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Effects of particle size on flotation performance in the separation of copper, gold and lead
Powder Technology 344 (2019) 654–664
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Effects of particle size on flotation performance in the separation of copper, gold and lead Jin-cheng Ran a,b,c,⁎, Xian-yang Qiu b,c, Zhen Hu b,c, Quan-jun Liu a, Bao-xu Song b,c, Yan-qing Yao b,c a b c
State Key Laboratory of Complex Non-ferrous Metal Resources Clean Utilization, Kunming Univer-sity of Science and Technology, Kunming, Yunnan 650093, China Guangdong Institute of Resources Comprehensive Utilization, Guangzhou, Guangdong 510650, China Guangdong Provincial Key Laboratory of Development and Comprehensive Utilization of Mineral Resources, Guangzhou, Guangdong 510650, China
a r t i c l e
i n f o
Article history: Received 27 October 2017 Received in revised form 26 November 2018 Accepted 8 December 2018 Available online 10 December 2018 Keywords: Flotation kinetic Separation flotation Particle size Separation efficiency Distribution index
a b s t r a c t In order to investigate the effect of particle size on the flotation performance in the separation of copper-goldlead, froth products of various size fractions were collected as a function of flotation time. The optimum dosage of potassium dichromate (K2Cr2O7) and sodium diethyldithiocarbamate (DDTC) were determined by flotation conditional tests. Six flotation kinetic models were used for fitting the experimental data of copper, gold and lead cumulative recovery using 1stOpt and Origin software. Flotation rate constant (k), the maximum recoveries values (R∞), and the multitude correlation coefficient (R2) of each model, as well as the separation efficiency (SE) and the distribution index (D.I.) were calculated to study the changing trend of flotation parameters for various size fractions. The results demonstrated that the favorable size fraction for the copper-gold-lead separation flotation was −74 + 20 μm. The classical first-order model was considered as the optimum model to adapt to the coppergold-lead separation flotation process in this investigation. The flotation rates of the coarser size fractions were greater than those with relatively finer size fractions, while longer flotation time may contribute to improving the recovery of the fine size fraction, and had little impact on the recovery of coarse-grained. The separation efficiency with respect to intermediate size fractions was greater than both the coarse and ultra-fine size fractions whether it is for copper-lead separation flotation or for gold-lead separation flotation. The most reasonable size fraction for gold enriched in the copper concentrate was −58 + 20 μm, while the coarse size fraction of −100 + 74 μm was found to be against to the selective enrichment of gold. © 2018 Elsevier B.V. All rights reserved.
1. Introduction Investigations of the flotation parameters to recycle fine/ultrafine gold particles from polymetallic sulfide ore, with the rapid depletion of mineral resources, have been a preoccupation for the mineral processing researchers. As a consequence, an effective method of flotation was developed to recycle or pre-enrichment the gold minerals from polymetallic sulfide ores, depending on the surface properties differences of the valuable minerals and the gangue minerals. Gold flotation performance is determined in aspect of many factors like flotation reagent, grinding fineness, pulp pH, gold occurrence state, conditioning intensity and grind media, etc. [1–3]. It is well known that particle size plays a critical role for the froth flotation, especially for flotation separation between two or more minerals [4,5]. Grinding is necessary to achieve one mineral liberates from other minerals, as a result, fine grinding of coarse-grained minerals is of ⁎ Corresponding author at: State Key Laboratory of Complex Non-ferrous Metal Resources Clean Utilization, Kunming University of Science and Technology, Kunming, Yunnan 650093, China. E-mail address: [email protected] (J. Ran).
https://doi.org/10.1016/j.powtec.2018.12.045 0032-5910/© 2018 Elsevier B.V. All rights reserved.
interest to the mineral processing plant for its higher energy consumption and cost [6,7]. However, the lower liberation of valuable minerals from the gangue minerals in the coarse size fractions causes more valuable minerals lost in the tailings. Poor flotation performances of the coarse and fine size fractions were obtained in comparison to the intermediate size [8,9]. The particle-bubble collision efficiency and coverage of collector for coarse mineral particles were lower than that of the optimum flotation particle sizes [10]. The low flotation rate of the fine/ ultra-fine particles was mainly attributed to lower collision efficiency of particle-bubble for their low mass and inertia [11]. Furthermore, another reason for the low flotation performance of fine/ultrafine particles is the lack of kinetic energy, which makes it difficult to form the three phase line of contact and display the thin water film between the particle and bubble [12]. Flotation kinetics is a method to study the relationship between the concentrations or recovery of minerals and flotation time, which can described as a function of recovery and rate using mathematical models [13–15]. Flotation kinetics was described as the probabilities of the occurrence of three successive events of particle-bubble collision, attachment and disengagement [16,17]. It can be summarized into three categories of first-order kinetic, second-order kinetic, and nonintegral-
J. Ran et al. / Powder Technology 344 (2019) 654–664 Table 1 Main element analysis results of ore sample.
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Table 3 Distribution of gold in major minerals.
Elements
Cu
Pb
Zn
S
Aua
SiO2
Minerals
Distribution of gold/%
Minerals
Distribution of gold/%
Contents/%
15.67
43.68
0.44
21.38
45.57
2.61
Native gold Pyrite Gangue Total
57.575 0.538 4.607 100.000
Chalcopyrite Galena Others
19.596 17.334 0.350
a
: g/t.
