Advertisement

Characterization of Crystallization Kinetics from Batch Experiments

  • Narayan S. Tavare
Part of the The Springer Chemical Engineering Series book series (PCES)

Abstract

The process analysis of various types of batch crystallizers operated in various modes is presented in Chapter 5. In this chapter, the techniques that are available to characterize crystallization kinetics of a crystallizing system in a batch crystallizer are discussed. In recent years there has been an increasing recognition of the importance of crystallization kinetics in assessing the design and performance of crystallizers. The characterization of crystallization kinetics in an environment typical of that encountered in industrial situations is therefore of utmost importance. Numerous techniques have been devised to measure and analyze crystal growth and, to a far lesser extent, nucleation. The experimental techniques developed to extract crystallization parameters as depicted in Figure 53 are based on phenomenological models and are closely related to those used in chemical reaction engineering. The classical approach to establish crystallization kinetics involves the isolation of the nucleation and growth processes and the determination of their kinetics separately by direct and/or indirect methods under different hydrodynamic conditions.

Keywords

Nucleation Rate Crystallization Kinetic Crystal Size Distribution Nucleation Kinetic Calcium Oxalate Monohydrate 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Bellman, R. and Kalaba, R., Quasilinearization and Non-linear Boundary Value Problems, American Elsevier, New York (1965).Google Scholar
  2. Bergmann, R. N., Kalaba, R. E. and Spingarn, K., “Optimizing inputs for diagnosis of diabetes: I Fitting a minimal model to data,” J. Optimization Theory Applic. 20, 47–63 (1976).CrossRefGoogle Scholar
  3. Bransom, S. H., Dunning, W. J. and Millard, B., “Kinetics of crystallization in solution,” Discuss. Farad. Soc. 5, 83–103 (1949).CrossRefGoogle Scholar
  4. Bourne, J. R. and Faubel, A., “Influence of agitation on the nucleation of ammonium sulfate,” in Jancic, S. J. and de Jong, E. J. (Eds.), Industrial Crystallization 81, North-Holland, Amsterdam,79–86(1982).Google Scholar
  5. Chambliss, C. W., Nucleation and Growth Kinetics in a Cooling Crystallizer, Ph. D. thesis, Iowa State University, Ames, Iowa (1966).Google Scholar
  6. Dauday, P. J. and de Jong, E. J., “The dynamic behaviour of NaCl crystallization in a 91 L MSMPR crystallizer,” in Jancic, S. J. and de Jong, E. J.(Eds.), Industrial Crystallization 84, Elsevier, Amsterdam, 447–451 (1984).Google Scholar
  7. Donnelly, J. K. and Quon, D., “Identification of parameters in systems of ordinary differential equations using quasilinearization and data perturbation,” Can. J. Chem. Eng. 48, 114–119 (1970).CrossRefGoogle Scholar
  8. Estrin, J., McNeil, T. J. and Weed, D. R., “A note on modeling laboratory batch crystallizations,” AIChEJ. 24, 728–731 (1978).CrossRefGoogle Scholar
  9. Garside, J. and Jancic, S. J., “Growth and dissolution of potash alum crystals in the subsieve size range,” AIChEJ. 22, 887–894 (1976).CrossRefGoogle Scholar
  10. Garside, J. and Jancic, S. J., “Measurement and scaleup of secondary nucleation kinetics for the potash alum-water system,” AIChE J. 25, 948–958 (1979).CrossRefGoogle Scholar
  11. Garside, J. and Shah, M. B., “Crystallization kinetics from MSMPR crystallizers,” Ind. Eng. Chem. Proc. Des. Dev. 19, 509–514 (1980).CrossRefGoogle Scholar
