Application of a 2-D Population Balance Model to a Pharmaceutical Crystallization Process

Population balance models (PBMs) have acquired increased popularity in the modeling of pharmaceutical crystallization processes. In this study, we develop and evaluate a two dimensional PBM as a tool to predict the crystal habit and the crystal size distribution obtained in the cooling crystallization of an active pharmaceutical ingredient. The crystallization system was found to exhibit minimal agglomeration, and a PBM with growth and secondary nucleation parameters was found to be an adequate descriptor for the system. Laboratory and plant (50 L scale) data was used to fit the model parameters and evaluate the model predictions. Two distinct crystal planes with independent secondary nucleation and growth properties were used to describe the evolution and distribution of the crystal properties. The model successfully captures the transition from rod-like particles with high aspect ratio to prisms-like structures. Also discussed are the strategies to model situations in which the seed acts as a source of heterogeneous nucleation.