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Typically, coarse dense mineral particles greater than 150 μm are difficult to float, and the recovery decreases progressively. Various physical parameters can be manipulated in an attempt to increase the recovery. These physical parameters are the following: liberation, turbulence in the flotation cell, pH, collector, frother type and dosage. The testwork discussed in this paper was performed for a copper-molybdenum operation that is experiencing coarse particle (>150 μm) losses in the tails. This operation uses Diesel No. 2 fuel and sodium ethyl xanthate for molybdenum and copper flotation, respectively and X-133 frother. In an attempt to increase coarse particle recovery, stronger collectors (potassium amyl xanthate, Aero 249 and Aero 3501) and frothers (FrothPro 618, FrothPro 630 and FrothPro 706) were used. The analysis was performed using the Analysis of Variance (ANOVA) approach. The conditions required by the ANOVA method were met. The results showed that the collector potassium amyl xanthate (PAX) with frothers X-133 and FrothPro 630 resulted in approximately 3% increase in copper rougher recovery relative to the baseline (sodium ethyl xanthate and X-133). The collectors and frothers did not have a significant effect on molybdenum recovery within the dosage limits investigated.

The maximum recovery of particles in flotation is typically in the 20 to 150 μm size range [

The froth phase is an extremely important part of flotation. If the froth phase is unstable, then the flotation performance, recovery and grade, will be poor. Froth stability is strongly influenced by particle size and hydrophobicity [

To obtain higher coarse particle flotation in conventional flotation cells, higher hydrophobicity (more collector and/or stronger collector) is needed to increase the detachment forces required to pull the particle from the air bubble [

The testwork presented in this paper was done for a copper-molybdenum operation that is experiencing fine particles (<20 μm) and coarse particle losses (>150 μm). The objective is to increase the coarse particle recovery by using stronger collectors (increasing surface hydrophobicity) and stronger frothers (higher glycol concentration). The collectors tested are the following: sodium ethyl xanthate (baseline), potassium amyl xanthate, Aero 3501 and Aero 249. The frothers used are the following: X-133 (baseline), FrothPro 618, FrothPro 630 and FrothPro 706. The FrothPro 618, FrothPro 630 and FrothPro 706 frothers have higher concentrations of glycol relative to the X-133 frother.

The paper also presents a strict statistical approach to assess the results. The ANOVA statistical approach was used to determine the significance of the results.

The ore was crushed to 2000 μm (−10 mesh), blended and split into 1 kg charges which were used in this testwork (grind curve determination and flotation).

A grind curve to achieve a P_{80} of 265 µm was developed using a lab scale mill. The grinding was done at 60% solids by weight, lime was added to the mill to achieve a pH of 10.3, and 20.6 µL of No 2 Diesel fuel was added to the mill. The dosage of Diesel No 2 fuel in the mill (20.6 μL) was kept constant throughout the testwork.

A lab scale mill (internal length of 40.64 cm and internal diameter of 20.32 cm) with ~14 kg of mild steel balls of assorted sizes (

The flotation tests were performed using a Denver laboratory machine with a 2 litre cell. The flotation testwork was based on the procedure indicated by the concentrator that provided the ore for testing. In all the flotation tests, concentrates 1, 2, 3 and 4 were collected for 45 seconds, 1.25 minutes, 3.0 minutes and 2.0 minutes, respectively for a total of 7 minutes. 0.648 g/t (0.0360 lb/st) of collector and 0.081 g/t (0.0045 lb/st) of X-133 frother were added at the beginning of the flotation test. In all of the flotation tests X-133 was added prior to concentrate 1. Whereas an additional 0.0405 g/t (0.0023 lb/st) of frother was added at the beginning of concentrates 3 and 4. The frother type added prior to concentrates 3 and 4 changed depending on the test. The pH was maintained at 10.3 using lime throughout the test.

The collectors used were the following: sodium ethyl xanthate (SEX), potassium amyl xanthate (PAX), Aero 3501 and Aero 249. The frothers used were the following: X-133, FrothPro 618, FrothPro 630 and FrothPro 706. All the tests were duplicated for a total of 32 flotation tests.

