Cooling Batch Crystallizer Research Articles

Metastable zone width and nucleation kinetics of vanillyl alcohol crystallization in various solvents

In this study, linear cooling batch crystallization of vanillyl alcohol using a laser power system was carried out to experimentally measure the metastable zone widths of vanillyl alcohol in selected solvents (ethanol, 2-propanol, and methyl cyanide) at various saturated temperatures (40, 50, and 60 °C), cooling rates (0.5, 1, 1.5, and 2 °C/min), and agitation speeds (300, 400 rpm). Besides, the sonocrystallization of vanillyl alcohol in ethanol was conducted for measuring MSZW at a various ultrasonic amplitudes (0 %, 25 %, 50 %, and 100 %) at a fixed temperature of 40 °C, cooling rate of 1 °C/min, and agitation speed of 300 rpm. For all three solvents, the MSZW decreases with saturation temperature, while it increases with cooling rate, and this trend doesn’t change for different agitation speeds. Three models—the self-consistent Nývlt-like model, the classical 3D nucleation theory model, and the simplified linear integral model based on classical nucleation theory (CNT)—were employed to estimate the nucleation kinetic parameters for vanillyl alcohol in three solvents. The goodness fit of the models were checked by the coefficient of determination (R-squared). The R-squared values reflected a very good fit between the experimental and predicted values and implied that the models are reliable to estimate nucleation kinetic parameters. Additionally, the interfacial energy between vanillyl alcohol and the solvents was observed to decrease with increasing temperature. Overall, the results indicate that a low nucleation order and low interfacial energy suggest weak solute–solvent interactions, making nucleation easier in the following order: methyl cyanide > ethanol > 2-propanol.

Optimal control of batch cooling crystallizers by using genetic algorithm

The formation of crystals from solutions plays a key role in various industrial applications. In this study, a new approach is presented into the optimal control of batch cooling crystallizers through a genetic algorithm. The Population balance is formularized for a typical batch crystallizer. The objective functions considered here are related to quality of products at the end of the batch. These functions are objective function of maximum mean weight size, closeness to the specified value and minimum coefficient of variation. By using an optimization algorithm (genetic algorithm), the minimum and maximum values of the objective function the input temperature parameter are obtained. The obtained results show that various trajectories can be used for cooling batch crystallizer based on objective functions. This method is applied for the potassium-nitrate system.

Evaluation of the Effect of Seed Preparation Method on the Product Crystal Size Distribution for Batch Cooling Crystallization Processes

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.

Kinetics of ( R, S)- and ( R)-mandelic acid in an unseeded cooling batch crystallizer

The objective of this work is to determine the nucleation and growth kinetics of ( R, S)-mandelic acid (( R,S)-MA) and ( R)-mandelic acid (( R)-MA) in aqueous solutions using an unseeded cooling crystallization process. To obtain the nucleation and growth kinetics, the solubility, metastable zone limits, and supersaturation were measured by in-situ attenuated total reflection Fourier transform infrared (ATR-FTIR) spectroscopy and focused beam reflectance measurement (FBRM). The nucleation rate and growth rate parameters were determined by a nonlinear optimization algorithm. The effects of initial concentration and cooling rate on supersaturation and the nucleation rate are also discussed.

Two-dimensional population balance model with breakage of high aspect ratio crystals for batch crystallization

A two-dimensional population balance model was developed for the description of breakage of crystals with high aspect ratios for a potassium dihydrogen phosphate (KDP) batch crystallization process. Two physical assumptions were made for the modelling. Firstly, the rate of breakage is proportional to the product of the frequency and impact energy of the collisions between the crystals and crystallizer equipment. Secondly, crystals become prone to breakage only when their aspect ratio exceeds a certain limit. Parameters for the rate of breakage were determined by fitting the breakage function in agitation experiments of suspended crystals in a crystallizer. These obtained parameters were validated in batch crystallization experiments. Since the growth rate of KDP is affected by low concentrations of multi-valent ions, Fe 3 + ions were used to control the crystal growth rate resulting in crystals with high aspect ratios. To be able to describe the effect of the used concentrations of Fe 3 + ions on the crystallization process, growth rate equations were derived, which account for the inhibitory effect on the growth rates along widths and lengths of crystals. The results obtained by solving the two-dimensional population balance model accompanied by crystal breakage were compared with seeded cooling batch crystallization experiments at various concentrations of FeCl 3 . The model described crystal breakage very well at a wide range of process conditions. Some discrepancies were observed during initial period of the crystallization, which are most likely caused by the growth model used.

