Parametric Optimization in Rougher Flotation Performance of a Sulfidized Mixed Copper Ore

Abstract

The dominant challenge of current copper beneficiation plants is the low recoverability of oxide copper-bearing minerals associated with sulfide type ones. Furthermore, applying commonly used conventional methodologies does not allow the interactional effects of critical parameters in the flotation processes to be investigated, which is mostly overlooked in the literature. To tackle this issue, the present paper aimed at characterizing the behavior of five key effective factors and their interactions in a sulfidized copper ore. In this context, dosage of collector (sodium di-ethydithiophosphate, 60–100 g/t), depressant (sodium silicate, 80–120 g/t) and frother (methyl isobutyl carbinol (MIBC), 6–10 g/t), pulp pH (7–11) and agitation rate (900–1300 rpm) were examined and statistically analyzed using response surface methodology. Flotation experiments were conducted in a Denver type agitated flotation cell at the rougher stage. The experimental results showed that increasing the pH (from 8 to 10) at low agitation rate (1000 rpm) enhanced the recovery from 80.36% to 85.22%, while at high agitation rate (1200 rpm), a slight declination occurred in the recovery. Meanwhile, increasing the collector dosage at a lower frother value (7 g/t), caused a reduction of about 4.44% in copper recovery owing to the interactions between factors, whereas at a higher frother level (9 g/t), the recovery was almost unchanged. The optimization process was also performed using the goal function approach, and maximum copper recovery of 92.75% was obtained using ~70 g/t collector, 110 g/t depressant, 7 g/t frother, pulp pH of 10 and 1000 rpm agitation rate.

1. Introduction

Copper is one of the most applicable elements in the metallurgical industries with a production of 10 Mt annually [1]. Treatment operations for copper extraction mostly focus on sulfide or oxide ores owing to the well-established metallurgical processes. With declining copper cut-off grades in sulfide- or oxide-type ore resources, the mixed sulfide-oxide deposits can be considered as an alternative and important source. However, their treatment from the mineral processing perspective is challenging with respect to the complexity of process mineralogy. It is estimated that about 80% of copper is produced from primary ores by the froth flotation, smelting, and refining and the rest of 20% is achieved by hydrometallurgical methods [2].

Flotation is one of the most widely used techniques to separate valuable minerals from gangue minerals in the mineral processing, because of its ability to treat low-grade and complex raw materials in the fine particle size ranges [3,4,5,6,7]. Froth flotation takes place in the presence of three different phases, including solid (particles), liquid (water) and gas (air bubbles). The physical and chemical properties of each phase play a fundamental role in the efficiency of the flotation process. This process for the mixed sulfide-oxide ores is traditionally carried out with two distinctive treatments including direct flotation by fatty acids and sulfidizing by a sulfidization agent such as Na₂S, NaHS, and (NH₄)₂S [8,9,10]. A principal issue involved in the flotation of mixed sulfide-oxide ores and the copper industry is the low recovery of oxide section. This is related to the surface properties of copper oxide minerals, which cannot respond well to traditional sulfide copper collectors [11].

Moreover, flotation operations depend on many factors including the minerals’ nature and structure (mineralogy, morphology and particle size), water chemistry, bubble size and velocity, particle residence time, stator and rotor configurations, hydrodynamic properties, pulp potential and pH, pulp density, air flowrate, and reagent types and dosages [3,6,12,13,14,15,16,17,18,19,20]. An understanding of the influence of these factors is essential to improve the flotation circuit performance. Technically, grade, recovery and selectivity index are commonly used as the most critical metallurgical parameters for this purpose. An increase of 1−2% in these parameters is economically very significant [17] and plays a remarkable role in the desirability of the flotation plants. In fact, an inefficient operation can cause an incorrect balance between grade and recovery, which leads to adverse shifts in the grade-recovery curve [21,22].

