A method of characteristics for solving population balance equations (PBE) describing the adsorption of impurities during crystallization processes

International audiencePossible hindering effects of impurities on the crystal growth were shown to take place because of the adsorption of impurity species on the crystal surface. Transient features of this adsorption were observed, such that the growth of a given crystal does not depend on supersaturation only, but also on the time a given particle spent in contact with impurities present in the mother liquor. Meanwhile, few kinetic models describe the effect of impurities on the growth of crystals in solution, and published models are usually derived from data obtained, thanks to specific experiments based on the evaluation of the growth rate of single crystals. Such models are obviously questionable because, in the industrial practice, distributed properties of crystals are actually involved. Considering the “time of contamination” of particles as a new internal variable is thus made necessary. This is the reason why a specific PBE resolution algorithm is presented in this paper. The numerical scheme for the resolution of PBEs is based on the method of characteristics and shown to allow fast and accurate simulation of transient features of the crystal size distribution in the particular case when the growth or nucleation rates are assumed to exhibit unsteady-state dynamics. The algorithm is finally used to simulate the isothermal desupersaturation crystallization of citric acid in water

Acoustic Emission: a new in-line and non-intrusive sensor for monitoring batch solution crystallization operations

International audienceAcoustic emission (AE) is shown to provide complex and in-depth information on both the liquid and the dispersed phases during batch cooling solution crystallization processes. Despite its complexity, such information might be highly valuable for process monitoring and control purposes owing to its non-intrusive features, its relative cheapness, and the very wide scope of its potential applications. Basic crystallization phenomena such as the onset of nucleation and the development of crystal growth, several key-process variables like the concentration of solid in suspension, and overall data describing the average particle size and the content in impurities of the crystallization medium are evaluated from real experimental data obtained at the lab-scale. AE is not claimed here to allow replacing "usual" particle sizes sensing technologies like image analysis or FBRM; it is rather suggested that the large amount of information contained in the acoustic data is quite interesting and deserves further investigation

PAT monitoring and PBE modelling of batch cooling solution crystallization in the presence of impurities

International audienceHindering effects of impurities on the crystal growth are usually assumed to result of the adsorption of impurity species on the crystal surface. In the presence of impurities the growth rate does not depend on supersaturation only, but also on the concentration of impurities and on the time a given particle spent in contact with inhibiting species (unsteady-state adsorption mechanisms). Few kinetic models describe such phenomena. Moreover, published models are derived from data obtained from specific experiments performed on singles crystals, which makes their application to real industrial crystallizers rather questionable. Indeed, for process engineering purposes, the available kinetic inhibition models accounting for the effect of impurities (e.g. Cabrera-Vermilyea or Kubota-Mullin's approaches), have to be evaluated in industrial situations where complex and distributed features of the crystallizing suspensions are involved (e.g. during batch solution crystallization). Population Balance Equations (PBE) modelling offers an invaluable simulation tool for such evaluation. With this aim in view, a comprehensive modelling approach based on in situ continuous and dispersed phase measurements, and specific PBE simulation was developed to represent and better understand the effect of impurities on the development of batch crystallization processes. The cooling solution crystallization of Ammonium Oxalate (AO) in water in the presence of various concentration of Nickel Sulphate was selected as a model system during this study. In situ measurements of supersaturation were performed using ATRFTIR spectroscopy and the CSD was assessed thanks to in situ image acquisition followed by off-line image processing. The experimental results were simulated after estimating crystallization kinetic parameters, including parameters of models describing the inhibiting adsorption of impurity on the growing crystal surfaces. Nonlinear optimization techniques were used to fit the experimental data to the simulated ones

Batch cooling solution crystallization of ammonium oxalate in the presence of impurities: Study of solubility, supersaturation, and steady-state inhibition