  12. Garside, J, Gibilaro, L. G. and Tavare, N. S., “Evaluation of crystal growth kinetics from a desupersaturation curve using initial derivatives,” Chem. Eng. Sci. 37, 1625–1628 (1982).CrossRefGoogle Scholar
  13. Garside, J. and Tavare, N. S., Research reports submitted to Separation Process Services (SPS), Harwell, Didcot, England (1982).Google Scholar
  14. Garside, J. and Tavare, N. S., Research report submitted to Separation Process Services (SPS), Harwell, Didcot, England (1983).Google Scholar
  15. Garside, J. and Tavare, N. S., “Simultaneous estimation of crystal nucleation and growth kinetics from batch experiments,” Chem. Eng. Res. Des. 64, 109–118 (1986).Google Scholar
  16. Gutwald, T. and Mersmann, A., “Determination of crystallization kinetics from batch experiments,” in Mersmann, A.(Ed.), Industrial Crystallization’ 90, Garmisch-Partenkirchen, Germany, 331–336(1990).Google Scholar
  17. Halfon, A. and Kaliguine, S., “Alumina trihydrate crystallization: Part I Secondary nucleation and growth rate kinetics,” Can. J. Chem. Eng. 54, 160–167 (1976).CrossRefGoogle Scholar
  18. Han, C. D., “Determination of crystal growth rate by analog computer simulation,” Chem. Eng. Sci. 22, 611–618 (1967).CrossRefGoogle Scholar
  19. Harano, Y. and Yamamoto, H., “Formation and growth of nuclei by secondary nucleation in agitated solution of K-alum,” J. Chem. Eng. Jpn. 13, 313–318 (1980).CrossRefGoogle Scholar
  20. Harano, Y. and Yamamoto, H., “Impurity effect of some amino acids on formation and growth of Lglutamic acid nuclei by secondary nucleation in agitated solution,” in Jancic, S. J. and de Jong, E. J.(Eds.), Industrial Crystallization 81, North Holland, Amsterdam, 137–145 (1982).Google Scholar
  21. Hiquily, N. and Laguerie, C, “On the interpretation of the metastable zone width in relation to crystallization kinetics,” in Proc. Technol. Proceedings, 6 (Industrial Crystallization’87), 107–110(1989).Google Scholar
  22. Hulburt, H. M. and Katz, S., “Some problems in particle technology,” Chem. Eng. Sci. 19, 555–574 (1964).CrossRefGoogle Scholar
  23. Hwang, M. and Seinfeld, J. H., “A new algorithm for the estimation of parameters in ordinary differential equations,” AIChEJ. 18, 90–93 (1972).CrossRefGoogle Scholar
  24. Jancic, S. J., Crystallization Kinetics and Crystal Size Distribution in Mixed Suspension Mixed Product Removal Crystallizers, Ph.D. thesis, University College, London (1976).Google Scholar
  25. Janse, A. H., Nucleation and Crystal Growth in Batch Crystallizers, Ph.D. thesis, Delft University of Technology, Delft, Holland (1977).Google Scholar
  26. Janse, A. H. and de Jong, E. J., “On the width of the metastable zone,” Trans. I. Chem. E. 56, 187–193 (1978).Google Scholar
  27. Jones, A. G., Budz, J., and Mullin, J. W., “Crystallization kinetics of potassium sulfate in an MSMPR agitated vessel,” AIChE J. 32 2002–2009 (1986).CrossRefGoogle Scholar
  28. Kane, S. G., Evans, T. W., Brian, P. L. T. and Sarofim, A. F., “Determination of the kinetics of secondary nucleation in batch crystallizers,” AIChE J. 20, 855–862 (1974).CrossRefGoogle Scholar
  29. Kalogerakis, N. and Luss, R., “Simplification of quasilinearization method for parameter estimation,” AIChEJ. 29, 858–866 (1983).CrossRefGoogle Scholar
  30. Klug, D. L. and Pigford, R. L., “The probability distribution of growth rates of anhydrous sodium sulphate crystals,” Ind. Eng. Chem. Res. 28, 1718–1725 (1989).CrossRefGoogle Scholar
  31. Kyprianidou-Leodidou, T. C. and Botsaris, G. D., “Freeze concentration of aqueous solutions,” in Myerson, A. S. and Toyokura, K. (Eds.), Crystallization as a Separation Process, ACS Symp. Ser. No. 438, American Chemical Society, Washington, D.C., 364–372 (1990).CrossRefGoogle Scholar
