Local Vs Global Estimability Analysis Of Population Balance Models For Crystallization Processes

Estimability and sensitivity analysis has been applied to a one-dimensional population balance model (PBM) that describes the dynamic evolution of the critical quality attributes (CQAs) for a batch cooling crystallization process in order to assess the estimability potential of the identified parameters. Hybrid non-convex optimization model-based approaches have been utilized for the identification of the crystallization kinetics. The results were validated by using experimental online and offline process analytical tools (PAT) for the determination of the evolution of mean crystal size and the solution concentration. Then the optimum subset of parameters was determined based on two different approaches: (1) a sequential orthogonalization of the sensitivity matrix and (2) a variance-based global sensitivity analysis approach. The estimability analysis revealed that due to the low information content of the data and correlation between the parameters, only 4 parameters out of 13 are identifiable, ascertaining that the model is over-parameterized. By applying this methodology the most influential and least correlated parameters could be identified more reliably, providing enhanced prediction capabilities of the overall dynamics of the studied crystallization process.