order, given dozens of flotation kinetic models existed: [18]. Many factors in existence affected the flotation kinetic, including mineral particles, flotation equipment, and chemical environment, etc. [19–21]. The essence of the flotation could be revealed through the study on the relationship of flotation process with time under the control of various influencing factors. Furthermore, flotation kinetics studies can also optimize the flotation process, and improve the flotation efficiency by building the optimal flotation kinetic models. Review of the literatures above indicates that a few papers reported the flotation kinetics of gold in the flotation separation of a gold-bearing polymetallic sulfide ore although the recovery of gold was being an important parameter. Yalcin and Kelebek [22] investigated the flotation behavior of a gold ore with respect to fineness of grind using flotation kinetic models, and the results of which indicated the second order kinetics is a more fitting model for both gold and pyrite. In addition, Eric et al. [23] investigated the flotation performance of gold in porphyry copper-gold ore by first-order flotation kinetics, which indicated that an increase in flotation time of copper rougher stage cannot result in the increase in gold recovery and some gold particles can only be recovered by pyrite flotation. However, none of these reported attentions had considered the selective enrichment of gold in the separation flotation process of polymetallic sulfide ore. In this paper, the cumulative recoveries of copper, gold and lead were used as the key parameters to study the effects of different particle sizes on the flotation performances in the separation flotation process. Six flotation kinetic models were applied in order to fit the experimental data generated from the ore with various size fractions of copper, gold and lead. Flotation rate constant (k), maximum recovery (R∞) and multitude correlation coefficient (R2) were selected as the evaluation parameters of flotation kinetics. Separation efficiency (SE) and distribution index (D.I.) were calculated to study the flotation performances of copper, gold and lead during the separation flotation process, and to investigate the selective enrichment of gold in the froth products. 2. Experimental 2.1. Materials 2.1.1. Ore samples The representative sample used in the flotation tests was obtained from a mine in Yunnan province, China. Elemental analysis of the ores was performed by wet chemical analysis method using inductively coupled plasma-atomic emission spectroscopy (ICP-APS), and the results are shown in Table 1. The sample contained 15.67% Cu, 43.68% Pb, and 45.57 g/t Au. Main mineral composition of the ores and balanced distribution of gold in the ores determined by mineral liberation analyzer (MLA) measurements are provided in Table 2 and Table 3, respectively. The major minerals of the ores are chalcopyrite, galena, pyrite and blende, Table 2 Mineral composition of ore sample. Minerals
Content/%
Minerals
Content/%
Chalcopyrite Blende Magnetite Feldspar Total
43.807 0.571 0.618 1.226 100.000
Galena Pyrite Quartz Others
50.254 1.339 2.150 0.035
among which quartz, feldspar and magnetite are major gangue minerals. The sum content of galena and chalcopyrite dispersed in the ore are up to 94.061%. Gold was dispersed in chalcopyrite and galena as micro-granular inclusions with a proportion of 19.596% and 17.334%, respectively, and native gold accounted for 57.575%. 2.1.2. Reagents In the flotation tests, potassium dichromate (K2Cr2O7), sodium diethyldithiocarbamate (DDTC) and methyl isobutyl carbinol (MIBC) were separately used as the lead depressant, the copper collector and frother. All reagents for tests are analytical grade. Tap water was used for the lab flotation tests. The chemical analysis results of the tap water are shown in Table 4. The contents of calcium and magnesium in the tap water are 12.47 mg/L and 4.18 mg/L, respectively. 2.2. Methods 2.2.1. Classification tests The ore samples for flotation tests were divided into two parts by sufficient blending and division after being crushed and grounded to b100 μm. One part of the samples was used for the full-scale flotation conditional tests, and another part was fractionated into five size fractions using Tyler screens (−100 + 74 μm, −74 + 58 μm, −58 + 43 μm, −43 + 20 μm, −20 μm) for the study of the particle size effect on Cu\\Au and Pb flotation separation. 2.2.2. Flotation tests 200 g ore sample was placed into a 500 mL flotation cell for the fullsize flotation tests or flotation kinetics tests. The impeller speed of flotation cell was set as 1340 rpm. For the full-size flotation tests, desired amounts of the depressant K2Cr2O7 and collector DDTC were separately added in the pulp and then the suspension was stirred for 5 min and 2 min, respectively. Subsequently, the frother MIBC with a dosage of 30 g/t was added and conditioned for 1 min. The flotation was conducted for 5 min. The optimum conditions were evaluated in terms of the recovery of copper, gold and lead during the separation flotation process. For the flotation kinetics tests in different sizes, six products were obtained by dividing the ore sample according to the phased recycle of 0–0.5 min, 0.5–1 min, 1–2 min, 2–3 min, 3–4 min, 4–5 min. The dosage of the reagents used in the flotation kinetics tests was the optimum conditions concluded from the full-size flotation tests. 2.2.3. Flotation kinetic calculation In this investigation, six flotation kinetic models were used to study the effects of various size fractions on the separation flotation, as shown in Table 5. The cumulative copper and gold recoveries of various size fractions after 0.5, 1, 2, 3, 4, and 5 mins of flotation time were fitted. The optimum initial values of the parameters of various models were obtained using the 1stOpt software, which was same as the optimum initial values used in calculation of the flotation rate constant (k), the Table 4 Element concentrations (mg/L) in tap water determined by ICP-MS. Element
Na
K
Ca
Mg
Fe
Cu
Zn
Pb
Mn
Concentration
38.41
3.10
12.47
4.18
0.024
0.051
0.037
b0.01
b0.01
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Table 5 Six flotation kinetic models used in this investigation [8,29–31]. No.
Name of model
Formula
1 2
Classical first-order model First-order model with rectangular distribution of flotabilities
R(t) = R ∞ [1 − exp (−kt)] RðtÞ ¼ R∞ f1− kt1 ½1− expð−ktÞg
3
Fully mixed reactor model
1 RðtÞ ¼ R∞ ð1− 1þt=k Þ
4
Improved gas/solid adsorption model
kt Þ RðtÞ ¼ R∞ ð1þkt
5
Second-order kinetic model
R∞ kt RðtÞ ¼ 1þR ∞ kt
6
Second-order model with rectangular distribution of flotabilities
RðtÞ ¼ R∞ f1− kt1 ½ln ð1 þ ktÞg
2
R(t) = fractional recovery at time t, R∞ = maximum recovery; k = rate constants.
maximum recoveries values (R∞), and the multitude correlation coefficient (R2) by the Origin software (Version 8.0). The R∞ values at different flotation time can be obtained using the six kinetic models (Table 5) fitted to the experimental data. The concept of separation efficiency was applied to calculate the difference of the cumulative recovery at the same time t between mineral 1 and mineral 2, which can be calculated by Eq. (1) [24–26]. SEðtÞ ¼ R1 ðt Þ−R2 ðt Þ
ð1Þ
A new quantity, namely, the distribution index (D.I.) or relative separation efficiency in the flotation system is defined as the absolute value of the ratio of the separation efficiency of the associated mineral 3 with mineral 1 (SE1) to the separation efficiency of the associated mineral 3 with the mineral 2 (SE2). DI is calculated by Eq. (2) R1 ðt Þ−R3 ðt Þ SE1 ¼ D:I: ¼ R2 ðt Þ−R3 ðt Þ SE2
ð2Þ
R1(t) represents the maximum recovery of the floated mineral in the froth produce during the separation process at time t, similarly, R2(t) represents the maximum recovery of the depressed mineral, and R3(t) represents the maximum recovery of the associated mineral.
