Emergence of falsified kinetics as a consequence of multi-particle interactions in dense-phase comminution processes

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Particle breakage during dense-phase comminution processes is significantly affected by mechanical multi-particle interactions, which are neglected in traditional discrete linear population model (DL-PBM). A discrete non-linear PBM (DNL-PBM) has been recently proposed to account for multi-particle interactions; however, the inverse problem, i.e., the estimation of the model parameters, has not been addressed. In this paper, a method for the estimation of DNL-PBM parameters is presented with a purpose of determining the consequences of neglecting multi-particle interactions in the traditional DL-PBM. The model parameters were obtained from a constrained, non-linear, least-squares minimization of the residuals between comminution data and discrete PBM prediction. Comminution data exhibiting multi-particle interactions were obtained from a DNL-PBM simulation followed by addition of 0%, 10%, and 20% random error. A comprehensive statistical analysis of the goodness of fit and certainty of the parameters was performed to discriminate the models. Using the estimated parameters, predictive capability of both models was further assessed by comparing their prediction with additional computer-generated data obtained with a different feed particle size distribution. The parameter estimation method was shown to be highly accurate and robust. DNL-PBM can predict the influence of different feed conditions better than DL-PBM when multi-particle interactions are significant. This study has demonstrated that neglecting multi-particle interactions in dense-phase comminution processes via the use of DL-PBM can lead to falsified kinetics with erroneous breakage functions.

Original languageEnglish (US)
Pages (from-to)5672-5683
Number of pages12
JournalChemical Engineering Science
Issue number22
StatePublished - Nov 15 2011

All Science Journal Classification (ASJC) codes

  • General Chemistry
  • General Chemical Engineering
  • Industrial and Manufacturing Engineering


  • Falsified kinetics
  • Multi-particle interactions
  • Parameter identification
  • Particle processing
  • Population balance
  • Simulation


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