Design Models for Continuous Crystallizers with Double Drawoff

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)