Crystallization from solutions and melts pp 50-58 | Cite as

# Design Models for Continuous Crystallizers with Double Drawoff

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*.

## Preview

Unable to display preview. Download preview PDF.

## Literature Cited

- 1.Hulburt, H. M., and T. Akiyama,
*Am. Chem. Soc. Chem. Eng. Symposium*, Boston, Mass. (1967).Google Scholar - 2.
- 3.
- 4.Randolph, A. D.,
*ibid.*, 424.Google Scholar - 5.
- 6.
- 7.

## Copyright information

© Springer Science+Business Media New York 1969