International audienceCompared with equilibrium data in pure solvent, variations of solubility are frequently observed in the presence of dissolved impurities. It is also well-known that impurities can inhibit the crystallization processes and lead to supersaturation barriers below which the growth of crystals is canceled. However, many papers dealing with the inhibiting effects of impurities in solution crystallization are rather unclear about the appropriate way of expressing the supersaturation in impure media. Indeed, as suggested in the present work, the latter can be defined either with respect to the solubility in pure solvent or in reference to the solubility of the impure solvent. Setting the correct reference for computing supersaturation in impure solutions is obviously a key issue for understanding and modeling the dynamics of elementary crystallization phenomena (i.e., primary and secondary nucleation, crystal growth, etc.) The present case study aims at clarifying this point. Solubility data were acquired by in situ ATR FTIR measurements of the concentration of ammonium oxalate in pure water and in impure water containing various concentrations of nickel sulfate dissolved as impurity. Supersaturation thresholds were observed and analyzed, according to the theoretical framework of the Kubota-Mullin impurity adsorption model. The experimental thresholds are attributed to the solubility drifts resulting from the pollution of the pure solvent by impurities. Finally we propose that the impurity-dependent solubility should be considered as the appropriate reference for defining supersaturation

Etude de l'émission acoustique lors de la cristallisation d'acide citrique avec transition de phase

National audienceDu fait de son caractère non intrusif et non destructif, l'émission acoustique (EA) est une technique attractive pour le suivi de cristallisations, bien que les rares résultats publiés à ce jour ne soient pas très probants. L'émission acoustique est produite par les processus mécaniques locaux qui résultent de l'apparition ou de la disparition de la phase solide, et de son interaction avec son environnement. Elle se présente sous la forme d'un grand nombre de salves pseudopériodiques séparées ou continues. Les signaux acoustiques sont acquis par un capteur piezo-électrique externe et traités en temps réel par un système d'acquisition et de traitement qui calcule et enregistre des paramètres globaux caractéristiques des salves (nombre de coups, amplitude, fréquence, énergie ...) A partir de la cristallisation de l'acide citrique présentée ici, on montre que les paramètres caractéristiques des salves pendant la cristallisation peuvent être reliés aux différentes étapes élémentaires de la transition de l'anhydre vers le monohydrate. Une analyse en composante principale des variables caractéristiques des salves a été effectuée qui permet de repérer les différentes étapes du procédé

Modélisation de cristallisations discontinues en solution en l'absence et en présence d'impuretés.

National audienceThe batch solution cooling crystallization of ammonium oxalate (AO) was performed in pure water and in the presence of dissolved impurities (NiSO4). The solute concentration was measured using in situ ATR FTIR spectroscopy and the crystal size distribution was estimated from in situ image acquisition and processing, using an immersed video acquisition probe. The experimental supersaturation trajectories show that the development of the crystallization is significantly inhibited by the presence of impurity. Such impurity effects, which were widely investigated at the scale of one single mono-crystal, were neither observed nor described in the case of a whole set of dispersed crystallizing particles. After identification of the nucleation and growth kinetics of AO in pure medium, the inhibition parameters were determined according to Kubota-Mullin's model. A mechanism of unsteady-state adsorption of impurity species at the growing crystal surface was identified, which allowed to satisfactorily represent the experimental results. A dynamic simulation model was thus proposed and developed using Population Balance Equations (PBE), which were solved thanks to a numerical method of characteristics.La cristallisation discontinue en solution de l'oxalate d'ammonium (OA) dans l'eau, en présence et en l'absence d'impuretés (NiSO4), a été conduite par refroidissement. La mesure de concentration en soluté a été réalisée grâce à la spectroscopie ATR FTIR in situ et le suivi granulométrique par analyse d'images acquises à l'aide d'un capteur vidéo in situ. Les trajectoires de sursaturation en présence de sulfate de nickel montrent que la cristallisation est considérablement inhibée par la présence de l'impureté. Ces effets d'impuretés, largement étudiés dans la littérature à l'échelle d'un monocristal n'ont jamais été observés et décrits sur l'ensemble d'une population de cristaux en suspension. Après avoir identifié les cinétiques de nucléation et de croissance de l'OA en milieu pur, les paramètres d'inhibition sont déterminés sur la base du modèle de Kubota-Mullin. Un mécanisme transitoire d'adsorption de surface de l'impureté a été identifié, dont la simulation permet de rendre compte des résultats expérimentaux. Un modèle de simulation dynamique par les équations de bilans de populations (EBP) a été développé et résolu à l'aide d'un algorithme numérique fondé sur la méthode des caractéristiques

