Improvement of Copper Recovery of Low-Grade Deposit Using Optimization of Flotation Process Parameters with Hydrofroth as a Frother ()
1. Introduction
The need to use complex or low-grade ores, whose average particle size is too small for efficient separation, and the high demand for metals are forcing us to resort to new technologies to process rock masses. Flotation is the main process for these rock masses [1]-[3]. According to [2] and [4]-[7], it is an essential physico-chemical process for particle separation, based on differences in surface properties of minerals. The behavior of the flotation technique is linked to the intrinsic characteristics of the ore, which evolve throughout the exploitation of the deposit [3] [8] [9]. In this context, optimizing flotation parameters and conducting a new ore characterization are paramount to continuously maintaining or improving concentrator performance [10]-[12]. However, the Kakula deposit contains indicated and inferred mineral resources with respective cut-off grades of 3% and 1% [13]. After a thorough study and careful analysis, the target grade for feeding the Kakula concentrator was 5%. Nevertheless, there are occasions when the mine feeds the concentrator with grades lower than this target value, impacting the operational performance of the concentrator. Consequently, it has become imperative to investigate the flotation behavior of ore feed at grades below the target grade. The Taguchi and multi-objective methods have proven effective for guiding research, considering the numerous study parameters and the desire to obtain valid and reliable conclusions efficiently and cost-effectively [14] [15]. The Taguchi approach shed light on experimental designs, which previously held less interest among industrial professionals due to a lack of pragmatism [16]. It clarified and simplified experimental designs by solving the problem of excessive trial numbers that scientists would have executed then, risking waiting even a year for results [17] [18]. This approach has been widely adopted in product design and optimization, quality engineering, and experimental methods. The principle of minimizing product or process variability through experimental planning and optimization forms the foundation for this method [19] [20]. The approach described will be applied in this study to establish a cause-and-effect relationship between specific parameters (referred to as factors) assumed to influence the phenomenon’s behavior, and others (referred to as responses) characterizing the outcome of this phenomenon. In reviewing the literature, the authors [21]-[25] worked on the flotation of copper sulfide minerals. Among the study parameters, the air flow rate as the study parameter was not considered in their experiments. The authors applied the Taguchi methodology for optimizing control variables; however, this method optimizes control variables and responses separately. Therefore, including the air flow rate parameter in our research and applying multi-objective optimization for all responses distinguishes our work as a unique case compared to recent studies in copper sulfide mineral flotation. Multi-objective optimization deals with problems with multiple objective functions to maximize or minimize [22].
The overall objective of this study is to improve the recovery of copper through froth flotation of ores from the Kakula deposit, while setting optimal parameters that lead to improved copper recovery efficiency and satisfactory copper grade. Specifically, it will be necessary to characterize the ores from the Kakula deposit, study their grindability, determine the influence of specific parameters on recovery yield and grade, and predict the optimal parameters of the model leading to optimal copper recovery yield and grade.
2. Materials and Methods
2.1. Materials
Flotation tests were conducted on a copper sulfide ore sample from the low-grade ore storage area at the Kakula mine in the southeastern part of the Democratic Republic of Congo (DRC). During the flotation tests, Sodium Isobutyl Xanthate (SIBX) was used as the collector (product of Axis House), Hydrofroth (HDF) was employed as a frother, and AERO (promoter) served as the secondary collector. The water used in our experiments originated from the Kakula wastewater treatment plant. The chemical characterization of the sample was carried out for various metals using the X-ray Fluorescence Spectroscopy (Niton™ XL5 Plus Handheld, Japan).
2.2. Methods
The study began with developing the Taguchi experimental design, followed by sample collection at the Kakula mine. The experiments were conducted in the Kakula concentrator laboratory. The research was concluded by statistical analysis of results using Minitab 21.4.0 software.
2.2.1. Experimental Setup
The tests were conducted using an Altso flotation machine with a parallelepiped cell capacity of 2.8 liters. The unit features a variable digital display of shaft rpm (revolutions per minute), allowing for precise agitator speed control, which is crucial for mastering aeration and agitation intensity. It also includes air pressure, flow control, and a digital timer for accurate test duration. The cell agitator’s rotation speed was set at 600 rpm. Various materials were employed to facilitate our experiments on the flotation machine, starting from sample collection to chemical analysis of the samples. A scoop and a bag were used for sample collection from the low-grade ore storage area at the mine. A laboratory jaw crusher and a RockLab were utilized for particle size reduction from + 8 mm to 2 mm. A rotary sample divider ensured sample representativeness. A series of sieves (25, 38, 53, 75, 106, 150 μm) was also used for particle size analysis and grindability studies. A laboratory rod mill was used for mineral grinding. A vacuum pump, filter paper, pans, an oven, and a plate, as well as a balance, pipettes (2 μl - 20 μl; 50 μl - 200 μl), and syringes (3, 5, 10 ml), were used respectively for filtering the rough and waste materials, containing the samples, drying the samples, weighing the samples, cleaning the mill, adding water to the cell, extracting the quantity of reagents, preparing the reagents, taking water to put in the mill, and holding the pulp.