  32. Larson, M. A. and Mullin, J. W., “Crystallization kinetics of ammonium sulfate,” J. Crystal Growth 20, 183–191 (1973).CrossRefGoogle Scholar
  33. Lee, E. S., Quasilinearization and Invariant Imbedding, Academic Press, New York (1968).Google Scholar
  34. Lee, H. H., “Determination of birth and growth rate of secondary nuclei: SSBR crystallizer,” AIChE J. 24, 535–537 (1978).CrossRefGoogle Scholar
  35. Lyapunov, A. N. and Kholmogateseva, E. P., “Determination of the growth rate of hydrarllite particles in an aluminate solution by linear growth of crystal faces,” J. Appl. Chem. USSR, 30, 1379–1384,1664-1668(1957).Google Scholar
  36. Marquardt, D. W., “An algorithm for least squares estimation of non-linear parameters,” J. Soc. Ind. Appl. Math. 11, 431–441 (1963).CrossRefGoogle Scholar
  37. Misra, C. and White, E. T., “Kinetics of crystallization of aluminium trihydroxide from seeded aluminate solution,” Chem. Eng. Symp. Ser. 110 67, 53–65 (1971).Google Scholar
  38. Mohamed, A. K. M., Tavare, N. S. and Garside, J., “Crystallization kinetics of potassium sulphate in a 1 m3 batch cooling crystallizer,” in Strathdee, G. L., Klein, M. O. and Melis, L. A. (Eds.), Crystallization and Precipitation, Pergamon Press, Oxford, 61–70 (1987).Google Scholar
  39. Molner, I., Halaz, S. and Blickle, T., “Determination of size-dependent crystal growth characteristics from batch experiments,” Chem. Eng. Sci. 45, 1243–1251 (1990).CrossRefGoogle Scholar
  40. Mullin, J. W. and Garside, J., “Crystallization of aluminium potassium sulphate: A study of assessment of crystallizer design data: I: Single crystal growth rates, II: Growth in a fluidized bed,” Trans. I. Chem. E. 45, 285–290,291-295 (1967)Google Scholar
  41. Mullin, J. W. and Garside, J., “Crystallization of aluminium potassium sulphate: A study of assessment of crystallizer design data: III: Growth and dissolution rates,” Trans. I. Chem. E. 46, 11–18 (1968).Google Scholar
  42. Mullin, J. W., Garside, J. and Gaska, C., “A laboratory scale fluidized bed crystallizer,” Chem. Ind. 41, 1704–1706 (1966).Google Scholar
  43. Mullin, J. W. and Nyvlt, J., “Design of continuous mixed suspension crystallizers,” Kristall und Technik 9, 144–155(1974).Google Scholar
  44. Nag Fortran Library, Mark 7, Numerical Algorithm Group Ltd., Oxford, England (1978).Google Scholar
  45. Nieman, R. E. and Fisher, D. G., “Parameter estimation using linear programming and quasilinearization,” Can. J. Chem. Eng. 50, 802–806 (1972).CrossRefGoogle Scholar
  46. Nyvlt, J., “Kinetics of crystallization from solution,” J. Crystal Growth 3/4, 377–383 (1968).CrossRefGoogle Scholar
  47. Nvylt, J., Industrial Crystallization: The State of the Art, Verlag Chemie, Weinheim (1978).Google Scholar
  48. Omran, A. M. and King, C. J., “Kinetics of ice crystallization in sugar solutions and fruit juices,” AIChE J. 20, 795–803 (1974).CrossRefGoogle Scholar
  49. Palwe, B. G., Chivate, M. R. and Tavare, N. S., “Growth kinetics of ammonium nitrate crystals in a draft tube baffled batch crystallizer,” Ind. Eng. Chem. Proc. Des. Dev. 24, 914–919 (1985).CrossRefGoogle Scholar
  50. Powell, M. J. D., “A method for minimizing a sum of squares of non-linear functions without calculating derivatives,” Computer J. 8, 303–307 (1965).CrossRefGoogle Scholar
  51. Prakash, R., Prakash, O. and Tavare, N. S., “Orthorhombic structure: a necessity in superconducting 1-2-3 compounds,” Pramana-J. Phys. 30, L597–L600 (1988).CrossRefGoogle Scholar
  52. Qiu, Y. and Rasmuson, A. C., “Nucleation and growth of succinic acid in a batch cooling crystallizer,” AIChE J. 36, 665–676 (1990a).CrossRefGoogle Scholar
