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

  • Robin Ahrens
  • Zahra Lakdawala
  • Andreas Voigt
  • Viktoria Wiedmeyer
  • Volker JohnEmail author
  • Sabine Le Borne
  • Kai Sundmacher


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.



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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© Springer Nature Switzerland AG 2020

Authors and Affiliations

  • Robin Ahrens
    • 1
  • Zahra Lakdawala
    • 2
  • Andreas Voigt
    • 3
  • Viktoria Wiedmeyer
    • 4
  • Volker John
    • 2
    • 5
    Email author
  • Sabine Le Borne
    • 1
  • Kai Sundmacher
    • 3
    • 6
  1. 1.Faculty of Electrical Engineering, Informatics and MathematicsInstitute of Mathematics, Hamburg University of TechnologyHamburgGermany
  2. 2.Weierstrass Institute for Applied Analysis and Stochastics (WIAS)BerlinGermany
  3. 3.Department Process Systems EngineeringOtto-von-Guericke-University MagdeburgMagdeburgGermany
  4. 4.ETH Zurich, Institute of Energy and Process EngineeringZurichSwitzerland
  5. 5.Freie Universität Berlin, Department of Mathematics and Computer ScienceBerlinGermany
  6. 6.Process Systems EngineeringMax Planck Institute for Dynamics of Complex Technical SystemsMagdeburgGermany

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