formula for approximate the Fuerstenau curves is obtained by combining two kinetic Eqs. (3) and (4), as shown in Eq. (5). The new parameter, k ¼ kk12 , was defined as a separation selectivity index, and the value of which can be calculated by fitting the flotation kinetics using Eq. (5) [27]. R ¼ R∞ ½1− expð−k1 t Þ
ð3Þ
Ra ¼ R∞ ½1− expð−k2 t Þ
ð4Þ
2
3 k1 Ra∞ −Ra k2 5 4 R ¼ R∞ 1− Ra∞
ð5Þ
where R and Ra are the Cu/Au recovery and Pb recovery in the concentration, respectively; R∞ and Ra∞ are the maximum Cu/Au recovery and Pb recovery in the concentrate, respectively; k1 and k2 are the firstorder flotation rate constants of the floated minerals (Cu/Au) and the depressed mineral (Pb); t is the flotation time. 3. Results and discussions
2.2.4. Fuerstenau upgrading curves analysis The Fuerstenau upgrading curves were used to characterize and analysis the flotation selectivity of different dosages of potassium dichromate and DDTC on the separation of Cu\\Pb and Au\\Pb. The Fuerstenau upgrading curves were obtained by combining the kinetic equations relating the recoveries to time of the two components and eliminating the parameter of time. In this study, the classical firstorder equations were used to describe the flotation kinetics of Cu, Pb and Au, which are shown in Eqs. (3) and (4). Then a mathematical
3.1. Particle size distribution The particle size distributions of the feeding for full-size flotation and the gold in the ore sample are shown as Fig. 1 (a) and (b), respectively. The cumulative yield of the fine size fraction (−20 μm) in the feeding was 32.30% and the distribution of gold was 32.92%. While the yield of the coarse size fraction (−100 + 74 μm) distribution in the feeding was 7.28% and the gold was 7.04%.
Fig. 1. Particle size distributions of the feeding for full-size flotation (a) and the gold in ore sample (b).
J. Ran et al. / Powder Technology 344 (2019) 654–664
3.2. Flotation tests 3.2.1. Effect of potassium dichromate dosage on the flotation performance The effects of potassium dichromate dosage on the flotation recovery of copper, lead and gold in the separation flotation are investigated, and the Fuerstenau upgrading curves of copper-lead system and goldlead system in the flotation pulp are shown in Fig. 2. The maximum Cu/Au recovery (R∞) and Pb recovery (Ra∞) in the concentrate are assumed to be 100%, then the Eq. (5) can be simplified to Eq. (6) [27]. 2 3 k1 100−Ra k2 5 R ¼ 10041− 100
ð6Þ
The term R2 was used to compare the fitting degree of the predicted results of models with different numbers of independent variables and different degrees of freedom [28]. It can be seen from Fig. 2 that the R2 values are all N0.99, which indicate a good fitting to the test data. The smallest values of the separation selectivity index k of 1.12 and 1.11 and the worst selectivity were observed for the copper-lead system and gold-lead system in the absence of potassium dichromate, respectively. The k values for the copper-lead system and gold-lead system were all present an increasing an initial increase and then a decrease tendency with the increase of potassium dichromate dosage, which indicated that excessive amounts of potassium dichromate will lead to
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low recoveries of copper and gold. The optimal k values (6.85 and 4.27) and the best selectivity in the separation of Cu\\Pb and Au\\Pb were all obtained at the potassium dichromate dosage of 800 g/t. 3.2.2. Effect of sodium diethyldithiocarbamate dosage on the flotation performance Fig. 3 shows the flotation performances of copper, lead and gold in different dosage of DDTC. The R2 values are all N0.99, which indicate a good fitting to the test data. With the increase of the DDTC dosage, the k values for the copper-lead system and gold-lead system were all present an increasing an initial increase and then a decrease tendency. Nevertheless, the collecting ability of DDTC for the impurity minerals (e.g. galena) also increased simultaneously, which led to lower k values and higher entrainment of impurities in the froth product. The maximum k values (6.85 and 4.27) and the best selectivity for the copper-lead system and gold-lead system were all obtained at the DDTC dosage of 30 g/t. In the froth flotation, in addition of flotation reagents, the particle size is another crucial parameter that affects the flotation recovery and separation efficiency. This paper focuses on the specific effects of the particle size on the copper, lead and gold separation flotation. The dosage of K2Cr2O4 and DDTC of 800 and 30 g/t was selected as optimal dosage in the various size fractions flotation study, respectively. It can be seen from the present discussions that gold is mainly enriched in the copper concentrate in the separation flotation. Therefore, the
Fig. 2. The Fuerstenau upgrading curves: relationship between the dosages of potassium dichromate and the separation performances of copper-lead (a) and gold-lead (b) (DDTC 30 g/t).
Fig. 3. The Fuerstenau upgrading curves: relationship between the dosages of DDTC and the separation performances of copper-lead (a) and gold-lead (b) (potassium dichromate 800 g/t).
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Fig. 4. Effects of the size fractions on the cumulative copper, gold and lead recovery in the separation process (K2Cr2O4 600 g/t, DDTC 30 g/t).
occupancy of gold in the copper concentrate was employed to evaluate the separation performance of copper, lead and gold, which was also considered as the recovery of gold in the size fractions flotation study. 3.2.3. Effects of the size fractions on the cumulative copper, gold and lead recovery in the separation flotation process The relationships between recovery of copper, gold and lead and flotation time of different size fractions are showed in Fig. 4. The cumulative recoveries of copper, gold and lead present an initial increase and then a decrease tendency with the increase of particle size, which is consistent with that of some other minerals investigated in previous reports [32–34]. The maximum recovery of gold was obtained with the size fraction −43 + 20 μm, followed by the −58 + 43 μm size fraction. In addition, the gold recovery of 68.14% was obtained with the size fraction of −74 + 58 μm, which indicated that the optimum size fraction of gold in the gold-lead separation flotation was −74 + 20 μm. The excessive coarse size fraction of −100 + 74 μm and the fine size fraction of −20 μm were considered to be detrimental to the recovery of gold in the process of separation flotation. Lower gold recovery of the coarse size fraction may be attributed to insufficient liberation of gold from the sulfide minerals (e.g. galena) and the increased probability of particle/bubble detachment during the flotation. On the one hand, more gold particles may be locked in composite particles with the coarse-grained galena particles and lost in the depressed products in the presence of potassium dichromate. On the other hand, excessive turbulence in the flotation cells and the high weight of gold particles is another important reason for a poor recovery of the coarse gold particles, which increase the gold particles detachment from bubbles [23,35]. For the fine particle
gold, the lower collision efficiency of fine/ultrafine gold particles or gold-carrier minerals with air bubbles are generally caused by its small mass and consequently low momentum in the flotation solution, resulting in a poor gold recovery [36–38]. Furthermore, the associated fine gangue particles and other sulfide mineral impurities coated on the surfaces of the gold particles form hydrophilic “armor” in the presence of potassium dichromate, preventing the adsorption of collector and reducing the capturing ability of gold particles by bubbles [39,40]. The optimum size fraction of copper in the separation flotation process was basically consistent with that of gold. It is worth noting that the maximum recovery of copper was obtained at the size fraction of −74 + 58 μm with a copper recovery of 89.34%, followed by the −43 + 20 μm and − 58 + 43 μm size fractions. Therefore, the optimum size fraction of copper in the Cu\\Au and Pb separation flotation was −74 + 20 μm. For lead, the recoveries present an initial increase and then a decrease tendency with the continuous increase of particle size as an entrainment impurity in the copper-gold concentrate. In particular, the lead flotation performance with various size fractions was consistent with that of copper, and the maximum recovery was obtained at the size fraction of −74 + 58 μm. 3.3. Flotation kinetics analyses 3.3.1. Kinetic analysis of various size fractions based on copper cumulative recovery Flotation kinetic fitting results of cumulative copper recovery of various size fractions as a function of flotation time are shown in Fig. 5 and Table 6. The maximum recovery (R∞) increased gradually from model 1
J. Ran et al. / Powder Technology 344 (2019) 654–664
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Fig. 5. Six kinetic models fitted to the copper cumulative recovery of various size fractions in the separation flotation process.
