Errors in the estimation of size-by-liberation flotation rate constants

The description of froth flotation kinetics has been acknowledged as an essential step towards gaining a more comprehensive understanding of flotation operations. Mathematical models have adopted either continuous or discrete descriptions of specific rate constants. Particularly, the latter framework makes it possible to link discrete specific rate constants to physical properties of the mineral particles, such as particle size and mineral liberation. One aspect of such models usually overlooked is the evaluation of the uncertainty involved in the computation of relevant variables intimately related with the flotation performance such as recovery and specific rate constants, among others. This work aims at assessing the error in the estimation of specific overall flotation rate constants from the P9 flotation model (Savassi, 1998).The case study presented in this work is based on Welsby et al. (2010). The error was computed using the derivative form of propagation error analysis without considering covariance terms. The specific variances of the different variables were obtained from measurements described in Welsby et al. (2010) or estimated based on the available literature. The estimated error was found to be sensitive to the specific variances. The error was estimated in two cases, namely best and worst case scenario. The average coefficients of variation of kij were 11% and 121% for the best and worst case scenario respectively. In the best case scenario, the major contributor to the variances of the discrete specific overall flotation rate constants is residence time, while in the worst case scenario the main contributor was the recovery expressed by size and liberation classes.The work has exposed the need for information on the uncertainties implicit in the measurements of flotation quantities, which is current by lacking.

Figure optionsDownload as PowerPoint slideHighlights
► Average coefficient of variation of kij was 11% best case scenario.
► Average coefficient of variation of kij was 121% worst case scenario.
► Contribution to variance of kij is Rij ≫ τ > Rw ≈ ENT for worst case scenario.