118–122.CrossRefGoogle Scholar
Berglund, K.A. & Larson, M.A. (1984). Modeling of growth rate dispersion of citric acid mono-hydrate in continuous crystallizers. AIChE J. 30: 280–287.CrossRefGoogle Scholar
Bourne, J.R. & Zabelka, M. (1980). The influence of gradual classification on continuous crystallization. Chem. Eng. Sci. 35: 533–542.CrossRefGoogle Scholar
Budz, J., Karpinski, P.H., & Nuruc, Z. (1984). Influence of hydrodynamics on crystal growth and dissolution in a fluidized bed. AIChE J. 30: 710–717.CrossRefGoogle Scholar
Canning, T.F. & Randolph, A.D. (1967). Some aspects of crystallization theory: Systems that violate McCabe's Delta Law. AIChE J. 13: 5–10.CrossRefGoogle Scholar
Chiang, C.L. (1980). An introduction to stochastic processes and their applications. New York; Krieger, pp. 396–435.Google Scholar
Fan, L.T., Fan, L.S., & Nassar, R. (1979). A stochastic model of the unsteady state age distribution in a flow system. Chem. Eng. Sci. 34: 1172–1174.CrossRefGoogle Scholar
Fan, L.T., Chou, S.T., & Hsu, J.P. (1987). Transient analysis of crystallization: Effect of the size-dependent residence time or classified product removal. AIChE Symp. Ser. 83(253):120–129.Google Scholar
Garside, J. & Jancic, S.J. (1978). Prediction and measurement of crystal size distributions for size-dependent growth. Chem. Eng. Sci. 33: 1623–1630.CrossRefGoogle Scholar
Girolami, M.W. (1984). Size dependent crystal growth: A manifestation of growth rate dispersion in the Potassium Alum-Water system. M.S. Thesis. North Carolina State University, Raleigh, North Carolina.Google Scholar
Hixson, A.W. & Knox, K.L. (1951). Effect of agitation on rate of growth of single crystals. Ind. Eng. Chem. 43: 2144–2151.CrossRefGoogle Scholar
Hsu, J.P. & Fan, L.T. (1987). Transient analysis of crystallization: Effect of the size-dependent growth rate. Chem. Eng. Commun. in press.Google Scholar
Karlin, S. & Taylor, H.M. (1981). A second course in stochastic processes. New York: Academic Press, pp. 534–535.Google Scholar
Karpinski, P.H. (1980). Crystallization as a mass transfer phenomenon. Chem. Eng. Sci. 35: 2321–2324.CrossRefGoogle Scholar
Karpinski, P.H. (1985). Importance of the two-step crystal growth model. Chem. Eng. Sci. 40: 641–646.CrossRefGoogle Scholar
Katz, S. & Shinnar, R. (1969). Particulate methods in probability systems. Ind. Eng. Chem. 61(4): 60–73.CrossRefGoogle Scholar
Larson, M.A., White, E.T., Ramanarayanan, K.A., & Berglund, K.A. (1985). Growth rate dispersion in MSMPR crystallizers. AIChE J. 31: 90–94.CrossRefGoogle Scholar
Margolis, G., Sherwood, T.K., Brian, P.L.T., & Sarofim, A.F. (1971). The performance of a continuous well stirred ice crystallizer. Ind. Eng. Chem. Fundam. 10: 439–452.CrossRefGoogle Scholar
McCabe, W.L. (1929). Crystal growth in aqueous solutions I-theory. Ind. Eng. Chem. 21: 30–33.CrossRefGoogle Scholar
Melikhov, I.V. & Berliner, L.B. (1981). Simulation of batch crystallization. Chem. Eng. Sci. 36: 1021–1034.CrossRefGoogle Scholar
Murray, D.C. & Larson, M.A. (1965). Size distribution dynamics in a slating out crystallizer. AIChE J. 11: 728–733.CrossRefGoogle Scholar
Nassar, R., Too, J.R., & Fan, L.T. (1984). Stochastic diffusion model for crystal size distribution in an open flow system. AIChE J. 30: 1014–1016.CrossRefGoogle Scholar
Nicolis, G. & Prigogine, I. (1977). Self-organization in nonequilibrium systems. New York: John Wiley & Sons, pp. 232.Google Scholar
Nyvlt, J., Sohnel, O., Matuchova, M., & Broul, M. (1985). The kinetics of industrial crystallization. New York: Elsevier, pp. 149–215.Google Scholar
Ramanarayanan, K.A., Athreya, K., & Larson, M.A. (1984). Statistical-mathematical modeling of CSD in continuous and batch crystallizers. AIChE Symp. Ser. 80 (214): 76–88.Google Scholar
Randolph, A.D. & Larson, M.A. (1962). Transient and steady-state size distribution in continuous mixed suspension crystallizers. AIChE J. 8: 639–645.CrossRefGoogle Scholar
Randolph, A.D. & Larson, M.A. (1971). Theory of particulate processes. New York: Academic Press.Google Scholar
Randolph, A.D. & White, E.T. (1977). Modeling size dispersion in the prediction of crystal size distribution. Chem. Eng. Sci. 32: 1067–1076.CrossRefGoogle Scholar
Rohatgi, V.K. (1976). An introduction to probability theory and mathematical statistics. New York: John Wiley & Sons, pp. 197–199.Google Scholar
Rousseau, R.W. & Howell, T.R. (1982). Comparison of simulated crystal size distribution control systems based on nuclei density and supersaturation. Ind. Eng. Chem. Process Des. Dev. 21: 606–610.CrossRefGoogle Scholar
Rousseau, R.W. & Woo, R. (1980). Effects of operating variables on potassium alum crystal size distribution. AIChE Symp. Ser. 76(193): 27–33.Google Scholar
Seinfeld, J.H. & Lapidus, L. (1974). Mathematical methods in chemical engineering, vol. 3, Process modeling, estimation, and identification. Englewood Cliffs, New Jersey: Prentice-Hall, Inc. pp. 197–288.Google Scholar
Sherwin, M.B., Shinnar, R., & Katz, S. (1967). Dynamic behavior of the well-mixed isothermal crystallizer. AIChE J. 13: 1141–1154.CrossRefGoogle Scholar
Too, J.R., Nassar, R., Chou, S.T., & Fan, L.T. (1986). Stochastic analysis of crystallization in an open flow system. J. of the Chin. Inst. of Ch.E. 17: 303–313.Google Scholar
Wey, J.S., Terwilliger, J.P., & Gingello, A.D. (1980). Analysis of AgBr precipitation in a continuous suspension crystallizer. AIChE Symp. Ser. on Design, Control and Analysis of Crystallization Processes 76 (193): 34–42.Google Scholar