Modeling of crystal growth and nucleation rates for pentaerythritol batch crystallization

The kinetics of crystallization – nucleation and crystal growth – was determined for a seeded batch cooling process. Several experiments were done utilizing always the same condition: initial concentration, seed mass and size distribution, and cooling rate. From one experiment to other the agitation speed was varied. As the utilized reactor is able to measure torque of the impeller, the power dissipated in agitation was monitored during the crystallization, as well as reactor temperature and turbidity of the suspension. Turbidity monitoring and the measurement of particle size distribution from seeds and final product allowed obtaining the evolution of the second moment of the particles during the crystallization. The crystallization process was modeled utilizing the Method of Moments and the nucleation and crystal growth kinetics were obtained from least-square minimization of calculated second moments of the crystals. A crystal growth kinetic was determined and the secondary nucleation rate was described as a function of dissipated power and as functions of impeller tip speed. Additional experiments were done, in which cooling rate, seed mass and seed size were varied. The calculated kinetics could satisfactorily describe the results of the additional experiments, corroborating the quality of the modeling.     

Effect of cooling mode on product crystal size in seeded batch crystallization of potassium alum

Potassium alum was crystallized by seeding in a batch crystallizer under controlled and natural cooling modes. Regardless of the cooling mode, the product crystal size distribution (CSD) became bi-modal at low seed concentrations because of enormous secondary nucleation. The mean mass size of the product was smaller for the natural cooling mode compared to that for the controlled cooling mode with more intensive secondary nucleation. On the other hand, at high seed concentrations, the product CSD became uni-modal with the same mean mass size for both cooling modes, where the crystallization was dominated by seed growth. The low supersaturation caused by the growth of enough seeds plays a key role to produce uni-modal size distribution with suppressed nucleation. Adhering of small crystals (secondary nuclei) to growing seed crystals is also considered to be another mechanism for generating uni-modal CSD.     

氯化钾间歇冷却结晶生长规律及粒度控制实验研究

采用聚焦光束反射测量技术（FBRM）考察了氯化钾（KCl）间歇冷却结晶过程中晶体成核和生长规律,重点研究了降温速率对KCl水溶液冷却时产生过饱和度的影响,以及添加晶种的相关条件（如晶种粒径和添加量等因素）与KCl晶体产品粒度的关系。同时,采用直接冷却刺激起晶产生“晶种”,并控制其生长达到控制晶体产品粒度的目的。结果表明,在添加晶种条件下,程序降温过程产生的低过饱和度不易引起爆发成核,且晶种的添加量决定着晶体产品的平均粒度与理想生长模型的偏差。另外,降温速率是冷却刺激起晶产生“晶种”粒径的关键因素。     

膜辅助添加晶种的过硫酸铵冷却结晶在线监测与过程调控

冷却结晶是经典的溶液结晶过程,常用于分离溶解度随温度变化较大的物质,制备高品质晶体产品。直接进行降温会导致成核速率不可控,得到的晶体产品质量差。在工业中通常选择在溶液结晶介稳区内投放适量晶种来诱导成核,但晶种制备过程复杂,而且成功的添加晶种过程取决于晶种的粒度分布、数量、投放时机和操作人员的经验等因素,降低了产品质量的批次重复性。本文利用聚四氟乙烯（PTFE）中空纤维膜组件为结晶溶液和冷却液提供换热界面,结晶溶液温度降低,在膜界面处形成较均匀的过冷度梯度,进而在低过饱和度下发生异相成核,实现膜辅助添加晶种的过硫酸铵冷却结晶过程调控。膜组件中产生的晶种进入结晶釜中继续生长,将成核和生长过程进行解耦。在线结晶检测系统捕捉到的照片证实了通过控制膜组件使用温度和时长两个操作参数便可得到具有较好的形貌、较窄的粒度分布的晶种。相比直接冷却结晶,在相近的降温速率下,膜辅助添加晶种过程制备的晶体产品具有更大的平均粒径,且粒度分布更集中,表面更加光滑。因此,膜辅助冷却结晶呈现了良好的成核控制能力,有望实现晶种自动制备和添加功能,为高附加值晶体产品的冷却结晶过程开发提供了新方向。     

Modeling batch crystallization processes: Assumption verification and improvement of the parameter estimation quality through empirical experiment design

