Kinetics in batch crystallization of lactose: Parameter estimation using a population balance model and process analytical technology

Batch crystallization is a critical step in the production of lactose, a key component in pharmaceutical formulations and food products. This study presents a comprehensive investigation into the kinetics of lactose crystallization, employing population balance modeling to simulate the time-dependent evolution of the crystal population during batch cooling crystallization. Experimental data for parameter estimation were obtained using process analytical technology (PAT). The model incorporates mutarotation, growth, secondary nucleation, and agglomeration kinetics, with parameters estimated from experimental observations. An adapted secondary nucleation model, based on the work of Agrawal et al. (2017) , which accounts for collision frequencies between particles, in combination with a size-independent agglomeration efficiency model, yielded the best agreement between simulation and experiment. Significant improvements in predictive accuracy were achieved through the implementation of a novel model extension: tracking the area density distribution alongside the traditional number density distribution. This addition ensures conservation of the surface area of primary crystals during agglomeration events, leading to higher predicted volumetric growth rates and a more accurate depletion profile of lactose in solution compared to the conventional 1D population balance model (PBM). The proposed model offers a useful tool for evaluating the influence of process parameters on product yield and particle size distribution, supporting improved design and control of the lactose crystallization process.