Mathematical design of continuous, isothermal crystallizers with homogeneous nucleation: a simplified approach

A simplified, systematic approach to the mathematical simulation of crystallizers is attempted by using the fundamental principles of mass conservation, via a population balance to the solid phase and a solute balance to both solid and liquid phases. A continuous, isothermal and isochoric crystallizer is assumed to be described by the MSMPR model under transient operating conditions with complete micromixing. The birth and death functions are assumed nil. Homogeneous nucleation is considered at a rate which is independent of the solution supersaturation. The growth rate of the crystals is described by McCabe's law. The possibility of solving the population balance and the mass balance independently is explored, and the conditions of validity for such an approach are found. The maximum linear dimension of crystal and the liquor concentration profile as functions of time are obtained. The approximation is found to be generally good for a period of time right after start-up of the crystallizer. A much wider range of time ensuring a satisfactory approximation is possible provided that the system and operation-dependent parameter takes small values.