Dhar et al. [23] studied the application of xanthate, dithiophosphate, thionocarbamate collectors, and their mixture for flotation of copper sulfides from Nussir ore. They found that xanthate and thionocarbamate with the ratio of 1 to 3 had the highest grade (29%) and copper recovery (98%). Hangone et al. [24] showed that the maximum copper recoveries could be obtained with the di-ethyl-dithiophosphate compared to that obtained with other thiol collectors at the same equivalent dosage. Asadi et al. [25] beneficiated a sequential sulfidization-flotation technique for copper oxide flotation taken from the Chahmora mine situated in Semnan province, Iran. They employed response surface methodology for evaluating and optimizing process performance. Their results indicated that a three-stage sulfidization was suitable for copper flotation to acquire a rougher concentrate with the grade and recovery of 9.28% and 81.15% under optimal conditions after 5 min sulfidization conditioning. Tijsseling et al. [26] examined the flotation behavior of mixed oxide with sulfide copper-cobalt minerals using different collectors. Their findings demonstrated that a dithiophosphate collector could recover over 90% of the copper sulfides, and 70% of the copper oxide minerals. Asghari et al. [27] investigated the improvement of copper recovery in an industrial flotation circuit (Sarcheshmeh copper mine), and stated that about 95% of overall copper lost in final tailing was in the rougher circuit while the rougher flotation recovery of mixed copper ore was 8% less than the sulfide ore. Additionally, the increase of collector and NaHS dosages along with the size reduction of coarse particles (>74 μm) of rougher tailing had a positive influence on the recovery. Following this, Ghodrati et al. [28] applied response surface methodology for the optimization of chemical reagents used in Miduk porphyry copper flotation. They reported that nearly 91.4% copper with the grade of 8.13% was recovered under optimal conditions including 5 g/t Z11, 34 g/t C-4132, 5 g/t A3477, 15 g/t AF65, and 8 g/t MIBC. Ávila-Márquez et al. [29] examined the flotation of a copper sulfide under acidic conditions using a xanthogen formate compound as a collector. They argued that the highest copper recovery was achieved about 97% at an initial collector concentration of 20 mg L⁻¹, a flotation time of 3 min, and pH of 2. The surface oxidation of mineral in copper sulfide flotation was investigated via Moimane et al. [30]. The investigations showed that the surface oxidation of copper sulfide minerals had some detrimental effects on their flotation performance. Also, it was identified that chalcocite flotation was much more sensitive to surface oxidation in comparison to chalcopyrite.

As considered in the literature, many research works have been performed on the optimization and evaluation of the main factors influencing the flotation process [6,17,25,26,27,28,31], but the information on the interaction between influential factors is limited. Meanwhile, each flotation operation has its own specifications and mineralogical properties based on its particular restrictions to achieve the highest recovery and, therefore, requires more detailed investigations. The present research is an attempt to fill this gap. Moreover, many experiments must be carried out to determine the optimal values of influential operating factors on the flotation performance, which is impossible due to the massive number of flotation condition sets. Hence, in this research work, the main and first-order interaction effects of the influential parameters on flotation behavior are characterized using response surface methodology combined with central composite design as an experimental design technique.

2. Theoretical Background

The conventional optimization technique of a multivariable system follows one factor at a time and its major disadvantage is disregarding interactive effects among the factors. Accordingly, it does not imply the complete effects of various factors on the process [32,33,34,35,36,37,38]. Additionally, this approach requires more data to determine optimal level, which is a time-consuming process and undesirable [39]. Thus, design of experiment (DOE) can be used for optimizing such multivariable systems as its successful application has been proven by many researchers in the mineral processing industry [17,40,41,42]. Response surface modeling (RSM) is one of the efficient techniques of DOE, which involves a combination of mathematical and statistical methods based on the multivariate non-linear model in which all factors are varied over a set of experimental runs. This technique is an invaluable, cost-effective and practical tool for analysis of processes and quantification of the relationship between the controllable inputs and the response surfaces (outputs) obtained even in the presence of complex interactions [32,33,43,44,45].

Generally, response surface methodology process involves five major steps containing (i) designing of a series of experiments, (ii) developing a mathematical model with the best fittings for a functional relationship between input factors and outputs, (iii) finding the optimal set of experimental factors that produce a maximum or minimum value of the response(s), (iv) predicting the response(s) and checking the adequacy of the model within the setup of the experiments, and (v) representing the direct and interaction effects of factors [42,43,44,45]. This technique includes different designs such as central composite design (CCD), Box–Behnken design (BBD), three-level factorial, and Doehlert, which CCD is one of the most popular designs used in the process optimization [32,33,45]. It is known that the CCDs with fractional factorial points are the best option to build statistical models in terms of the number of required experiments and quality of the data obtained [46].

In a CCD, the number of experiments (N) is determined according to Equation (1):

$$N=2^{\left(n-p\right)}+2n+n_c$$

(1)

where n is the number of factors and p is fraction of the number of factors (p = 0 is for full factorial design), n_c is number of central runs to estimate experimental error and 2n represents axial runs. In addition, all factors are studied in five levels (−α, −1, 0, +1, +α), where the value of α is the star (axial) point and is measured by the following formula [45,47,48]:

$$\alpha ={(2^{\left(n-p\right)})}^{\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$4$}\right.}$$

(2)

Two significant models, including first-order model (Equation (3)) and second-order polynomial model (Equation (4)) are typically applied in RSM methodology.

$$Y={\beta }_0+{\displaystyle \sum }_{i=1}^k{\beta }_i{x}_i+\epsilon$$

(3)

$$Y={\beta }_0+{\displaystyle \sum }_{i=1}^k{\beta }_i{x}_i+{\displaystyle \sum }_{i=1}^k{\beta }_{ii}{x}_i^2+{\displaystyle \sum }_{1\le i\le j}^k{\beta }_{ij}{x}_i{x}_j+\epsilon$$

(4)

in which Y exhibits the predicted response; k depicts the number of factors; β₀ displays a constant term; β_i denotes the linear coefficients; x_i represents the independent variables or factors; β_ii depicts the quadratic coefficients; β_ij indicates the interaction coefficients; and ε is the error.

