Generalization and numerical investigation of QMOM

R. Grosch, H. Briesen, W. Marquardt, M. Wulkow

Research output: Contribution to journalArticlepeer-review

50 Scopus citations


A generalized framework is developed for the quadrature method of moments (QMOM), which is a solution method for population balance models. It further evaluates the applicability of this method to industrial suspension crystallization processes. The framework is based on the concepts of generalized moments and coordinate transformations, which have been used already in earlier solution approaches. It is shown how existing approaches to QMOM are derived from the suggested unified framework. Thus, similarities and differences between the various QMOM methods are uncovered. Further, potential error sources involved in the different approaches to QMOM are discussed and assessed by means of a series of test cases. The test cases are selected to be challenging. The error in the QMOM solution is evaluated by comparison to an adaptive, error controlled solution of the population balance. The behavior of a range of different QMOM formulations is analyzed by means of numerical quadrature, dynamic simulation, as well as numerical continuation and bifurcation analysis. As a result of this detailed analysis, some general limitations of the method are detected and guidelines for its application are developed. This article is limited to lumped population balance models with one internal coordinate.

Original languageEnglish
Pages (from-to)207-227
Number of pages21
JournalAIChE Journal
Issue number1
StatePublished - Jan 2007
Externally publishedYes


  • Crystallization
  • Gaussian quadrature
  • Integral approximation
  • Method of moments
  • Numerical investigation
  • Population balance


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