Maximizing similarity: Using correlation coefficients to calibrate kinetic parameters in population balance models

Crystallization plays a crucial role as a separation and purification technique, particularly in the chemical and pharmaceutical industries. By adjusting process parameters, the productivity, product quality, and efficiency of downstream processes can be improved. In complex processes, model-based design becomes invaluable. Population Balance Models (PBMs) have successfully aided the chemical industry in achieving more effective production processes for decades. These models can utilize various input data sources to identify the dominant mechanisms and calibrate model parameters. While inline particle monitoring tools serve as excellent qualitative descriptors, challenges arise from experimentation and data interpretation, hindering their direct application in the kinetic parameter estimation of PBMs. In this study, we present a novel approach that utilizes information from inline particle monitoring tools for the kinetic parameter estimation of PBMs, bypassing the associated obstacles. Our pioneering approach relies on offline product size data and the correlation-based utilization of inline particle monitoring information. The paper compares this novel strategy with two parameter estimation techniques: the classical method using solute concentration and product size data and a somewhat naïve approach, which assumes that the inline particle monitoring data can directly be compared with the simulations. The prediction capabilities are evaluated through two in-silico case studies. The results indicate that the precision and predictive capability of the correlation-based technique are comparable to the classical approach, both for noisy data and for a system undergoing significant agglomeration and deagglomeration. The use of Pearson's correlation coefficient yields the best results in the novel cases. These findings in in-silico datasets provide a foundation and motivation for the practical application of this idea, unleashing the so-far hidden model development potential of such measurements.