On the Mineral Recovery Estimation in Cu/Mo Flotation Plants

"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, ?, 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 ? 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.IntroductionMass balances have been extensively used in flotation processes to determine the mass flowrates (production) and mineral recovery (efficiency) of valuable minerals. Simple relationships for steadystate processes based on the feed, concentrate and tail grades can be obtained by taking a black-box approach. However, the calculation of concentrate flowrates from different components of the system, such as size fractions, chemical elements or minerals, does not satisfy the mass-conservation principle because of measurement errors (Smith and Ichiyen, 1973; Romagnoli and Sánchez, 2000). Mass-balance data reconciliation allows for obtaining a unique solution that satisfies the total and component mass balances, making small adjustments to the process data and taking advantage of the information redundancy (Narasimhan and Jordache, 2000). This methodology, which is based on a constrained weighted least-squares minimization, has proved to be robust when measurement errors are normally distributed, in the absence of gross errors.Commercial software has been developed to conduct massbalance data reconciliation in flotation processes, including MATBAL (Algosys, 2002), BILMAT (Algosys, 2013), JKMultibal (JKTech, 2013), BILCO (Caspeo, 2013) and HSC Chemistry (Outotec, 2013), which accomplish the reconciliation using known data accuracy in the optimization problem. The data accuracy can be obtained by sampling a stream n times in a run, known as repeats, each with independent chemical assays. Some unmeasured variables can be estimated using the measuring redundancy and sensor location. At present, grade and flow rate sensors may be incorporated in flotation to conduct real-time mass balances. However, a lack of sensor calibration and maintenance for suitable online measurements hinders the quality of the information. In"