In this work, experimental data of different batches was used for estimation of the kinetic parameters for the secondary nucleation framework of Gahn and Mersmann [Gahn, C. and Mersmann, A., 1999. Brittle fracture in crystallization processes. Chem. Eng. Sci. 54, 1273–1292].An empirical experiment design procedure was used to design an informative batch experiment through optimization of the seed quality, size and mass and process conditions at seeding. The parameters estimated using the data of the designed experiment showed smaller magnitudes of the confidence ellipsoids and standard deviations as compared to those obtained by using the data of conventional (un)seeded batch experiments. It was shown that the designed experiment allowed reducing uncertainty in the initial conditions, namely, the mass and crystal size distribution of the initial population of crystals and the initial supersaturation.It was also demonstrated that the main reason for the model/process mismatch was the origin of nuclei. Dynamic experimental data could be described better if the state of the crystals forming the crystallization system corresponded to the assumptions of the used kinetic model. Differences in the crystal surface properties, shape, and strain content could be responsible for a divergent nucleation and growth behavior in batches that were initiated either by primary nucleation, seeding with small ground seeds or seeding with coarse crystals from the product of the previous batch.     

硫酸镍间歇结晶过程的工艺优化

文章采用聚焦光束反射测量仪(FBRM)研究了硫酸镍间歇结晶过程晶体的成核和生长规律,考察了搅拌桨形式、降温方式、搅拌速率、晶种添加量和晶种粒度对结晶过程中结晶动力学的影响。结晶工艺条件优化后,得到了粒径大、晶型好、分布均匀的晶体产品,为硫酸镍间歇结晶过程的工艺优化和工业放大提供了依据。     

Towards predictive simulation of single feed semibatch reaction crystallization

A population balance model is developed over single-feed semi-batch reaction crystallization of benzoic acid. The model is evaluated by comparison with experimental data, and simulations are carried out to advance the understanding of the process. The model accounts for chemical reaction, micro and mesomixing, primary nucleation, crystal growth and growth rate dispersion (GRD). Two mechanistic mixing models are evaluated: the segregated feed model and the engulfment model (E-model) with mesomixing. When the mixing is described by the E-model (engulfment model) and GRD is accounted for, the model quite well captures the influence of reactant concentrations, agitation rate, feed point location, feed pipe diameter, total feeding time and crystallizer volume, on the product weight mean size. When using the SF-model (segregated feed model) the results are less satisfactory. The kinetics of nucleation and crystal growth have a great impact on the results of the simulations, influencing the product weight mean size as well as the response to changes in the processing conditions. A new set of kinetic data for benzoic acid derived from semi-batch experimental results are presented.     

Stochastic simulation for morphological development during the isothermal crystallization of semicrystalline polymers: A case study of syndiotactic polypropylene

A stochastic simulation scheme for predicting morphological development during nucleation and subsequent crystal growth based on predetermined crystallization kinetic data of a semicrystalline polymer under quiescent isothermal conditions is proposed. Based on previously obtained crystallization kinetic data for syndiotactic polypropylene (s‐PP) used as the input information, the simulation scheme was successful in predicting the morphological development of s‐PP during isothermal crystallization from the melt state. The predicted development of crystallinity during crystallization was reanalyzed with the Avrami macrokinetic model, and good agreement between the predicted and theoretical values for s‐PP was observed. On the basis of this simulation scheme, both the spherulite size and its distribution during the course of crystallization could also be predicted. Although the spherulitic growth rate influenced both the spherulite size and its distribution during the course of crystallization, it had no effect on the final spherulitic morphology or the resulting average spherulitic size. © 2008 Wiley Periodicals, Inc. J Appl Polym Sci, 2009     

Kinetics of nucleation and growth of L-sorbose crystals in a continuous MSMPR crystallizer with draft tube: Size-independent growth model approach

The experimental data concerning kinetics of a continuous mass crystallization in L-sorbose - water system are presented and discussed. Influences of L-sorbose concentration in a feeding solution and mean residence time of suspension in a working volume of laboratory DT MSMPR crystallizer on the resulting crystal size distributions, thus on the nucleation and growth kinetics, were determined. The 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 investigated range of crystallizer productivity (220–2,200 kg of L-sorbose crystals m⁻³ h⁻¹), a crystal product of mean size Lm from 0.22 to 0.28 mm and CV from 68.8 to 44.0% was withdrawn. The values of linear growth rate show increasing trend (from 6.6·10⁻⁸ to 7.6·10⁻⁸ m s⁻¹) with the productivity enlargement (assuming constant residence time τ=900 s). Occurrence of secondary nucleation phenomena within the circulated suspension, resulting from the crystals attrition and breakage was observed. The parameter values in a design equation, matching linear growth rate and suspension density with nucleation rate were determined.     

