Batch flotation kinetics: Fractional calculus approach. (June 2015)

• Record Type: Journal Article
• Authors: Vinnett, L.; Alvarez-Silva, M.; Jaques, A.; Hinojosa, F.; Yianatos, J.
• Is Part Of: Minerals engineering. Volume 77(2015)
• Page Start: 167
• Page End: 171
• Publication Date: 2015-06
• Subjects: Flotation kinetics -- Batch flotation -- Fractional calculus approach; Mines and mineral resources -- Periodicals; Ressources minérales -- Périodiques; Mines and mineral resources; Periodicals; Electronic journals; 622
• DOI: 10.1016/j.mineng.2015.03.020
• Languages: English
• ISSNs: 0892-6875

Abstract

Abstract : Graphical abstract: Molybdenum recovery as a function of time. Comparison between fractional calculus approach and single parameter models (left); and comparison between fractional calculus approach and Gamma model (right). Highlights: A model to describe flotation kinetics based on fractional calculus was presented. The model has 3 parameters: derivative order, fractional rate and maximum recovery. The model was fitted to Cu/Mo flotation data and compared to other model structures. The proposed model gave suitable results, comparable to distributed Gamma model. The model structure allowed describing slow flotation processes. Abstract: As in many separation processes, design of flotation systems is governed by kinetics, which is a function of chemical, physical and machine parameters. Several kinetic models have been presented in literature, those based on a homogeneous chemical reactions being the most widespread. In this technical note an alternative approach based on the use of fractional calculus to describe batch kinetic characterization is presented. Batch flotation test data for porphyry ores of copper and molybdenum were used to compare the fractional calculus approach with first-order models. Comparisons include single rate constants as well as distributed rate constants (i.e., rectangular and Gamma distributions). Results showed a derivative order lower than 1, ranging from 0.60 to 0.95, which is related to a retarded flotation response at the beginning of the process. The fractional calculus approach was in all cases superior to the rectangular distributed kinetic constant, but comparable to the Gamma distribution approach. The proposed approach gives acceptable results for slow flotation processes, which is in good agreement with Gamma distributions with high fraction of slow rate constants.