2.2.2. Origin of Sample
To successfully conduct the tests, a sample of 100 kg of low-grade ore was collected from the low-grade ore storage area on the Kakula underground mine. Fifteen sample points were randomly targeted on the low-grade ore storage area to ensure representativeness of the sample.
2.2.3. Mineralogy of Kakula Deposit
Based on the previous study on the mineralogy of the Kakula deposit conducted by XPS Expert Process Solutions, the Kakula ore is rich in chalcocite. Other major mineral phases are bornite and chalcopyrite. Gangue minerals are quartz, feldspar, micas, and chlorite. Fe oxides and carbonates are minor phases [13]. This work assumes that the ore sample contains the same mineral phase.
2.2.4. Experimental Procedure for the Grindability Study
The sample, as received, consisted of coarse particles larger than 8 mm. Initially, it underwent primary crushing using a laboratory jaw crusher and secondary crushing in the rock lab. Subsequently, the ore was subjected to wet grinding at various intervals to determine the correlation between particle size and grinding time. The mill was wet fed with 0.835 kg, 1.035 kg, and 1.295 kg, respectively, corresponding to 25%, 30%, and 35% solid percentages. Grinding time was determined for the 15%, 20%, and 25% rejection range on the 53 µm sieve, following variations in solid percentage.
2.2.5. Experimental Flotation Plan
Based on previous studies and literature, the air flow rate is not considered as a parameter. This study chose the percentage solids, air flow rate, oversize at 53µm, collector dosage, frother dosage, and secondary collector dosage as the six main parameters to be investigated. According to the Taguchi design methodology, three levels were chosen for each parameter as illustrated in Table 1. Considering the six parameters and the relevant three levels, a Taguchi orthogonal array (L27) was established to execute the experiment. The Kakula Concentrator's operational Conditions inspired the selection of three levels for each factor. Twenty-seven experiments were therefore conducted as shown in Table 2. Numbers one (1) to three (3) in Table 2 are the relative levels of the parameters indicated in Table 1. In this study, interactions between parameters were not taken into consideration.
Table 1. Controllable factors and their levels.
Parameter |
Code |
Unit |
Levels |
I |
II |
III |
Solid mass percentage |
A |
% |
25 |
30 |
35 |
Oversize at 53 µm |
B |
µm |
15 |
20 |
25 |
Air flow rate |
C |
l/mina |
6 |
8 |
10 |
SIBX dosage |
D |
g/tb |
206 |
256 |
306 |
Hydrofroth dosage |
E |
g/t |
103 |
133 |
163 |
AERO dosage |
F |
g/t |
10 |
30 |
50 |
Note: aLitter per min, bgram per ton.
In experiments based on the Taguchi design, signal-to-noise (SN) ratios are recommended for optimizing process parameters [20] [26]. The term Signal-to-Noise Ratio (SN) establishes a relationship between the average of the response (signal) and the dispersion of the response concerning the noise (background noise) [15]. The SN ratios can then be calculated based on the required response characteristics, i.e., “larger is better”, “smaller is better”, and “nominal is better”. In this study, the aim is to increase recovery yield and copper content. Therefore, SN ratios for “larger is better” and smaller is better were selected and calculated using response values. The SN ratio for this scenario was determined using Equations (1) and (2) [22]:
(1)
(2)
Where n is the number of repetitions of experiments, and
is the response value (recovery) of the i-th experiment, and j successively takes the values
.
Table 2. Taguchi Orthogonal array (L27) for influencing factors and their levels coded with actual values in brackets.
Row |
Controllable factors |
A |
B |
C |
D |
E |
F |
1 |
1 (25) |
1 (15) |
1 (6) |
1 (206) |
1 (103) |
1 (10) |
2 |
1 (25) |
1 (15) |
1 (6) |
1 (206) |
2 (133) |
2 (30) |
3 |
1 (25) |
1 (15) |
1 (6) |
1 (206) |
3 (163) |
3 (50) |
4 |
1 (25) |
2 (20) |
2 (8) |
2 (256) |
1 (103) |
1 (10) |
5 |
1 (25) |
2 (20) |
2 (8) |
2 (256) |
2 (133) |
2 (30) |
6 |
1 (25) |
2 (20) |
2 (8) |
2 (256) |
3 (163) |
3 (50) |
7 |
1 (25) |
3 (25) |
3 (10) |
3 (306) |
1 (103) |
1 (10) |
8 |
1 (25) |
3 (25) |
3 (10) |
3 (306) |
2 (133) |
2 (30) |
9 |
1 (25) |
3 (25) |
3 (10) |
3 (306) |
3 (163) |
3 (50) |
10 |
2 (30) |
1 (15) |
2 (8) |
3 (306) |
1 (103) |
2 (30) |
11 |
2 (30) |
1 (15) |
2 (8) |
3 (306) |
2 (133) |
3 (50) |
12 |
2 (30) |
1 (15) |
2 (8) |
3 (306) |
3 (163) |
1 (10) |
13 |
2 (30) |
2 (20) |
3 (10) |
1 (206) |
1 (103) |
2 (30) |
14 |
2 (30) |
2 (20) |
3 (10) |
1 (206) |
2 (133) |
3 (50) |
15 |
2 (30) |
2 (20) |
3 (10) |
1 (206) |
3 (163) |
1 (10) |
16 |
2 (30) |
3 (25) |
1 (6) |
2 (256) |
1 (103) |
2 (30) |
17 |
2 (30) |
3 (25) |
1 (6) |
2 (256) |
2 (133) |
3 (50) |
18 |
2 (30) |
3 (25) |
1 (6) |
2 (256) |
3 (163) |
1 (10) |
19 |
3 (35) |
1 (15) |
3 (10) |
2 (256) |
1 (103) |
3 (50) |
20 |
