Modeling Pharmaceutical Batch Cooling Crystallization Processes Using Computational Fluid Dynamics Coupled with a One-Dimensional Population Balance Model.

The batch cooling crystallization of the α polymorphic form of l-glutamic acid from aqueous solution in a kilo-scale 20 L pharmaceutical batch crystallizer is simulated using a multiphase computational fluid dynamics (CFD) model coupled with a one-dimensional population balance equation (PBE). The predicted three-dimensional spatial and temporal distributions of turbulent kinetic energy, supersaturation, nucleation rate, and solid volume fraction provide a high fidelity and very detailed insights into the interplay between crystallizer hydrodynamics and crystallization process kinetics and their resultant impact upon the resulting crystal size distributions (CSDs). Comparison of the CFD-PBE modeling results with published experimental data (Liang, 2002) demonstrates the model's predictive capability by reproducing the measured final CSDs with an acceptable degree of accuracy. An increase in impeller speed is found to increase both the measured and predicted CSD curves shift toward smaller particles sizes. In terms of the spatial variations of process parameters, the evolution of CSD during the crystallization process reveals significant variation of the evolving CSD at the early stages (between 45 and 40 °C) of the crystallization process, which is relatively invariant in the later stages (between 30 and 20 °C), consistent with the reduction of solution supersaturation within the batch process. The simulation results under different agitation rates reveal that at the higher rates, smaller crystals are produced due to a greater level of turbulence and higher supersaturation at an early stage of the process. Detailed sensitivity analysis on the effect of crystallization kinetics on the predicted CSD emphasizes the need for using reliable kinetic data relevant to the crystallization conditions being simulated.