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

[1]  R. Braatz,et al.  Solute concentration prediction using chemometrics and ATR-FTIR spectroscopy , 2001 .

[2]  D. L. Ma,et al.  Robust identification and control of batch processes , 2003, Comput. Chem. Eng..

[3]  Z. Nagy,et al.  Comparative performance of concentration and temperature controlled batch crystallizations , 2008 .

[4]  W. K. Burton,et al.  The growth of crystals and the equilibrium structure of their surfaces , 1951, Philosophical Transactions of the Royal Society of London. Series A, Mathematical and Physical Sciences.

[5]  J. Mullin,et al.  Interpretation of crystallization induction periods , 1988 .

[6]  Herman J. M. Kramer,et al.  Process Modeling of the Polymorphic Transformation of l-Glutamic Acid , 2004 .

[7]  D. Verdoes,et al.  Determination of nucleation and growth rates from induction times in seeded and unseeded precipitation of calcium carbonate , 1992 .

[8]  ScienceDirect.  Progress in crystal growth and characterization of materials , 1990 .

[9]  J. Nývlt.  Nucleation and growth rate in mass crystallization , 1984 .

[10]  Hans Leuenberger,et al.  Pharmaceutical powder technology — from art to science: the challenge of the FDA's Process Analytical Technology initiative , 2005 .

[11]  Lawrence X. Yu,et al.  Applications of process analytical technology to crystallization processes. , 2004, Advanced drug delivery reviews.

[12]  Jukka Rantanen,et al.  IR spectroscopy together with multivariate data analysis as a process analytical tool for in-line monitoring of crystallization process and solid-state analysis of crystalline product. , 2005, Journal of pharmaceutical and biomedical analysis.

[13]  M. Mazzotti,et al.  In Situ Monitoring and Modeling of the Solvent-Mediated Polymorphic Transformation of l-Glutamic Acid , 2006 .

[14]  D. L. Ma,et al.  Optimal model-based experimental design in batch crystallization , 2000 .

[15]  G. Févotte.  New perspectives for the on-line monitoring of pharmaceutical crystallization processes using in situ infrared spectroscopy. , 2002, International journal of pharmaceutics.

[16]  A. Mersmann,et al.  Estimation of metastable zone width in different nucleation processes , 2001 .

[17]  Study of growth kinetics of ammonium oxalate monohydrate crystals from aqueous solutions , 1994 .

[18]  F. Puel,et al.  On-line ATR FTIR measurement of supersaturation during solution crystallization processes. Calibration and applications on three solute/solvent systems , 2001 .

[19]  Effect of Cu(II) ions on the growth of ammonium oxalate monohydrate crystals from aqueous solutions: growth kinetics, segregation coefficient and characterisation of incorporation sites , 2000 .

[20]  A. Seidel-Morgenstern,et al.  Numerical solutions of population balance models in preferential crystallization , 2008 .

[21]  Heiko Briesen,et al.  Simulation of crystal size and shape by means of a reduced two-dimensional population balance model , 2006 .

[22]  Jean-Charles Pinoli,et al.  Novel image analysis method for in situ monitoring the particle size distribution of batch crystallization processes , 2010, J. Electronic Imaging.

[23]  H. Wu,et al.  Quality-by-Design (QbD): An integrated process analytical technology (PAT) approach for a dynamic pharmaceutical co-precipitation process characterization and process design space development. , 2011, International journal of pharmaceutics.

[24]  Peter J. Jansens,et al.  Two-dimensional population balance model with breakage of high aspect ratio crystals for batch crystallization , 2008 .

[25]  Nick Hallas,et al.  Crystallization and Precipitation , 1988 .

[26]  A. Chernov.  Notes on interface growth kinetics 50 years after Burton, Cabrera and Frank , 2004 .

[27]  J. Garside,et al.  Direct observation of secondary nuclei production , 1978 .

[28]  M. Mazzotti,et al.  Effect of temperature on the nucleation kinetics of α L-glutamic acid , 2009 .

