Industrial batch crystallization of a plate-like organic product. In situ monitoring and 2D-CSD modelling: Part 1: Experimental study

Experimental results obtained during the batch cooling solution crystallization of a fine organic compound in aqueous ethanol solvent are presented. The process monitoring was ensured through in-line, in situ ATR FTIR spectroscopy, providing continuous solute concentration estimates. Off-line image analysis was also performed to yield discrete-time measurements of the 2D-crystal size distribution (CSD) of the platelet-like particles. The decisive effect of secondary nucleation on both the course of supersaturation and CSD was highlighted through the qualitative analysis of selected batch runs, particular attention being focused on the seeds size and weight. At least two nucleation mechanisms allow explaining the experimental results: the introduction of seeds causes a significant burst of surface nucleation and the continuation of the cooling process, through the generation of continuous supersaturation, allows activated secondary nucleation to take place.     

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。     

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.     

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。     

A study on crystallization kinetics of pentaerythritol in a batch cooling crystallizer

The crystallization kinetics of pentaerythritol (PeE) in aqueous solution in the presence of impurity or not in a batch cooling crystallizer was explored. Also, the solubility and the nucleation and crystal growth kinetics of PeE in aqueous solution were investigated. A second-order dependence of PeE growth rate on supersaturation is observed in pure PeE-water system. The crystal growth rate of PeE-water system in the presence of impurity is proportional to the supersaturation to the 3.5 power. The nucleation and crystal growth behaviors for PeE-water system in a batch cooling crystallizer were grasped according to Mersmann's criteria. The nucleation in this crystallizer was found to act with heterogeneous nucleation. In this system, it suggests that the crystal growth is controlled by a complex mechanism behavior of surface integrated and diffusion limited. Simplified relation was derived for calculation of mean crystal size of product crystals from the batch cooling crystallizer. The obtained relation was verified by a set of experiments.     

基于PBM的L-谷氨酸粒度分布控制优化

针对β型L-谷氨酸冷却结晶过程,为获取期望粒度分布,采用特征曲线法（MOCH）来建立关于粒度相关生长率的种群平衡方程（PBE）,然后通过对种群平衡模型（PBM）参数辨识后确定最优过饱和度及控温曲线。由于辨识模型参数的目标函数具有非线性和非凸型性,因而采用少量经济性的批量冷却结晶实验,结合图像分析晶种和产品粒度分布得到的统计数据,拟合模型参数。根据实际要求的结晶过程时间,为达到目标粒度分布,通过优化结晶过程的过饱和度获得最优调温曲线,实现基于恒定过饱和度的晶体生长过程优化控制。实验结果表明通过优化的控温曲线,实现了基于最优过饱和度控制的期望目标粒度分布。     

Simulation of batch crystallization

The closed mathematical model of a well-mixed batch crystallizer has been presented. This model takes into consideration crystals growth rate fluctuations producing an increased spread of crystal sizes. The numerical methods for solving partial integro-differential system of this model equations are proposed for the cases of when growth rate is expressible as product of supersaturation and size functions.Simultaneous population and mass balance equations have been calculated together with power law kinetics of nucleation and growth to determine crystal-size distribution functions (CSD), variation coefficients (CV), produced crystal sizes and numbers. The case of size-dependent crystal growth determined by sequential processes of diffusion and surface reaction is also investigated.The computer results are presented in the dimensionless form as functions on both diffusion and fluctuation Peclet numbers and dimensionless cooling rate. In particular, it has been established that the CV of weight CSD increases approximately twice due to fluctuations and becomes close to 40%; the CV also increases owing to the decrease of cooling rate and approaches 28%. Some formulae are suggested for predicting the kinetics of crystallization (or precipitation) and determining the kinetic parameters of crystals growth and nucleation.     

Seeded Induction Period and Secondary Nucleation of Lithium Carbonate

Seeded nucleation of lithium carbonate in aqueous solution during reactive crystallization was monitored by FBRM (focused beam reflectance measurement) and PVM (particle video microscope). The impacts of operating variables, such as seed size and loading, stirring speed, on induction period and secondary nucleation were investigated and explained by an adsorption model. The results show that seed surface area plays an important role in secondary nucleation, for more surface area has higher adsorption capacity and consumes more supersaturation on seed growth, thus restrains nucleation better. A method through comparison between pure breakage/attrition and nucleation process was put forward to distinguish attrition-induced and surface-induced nucleations quantitatively, which can reveal the contributions of different nucleation mechanisms. The nucleation processes in different conditions were studied, the principles and valuable experimental data were obtained for seeding approach primarily. FBRM and PVM are useful on-line apparatuses to facilitate seed selection and seeding optimization.     

