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Advances in numerical methods for the solution of population balance equations for disperse phase systems

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Abstract

Accurate prediction of the evolution of particle size distribution is critical to determining the dynamic flow structure of a disperse phase system. A population balance equation (PBE), a non-linear hyperbolic equation of the number density function, is usually employed to describe the micro-behavior (aggregation, breakage, growth, etc.) of a disperse phase and its effect on particle size distribution. Numerical solution is the only choice in most cases. In this paper, three different numerical methods (direct discretization methods, Monte Carlo methods, and moment methods) for the solution of a PBE are evaluated with regard to their ease of implementation, computational load and numerical accuracy. Special attention is paid to the relatively new and superior moment methods including quadrature method of moments (QMOM), direct quadrature method of moments (DQMOM), modified quadrature method of moments (M-QMOM), adaptive direct quadrature method of moments (ADQMOM), fixed pivot quadrature method of moments (FPQMOM), moving particle ensemble method (MPEM) and local fixed pivot quadrature method of moments (LFPQMOM). The prospects of these methods are discussed in the final section, based on their individual merits and current state of development of the field.

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Author information

Authors and Affiliations

  1. Department of Mechanical Engineering and Automation, School of Mechanical Engineering, Xi’an Jiaotong University, Xi’an, 710049, China

    JunWei Su

  2. Key Laboratory of Mechanics on Disaster and Environment in Western China, Ministry of Education, Lanzhou, 730000, China

    ZhaoLin Gu

  3. Department of Environmental Science and Technology, School of Human Settlements and Civil Engineering, Xi’an Jiaotong University, Xi’an, 710049, China

    ZhaoLin Gu

  4. Department of Chemical Engineering, Imperial College London, London, SW7 2AZ, UK

    X. Yun Xu

Authors
  1. JunWei Su
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  2. ZhaoLin Gu
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  3. X. Yun Xu
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Corresponding author

Correspondence to ZhaoLin Gu.

Additional information

Supported by the National Basic Research Program of China (Grant No. 2004CB720208), the National Natural Science Foundation of China (Grant Nos. 40675011 & 10872159), and the Key Laboratory of Mechanics on Disaster and Environment in Western China

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Su, J., Gu, Z. & Xu, X.Y. Advances in numerical methods for the solution of population balance equations for disperse phase systems. Sci. China Ser. B-Chem. 52, 1063–1079 (2009). https://doi.org/10.1007/s11426-009-0164-2

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  • DOI: https://doi.org/10.1007/s11426-009-0164-2

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