to model 6, while the R∞ values of models 3–5 are basically equivalent. The R∞ values of −58 μm size fractions obtained from a model is larger than that of +58 μm size fractions. It revealed that fine size fractions (−58 μm) have a high flotation recovery, while coarse size fractions (+58 μm) exhibit poor flotation recovery. Different rate constants (k) obtained from six models fitted presented different changing trends. In addition to the model 3, the k values obtained from the other models decreased with the decreasing of the particle size, which indicates the
fact of that k value of the coarse size fractions is greater than that of the fine size fractions. This suggested that coarse size fraction (−100 + 74 μm) can be stabilized in a relative short time, and a longer flotation time may not increase the recovery of coarse size fractions, while fine size fractions need a longer time to get a higher flotation recovery. It can be seen from Fig. 5 that the R2 values of the six models are all N0.97, which indicate a good fitting of all kinetic models to the test data. Furthermore, the R2 values of model 1 for all of the size fractions
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Table 6 Parameters obtained from six kinetic models fitted to the copper cumulative recovery of various size fractions. Models
Model 1 Model 2 Model 3 Model 4 Model 5 Model 6
−100 + 74 μm
−74 + 58 μm
−58 + 43 μm
−43 + 20 μm
−20 μm
R∞ (%)
k (min−1)
R∞ (%)
k (min−1)
R∞ (%)
k (min−1)
R∞ (%)
k (min−1)
R∞ (%)
k (min−1)
73.8844 82.0640 85.2241 85.2241 85.2241 91.2703
1.4130 2.8387 0.5707 1.7523 0.0206 3.8562
89.6151 100.1128 106.8881 106.8881 106.8881 116.3419
1.1446 2.2853 0.7778 1.2857 0.0120 2.6788
90.9506 106.0254 119.1730 119.1730 119.1730 135.1478
0.6600 2.2853 0.7778 1.2857 0.0120 2.6788
93.3025 110.4564 126.9019 126.9019 126.9019 146.0943
0.5681 1.0071 2.0813 0.4805 0.0038 0.8791
84.7331 100.6023 116.2094 116.2094 116.2094 134.2599
0.5332 0.9406 2.2512 0.4442 0.0038 0.8076
Fig. 6. Six kinetic models fitted to the gold cumulative recovery of various size fractions in the separation flotation process.
J. Ran et al. / Powder Technology 344 (2019) 654–664
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Table 7 Parameters obtained from six kinetic models fitted to the gold cumulative recovery of various size fractions. Models
Model 1 Model 2 Model 3 Model 4 Model 5 Model 6
−100 + 74 μm
−74 + 58 μm
−58 + 43 μm
−43 + 20 μm
−20 μm
R∞ (%)
k (min−1)
R∞ (%)
k (min−1)
R∞ (%)
k (min−1)
R∞ (%)
k (min−1)
R∞ (%)
k (min−1)
48.7544 53.6514 56.3138 56.3138 56.3138 60.3490
1.4016 2.8998 0.5781 1.7300 0.0307 3.7974
68.3633 76.4245 82.4776 82.4776 82.4776 88.9457
1.1340 2.2608 0.8138 1.2287 0.0149 2.6382
76.8659 89.4671 100.4119 100.4119 100.4119 113.7526
0.6827 1.2509 1.6016 0.6244 0.0062 1.1789
80.4492 95.4671 110.0264 110.0264 110.0264 126.9389
0.5471 0.9647 2.1867 0.4573 0.0042 0.8333
69.9873 93.2567 97.4084 96.4440 96.4440 111.6311
0.5216 0.9166 2.3733 0.4307 0.0045 0.7803
flotation tests were basically the largest among the six investigated models, which showed that the model 1 exhibited more reasonable for fitting the flotation separation test results. 3.3.2. Kinetic analysis of various size fractions based on gold cumulative recovery The cumulative gold recovery at different time with various size fractions in separation flotation was fitted to the six kinetic models, and the results are shown in Fig. 6 and Table 7. In general, the R∞ values increased gradually from model 1 to model 6, which showed a same changing trend with that of copper. The greatest R∞ values were obtained from the −43 + 20 μm size fractions for all six kinetic models, which presented the difference from the gold recovery as a function of flotation time with various size fractions that have been shown in Fig. 4. The coarse size fractions (+74 μm) exhibited the poorest recovery for whichever model was fitted, which was consistent with that of the copper recovery (Fig. 6). The changing trends of k values of gold with various size fractions in the separation flotation process were similar to those of copper (Table 6). Except for model 3, the order of the k values of each size fraction is −100 + 74 μm N −74 + 58 μm N −58 + 43 μm N −43 + 20 μm N −20 μm for all the kinetic models. It indicated that a similar flotation rate difference between copper and gold with various size fractions may be used to illustrate the concomitant of copper and gold in the separation flotation. As is shown in Fig. 6, the R2 values of all six models are N 0.97, which indicated that all models gave an excellent fit to the test data. Furthermore, the maximum R2 values of five size fractions all appeared in model 1, which meant that model 1 was more reasonable than others for fitting the gold recovery as a function of flotation time in the separation flotation process. Particularly, the R∞ values of the six kinetic models with some size fractions were N100% for fitting the copper or gold recovery as a function of flotation time in the separation flotation process. However, the theoretical maximum recovery of flotation, as well as the R∞ values calculated from all six kinetic models, was 100%. Nevertheless, it did not suggest that the six models are not reasonable for fitting the data obtained from the separation flotation tests. A larger data would be obtained by fitting from the kinetic models for its larger original test data and lower convergence speed. Therefore, the R2 values of the kinetic models with various size fractions were considered to be the criterion for the fitting correlation, which present an excellent agreement with the changing trend of the cumulative recovery when the R2 value is close to 1. 3.3.3. Kinetic analysis of various size fractions based on lead cumulative recovery In the separation flotation process, lead was enriched in the coppergold concentrate as an entrainment impurity. The kinetic studies of lead were conducted by fitting to the six kinetic models to investigate the entrainment cumulative recovery at different time with various size fractions in the froth products, and the results are shown in Fig. 7 and Table 8. The R∞ values of fine size fraction (−58 μm) were greater compared with the coarse size fraction (−100 + 58 μm), which exhibited a
