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Abstract:
To design and optimize crystallization based separation processes usually mathematical process models are used. One possibility for modelling such processes is the population balance approach [1]. To have predictive capabilities the kinetic and physical constants inside the models have to be known. Usually the kinetic constants are obtained via fitting model predictions to experimental data.
In this work a parameterization of a reduced model, based on the Method of Moments, is exemplified with two case studies. The first case study presented is the seeded isothermal crystallization of L-threonine in water. A second more challenging case study is the “auto seeded” polythermal preferential crystallization [2] in the system DL-threonine/water. For both examples experiments were carried out in a 1 liter scale. Input for the parameter estimation are the concentration trajectories measured with the combined use of polarimetry (POLARmonitor, IBZ Messtechnik Hannover) and densimetry (DE40, Mettler-Toledo) and the particle counts monitored with the help of a FBRM-probe (lasentec, Mettler-toledo, D600 field unit).
Two statistical methods are presented to quantify the confidence intervals and reliability of the estimated parameters. One possibility is based on the calculation of sensitivities followed by an analysis of the Fisher information. Another option is the estimation of the confidence intervals with a modified monte-carlo method, the so called bootstrap method [3].
Based on the analysis of preliminary experiments sequel experiments are designed in such a way that the reliability of the estimated model parameters is increased. The experimental conditions that can be varied to design the experiments are the seed mass or size, the crystallization temperature or the temperature profiles respectively.
[1] Randolph, A. D., Larson M. A. (1988). Theory of particulate processes. Academic press, San Diego.
[2] Coquerel, G., Petit, M.-N., Bouaziz, R. (2000). Method of resolution of two enantiomers by crystallization. United States Patent, Patent number: 6,022,409.
[3] Efron, B., Tibshirani (1993): An introduction to the bootstrap. Chapman and Hall/CRC.
