A comparison of the predictability of batch flotation kinetic models. (December 2016)

• Record Type: Journal Article
• Authors: Alvarez-Silva, M.; Vinnett, L.; Langlois, R.; Waters, K.E.
• Is Part Of: Minerals engineering. Volume 99(2016)
• Page Start: 142
• Page End: 150
• Publication Date: 2016-12
• Subjects: Flotation kinetics -- Kinetic models -- Predictability -- Fractional calculus -- Flotation -- Pyrite -- Calcite; Mines and mineral resources -- Periodicals; Ressources minérales -- Périodiques; Mines and mineral resources; Periodicals; Electronic journals; 622
• DOI: 10.1016/j.mineng.2016.08.019
• Languages: English
• ISSNs: 0892-6875

Abstract

Highlights: Batch flotation data of pyrite and calcite were used to compare kinetic models. Three first-order and one fractional models were investigated. The single rate constant and gamma models were the most effective modelling this system. Gamma was the most robust model, capable of reducing to a single constant system. Abstract: Batch flotation test data of a mixture of pyrite and calcite were used to compare regression parameters of four kinetic model structures. The work included the use of unoxidized or a mixture of partially oxidized pyrite (by microwave irradiation). The objective of floating oxidized pyrite was to have mineral particles with different floatability, closer to a real situation. The models considered include: single rate constant, distributed rate constants ( i.e. rectangular and gamma distributions), and a recently introduced approach based on fractional calculus. Such models were selected due to their good tradeoff between simplicity and accuracy. The regressions were performed (1) taking all the data points and comparing the mean square error ( MSE ) and adjusted correlation factor R Adj 2 as indicators of the goodness of fit; and (2) taking the first data points while neglecting the last ones (from 1 to 3) and observing the variability of the model parameters and the prediction of maximum recovery ( R∞ ). For the latter regression scheme, besides MSE and R Adj 2, a predictive factor, E, was defined by subtracting the final measured recovery from the calculation obtained by the model. This allowed to measure the ability of each model to extrapolate the omitted points on the recovery vs. time curve. Results from this study showed that the single constant model had a satisfactory performance with the advantage of having the least parameters compared to the other structures. The gamma model was effective and robust. The rectangular model gave an acceptable goodness of fit but overestimated the maximum and final recovery. Finally, the fractional calculus approach gave the best goodness of fit, overall, but failed in predicting the maximum recovery, which occurred when the derivative order was greater than 1.