ASL model for prediction of CSD in a continuous crystallizer

A Monte Carlo simulation scheme is proposed for crystal size distribution (CSD) in a continuous crystallizer for size dependent growth rate. Crystal growth rates are described by Abegg, Stevens, and Larson (ASL) model. The proposed model is used to predict CSD from potassium carbonate crystallizer. The agreement between theory and available data confirms the validity of the model.     

Graphical Representation of Various Models for Crystal Size Distribution in Continuous Flow Crystallizers

Plots of crystal size distribution of the following crystallizer models are compared: an ideal continuous-flow MSMPR (mixed suspension, mixed product removal) crystallizer with a zero as well as non-zero initial crystal size, an MSMPR crystallizer with size dependent growth of crystals, an MSMPR crystallizer with missing fines, an MSMPR crystallizer with agglomerative growth, and a series of MSMPR crystallizers simulating a crystallizer with nonideal agitation. The shape of the individual size distribution curves can serve as a diagnostic criterion in determination of the most probable model of crystallization.     

Monte Carlo Simulation of Transient CSD in a Continuous Crystallizer under Stochastic Dispersion Effects

Monte Carlo simulation is a very powerful tool for simulation of transient and steady state crystal size distribution (CSD) in a continuous crystallizer under stochastic dispersion effects. In the present work, transient CSD in a continuous crystallizer has been reported when shape factor and growth rate dispersions conform to normal distribution. For the steady state run, the algorithm reported by Sen Gupta and Dutta elsewhere has been used to validate the results obtained in the present work when the steady state is reached.     

Two parameter kinetic equation of size dependent crystal growth

The previously proposed hyperbolic, three parameter empirical model of size dependent crystal growth can be reduced to the two parameter one of the form This simplification reduces dimension of the least squares correlation of crystal size distribution in MSMPR crystallizer thus saving amount of calculations with a negligible loss of accuracy estimated by means of the mean residual square deviation. The additional advantage is that a differential balance of crystal number in MSMPR crystallizer can be solved analytically for the simplest case of the exponential function of secondary nuclei size distribution. Correlations for single experiment with ammonium alum are presented.     

Analysis of Transient Crystal Size Distribution in a Continuous Sodium Chloride Crystallizer

This work deals with the transient analysis of crystal size distribution (CSD) in a continuous sodium chloride crystallizer. The crystallization is assumed to take place under diffusion controlled conditions and the crystal growth models reported by Sen Gupta and Dutta elsewhere have been used. Monte Carlo (MC) scheme has been employed for simulation purposes. The simulation results have been compared with the available experimental data at steady state.     

Mathematical model of particle size distribution of crystals taking into account the growth dispersion

This paper presents a mathematical model to describe the effect which the growth dispersion has on the particle-size distribution of crystals which are formed in a crystallizer with an ideally mixed suspension and ideal product discharge (MSMPR crystallizer). This model starts from a number density distribution of crystals, which shows dependence on the process duration, the rate of crystal growth and the crystal size. The model differs from the diffusion model. The distribution data calculated are in agreement with distribution data measured and published by a number of other authors. The influence of the two parameters b and r_LH on the mathematically determined frequency distributions is being studied.     

Isotopic method for studying the kinetics of crystal growth

An experimental method for studying the kinetics of crystal growth based on the knowledge of crystal size distribution in the crystallizer is presented. Residence time distribution was determined using the radioactive isotopes technique. The method was employed to determine the magnesium sulphate growth kinetics in high temperature conditions.     

Effect of mixing on the crystal size distribution of borax decahydrate in a batch cooling crystallizer

The effect of the impeller speed upon the metastable zone width, supersaturation level, crystal growth and the crystal size distribution of borax decahydrate have been investigated to find operating conditions of a batch cooling crystallizer. The importance of impeller speed was studied in baffled stirred crystallizer with a volume of about 2 dm³, equipped with four straight blade turbine (4-SBT) cooling at a constant cooling rate. The metastable zone width was determined by visual method, while concentration changes during the process were monitored in line using ion-selective electrode. The crystal size distribution was determined by optical microscope and sieve analysis respectively. The power consumption measurements were performed for all impeller speeds examined as well. On the basis of the experimental results and observations it is evident that in an agitated batch crystallizer the above mentioned parameters are significantly influenced by hydrodynamic regime in the system determined by impeller used and its revolution speed.     