  53. Qiu, Y. and Rasmuson, A. C, “Crystal growth rate parameters from isothermal desupersaturation experiments,” Chem. Eng. Sci. 46, 1659–1667 (1990b).Google Scholar
  54. Randolph, A. D. and Larson, M. A., Theory of Particulate Processes, Academic Press, New York (1971).Google Scholar
  55. Randolph, A. D. and Rajagopal, K., “Direct measurement of crystal nucleation and growth rate kinetics in a backmixed crystal slurry: Study of the K2SO4 system.,” Ind. Eng. Chem. Fundam. 9, 165–171 (1970).CrossRefGoogle Scholar
  56. Randolph, A. D. and Cise, M. D., “Nucleation kinetics of the potassium sulphate-water system,” AIChE J. 18, 798–807 (1972).CrossRefGoogle Scholar
  57. Randolph, A. D. and Sikdar, S. K., “Effect of a soft impeller coating on the net formation of secondary nuclei,” AIChE J. 20, 410–412 (1974).CrossRefGoogle Scholar
  58. Randolph, A. D. and Sikdar, S. K., “Creation and survival of secondary crystal nuclei: the potassium sulfate-water system,” Ind. Eng. Chem. Fundam. 15, 64–71 (1976).CrossRefGoogle Scholar
  59. Rawlings, J. R., Miller, S. M. and Witkowski, W. R., “Model identification and control of solution crystallization processes: A review,” Ind. Eng. Chem. Res. 32, 1275–1296 (1993).CrossRefGoogle Scholar
  60. Rosen, H. N. and Hulburt, H. M., “Continuous vacuum crystallization of potassium sulfate,” Chem. Eng. Prog. SympSer. No. 110 67, 18–26 (1971).Google Scholar
  61. Rumford, F. and Bain, J., “The controlled crystallization of sodium chloride,” Trans. Inst. Chem. Eng. 38, 10–20 (1960).Google Scholar
  62. Seinfeld, J. H., “Identification of parameters in partial differential equations,” Chem. Eng. Sci. 24, 65–74(1969).CrossRefGoogle Scholar
  63. Seinfeld, J. H. and Chan, W. H., “Estimation of parameters in partial differential equations,” Chem. Eng. Sci. 26, 753–766 (1971).CrossRefGoogle Scholar
  64. Seinfeld, J. H. and Gavalas, G. R., “Analysis of kinetic parameters from batch and integral experiments,” AIChE J. 16, 644–647 (1970).CrossRefGoogle Scholar
  65. Seinfeld, J. H. and Lapidus, L., Mathematical Methods in Chemical Engineering, Prentice Hall, Englewood Cliffs, New Jersey (1974).Google Scholar
  66. Shi, Y, Liang, B. and Hartel, R. W., “Crystallization of ice from aqueous solutions in suspension,” in Myerson, A. S. and Toyokura, K. (Eds.), Crystallization as a Separation Process, ACS Symp. Sen No. 438, American Chemical Society, Washington, D.C., 316–328 (1990).CrossRefGoogle Scholar
  67. Shirai, Y, Nakanishi, K., Matsuno, R. and Kamikubo, T., “On the kinetics of ice crystallization in batch crystallizers,”AIChE J. 31, 676–682 (1985).CrossRefGoogle Scholar
  68. Sowul, L. and Epstein, M. A. F., “Crystallization kinetics of sucrose in a CMSMPR evaporative crystallizer,” Ind. Eng. Chem. Proc. Des. Dev. 20, 197–203 (1981).CrossRefGoogle Scholar
  69. Stocking, J. H. and King, C. J., “Secondary nucleation of ice in sugar solutions and fruit juices,” AIChE J. 22, 131–140(1976).CrossRefGoogle Scholar
  70. Tavare, N. S., “Growth kinetics of ammonium sulphate in a batch cooling crystallizer using initial derivatives,” AIChE J. 31, 1733–1735 (1985).CrossRefGoogle Scholar
  71. Tavare, N. S., “Crystallization kinetics from transients of an MSMPR crystallizer,” Can J. Chem. Eng. 64, 752–758 (1986).CrossRefGoogle Scholar
  72. Tavare, N. S., “Batch crystallizers: A review,” Chem. Eng. Commun. 61, 259–318 (1987).CrossRefGoogle Scholar
  73. Tavare, N. S., “Comments on ‘The probability distribution of growth rates of anhydrous sodium sulphate,’” Ind. Eng. Chem. Res. 30, 803–804 (1991).CrossRefGoogle Scholar
