On the Sensitivity of Kinetic Modeling to the Selection of Flotation Intervals in Batch Tests

Batch tests were conducted to recover copper minerals by flotation. Seven intervals (cumulative flotation times) were chosen to characterize flotation kinetics in terms of maximum recoveries, R∞, and flotation rate distributions, f(k). The responses were subsampled, removing one datapoint at a time to obtain seven datasets with six time-recovery datapoints. The main objective of this subsampling procedure was to assess the sensitivity of the R∞–f(k) estimates to moderate changes and arbitrary selection of flotation intervals in batch tests. These datasets were fitted to the Single Flotation Rate (SFR), Rectangular, and Gamma models. The R∞–f(k) pairs proved to be sensitive to changes in the flotation intervals, particularly under poor model fitting and noisy kinetic responses. The former was observed with the SFR model in all cases and with the Rectangular model in one test, whereas the latter was observed with the Gamma model for the noisiest kinetic response, showing a trend to overfitting. A simplified scale-up procedure was performed, showing significant uncertainties in the predicted recoveries when the R∞–f(k) pairs were strongly influenced by different flotation intervals. The scale-up results presented a variability that was directly justified by the R∞–f(k) uncertainties, caused by the arbitrary selection of flotation intervals in the batch tests. The analysis highlights the need for more robust experimental designs in kinetic characterizations, particularly for the prediction of metallurgical results at a large scale.