In this study, the experimental data are analyzed statistically using Design Expert software (Demo version 7.0.0, from Stat-Ease Inc., Minneapolis, MN, USA) and factors are studied with their codified values for uniform comparison according to the following equation:

$$x_i=\frac{X_i-X_0}{\Delta \mathrm{X}}$$

(5)

where x_i implies the dimensionless coded value of the ith factor, X_i denotes the actual value of the factor, X₀ represents the value of X_i at the center point and ΔX is the step change value [41].

3. Experimental Procedure

3.1. Material and Grinding and Sulfidization Processes

The initial mixed sulfide-oxide copper bulk sample (nearly 100 kg) was provided from Abbas Abad copper mine, located in the northeast of Semnan Province, Iran. The samples were prepared after two stages of laboratory comminution including crushing in a jaw crusher and a roll crusher followed by grinding by a standard Bond ball mill. Firstly, the given sample was crushed using a jaw crusher (Fritsch 01.703, Fritsch, Idar-Oberstein, Germany) to reach a particle size finer than 10 mm. After that, samples were crushed twice by a roll crusher to achieve particles less than 4 mm in diameter. The samples were homogenized and subsequently split by means of cones and riffles. Ultimately, the representative samples were chemically analyzed via X-ray fluorescence spectrometer (XRF Shimadzu-1800, Shimadzu Corporation, Kyoto, Japan) and X-ray diffraction (XRD, Unisantis XMD300, Unisantis, Georgmarienshűtte, Germany) as shown in

Table 1. Chemical analysis of the representative sample obtained from Abbas Abad copper mine (wt.%).

Composition	SiO2	CaO	Fe2O3	K2O	MnO	TiO2	BaO	Al2O3
Content	52.10	6.90	6.34	4.52	0.21	0.71	0.09	17.64
Composition	SO3	P2O5	MgO	Sr	Na2O	Cu *	L.O.I **
Content	0.19	0.61	2.71	0.11	2.66	0.42	4.79

* It composed of 0.22 (wt.%) copper sulfide and 0.2 (wt.%) copper oxide. ** L.O.I. is loss on ignition.

and

Table 2. The X-ray diffraction (XRD) analysis results obtained from Abbas Abad copper ore sample (wt.%).

Compound	Chemical Composition	S-Q	System
Anorthite, sodian, ordered	(Ca,Na)(Al,Si)2Si2O8	16.4	Triclinic
Albite, calcian, ordered	(Na,Ca)Al(Si,Al)3O8	13.2	Triclinic
Microcline, intermediate	KAlSi3O8	11.7	Triclinic
Sanidine, disordered	K(Si3Al)O8	10.5	Monoclinic
Orthoclase	KAlSi3O8	9.4	Monoclinic
Magnesioferrite, high, syn	MgFe2O4	7.0	Cubic
Diopside, aluminian	Ca(Mg,Fe,Al)(Si,Al)2O6	5.8	Monoclinic
Calcite, syn	CaCO3	5.3	Hexagonal
Magnetite	FeO·Fe2O3	4.4	Cubic
Montmorillonite-14A	Na0.3(Al,Mg)2Si4O10(OH)2·xH2O	3.1
Bytownite, low	0.23NaAlSi2O8·0.77CaAl2Si2O8	2.5	Triclinic
Andesine, low	0.62NaAlSi2O8·0.38CaAl2Si2O8	2.4	Triclinic
Chlorite	(Mg,Fe)5(Al,Si)5O10(OH)8	2.3	Monoclinic
Biotite-2 ITM1 RG	KMg3(Si3Al)O10(OH)2	2.1	Monoclinic
Hematite	Fe2O3	2.0	Hexagonal
Kaolinite 1T	Al2Si2O5(OH)4	1.9	Triclinic

, respectively.

Table 1 presents the chemical characterization of the representative samples using XRF, and it confirms the presence of 0.42 (wt.%) copper in the sample studied. Copper minerals of the ore exist in two forms of both oxide (malachite) and sulfide (chalcocite and covellite) minerals. More detailed information in this regard can be found elsewhere [5]. Table 2 demonstrates the XRD analysis of the representative sample. The results demonstrate that the main gangue minerals are silicates and also altered minerals of aluminosilicate, montmorillonite and kaolinite are found in the ore.

