Design Models for Continuous Crystallizers with Double Drawoff

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.

A particle balance model is developed for a well-stirred continuous crystallizer with two discharge streams, one containing only fines and mother liquor and one containing the average contents of the crystallizer. Steady state equations for the operation of such a system are developed and examined for conditions leading to cyclic variation of crystal size. Computational procedures are used which can be extended to more detailed and more realistic models.

Denis G. Stefango is with the Horson Process Division, Chicago Bridge and Iron Company, Chicago, Illinois.