3 (35) |
1 (15) |
3 (10) |
2 (256) |
2 (133) |
1 (10) |
21 |
3 (35) |
1 (15) |
3 (10) |
2 (256) |
3 (163) |
2 (30) |
22 |
3 (35) |
2 (20) |
1 (6) |
3 (306) |
1 (103) |
3 (50) |
23 |
3 (35) |
2 (20) |
1 (6) |
3 (306) |
2 (133) |
1 (10) |
24 |
3 (35) |
2 (20) |
1 (6) |
3 (306) |
3 (163) |
2 (30) |
25 |
3 (35) |
3 (25) |
2 (8) |
1 (206) |
1 (103) |
3 (50) |
26 |
3 (35) |
3 (25) |
2 (8) |
1 (206) |
2 (133) |
1 (10) |
27 |
3 (35) |
3 (25) |
2 (8) |
1 (206) |
3 (163) |
2 (30) |
2.2.6. Flotation Test Experimental Procedure
The flotation test was conducted according to the Kamoa standard. The flotation time was 40 minutes, with an additional 14 minutes of conditioning (5 minutes for the first adding reagent, 3 minutes for the second, and 2 minutes for the third until five adding reagent). Before beginning the flotation test, the pH of the pulp was fixed at 8.66. For each trial, five (5) concentrate fractions were removed, along with the tailing fraction. The flotation test process carried out during the study can be summarized in Figure 1. The method of obtaining pulp with a well-defined solid percentage was first carried out through wet grinding. Next, a 5-minute conditioning step was performed by adding 60% SIBX, 57% Hydrofroth, and 100% AERO. The reagents, such as SIBX, Hydrofroth, and AERO, were prepared at 1%, 97%, and 50%, respectively.
Figure 1. Flotation test experimental procedure.
The amount of metal copper recovered was calculated using Equation (3), which is based on assays alone of the feed (f), tailings (t), and concentrate (c) [9]:
(3)
2.2.7. Analysis of Variance
The theory of analysis of variance (ANOVA) aims to analyze a situation where the effect of one or more factors on a variable is investigated. In other words, it is a method for studying the variability of a product based on a set of production factors that can be systematically controlled [22] It uses statistical tests to evaluate the variation between groups (intergroup variance) compared to the variation within groups (intragroup variance). More formulas used in ANOVA can be shown in Table 3.
Table 3. Formulas in analysis of variance [22].
Parameters |
Formulas |
Equation |
Total sum of squared
deviations |
|
(4) |
Sum of squared deviations |
|
(5) |
Sum of squared error |
|
(6) |
Variance |
|
(7) |
Total degrees of freedom of the result |
|
(8) |
Variance ratio |
|
(9) |
Pure sum of squares of each factor |
|
(10) |
Contribution of each
parameter to the response |
|
(11) |
In Equations (4) and (5), N is the total number of observations or experiments, Yi is the metal recovery for the itch experiment. In Equations (6) and (7), p is one of the experiment’s parameters, and j is the level number of this p parameter. NK is the number of levels for each parameter (3 in this case), and
is the degrees of freedom for the p parameter. In Equation (8), (fT) is the total degrees of freedom of the result and is equal to the total number of experiments (27 in this case) minus one. In Equation (9), VE is the error’s mean square (variance). This is used to evaluate the significance of the parameters on the response. Minitab breaks down the SS Regression or SS treatments component into the amount of variation explained by each term using both the sequential sum of squares (Seq SS) and adjusted sum of squares (Adj SS) after Minitab defines the mean square Adjusted (MS Adj) to determine the F-Value as presented in Equations (10) and (11).
2.2.8. Performance Prediction by Taguchi Method
The Taguchi methodology operates on the principle that the trial corresponding to the optimal conditions found may or may not be conducted during the experimentation phase, but the prediction of the performance value of the experiment can be made based on the prediction function represented by Equation (12) [8].
(12)
With T representing the sum of all trial responses, n the total number of trials, and
the average responses at level i, j, etc.
2.2.9. Performance Prediction by Multi-Objective Method
To optimize all outcomes simultaneously, a compromise is necessary. Based on [22], the desirability function is the most effective way to achieve this. Minitab Software was used to calculate composite desirability as the weighted geometric mean of the individual desirability for each response. This mathematical approach ensures that if any individual’s desirability is zero (implying that one response is unacceptable), the composite desirability will also be zero, thereby highlighting a critical failure point. The formula for composite desirability is given by (Equation (13)):
(13)
represents the individual desirability score for the i-th response.
denotes the importance value assigned explicitly to the i-th response, reflecting its relative priority. n is the total number of responses included in the optimization. We fixed
at 10, 10, 5, 5 for the recovery, silica yield, mass pull, and copper content responses.
