Chapter 14
Numerical Methods for Coupled
Population Balance Systems Applied
to the Dynamical Simulation
of Crystallization Processes
Robin Ahrens, Zahra Lakdawala, Andreas Voigt, Viktoria Wiedmeyer,
Volker John, Sabine Le Borne, and Kai Sundmacher
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
R. Ahrens · S. Le Borne
Faculty of Electrical Engineering, Informatics and Mathematics,
Institute of Mathematics, Hamburg University of Technology,
Am Schwarzenberg-Campus 3, 21073 Hamburg, Germany
e-mail: robin.ahrens@tuhh.de
S. Le Borne
e-mail: leborne@tuhh.de
Z. Lakdawala · V. John (B)
Weierstrass Institute for Applied Analysis and Stochastics (WIAS),
Mohrenstr. 39, 10117 Berlin, Germany
e-mail: john@wias-berlin.de
Z. Lakdawala
e-mail: lakdawala@wias-berlin.de
A. Voigt · K. Sundmacher
Department Process Systems Engineering, Otto-von-Guericke-University Magdeburg,
Universitätsplatz 2, 39106 Magdeburg, Germany
e-mail: andreas.voigt@ovgu.de
K. Sundmacher
e-mail: sundmacher@mpi-magdeburg.mpg.de
© Springer Nature Switzerland AG 2020
S. Heinrich (ed.), Dynamic Flowsheet Simulation of Solids Processes,
https://doi.org/10.1007/978-3-030-45168-4_14
475
Numerical Methods for Coupled
Population Balance Systems Applied
to the Dynamical Simulation
of Crystallization Processes
Robin Ahrens, Zahra Lakdawala, Andreas Voigt, Viktoria Wiedmeyer,
Volker John, Sabine Le Borne, and Kai Sundmacher
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
R. Ahrens · S. Le Borne
Faculty of Electrical Engineering, Informatics and Mathematics,
Institute of Mathematics, Hamburg University of Technology,
Am Schwarzenberg-Campus 3, 21073 Hamburg, Germany
e-mail: robin.ahrens@tuhh.de
S. Le Borne
e-mail: leborne@tuhh.de
Z. Lakdawala · V. John (B)
Weierstrass Institute for Applied Analysis and Stochastics (WIAS),
Mohrenstr. 39, 10117 Berlin, Germany
e-mail: john@wias-berlin.de
Z. Lakdawala
e-mail: lakdawala@wias-berlin.de
A. Voigt · K. Sundmacher
Department Process Systems Engineering, Otto-von-Guericke-University Magdeburg,
Universitätsplatz 2, 39106 Magdeburg, Germany
e-mail: andreas.voigt@ovgu.de
K. Sundmacher
e-mail: sundmacher@mpi-magdeburg.mpg.de
© Springer Nature Switzerland AG 2020
S. Heinrich (ed.), Dynamic Flowsheet Simulation of Solids Processes,
https://doi.org/10.1007/978-3-030-45168-4_14
475