(516a) Optimal Control of Crystal Shape and Nucleation in Crystallization Processes

Multiple-objective optimization problems of system with two internal coordinates in seeded batch crystallization are solved nearly analytically by adapting a framework developed by Bajcinca (Bajcinca, 2011; Bajcinca, 2013), which combines method of moments and method of characteristics to quantify the seed-grown and nucleus-grown crystals before applying optimal control theory. Objective functions considered in this work includes crystal shape, nucleated number, and nucleated volume.

A case study based on crystallization of dihydrogen potassium phosphate with water as solvent (Ma et al. 2002) is used to analyze the similarities and differences between control strategies for single- and two-dimensional crystallization systems. It is found that the achievable interval of product aspect ratio is not broad if only one growth stage (growth and dissolution cycling is disallowed) is applied, which is consistent with previous findings (Bötschi et al., 2018). From the point of view of inhibiting nucleation, there is an optimal product aspect ratio if either nucleated number or nucleated volume is set to be the single objective. The results also show that there is significant trade-off between nucleated number and volume by plotting the Pareto-optimal fronts with product aspect ratio as a constraint, which is consistent with results for single-dimensional crystallization systems (Tseng et al., 2019). The trade-off is particularly strong when the target product aspect ratio is near the midpoint of the feasible interval. Another finding in this work is that, unlike the single dimensional case (Hofmann and Raisch, 2010) the batch time constraint is not always active when value of aspect ratio constraint is large or in the middle of each Pareto-optimal front since a larger growth rate is required to meet the aspect ratio requirement.

This work provides understanding about the relationship between product aspect ratio, minimal nucleated number and nucleated volume with corresponding optimal control strategy, which enables engineers to have insight into the optimal operating policy for multi-dimensional crystallization systems.

References

Bötschi, S.; Rajagopalan, A. K.; Morari, M.; Mazzotti, M., Feedback Control for the Size and Shape Evolution of Needle-like Crystals in Suspension. I. Concepts and Simulation Studies. Crystal Growth & Design 2018, 18 (8), 4470-4483.

Bajcinca, N.; de Oliveira, V.; Borchert, C.; Raisch, J.; Sundmacher, K., Optimal control solutions for crystal shape manipulation. In Computer Aided Chemical Engineering, Pierucci, S.; Ferraris, G. B., Eds. Elsevier: 2010; Vol. 28, pp 751-756.

Bajcinca, N., Analytic solutions to optimal control problems in crystal growth processes. Journal of Process Control 2013, 23 (2), 224-241.

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

Tseng, Y.-T.; Pan, H.-J.; Ward, J. D., Pareto-optimal fronts for simple crystallization systems using Pontryagin’s minimum principle. Industrial & Engineering Chemistry Research 2019, 58 (31), 14239-14251.

Hofmann, S.; Raisch, J. In Application of optimal control theory to a batch crystallizer using orbital flatness, 16th Nordic Process Control Workshop, Lund, Sweden, 2010; pp 25-27.