(612d) Optimal Crystal Size Control Using a Continuous Plug Flow Crystallization Configuration with Recycle

This work focuses on mathematic modelling and control of a continuous plug flow crystallizer (PFC) and provides an optimal control strategy to produce crystals with desired size distributions. Mass, energy and population balance equations are presented to describe the spatio-temporal evolution of the entire crystallization processes. It is known that due to the short residence times, the PFC systems do not operate at equilibrium conditions. The yield of PFCs is usually less than the yield in the equivalent batch processes [1]. More precisely, in [1], it was shown that the extraction position and the recycling ratio can be used to enhance the yield and control the crystal size distribution. Therefore, in the present work, the recycle configuration is considered in the PFC systems.

Motivated by [2], the novel mathematica models were provided in [3]. Consequently, the jacket temperatures and the superficial velocity were studied and optimized to realize the control of the crystal size and shape distributions throughout PFC system.

Motivated by the above, in the present work, we are considering simultaneously the optimal design and control for the continuous PFC system to achieve the high yield, the low equipment costs and the desired crystal size distribution. In particular, the method of moment is applied to the population balance model to derive a reduced-order moment model. First, based on the steady-state models, design variables for the recycle-type PFC such as tubing lengths, the extraction position and jacket temperatures for each segment of the PFC are analyzed and optimized to minimize experimental equipment costs and maximize the yield, while ensuring the desired crystal sizes. Then, the dynamic mathematic models for crystal concentrations, PFC temperatures and crystal populations are involved. Given the designed PFC configuration, the jacket temperatures, the superficial velocity and the recycling ratio are investigated and optimized in order to minimize the squared deviation of the average crystal size from the set-points throughout the PFC.

[1] Cogoni, Giuseppi, B. P. de Souza, and Patrick J. Frawley. ``Particle Size Distribution and yield control in continuous Plug Flow Crystallizers with recycle." Chemical Engineering Science 138 (2015): 592-599.

[2] Liu, Jing J., Yang D. Hu, and Xue Z. Wang. ``Optimization and control of crystal shape and size in protein crystallization process." Computers & Chemical Engineering 57 (2013): 133-140.

[3] Kwon, Joseph Sang-Il, et al. ``Crystal shape and size control using a plug flow crystallization configuration." Chemical Engineering Science 119 (2014): 30-39.