A high-order moment-conserving method of classes (HMMC) based population balance model for mechanical flotation cells

Manjunath Basavarajappa*, Ville Alopaeus, Roe Hoan Yoon, Sanja Miskovic

*Corresponding author for this work

Research output: Contribution to journalArticleScientificpeer-review

3 Citations (Scopus)


In this paper, a high-order moment-conserving method of classes (HMMC) model is developed to predict bubble size distribution, number mean and Sauter mean diameters (SMD) in mechanical flotation cells. The population balance model (PBM) uses vessel averaged turbulence kinetic energy dissipation rate and gas hold-up as model inputs along with initial bubble size distribution. Experimental measurements are made in a 0.8 m3 pilot scale XCELLTM mechanical flotation cell at different aeration rates and impeller tip speeds. All the experimental measurements using MIBC frother are performed at frother dosage value over critical coalescence concentration (CCC), therefore, coalescence process is not considered in the PBM. Nonlinear least squares function (lsqnonlin) and constrained nonlinear multivariable minimization function (fmincon) available in the MATLAB optimization toolbox are used. Three breakage models, namely, Coulaloglou and Tavlarides (1977), Chen et al. (1998), and Alopaeus et al. (2002), each requiring estimation of adjustable parameters from the experimental data are selected. Also, 95% confidence intervals for estimated breakage parameters are calculated using a bootstrap based re-sampling technique. The developed model is capable of providing acceptable predictions of bubble size distribution, number mean diameter, and SMD for a reasonably wide range of operating conditions and has the potential to be developed further for three phase air-water-solid systems.

Original languageEnglish
Pages (from-to)36-52
Number of pages17
JournalMinerals Engineering
Publication statusPublished - 1 Jul 2017
MoE publication typeA1 Journal article-refereed


  • Flotation cell
  • High-order moment conserving method of classes (HMMC)
  • Parameter estimation
  • Population balance model
  • Sauter mean diameter (D) estimation

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