Critical seed loading from nucleation kinetics

A method is presented for preparing critical seed loading diagrams for nonaggregating systems knowing only the nucleation kinetics. This is advantageous because it is much less time‐consuming than developing and solving a complete batch process model including solubility expressions and growth rate kinetics. Furthermore, there are many more reports available in the literature of nucleation kinetics alone than there are of complete batch crystallization process models, because expressions for the nucleation rate as a function of crystal growth rate can be rapidly determined from mixed‐suspension, mixed‐product‐removal (MSMPR) data without measuring the supersaturation. The results for 43 systems show that there is a great deal of variability in the critical seed loading, and a single correlation is inadequate to describe the relationship between critical seed loading and seed size. For a seed size of 10 µ, seed loading can effectively suppress nucleation in 92% of cases, while for seeds of size 50, 100, and 200 µ, seed loading can suppress nucleation in 74, 61, and 39% of cases, respectively. © 2014 American Institute of Chemical Engineers AIChE J, 60: 1645–1653, 2014     

Membrane assisted cooling crystallization: Process model,nucleation, metastable zone,and crystal size distribution

The membrane assisted cooling crystallization was proposed and investigated by the simulation and experiments. The developed process model concerned the supersaturation evolution on the membrane interface, the combined nucleation rate in the crystallizer. The impact of different membrane on reducing the nucleation barrier was investigated by introducing the metastable zone width theory. The influence of membrane distillation conditions on the crystal nucleation and growth kinetic was uncovered based on the simulation and experiments results. The experimental results indicated that membrane assisted cooling mode with optimized profiles did improve the crystal size distribution and crystal habit comparing with conventional cooling mode. Terminal coefficient of variation decreased from 55.4 to 33.9 under similar mean crystal growth rate, 2.27 × 10^?7 m s^?1 (conventional cooling) and 1.98 × 10^?7 m s^?1 (membrane assisted cooling). Finally, the brief summary on the advantages and key issues of this propose membrane assisted crystallization operation were concluded. © 2015 American Institute of Chemical Engineers AIChE J, 62: 829–841, 2016     

SEEDING EFFECT ON CRYSTAL GROWTH IN HYDROTHERMAL SYNTHESIS OF LAYERED OCTOSILICATE

In the hydrothermal synthesis process of layered octosilicate ilerite, seed crystals were added to the starting solution (water glass) for control of the crystallization rate. Octosilicate platelets of 4.4 μm and their ground products with a size less than 1 μm were used as the seed. The crystallization rate increased with an increase in the additional amount of platelet seed. The crystalline products were obtained even if the seed had a relatively low crystallinity. The size of products depended strongly on both the additional amount and size of seed. When the seed-loading mass ratio of seed to the starting solution was 0.01, the crystal growth was a maximum and the size of products was about twice of that of seed. However, in the use of the ground seed, a finer product was obtained at the optimum seed-loading mass ratio due to increase in the number of seed crystals. To control crystal growth for reducing synthesis time and for obtaining crystals of a specific size, both number and size of seed crystals must be optimized because the silanol groups on the edge of seed crystals added become new reaction sites of crystallization.     

Modeling and control of protein crystal shape and size in batch crystallization

In this work, the modeling and control of a batch crystallization process used to produce tetragonal hen egg white lysozyme crystals are studied. Two processes are considered, crystal nucleation and growth. Crystal nucleation rates are obtained from previous experiments. The growth of each crystal progresses via kinetic Monte Carlo simulations comprising of adsorption, desorption, and migration on the (110) and (101) faces. The expressions of the rate equations are similar to Durbin and Feher. To control the nucleation and growth of the protein crystals and produce a crystal population with desired shape and size, a model predictive control (MPC) strategy is implemented. Specifically, the steady‐state growth rates for the (110) and (101) faces are computed and their ratio is expressed in terms of the temperature and protein concentration via a nonlinear algebraic equation. The MPC method is shown to successfully regulate both the crystal size and shape distributions to different set‐point values. © 2013 American Institute of Chemical Engineers AIChE J, 59: 2317–2327, 2013     

Impeller geometry effect on crystallization kinetics of borax decahydrate in a batch cooling crystallizer

The effects of impeller type and diameter in a batch cooling crystallizer on the nucleation and crystal growth kinetics as well as on the shape and size distribution of borax decahydrate crystals were investigated. Two different types of impellers of various sizes were applied. Chosen impeller configurations generate completely different fluid flow patterns in the crystallizer what allows to investigate the influence of the axial and radial flow on the kinetic parameters as well. The nucleation in crystallizer was taking place by the heterogeneous nucleation mechanism at all mixing conditions. The number of crystals formed by this mechanism increases as ratio D/d_T decreases and it is higher when an axial flow pattern in crystallizer has been developed. The crystal growth rate increases with increasing the impeller size in observed supersaturation range. The radial impeller defined by ratio D₂/d_T = 0.58 could be considered as viable option for growth of borax crystal, since the further enlargement of this ratio does not increase growth rate and can only cause higher power consumption. The maxima in the coarser and finer fractions of CSD indicate a different influence of mixing conditions on the crystal grow and secondary nucleation. An axial flow pattern in crystallizer favors agglomeration of growing crystals increasing that way product mean crystal size, while radial flow results with more regular shape of borax crystals.     

