Modeling of Nucleation and Growth Kinetics for Unseeded Batch Cooling Crystallization

Both primary and secondary nucleation rates are considered in a model developed for unseeded batch crystallization. A carefully designed strategy was employed to minimize the effects of the stochastic nature of induction time; nucleation was induced at designed supersaturations on known temperature plateaus. Crystallization kinetics of paracetamol from ethanolic solutions were extracted from measurements of in situ solute concentrations and combined with sieve (ex situ) data on the final product. Parameters in models for primary and secondary nucleation and for crystal growth rate were estimated by fitting a full population balance model to the measurements, and the evolution of the crystal size distribution was compared against in situ estimation from focused-beam reflectance measurements using the technique that we previously developed. The resulting models suggest that primary nucleation produces fewer surviving crystals than had been expected and that most of the product crystals from the process involving a temperature plateau result from secondary nucleation.