Population balance models (PBMs) are well-established modeling techniques that capture the highly nonlinear nature of crystallization kinetics. Numerous studies have demonstrated that the successful implementation of PBMs can facilitate process intensification and enable the precise development of recipes that consider multiple critical quality attributes. However, effectively integrating PBMs into crystallization process development necessitates addressing several key aspects: selecting an appropriate model structure that accurately represents the crystallization mechanisms, refining model parameters to reduce uncertainty, and accounting for non-ideal mixing effects during mathematical model development [2,3]. While considerable research has focused on model discrimination, parameter precision improvement, and enhancing computational efficiency in solving PBMs using in-silico or lab-scale experimental data, the influence of mixing effects on population balance modeling remains largely unexplored. This gap is primarily due to the computational costs associated with coupling Computational Fluid Dynamics (CFD) with PBMs in crystallization processes, as well as the scarcity of data from pilot plant operations.
Mixing plays a crucial role in crystallization processes, directly influencing factors such as supersaturation—the driving force behind most crystallization mechanisms—and energy dissipation due to stirring, which can induce particle breakage or secondary nucleation [4-6]. CFD modeling offers a simplified approach to simulate mixing by dividing the system into interconnected, well-mixed compartments, each represented by ordinary differential equations. This method captures essential mixing dynamics without the computational intensity of full-scale CFD simulations. When integrated with PBMs, which describe the distribution and evolution of particle sizes, compartmental CFD models enhance the accuracy of scale-up designs in crystallization. By providing detailed insights into local mixing effects, they enable more precise predictions of crystal size distributions and process outcomes, facilitating the development of efficient and scalable crystallization processes [7].
In this study, we present an industrial case of cooling-antisolvent crystallization utilizing compartmental-population balance modeling for scale-up design. Various lab-scale experiments were conducted based on different decision variables—such as seed loading, antisolvent addition rate, and cooling rate—to provide experimental inputs for model training. Multiple model candidates were evaluated using various statistical criteria, and additional experiments were performed to reduce the uncertainty of the optimal model. Subsequently, mixing-related parameters were incorporated and estimated by training the model with experimental data from different scales, following a systematic mathematical modeling workflow for scale-up. Finally, validation experiments were conducted to demonstrate the benefits of digital design in crystallization process development.
Reference:
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[5] Raponi, A.; Romano, S.; Battaglia, G.; Buffo, A.; Vanni, M.; Cipollina, A.; Marchisio, D. "Computational Modeling of Magnesium Hydroxide Precipitation and Kinetics Parameters Identification." Cryst Growth Des 2023, 23 (7), 4748–4759.
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