Journal
CHEMICAL ENGINEERING SCIENCE
Volume 61, Issue 23, Pages 7795-7804Publisher
PERGAMON-ELSEVIER SCIENCE LTD
DOI: 10.1016/j.ces.2006.09.014
Keywords
population balance equation; method of moments; method of weighted residuals; quadrature approximation
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Population balance models are generally computationally intensive, so in many practical applications only a few moments of the density function are computed, minimizing the computational costs. Nevertheless, the moment formulation contains an excess of unknowns with respect to equations denoting a closure problem. One possible solution to this closure problem might be to apply a numerical quadrature approximation. In this work, the relationship between the quadrature approximation and the well-known method of weighted residuals (MWR) is discussed. An important result obtained in this work is that the problem of reconstruction of the density function is avoided using the MWR version of the quadrature approximation. Numerical experiments are performed in order to elucidate the advantages and disadvantages of the quadrature approximations. (c) 2006 Elsevier Ltd. All rights reserved.
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