CRYSTALLIZATION KINETICS AND PRODUCT PURITY OF α-GLUTAMIC ACID CRYSTAL

A continuous mixed-suspension mixed-product removal lpar;CMSMPR) crystallizer was used to study the crystallization kinetics and product purity of glutamic acid crystal in pure solution and impure solution with L-phenylanaline as the impurity. Under the assumption that the crystal growth rate was a function of crystal size, the population balance equation was solved to give the crystal growth and nucleation rates by use of the steady-state population density data. The crystal growth and nucleation rates were suppressed by the presence of impurity. The impurity contents in the crystal products, which were analyzed by a HPLC pre-column method, were found to be related to crystal size, supersaturation, and impurity concentration of solution     

青霉素亚砜结晶生长与成核动力学

利用Mydlarz 和 Jones 模型（MJ2）,对乙酸丁酯中青霉素亚砜的成核与生长动力学进行研究。通过矩量法对MJ2模型进行处理后,利用晶体产品的粒度分布计算得到青霉素亚砜的生长速率与成核速率,然后利用最小二乘法拟合回归求解出成核与生长动力学方程参数。通过实验设计考察了过饱和度、温度与搅拌速度对青霉素亚砜晶体成核和生长过程的影响。研究表明青霉素亚砜晶体生长速率随过饱和度比的增加呈现指数型增长,确定青霉素亚砜晶体生长属于晶体表面生长控制过程。由于高速搅拌会增加青霉素亚砜晶体的破碎,促进了二次成核过程,随着搅拌速度的增加,晶体生长速率出现小幅下滑,而成核速率则明显升高。青霉素亚砜成核与生长动力学研究将有助于工业生产过程优化。     

On the use of process analytical technologies and population balance equations for the estimation of crystallization kinetics. A case study

The batch cooling solution crystallization of ammonium oxalate was performed in water at various constant cooling rates. Measurements of the solute concentration were obtained using in situ attenuated total reflectance fourier transform infrared (ATR‐FTIR) spectroscopy, and final estimates of the crystal size distribution (CSD) were computed; thanks to in situ image acquisition and off‐line image analysis. The crystallization process was then simulated using population balance equations (PBEs). Estimates of the nucleation and the growth parameters were computed through model/experiments fitting. According to the cooling rate, the PBE model allowed distinguishing between two distinct crystallization regimes, separated by an “intermediate regime.” The respective contributions and shortcomings of solute concentration measurements and granulometric data to the identification of nucleation and growth kinetic parameters are analyzed and discussed. It is shown in particular that no real separate estimation of nucleation and growth parameters can be obtained in the absence of CSD data. © 2011 American Institute of Chemical Engineers AIChE J, 2012     

Crystal Growth in Drowning‐Out Crystallization using a T‐Mixer

The kinetics of nucleation and crystal growth in drowning‐out crystallization using a T‐mixer were estimated using crystal size distribution, taking into account a size‐independent growth. At the conditions of the feed compositions investigated, the product weight mean size changed from 7–29 μm when the residence time varied between 0.32 and 0.61 s. Nucleation and growth rates were expressed simply as a function of the residence time. The T‐mixer can be used to generate high levels of supersaturation due to inducing micro‐mixing effects. The particle size correlated well with the ratio of growth rate to nucleation rate. Finally, the particle size obtained in drowning‐out crystallization using a T‐mixer was found to be proportional to the 1.69^th power function of the residence time.     

氯氧化铋反应结晶动力学研究

在铋盐水解制备氯氧化铋的反应结晶过程中,控制氯氧化铋晶体成核和生长速率可影响氯氧化铋晶体的形貌、粒径和分散性。为此,选用间歇动态法研究了氯氧化铋晶体成核与生长动力学,采用矩量变换法建立了结晶过程动力学模型,并用最小二乘法对实验数据进行多元线性回归,获取了动力学模型参数。研究结果表明：当氯氧化铋晶体粒度≥3 μm时,其晶体生长速率符合粒度无关生长模型;晶浆悬浮密度和过饱和度对成核速率均有显著影响;溶液过饱和度对成核速率的影响较生长速率的影响更为显著。