Then, 1100 g representative samples were ground by a laboratory Bond ball mill (12 × 5 in, Denver, England) at an optimal time of 22 min [5] with a solid percentage of 70% w/w to reach 80% passing ∼80 µm. This particle range is identified as the most favorable size for copper flotation in several works conducted by the authors [49,50,51,52]. The sieve analysis of mill product (flotation feed) is presented in

Table 3. Sieve analysis of flotation feed sample studied.

Sieve Size (µm)	Mass Retained on Each Sieve (g)	% Weight Retained on Each Sieve	Cumulative % Weight Retained	Cumulative % Weight Passing
2000	4.38	1.41	1.41	98.59
841	1.85	0.59	2.00	98.00
595	0.71	0.23	2.23	97.77
400	0.50	0.16	2.39	97.61
297	1.05	0.34	2.73	97.27
210	3.50	1.12	3.85	96.15
149	7.20	2.31	6.16	93.84
105	18.60	5.97	13.13	87.87
74	30.30	9.72	21.85	78.15
53	28.50	9.14	30.99	69.01
37	45.10	14.97	45.46	54.54
−37	170.03	54.55	100.00	0.00
Sum	311.72	100.00

. It should be mentioned that samples studied are in the oxide and sulfide forms (50% copper sulfide and 50% copper oxide) and their simultaneous flotation is difficult due to different behavior of oxide and sulfide minerals. Therefore, the mechanochemical sulfidization process was applied to sulfidize the oxide copper in the grinding stage. Milling was carried out on the representative sample by adding the sulfur at a value of 0.5% based on ball mill feed weight. We presented this novel process of sulfidization in our previous work, which detailed information was provided there [5].

3.2. Flotation Experiments

Rougher flotation experiments were carried out using a 3 L Denver flotation machine with a solid percentage of about 30% w/w at the desired impeller speed (900–1300 rpm). Lime (Ca(OH)₂) was applied to modify the pH at a targeted level (7–11) during the flotation process. It should be noted that all experiments were carried out using tap water. First, sodium silicate was utilized as a depressant agent of silicate gangue minerals at predetermined values of 80–120 g/t and after 5 min sodium di-ethyldithiophosphate (DTP, Na₃PS₂O₂) was added as a collector at desired values (60–100 g/t). Then, after 3 min conditioning, MIBC (methyl isobutyl carbinol, (CH₃)₂CHCH₂CH(OH)CH₃) as broadly used frother was added into the cell at required values (6–10 g/t). After 1 min, flotation cell was aerated, and froth was collected for 13 min with scraping interval of every 20 s. After each test, the tailings and concentrates were filtered, dried, weighed and assayed for copper content.

4. Results and Discussions

4.1. Design of Experiments

According to the RSM-CCD methodology, 29 sets of experiments (N = 2^{(5 − 1)} + 2 × 5 + 3 = 29) with a suitable combination of the amounts of collector, depressant, frother, pH and agitation speed were designed and conducted. The factors and their levels in coded and actual units are presented in

Table 4. The main factors influencing the copper flotation process and their levels.

Factors	Symbol	Coded Levels
		−2	−1	0	+1	+2
		Actual Levels
Collector dosage (g/t)	A	60	70	80	90	100
Depressant dosage (g/t)	B	80	90	100	110	120
Frother dosage (g/t)	C	6	7	8	9	10
pH	D	7	8	9	10	11
Agitation speed (rpm)	E	900	1000	1100	1200	1300

. It needs to be pointed out that the length of the axial (star) points was chosen based on Equation (2); (α = (2^{(5 − 1)})^1/4 = 2).

Table 5. Central composite design (CCD) matrix and experimental (measured) values of copper recovery.

Run	A	B	C	D	E	Cu Recovery (%)
1	90	110	7	10	1000	86.90
2	80	100	8	11	1100	86.51
3	80	100	10	9	1100	82.14
4	80	100	8	9	1100	82.32
5	70	110	9	10	1000	82.19
6	90	110	9	10	1200	83.53
7	60	100	8	9	1100	79.60
8	80	100	6	9	1100	86.27
9	70	90	7	8	1200	86.55
10	70	90	9	8	1000	79.17
11	90	90	7	8	1000	83.47
12	90	90	9	8	1200	85.74
13	70	90	9	10	1200	80.9
14	70	110	7	10	1200	87.64
15	80	100	8	9	1100	82.28
16	90	110	7	8	1200	81.00
17	70	90	7	10	1000	92.4
18	90	90	7	10	1200	83.71
19	70	110	7	8	1000	87.21
20	80	100	8	9	900	84.64
21	70	110	9	8	1200	88.34
22	90	110	9	8	1000	78.35
23	90	90	9	10	1000	85.03
24	80	120	8	9	1100	84.32
25	100	100	8	9	1100	76.88
26	80	100	8	9	1300	84.98
27	80	100	8	7	1100	81.74
28	80	100	8	9	1100	78.98
29	80	80	8	9	1100	77.45

also shows the design matrix of the variables and the corresponding responses for each experiment.

