Mathematical modelling and analysis of dynamic behaviour for seeded batch potash alum crystallization process (original) (raw)
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ASEAN Journal of Chemical Engineering
The driving force of the cooling crystallization process is supersaturation, where the supersaturation level during the crystallization process is crucial to grow the crystal sufficiently. Nucleation and crystal growth rates are two concurrent phenomena occurring during crystallization. Both are supersaturation functions that determine the growth of seed crystals and the formation of fine crystals. Trade-offs between nucleation and crystal growth are essential for achieving the large size of seed crystals with the minimum number of fine crystals. Thus, the objective of this study is to analyze the effects of nucleation and crystal growth rates on final product quality, which is crystal size distribution (CSD). Modeling of the crystallization process using a potash alum case study is highlighted and simulated using Matlab software. Then, the effects of nucleation rate, crystal growth rate, and both nucleation and crystal growth rates on CSD are evaluated using local sensitivity analy...
Elsevier Ltd, 2023
The effects of different seed forms on crystal product distribution are presented for optimizing crystal size distribution (CSD) in the case of seeded batch cooling crystallization process. Three different seed distributions and quality are introduced as variable parameter for CSD control of seeded batch crystallization process via simulation in Matlab software. Similar implementation is conducted in the experimental study using the same operating conditions and parameters. Cubic cooling profile is adapted as the temperature profile for potash alum crystallization system due to its ability to control secondary nucleation. The experimental data obtained from laboratory works are validated the simulation results from Matlab where good agreement has been achieved. In terms of mean crystal size of the final CSD, the seed profile with 0.29 standard deviation labelled Sieved Seed 2, produces the best seed profile for seeded batch potash alum crystallization process because it has the largest size of crystals at mean crystal size of 500 lm grown from 90 lm of seed crystals. However, considerable fine crystals at mean crystal size of 30 lm are also obtained indicating trade-off between large size of crystals and fine crystals are needed. In conclusion, this work highlights the effects of different seed quality in terms of distribution and shape on crystal size distribution as one of the important quality specifications in crystallization process and demonstrates narrow distribution of seed crystals as recommendation on the best seed quality for producing desired CSD.
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.
The Canadian Journal of Chemical Engineering, 1989
Crystallization kinetics of KC1 in a 2 1.8L continuous mixed-suspension-mixed-product-removal (CMSMPR) potash cooling crystalliier are determined using the method of s-plane analysis (Tavare, 1986). Feed saturated in refined potash, nearly saturated in NaCl and containing 0.75 g of MgSO, per 100 g of water is cooled from 54°C to 38°C by two concentric cooling coils. The crystallizer is brought to steady-state and then perturbed by a change in the crysallizer temperature from 38°C to 32°C. Samples are withdrawn every 15 minutes by means of a specially devised sample trap which permits representative sample removal. Samples are sized using sieve-analysis. The crystallization kinetics are correlated as B" =49.618 Les cin6tiques de cristallisation du KCI dans un cristalliseur de refroidissement de potasse B retrait de produit mixte et de suspension mixte en rkgime continu sont dkterminhs en utilisant la m6thode d'andyse du plans (Tavare, 1986). L'alimentation saturh en potasse raffinke, quasi satur6e en NaCl et contenant 0,75 g de MgSO, par 100 g d'eau est refroidie de 54 B 38°C par deux serpentins de refroidissement concentnques. Le cristalliseur est amen6 en r6gime permanent puis perturb6 en faisant passer la tempkrature de 38 B 32°C. Des 6chantillons sont pr6lev6s toutes les 15 minutes au moyen d'un collecteur swialement c o n y B cette fin et qui permet le retrait d'khantillons reprksentatifs. Les khan-tiUons sont s6par6s par analyse granulom6trique. Les cin6tiques de cristallisation sont corr616s sous la forme B" = 49,618
Computers & Chemical Engineering, 2011
Crystallization is a widely used unit operation for the production of pharmaceuticals, fertilizers, and fine chemicals. A commonly used crystallization operational objective is to produce large crystals under minimum nucleation rates. For cooling crystallization there are two key methods for minimizing nucleation, programmed cooling and seeding. In this paper, we evaluate the cooling and seeding methods through the detailed modeling of nucleation phenomena coupled with a population balance and dynamic optimization of this mathematical formulation. Extensive simulation results showed that initial seeding parameters, as proclaimed by others, do have a significant effect on the final product crystal size distribution. It also showed the significance of a combined seeding-cooling approach where a joint cooling and seeding optimization gives superior performance to just optimizing the seed. Importantly, the developed model was highly instrumental in rapidly determining optimal combined seeding-cooling profiles via dynamic model-based optimizations.
Feedback control of crystal size distribution in a continuous cooling crystallizer
The Canadian Journal of Chemical Engineering, 1991
Control of crystal size distribution (CSD) in a 21.8 L continuous cooling KCI crystallizer was attempted. Feed saturated at 54°C with potash, nearly saturated with NaCl and containing 0.75 g MgS04/100 g of H,O was cooled to the crystallizer temperature at 40°C. The control scheme consisted of a proportional-integral controller with the rate of fines dissolution/removal as the input variable and the fines suspension density (crystals smaller than 150 pm) as the output variable. The measuredicontrolled variable was a temperature difference, AT, corresponding to the temperature of a slurry sample containing representative fines, before and after the fines were dissolved by heating. An increase in the product weight-mean crystal size and a decrease in the coefficient of variation of product were observed in the controlled runs.
