Article Abstract

A numerical conditioning analysis for mineral recovery estimation was performed for industrial flotation plants, considering the copper (Cu), molybdenum (Mo) and iron (Fe) separability. A modified relative condition number, χ, was presented that allowed sensitivity analysis to be evaluated for the component recovery by means of an analytical formula. This closed form made it possible for the error propagation to be determined from feed, concentrate and tail grades with different orders of magnitude. The χ parameter can be evaluated using available grade data from the design criteria or historical mass balances, in which the variability is typically unknown. Reconciled data from different Cu/Mo concentrators were employed to evaluate the effect of small numerical disturbances in the grade data on the mineral recovery estimation. Higher error propagation was typically observed for Fe. The Mo minerals presented numerical problems, mainly in second cleaners and in the first cell of rougher banks. Lower condition numbers were observed for Cu due to the higher flotation rates.

  Mass-balance data reconciliation without redundancy was evaluated for a typical Cu/Mo flotation circuit using relative error minimization. Significant relative errors in the mineral recovery estimation were obtained with nonreconciled data in ill-conditioned problems. Negligible improvements in the mineral recovery estimation because of the data reconciliation with regard to the nonreconciled approach were obtained in well-conditioned problems. In addition, the improvements in mineral recovery estimation by using Cu, Mo and Fe in the data reconciliation were nonsignificant with respect to using only the best-conditioned component in well- and ill-conditioned problems.

  Despite the effort in data reconciliation and data repetition, poor performance may be obtained in ill-conditioned problems, which can deteriorate the flotation rate characterization. The error propagation has a negative impact on the mineral recovery of the first cell, which may significantly bias the flotation rate characterization of both valuable and nonvaluable elements.