  74. Tavare, N. S. and Chivate, M. R., “Growth and dissolution kinetics of potassium sulphate crystals in a fluidized bed crystallizer,” Trans. Inst. Chem. Eng. 57, 35–42 (1979).Google Scholar
  75. Tavare, N. S. and Garside, J., “Estimation of crystal growth and dispersion parameters using pulse response techniques in batch crystallizers,” Trans. Inst. Chem. Eng. 60, 334–344 (1982).Google Scholar
  76. Timm, D. C. and Larson, M. A., “Effects of nucleation kinetics on the dynamic behaviour of a continuous crystallizer,” AIChEJ. 14, 452–457 (1968).CrossRefGoogle Scholar
  77. Toyokura, K., Yamazoe, K., Magri, J., Yago, N. and Ayoma, Y., “Secondary nucleation of potash alum” In Mullin, J. W. (Ed.), Industrial Crystallization, Plenum Press, New York, 41–49 (1976).CrossRefGoogle Scholar
  78. Toyokura, K., Uchiyama M., Kawai M., Akutsu, H. and Ueno, T., “Secondary nucleation of KA1(SO4)2 12H2O, MgSO4 7H2O and CuSO4 5H2O,” in Jancic, S. J. and de Jong, E. J.(Eds.), Industrial Crystallization, North-Holland, Amsterdam, 87–96 (1982).Google Scholar
  79. Verigin, A. N., Shuhuplyak, I. A., Mikhalev, M. F. and Kulikov, V. N., “Investigation of crystallization kinetics with programmed variation of the solution temperature,” J. Appl.Chem. USSR 52, 1801–1803 (1980).Google Scholar
  80. Wang, B. C. and Luss, R., “Increasing the size of region of convergence for parameter estimation through the use of shorter data length,” Int. J. Control 31, 947–972 (1980).CrossRefGoogle Scholar
  81. Wey, J. S. and Estrin, J., “Modelling the batch crystallization process. The ice-brine system,” Ind. Eng. Chem. Process Des. Dev. 12, 236–246 (1973).CrossRefGoogle Scholar
  82. Wey, J. S. and Terwilliger, J. P., “Letter to the Editor: Comments on Lee’s communication, (AIChE J. 24, 535–537 (1978)),”CrossRefGoogle Scholar
  83. Wey, J. S. and Terwilliger, J. P., “Letter to the Editor: Comments on Lee’s communication, AIChE J. 25, 208 (1979).CrossRefGoogle Scholar
  84. Will, E. J., Bijvolet, O. L. M., Blomen, L. J. M. J. and Linden, H. V. D., “Growth kinetics of calcium oxalate monohydrate: I: Method and validation,” J. Crystal Growth 64,297–305 (1983a).CrossRefGoogle Scholar
  85. Will, E. J., Bijvolet, O. L. M., Blomen, L. J. M. J. and Linden, H. V. D., “Growth kinetics of calcium oxalate monohydrate: II: variation of seed concentration.” J. Crystal Growth 64, 306–315 (1983b).CrossRefGoogle Scholar
  86. Will, E. J., Bijvolet, O. L. M., Blomen, L. J. M. J. and Linden, H. V. D., “Growth kinetics of calcium oxalate monohydrate: III: Variation of solution composition,” J. Crystal Growth 64, 316–325 (1983c).CrossRefGoogle Scholar
  87. Witkowski, W. R., Miller, S. M. and Rawlings, J. B., “Light scattering measurements to estimate kinetic parameters of crystallization,” in Myerson, A. S. and Toyokura, K. (Eds.), Crystallization as a Separation Process, ACS Symp. Ser. No.438, American Chemical Society, Washington, D.C., 102–114(1990).CrossRefGoogle Scholar
  88. Xugen, V. T. and Svrcek, W. Y, “On equivalence of the Gauss-Newton techniques, the parameter influence coefficient technique and the quasilinearization technique in dynamic system identification by least squares,” J. Optimization Theory Applic. 22, 117–123 (1977).CrossRefGoogle Scholar
  89. Youngquist, G. R. and Randolph, A. D., “Secondary nucleation in a class II system, ammonium sulfate-water,”, AIChE J. 18, 421–429 (1972).CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 1995

Authors and Affiliations

  • Narayan S. Tavare
    • 1
  1. 1.University of Manchester Institute of Science and Technology (UMIST)ManchesterUK

Personalised recommendations