Investigation of dynamic processes in cooling crystallizer in case of needle-shape crystal production
Keywords:
cooling crystallization, needle-like crystals, bi-dimensional population balance model, moment method, simulationAbstract
A mathematical model is presented for investigating the dynamics of continuous cooling crystallizers, developing a bi-dimensional population balance model. The mixed set of ordinary and partial differential equations of the population balance model is solved by applying the moment method and developing computer programs in MATLAB environment. The marginal population density functions are approximated by means of the gamma distribution using the steady state marginal moments. Numerical experiments involve a detailed study of interactions of the cooling profile and the crystallization kinetics, as well as investigation of transients being important in control, and the oscillations arising in those. Application of the bi-dimensional population balance model allows studying crystallization processes producing either needle- or plate-like habit crystalline products.
References
Blickle, T., Lakatos, B., Mihálykó, Cs. (2001): Szemcsés rendszerek matematikai modelljei. A kémia újabb eredményei-89. Akadémiai Kiadó, Budapest. 173–348. p.
Borsos, Á. (2009): Hűtéses kristályosítók modellezése és optimalizálása. Diplomadolgozat. Pannon Egyetem, Veszprém.
Lakatos, B. G. (2007): Population balance modelling of crystallisation processes. Hung. J. Ind. Chem., 35. 7–17.
Lakatos, B. G., Mihálykó, Cs., Blickle, T. (2006), Modelling of interactive populations of disperse systems. Chem. Eng. Sci., 61(1), 54–62. https://doi.org/10.1016/j.ces.2005.01.045
Ma, C. Y., Wang, X. Z., Roberts, K. J. (2007): Multi-dimensional population balance modelling of the growth of rod-like L-glutamic acid crystals using growth rates estimated from in-process imaging. Advanced Powder Technology, 18(6), 707–723. https://doi.org/10.1163/156855207782514932
Ma, D. L., Tafti, D. K., Bratz, R. D. (2002): High-resolution simulation of multidimensional crystal growth. Ind. Eng. Chem. Res., 41(25), 6217–6223. https://doi.org/10.1021/ie010680u
Puel, F., Févotte, G., Klein, J. P. (2003a): Simulation and analysis of industrial crystallization process through multidimensional population balance. Part 1: a resolution algorithm based on the method of classes. Chem. Eng. Sci., 58(16), 3715–3727. https://doi.org/10.1016/S0009-2509(03)00254-9
Puel, F., Févotte, G., Klein, J. P. (2003b): Simulation and analysis of industrial crystallization process through multidimensional population balance equations. Part 2: a study of semi-batch crystallization. Chem. Eng. Sci., 58(16), 3729–3740. https://doi.org/10.1016/S0009-2509(03)00253-7
Ramkrishna, D. (2000): Population Balances, Theory and Applications to Particulate Systems in Engineering. Academic Press, San Diego.
Randolph, A. D., Larson, M. A. (1988): Theory of Particulate Processes. Academic Press, New York. https://doi.org/10.1016/B978-0-12-579652-1.50007-7
Tavare, N. S., (1995): Industrial Crystallization. Process Simulation, Analysis and Design. Plenum Press, New York.
Ulbert, Zs. (2002): Kristályosítók dinamikus folyamatainak modellezése és szimulációja. Phd dolgozat, Veszprémi Egyetem, Veszprém.
Ulbert, Zs., Lakatos, G. B. (2007): Dynamic simulation of crystallization processes: Adaptive finite element collocation method. AIChE Journal, 53(12), 3089–3107. https://doi.org/10.1002/aic.11303
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Copyright (c) 2011 Borsos Ákos, Lakatos G. Béla
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