A combined D-optimal and estimability model-based design of experiments of a batch cooling crystallization process

In this work, a systematic methodology is proposed to help develop model-based design of experiments to build robust and reliable mathematical model of a batch crystallization process. The cooling crystallization of paracetamol in water and propanol is used as the case study. The mathematical model consists in the mass balance and a set of population balance equations, involving primary and secondary nucleation, growth, agglomeration, breakage and dissolution kinetics. Firstly, a structural identifiability approach is used to investigate whether the model parameters can be determined uniquely with an idealized input-output behavior of the process. The approach is also critical to determine the minimum set of required observable outputs and help discriminate model candidates. A novel Model-Based Design of Experiments (MBDoE) is then proposed based on the combination of the D-optimality criterion and the estimability analysis. The objective is to reduce the uncertainties in the model parameters by enhancing the data information content and help maximize the estimability potential of all model parameters while reducing correlation amongst them. Moreover, a new operating strategy based on temperature cycling is used in a sequential design of experiment to maximize data information content from one single experiment while reducing the experimental burden and inherent wastes.