Population Balance Models for Batch Crystallization

Abstract

The conservation equation for the mean number of crystals of size L to L + dL, n(L) dL, in a sample of a crystallizing suspension (or magma) is frequently called the “population balance.” As formulated by Randolph and Larson (6) and by Hulburt and Katz (3), for a batch crystallizer it takes the form $$\frac{{\partial n}} {{\partial t}} = \frac{\partial } {{\partial L}}(Gn) = B - D$$ (1) The linear growth rate, G, the nucleation rate, B, and the crystal loss rate, D, are all functions of the supersaturation and possibly crystal size, magma density, temperature and degree of agitation. The mother liquor concentration, C, (kg/m3 of clear liquor) is related to the magma density, W, (kg crystals/m3 suspension) through the volume fraction of crystals in the suspension, Vm, $${V_m} = W/{\rho _c}$$ (2) $${\rho _c}{V_m} = (1 - {V_m})C = {\rho _c}{V_{mo}} + (1 - {V_{mo}}){C_o} = const.$$ (3).