Copper | Iron | Molybdenum | Total Sulphur | |
---|---|---|---|---|

Average (%) | 0.275 | 1.81 | 0.0136 | 0.70 |

St. Deviation | 2.95 × 10^{−3 } | 4.34 × 10^{−2 } | 1.11 × 10^{−3 } | 1.19 × 10^{−16 } |

RSD (%) | 1.07 | 2.40 | 8.16 | 1.70 × 10^{−14 } |

Ball Diameter (inches) | # of Balls | Ball Distribution (%) |
---|---|---|

1.50 | 16 | 5.32 |

1.25 | 25 | 8.38 |

1.00 | 38 | 12.78 |

0.75 | 87 | 29.35 |

0.625 | 131 | 44.17 |

Reagent | Dosage (g/t) | Conditioning Time (Minutes) | Stage | Flotation Time (Minutes) | Total Flotation Time (Minutes) |
---|---|---|---|---|---|

Collector | 0.648 | 1.0 | Conc 1 | 0.75 | 0.75 |

X-133 | 0.081 | 0.5 | |||

Conc 2 | 1.25 | 2.0 | |||

Frother | 0.0405 | 1.0 | Conc 3 | ||

3.0 | 5.0 | ||||

Frother | 0.0405 | 1.0 | Conc 4 | ||

2.0 | 7.0 |

*pH of 10.3 was maintained using lime throughout the test.

Collector | Frother - Concentrate 1 | Frother - Concentrate 3 | Frother - Concentrate 4 |
---|---|---|---|

PAX | X-133 | X-133 | X-133 |

Aero 3501 | X-133 | X-133 | X-133 |

Aero 249 | X-133 | X-133/FrothPro 618 | X-133/FrothPro 618 |

Aero 249 | X-133 | X-133/FrothPro 706 | X-133/FrothPro 706 |

PAX | X-133 | X-133/FrothPro 630 | X-133/FrothPro 630 |

Aero 3501 | X-133 | X-133 | X-133 |

SEX | X-133 | X-133 | X-133 |

Aero 249 | X-133 | X-133/FrothPro 618 | X-133/FrothPro 618 |

PAX | X-133 | X-133/FrothPro 630 | X-133/FrothPro 630 |

Aero 249 | X-133 | X-133 | X-133 |

SEX | X-133 | X-133/FrothPro 706 | X-133/FrothPro 706 |

Aero 3501 | X-133 | X-133/FrothPro 706 | X-133/FrothPro 706 |

Aero 3501 | X-133 | X-133/FrothPro 618 | X-133/FrothPro 618 |

Aero 249 | X-133 | X-133 | X-133 |

SEX | X-133 | X-133/FrothPro 618 | X-133/FrothPro 618 |

PAX | X-133 | X-133/FrothPro 706 | X-133/FrothPro 706 |

Aero 3501 | X-133 | X-133/FrothPro 630 | X-133/FrothPro 630 |

SEX | X-133 | X-133/FrothPro 630 | X-133/FrothPro 630 |

Aero 249 | X-133 | X-133/FrothPro 706 | X-133/FrothPro 706 |

PAX | X-133 | X-133/FrothPro 706 | X-133/FrothPro 706 |

Aero 3501 | X-133 | X-133/FrothPro 630 | X-133/FrothPro 630 |

SEX | X-133 | X-133/FrothPro 618 | X-133/FrothPro 618 |

Aero 3501 | X-133 | X-133/FrothPro 706 | X-133/FrothPro 706 |

Aero 249 | X-133 | X-133/FrothPro 630 | X-133/FrothPro 630 |

SEX | X-133 | X-133/FrothPro 706 | X-133/FrothPro 706 |

PAX | X-133 | X-133/FrothPro 618 | X-133/FrothPro 618 |
---|---|---|---|

Aero 249 | X-133 | X-133/FrothPro 630 | X-133/FrothPro 630 |

SEX | X-133 | X-133/FrothPro 630 | X-133/FrothPro 630 |

Aero 3501 | X-133 | X-133/FrothPro 618 | X-133/FrothPro 618 |

PAX | X-133 | X-133 | X-133 |

PAX | X-133 | X-133/FrothPro 618 | X-133/FrothPro 618 |

SEX | X-133 | X-133 | X-133 |

The flotation products were dried at ~35˚C. The concentrates were weighed and pulverized for assaying. The tails were weighed and passed through a 300 µm screen to break-up any clumps. Then, they were homogenized for 1 hour using a V-blender and split into 8 sub-samples using a laboratory spin riffler. Two tails sub-samples were pulverized and sent for assaying. Also, these tails sub-samples were used for mineralogy if necessary.

