Zyklische Prozessführung zur Formgebung facettierter Kristalle
Chemische und Thermische Verfahrenstechnik
Zusammenfassung der Projektergebnisse
In this project, a novel crystallization process composed of growth-dissolution cycles was realized and controlled in a closed loop manner, to manipulate the crystal shape distribution towards a desired final shape distribution. Concerning modeling and control aspects, one of the key contributions of this project has been the extension of a particular generalized moment model approach to cases with a wider range of size-dependent growth functions, size-dependent particle removal and two internal coordinates. This work on modeling has laid the foundation for efficient calculation of optimal control profiles (unimodal operation) in the context of crystal shaping applications involving a fines removal apparatus. Optimal control profiles were “robustified” via feedback control and the resulting overall control strategy was successfully implemented in a laboratory at OvGU Magdeburg. A crystallization test stand was built, which allowed for fast switches of the crystallizer temperature and therefore for fast switches between supersaturated and undersaturated conditions. The crystallizer was modeled by using energy and mass balances as well as a morphological population balance to account for changes in the crystal shape distribution over time. With this model, a policy for supersaturation control was derived, that was furthermore used to determine the face-specific growth and dissolution kinetics of KDP at constant supersaturations and temperatures. It was found that the growth of KDP at low supersaturations, and in particular the growth of the 100 faces, is strongly influenced by impurities present in the solution, whereas the growth rates are linearly dependent on the supersaturation level at higher supersaturations. The dissolution kinetics were found to be linearly dependent on the level of undersaturation and similar for both face types of KDP, indicating that dissolution is limited by bulk diffusion processes. The crystallization processes were observed with a flow through microscope, and the crystal shape distributions were reconstructed based on the video frames that were collected with this microscope. The algorithms which were used for the shape estimation were implemented in such a way, that the evolution of the crystal shape distribution over time could be observed in real time during the crystallization process. Using these real time observations, the crystal shape distribution could be controlled in a closed loop manner during cyclic growth-dissolution processes. It was shown that the region of crystal shapes which is attainable by pure growth processes can be expanded by the application of additional dissolution steps, and hence more crystal shapes can be reached by this process concept. Due to the methods for supersaturation control and the availability of measurements of the crystal shape distribution, the cyclic process could be controlled very well in terms of supersaturation levels and a cyclic crystallization between a minimal and maximal crystal volume. Finally, the desired final crystal shape could be reached with high precision, proving the efficiency of the control strategies and routines that were developed in this project.
Projektbezogene Publikationen (Auswahl)
- (2017) Optimal control of univariate and multivariate population balance systems involving external fines removal. Chemical Engineering Science 168 101–123
Hofmann, S.; Bajcinca, N.; Raisch, J.; Sundmacher, K.
(Siehe online unter https://doi.org/10.1016/j.ces.2016.12.032) - Estimation of crystal shape distributions from microscopic images. In H. Qu, editor, Proceedings of BIWIC 2013, 20th International Workshop on Industrial Crystallization, pages 215–222, 2013
Holger Eisenschmidt, Andreas Voigt, and Kai Sundmacher
- Method of moments over orthogonal polynomial bases. Chemical Engineering Science, 119(0):295–309, 2014
Naim Bajcinca, Steffen Hofmann, and Kai Sundmacher
(Siehe online unter https://doi.org/10.1016/j.ces.2014.07.014) - Approximate ODE models for population balance systems. Computers & Chemical Engineering, 74(0):158–168, 2015
Naim Bajcinca, Steffen Hofmann, Dmytro Bielievtsov, and Kai Sundmacher
(Siehe online unter https://doi.org/10.1016/j.compchemeng.2014.12.015) - Face-specific growth and dissolution kinetics of potassium dihydrogen phosphate crystals from batch crystallization experiments. Crystal Growth & Design, 15(1):219–227, 2015
Holger Eisenschmidt, Andreas Voigt, and Kai Sundmacher
(Siehe online unter https://doi.org/10.1021/cg501251e) - Generalizing ODE modeling structure for multivariate systems with distributed parameters. IFAC- PapersOnLine, 48(8):240–247, 2015. 9th IFAC Symposium on Advanced Control of Chemical Processes ADCHEM 2015, Whistler, Canada, June 7–10, 2015
Naim Bajcinca, Steffen Hofmann, Holger Eisenschmidt, and Kai Sundmacher
(Siehe online unter https://doi.org/10.1016/j.ifacol.2015.08.188) - Model-based observation and design of crystal shapes via controlled growth-dissolution cycles. In Jakob K. Huusom Krist V. Gernaey and Rafiqul Gani, editors, 12th International Symposium on Process Systems Engineering and 25th European Symposium on Computer Aided Process Engineering, volume 37 of Computer Aided Chemical Engineering, pages 1673–1678. Elsevier, 2015
Holger Eisenschmidt, Naim Bajcinca, and Kai Sundmacher
(Siehe online unter https://doi.org/10.1016/B978-0-444-63577-8.50124-8) - Optimal control of crystal shapes in batch crystallization experiments by growth-dissolution cycles. Crystal Growth & Design, 16(6):3297–3306, 2016
Holger Eisenschmidt, Naim Bajcinca, and Kai Sundmacher
(Siehe online unter https://doi.org/10.1021/acs.cgd.6b00288)