Since the objective was to investigate and optimize the influential operational factors on the flotation of copper, the copper recovery, R (%) was considered as the process response and calculated by Equation (6).

$$R=\frac{C_{1}c}{Ff}\times 100$$

(6)

where F (g) and C₁(g) depict the dry weight of feed and concentrate and f (%) and c (%) represent the % grade of feed and concentrate, respectively [12].

4.2. Model Construction for Cu Recovery

To understand the behavior of factors and process, it is essential to select an appropriate model. Hence, various models were fitted to the flotation data and assessed by analysis of variance (ANOVA) in terms of the quality and accuracy of the models fitted (

Table 6. Statistical analysis of models for modeling rougher flotation of copper.

Source	SS	DF	MS	F-Value	p-Value
Analysis of Variance (ANOVA) of Models
Mean versus Total	2.02 × 105	1	2.02 × 105
Linear versus Mean	94.81	5	18.96	1.61	0.1985
2FI versus Linear	136.74	10	13.67	1.32	0.3153
Quadratic versus 2FI	93.75	5	18.75	3.64	0.0517	Suggested
Cubic versus Quadratic	21.25	5	4.25	0.64	0.6925	Aliased
Residual	19.99	3	6.66
Total	2.02 × 105	29	6977.64
Analysis of Lack of Fit
Linear	264.38	21	12.59	3.43	0.2502
2FI	127.64	11	11.6	3.16	0.265
Quadratic	33.89	6	5.65	1.54	0.445	Suggested
Cubic	12.64	1	12.64	3.44	0.2048	Aliased
Pure Error	7.35	2	3.67
Statistical Analysis Summary of Models
Source	Std. Dev.	R-Square	PRESS
Linear	3.44	0.2587	443.19
2FI	3.22	0.6317	1579.43
Quadratic	2.27	0.8875	873.73			Suggested
Cubic	2.58	0.9455	14,359.54			Aliased

SS—sum of squares; DF—degrees of freedom; MS—mean squares; PRESS—predicted residual error sum of squares.

).

The ANOVA was introduced by Fisher, who developed it to solve agricultural problems. It enables an assessment of the influence of certain controlled factors on the outcome of an experiment. An analysis of variance can be carried out according to two schemes. The first is to study the variance for the single classification; the second scheme provides for multivariate data analysis. However, the fundamental disadvantage of ANOVA is considered as the impact of only one variable dependent on a certain phenomenon. Wilks met the problem with his multidimensional analysis of variance (MANOVA), which allows a simultaneous examination of relations between two or more independent variables of type and two or more dependent variables of quantitative type. Hence, both ANOVA and MANOVA turn out to be useful in the study of grained mineral properties and their impact on the beneficiation effects [53,54,55,56].

Table 6 shows that a quadratic model is more significant than other models. According to ANOVA in Table 6, F-value for the model (3.64) and the lack of fit is 1.54 indicating that a quadratic polynomial model with R² of 0.8895 is adequate and capable in approximating the response surface and representing the system under the given experimental domain. Therefore, a quadratic polynomial model (Equation (4)) was fitted to experimental data. After removing the very insignificant interaction terms (p-value > 0.1), the final equation representing the recovery of Cu was achieved as a function of collector (A), depressant (B) and frother (C) dosages, pH (D) and agitation speed (E). Equation (7) is the final formula developed based on coded factors:

$$\begin{array}{ll}R=& 80.51-0.92\times \mathrm{A}+0.50\times \mathrm{B}-1.41\times \mathrm{C}+0.92\times \mathrm{D}+0.14\times \mathrm{E}-0.91\times \mathrm{A}\times \mathrm{B}\\ & +1.3\times \mathrm{A}\times \mathrm{C}+1.55\times \mathrm{C}\times \mathrm{E}-1.51\times \mathrm{D}\times \mathrm{E}+1.14\times {\mathrm{C}}^2+1.12\times {\mathrm{D}}^2\\ & +1.29\times {\mathrm{E}}^2\end{array}$$

(7)

From the analysis of Equation (7), because of the individual variables (A, B, C, D and E) and assuming the remaining four mean values equal to zero, it occurs that the maximum values do not exceed 86.83% (R_max(A) = 81.43%; R_max(B) = 81.51%; R_max(C) = 82.25%; R_max(D) = 86.83%; R_max(E) = 85.98%), while R_opt = 92.40%, which is the confirmation that the interactions between individual variables influence the result significantly.

