First-order flotation kinetics models and methods for estimation of the true distribution of flotation rate constants

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To improve their versatility, many first-order flotation kinetics models with distributions of flotation rate constants were redefined so that they could all be represented by the same set of three model parameters. As a result, the width of the distribution become independent of its mean, and parameters of the model and the curve fitting errors, became virtually the same, independent of the chosen distribution function. For the modified three-parameter models, the curve fitting errors were much smaller and their robustness, measured by PRESS residuals, was much better when compared to the corresponding two-parameter models. Three different methods were compared to perform flotation kinetics analysis and estimate model parameters. In Method I, recovery vs. time data were used to obtain model parameters. No significant insight into the distribution of rate constants could be obtained because the distributions were presupposed. In Method II, the froth products were fractionated into several size fractions and the data for each fraction were fitted to a model. This task was easy to perform and the method could describe the flotation kinetics reasonably well. In method III, flotation products were fractionated into many size-specific gravity fractions. The procedure involved a large amount of time and effort and it generated relatively large errors. Based on the analysis presented in this article, it was concluded the smallest errors were obtained with Method II. The overall distribution of flotation rate constants could be obtained from a weighted average of the distributions of individual size fractions. The distributions so obtained were demonstrated to be less sensitive to the choice of the model used to represent the kinetics of individual size fractions, and therefore can be assumed to be “true” representation of the flotation rate distribution.