A high-order moment-conserving method of classes (HMMC) based population balance model for mechanical flotation cells. (July 2017)

• Record Type: Journal Article
• Authors: Basavarajappa, Manjunath; Alopaeus, Ville; Yoon, Roe-Hoan; Miskovic, Sanja
• Is Part Of: Minerals engineering. Volume 108(2017)
• Page Start: 36
• Page End: 52
• Publication Date: 2017-07
• Subjects: Population balance model -- High-order moment conserving method of classes (HMMC) -- Flotation cell -- Sauter mean diameter (D32) estimation -- Parameter estimation; Mines and mineral resources -- Periodicals; Ressources minérales -- Périodiques; Mines and mineral resources; Periodicals; Electronic journals; 622
• DOI: 10.1016/j.mineng.2017.01.015
• Languages: English
• ISSNs: 0892-6875

Abstract

Graphical abstract: Highlights: A PBM based on HMMC is developed for gas-liquid flows in flotation cell. Experimental BSD measurements are made using an ex-situ bubble sampling method. Three breakage rate models are used and their adjustable parameters are evaluated. Good match is found for number mean diameter but SMD is under-predicted. 95% confidence intervals on point estimates of parameters are calculated. Abstract: 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 m 3 pilot scale XCELL TM 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.