(514d) Simulation of the Crystal Shape Distribution in the Presence of Growth Modifiers

Crystal shape and its distribution are of great interest due to the crucial role it plays in determining the quality of the final products and the efficiency of downstream processes.  Selected additives as growth modifiers (GMs) are often used in the industries to achieve the desired crystal shape distribution. Thus, prediction and control of crystal shape distribution are necessary for product design, quality control and economical operation point of view. Morphological population balance modelling (PBM) is widely used as a tool to describe the evolution of crystal shape distribution in a crystallizer [1,2,3]. Despite the fact that the effect of impurities (often called additives or growth/nucleation modifiers) on the crystal shape has been demonstrated in many experimental studies, most of the previous works related to the modelling of crystal shape distributions consider only the effect of operating conditions such as supersaturation, cooling profile and seed distribution  on the crystal shape distribution. Recently the effect of GMs has been incorporated in single dimensional PBM model, to explain the effect of GMs on the overall growth of particles and on the crystal size distribution (CSD) [4]. However, to the best of our knowledge, no work has been presented in the literature, which incorporates the effect of growth modifiers on the evolution of crystal shape distribution.

In this work, we present a modelling framework and simulation results that can be used to predict the  evolution of crystal shape distribution in a crystallizer in the presence of GM. The growth rate of the crystals depends not only on the concentration of the GM, but also the time during which the crystals are exposed to the GM in the mother liquor [5].  These two aspects have recently been incorporated in a mono-dimensional PBM proposed by Fevotte and Fevotte [4]. We further extend this model to a multi-dimensional PBM so that morphological PBM describing the evolution of crystal shape distribution can also be incorporated.

Following the model by Kubota and Mullin [6], the growth rate dependence on the GM concentration is described by surface coverage of the adsorbed species on the growing crystal and a proportionality constant denoting the effectiveness of the adsorbed species.  On the other hand, in order to track the contact time of the crystals with GM, the density function is redefined with an additional property that takes into account the exposure time of the crystals to impurity. It is assumed that the transient coverage process can be described by a first order dynamics. The resulting PBMs are simulated using commercially available software gCRYSTAL (Process Systems Enterprise, UK) for 1D problems. On the other hand, well-established high resolution finite volume technique is used for simulation of all the 1D and multidimensional problems [7]. This study would be very useful in understanding the effect of GM as well as in achieving tailored crystal shape distribution.

References

[1] C. Borchert, N. Nere, D. Ramkrishna, A. Voigt and K. Sundmacher. On the prediction of crystal shape distributions in a steady-state continuous crystallizer. Chem. Eng. Sci., 64(4): 686-696, 2009.

[2] G. Yang, N. Kubota, Z. Sha, M. Louhi-Kultanen and J. Wang. Crystal shape control by manipulating supersaturation in batch cooling crystallization. Cryst. Growth Des., 6(12):2799-2803, 2006.

[3] C. Y. Ma and X. Z. Wang. Model identification of crystal facet growth kinetics in morphological population balance modeling of l-glutamic acid crystallization and experimental validation. Chem. Eng. Sci., 70(0):22-30, 2012. 

[4] 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.

[5] N. Kubota. Effect of impurities on growth kinetics. Cryst. Res. Technol., 36(8-10):749-769, 2001.

[6] N. Kubota and J. W. Mullin. A kinetic model for crystal growth from aqueous solution in the presence of impurity. J. Crys. Grow., 152(3):203-208, 1995.

[7] R. Gunawn, I. Fusman and R. D. Braatz. High resolution algorithm for multidimensional population balance equations. AIChE J, 50:2738-2749, 2006.