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#### Effect of the modeling approach on the quality of estimated kinetic parameters for a crystallization case study

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##### Citation

Haida, H., Czapla, F., Elsner, M. P., Lorenz, H., & Seidel-Morgenstern, A. (2008).
*Effect of the modeling approach on the quality of estimated kinetic parameters for a crystallization
case study*. Poster presented at BIWIC 2008 - 15th International Workshop on Industrial Crystallization, Magdeburg,
Germany.

Cite as: http://hdl.handle.net/11858/00-001M-0000-0013-94C3-E

##### Abstract

This study compares three solution strategies of a chosen crystallization model by analyzing statistical properties of estimated model parameters. There are different approaches to solve crystallization models that are based on the concept of population balances. In this case study (i) a finite discretization of the population balance, (ii) the conventional method of moments and (iii) the quadrature method of moments as reduced model formulations [3] are compared. The used model incorporates the kinetics of crystal growth and secondary nucleation. To parameterize these kinetics four free parameters have to be estimated. Typically crystallization experiments are carried out and kinetic parameters are estimated for each of the mentioned model strategies by fitting the model to the gathered data. The statistical properties of the estimated parameters are
used to compare the solutions strategies. Using L-Threonine in water as a model system isothermal seeded crystallization
experiments are carried out in a stirred 1-L-vessel.By means of refractive index measurement and optical rotation measurement, respectively, the concentrations are monitored. The particulate phase is monitored using a Focused Beam Reflectance Measurement Probe (FBRM). The particle size distribution of the seed crystals is obtained by microscopic image analysis. Using the data from experiments carried out under different conditions a parameter estimation is done for each of the three mentioned strategies to solve the population balance model. In each case the estimated parameters are evaluated by means of their statistical properties, e.g. parameter sensitivity, confidence intervals and correlation coefficients gained from the Fisher Information Matrix [4]. Moreover an identifiability index is used to quantify the
model evaluate [2, 1].