Dimensionless Framework for Seed Recipe Design and Optimal Control of Batch Crystallization

Abstract

In order to study and propose guidelines for the design and control of batch crystallization systems with different growth and nucleation parameters, optimal control theory and a dimensionless batch crystallization model are applied to solve multi-objective optimization problems in a nearly analytical and computationally efficient way. Optimal growth rate trajectories and the corresponding critical seed recipes (seed loading ratio and seed mean size that make nucleated mass negligible) representing a suitable trade-off between two objective functions (number of nuclei and nucleated mass) are derived for 32 chemical systems. The results are also compared with results from applying supersaturation control, a strategy that can be implemented without a kinetic model. The analysis suggests that the benefit from applying an optimal growth rate trajectory is significant only when the sensitivity of nucleation rate to supersaturation is significantly greater than that of the growth rate. Furthermore, the width of the crystal size distribution has little effect on the critical seed recipe. The effect of the batch time on the critical seed loading ratio is also studied for individual systems. It is found that increasing batch time helps to reduce the seed loading requirement for systems in which the nucleation rate is highly sensitive to supersaturation.

Progress and Opportunities for Utilizing Seeding Techniques in Crystallization Processes

“…One method is to develop a specified production process that satisfies the GMP requirements and use this process to specifically produce the desired seed crystals. , Another solution is to develop new seeding strategies that can beneficially avoid or eliminate the need for GMP seed preparation. , With the improvement in product quality and regulatory requirements, it seems difficult to cope with the problems mentioned above using existing approaches. Without the sake of completeness, the following three topics can be used to categorize some progress that has been made in recent years and may be considered valuable directions toward improving existing seeding techniques or developing new technologies: The multiple-pass seeding technique is a potential alternative for improving the operating flexibility; this technique can be used to deploy seed recipes with different sizes and masses according to the optimized control strategies and then treats seeding as a processing variable with an adjustable degree of freedom (e.g., the dynamic seeding technique , ) for specified product-property control (e.g., CSD). New directions in the development of seeding strategies involve designing seed-loading modes, integrating external seeding techniques with auxiliary technologies (such as milling and gassing) and upstream or downstream operations, and mapping seed behavior by computational fluid dynamics (CFD) simulations to improve seeding effectiveness. New directions in the development of seeding-control approaches include the use of mechanistic, data-driven or hybrid modeling approaches, multiobjective optimization control techniques, and robust and intelligent control methodologies to improve the control level, robustness and intelligent management of the crystallization process. , …”

“…New directions in the development of seeding-control approaches include the use of mechanistic, data-driven or hybrid modeling approaches, multiobjective optimization control techniques, and robust and intelligent control methodologies to improve the control level, robustness and intelligent management of the crystallization process. , …”

“…• New directions in the development of seeding-control approaches include the use of mechanistic, data-driven or hybrid modeling approaches, multiobjective optimization control techniques, and robust and intelligent control methodologies to improve the control level, robustness and intelligent management of the crystallization process. 124,125 In addition, most industrial crystallizer designs lack effective actuators to meet the desired control objectives, e.g., producing a product with a defined CSD, and the effectiveness of existing implementation strategies is quite limited. 59,113 It is noteworthy that the improper use of process actuators can have harmful effects similar to those caused by intentional process disturbances.…”

Optimal Control of Batch Crystallization Processes with Primary Nucleation

“…Hofmann and Raisch further showed that nearly analytical solutions to certain optimization problems can be obtained by Pontryagin’s Minimum Principle (PMP) , if the feedback of nucleated crystal mass is neglected . Using this framework, several problems in optimization of seeded batch crystallization processes have been solved. − The method has been found to be very accurate and computationally efficient.…”

Membrane-Assisted Cooling Crystallization for Interfacial Nucleation Induction and Self-Seeding Control

“…Crystallization is an important separation and purification technology for the fine chemical manufacture, pharmaceutical engineering, and biochemical engineering. , Cooling crystallization, one of the most classic crystallization processes, is mostly controlled by adding seed crystals within the metastable zone to induce nucleation and obtain the solid product. − A successful seeding operation relies on a lot of aspects, namely, seed size and amount, time point and place of addition, experience of the operator, etc. Researchers are working to screen or generate seed crystals by using molecular sieves or additional physical fields, − or via optimizing the operation route. − In addition, nucleation and crystal growth kinetics in the crystallizer have a substantial impact on crystal product quality and have a fundamental role in the downstream processing.…”