A Novel Statistical Insight to Selection of the Best flotation Kinetic Model

Many flotation kinetics models have been studied in the literature. Their applicability was extensively investigated and argued in detail. However, model selection criteria were not adequately discussed from the statistical points of view. In this investigation, the kinetic behavior of a complex copper sulfide ore was studied in a mechanical Denver flotation cell focusing on flotation kinetics of chalcopyrite, pyrite and molybdenite. Different flotation kinetics models including nine common empirical models and four mathematical models namely Hill, Chapman (Sigmodial function), single rectangular (Hyperbola equation) and exponential were applied to the experimental data. In addition to assessment of the goodness of fit criterion for each model, a factor of model complexity was considered using information criteria (IC) (i.e. Bayesian information (BIC), low of iterated logarithm (LILC) and Akaike information (AIC) indices). The obtained results showed that the IC indices could simply manifest the best-fitted model to the experimental data. Whereas, the coefficient of determination values (R2) were relatively same for all models. By taking the R2 and model complexity criteria into account, the exponential model was chosen as the best representative mathematical model to demonstrate chalcopyrite kinetic behavior. However, Chapman model was selected as the best one for the flotation of pyrite and molybdenite. In case of the common first-order flotation kinetics models, fast and slow flotation kinetic model (Kelsall) was reasonably fitted the best to the given data of chalcopyrite. However, the gas/solid kinetics adsorption model was chosen as the best-fitted one for pyrite and molybdenite. Furthermore, it was found that mathematical models represent better results in association with flotation kinetic behavior of chalcopyrite, pyrite and molybdenite due to the consideration of more parameters in modeling. Finally, it was concluded that the IC indices must be applied to the process of model selection due to consideration of goodness of fit, complexity of a model and model consistency.