Batch flotation kinetics: Fractional calculus approach

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.