Crystal Growth & Design, 2010
This paper provides an experimental and simulation based analysis of the effect of seed quality on the shape of the product crystal size distribution of a seeded batch cooling crystallization process. Various seeds were prepared using different protocols, involving milling, washing, and sieving. The cooling batch crystallization processes of potassium dichromate in water with the different seeds were monitored using process analytical technologies (PAT), such as attenuated total reflectance (ATR) UV/vis spectroscopy, focused beam reflectance measurement (FBRM), and online laser diffraction for real-time crystal size distribution measurement. A population balance model with apparent size-dependent growth, which incorporates the effect of growth rate dispersion, is used to simulate the evolution of the crystal size distribution (CSD) using the different seed distributions as initial conditions. The simulation results were in good agreement with the experimental product CSD, when the good quality crystalline seed was used with no fines. However, the mean crystal size of the product was overpredicted by the growth-only model, when milled seeds were used with different fine contents. This was caused mainly by the excessive initial breeding, due to the different surface properties resulting from the preparation method, the Ostwald ripening promoted by the fines, and the pronounced agglomeration observed in these cases during the experiments. The simulation and experimental results provide evidence of the importance of consistent and well-defined seed quality and suitable preparation procedures for high quality crystalline products.
Chemical Engineering Science, 2010
The paper presents a novel quality-by-design framework for the design of optimal seed recipes for batch cooling crystallisation systems with the aim to produce a desired target crystal size distribution (CSD) of the product. The approach is based on a population balance model-based optimal control framework, which optimizes the compositions of seed blends, based on seed fractions that result from standard sieve analysis. The population balance model is solved using a combined quadrature method of moments and method of characteristics (QMOM-MOCH) approach for the generic case of apparent size-dependent growth. Seed mixtures are represented as a sum of Gaussian distributions, where each Gaussian corresponds to the seed distribution in a particular sieve size range. The proposed methods are exemplified for the model system of potassium dichromate in water, for which the apparent size-dependent growth kinetic parameters have been identified from laboratory experiments. The paper also illustrates the simultaneous application of in situ process analytical tools, such as focused beam reflectance measurement (FBRM) for nucleation detection, attenuated total reflection (ATR) UV/Vis spectroscopy for concentration monitoring, as well as the in-line use of laser diffraction particle sizing for real-time CSD measurement.
Control of crystal size distribution in a batch cooling crystallizer
Canadian Journal of Chemical Engineering, 1990
A control scheme for crystal size distribution (CSD) in a batch crystallizer, based on indirect measurement of fines suspension density and manipulation of fines dissolving rate, is proposed and implemented on a 27 L laboratory batch cooling crystallizer using the potash alum-water system. The measured variable was a temperature difference related to the fines suspension density detected by a new fines sampling/suspension density measuring device proposed by Rohani and Paine (1987). Servo-control of the fines suspension density was achieved using a conventional PI control mode. Two different cooling policies, namely, linear cooling and isothermal operation were examined and improvement in the final CSD was observed in both cases. The weight-mean crystal size and the coefficient of variation of the end product showed a maximum improvement (larger mean size and smaller coefficient of variation) of 80% and 31% over the uncontrolled experiments, respectively. The weight fraction of fines (smaller than 150 μm) in the end product was decreased by a maximum of 99% over the uncontrolled run. Higher overall rates of fines dissolution led to a more uniform product with a larger weight-mean crystal size at the expense of a small reduction in the rate of solids make.Un schéma de contrôle de la distribution de taille des cristaux dans un cristalliseur discontinu, basé sur la mesure indirecte de la densité de suspension des fines et la manipulation du taux de dissolution des fines, est proposé et utilisé sur un cristalliseur à refroidissement discontinu de laboratoire d'une capacité de 27 L avec un système alun de potasse-eau. La variable mesurée est une différence de température reliée à la densité de suspension des fines détectée par un nouveau dispositif de mesure d'échantillons de fines et de densité de suspension proposé par Rohani et Paine (1987). On a effectué la servorégulation de la densité de suspension des fines en utilisant un mode de contrôle PI classique. Deux procédures de refroidissement différentes ont été étudiées, à savoir le refroidissement linéaire et le fonctionnement isotherme, et on a observé une amélioration de la distribution finale de taille des cristaux dans les deux cas. La taille des cristaux de poids moyen et le coefficient de variation du produit final montrent une amélioration maximale (taille moyenne plus grande et coefficient de variation plus petit) de 80 et 31% pour les expériences non régulées, respectivement. La fraction de poids des fines (inférieure à 150 μm) dans le produit final est réduite jusqu'à 99% lors du cycle non régulé. Des vitesses globales supérieures de dissolution des fines donnent un produit plus uniforme avec une taille des cristaux de poids moyen plus grande au détriment d'une légère réduction de la vitesse de formation des solides.