Separation of para-xylene from xylene mixture via crystallization

Crystallization kinetics of para-xylene from xylene isomers mixture using a lab-scale cooling batch crystallizer were determined. The cooling batch crystallizer type is simple, flexible and requires less process development. Dynamic mass and population balances were used to model the batch crystallizer. The model equations were solved using the numerical method of lines; a new proposed solution method. The kinetic parameters of nucleation and growth rates were estimated by measuring the concentration and the total mass of para-xylene suspended crystals during the process time. A nonlinear optimization technique was then applied to estimate the parameters. The effect of the cooling strategy on the estimated parameters was studied. It was found that model predictions using the optimum estimated parameters were in good agreement with the experimental results under various cooling strategies. The optimal kinetic parameters were then used to find the optimum cooling strategy to maximize the yield of para-xylene crystals which have an average size greater than 0.5 mm. A new objective function was formulated and also, a nonlinear optimization technique was applied to find the optimum cooling strategy to achieve this product characterization. The optimization technique converged successfully and the proposed objective function was found to be effective to optimize the para-xylene crystallization process.

Mathematical Model of the Dissolution Stage in Cooling Batch Crystallization

Experiments were performed in a cooling batch crystallizer to develop a phenomenological model that represents the dissolution stage in crystallization. Two models were used: a theoretical and a black box, comparing their results with the experimental ones through the simulation of these models (use the mean and the standard deviation of crystal size like comparative means). The theoretical model was obtained by population's balance, mass and energy balances, and constitutive relations (decrease speed and production‐reduction speed). The black box model consisted of a set of equations, which are functions of the mean, standard deviation, agitation speed and time.

DYNAMIC OPTIMAL CONTROL OF BATCH CRYSTALLIZATION PROCESSES

This work applies an on-line optimal control strategy developed by Zhang (2001) to two cooling batch crystallization processes. The algorithm initially finds the optimal crystallizer temperature and subsequently uses a feedback control system in order to achieve the desired final product quality of the crystals expressed in terms of the final crystal size distribution. In both batch processes, it is shown that the on-line optimal control approach provides better final product quality as compared with a simplified optimal cooling policy. The improvement is especially noticeable in the presence of plant/model mismatch or errors in the initial conditions.

Ammonium Sulfate Crystallization in a Cooling Batch Crystallizer

Abstract Crystallization kinetics of ammonium sulfate crystals are determined in a 25-L draft tube baffled, agitated crystallizer from a series of batch cooling experiments performed in an integral mode. The method of s-plane analysis for relative nucleation kinetics and the method of initial derivatives for growth rate kinetics are used to establish conventional kinetic expressions. A simulation technique is developed to calculate the product population density functions for the same system in a seeded cooling batch crystallizer configuration.

Batch crystallization of KCl in the presence of soluble and insoluble impurities

Abstract Crystallization of KCl from an aqueous solution co-saturated with NaCl and KCl in the presence of small amounts of magnesium sulphate, calcium sulphate, ferric chloride, chromium nitrate and insoluble silica powder over size ranges of 20-30 μm, 90-106 μm and 180-212 μm is studied in a 750 ml controlled cooling batch crystallizer. Scanning electron microscopy is used to study the crystal habit and polycrystals formation in each case. Crystal size distribution and crystal yield are reported for each impurity. Growth kinetic constant of KCl crystals in presence of each admixture is estimated by comparing the simulated and the measured product crystal size distributions.

A simplified approach to the operation of a batch crystallizer

AbstractA 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.

Self-tuning control of crystal size distribution in a cooling batch crystallizer

In this paper the theoretical basis of a control scheme, previously implemented on a laboratory scale potash alum batch cooling cystallizer (Rohani , Can. J. chem. Engng, in press, 1990), is presented. A comparison is made between the experimental and simulation results. A mathematical model of a seeded batch cooling crystallizer equipped with a fines dissolving loop and a fines suspension measuring device is developed. The mean crystal size and the coefficient of variation of an ideal batch crystallizer are derived analytically and it is shown that a batch crystallizer utilizing the proposed control scheme approaches the ideal case. Using the traditional control schemes based on operation along an optimal cooling trajectory results in a terminal CSD far from the ideal case. It is also shown that due to the time-varying characteristics of a batch crystallizer, a minimum variance self-tuning controller renders tighter control and improves the product CSD to a larger extent (a smaller coefficient of variation and a larger mean crystal size of the weight distribution) when compared with a conventional PI-controller.

Scale-up of agitated crystallizers; Cooling batch crystallization of potassium aluminium sulphate

The crystallization of potassium aluminium sulphate was conducted by cooling a solution saturated at 70°C to a temperature of 25°C at three various cooling rates. The measurements were performed on a small scale (160 cm3) and a large laboratory scale (0.021 m3). The mean size of product crystals was determined by sieve analysis, and the system constant, BN, was calculated using previously derived relations. The BN value is the same, within experimental error, for all the experiments and scales, indicating that agitated-vessel cooling crystallizers can be modelled successfully even on a very small laboratory scale.