Simultaneous preferential crystallization in a coupled, batch operation mode—Part I: Theoretical analysis and optimization (original) (raw)
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AIChE Journal, 2017
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A simplified approach to the operation of a batch crystallizer
Canadian Journal of Chemical Engineering, 1990
A general model for a seeded cooling batch crystallizer based on first principles is developed, incorporating either size-dependent or size-independent growth rates. A simple approach is proposed to obtain temperature-time trajectories at constant supersaturation or nucleation rate, without resorting to optimization techniques. Cooling curves at constant supersaturation, which lead to a substantial improvement (a smaller coefficient of variation and a larger mean size) of the terminal crystal size distribution, can be determined even in the absence of precise nucleation and growth kinetics, whereas properties related to the crystal size distribution are sensitive to such kinetics. Experimental results for the potassium sulfate-water system, potash alum-water system, and hexamethylenetetramine in ethanol, methanol, and 2-propanol/water are predicted reasonably well by the model. Extension to any type of batch crystallization with super-saturation induced by means other than cooling, such as reactive precipitation and salting out, is briefly discussed.On a mis au point un modèle général pour un cristalliseur discontinu inoculé à refroidissement basé sur les premiers principes, qui utilise des vitesses de croissance dépendant ou non de la taille. On propose une méthode simple pour obtenir des trajectoires temps-température à sursaturation ou à vitesse de nucléation constantes, sans faire appel à des techniques d'optimisation. Des courbes de refroidissement à sursaturation constante, qui entra îne une amélioration substantielle (coefficient de variation plus petit et taille moyenne plus grande) de la distribution terminale de taille des cristaux, peuvent être déterminées même en l'absence de nucléation précise et de cinétique de croissance, alors que les propriétés liées à la distribution de taille des cristaux sont sensibles à ces cinétiques. Les résultats expérimentaux pour le système sulfate de potassium-eau, alun de potasse-eau et hexaméthylènetétramine dans l'éthanol, le méthanol et le 2-propanol-eau sont prédits raisonnablement bien par le modèle. On analyse brièvement la possibilité d'étendre le modèle à n'importe quelle méthode de cristallisation discontinue oú la sursaturation est provoquée autrement que par refroidissement, comme la précipitation réactive et le désalaee.
Determination of Operating Conditions for Controlled Batch Cooling Crystallization
Chemical Engineering & Technology, 2006
ABSTRACT In batch cooling crystallization, the supersaturation courses, obtained at different operating conditions, directly influence the crystallization kinetics. Therefore, the product sizes obtained strongly depend on the operating conditions. In order to control the supersaturation level during batch processes, a cooling model was introduced which included the seeding conditions, cooling rate, batch time, and crystallization kinetics. The cooling profiles, which maintain the different constant levels of supersaturation, were, therefore, predicted by numerically solving the model equation. Furthermore, the mean product sizes, obtained with the different specified cooling profiles, were simulated using the mass balance and the moment transformation of the population balance. Based on the simulation results, the relationship between the operating conditions, the supersaturation level, and product size was established. Hence, a strategy to select the appropriate operating conditions, in order to meet the required mean product size, was demonstrated. The results highlight that, by using the developed strategy, the batch cooling crystallization can be operated at optimal conditions, e.g., short batch time, slow cooling rate, or low seed loading. A potassium dihydrogen phosphate (KDP) system was selected for the case study.
Mathematical modeling and kinetic parameter estimation in batch crystallization
AIChE Journal, 2004
A dynamic model of a batch crystallizer was used to estimate the kinetic parameters in a sugar cane crystallization process. The mathematical model included mass, energy, and population balance differential equations, and empirical relationships (power-law-type) for nucleation, growth, and production-reduction rates. Experimental data were obtained from runs carried out at different agitation and cooling profiles. A nonlinear optimization process was used to fit 11 kinetic parameters to experimental data. The overall experimental error was estimated in 7.71% and the average asymptotic error of all kinetic parameters was less than 2%. The nucleation rate was favored by high agitation speed and natural cooling profiles. The maximum growth rate was reached when supersaturation was at a maximum. There was a no clear effect of agitation profiles on growth. The overall effect of the term production-reduction was in all cases positive, with the largest values found for natural cooling profiles.
Chemical Engineering Science, 2011
A systematic procedure for synthesizing the multi-stage crystallization process was developed for resolution of enantiomeric mixtures involving solid solutions in the crystalline phase. The model compound investigated was citalopram oxalate, which revealed a complete solid solution in the solid phase. The counter-current multi-stage batch crystallization was suggested to isolate the target enantiomer from enantiomerically enriched mixtures. The solid-liquid equilibria in the presence of a solvent and the distribution diagrams were quantified and used in designing the crystallization process and defining adequate processing conditions. Different flowsheet schemes were considered and compared with respect to the process performance. The design procedure was verified by the experimental separation of enantiomeric mixtures of citalopram.
Chemical Engineering Science, 2003
A bi-dimensional population balance model was presented in the previous part of this series of papers to simulate the time variations of two characteristic sizes of hydroquinone particles during crystallization. The multidimensional population balance equations combined with kinetic models and mass balance equations were shown to allow the simulation of the solution crystallization of hydroquinone characterized by a rod-like habit. Semi-continuous isothermal operations were performed at the lab-scale in the presence of various additive concentrations. Both the experimental solute concentration trajectory and the ÿnal bi-dimensional crystals size distribution were correctly predicted by the model. The simulated elongation shape factor characterizing the crystal shape was therefore in agreement with the experimental one. Due to the use of tailor-made additive, inhibition e ects were observed to a ect both primary nucleation and growth kinetics in the length direction. For secondary nucleation, indirect e ects were assumed to occur which allowed satisfactory predictions of the ÿnal number of ÿne particles. The representation of the kinetics involved required the evaluation of a set of nine parameters. As a result it was observed that the elongation ratio characterizing the shape of the rod-like particles increases with the length in a nonlinear way. A major interest of the two-dimensional model lies in its ability to relate the time variations of the crystal habit: the particles lengthen in the ÿrst moments of their growth and then progressively get thicker until the end of the process. ?