Modeling, Simulation and Optimization of Process Chains

  • Michele Spinola
  • Alexander Keimer
  • Doris Segets
  • Lukas Pflug
  • Günter LeugeringEmail author


Processes in the field of chemical engineering do not consist of one single step, but typically a high number of strongly interconnected unit operations linked with recycling streams. This inherent complexity further exacerbates when distributed particle properties, i.e., dispersity, must be considered, noteworthy being the case whenever particulate products are in focus. Out of all five possible dimensions of dispersity (size, shape, composition, surface and structure) particle size most often determines the efficiency of particulate products. Thus, its optimization is key to reach tailored handling and end product properties. In this work, a model-based optimization tool for particle synthesis was elaborated which is often the first step of a process chain. It is described by population balance equations relying on the method of characteristics for the numerical simulation and on the usage of gradient information to enhance the performance of the optimization. The presented scheme to optimize time-dependent process conditions in a time efficient manner is applicable for a wide range of particle syntheses.


Ripening Method of characteristics Population balance equation Gradient-based optimization Sensitivity Adjoint 



The authors gratefully acknowledge financial support from the German Research Foundation within the priority program SPP 1679 “DYNSIM-FP” LE 595/30-2 and the travel funding provided by the “Bavaria California Technology Center”.


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© Springer Nature Switzerland AG 2020

Authors and Affiliations

  • Michele Spinola
    • 1
  • Alexander Keimer
    • 2
  • Doris Segets
    • 3
  • Lukas Pflug
    • 4
    • 5
  • Günter Leugering
    • 6
    Email author
  1. 1.Department of Mathematics, Applied Analysis (Alexander von Humboldt-Professorship)Friedrich-Alexander-Universität Erlangen-Nürnberg (FAU)ErlangenGermany
  2. 2.UC Berkeley, Institute of Transportation Studies (ITS)BerkeleyUSA
  3. 3.Process Technology for Electrochemical Functional MaterialsInstitute for Combustion and Gas Dynamics-Reactive Fluids (IVG-RF), and Center for Nanointegration Duisburg-Essen (CENIDE)DuisburgGermany
  4. 4.Central Institute for Scientific ComputingFriedrich-Alexander-Universität Erlangen-Nürnberg (FAU)ErlangenGermany
  5. 5.Department of Mathematics, Chair of Applied Mathematics (Continuous Optimization)Friedrich-Alexander-Universität Erlangen-Nürnberg (FAU)ErlangenGermany
  6. 6.Department of Mathematics, Applied Mathematics 2Friedrich-Alexander-Universität Erlangen-Nürnberg (FAU)ErlangenGermany

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