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

## TL;DR

This paper uses advanced modeling to simulate and understand how cooling crystallization affects crystal size in pharmaceutical production.

## Contribution

A novel CFD-PBE coupling approach is applied to kilo-scale pharmaceutical crystallization for detailed process insights.

## Key findings

- Higher impeller speeds lead to smaller crystal sizes due to increased turbulence and supersaturation.
- Crystal size distribution varies significantly during early cooling stages but stabilizes later.
- Reliable kinetic data is crucial for accurate CFD-PBE predictions of crystal size distributions.

## Abstract

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.