A quadratic model was established for each response as a function of the control variables. This was done to determine the relationship between the technological performance factors (copper recovery, mass pull, copper content, and silica yield) and the control parameters. Several models were tested before considering the models presented in Table 17.
(14)
Where
are input factors that influence the responses y;
are constant parameters of the model, and
is the random error. Furthermore, cross-factors and variables were applied to the models to ensure fit. Statistical parameters such as R² and S (a parameter accounting for residuals) were a guide for good model fit.
3. Results and Discussion
This section summarizes the findings regarding copper flotation performance in the supplied sulfide ores. It is also dedicated to data analysis and identifying the optimal levels for all control parameters.
3.1. Chemical and Sieve Assay Analysis of the Sample
Table 4 details the chemical analysis of the sample examined in this study. The analysis revealed a copper concentration of 4.29%, alongside a significant silica presence of 55.81%, which poses a considerable challenge for the process. Figure 2 visualizes the results of the particle size chemical analysis conducted on the ore sample. This figure shows that a significant proportion of copper is below 53 µm. These findings corroborate the metallurgical test results reported recently during feasibility studies related to the Kakula deposit [13].
Table 4. The chemical composition of the ore sample from the Kakula mine.
Component % |
Cu |
SiO2 |
MgO |
Ca |
Fe |
4.29 |
55.81 |
4.37 |
0.67 |
5.01 |
Figure 2. Sieve assay analysis results for Cu from the Kakula mine ore.
Based on the grindability study results presented with the equations of the curves below (Figure 3), the times required were determined (see Table 5) to achieve 15%, 20%, and 25% oversize at 53 µm sieve.
Figure 3. Grindability curves: Each equation determined the grind time at 15.20, and 25% oversize at +53 µm. y represents the oversize at +53 µm, and x represents the grind time(min).
Table 5. Grinding results at various times.
Sample Types |
Oversize at 53 µm (%) |
Grinding time (min) |
Sample (25% solid) |
15 |
18.9 |
20 |
16.6 |
25 |
14.8 |
Sample (30% solid) |
15 |
20.7 |
20 |
18.1 |
25 |
16 |
Sample (35% solid) |
15 |
30.5 |
20 |
26.1 |
25 |
22.8 |
3.2. Results of Copper Metal Recovery
The average recovery of copper by flotation and the copper content for the various combinations of process parameters and levels are shown in Table 6. The highest recovery of copper of 95,45% into the concentrate occurred in the 24th experiment run (% solids = 35; oversize at 53 µm = 20%; air flow rate = 6l/min; SIBX dosage = 306 g/t; HDF dosage = 163g/t; AERO dosage = 30 g/t) and the lowest (86.88%) was recorded in the 27th experiment run ((% solids = 35; oversize at 53 µm = 25%; air flow rate = 8l/min; SIBX dosage = 206g/t; HDF dosage = 163g/t; AERO dosage = 30g/t). The highest copper content of 12.30% of the concentrate, occurred in the 18th experiment run.
Table 6. Experimental results for Cu metal.
Row |
A |
B |
C |
D |
E |
F |
R_Cu |
%Cu |
Mass pull |
Silica yield |
1 |
25 |
15 |
6 |
206 |
103 |
10 |
91.90 |
11.98 |
43.42 |
39.93 |
2 |
25 |
15 |
6 |
206 |
133 |
30 |
92.70 |
12.02 |
44.19 |
40.71 |
3 |
25 |
15 |
6 |
206 |
163 |
50 |
94.62 |
6.76 |
54.30 |
51.19 |
4 |
25 |
20 |
8 |
256 |
103 |
10 |
93.85 |
7.33 |
49.98 |
44.33 |
5 |
25 |
20 |
8 |
256 |
133 |
30 |
94.33 |
7.09 |
51.59 |
47.27 |
6 |
25 |
20 |
8 |
256 |
163 |
50 |
94.92 |
6.81 |
55.25 |
52.36 |
7 |
25 |
25 |
10 |
306 |
103 |
10 |
94.34 |
7.42 |
51.58 |
49.44 |
8 |
25 |
25 |
10 |
306 |
133 |
30 |
94.78 |
7.08 |
52.98 |
49.02 |
9 |
25 |
25 |
10 |
306 |
163 |
50 |
94.29 |
7.60 |
48.94 |
46.16 |
10 |