similar trend with the fitting results of the copper and gold as a function of flotation in the separation flotation. It should be noted that the changing trends of k and R∞ values (Table 8) from model 1 to model 6 were all consistent with the copper and gold although potassium dichromate existed in the pulp as the lead depressant, the only difference was that the k and R∞ values (Table 6 and Table 7) obtained from all the six kinetic models were much smaller than the fitting results of copper and gold. The lead fitting results of the six kinetic models with various size fractions were shown in the Fig. 7. In general, the R2 values obtained from the calculated using all the six kinetic models were N0.97, which indicated that a good fit to the test data. Model 1 presents a more excellent fit to the lead recovery as a function of flotation time in the separation flotation process, and the R2 values obtained from the model 1 with various size fractions were all N0.99, which were the biggest among the investigated models. Therefore, the model 1 was considered to be the most reasonable model for fitting the lead recovery in the separation flotation process. 3.3.4. Separation efficiency of various size fractions After the comparisons of R2 values obtained from the six kinetic models of copper, gold and lead with various size fractions, model 1 was concluded to be the most reasonable model for fitting the separation flotation process. Therefore, the separation efficiency (SE) among copper, gold and lead was calculated on basis of the classical firstorder model (model 1). Furthermore, the sum content of galena and chalcopyrite dispersed in the ore are up to 94.061% (Table 2), which means that the separation flotation of the ore can be considered as the separation between chalcopyrite, gold and galena. The separation efficiency (SE) was used to assess the flotation separation performance of one mineral from another mineral. The SE of copper-lead and gold-lead as a function of flotation time with various size fractions of the ore sample in separation flotation process are shown in Fig. 8 (a) and (b), respectively. As can be seen from Fig. 8 (a), in the copper-lead separation flotation, the values of SE present an initial increase and then a decreasing tendency with the continuous increase of particle size, and the maximum value of SE was obtained with the size fraction −74 + 58 μm, followed by the −43 + 20 μm size fraction and − 58 + 43 μm size fraction, which meant that the optimum separation flotation size fraction of copper-lead was −74 + 20 μm. The poor copper recovery of the fine particle size was contributed to a lower SE value of −20 μm size fraction as the slight changing trend of lead recovery with the particle size increased, which has been shown in the Fig. 4. Furthermore, the lowest value of SE was obtained from the size fraction of −100 + 74 μm, which suggested that excessive coarse size fraction and the ultra-fine size fraction depressed the separation of copper and gold in the froth flotation. The similar changing trend was also presented on the curves of goldlead separation efficiency with various size fractions as a function of flotation time, and the results are shown in Fig. 8 (b). In view of the values of SE, the favorable particle size fractions for gold-lead separation flotation are −43 + 20 μm and − 58 + 43 μm, while the negative particle size fractions are −20 μm and − 100 + 74 μm. Therefore, in all the
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Fig. 7. Six kinetic models fitted to the lead cumulative recovery of various size fractions in the separation flotation process.
Table 8 Parameters obtained from six kinetic models fitted to the lead cumulative recovery of various size fractions in the separation flotation process. Models
Model 1 Model 2 Model 3 Model 4 Model 5 Model 6
−100 + 74 μm
−74 + 58 μm
−58 + 43 μm
−43 + 20 μm
−20 μm
R∞ (%)
k (min−1)
R∞ (%)
k (min−1)
R∞ (%)
k (min−1)
R∞ (%)
k (min−1)
R∞ (%)
k (min−1)
19.5860 21.5389 22.5920 22.5920 22.5920 24.1948
1.4131 2.9293 0.5707 1.7524 0.0776 3.8564
26.4999 29.6012 31.6022 31.6022 31.6022 34.7386
1.1453 2.2876 0.7768 1.2873 0.0407 2.5950
27.2613 31.6817 35.4877 35.4877 35.4877 40.1446
0.6943 1.2765 1.5632 0.6397 0.0180 1.2116
28.2890 33.1649 38.1002 38.4812 38.1002 43.8629
0.5479 0.9925 2.1126 0.4628 0.0124 0.8660
25.7034 30.2714 35.0670 35.0670 35.0670 40.5893
0.5103 0.9171 2.3210 0.4309 0.0123 0.7806
J. Ran et al. / Powder Technology 344 (2019) 654–664
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Fig. 8. Separation efficiency as a function of flotation time: (a) copper-lead; (b) gold-lead.
experiments of copper-lead separation flotation and gold-lead separation flotation, the separation efficiency of the intermediate size fractions is the highest. A lower SE value of gold-lead for the coarse size fraction may be due to insufficient liberation of gold from galena or other gangue minerals. Furthermore, the low SE value of coarse size fractions may be explained by the lower collector DDTC dosage of 30 g/t, which was used to reduce the entrainment of impurity minerals (e.g. galena) in the separation flotation. While for the ultra-fine particle size minerals, the low SE value of gold-lead separation flotation may without relation to insufficient liberation. The main reason is due to low bubble collision efficiency or insufficient kinetic energy to collide and initiate the attachment process for the native gold and gold-carrier minerals under multi-phase flotation solution system [41,42]. In particular, the values of SE of gold-lead separation flotation for the same size fractions are all smaller than those of copper-lead separation flotation. In addition, the SE values of coarse size fractions can be stabilized in a relative short time despite the minimum separation efficiency (SEmin) values were obtained from the maximum size fraction of −100 + 74 μm, while fine size fractions need a longer time to obtain a higher SE values.
rates of the associated Au in the flotation separation of Cu\\Pb for investigating mineral flotation separation and performances. The distribution index (D.I.) was introduced in this investigation to study the distribution rates of gold with various size fractions in the separation flotation, and the results are provided in Fig. 9. The lower the D.I. value was, the easier the gold was enriched in froth produce (copper concentrate). Considering all the size fractions, the lowest D.I. value appeared with the size fraction of −43 + 20 μm, followed by −58 + 43 μm size fraction, which meant that the favorable particle size fraction for gold enriched in the copper concentrate was −58 + 20 μm. In contrast to the cumulative recovery of gold with various size fractions, the greatest D.I. value was appeared with the coarse size fraction of −100 + 74 μm, which indicated that the worse selective enrichment of gold in the copper concentrate was of the −100 + 74 μm size fraction during the separation flotation process, possibly since the insufficient liberation of gold from the lead minerals. While the fine size fraction (−20 μm) presented a relative high selectivity enrichment although the recovery was lower than that of the size fraction of −74 + 58 μm (Fig. 4). 4. Conclusions
3.3.5. Distribution indexes of various size fractions The selectivity enrichment of associated elements in the flotation separation of two host minerals is very important for mineral processing, especially when the associated minerals are priced only in foam products. Therefore, it is of great significance to analyze the distribution
Fig. 9. Distribution indexes of gold with various size fractions during the separation flotation as a function of flotation time.