[29]  Debasis Sarkar,et al.  In situ particle size estimation for crystallization processes by multivariate image analysis , 2009 .

[30]  Ying Zhou,et al.  Critical evaluation of image processing approaches for real-time crystal size measurements , 2009, Comput. Chem. Eng..

[31]  Doraiswami Ramkrishna,et al.  Population Balances: Theory and Applications to Particulate Systems in Engineering , 2000 .

[32]  Marco Mazzotti,et al.  Monitoring the particle size and shape in the crystallization of paracetamol from water , 2010 .

[33]  Zoltan K. Nagy,et al.  Simultaneous Quadrature Method of Moments for the Solution of Population Balance Equations, Using a Differential Algebraic Equation Framework , 2009 .

[34]  Zoltan K. Nagy,et al.  Optimal seed recipe design for crystal size distribution control for batch cooling crystallisation processes , 2010 .

[35]  K. Sangwal,et al.  Effect of Cr(III) ions on the growth kinetics of ammonium oxalate monohydrate crystals from aqueous solutions , 2001 .

[36]  Zoltan K. Nagy,et al.  Model based robust control approach for batch crystallization product design , 2009, Comput. Chem. Eng..

[37]  Reginald B. H. Tan,et al.  Recent Advances in Crystallization control: An Industrial Perspective , 2007 .

[38]  Keshra Sangwal,et al.  Additives and Crystallization Processes , 2007 .

[39]  K. Sangwal.  Kinetic effects of impurities on the growth of single crystals from solutions , 1999 .

[40]  D. Verdoes,et al.  Induction time and metastability limit in new phase formation , 1991 .

[41]  François Févotte,et al.  A method of characteristics for solving population balance equations (PBE) describing the adsorption of impurities during crystallization processes , 2010 .

[42]  François Puel,et al.  Industrial batch crystallization of a plate-like organic product. In situ monitoring and 2D-CSD modelling: Part 1: Experimental study , 2007 .

[43]  Marco Mazzotti,et al.  Measurement of 3D particle size distributions by stereoscopic imaging , 2010 .

[44]  Effect of Supersaturation and Temperature on the Growth Morphology of Ammonium Oxalate Monohydrate Crystals Obtained from Aqueous Solutions , 1996 .

[45]  Marco Mazzotti,et al.  Monitoring size and shape during cooling crystallization of ascorbic acid , 2009 .

[46]  Z. Nagy,et al.  Determination of the Kinetic Parameters for the Crystallization of Paracetamol from Water Using Metastable Zone Width Experiments , 2008 .

[47]  Gilles Fevotte,et al.  A population balance model of the solution-mediated phase transition of citric acid , 2007 .

[48]  Solution and analysis for crystallization with agglomeration , 1994 .

[49]  G. Févotte,et al.  Comparison between approaches for the experimental determination of metastable zone width: A case study of the batch cooling crystallization of ammonium oxalate in water , 2012 .

[50]  H. Briesen.  Two-dimensional population balance modeling for shape dependent crystal attrition , 2009 .

[51]  Doraiswami Ramkrishna,et al.  A coalescence redispersion model for drop-size distributions in an agitated vessel , 1976 .

[52]  François Puel,et al.  Industrial batch crystallization of a plate-like organic product. In situ monitoring and 2D-CSD modelling. Part 2: Kinetic modelling and identification , 2007 .

[53]  Amornchai Arpornwichanop,et al.  Improvement of batch crystallization control under uncertain kinetic parameters by model predictive control , 2011 .

[54]  Bostjan Likar,et al.  Digital imaging as a process analytical technology tool for fluid-bed pellet coating process. , 2010, European Journal of Pharmaceutical Sciences.

[55]  K. Sangwal.  Growth kinetics and surface morphology of crystals grown from solutions: Recent observations and their interpretations , 1998 .

[56]  L. L. Simon,et al.  Endoscopy-Based in Situ Bulk Video Imaging of Batch Crystallization Processes , 2009 .