The mineralogical characterization was done using an automated scanning electron microscope (TESCAN Integrated Mineral Analyzer—TIMA). The feed and selected flotation tailings were sieved into size fractions. Polished sections of 30 mm diameter were prepared from each size fraction. Two polished sections were prepared from each size fraction coarser than 150 µm. This was done to analyze more particles. For the size fractions 150 µm and finer only one polished section was prepared. The TIMA run was done at 25 kV of acceleration voltage and 5 nA of beam current analyzing spots on the particles every 5 µm (high resolution map mode).

The mineralogical characterization was done for each size fraction of the feed. This is known as a size-by-size mineralogical characterization. This approach yields a large amount of data. 3D plots allow illustrating large amount of data.

The Y-axis gives the cumulative percentage of the molybdenite that is in the size fraction indicated in the X-axis at several liberation classes indicated by the Z-axis (also shown as the bar colour).

Collector | X-133 | X-133/FrothPro 618 | X-133/FrothPro 630 | X-133/FrothPro 706 |
---|---|---|---|---|

SEX | 82.48 | 79.90 | 84.13 | 83.19 |

82.42 | 80.20 | 85.59 | 81.05 | |

PAX | 82.02 | 80.19 | 85.16 | 86.29 |

81.54 | 85.60 | 86.63 | 84.57 | |

Aero 3501 | 80.99 | 82.14 | 83.30 | 81.36 |

83.34 | 82.94 | 79.63 | 81.20 | |

Aero 249 | 83.42 | 80.44 | 82.46 | 82.09 |

79.78 | 81.85 | 81.22 | 78.32 |

Collector | X-133 | X-133/FrothPro 618 | X-133/FrothPro 630 | X-133/FrothPro 706 |
---|---|---|---|---|

SEX | 71.36 | 74.21 | 73.14 | 79.62 |

65.05 | 63.77 | 77.07 | 75.44 | |

PAX | 73.10 | 81.28 | 76.42 | 68.84 |

70.43 | 73.62 | 79.15 | 77.16 | |

Aero 3501 | 73.46 | 73.32 | 75.29 | 74.73 |

75.19 | 76.40 | 65.66 | 80.50 | |

Aero 249 | 76.49 | 72.61 | 75.67 | 73.86 |

74.46 | 72.93 | 79.29 | 71.47 |

The ANOVA analysis is used by experimenters in various fields of research to test the effect of dependent variables on independent variables [

A two variable ANOVA analysis was performed. The theory is presented below [

SS collector = ( 1 b n ) ∑ i = 1 a y i .. 2 − ( y … 2 a b n ) (1)

SS frother = ( 1 a n ) ∑ j = 1 b y . j . 2 − ( y ... 2 a b n ) (2)

where

SS_{collector} is the sum of squares for the collectors

SS_{frother} is the sum of squares for the frothers

b is the number of frothers used in the testwork

a is the number of collectors used in the testwork

n is the number of replicates (in this testwork n = 2)

y_{i}_{.} is the total of the observations for collector i

y_{.j}_{.} is the total of the observations for frother j

y_{...} represents the grand total of all observations

SS total = ∑ i = 1 a ∑ j = 1 b ∑ k = 1 n y i j k 2 − y … 2 a b n (3)

where

SS_{total} is the total sum of squares

y_{ijk} is the observation ijk. This represents each observation for every collector i and frother j.

SS interaction = 1 n ∑ i = 1 q ∑ j = 1 b y i j . 2 − y … 2 a b n − SS collector − SS frother (4)

SS error = SS total − SS collector − SS frother − SS interaction (5)

y_{ij}_{.} is the sum of the observations of collector i and frother j or the sum of the replicates for collector i and frother j. The mean square is the sum of square divided by the degrees of freedom.

