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Design Models for Continuous Crystallizers with Double Drawoff

  • Hugh M. Hulburt
  • Denis G. Stefango
Chapter

Abstract

Models for the performance of continuous crystallizers have been proposed and examined by Saeman (6), Randolph and Larson (5), Murray and Larson (3), Randolph (4), and Sherwin, Shinnar, and Katz (7) and have been set in the context of the general population balance treatment by Hulburt and Katz (2). Let f(r, x; t) be the number of crystals of size r per unit volume of crystallizer per unit size at a given position x and moment t. The balance equation for f then reads
$$\frac{{\partial f}} {{\partial t}} + \frac{\partial } {{\partial x}}\left( {\dot xf} \right) + \frac{\partial } {{\partial r}}\left( {\dot rf} \right) = h\left( {r;x;t} \right)$$
(1)

The life history of a crystal is defined by its size r(t) and its location in the crystallizer x(t). It can be represented as a trajectory in x, r space, the phase space of the process. At some point (x 0, r 0) the crystal is born by nucleation or by injection from outside, and at some point (x 1, r 1) it leaves the crystallizer. In the absence of agglomeration, each crystal follows a continuous trajectory from (x 0, r 0) to (x 1, r x ). Then f(x, r; t) is the density of phase points about (x, r) at the moment t.

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Literature Cited

  1. 1.
    Hulburt, H. M., and T. Akiyama, Am. Chem. Soc. Chem. Eng. Symposium, Boston, Mass. (1967).Google Scholar
  2. 2.
    Hulburt, H. M., and S. Katz, Chem. Eng. Sci., 19, 555 (1964).CrossRefGoogle Scholar
  3. 3.
    Murray, D. C, and M. A. Larson, AlChE J., 11, 728 (1965).CrossRefGoogle Scholar
  4. 4.
    Randolph, A. D., ibid., 424.Google Scholar
  5. 5.
    Randolph, A. D., and M. A. Larson, ibid., 8, 639 (1962).Google Scholar
  6. 6.
    Saeman, W. C., ibid., 2, 107 (1956).Google Scholar
  7. 7.
    Sherwin, M. B., Reuel Shinnar, and Stanley Katz, ibid., 13, 1141 (1967).Google Scholar

Copyright information

© Springer Science+Business Media New York 1969

Authors and Affiliations

  • Hugh M. Hulburt
    • 1
  • Denis G. Stefango
    • 1
  1. 1.Northwestern UniversityEvanstonUSA

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