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Numerical Methods for Coupled Population Balance Systems Applied to the Dynamical Simulation of Crystallization Processes

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Dynamic Flowsheet Simulation of Solids Processes

Abstract

Uni- and bi-variate crystallization processes are considered that are modeled with population balance systems (PBSs). Experimental results for uni-variate processes in a helically coiled flow tube crystallizer are presented. A survey on numerical methods for the simulation of uni-variate PBSs is provided with the emphasis on a coupled stochastic-deterministic method. In this method, the equations of the PBS from computational fluid dynamics are solved deterministically and the population balance equation is solved with a stochastic algorithm. With this method, simulations of a crystallization process in a fluidized bed crystallizer are performed that identify appropriate values for two parameters of the model such that considerably improved results are obtained than reported so far in the literature. For bi-variate processes, the identification of agglomeration kernels from experimental data is briefly discussed. Even for multi-variate processes, an efficient algorithm for evaluating the agglomeration term is presented that is based on the fast Fourier transform (FFT). The complexity of this algorithm is discussed as well as the number of moments that can be conserved.

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Acknowledgements

The work at this report was supported by the grants JO329/10-3, BO4141/1-3, and SU189/6-3 within the DFG priority programme 1679: Dynamic simulation of interconnected solids processes.

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Authors and Affiliations

  1. Faculty of Electrical Engineering, Informatics and Mathematics, Institute of Mathematics, Hamburg University of Technology, Am Schwarzenberg-Campus 3, 21073, Hamburg, Germany

    Robin Ahrens & Sabine Le Borne

  2. Weierstrass Institute for Applied Analysis and Stochastics (WIAS), Mohrenstr. 39, 10117, Berlin, Germany

    Zahra Lakdawala & Volker John

  3. Department Process Systems Engineering, Otto-von-Guericke-University Magdeburg, Universitätsplatz 2, 39106, Magdeburg, Germany

    Andreas Voigt & Kai Sundmacher

  4. ETH Zurich, Institute of Energy and Process Engineering, Sonneggstrasse 3, 8092, Zurich, Switzerland

    Viktoria Wiedmeyer

  5. Freie Universität Berlin, Department of Mathematics and Computer Science, Arnimallee 6, 14195, Berlin, Germany

    Volker John

  6. Process Systems Engineering, Max Planck Institute for Dynamics of Complex Technical Systems, Sandtorstr. 1, 39106, Magdeburg, Germany

    Kai Sundmacher

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  1. Robin Ahrens
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Correspondence to Volker John .

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  1. Institute of Solids Process Engineering and Particle Technology, Hamburg University of Technology, Hamburg, Germany

    Stefan Heinrich

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Ahrens, R. et al. (2020). Numerical Methods for Coupled Population Balance Systems Applied to the Dynamical Simulation of Crystallization Processes. In: Heinrich, S. (eds) Dynamic Flowsheet Simulation of Solids Processes. Springer, Cham. https://doi.org/10.1007/978-3-030-45168-4_14

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