(633b) Multi-Objective Optimization of Simple Crystallization Systems

Multiple-objective optimization problems in seeded batch crystallization are solved for two chemical systems using the method of moments and a transformation proposed by Raisch and coworkers (Vollmer and Raisch, 2003; Vollmer and Raisch, 2006; Hofmann and Raisch, 2010). Six sets of two objective functions are considered: The nucleated mass and the number of nuclei; the crystal number mean size and the nucleated mass; the weight mean coefficient of variation and the weight mean size; the number mean coefficient of variation and the number of nuclei; the batch time and the nucleated mass; and the batch time and the number mean size.

The results show that if one objective is based on higher moments of the nucleated crystals (e.g. the nucleated mass) while the other is based on lower moments (e.g. the number of nuclei or the number mean size of the crystals), the Pareto-optimal front is relatively wide, indicating significant competition between the two objectives. This finding is consistent with the conclusion in previous work (Ma et al., 2002; Ward et al. 2006; Tseng and Ward, 2017). In these cases, a constant growth rate trajectory may represent a good trade-off between two objectives. By contrast, if both objectives are based on higher moments or both objectives are based on lower moments, the trade-off between the two objectives become less significant and the optimal trajectories for each single objective are similar.

This work identifies and quantifies an inherent trade-off that sometimes occurs between objective functions in batch crystallization process. Understanding this tradeoff and the circumstances under which it arises can help engineers to determine effective operating recipes for such processes. The results are illustrated with case studies based on crystallization of potassium nitrate (Miller and Rawlings, 1994) and Pentaerythritol (Bernardo and Giulietti, 2010).

References

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Ma, D. L., Tafti, D. K., Braatz, R. D., 2002. Optimal control and simulation of multidimensional crystallization processes. Computers & Chemical Engineering 26 (7-8), 1103-1116.

Miller, S. M., Rawlings, J. B. (1994). Model identification and control strategies for batch cooling crystallizers. AIChE Journal, 40, 1312–1327.

Tseng, Y. T., Ward, J. D. (2017). Comparison of objective functions for batch crystallization using a simple process model and Pontryagin's minimum principle. Computers & Chemical Engineering 99, 271-279.

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Ward, J. D., Mellichamp, D. A., Doherty, M. F. (2006). Choosing an operating policy for seeded batch crystallization. AIChE Journal 52, (6), 2046–2054.