30 |
15 |
8 |
306 |
103 |
30 |
94.29 |
12.02 |
48.65 |
45.28 |
11 |
30 |
15 |
8 |
306 |
133 |
50 |
94.48 |
11.64 |
49.62 |
45.80 |
12 |
30 |
15 |
8 |
306 |
163 |
10 |
92.62 |
10.07 |
48.31 |
45.19 |
13 |
30 |
20 |
10 |
206 |
103 |
30 |
94.31 |
11.66 |
50.95 |
47.91 |
14 |
30 |
20 |
10 |
206 |
133 |
50 |
94.30 |
11.10 |
51.76 |
48.30 |
15 |
30 |
20 |
10 |
206 |
163 |
10 |
93.85 |
11.95 |
49.58 |
18.35 |
16 |
30 |
25 |
6 |
256 |
103 |
30 |
92.76 |
9.76 |
48.94 |
45.46 |
17 |
30 |
25 |
6 |
256 |
133 |
50 |
93.88 |
11.96 |
49.37 |
45.84 |
18 |
30 |
25 |
6 |
256 |
163 |
10 |
93.98 |
12.30 |
49.10 |
45.66 |
19 |
35 |
15 |
10 |
256 |
103 |
50 |
93.73 |
11.06 |
55.69 |
52.80 |
20 |
35 |
15 |
10 |
256 |
133 |
10 |
94.89 |
9.38 |
57.76 |
55.09 |
21 |
35 |
15 |
10 |
256 |
163 |
30 |
95.10 |
10.01 |
61.67 |
59.26 |
22 |
35 |
20 |
6 |
306 |
103 |
50 |
92.74 |
11.64 |
51.83 |
51.79 |
23 |
35 |
20 |
6 |
306 |
133 |
10 |
93.51 |
10.61 |
58.27 |
53.96 |
24 |
35 |
20 |
6 |
306 |
163 |
30 |
95.45 |
7.62 |
57.96 |
55.42 |
25 |
35 |
25 |
8 |
206 |
103 |
50 |
93.50 |
7.89 |
45.96 |
43.08 |
26 |
35 |
25 |
8 |
206 |
133 |
10 |
92.91 |
10.01 |
52.11 |
50.48 |
27 |
35 |
25 |
8 |
206 |
163 |
30 |
86.88 |
7.62 |
60.56 |
57.76 |
3.3. Effect of Different Parameters on Responses
To determine the effect that each parameter has on the responses (copper recovery, copper content, mass pull, and Silica yield), the signal-to-noise ratio (SN) was calculated for each experiment. The SN ratio is based on “larger is better” (Equation (1)) or “smaller is better” (Equation (2)). The average SN ratios of each level of the six parameters for the flotation of copper were calculated and listed in Tables 7-10. Delta values, which show the relative significance of the factors, were also calculated as the difference between the maximum and minimum average values. Based on this, the collector SIBX dosage was the most influential factor affecting the copper recovery response. The Hydrofroth dosage had the least influence on copper recovery response. Furthermore, Solid mass percentage is the most influential factor affecting the copper content, Mass pull, and Silica yield responses.
Table 7. Average SN values for copper recovery at three levels of parameters and delta statics.
Code |
Flotation
parameter |
Level 1 |
Level 2 |
Level 3 |
Delta
(max-min) |
Rank |
A |
Solid mass
percentage |
39.46 |
39.45 |
39.38 |
0.07 |
4 |
B |
Oversize at 53 µm |
39.44 |
39.48 |
39.37 |
0.10 |
3 |
C |
Air flow rate |
39.42 |
39.37 |
39.50 |
0.12 |
2 |
D |
SIBX dosage |
39.35 |
39.48 |
39.47 |
0.13 |
1 |
E |
Hydrofroth dosage |
39.42 |
39.46 |
39.42 |
0.04 |
6 |
F |
Aero dosage |
39.42 |
39.40 |
39.47 |
0.06 |
5 |
Table 8. Average SN values for copper content at three levels of parameters and delta statics.
Code |
Flotation
parameter |
Level 1 |
Level 2 |
Level 3 |
Delta
(max-min) |
Rank |
A |
Solid mass
percentage |
18.09 |
21.10 |
19.49 |
3.02 |
1 |
B |
Oversize at 53 µm |
20.34 |
19.36 |
18.97 |
1.37 |
3 |
C |
Air flow rate |
20.26 |
18.84 |
19.57 |
1.43 |
2 |
D |
SIBX dosage |
19.90 |
19.38 |
19.39 |
0.52 |
6 |
E |
Hydrofroth dosage |
19.90 |
19.93 |
18.84 |
1.09 |
4 |
F |
Aero dosage |
19.96 |
19.29 |
19.42 |
0.67 |
5 |
Table 9. Average SN values for mass pull at three levels of parameters and delta statics.
Code |
Flotation
parameter |
Level 1 |
Level 2 |
Level 3 |
Delta
(max-min) |
Rank |
A |
Solid mass
percentage |
34.00 |
33.91 |
34.89 |
0.99 |
1 |
B |
Oversize at 53 µm |
34.18 |
34.47 |
34.14 |
0.34 |
5 |
C |
Air flow rate |
34.08 |
34.18 |
34.53 |
0.46 |
4 |
D |
SIBX dosage |
33.99 |
34.50 |
34.30 |
0.51 |
3 |
E |
Hydrofroth dosage |
33.90 |
34.29 |
34.61 |
0.70 |
2 |
F |
Aero dosage |
34.14 |
34.45 |
34.21 |
0.31 |
6 |
Table 10. Average SN values for silica yield at three levels of parameters and delta statics.