4.3. Model Validation and Statistical Evaluation

After modeling, the data were statistically analyzed at 95% confidence level to evaluate the significance of the model and determine the rank of important factors. ANOVA was used for this purpose, the results of which are presented in

Table 7. ANOVA for response surface modeling (RSM) quadratic model.

Source	SS	DF	MS	F-Value	p-Value
Model	296.79	12	24.73	5.67	0.0009	Significant
A-Collector (g/t)	20.37	1	20.37	4.67	0.0461
B-Depressant (g/t)	5.93	1	5.93	1.36	0.2606
C-Frother (g/t)	47.86	1	47.86	10.98	0.0044
D-pH	20.19	1	20.19	4.63	0.0470
E-Agitation rate (rpm)	0.47	1	0.47	0.11	0.7461
AB	13.2	1	13.2	3.03	0.1011
AC	26.96	1	26.96	6.19	0.0243
CE	38.6	1	38.6	8.85	0.0089
DE	36.51	1	36.51	8.38	0.0106
C2	35.12	1	35.12	8.06	0.0119
D2	33.9	1	33.9	7.78	0.0131
E2	45.03	1	45.03	10.33	0.0054
Residual	69.75	16	4.36
Lack of Fit	62.4	14	4.46	1.21	0.5413	Not significant
Pure Error	7.35	2	3.67
Cor Total	366.54	28
Std. Dev.	2.09
R-Squared	0.8097
Adequate Precision	9.57
PRESS	218.84

. As considered in Table 7, R² is 0.8097, which indicates that the model can explain 80.97% of the variability in Cu recovery. The predictive copper recoveries by the model (Equation (7)) were plotted against the actual values (Figure 1a). Additionally, the values of the conformity factor η² were listed in

Table 8. The proportion of total variance explained by the certain experimental effect.

${{\mathit{\eta }}^2}_{\mathit{m}\mathit{o}\mathit{d}\mathit{e}\mathit{l}}$	${{\mathit{\eta }}^2}_{\mathit{C}}$	${{\mathit{\eta }}^2}_{{\mathit{E}}^2}$	${{\mathit{\eta }}^2}_{\mathit{C}\mathit{E}}$	${{\mathit{\eta }}^2}_{\mathit{D}\mathit{E}}$	${{\mathit{\eta }}^2}_{{\mathit{C}}^2}$	${{\mathit{\eta }}^2}_{{\mathit{D}}^2}$	${{\mathit{\eta }}^2}_{\mathit{A}\mathit{C}}$	${{\mathit{\eta }}^2}_{\mathit{A}}$	${{\mathit{\eta }}^2}_{\mathit{D}}$	Σ (%)
80.97	12.78	12.03	10.31	9.75	9.38	9.06	7.20	5.44	5.39	81.34

, which expresses the percentage of variance explained by the effect of individual and combined factors.

Adequate precision comprises the predicted value at the design points, the average prediction error and a ratio greater than 4 is desirable [6,38]. In this study, it was found to be a ratio of 9.57 (Table 7), which shows the model’s ability. The adequacy of the predictive model generated for the copper recovery is further demonstrated from the residual normal probability plot in Figure 1b. The data presented in Figure 1b closely follows the straight line showing that there is no requirement of actual data transformations. It can be concluded that the deviation between the predicted and experimental values are distributed normally and the suggested model is well-fitted to data. This further supports the validity of the second-order model to predict copper recovery.

In addition to the model adequacy, ANOVA was employed to determine the relative significance and the influential degree of factors. The essential parameters were ranked based on the p-, F-values and conformity factor η². It can be considered from Table 7 and Table 8 that the significance degree of the important terms is in the order of frother > quadratic effect of agitation rate > interactive effect between frother and agitation speed > interaction effect between pH and agitation speed > quadratic effect of frother > quadratic effect of pH > interactive effect between collector and frother > linear effect of collector > linear effect of pH.

4.4. Influence of Factors and Their Interactions on Recovery

The 3D response surface graphs were depicted to identify the individual, interaction effects and generally combined impacts of factors studied on the copper recovery (Figure 2, Figure 3, Figure 4 and Figure 5).

Figure 2 indicates the 3D response surface (Figure 2b), contour plots (Figure 2a) and the interactive impact (Figure 2c) of collector and depressant on the copper flotation when other experimental factors were constant at the central values (pH = 9, frother dosage = 8 g/t and agitation rate = 1100 rpm).

