Data and Computations to Determine Time Corresponding to Maximum Separation Efficiency (Figure 12.58), and to Determine Flotation Rate Constant (Figure 12.59)
1. Maximum separation efficiency (Figure 12.58)
| 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 |
| Time (min) | Mass % | Assay (%) | Units (Mass % X % PbS) | Rec PbS (%) | Cum R PbS (%) | Units (Mass % X % G) | Rec G (%) | Cum R G (%) | CR PbS- CR G (%) | ||
| Pb | PbS | G | |||||||||
| 0.5 | 3.29 | 72.9 | 84.18 | 15.82 | 276.95 | 37.25 | 37.25 | 52.05 | 0.56 | 0.56 | 36.69 |
| 1 | 2.12 | 66.9 | 77.25 | 22.75 | 163.77 | 22.03 | 59.28 | 48.23 | 0.52 | 1.08 | 58.20 |
| 1.5 | 1.88 | 51.7 | 59.7 | 40.3 | 112.24 | 15.10 | 74.38 | 75.76 | 0.82 | 1.90 | 72.48 |
| 2 | 1.44 | 37.5 | 43.3 | 56.7 | 62.35 | 8.39 | 82.77 | 81.65 | 0.88 | 2.78 | 79.98 |
| 4 | 4.28 | 19.2 | 22.17 | 77.83 | 94.89 | 12.76 | 95.53 | 333.11 | 3.60 | 6.38 | 89.15 |
| 6.5 | 3.53 | 2.41 | 2.78 | 97.22 | 9.81 | 1.32 | 96.85 | 343.19 | 3.71 | 10.09 | 86.76 |
| 10 | 4.82 | 0.82 | 0.95 | 99.05 | 4.58 | 0.62 | 97.47 | 477.42 | 5.16 | 15.25 | 82.22 |
| 14 | 3.87 | 0.82 | 0.95 | 99.05 | 3.68 | 0.49 | 97.96 | 383.32 | 4.14 | 19.39 | 78.57 |
| 20 | 4.33 | 0.49 | 0.57 | 99.43 | 2.47 | 0.33 | 98.29 | 430.53 | 4.65 | 24.04 | 74.26 |
| Tails | 70.44 | 0.16 | 0.18 | 99.82 | 12.68 | 1.71 | 100.00 | 7031.32 | 75.96 | 100.00 | 0.00 |
| Head | 100.00 | 6.44 | 7.43 | 92.57 | 743.41 | 100.00 | 9257.00 | 100.00 | |||
Column 4: conversion of Pb assay to PbS
Column 5: determination of gangue (G) assay, 100-column 3b
Column 6: intermediate step in calculation for recovery of PbS, column 2×column 4
Column 7: determination of increment PbS recovery, column 6/Σ column 6 (“head”)
Column 8: cumulative recovery of PbS (or Pb)
Column 9: intermediate step in calculation for recovery of G, column 2×column 5
Column 10: determination of increment G recovery, column 6/Σ column 9 (“head”)
Column 11: cumulative recovery of G
Column 12: determination of separation efficiency, column 8 – column 11
Maximum separation efficiency is determined from:
a. plot of Column 12 (CR PbS−CR G) versus time; and
b. from plot of increment Pb grade (assay, %Pb, column 3) versus time, both given in Figure 12.58
2. Determination of flotation rate constant: disappearance plot (Figure 12.59)
| 1 | 2 | 3 |
| Time (min) | Cum R PbS (%) | 1−Cum R/100 |
| 0.5 | 37.25 | 0.6275 |
| 1 | 59.28 | 0.4072 |
| 1.5 | 74.38 | 0.2562 |
| 2 | 82.77 | 0.1723 |
| 4 | 95.53 | 0.0447 |
| 6.5 | 96.85 | 0.0315 |
| 10 | 97.47 | 0.0253 |
| 14 | 97.96 | 0.0204 |
| 20 | 98.29 | 0.0171 |
Column 2: same as column 8 above
Column 3: calculation of mass remaining, converted to fraction
From the plot of column 3 (1−Cum R/100) versus time (the “disappearance plot,” Figure 12.59), the first 2 min give good approximation to simple first order, with k=0.88 min−1.
In principle the same computations could be applied to gangue. In that case you will find an R∞ is required to fit the data (i.e., Eq. (12.51)); and, of course, it assumes gangue recovery also follows first-order kinetics which is likely not the case, especially as entrainment tends to be an important factor in batch tests.