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.     

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.     

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.     

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)     

Determination of reactive crystallization kinetics of 5‐(difluromethoxy)‐2‐mercapto‐1H‐benzimidazole in a batch crystallizer

5‐(difluromethoxy)‐2‐mercapto‐1H‐benzimidazole (DMB) was crystallized via the reaction between sodium salt of DMB and acetic acid. In this work, we firstly measured the solubility data of DMB in binary ethanol‐water mixture at different temperatures. Then, the reactive crystallization kinetics of DMB was determined in the batch crystallizer. Based on the population balance and mass balance, the kinetics model of reactive crystallization process of DMB was established. And the nucleation rate, size‐independent crystal growth and agglomeration kernel were determined by method of classes. Finally, based on the population balance, numeric simulation was done using the above crystallization kinetics in order to verify its reliability.     

A method for determination of size-dependent crystal growth kinetics from batch experiments (I). One-experiment estimation

The method developed for determining size-dependent crystal growth kinetics makes use of the assumption that the linear growth rate is a product of a size-dependent factor and a supersaturation-dependent one. The transformed form of the population balance equation, obtained by means of this assumption, is the basis of the evaluation utilizing measurement data from one seeded batch crystallization experiment, namely the size distributions of the seed and product crystals as well as the supersaturation course. The application of the method is illustrated by evaluating an experiment with potash alum crystals.     

Continuous reaction crystallization of struvite from phosphate(V) solutions containing calcium ions

Continuous reaction crystallization of struvite from water solutions containing phosphate(V) (1.0 mass%) and calcium ions (from 0.01 to 0.20 mass%) was investigated. Process was carried out in temperature 298 K in continuous DT MSMPR type crystallizer with internal circulation of suspension. Influence of pH (from 9 to 11) and mean residence time of suspension in crystallizer (from 900 to 3600 s) on product crystal size distribution, mean size, population homogeneity and shape of crystals, as well as chemical composition of solid phase was tested. Within the investigated process parameter ranges struvite crystals of mean size from 18 to ca. 50 μm were produced. With the increase in calcium ions concentration in a feed mean crystal size decreased from 34.2 to 18.4 μm (pH 9, τ 900 s). Coexistence of struvite and hydroxyapatite crystals in the solid product was confirmed analytically (Ca content in solid product from 0.3 to 8.4 mass%). Presence of calcium ions favoured crystallization of struvite in a form of tubular crystals, characterized by lengthwise cracks and irregular edges. Co–precipitated hydroxyapatite particles showed relatively small sizes, even below 1 μm, forming agglomerates on the surface of larger struvite crystals and individual agglomerates. (© 2011 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Rate of sodium chloride attrition fragment generation in a mixed‐suspension crystallizer

Attrition of crystals in industrial crystallization is the major source of secondary nucleation and has strong effects on product quality. This work describes attrition in industrial crystallizers using an empirical engineering model based on dimensionless groups describing crystal properties, suspension properties, and crystallizer geometry and operating conditions. Here the attrition rate of sodium chloride crystals in a small scale mixed‐suspension crystallizer is studied, varying the following parameters: impeller speed, parent crystal size, suspension density, draft‐tube impeller clearance, off‐bottom impeller clearance, impeller type, and impeller material. It was found that the attrition rate depends on most of the variables investigated. The direction of the dependence is predictable based on intuitive modeling. An empirical power law model based on dimensionless groups predicted by Buckingham‐Pi theory (using variables mentioned above) gives a good fit to the data.     

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.     

Synthesis of Submicron Silicalite‐1 Crystals from Clear Solutions

Discrete and monodisperse submicron crystals of silicalite‐1 with a mean size of 0.3 μ m were synthesized from clear crystallization solutions. The effects of silica content, alkalinity of batch and the nature of silica source on the product yield, crystal morphology and particle size distribution were investigated. The crystal shape was sphere‐like or hexagonal twinned disks when silicic acid was the silica source. Change of silica source to sodium silicate solution leads to the formation of rounded‐edged‐hexahedron crystals. Silica content of batch does not influence crystal morphology. Alkalinity of clear crystallization solution has a strong effect both on the particle size distribution and yield of product. Increase of alkalinity caused bimodal particle size distribution and decrease of yield.     

The estimation of crystallization kinetics from linear in n(L) versus L steady-state data including growth rate dispersion

A discussion of modelling of nucleation and crystal growth kinetics is presented for those mixedsuspension, mixed product removal (MSMPR) crystallizer data available in the literature, for which log population density data appears to be a linear function of crystal size. The modelling crystallization kinetics is done twice – once assuming that the system is obeying McCabe's Δ law, and again when the crystals exhibit growth rate dispersion (GRD). In the latter case the gamma, inverse gamma, log-normal, beta, Fisher, sum of two gammas, sum of two inverse gammas, sum of two log-normal, and sum of two constant rates of growth rate dispersion models are used for crystal growth rate estimation. Finally, McCabe's and GRD predictions are compared with the size-dependent growth rate estimations.     

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)     

Effect of seeded surface area on crystal size distribution in glycine batch cooling crystallization: a seeding methodology

In batch cooling crystallization, if the seeding process is not carefully carried out, the crystal size distribution (CSD) is dispersed. The aim of this work is to determine the optimal conditions for seeding operations. Results show that the CSD is controlled if the seed surface area reaches a specific value called critical surface S_c. Nevertheless, S_c is not the only parameter to be considered. The mean crystal size of the product obtained actually depends on the size of the seeds used because of the growth rate distribution. In fact, seeds behave differently according to their crystal sizes, which accounts for the difference in crystal growth rates. Rules are proposed for seeding with the view to obtain a uni-modal CSD and a final product size predefined by the seed crystals.     

