Antisolvent Crystallization of carbamazepine dihydrate: comparing constant growth rate, size-dependent growth, and growth rate dispersion models

Various models have been proposed to describe the kinetics of the processes involved in the continuous crystallization of pharmaceutical solutes. In many of these models, the growth rate of crystals (m/s) is assumed to be independent of the size of the crystals. While this assumption leads to reasonable correspondence between the simulated and experimental mean particle size and solute concentration at steady state, it fails to capture the spread of the particle size distribution (PSD) accurately, especially the tail toward the lower particle sizes. Two types of models, namely, dispersion of growth rate and size dependent growth rate, have been proposed for improving the accuracy in predicting PSD. In this work, we evaluated some of these variable growth rate models for simulating the continuous antisolvent crystallization of irregularly shaped carbamazepine dihydrate (CBZ-DH) crystals. The variable growth rate models (dispersion as well as size dependent growth) are implemented in a general-purpose population balance model (PBM) based on a tank-in-series framework. The PBM was used to simulate recently published experimental data from continuous antisolvent crystallization of CBZ-DH. Sensitivity analysis with respect to key parameters was carried out. Based on the comparison of the simulated and experimental results, specific recommendations on selecting a variable growth model have been made. The presented approach, model, and results will be useful for enhancing the fidelity of models of continuous crystallizers.