Code |
Flotation
parameter |
Level 1 |
Level 2 |
Level 3 |
Delta
(max-min) |
Rank |
A |
Solid mass
percentage |
−33.50 |
−32.40 |
−34.50 |
2.10 |
1 |
B |
Oversize at 53 µm |
−33.62 |
−33.02 |
−33.61 |
0.60 |
4 |
C |
Air flow rate |
−33.53 |
−33.58 |
−33.14 |
0.44 |
6 |
D |
SIBX dosage |
−32.55 |
−33.90 |
−33.80 |
1.35 |
2 |
E |
Hydrofroth dosage |
−33.35 |
−33.68 |
−33.22 |
0.46 |
5 |
F |
Aero dosage |
−32.66 |
−33.88 |
−33.71 |
1.22 |
3 |
The level of a parameter with the highest average SN ratio corresponds to a better performance and gives the best combination level. Therefore, the optimal levels of flotation parameters have the most significant average SN ratio. The optimum levels of parameters for recovery of copper are solid mass percentage, 25% (Level 1); oversize at 53 µm, 20% (Level 2); air flow rate, 10 l/min (Level 3); SIBX dosage, 256 g/t (Level 2); Hydrofroth dosage, 133 g/t (Level 2); and AERO dosage, 50 g/t (Level 3). As far as, the optimum levels of parameters for copper content response are solid mass percentage, 30% (Level 2); oversize at 53 µm, 15% (Level 1); air flow rate, 6 l/min (Level 1); SIBX dosage, 206g/t (Level 1); Hydrofroth dosage,133 g/t (Level 2); and AERO dosage, 10 g/t (Level 1). The optimum levels of parameters for mass pull response are solid mass percentage, 35% (Level 3); oversize at 53 µm, 20% (Level 2); air flow rate, 10 l/min (Level 3); SIBX dosage,256 g/t (Level 2); Hydrofroth dosage,163 g/t (Level 3); and AERO dosage, 30 g/t (Level 2). The optimum levels of parameters for silica yield response are solid mass percentage, 30% (Level 2); oversize at 53 µm, 20% (Level 2); air flow rate, 10 l/min (Level 3); SIBX dosage,206g/t (Level 1); Hydrofroth dosage, 163 g/t (Level 3); and AERO dosage, 10 g/t (Level 1). A plot of the graph of the parameter against its response on each level is referred to as the main effect, and it indicates the general trend of influence of each parameter (Figure 4).
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Figure 4. The main effects of the process parameter on copper recovery, copper content, mass pull, and silica yield, respectively.
3.4. Analysis of Variance (ANOVA) Results
The parameters that significantly affected responses were investigated using the analysis of variance (ANOVA). The analysis of variance for copper recovery shows that at a confidence level of α = 0.95, the calculated F-values for parameters A (F = 0.62), B (F = 1.12), C (F = 1.54), D (F = 2.05), E (F = 0.26), and F (F = 0.42) not exceed the critical F-value read from Fisher tables (F (2,14) = 3.739) (Table 11). None of these factors significantly affects the recovery of copper at the tested confidence level of 95%. Regarding importance, the critical probabilities or p-values for A, B, C, D, E, and F parameters are 0.553, 0.354, 0.249, 0.165, 0.776, and 0.667, respectively. This allows us to judge the D parameter as the most significant, as it has the least critical probability.
Table 11. ANOVA table for copper recovery (at 95% confidence interval).
Source |
DF |
Seq SS |
Adj SS |
Adj MS |
F-Value |
P-Value |
A |
2 |
0.02895 |
0.02895 |
0.014477 |
0.62 |
0.553 |
B |
2 |
0.05244 |
0.05244 |
0.026218 |
1.12 |
0.354 |
C |
2 |
0.07213 |
0.07213 |
0.036064 |
1.54 |
0.249 |
D |
2 |
0.09607 |
0.09607 |
0.048036 |
2.05 |
0.165 |
E |
2 |
0.01208 |
0.01208 |
0.006039 |
0.26 |
0.776 |
F |
2 |
0.01956 |
0.01956 |
0.009778 |
0.42 |
0.667 |
Residual Error |
14 |
0.32777 |
0.32777 |
0.023412 |
|
0.553 |
Total |
26 |
0.60900 |
|
|
|
|
Analysis of variance for copper content in concentrate shows that at a confidence level of α = 0.95, the calculated F-values for parameters A (F = 12.7) exceed the critical F-value read from Fisher tables (F (2,14) = 3.739) (Table 12). This parameter is therefore statistically significant for copper content. Regarding importance, A’s critical probabilities or p-value is 0.001 (<5%). This allows us to judge the A parameter as the most significant. Furthermore, the A parameter is statistically significant for mass pull and silica yield (Table 13 and Table 14).
Table 12. ANOVA table for copper content (at 95% confidence interval).
Source |
DF |
Seq SS |
Adj SS |
Adj MS |
F-Value |
P-Value |
A |
2 |
40.982 |
40.982 |
20.4910 |
12.17 |
0.001 |
B |
2 |
8.957 |
8.957 |
4.4784 |
2.66 |
0.105 |
C |
2 |
9.155 |
9.155 |
4.5775 |
2.72 |
0.101 |
D |
2 |
1.624 |
1.624 |
0.8119 |
0.48 |
0.627 |
E |
2 |
6.938 |
6.938 |
3.4692 |
2.06 |
0.164 |
F |
2 |
2.273 |
2.273 |
1.1366 |
0.68 |
0.525 |
Residual Error |
14 |
23.565 |
23.565 |
1.6832 |
|
|
Total |
26 |
93.494 |
|
|
|
|
Table 13. ANOVA table for mass pull (at 95% confidence interval).
