(385e) Sparse Data-Driven Modeling of Crystallization Processes

Solution crystallization is an important unit operation in the fine chemicals, food, agrochemical, and pharmaceutical industries for the production of high added-value products in crystalline form.^1,2 Crystallization processes are commonly described by population balance models. The population balance model is an integro-partial differential equation describing the dynamic development of crystal quality attributes such as the size distribution by accounting for crystallization kinetics, including nucleation, growth, agglomeration, and breakage. The population balance model can enable improved process design, a systematic evaluation of process alternatives, and the development of model-based control strategies³ which are better capable of coping with process disturbances and input-output constraints compared to model-free strategies. However, the development of population balance models for industrial crystallizers is challenging due to the high sensitivity of crystallization kinetics on supersaturation and mixing. Additionally, the functional forms of the kinetic expressions for the various crystallization mechanisms being modelled are often unknown and are generally chosen based on trial-and-error.

High quality real time crystallization data are now readily available in industry due to recent advancements in process analytical technology (PAT) tools.⁴ Such high quality data can be used to develop mathematical models for crystallization processes. Data-driven methods such as symbolic regression based on evolutionary computations^5,6, physics informed neural networks (PINN)⁷, and the sparse identification of nonlinear dynamics (SINDy)⁸ methodologies can lead to the discovery of first-principle models from data and thus overcome some of the challenges encountered in developing interpretable first-principle models. The SINDy approach identifies models by leveraging the inherent sparsity available in most physical systems of interest without performing a combinatorial brute-force search which can be computationally intractable.⁸ Despite the promising potential of the SINDy approach, its application to modelling crystallization processes has not been characterized yet.

The objective of this work is to characterize the performance of the sparse data-driven methodology, SINDy, for modelling crystallization processes. Three case studies with increasing complexities are presented. As a benchmark, the SINDy approach is first characterized for the identification of crystallization kinetics in a mixed-suspension mixed-product-removal crystallizer using in silico data followed by the identification of crystallization kinetics from experimental data obtained from seeded protein crystallization and the cooling crystallization of paracetamol in batch. Considerable agreements are obtained between the data-driven model and the experiments. The SINDy approach holds promise for developing model-based control strategies for crystallization processes due to the relatively low computational cost associated with identifying crystallization models.

References

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