Abstract

Gas dispersion properties have been proved to be a key feature of the flotation process. In particular, bubble surface area flux (Sb), derived from a combination of gas rate and the Sauter mean diameter (D32), has received considerable attention, being reported to be related to flotation rate constant and thus with flotation performance. Therefore, Sb is among the potential variables to control in order to achieve a target metallurgical performance. Unfortunately, important information related to the shape of the bubble size distribution, such as multi-modal, narrowness and tail behavior is completely lost in the D32 derivation. Therefore, formal control strategies should take into account the Sb value in conjunction with the shape of the bubble size distribution, which must be estimated on-line from sequential bubble size data points. This work details the application of a Gaussian mixture model (GMM) to represent the whole underlying bubble size density function. A recursive version of the classical expectation-maximization EM algorithm is used to estimate on-line the Gaussian mixture parameters from a sequence of data inputs. Results show that a low order GMM can represent reasonably well the bubble size density function. In addition, on-line estimates of the D32 can be obtained directly from the Gaussian mixture parameters.