On the use of process analytical technologies and population balance equations for the estimation of crystallization kinetics. A case study (original) (raw)
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Crystal Growth & Design, 2013
When compared to 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 cancelled. 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 thanks to 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 Kubota-Mullin impurity adsorption model. The experimental thresholds are confronted to the solubility drifts resulting from the
Reactive Crystallization of Calcium Oxalate: Population Balance Modeling
Chemical and Biochemical Engineering Quarterly, 2018
Reactive crystallization of calcium oxalate has been studied to determine particle size distribution for calcium oxalate precipitation using population balance model with method of moments. The model is formulated and tested for single feed semi-batch reactive crystallization of calcium oxalate with reactants calcium chloride and sodium oxalate with literature data. The simulated results include local supersaturation distribution, number of particle distribution, mass of particle crystallized, particle size, nucleation and growth rate during the process. The model results are in good agreement with available experimental data from literature.
International Journal of Chemical Reactor Engineering, 2008
The batch cooling crystallization of an industrial active pharmaceutical ingredient that exhibits a needle-like habit was investigated. A model of the time variations of key physical properties of particles (crystal size distribution CSD and specific area) was designed using an approach based on the simple population balance equation. The experiments were monitored thanks to three in-situ process analytical sensors (Mid-IR spectroscopy, in-situ microscopy and laser backscattering). Primary and secondary surface nucleation mechanisms as well as growth of the main crystal dimension (length) were described resulting in a six parameter model. The model roughly represents the effects of different cooling strategies on the supersaturation profile, the CSD and the specific area of the final particles. First, a very weak primary nucleation occurs leading to an initial population of a few large crystals. A second population of crystals is generated afterwards through secondary nucleation mec...
Nonlinear kinetic parameter estimation for batch cooling seeded crystallization
Aiche Journal, 2004
Kinetic parameter estimation for most batch crystallization processes is necessary because nucleation and crystal growth kinetic parameters are often not available. The existing identification methods are generally based on simplified population balance models such as moment equations, which contain insufficient information on the crystal size distribution (CSD). To deal with these problems, a new optimization-based identification approach for general batch cooling seeded crystallization is proposed in this study. The final-time CSD is directly used for identification. A novel effective method for solving the population balance equation is developed and used to identify nucleation and growth kinetic parameters. Cooling crystallization of ammonium sulfate in water was experimentally investigated, where the concentration was measured by an on-line density meter and the final-time CSD was analyzed by a Malvern Mastersizer 2000. Kinetics for ammonium sulfate are determined based on cooling crystallization experiments. Applying these kinetics in simulation provides a good prediction of the product CSD. © 2004 American Institute of Chemical Engineers AIChE J, 50: 1786–1794, 2004
Calcium oxalate crystallization kinetics from calorimetric measurements
Thermochimica Acta, 1997
The kinetics of calcium oxalate monohydrate precipitation effected by mixing aqueous solutions of calcium chloride and sodium oxalate together in the stoichiometric ratio at 25 and 37°C, were studied using an isoperibolic reaction twin calorimeter. A method for inferring the crystal growth kinetic parameters from experimental progress curve giving the time development of the integral heat evolved during the precipitation is suggested and verified. Results obtained for calcium oxalate monohydrate compare favourably with those obtained with conventional techniques for studying crystallization. ',C 1997 Elsevier Science B.V.
Crystal Research and Technology, 2007
The results of an in situ investigation of the effect of four different bi-and trivalent cations (Fe(III), Cu(II), Mn(II) and Cr(III)) on the displacement velocity of individual growth steps on the (110) face of ammonium oxalate monohydrate crystals as a function of supersaturation are described and discussed. It was observed that: (1) at a particular temperature of pure solutions and solutions containing impurities, the velocity v of movement of the [110] growth steps is always greater than that of the [111] steps, (2) fluctuations in the velocity of individual growth steps occur in all solutions containing similar concentrations of different impurities, (3) the value of kinetic coefficient β for growth steps decreases with an increase in the concentration c i of Cu(II) impurity, but that for dissolution steps does not depend on c i ; moreover, the value of kinetic coefficient β for growth steps is higher than that of dissolution steps, and (4) in the presence of Mn(II) and Cr(III) impurities, the kinetic coefficient β for dissolution steps is several times greater than that for growth steps. The results are explained from the standpoint of Kubota-Mullin model of adsorption of impurities at kinks in the steps and the stability of dominating complexes present in solutions. Analysis of the results revealed that: (1) the effectiveness of different impurities in inhibiting growth increases in the order: Fe(III), Cu(II), Mn(II), and Cr(III), and this behavior is directly connected with the stability and chemical constitution of dominating complexes in saturated solutions, (2) fluctuations in the velocity of growth steps is associated with the effectiveness of an impurity for adsorption; the stronger the adsorption of an impurity, the higher is the fluctuation in step velocity v, and (3) depending on the nature of the impurity, the kinetic coefficient for the dissolution steps can remain unchanged or can be higher than that of the growth steps.
Analysis of crystallization kinetics
Materials Science and Engineering: A, 1997
A realistic computer model for polymorphic crystallization (i.e., initial and final phases with identical compositions), which includes time-dependent nucleation and cluster-size-dependent growth rates, is developed and tested by fits to experimental data. Model calculations are used to assess the validity of two of the more common approaches for the analysis of crystallization data. The effects of particle size on transformation kinetics, important for the crystallization of many systems of limited dimension including thin films, fine powders, and nanoparticles, are examined.