It can be seen in Figure 2 that, at low levels of collector dosage (70 g/t), increasing the value of depressant (sodium silicate) from 90 to 110 g/t results in an improvement in the recovery of copper (from 80.03% to 82.84%). This might be related to the fact that the presence of sodium silicate in flotation pulp leads to the increase in the load on the particle surface, favorable dispersion of fine particles and consequently satisfactory results of flotation performance. Moreover, a higher dosage of sodium silicate helps to upgrade the flotation performance by the depression of silicate minerals [25,57]. According to Park and Jeon [58], sodium silicate is habitually used for a dispersant/depressant. Based on the chemical reactions (Equations (8)–(10)), three anionic species are formed in the pulp, viz. ${\mathrm{OH}}^{-}$, ${\mathrm{HSiO}}_3^{-}$, and ${\mathrm{SiO}}_3^{2-}$. The OH⁻ ion enhances the pH of pulp, while ${\mathrm{HSiO}}_3^{-}$ and ${\mathrm{SiO}}_3^{2-}$ are the main depressing/dispersing species of silicates. A stable dispersion of the particles in the pulp is attributed to repulsion between anionic species and minerals. This phenomenon desirably prevents a slime coating on the mineral surfaces. Consequently, it promotes the adsorption rate of collectors and subsequently, copper floatability.

$${\mathrm{Na}}_2{\mathrm{SiO}}_3+2{\mathrm{H}}_2\mathrm{O}\leftrightarrow {\mathrm{H}}_2{\mathrm{SiO}}_3+2{\mathrm{Na}}^{+}+2{\mathrm{OH}}^{-}$$

(8)

$${\mathrm{H}}_2{\mathrm{SiO}}_3\leftrightarrow {\mathrm{HSiO}}_3^{-}+{\mathrm{H}}^{+}$$

(9)

$${\mathrm{HSiO}}_3^{-}\leftrightarrow {\mathrm{SiO}}_3^{2-}+{\mathrm{H}}^{+}$$

(10)

Furthermore, the increase in DTP collector dosage in the range studied (70–90 g/t) leads to a reduction in the recovery (Figure 2 and Figure 3), because of the micellization phenomenon for the additional values of the collector in the range investigated [59,60].

According to Dhar et al. [61], the mechanism of copper mineral flotation with dithiophosphates is in conjunction with chemical adsorption by the formation of cuprous DTP in neutral and slightly alkaline conditions. Also, Roy et al. [62] reported that the adsorption of this collector type occurs very quickly on the surface of sulfide minerals and at the first few seconds after the addition of the collector. Meanwhile, for the frother, a similar trend with the collector is observable (Figure 3). Although there is a linear relationship between Cu recoveries with collector dosage, it is quadratic for the frother. Figure 3a–c demonstrates that at low levels of frother (7 g/t), the increment in the amount of collector causes attenuation in copper recovery (from 85.29% to 80.85%) and at low values, it was almost unchanged. Furthermore, an increase in the collector dosage (from 70 to 90 g/t) leads to a slight increase in copper recovery. According to Figure 3a–c, the maximum copper recovery is obtained at the collector and frother dosages of 70 g/t and 7 g/t, respectively. It can also be seen that changing the collector consumption results in only a minor influence on the flotation of copper in the range tested; however, it was statistically significant. This effect can be described by the micellization phenomenon in the range tested [59].

Figure 4 and Figure 5 exhibit the response surface graphs of the copper recovery as a function of agitation rate with frother and pH. It is seen that the recovery is very sensitive and effective to change in the agitation rate, frother dosage and pulp pH, and there is a quadratic relationship between these factors with copper recovery.

According to Fornasiero and Filippov [63] as well as Hassanzadet et al. [64] a high impeller speed in the flotation cell is essential for maximum particle–bubble collision frequency, but an intensive agitation is detrimental as the coarser particles detach from the bubbles and recovery reduces. According to Figure 4, at high levels of frother (9 g/t), the increase of the agitation rate from 1000 to 1200 rpm causes an increase in copper recovery from 79.84% to 83.22%. Also, the findings in Figure 5 indicate that at low levels of agitation speed (1000 rpm), copper recovery enhances from 80.36% to 85.22% when pH exceeds from 8 to 10. Increasing the copper recovery into the concentrate at the highest pH-value is related to the stability of froth and the greater ability to carry particles by bubbles. The optimal pH was found to be 10.