Seed loading effects on the mean crystal size of acetylsalicylic acid in a continuous‐flow crystallization device

This study investigates the effects of seed loading on the mean crystal size of the model substance, acetylsalicylic acid, crystallized from ethanol in a continuously seeded tubular crystallizer. A hot, highly concentrated ethanolic acetylsalicylic acid solution was mixed with an acetylsalicylic acid‐ethanol seed suspension. Subsequent cooling of the slurry in the tubing promoted supersaturation and hence crystal growth. The tubular shape of the 15 m‐long crystallizer with an inner diameter of 2 mm enabled narrow residence time distributions of the crystals in the pipe and excellent temperature control in the radial direction and along the tubing. Crystals entering the crystallizer had both identical growth conditions in each section and about the same time for crystal growth. Narrow crystal size distributions were achieved with decreasing differences in the volume‐mean‐diameter sizes of the seed and product crystals as seed loadings increased. Decreasing the seed size had a similar effect as increasing the seed loading, since in that case the same amount of seed mass resulted in more individual seed particles. Altering the arrangement of the coiled crystallizer with respect to spatial directions (horizontal, vertical) did not lead to a significantly different outcome. All experiments produced considerably larger product crystals in comparison to the seeds despite relatively short crystallization times of less than 3 min. Moreover, product mass gains of a few hundred percent at a g/min‐scale were achieved. Similarities in product crystal samples taken at different times at the outlet of the crystallizer showed that steady‐state conditions were rapidly reached in the continuous flow crystallization device. (© 2011 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Comparison Study of Mixing Effect on Batch Cooling Crystallization of 3‐Nitro‐1,2,4‐triazol‐5‐one (NTO) Using Mechanical Stirrer and Ultrasound Irradiation

The insensitive explosive 3‐Nitro‐1,2,4‐triazol‐5‐one (NTO) has been recrystallized from water in an effort to prepare crystals with smaller size and narrower distribution in a batch cooling crystallizer. Two mixing devices, i.e., a mechanically stirred system with and without ultrasound in aqueous media were employed to compare the mixing effect on the crystallization. Under ultrasound irradiation, the metastable zone width was significantly reduced by more than 2 fold and the crystal size was shifted from 140∼160 μm to 50∼70 μm with a narrower CSD compared to the mechanically stirred system. However in the mechanical stirrer, the mixing effect on NTO crystallization was negligible if the impeller speed was sufficient to suspend all crystals in the crystallizer. It was found that the crystal growth was not influenced by mixing. We suggest that the NTO crystals were formed by primary heterogeneous nucleation that is common in batch cooling system. Finally, the population balance model (PBM), with the empirical nucleation and growth kinetic expressions, was solved numerically to predict the crystal size and the CSD with batch time, and the results were in good agreement with the experimental data.     

Seeded batch crystallization of ammonium aluminum sulfate from aqueous solution

Seed crystals of ammonium aluminum sulfate ((NH₄)Al(SO₄)₂··12H₂O) were grown in aqueous solution by cooling. The temperature of a crystallizer was lowered with no control by circulating cooling water through the jacket. It fell in an exponential manner. The effects of seed amount and size on the product crystal size distribution were examined. The product crystals obtained were of narrow and uni-modal size distribution with suppressed secondary nucleation if seed crystals were loaded more than a critical value. The critical value was determined and well compared with previously reported values for other material systems. This crystallization technique does not need any prior knowledge of the kinetics of crystal growth and nucleation. It is simple and robust, and can be easily applied to an existing crystallizer without installing any additional control systems.     

Modelling of Growth Rate for MSMPR Crystallizer Data

One of the most important applications of the population balance approach to MSMPR crystallizer modelling is the recovery of crystal nucleation and growth rates data from steady-state crystal size distributions (RANDOLPH, LARSON). A large number of studies have confirmed that both size-dependent (growth rate is a function of crystal size) and growth rate dispersion (crystals of the same size do not have the same growth rate), causes nonlinearities which limit the usefulness of the RANDOLPH and LARSON approach. A discussion of modelling of crystal growth kinetics for simulated and real MSMPR crystallizer data is presented. In the former case, both linear and non-linear log population density distributions are used. The modelling of growth kinetics is done twice – once assuming that growth rate dispersion is a source of curvature in the log population density vs size data plot and, again when this curvature is caused by size-dependent growth. Calculations clearly indicate that even for crystallizing systems which follow the McCabe's δL law, both growth rate dispersion and size-dependent growth models lead to proper estimation of growth kinetics. When log population density vs size data plots exhibit curvature, however, use of the size-dependent growth rate approach gives more reliable growth kinetics across a broad crystal size range than those obtained from modelling of growth kinetics by growth rate dispersion.     