Transition from nucleation and growth to Ostwald ripening

Condensation phase transitions from metastable fluids occur by nucleation with accompanying cluster growth and eventual Ostwald ripening. In closed batch systems the supersaturation declines as clusters nucleate and grow, causing an increase in the stable critical nucleus size. During ripening the subcritical clusters are considered to dissolve spontaneously, so that their mass is released to contribute to further growth of remaining clusters. A model based on the dynamics of cluster size distributions (CSDs) represents this sequence of phenomena in terms of four-dimensionless parameters: initial supersaturation, power on the cluster-mass expression for the growth rate coefficient, and parameters for nucleation rate and Gibbs-Thomson effect. A numerical solution of the scaled governing equations for CSD and supersaturation shows the transition from nucleation and growth to ripening, which can occur over a relatively long time period, thus separating the stages. The asymptotic ripening stage shows a power law increase in average cluster mass as the CSD evolves to (minimum) polydispersity index of unity.     

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     

Crystallization and precipitation

This paper deals with the design and operation of cooling and evaporation crystallizers and precipitators for reaction crystallization. It will be shown that the median crystal size, L₅₀, of a crystalline product and the crystal size distribution (CSD) mainly depend on the crystallization kinetics, e.g. the rates of nucleation and crystal growth, and that these kinetics are controlled by supersaturation. Therefore, the main objective in crystallization and precipitation is to choose and to maintain the optimal supersaturation with respect to product quality at all times and all locations in the crystallizer or precipitator.     

Determination of Nucleation and Crystal Growth Kinetics in Hostile Environment – Application to the Tetravalent Uranium Oxalate U(C2O4)2. 6H2O

A specific apparatus and an original batch method are developed for, respectively, nucleation and crystal growth rate measurements in a hostile environment, such as glove box. Primary nucleation and crystal growth kinetic rates for uranium oxalate are measured over a wide range of temperatures and solution concentrations. The nucleation rate obeys the Volmer‐Weber equation, with activation energies of 182 kJ.mol^?1 for the homogeneous nucleation and 102 kJ.mol^?1 for the heterogeneous one. The crystal growth rate is first order with respect to the supersaturation and controlled by a surface integration mechanism, characterized by a 29 kJ.mol^?1 activation energy.     

The critical conditions for secondary nucleation of silica colloids in a batch Stöber growth process

In this work, we determined experimentally the critical total surface area of silica seeds in the solution to avoid the formation of new particles (i.e. secondary nucleation) in a batch Stöber growth process. This critical surface area corresponded to the balance between the generation rate of reaction intermediate from the hydrolysis of TEOS and its consumption rate via the growth of existing seeds. Further calculation showed that the secondary nucleation was probably related to the average distance between seed particles. When the distance between seeds exceeded a critical value for each growth condition, i.e. for each generation rate, one would then observe secondary nucleation. Otherwise, simple growth was observed. Higher generation rate corresponded to shorter distance.     

A simplified approach to the operation of a batch crystallizer

A 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.     

Alumina trihydrate crystallization. Part 1. Secondary nucleation and growth rate kinetics

The kinetics of crystallization of alumina trihydroxide (hydrargillite) from caustic aluminate solutions of industrial composition (second stage BAYER process) were studied in a laboratory batch isothermal crystallizer. The yield and crystal size distribution of precipitate with time were obtained by varying the initial seed concentration. In this paper, the mass balance was used to determine nucleation and growth rate kinetics. First, from among the laws available in the literature, those which applied to alumina trihydrate crystallization were defined (model A). Kinetic constants of this model were calculated from experimental results. Then, a model based on a secondary nucleation mechanism was proposed (model B) that fits experimental data, and explains the induction periods found in the decomposition of aluminate solutions, even when seeds are present.     

KNO3-H2O溶液间歇结晶动力学

基于ΔL定律推导了晶体线性生长速率的数学表达式，利用已建立的溶液间歇结晶动力学实验研究手段实现了溶液透光率和浓度的在线测量.利用经验模型关联线性生长速率和相对过饱和度求取了生长动力学参数，并与文献值进行了比较.结果发现：对于自发成核结晶过程，综合动态透光率、过饱和度和经验模型可对成核和生长阶段进行定性识别.     

Attrition and secondary nucleation in crystallizers

The mean crystal size of coarse crystalline products is determined by secondary nucleation and crystal growth. Secondary unclei are mainly produced by contacts of crystals with parts of the crystallizer or with other crystals. As a consequence, attrition effects are very important. In this paper, a model is proposed in order to calculate the attrition rate of crystals, depending on the physical properties of the crystalline product, the geometry of the crystallizer and on the operating conditions such as the stirrer speed or the suspension density. The effective rate of secondary nucleation can be expressed in terms of the attrition rate by introducing effective values for number and size of attrition particles. Finally, a scale-up criterion based on this model is derived. This criterion allows to predict effective rates of secondary nucleation and mean crystal sizes if data obtained in a laboratory crystallizer are available.     

KNO3-H2O溶液间歇结晶动力学

基于ΔL定律推导了晶体线性生长速率的数学表达式,利用已建立的溶液间歇结晶动力学实验研究手段实现了溶液透光率和浓度的在线测量.利用经验模型关联线性生长速率和相对过饱和度求取了生长动力学参数,并与文献值进行了比较.结果发现：对于自发成核结晶过程,综合动态透光率、过饱和度和经验模型可对成核和生长阶段进行定性识别.