Source |
DF |
Seq SS |
Adj SS |
Adj MS |
F-Value |
P-Value |
A |
2 |
5.3760 |
5.3760 |
2.6880 |
8.73 |
0.003 |
B |
2 |
0.6004 |
0.6004 |
0.3002 |
0.98 |
0.401 |
C |
2 |
1.0259 |
1.0259 |
0.5130 |
1.67 |
0.224 |
D |
2 |
1.1913 |
1.1913 |
0.5956 |
1.93 |
0.181 |
E |
2 |
2.2399 |
2.2399 |
1.1200 |
3.64 |
0.053 |
F |
2 |
0.4692 |
0.4692 |
0.2346 |
0.76 |
0.485 |
Residual Error |
14 |
4.3100 |
4.3100 |
0.3079 |
|
|
Total |
26 |
15.2128 |
|
|
|
|
Table 14. ANOVA table for Silica Yield (at 95% confidence interval).
Source |
DF |
Seq SS |
Adj SS |
Adj MS |
F-Value |
P-Value |
A |
2 |
5.3760 |
5.3760 |
2.6880 |
8.73 |
0.003 |
B |
2 |
0.6004 |
0.6004 |
0.3002 |
0.98 |
0.401 |
C |
2 |
1.0259 |
1.0259 |
0.5130 |
1.67 |
0.224 |
D |
2 |
1.1913 |
1.1913 |
0.5956 |
1.93 |
0.181 |
E |
2 |
2.2399 |
2.2399 |
1.1200 |
3.64 |
0.053 |
F |
2 |
0.4692 |
0.4692 |
0.2346 |
0.76 |
0.485 |
Residual Error |
14 |
4.3100 |
4.3100 |
0.3079 |
|
|
Total |
26 |
15.2128 |
|
|
|
|
3.5. Prediction Results of the Optimum Performance by Taguchi Method
Table 15. Predicted SN and responses at optimum conditions.
Target |
A |
B |
C |
D |
E |
F |
Predicted value |
SN |
Response (%) |
Copper recovery (max) |
25 |
20 |
10 |
256 |
133 |
50 |
39.69 |
96.4 |
Copper content (max) |
30 |
15 |
6 |
206 |
133 |
10 |
23.71 |
14.2 |
Mass pull |
35 |
20 |
10 |
256 |
163 |
30 |
34.58 |
56.3 |
Silica yield |
30 |
20 |
10 |
206 |
163 |
10 |
-29.89 |
35.4 |
The established optimal conditions, defined by specific levels of factors A to F, enabled the maximization of the signal-to-noise ratio (SN) for copper recovery and content, as well as for mass pull (M_Pull), while minimizing silica yield (S_Y) (Table 15). This optimization suggests improved process stability in the face of operational parameter fluctuations. Although copper recovery reaches a high level (96.4%) under these ideal conditions, a trade-off is evident with the silica yield (35.4%). To overcome this imbalance, a multi-objective approach would prove essential to simultaneously improve copper recovery and minimize silica entrainment in the concentrate.
3.6. Prediction Results of the Optimum Performance Using
Multi-Objective Method
The Taguchi method identified the best values for each outcome. However, a multi-objective approach was necessary for this study to prove essential to obtain optimal parameters that can improve copper recovery and minimize silica yield. Table 16 provides statistical parameters such as R2 and S (a parameter accounting for residuals). A quadratic model was established for each response as a function of the control variables (Table 17).
Table 16. Summary of models.
Reponses |
Statistical parameters |
S |
R2 |
R_Cu |
1.71638 |
69.42% |
M_pull |
2.23661 |
93.65% |
%_Cu |
1.29,73 |
89.01% |
S_Y |
6.45793 |
80.70% |
Table 17. Mathematical models obtained.
Terms |
Coefficients |
R_Cua |
%Cu |
M_pullb |
S_Yc |
A |
62.8 |
−33.3 |
59.1 |
204 |
B |
0.87 |
6.35 |
−9.41 |
−19.28 |
C |
1.61 |
−1.291 |
3.42 |
−1.06 |
D |
−2.56 |
−6.51 |
−0.03 |
8.2 |
E |
0.065 |
−0.100 |
0.673 |
0.882 |
F |
−0.026 |
0.058 |
−0.189 |
−0.54 |
A*A |
0.381 |
−0.097 |
0.666 |
1.08 |
B*B |
−0.0100 |
−0.1000 |
0.1366 |
0.277 |
C*C |
−0.0286 |
0.0110 |
−0.0693 |
0.064 |
D*D |
0.216 |
0.291 |
0.198 |
−0.095 |
E*E |
−0.000298 |
0.000118 |
−0.000838 |
−0.00125 |
F*F |
−0.000257 |
−0.001035 |
0.00144 |
0.00200 |
A*E |
0.00070 |
0.00046 |
−0.00076 |
−0.00059 |
A*F |
−0.00152 |
−0.00327 |
0.01977 |
0.0387 |
B*E |
−0.00474 |
0.00721 |
−0.0288 |
−0.0600 |
B*F |
−0.00235 |
0.00670 |
−0.00627 |
−0.0149 |
C*E |
−0.00763 |
−0.00628 |
0.0048 |
0.0151 |
C*F |
−0.0017 |
0.01373 |
−0.0251 |
−0.0702 |
D*E |
−0.0152 |
−0.0058 |
0.0287 |
0.0863 |
|
0.000754 |
0.000253 |
−0.001707 |
−0.00144 |
Note: aCopper Recovery, bMass pull, cSilica yield.
