Assessment of flotation kinetics modeling using information criteria; case studies of elevated-pyritic copper sulfide and high-grade carbonaceous sedimentary apatite ores

Abstract

Despite flotation kinetic modeling is well discussed in the literature, its evaluation from overfitting, the number of model parameters and model complexities have not been adequately addressed. Flotation kinetic behavior of two deposits including an elevated-pyritic (Cu/S = 0.21) complex copper sulfide ore and a high-grade carbonaceous sedimentary apatite (P₂O₅ ≥ 25%) ore were investigated. The flotation kinetic experiments were carried out in a mechanically agitated batch flotation cell. Different flotation kinetic models including seven common empirical and initially four mathematical models were applied to the experimental data. In addition to assessment of the goodness of fit (GOF) for each model, a factor of model complexity was considered using advanced statistical techniques (i.e. Bayesian information (BIC), low of iterated logarithm (LILC) and Akaike information (AIC) indices). The results confirmed that flotation kinetic modeling significantly depends on the feed type. The empirical models were found more sensitive than the mathematical ones to the ore properties and the mineral types. Furthermore, the mathematical models demonstrated relatively favorable results than the practical models concerning the variation of ore properties due to the consideration of more parameters in the modeling. Finally, it was concluded that the IC indices must be applied to the process of model selection owing to consideration of GOF, the complexity of a model and model consistency. The IC was introduced as a more reliable indicator than the common regression approach for evaluating, sequential ordering and selecting the suitable flotation kinetic models. Further studies are required for model’s generalizability from a statistical point of view.

Graphical Abstract

Keywords:

• Flotation kinetic modeling
• goodness of fit
• information criteria
• flotation rate constant
• Bayesian information

Acknowledgement

Authors intend to sincerely appreciate Helmholtz-Institute Freiberg for Resource Technology (Germany) for supporting this research. In addition, we would like to extend our gratitude to all reviewers for their constructive comments and invaluable remarks.