MS collector = SS collector a − 1 (6)

MS frother = SS frother b − 1 (7)

MS interaction = SS interaction ( a − 1 ) ( b − 1 ) (8)

MS error = SS error a b ( n − 1 ) (9)

where

MS_{collector} is the mean square of the collectors

MS_{frother} is the mean square of the frothers

MS_{interaction} is the mean square of the interaction between the collectors and frothers

MS_{error} is the mean square of the error

For the collectors the F_{o} is defined as:

F o = MS collector MS error (10)

For the frothers the F_{o} is defined as:

F o = MS frother MS error (11)

For the interaction between the collectors and frothers the F_{o} is defined as:

F o = MS interaction MS error (12)

where

F_{o} is a constant in the f distribution.

The F_{o} value is compared to the critical f value in the f distribution. The f critical value is obtained for a certain confidence level, the degrees of freedom for the variable in question and degrees of freedom of error. If the F_{o} is greater than the f critical, then the variable in question has a significant effect on the output (mineral recovery).

_{o} versus the f critical values indicate that

Source of Variation | Sum of Squares | Degrees of Freedom | Mean Square | Fo | f_{critical}_{ } | P value | Significant |
---|---|---|---|---|---|---|---|

Collector | 34.18 | 3 | 11.39 | 3.98 | 3.24 | 0.027 | Yes |

Frother | 15.80 | 3 | 5.27 | 1.84 | 3.24 | 0.181 | No |

Interaction | 36.38 | 9 | 4.04 | 1.41 | 2.54 | 0.263 | No |

Error | 45.82 | 16 | 2.86 | ||||

Total | 132.18 | 31 |

the collectors had a significant impact on copper recovery (5% the effect was due to chance). The frothers and the interaction between the collectors and frothers were not significant. However, before accepting these results, we have to check for the normality of the residuals, constant variance as well as the relationship between the residuals versus run order of the tests and copper recovery versus run order. This analysis is discussed below.

The residuals of the tests have to be normally distributed. The residual is defined as follows:

Residual = Recovery of metal in test − average ( recovery of test 1 and recovery of test 2 ) (13)

Standardized value of residual = residual MS error (14)

The standardized values of the points not on the normality line (indicated by the arrows) are 1.59. These are less than 2.0, thus they are not outliers [

whether the variance is constant. For copper recoveries below ~83% the variance is constant, whereas, the variance for copper recoveries above ~83% is lower (dotted red circle in

To establish whether the variance is constant, the modified Levene test for equal variance was performed. This procedure is robust in departures from normality and can be calculated by the equation below [

d i j = Absolute ( y i j − median of treatment ) (15)

where

d_{ij} represents the deviation from treatment median for observation ij

y_{ij} represents the observation ij

ij represents variable A at the i^{th} and variable B at the j^{th} level

The null hypothesis is that the variance is constant, and the alternate hypothesis is the variance is not constant.

_{ij}) for the modified Levene

test of the observations for the collectors (copper recovery).

_{o} is not greater than the f critical, thus, the variance for the collectors is constant, or we do not reject the null hypothesis.

_{ij}) for the modified Levene test of the observations for the frothers (copper recovery).

_{o} is not greater than the f critical, thus, the variance for the frothers is constant, or we do not reject the null hypothesis.

Collector | X-133 | X-133/FrothPro 618 | X-133/FrothPro 630 | X-133/FrothPro 706 |
---|---|---|---|---|

SEX | 0.03 | 2.55 | 1.68 | 0.74 |

0.03 | 2.25 | 3.14 | 1.40 | |

PAX | 2.85 | 4.68 | 0.30 | 1.43 |

3.33 | 0.70 | 1.77 | 0.30 | |

Aero 3501 | 3.88 | 2.73 | 1.57 | 3.51 |

1.59 | 1.19 | 2.12 | 0.55 | |

Aero 249 | 1.89 | 1.10 | 0.32 | 0.56 |

1.76 | 0.32 | 0.93 | 3.22 |

Source of Variation | Sum of Squares | Degrees of Freedom | Mean Square | Fo | f_{critical}_{ } | P value | Significant |
---|---|---|---|---|---|---|---|