The obtained models were applied to the multi-objective method’s algorithm using Minitab 21.4.0 software. Thus, the optimized results are visualized in Figure 5. It can be seen that to achieve the best overall results (95.4% copper recovery, 48.0% mass pull, 12.2% copper content, and 24.8% silica yield), the following control variables should be used: 28.53% mass solid percentage, 21.1% oversize at 53 µm sieve, 10 l/min air flow rate, 249.4 g/t of SIBX, 163.0 g/t of Hydrofroth, and 10 g/t of AERO.
Figure 5. Optimization plot for all responses using Minitab 21.4.0 software.
Comparing the results obtained by the Taguchi and multi-objective methods, the multi-objective approach contributes more to minimizing silica, 24% versus 35%. This means a small percentage of silica would be carried into the concentrate.
4. Conclusions
Given the variability in ore grade, achieving high recovery rates and maintaining an optimal copper grade was critical. The current study explored improving copper recovery from the Kakula low-grade deposit using flotation process optimisation. This research employed the Taguchi experimental design and multi-objective optimisation to determine the most effective flotation parameters. Key factors investigated included solid mass percentage, air flow rate, particle size, frother dosage (HYDOFROTH), collector dosage (SIBX), and secondary collector dosage (AERO). The main conclusion of this study within the levels of process parameters selected is:
1) For Taguchi method, the optimum conditions for maximum copper recovery are solid mass percentage, 25%; oversize at 53 µm, 20%; air flow rate, 10 l/min; SIBX dosage, 256 g/t; Hydrofroth dosage, 133 g/t; and AERO dosage, 50 g/t collector dosage, 80 g/t. For maximum copper content in concentrate, the optimum conditions are solid mass percentage, 30%; oversize at 53 µm, 15%; air flow rate, 6 l/min; SIBX dosage, 206 g/t; Hydrofroth dosage, 133 g/t; and AERO dosage, 10 g/t. For maximum mass pull response, the optimum condition are solid mass percentage, 35% (Level 3); oversize at 53 µm, 20% (Level 2); air flow rate, 10 l/min (Level 3); SIBX dosage, 256 g/t (Level 2); Hydrofroth dosage, 163 g/t (Level 3); and AERO dosage, 30 g/t (Level 2). The optimum levels of parameters for silica yield response are solid mass percentage, 30% (Level 2); oversize at 53 µm, 20% (Level 2); air flow rate, 10 l/min (Level 3); SIBX dosage, 206 g/t (Level 1); Hydrofroth dosage, 163 g/t (Level 3); and AERO dosage, 10 g/t (Level 1). The predicted values for copper recovery, copper content, mass pull, and silica yield at the optimum conditions are: 96.38%, 14,18%, 56.3%, and 35.4%, respectively. For the Taguchi method, despite having better Copper recovery, a potential entrainment of silica into the concentrate is noted. Working with the operating conditions proposed by this method requires additional cleaning steps to eliminate entrained silica in the concentrate.
2) The best overall results for the multi-objective method are 95.4% copper recovery, 48.0% mass pull, 12.2% copper content, and 24.8% silica yield. The following control variables should be used: 28.53% mass solid percentage, 21.1% oversize at 53 µm sieve, 10 l/min air flow rate, 249.4 g/t of SIBX, 163.0 g/t of Hydrofroth, and 10 g/t of AERO. The multi-objective approach contributes more to minimizing silica, 24% versus 35%.
3) The relative significance of flotation parameters (based on the difference between max and min. average values) was that the collector SIBX dosage was the most influential factor affecting the copper recovery response. The Hydrofroth dosage had the least influence on copper recovery response. Furthermore, solid mass percentage is the most influential factor affecting the copper content, mass pull, and silica yield responses.
4) Based on ANOVA and at a 95% confidence level, the collector dosage SIBX parameter is the most significant, as it has the lowest critical probability. Solid mass percentage is statistically significant for copper content in concentrate, mass pull, and silica yield.
5) The finding in this study constitutes a basis for the comprehension of the flotation of Kakula ores. Still, it would be necessary to carry out pilot-scale tests for these findings and consider the economic approach of the proposed processes, energy consumption, and water consumption for future research.
Acknowledgements
The authors gratefully acknowledge Kamoa Copper SA for permitting experiments in their metallurgical laboratories. Special thanks are also extended to SGS SA for their invaluable assistance in characterizing the ore sample.
Author Contributions
Conceptualization and methodology, B.O.-N, K.-T, and P.K.-T; formal analysis and investigation, B.O.-N; writing—original draft preparation, B.O.-N; writing—review and editing, B.O.-N, A.K.-K, K.-T, J.H.-M, and A.W; Supervision, K.-T and A.K.-K. All authors have read and agreed to the published version of the manuscript.