Statistical Analyses of a Population Balance Model of a Batch Crystallization Process

Crystallization is a widely employed separation technique that has received significant attention due to its industrial relevance, notably in the pharmaceutical industry. While numerous studies have described the underlying kinetic crystallization phenomena using population balance models, simplifying assumptions are usually considered, such as disregarding variable correlations without accounting for the statistical and numerical consequences. Therefore, this lack of detailed statistical analyses can compromise the reliability of at least some of these results. In this regard, the present work performs the statistical characterization of a potassium sulfate crystallization process with the help of population balance models. In order to do that, the model parameters were determined using reparameterization procedures and experimental data collected from multiple batches to mitigate the undesired effects of high correlation in measured variables, which characterize these experimental systems and respective model parameters. It is shown that the proposed approach can successfully represent the solute concentration, the zeroth-order moment, and the ratios between higher-order and zeroth-order moments, considering the available experimental data set. Particularly, the particle swarm optimization (PSO) method was applied for the characterization of the confidence regions of the parameter values. The obtained results indicate that the model-based quantitative analysis of crystallization models can significantly benefit from more statistical interpretation of parameter estimates and variable correlation effects.