A stratified Monte Carlo simulation of CSD in a continuous crystallizer for size-dependent growth

This work deals with the prediction of crystal size distribution (CSD) in a continuous crystallizer for size-dependent growth. Crystal growth rates are described by Abegg, Stevens, and Larson (ASL) model. Stratified Monte Carlo method has been employed to evaluate the integrals involved in the classical moment equation for prediction of CSD. The simulation results have been compared with the available experimental data of K₂CO₃ · 1.5 H₂O crystals in a continuous crystall lizer.     

Optimierung der Kühlungskristallisation mittels Vermischung einer kalten und einer warmen Lösung

Heated saturated solutions were directly mixed with cold ones in a fluidization crystallizer. Crystals were continuously drawn from the fluid layer, and the outflowing mother liquor of the upper part of this layer recooled and inflown into the crystallizer again. A model enabled to determine that optimum common temperature referring to the given initial solutions, and the temperature of the outflowing mother liquor, when the main part of the crystals precipitates. — The portions of crystals referring to the theoretically found optimum common temperature of the solution in the crystallizer and to the whole circulation process, were determined. We examined the validity of the theoretically found values by experiment and the influence of cooling parameters on crystal size distribution as well as on the productivity of the crystallizer.     

Crystallization of vitamin C in a continuous DT MSMPR crystallizer – Size independent growth kinetic model approach

The experimental results concerning continuous mass crystallization process in L(+)‐ascorbic acid – water system are presented and discussed. Influence of L(+)‐ascorbic acid concentration in a feeding solution and mean residence time of suspension in laboratory DT MSMPR crystallizer on product crystal size distribution as well as nucleation and growth kinetics were determined. Kinetic parameter values were evaluated on the basis of size–independent growth (SIG) kinetic model (McCabe's ΔL law). It was observed, that within the examined range of crystallizer productivity (120–1600 kg LAA crystals m^–3h^–1) crystal product population of mean size L_m from 0.2 to 0.3 mm and CV from 66.6 to 49% is withdrawn. Linear growth rate values present decreasing trend (from ca. 7 · 10^–8 to ca. 6 · 10^–8 m s^–1) with the productivity increase (assuming constant mean residence time of suspension τ = 900 s). Occurrence of secondary nucleation within the circulated and mixed suspension, resulting from crystal attrition and breakage, was observed. The parameter values in design equation connecting linear growth rate and suspension density with nucleation rate were determined. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

The effect of crystal surface roughness on impurity adsorption

The effect of crystal surface roughness on impurity adsorption was investigated in a fluidized bed crystallizer and in a batch crystallizer. The crystallisation of sucrose in pure and impure systems was the study subject. Calcium chloride was utilized as impurity in this work. The results show that the impurity adsorption is growth rate dependent and is strongly influenced by the crystal surface properties. Crystals with high surface roughness have lower impurity adsorption. Based on experimental evidences, a new theoretical model is proposed to quantify the surface roughness influence on the impurity adsorption, allowing, by operating at the more adequate supersaturation, to control the impurity transfer into crystals. The used impurity does not have a significant influence on the growth rates at the studied temperatures. (© 2009 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

The Effect of Volume Shape Factor on the Crystal Size Distribution of Fragments due to Attrition

The effect of volume shape factor on crystal size distribution (CSD) is usually ignored to simplify the analysis of population balance equation. In the present work, the CSD of fragments generated from a mechanically stirred crystallizer as the result of attrition mechanism has been reported when the volume shape factor conforms to normal distribution. The physical model of GAHN and MERSMANN which relates the attrition resistance of a crystalline substances to its mechanical properties has been employed. The simulation of fragment size distribution was performed by Monte Carlo (MC) technique. The results are compared with those reported by GAHN and MERSMANN.     

Continuous Recrystallization in a Double Crystallizer

This paper deals with a simple model of steady state recrystallization in a double crystallizer. Equations describing the particle size distribution are formulated and solved. The relations between resulting particle size distribution and working conditions of the double crystallizer are discussed.     

Crystallization kinetics of MgSO4·12H2O from different scales of batch cooling scraped crystallizers

For reliably scaling up of crystallizers, a full kinetic model is required in addition to heat, mass and population balances. A method for extracting nucleation and growth kinetic parameters for scaling‐up seeded batch cooling crystallization was developed and demonstrated with a 15 L and in a 115 L scraped crystallizer using MgSO₄·12H₂O as the model system. The method includes fitting the time resolved measured solute concentration and the crystal size distributions with a dynamic population‐based model. The kinetic parameters extracted from the bench‐scale crystallizer agree with those obtained from the pilot scale, confirming that they can be employed for design purposes. (© 2006 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)