In this investigation, the effects of particle size on flotation parameters of copper-gold and lead were studied by flotation kinetic analysis using the determinate reagent dosages. Flotation conditional tests were carried out to find out the optimum dosage for flotation kinetic study with various size fractions. Six flotation kinetic models were adopted for fitting the test data of copper, lead and gold recovery. The origin 8.0 software was employed for calculation of the flotation rate constant (k), the maximum recoveries values (R∞), and the multitude correlation coefficient (R2) of each model, as well as the separation efficiency (SE) and the distribution index (D.I.) of each size fraction. The major conclusions of this investigation are as follows: (1) Whichever for copper, gold or lead, the minimum flotation recoveries were obtained with the coarse size fraction (−100 + 74 μm). The maximum gold recovery of 73.88% was obtained with the size fraction of −43 + 20 μm, and the maximum copper recovery of 89.34% and the maximum entrainment lead recovery of 26.43% were obtained with the −74 + 58 μm size fraction. Considering the flotation performances of copper and gold, the optimum size fraction in the flotation separation of Cu\\Au minerals from Pb components was −74 + 20 μm. (2) The classical first-order model (Model 1) was considered to be most reasonable for fitting the recoveries of copper, gold and lead as a function of flotation time during the separation flotation process. For the copper, gold and lead, the maximum fitting
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recoveries were all obtained with the size fraction of −43 + 20 μm, and the flotation rates of the coarse size fraction (−100 + 74 μm) were all greater than those of the fine size fraction (−20 μm). The recovery of coarse size fractions can be stabilized in a relative short time, while longer flotation time may improve the recovery of the fine size fraction. (3) In all the experiments of copper-lead separation flotation and gold-lead separation flotation, the separation efficiency of the intermediate size fractions is greater than that of the coarse or ultra-fine size fractions. Based on the SE of copper-lead, the maximum value of SE was obtained with the size fraction of −74 + 58 μm (62.91%), followed by −43 + 20 μm size fraction (61.08%). While based on the SE of gold-lead, the SEmax appeared with the size of −43 + 20 μm (48.00%), followed by the size of −58 + 43 μm (47.48%). (4) The distribution index also exhibits a fact that the most reasonable size fraction for gold enriched in the copper concentrate was −58 + 20 μm, and a relative lower value of D.I. was obtained with the intermediate particle size fraction (−58 + 20 μm). While the greatest D.I. value was obtained with the coarse size fraction of −100 + 74 μm, which indicated that the worst selective enrichment of gold in the copper concentrate was of the coarse size fraction of −100 + 74 μm. Acknowledgements The authors would like to acknowledge the financial funded by the Research Fund Program of Guangdong Provincial Key Laboratory of Development and Comprehensive Utilization of Mineral Resources (Grant No. 2017B030314046). References [1] S. Sen, A. Seyrankaya, Y. Cilingir, Coal-oil assisted flotation for the gold recovery, Miner. Eng. 18 (2005) 1086–1092. [2] L. Valderrama, J. Rubio, High intensity conditioning and the carrier flotation of gold fine particles, Int. J. Miner. Process. 52 (1998) 273–285. [3] A. Rabieh, B. Albijanic, J.J. Eksteen, A review of the effects of grinding media and chemical conditions on the flotation of pyrite in refractory gold operations, Miner. Eng. 94 (2016) 21–28. [4] P.B. Kowalczuk, O. Sahbaz, J. Drzymala, Maximum size of floating particles in different flotation cells, Miner. Eng. 24 (2011) 766–771. [5] J. Drzymala, Characterization of materials by Hallimond tube flotation, part 3. Maximum size of floating and interacting particles, Int. J. Miner. Process. 55 (1999) 203–218. [6] S. Farrokhpay, H.R. Manouchehri, S. Grano, Effect of feed classification by hydrocycloning on copper recovery in flotation, Can. Metall. Q. 49 (2010) 107–112. [7] D. Dziki, The crushing of wheat kernels and its consequence on the grinding process, Powder Technol. 185 (2008) 181–186. [8] N.-N. Zhang, C.-C. Zhou, J.-H. Pan, W.-C. Xia, C. Liu, M.-C. Tang, S.-S. Cao, The response of diasporic-bauxite flotation to particle size based on flotation kinetic study and neural network simulation, Powder Technol. 318 (2017) 272–281. [9] S. Farrokhpay, D. Fornasiero, Flotation of coarse composite particles: effect of mineral liberation and phase distribution, Adv. Powder Technol. 28 (2017) 1849–1854. [10] G.J. Jameson, Advances in fine and coarse particle flotation, Can. Metall. Q. 49 (2013) 325–330. [11] H.J. Schulze, B. Radoev, Th. Geidel, H. Stechemesser, E. Töpfer, Investigations of the collision process between particles and gas bubbles in flotation - a theoretical analysis, Int. J. Miner. Process. 27 (1989) 263–278.