Monitoring solvent-mediated phase transitions using acoustic emission

National audienceDu fait de son caractère non intrusif et non destructif, l'émission acoustique (EA) est une technique attractive pour le suivi de cristallisations, bien que les rares résultats publiés à ce jour ne soient pas très probants. L'émission acoustique est produite par les processus mécaniques locaux qui résultent de l'apparition ou de la disparition de la phase solide, et de son interaction avec son environnement. Elle se présente sous la forme d'un grand nombre de salves pseudo-périodiques séparées ou continues. Les signaux acoustiques sont acquis par un capteur piézo-électrique externe et traités en temps réel par un système d'acquisition et de traitement qui calcule et enregistre des paramètres globaux caractéristiques des salves (nombre de coups, amplitude, fréquence, énergie ...) A partir de la cristallisation de l'acide citrique présentée ici, on montre que les paramètres caractéristiques des salves pendant la cristallisation peuvent être reliés aux différentes étapes élémentaires de la transition de l'anhydre vers le monohydrate. Une analyse en composante principale des variables caractéristiques des salves a été effectuée qui permet de repérer les différentes étapes du procédé

Mesure de la distribution de taille de cristaux aciculaires par analyse d'images d'une sonde video in situ

National audienceThe batch cooling crystallization of ammonium oxalate (AO) in water was investigated in order to design a dynamic model of the process in both pure and impure solvent. The solute concentration was measured using in situ ATR FTIR spectroscopy while the solid dispersed phase was monitored through in situ image acquisition, using an immersed CCD video probe. In order to evaluate the particle size distribution (PSD) an algorithm for the processing of video 2D images of AO crystals was developed. The algorithm is intended to enable reliable crystal size measurements; the specificity of the system under investigation being related to the acicular shape of AO crystals. In particular, a major difficulty arises from the many overlapping particles which have to be differentiated prior to their size measurement. After segmentation, the identification of particles was mostly based upon a refined method for the detection of corners followed by the reconstruction of the crystals perimeters. The efficiency of the method was evaluated through comparison between the automatic image processing measurements and measurements performed by a trained human operator. More than 80% of AO particles are satisfactorily detected in suspension, even fuzzy crystals, provided that their corners are unbroken.La cristallisation discontinue d'oxalate d'ammonium (OA) a été étudiée en vue de la mise au point d'un modèle dynamique du procédé en solvant pur ou contaminé par des impuretés dissoutes. La concentration en soluté a été mesurée par spectroscopie ATR FTIR in situ, tandis que la phase solide dispersée était suivie par une sonde vidéo CCD immergée permettant l'acquisition d'images. En vue d'évaluer la distribution des tailles de particules (DTP), un algorithme de traitement des images vidéo bidimensionnelles des cristaux d'OA a été mis au point. Cet algorithme vise à assurer une mesure fiable de la taille des cristaux ; la spécificité du système étudié ici étant essentiellement liée à la forme aciculaire des cristaux. En particulier, une difficulté majeure du traitement provient du grand nombre de particules superposées qui doivent être différenciées avant la mesure de leur taille. Après segmentation, l'identification des particules a été essentiellement basée sur une technique de détection des coins, permettant ensuite une reconstruction du périmètre des cristaux. L'efficacité de la méthode a ensuite été évaluée par comparaison du traitement automatique avec celui effectué manuellement par un opérateur humain. Plus de 80% des particules d'OA en suspension ont été évaluées de façon satisfaisante, même les cristaux présentant une image floue on été identifiés, à condition que leurs coins soient intacts

Solubility prediction of weak electrolyte mixtures

International audienceThe solubility of materials is a thermodynamic variable that depends on their chemical composition and with temperature. Solubility is also affected by the pH, by the presence of additional species in the solution, and by the use of different solvents. On electrolyte, the calculation of solubility requires that the mean ionic activity coefficient be known along with a thermodynamic solubility product