Model for a Cascade Crystallizer in the Presence of Growth Rate Dispersion

A model is developed based on the population balance to relate the resulting crystal size distribution (CSD) from a cascade of mixed suspension, mixed product removal (MSMPR) crystallizers to the growth rate distributions of each stage. This model employs the constant crystal growth (CCG) model, in which it is assumed that an individual crystal has an inherent, constant growth rate, but different crystals might have different inherent growth rates. An explicit recursion formula between the first three moments of the resulting crystal size distribution and the first three moments of growth rate distributions of each stage is presented for a N-stage MSMPR crystallizer. A computer program has been developed to predict the CSD from a three-stage MSMPR crystallizer with continuous seeding into the first stage and growth in the subsequent stages. The model is solved simultaneously with the mass balance by using power law growth kinetics. The CSD in each stage is assumed as a gamma distribution to compute the mean crystal size, production rate, and coefficient of variance.