Collector | 3.88 | 3 | 1.29 | 0.84 | 2.93 | 0.483 | No |

Error | 42.92 | 28 | 1.53 | ||||

Total | 46.80 |

Collector | X-133 | X-133/FrothPro 618 | X-133/FrothPro 630 | X-133/FrothPro 706 |
---|---|---|---|---|

SEX | 0.26 | 1.25 | 0.42 | 1.47 |

0.20 | 0.95 | 1.88 | 0.68 | |

PAX | 0.20 | 0.96 | 1.45 | 4.57 |

0.68 | 4.42 | 2.92 | 2.85 | |

Aero 3501 | 1.23 | 1.0 | 0.42 | 0.37 |

1.12 | 1.80 | 4.09 | 0.53 | |

Aero 249 | 1.20 | 0.71 | 2.50 | 0.37 |

2.44 | 0.71 | 1.26 | 3.41 |

Source of Variation | Sum of Squares | Degrees of Freedom | Mean Square | F_{o} | f_{critical}_{ } | P value | Significant |
---|---|---|---|---|---|---|---|

Frother | 7.87 | 3 | 2.62 | 1.79 | 2.93 | 0.172 | No |

Error | 40.96 | 28 | 1.46 | ||||

Total | 48.83 |

residuals versus run order, respectively. There should be no trends in these graphs. If there are trends, then something went wrong with the experiments or the results are biased. In both figures there is no trend in that data, which is acceptable.

All the conditions for the ANOVA were met for copper recovery, thus, conclusions can be made with high level of confidence regarding the effects of collectors and frothers on copper recovery.

As discussed, the collectors had a significant impact on copper recovery. However, in order to determine which collector(s) had a significant impact on copper recovery, the Fisher Least Significance Method analysis was used at the 90% and 95% confidence level.

The equation for the Fisher Least Significance Method is shown below [

LSD = t α 2 , d f 2MS error n (16)

where

t α 2 , d f is the critical t value from t distribution at 100 (1 − α) confidence with df degrees of freedom

MS_{error} is the mean square of error

n is the number of replicates

LSD is the minimum difference between the observations required for a confidence at 100 (1 − α)

The Fisher Least Significance difference showed that the following conditions are significant at the 95% confidence level (copper recovery).

1) PAX & X-133/FrothPro 630 and PAX & X-133

2) PAX & X-133/FrothPro 630 and Aero 3501 & X-133

3) PAX & X-133/FrothPro 630 and Aero 249 & X-133

4) PAX & X-133/FrothPro 630 and SEX & X-133/FrothPro 618

5) PAX & X-133/FrothPro 630 and Aero 249 & X-133/FrothPro 618

6) PAX & X-133/FrothPro 630 and Aero 3510 & X-133/FrothPro 630

7) PAX & X-133/FrothPro 630 and Aero 249 & X-133/FrothPro 630

8) PAX & X-133/FrothPro 630 and SEX & X-133/FrothPro 706

9) PAX & X-133/FrothPro 630 and Aero 3510 & X-133/FrothPro 706

10) PAX & X-133/FrothPro 630 and Aero 249 & X-133/FrothPro 706

11) PAX & X-133/FrothPro 706 and PAX & X-133

12) PAX & X-133/FrothPro 706 and Aero 249 & X-133

13) PAX & X-133/FrothPro 706 and SEX & FrothPro 618

14) PAX & X-133/FrothPro 706 and Aero 249 & FrothPro 618

15) PAX & X-133/FrothPro 706 and Aero 3501 & X-133/FrothPro 630

16) PAX & X-133/FrothPro 706 and Aero 249 & X-133/FrothPro 630

17) PAX & X-133/FrothPro 706 and SEX & X-133/FrothPro 706

18) PAX & X-133/FrothPro 706 and Aero 3501 & X-133/FrothPro 706

19) PAX & X-133/FrothPro 706 and Aero 249 & X-133/FrothPro 706

The test that resulted in the highest copper recovery is PAX & X-133/FrothPro 630. As mentioned earlier, the baseline (SEX and X-133) is currently used in the operation in question; thus, we would like to know the confidence level of the difference in copper recovery between the test with the highest copper recovery and the baseline. Thus, the Fisher Least Squared at the 90% confidence level was performed.