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.     

Nucleation and growth kinetics for the crystallization of ice from dextrose solutions in a continuous stirred tank crystallizer with supercooled feed

The crystallization of ice in aqueous dextrose solutions is studied in an adiabatic continuous stirred tank crystallizer with a supercooled feed stream. The effective diameter of the ice crystals was determined for various values of mean crystal residence time, feed supercooling, magma density, stirring rate, and dextrose concentration. For all process conditions the supercooling was measured at 9-12 different locations in the crystallizer. These local supercoolings were averaged algebraically to yield the bulksupercooling. From the experimental results growth and nucleation rates have been calculated. By comparing the experimental growth rates to growth rates calculated by means of a mathematical model kinetics for the inbuilding of water molecules into the ice lattice have been determined. The growth rate appears to be directly proportional to the interface supercooling. The rate constant decreases exponentially with increasing weight percentage of dextrose in the solution. The nucleation rate was found to be directly proportional to total crystal surface per unit volume of suspension and proportional to the bulksupercooling to the power 2.1. Nucleation is believed to occur by breakage of dendrites from the surface of parent crystals.     

Influence of essential and non‐essential amino acids on calcium oxalate crystallization

The investigation on the mechanism of nucleation and growth of crystals at organic‐inorganic interfaces is crucial for understanding biological and physiological calcification processes such as the formation of urinary stones. The effects of five different amino acids on the crystallization of calcium oxalate have been investigated at pH 4.5 and 37 °C in aqueous solutions in the batch type crystallizer. The products were characterized by Scanning Electron Microscopy (SEM), Fourier Transfer Infrared Spectroscopy (FT/IR) and X‐Ray diffraction (XRD) analysis. Crystal size distribution (CSD) and filtration rate measurements were done. In order to determine the adsorption characteristics of amino acids on the calcium oxalate crystal surfaces, zeta potential measurements were also done and discussed. The results indicate that in the presence of all investigated amino acids, calcium oxalate monohydrate (COM) crystals were preferentially produced, but the crystal morphology varied with amino acid types and concentrations. Various crystal morphologies such as elongated hexagonal, coffin or platy habits were observed. In the presence of all investigated amino acids, the calcium oxalate crystallized in a monohydrate form. Electrostatic/ionic interaction, different adsorption properties and special functional effects of amino acids led to find different crystal morphology. (© 2010 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Influence of various factors on the liquid/liquid diffusion crystallization of proteins

From a numerical simulation of pre-nucleation solute transport in the liquid/liquid diffusion crystallization of proteins, it is derived that there are various factors influencing the spatial and temporal distributions of supersaturation. They include the ratio of the length of the protein solution to that of the salt solution in a tube crystallizer, the initial concentrations of protein and salt, and the initial salt concentration in the protein solution. Their influences on the protein crystallization have been demonstrated by the corresponding experiments of gel crystal growth. It may be deduced that the experimental conditions for the liquid/liquid diffusion growth of protein crystals could be optimized under given conditions in order to develop the advantages of this method.     

Study of phosphoric acid crystallization using a focused beam reflectance measurement method

A way for restoring the crystal size distributions (CSD) from measured chord length distributions (CLD) was reported in this paper. The kinetics of phosphoric acid crystallization process was investigated in cooling mode using focused beam reflectance measurement (FBRM) and digital photo technique. In order to restore the CSD from measured CLD and verify the reliability of FBRM data, digital photo technique in real time and optical microscope were applied in large crystal size and small range, respectively. Results indicated a converting constant A existed between CLD and CSD when crystal growth follows size‐independent growth (Mcabe's ΔL law) law. It was verified by Malvern particles size analysis method. The converting constant A varied with crystal morphology. The crystal growth order increased with the stirring increasing speed during phosphoric acid crystallization process. The trend was especially notable at higher speed situations. It can illustrate that the state of phosphoric acid hemihydrate crystal growth was controlled by both diffusion and surface‐integration with the increasing stirring speed. (© 2010 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Kinetic studies on the influence of temperature and growth rate history on crystal growth

Crystallization experiments of sucrose were performed in a batch crystallizer to study the effect of temperature and growth rate history on the crystal growth kinetics. In one of the growth methods adopted, the isothermal volumetric growth rate (R_V) is determined as a function of supersaturation (S) at 35, 40 and 45 ºC. In the other, crystals are allowed to grow at constant supersaturation by automatically controlling the solution temperature as the solute concentration decreased. Using the latter method R_V is calculated as the solution is cooled. The obtained results are interpreted using empirical, engineering and fundamental perspectives of crystal growth. Firstly, the overall activation energy (E_A) is determined from the empirical growth constants obtained in the isothermal method. The concept of falsified kinetics, widely used in chemical reaction engineering, is then extended to the crystal growth of sucrose in order to estimate the true activation energy (E_T) from the diffusion‐affected constant, E_A. The differences found in the isothermal and constant supersaturation methods are explained from the viewpoint of the spiral nucleation mechanism, taking into account different crystal surface properties caused by the growth rate history in each method. Finally, the crystal growth curve obtained in the batch crystallizer at 40 ºC is compared with the one obtained in a fluidized bed crystallizer at the same temperature. Apparently divergent results are explained by the effects of crystal size, hydrodynamic conditions and growth rate history on the crystallization kinetics of sucrose. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)