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Effects of particle size on flotation performance in the separation of copper, gold and lead Jin-cheng Ran a,b,c,⁎, Xian-yang Qiu b,c, Zhen Hu b,c, Quan-jun Liu a, Bao-xu Song b,c, Yan-qing Yao b,c a b c
State Key Laboratory of Complex Non-ferrous Metal Resources Clean Utilization, Kunming Univer-sity of Science and Technology, Kunming, Yunnan 650093, China Guangdong Institute of Resources Comprehensive Utilization, Guangzhou, Guangdong 510650, China Guangdong Provincial Key Laboratory of Development and Comprehensive Utilization of Mineral Resources, Guangzhou, Guangdong 510650, China
a r t i c l e
i n f o
Article history: Received 27 October 2017 Received in revised form 26 November 2018 Accepted 8 December 2018 Available online 10 December 2018 Keywords: Flotation kinetic Separation flotation Particle size Separation efficiency Distribution index
a b s t r a c t In order to investigate the effect of particle size on the flotation performance in the separation of copper-goldlead, froth products of various size fractions were collected as a function of flotation time. The optimum dosage of potassium dichromate (K2Cr2O7) and sodium diethyldithiocarbamate (DDTC) were determined by flotation conditional tests. Six flotation kinetic models were used for fitting the experimental data of copper, gold and lead cumulative recovery using 1stOpt and Origin software. Flotation rate constant (k), the maximum recoveries values (R∞), and the multitude correlation coefficient (R2) of each model, as well as the separation efficiency (SE) and the distribution index (D.I.) were calculated to study the changing trend of flotation parameters for various size fractions. The results demonstrated that the favorable size fraction for the copper-gold-lead separation flotation was −74 + 20 μm. The classical first-order model was considered as the optimum model to adapt to the coppergold-lead separation flotation process in this investigation. The flotation rates of the coarser size fractions were greater than those with relatively finer size fractions, while longer flotation time may contribute to improving the recovery of the fine size fraction, and had little impact on the recovery of coarse-grained. The separation efficiency with respect to intermediate size fractions was greater than both the coarse and ultra-fine size fractions whether it is for copper-lead separation flotation or for gold-lead separation flotation. The most reasonable size fraction for gold enriched in the copper concentrate was −58 + 20 μm, while the coarse size fraction of −100 + 74 μm was found to be against to the selective enrichment of gold. © 2018 Elsevier B.V. All rights reserved.
1. Introduction Investigations of the flotation parameters to recycle fine/ultrafine gold particles from polymetallic sulfide ore, with the rapid depletion of mineral resources, have been a preoccupation for the mineral processing researchers. As a consequence, an effective method of flotation was developed to recycle or pre-enrichment the gold minerals from polymetallic sulfide ores, depending on the surface properties differences of the valuable minerals and the gangue minerals. Gold flotation performance is determined in aspect of many factors like flotation reagent, grinding fineness, pulp pH, gold occurrence state, conditioning intensity and grind media, etc. [1–3]. It is well known that particle size plays a critical role for the froth flotation, especially for flotation separation between two or more minerals [4,5]. Grinding is necessary to achieve one mineral liberates from other minerals, as a result, fine grinding of coarse-grained minerals is of ⁎ Corresponding author at: State Key Laboratory of Complex Non-ferrous Metal Resources Clean Utilization, Kunming University of Science and Technology, Kunming, Yunnan 650093, China. E-mail address: [email protected] (J. Ran).
https://doi.org/10.1016/j.powtec.2018.12.045 0032-5910/© 2018 Elsevier B.V. All rights reserved.
interest to the mineral processing plant for its higher energy consumption and cost [6,7]. However, the lower liberation of valuable minerals from the gangue minerals in the coarse size fractions causes more valuable minerals lost in the tailings. Poor flotation performances of the coarse and fine size fractions were obtained in comparison to the intermediate size [8,9]. The particle-bubble collision efficiency and coverage of collector for coarse mineral particles were lower than that of the optimum flotation particle sizes [10]. The low flotation rate of the fine/ ultra-fine particles was mainly attributed to lower collision efficiency of particle-bubble for their low mass and inertia [11]. Furthermore, another reason for the low flotation performance of fine/ultrafine particles is the lack of kinetic energy, which makes it difficult to form the three phase line of contact and display the thin water film between the particle and bubble [12]. Flotation kinetics is a method to study the relationship between the concentrations or recovery of minerals and flotation time, which can described as a function of recovery and rate using mathematical models [13–15]. Flotation kinetics was described as the probabilities of the occurrence of three successive events of particle-bubble collision, attachment and disengagement [16,17]. It can be summarized into three categories of first-order kinetic, second-order kinetic, and nonintegral-
J. Ran et al. / Powder Technology 344 (2019) 654–664 Table 1 Main element analysis results of ore sample.
655
Table 3 Distribution of gold in major minerals.
Elements
Cu
Pb
Zn
S
Aua
SiO2
Minerals
Distribution of gold/%
Minerals
Distribution of gold/%
Contents/%
15.67
43.68
0.44
21.38
45.57
2.61
Native gold Pyrite Gangue Total
57.575 0.538 4.607 100.000
Chalcopyrite Galena Others
19.596 17.334 0.350
a
: g/t.
order, given dozens of flotation kinetic models existed: [18]. Many factors in existence affected the flotation kinetic, including mineral particles, flotation equipment, and chemical environment, etc. [19–21]. The essence of the flotation could be revealed through the study on the relationship of flotation process with time under the control of various influencing factors. Furthermore, flotation kinetics studies can also optimize the flotation process, and improve the flotation efficiency by building the optimal flotation kinetic models. Review of the literatures above indicates that a few papers reported the flotation kinetics of gold in the flotation separation of a gold-bearing polymetallic sulfide ore although the recovery of gold was being an important parameter. Yalcin and Kelebek [22] investigated the flotation behavior of a gold ore with respect to fineness of grind using flotation kinetic models, and the results of which indicated the second order kinetics is a more fitting model for both gold and pyrite. In addition, Eric et al. [23] investigated the flotation performance of gold in porphyry copper-gold ore by first-order flotation kinetics, which indicated that an increase in flotation time of copper rougher stage cannot result in the increase in gold recovery and some gold particles can only be recovered by pyrite flotation. However, none of these reported attentions had considered the selective enrichment of gold in the separation flotation process of polymetallic sulfide ore. In this paper, the cumulative recoveries of copper, gold and lead were used as the key parameters to study the effects of different particle sizes on the flotation performances in the separation flotation process. Six flotation kinetic models were applied in order to fit the experimental data generated from the ore with various size fractions of copper, gold and lead. Flotation rate constant (k), maximum recovery (R∞) and multitude correlation coefficient (R2) were selected as the evaluation parameters of flotation kinetics. Separation efficiency (SE) and distribution index (D.I.) were calculated to study the flotation performances of copper, gold and lead during the separation flotation process, and to investigate the selective enrichment of gold in the froth products. 