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Title: Simultaneous quadrature method of moments for the solution of population balance equations, using a differential algebraic equation framework
Authors: Gimbun, Jolius
Nagy, Zoltan K.
Rielly, Chris D.
Keywords: Population balance modeling
Particulate dynamics
Numerical simulation
Issue Date: 2009
Publisher: © American Chemical Society
Citation: GIMBUN, J., NAGY, Z.K. and RIELLY, C.D., 2009. Simultaneous quadrature method of moments for the solution of population balance equations, using a differential algebraic equation framework. Industrial and Engineering Chemistry Research, 48 (16), pp. 7798–7812
Abstract: The quadrature method of moments (QMOM) is a recent technique of solving population balance equations for particle dynamics simulation. In this paper, an alternative solution for the QMOM is described and thoroughly tested, which is based on the formulation and simultaneous solution of a semiexplicit differential algebraic equation (DAE) system. The DAE system consists of the ordinary differential equations resulting from the application of the method of moments, as well as a system of non-linear algebraic equations derived by applying the quadrature theory for the approximation of the moments. It is shown that the proposed approach provides an efficient procedure for evolving the quadrature abscissas and weights from the QMOM. The Jacobian matrix of the DAE system is provided analytically to make the solution more robust. The DAE-QMOM method was compared to the well established method for solving QMOM based on the product difference (PD) algorithm. The numerical results are compared to the analytical solutions in the case of breakage, aggregation, growth and nucleation mechanisms. Excellent agreements were found on the moment evolution predicted by both methods. However, the DAE-QMOM method was found to be more accurate and robust than the PDQMOM in some cases. Additionally, the DAE-QMOM is also capable of providing the solution significantly faster than the PD-QMOM method.
Description: This article is restricted access. The article was published in the journal, Industrial and Engineering Chemistry Research [© American Chemical Society]. It is available at: http://dx.doi.org/10.1021/ie900548s
Version: Closed access
DOI: 10.1021/ie900548s
URI: https://dspace.lboro.ac.uk/2134/5327
ISSN: 0888-5885
Appears in Collections:Closed Access (Chemical Engineering)

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