Modelling Batch Systems Using Population Balances

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58 pages
One-dimensional population balances are used as a modelling tool for a variety of chemical processes.
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Sobre o autor

Peter Dybdahl Hede has a M.Sc. and PhD degree in Chemical Engineering from the Technical University of Denmark and a Business Diploma (HD) in Finance from the Copenhagen Business School. Working as Customer Solutions Application Manager in a large biotech company Peters´ areas of expertise spans from...


One-dimensional population balances are used as a modelling tool for a variety of chemical processes. In particle technology population balances are typically used for modelling agglomeration processes – e.g. in fluid bed granulation processes. In this text the population balances are introduced and fully derived with focus on each of the terms in the balance. The text is an excellent starting point for beginners and thus you will be familiar with the basic principles and theory within this relevant chemical engineering field on a bachelor or master-of-science level.

The present text introduces the use of population balances in the context of batch wet granulation and coating systems and it reviews the latest achievements and proposals in the scientific literature in this field. The nature and framework of population balance theory are highlighted and one-dimensional population balances are introduced from scratch. This may seems tedious at first but the derivation of even the simplest population balances is nevertheless not an easy task, and it is in fact difficult to find complete derivations elsewhere in literature. In addition to the introduction of the different terms in the population balances, a brief historical review of coalescence kernels for the one-dimensional balances is presented. Next, a brief introduction to multi-dimensional balances is given hereby presenting some of the recent suggestions of two- and four-dimensional balances. Further, population balance solution techniques are introduced in terms of two simple analytical solutions besides an introduction to the field of numerical solution techniques. A number of the latest advances in the various available numerical solution techniques are further presented.

The text is aimed at undergraduate university or engineering-school students working in the field of mathematical or chemical and biochemical engineering. Newly graduated as well as experienced engineers may also find relevant new information as emphasis is put on the newest scientific discoveries and proposals presented in recent years of scientific publications. It is the hope that the present introductory text will be helpful to the reader – particularly in the first stages of the process of working with population balances. The comprehensive literature list may also hopefully be an inspiration for further reading.

I alone am responsible for any misprints or errors and I will be grateful to receive any critics and/or suggestions for further improvements.

Copenhagen, September 2006

Peter Dybdahl Hede

  1. Modelling Batch Fluid Bed Granulation Processes Using Population Balances
    1. The nature and framework of population balances
    2. One-dimensional population balances for fluid bed batch systems
    3. Multi-dimensional population balances
    4. Solving one-dimensional population balances
    5. Inverse problems in population balances
  2. Summary
  3. Table of symbols
  4. Literature
  5. Notes