(45d) Optimization and Control of Growth Modifier Concentration Profile for Achieving Target Crystal Shape Distribution

The crystal product quality, functionality and properties such as flow characteristics are greatly influenced by the crystal shape distribution. In order to obtain desired crystal shape, growth modifiers (GMs) are often used as additives [1]. The objective of this work is to determine the optimal concentration profile of the GMs that is required for the desired crystal shape distribution and subsequently use a simple control configuration for achieving the target crystal shape distribution. The optimal profile is achieved by formulating and solving an optimization problem. The formulation of the problem involves description of crystal shape distribution using multidimensional population balance model (PBM) in combination with Kubota-Mullin’s model for the pinning mechanism of GM molecules on crystal face to take into account the possible hindering or promoting effect of GM on crystal growth [2,3].  The Kubota-Mullin’s model uses surface coverage of the adsorbed species on the growing crystal and a proportionality constant denoting the effectiveness of the adsorbed species [2]. Finally, a simple feedback PI control configuration is implemented which manipulates the GM concentration profile in the crystallizer [4]. With this control implementation, it is demonstrated that the desired crystal shape distribution can be achieved.

References

[1] M.  A. Lovette, A. R. Browning, D. W. Griffin, J. P. Sizemore, R. C. Snyder and M. F. Doherty. Crystal Shape Engineering. Ind. Eng. Chem. Res., 47:9812-9833, 2008.

[2] N. Kubota. Effect of Impurities on the Growth Kinetics of Crystals. Cryst. Res. Technol., 36:749-769, 2001.

[3] F. Fevotte and G. Fevotte. A method of characteristics for solving population balance equations (PBE) describing the adsorption of impurities during crystallization processes. Chem. Eng. Sci., 65(10):3191-3198, 2010.

[4] D. B. Patience and J. B. Rawlings. Particle-Shape Monitoring and Control in Crystallization Processes. AIChE J., 47(9):2125:2129, 200