Comparison of One-Dimensional and Two-Dimensional Population Balance Models for Optimization of a Crystallization Process for a Needle-Shaped Active Pharmaceutical Ingredient

The two-dimensional population balance model (2D PBM) introduces the enhanced capability of modeling two different sets of growth kinetics, which can offer advantages to modeling crystallization processes that generate needle-like particles, a commonly encountered active pharmaceutical ingredient (API) morphology. Although one-dimensional population balance model (1D PBM) can be utilized effectively to model nonequant morphologies with the selection of appropriate shape factors, it cannot account for morphology or aspect ratio changes that can occur during the crystallization process. In this work, the advantage of the 2D PBM for an industrial crystallization process that generates needle-shaped API is highlighted by comparing the 1D PBM and 2D PBM results. The API utilized for this work had extremely slow desupersaturation and was not able to achieve solubility concentration despite an ∼50 h seed bed age. While the 1D PBM is useful in optimizing the crystallization process to enhance desupersaturation behavior, the 1D PBM did not match the particle size quantiles and, thus, could not be utilized to probe the impact of crystallization process parameters on the particle aspect ratio (AR). The 2D PBM was necessary to model the particle size quantiles and was utilized to further optimize process conditions for minimizing the particle aspect ratio. Simulations utilizing the 2D PBM indicated that, regardless of antisolvent addition rate or seed morphology, the final material would still have a high aspect ratio. This knowledge saved the investment of much time and effort in trying to minimize particle AR with changes in crystallization processing parameters alone and, thus, highlights the utility of the 2D PBM to the pharmaceutical industry.