Parameterization of population balance models for polythermal auto seeded preferential crystallization of enantiomers

Abstract

For analysis, design and model-based control of crystallization processes typically population balance models or reduced models derived therefrom are used. Usually the kinetic parameters in these models are determined analyzing measured concentration trajectories and/or particle size distributions using parameter estimation procedures. In the case of preferential crystallization of enantiomers the analysis of experiments is complex since there are two “competing” crystal populations. In this field often batch processes are performed using seeds of the desired enantiomer. Currently, it is in particular challenging to quantify and optimize a new concept: e.g. the so-called “ auto seeded programmed polythermal preferential crystallization” (“as3pc” [Coquerel, G., Petit, M.-N., Bouaziz, R., 2000. Method of resolution of two enantiomers by crystallization. United States Patent, Patent number: 6,022,409]). In order to design and optimize this process the temperature dependent kinetic constants for crystal growth, nucleation and dissolution have to be known. In this work a reduced model for this auto seeded process is presented. The general identifiability of the model parameters is investigated along with some suggestions on how to reparameterize the kinetic terms involved. The values of the identified key parameters are estimated using conventional least square optimization using experimental data determined for the model system threonine/water. Parameter confidence and cross correlation are discussed and finally the model is validated using experiments not used for parameter estimation.