If a 90% confidence level is considered.

LSD = t 0.05 , 16 2 × 2.86 2 (17)

where t_{0.05,16} = 1.746

LSD = 2.95

The difference between the copper recovery of the baseline (SEX and X 133) and PAX & X-133/FrothPro 630 has to be at least 2.95%. The test with PAX & X-133/FrothPro 630 resulted in a copper difference of 3.44%. Therefore, the copper recovery increase between the conditions PAX & X-133/FrothPro 630 and SEX &X-133 is 3.44% at the 90% confidence level.

In order to confirm at which particle ranges the recovery increased, a size-by-size mineralogical analysis on the tails was done as well as a size by size recovery. The mass pull for these tests was low; thus, obtaining enough concentrate sample for mineralogy was not possible.

size-by-size for SEX & X-133 and PAX & X-133/FrothPro 630. The size-by-size copper recovery was calculated by subtracting the amount of chalcopyrite in the feed and tails. The raw size-by-size copper recovery data (there was not enough mass in the concentrates to perform data reconciliation) showed that higher copper recovery was achieved at 150 μm for the test conducted with SEX & PAX & X-133/FrothPro 630 compared to that obtained with the baseline. Thus, at sizes 212 μm and higher, conventional flotation was not effective at recovering coarse particles regardless of the reagents used.

_{o} parameters are not greater than the f critical parameters (95% confidence level) for the collectors, frothers and interaction between the collectors and frothers.

Source of Variation | Sum of Squares | Degrees of Freedom | Mean Square | Fo | f_{critical}_{ } | P value | Significant |
---|---|---|---|---|---|---|---|

Collector | 30.44 | 3 | 10.15 | 0.67 | 3.24 | 0.583 | No |

Frother | 44.24 | 3 | 14.75 | 0.97 | 3.24 | 0.431 | No |

Interaction | 221.94 | 9 | 24.66 | 1.63 | 2.54 | 0.189 | No |

Error | 242.78 | 16 | 15.17 | ||||

Total | 539.41 |

graphs should be scattered or there should not be any trend. If there was a trend, then the data would be biased or an undesirable event could have happened, thus, influencing the data. There are no trends. Therefore, this requirement is met. All the requirements of the molybdenum recovery are met, thus, the ANOVA conclusions are reliable.

The improvements made with PAX and X-133/FrothPro 630 were confirmed using statistical analysis. This approach should be used with all testing conducted in metallurgy. Therefore, the metallurgist and management can make important decisions with a good level of confidence.

The testwork shows that both a stronger collector and frother (higher glycol concentration) are required for coarse particle recovery. The stronger collector for higher hydrophobicity of the recoverable mineral and a stronger frother to support the coarser particles in the froth phase.

In the plant there are other factors that need to be considered. If large flotation cells are used, for example, 300 m^{3}, then the operator has to ensure that enough frother is added to have a stable froth. Also, froth crowders may be considered to reduce the residence time of the particles in the froth phase before entering the launders. Reducing this time will reduce particle drop back to the pulp phase.

· The Analysis of Variance (ANOVA) analysis was used to establish whether the effects of the collectors and frothers on copper and molybdenum recoveries were significant. All the requirements of the ANOVA methodology were met; thus, the conclusions derived from the ANOVA analysis are reliable.

· The condition with PAX & X-133/FrothPro 630 resulted in the highest copper recovery gain relative to the baseline (SEX & X-133). The copper recovery gain was approximately 3%.

· The collectors and frothers did not have a significant effect on molybdenum recovery.

The authors are grateful for the good laboratory testwork performed by Raymond Chevrier. The contribution of the Canmet Mining Analytical Services Group is gratefully acknowledged.

The authors declare no conflicts of interest regarding the publication of this paper.

Feo, T.D. and Lastra, R. (2019) Effects of Collectors and Frothers on Copper and Molybdenum Coarse Particle Recoveries—A Statistical Approach. Journal of Minerals and Materials Characterization and Engineering, 7, 117-136. https://doi.org/10.4236/jmmce.2019.73009