According to Somasundaran and Wang [65], Liu et al. [66] and Gu et al. [67], the presence of sulfur ions is a function of pH. It can be concluded that H₂S, HS^– and S^2– form species are predominant at low (pH < 7), medium (pH 7–12) and high pH > 12 pH range, respectively. Therefore, it can be concluded that the optimal pH of flotation is located in the range where HS⁻ is predominant species. HS⁻ is easily absorbed on the surface of oxide minerals and produces a sulfidized surface film (such as CuS) and subsequently activates the oxides flotation. It is also mentioned that generally, the copper flotation takes place in the area on the Eh-pH diagram where the hydrophobic species of CuEX(s) is formed. In contrast, the depression of copper occurs in the stability area of Cu(OH)₂(s) and (EX)₂(aq) compounds. This behavior indicates that the reduction of copper recovery in the values of pH >10 may be owing to the formation of Cu(OH)₂(s) instead of CuEX(s) [25]. In this context, Fairthorne et al. [68] demonstrated that reducing recovery at high pH may be due to the generation of fresh spots on mineral surfaces during grinding, and the metal hydroxide precipitation. Additionally, Grano et al. [69,70] expressed that surface of sulfide mineral (e.g., chalcopyrite) is significantly influenced by pulp pH and the formation of iron oxyhydroxides on the surface of minerals at alkaline pHs prevents the adsorption of DTP and depresses the flotation. Additionally, these behaviors can be further described in Figure 4c and Figure 5c, which show interaction effects between agitation speed with frother dosage and pH, respectively.

4.5. Process Optimization

The flotation process parameters were optimized using the DX software package and goal function approach to maximize the recovery of copper within the experimental range, the results of which are displayed in Figure 6. Figure 6 demonstrates the optimal conditions suggested by the software. It is found that the maximum copper recovery can be obtained around 92.75% with a desirable amount of 100% (Desirability = 1). The optimal operating conditions suggested by DOE software were: collector dosage of ~70 g/t, depressant amount of ~110 g/t, frother dosage of 7 g/t, pulp pH of ~10 and agitation rate of ~1000 rpm. Two confirmation experiments were also performed to validate the model suggested under optimal condition. The recovery average of two flotation tests was determined to be 90.16%, which indicates the high accuracy of the model.

Figure 7a,b imply the relative significance of factors and the trend of factors for movement towards the optimal point, respectively. Perturbation plots help to compare the impact of all the factors at a particular point in the design space. A steep slope or curvature in a factor exhibits that the response variable (copper recovery) is sensitive to that factor. It is observed from Figure 7a the frother (C) and collector (A) dosages and the value of pH are the most critical factors on the recovery of copper. It can also be seen in Figure 7b that changing the value of factors toward the optimal point reduced the recovery of copper. The copper recovery increased with an increase in the depressant (B) and pH (D) dosages and also a decrease in the amount of the frother (C) and collector (A) amounts and agitation rate (E). In addition, it can be considered that the recovery of copper was a linear function of A and B and a quadratic function of C, D and E in the range studied. This behavior was already discussed in previous sections from a technical point of view.

5. Conclusions

The rougher flotation behavior of a sulfidized copper ore was studied by a series of batch flotation experiments. Response surface modeling based on central composite design was applied to optimize and evaluate the effects of collector, depressant and frother dosages, solution pH and agitation rate on the copper recovery. ANOVA and 3D response surface plots were applied to investigate the behavior of copper flotation. The major conclusions can be summarized as follows:

• A quadratic mathematical model (with R² of 0.8097) was developed to predict the copper recovery as a function of influential factors after validation and confirmation through several strong methods.
• ANOVA indicated that the linear effects of collector, frother and pH, the interaction effects of frother with collector and agitation rate and pH with agitation rate, the quadratic effects of frother, pH and agitation were significant on the copper recovery. Also, the significance degree of factors was obtained as frother dosage > agitation rate² > frother × agitation speed > pH × agitation speed > frother dosage² > pH² > collector × frother > collector dosage > pH.
• According to the 3D response surface graphs: (a) the recovery of copper improved about 2.81% by increasing the amount of depressant (sodium silicate) at low levels of collector dosage (70 g/t); (b) the copper recovery decreased by increasing the amount of dithiophosphate collector at high levels of frother (about 4.44%) and conversely at low values, the increase of the collector value to 90 g/t had no significant effect on the recovery; (c) changing the collector dosage had limited effects on the floatability of copper in the range tested and the recovery reduced with enhancing the value of collector dosage; (d) at low values of agitation rate, raising the pH increased significantly the copper recovery, while at high values of agitation, a slight reduction occurred in the recovery.
• Using an experimental design and goal function approach, the optimal levels of factors were determined to be ~70 g/t for collector, 110 g/t for depressant, 7 g/t for frother, 10 for pulp pH and 1000 rpm for agitation rate with a prediction of 92.75% copper recovery. Under these conditions, the desirability of the optimal condition was found to be 1. Confirmatory experiments were also conducted to assess the model suggested under the optimal condition predicted, and the results showed that the developed model was reliable and helpful for predicting the copper recovery.