2. Experimental 2.1. Materials 2.1.1. Ore samples The representative sample used in the flotation tests was obtained from a mine in Yunnan province, China. Elemental analysis of the ores was performed by wet chemical analysis method using inductively coupled plasma-atomic emission spectroscopy (ICP-APS), and the results are shown in Table 1. The sample contained 15.67% Cu, 43.68% Pb, and 45.57 g/t Au. Main mineral composition of the ores and balanced distribution of gold in the ores determined by mineral liberation analyzer (MLA) measurements are provided in Table 2 and Table 3, respectively. The major minerals of the ores are chalcopyrite, galena, pyrite and blende, Table 2 Mineral composition of ore sample. Minerals
Content/%
Minerals
Content/%
Chalcopyrite Blende Magnetite Feldspar Total
43.807 0.571 0.618 1.226 100.000
Galena Pyrite Quartz Others
50.254 1.339 2.150 0.035
among which quartz, feldspar and magnetite are major gangue minerals. The sum content of galena and chalcopyrite dispersed in the ore are up to 94.061%. Gold was dispersed in chalcopyrite and galena as micro-granular inclusions with a proportion of 19.596% and 17.334%, respectively, and native gold accounted for 57.575%. 2.1.2. Reagents In the flotation tests, potassium dichromate (K2Cr2O7), sodium diethyldithiocarbamate (DDTC) and methyl isobutyl carbinol (MIBC) were separately used as the lead depressant, the copper collector and frother. All reagents for tests are analytical grade. Tap water was used for the lab flotation tests. The chemical analysis results of the tap water are shown in Table 4. The contents of calcium and magnesium in the tap water are 12.47 mg/L and 4.18 mg/L, respectively. 2.2. Methods 2.2.1. Classification tests The ore samples for flotation tests were divided into two parts by sufficient blending and division after being crushed and grounded to b100 μm. One part of the samples was used for the full-scale flotation conditional tests, and another part was fractionated into five size fractions using Tyler screens (−100 + 74 μm, −74 + 58 μm, −58 + 43 μm, −43 + 20 μm, −20 μm) for the study of the particle size effect on Cu\\Au and Pb flotation separation. 2.2.2. Flotation tests 200 g ore sample was placed into a 500 mL flotation cell for the fullsize flotation tests or flotation kinetics tests. The impeller speed of flotation cell was set as 1340 rpm. For the full-size flotation tests, desired amounts of the depressant K2Cr2O7 and collector DDTC were separately added in the pulp and then the suspension was stirred for 5 min and 2 min, respectively. Subsequently, the frother MIBC with a dosage of 30 g/t was added and conditioned for 1 min. The flotation was conducted for 5 min. The optimum conditions were evaluated in terms of the recovery of copper, gold and lead during the separation flotation process. For the flotation kinetics tests in different sizes, six products were obtained by dividing the ore sample according to the phased recycle of 0–0.5 min, 0.5–1 min, 1–2 min, 2–3 min, 3–4 min, 4–5 min. The dosage of the reagents used in the flotation kinetics tests was the optimum conditions concluded from the full-size flotation tests. 2.2.3. Flotation kinetic calculation In this investigation, six flotation kinetic models were used to study the effects of various size fractions on the separation flotation, as shown in Table 5. The cumulative copper and gold recoveries of various size fractions after 0.5, 1, 2, 3, 4, and 5 mins of flotation time were fitted. The optimum initial values of the parameters of various models were obtained using the 1stOpt software, which was same as the optimum initial values used in calculation of the flotation rate constant (k), the Table 4 Element concentrations (mg/L) in tap water determined by ICP-MS. Element
Na
K
Ca
Mg
Fe
Cu
Zn
Pb
Mn
Concentration
38.41
3.10
12.47
4.18
0.024
0.051
0.037
b0.01
b0.01
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Table 5 Six flotation kinetic models used in this investigation [8,29–31]. No.
Name of model
Formula
1 2
Classical first-order model First-order model with rectangular distribution of flotabilities
R(t) = R ∞ [1 − exp (−kt)] RðtÞ ¼ R∞ f1− kt1 ½1− expð−ktÞg
3
Fully mixed reactor model
1 RðtÞ ¼ R∞ ð1− 1þt=k Þ
4
Improved gas/solid adsorption model
kt Þ RðtÞ ¼ R∞ ð1þkt
5
Second-order kinetic model
R∞ kt RðtÞ ¼ 1þR ∞ kt
6
Second-order model with rectangular distribution of flotabilities
RðtÞ ¼ R∞ f1− kt1 ½ln ð1 þ ktÞg
2
R(t) = fractional recovery at time t, R∞ = maximum recovery; k = rate constants.
maximum recoveries values (R∞), and the multitude correlation coefficient (R2) by the Origin software (Version 8.0). The R∞ values at different flotation time can be obtained using the six kinetic models (Table 5) fitted to the experimental data. The concept of separation efficiency was applied to calculate the difference of the cumulative recovery at the same time t between mineral 1 and mineral 2, which can be calculated by Eq. (1) [24–26]. SEðtÞ ¼ R1 ðt Þ−R2 ðt Þ
ð1Þ
A new quantity, namely, the distribution index (D.I.) or relative separation efficiency in the flotation system is defined as the absolute value of the ratio of the separation efficiency of the associated mineral 3 with mineral 1 (SE1) to the separation efficiency of the associated mineral 3 with the mineral 2 (SE2). DI is calculated by Eq. (2) R1 ðt Þ−R3 ðt Þ SE1 ¼ D:I: ¼ R2 ðt Þ−R3 ðt Þ SE2
ð2Þ
R1(t) represents the maximum recovery of the floated mineral in the froth produce during the separation process at time t, similarly, R2(t) represents the maximum recovery of the depressed mineral, and R3(t) represents the maximum recovery of the associated mineral.
formula for approximate the Fuerstenau curves is obtained by combining two kinetic Eqs. (3) and (4), as shown in Eq. (5). The new parameter, k ¼ kk12 , was defined as a separation selectivity index, and the value of which can be calculated by fitting the flotation kinetics using Eq. (5) [27]. R ¼ R∞ ½1− expð−k1 t Þ
ð3Þ
Ra ¼ R∞ ½1− expð−k2 t Þ
ð4Þ
2
3 k1 Ra∞ −Ra k2 5 4 R ¼ R∞ 1− Ra∞
ð5Þ
where R and Ra are the Cu/Au recovery and Pb recovery in the concentration, respectively; R∞ and Ra∞ are the maximum Cu/Au recovery and Pb recovery in the concentrate, respectively; k1 and k2 are the firstorder flotation rate constants of the floated minerals (Cu/Au) and the depressed mineral (Pb); t is the flotation time. 3. Results and discussions
2.2.4. Fuerstenau upgrading curves analysis The Fuerstenau upgrading curves were used to characterize and analysis the flotation selectivity of different dosages of potassium dichromate and DDTC on the separation of Cu\\Pb and Au\\Pb. The Fuerstenau upgrading curves were obtained by combining the kinetic equations relating the recoveries to time of the two components and eliminating the parameter of time. In this study, the classical firstorder equations were used to describe the flotation kinetics of Cu, Pb and Au, which are shown in Eqs. (3) and (4). Then a mathematical
3.1. Particle size distribution The particle size distributions of the feeding for full-size flotation and the gold in the ore sample are shown as Fig. 1 (a) and (b), respectively. The cumulative yield of the fine size fraction (−20 μm) in the feeding was 32.30% and the distribution of gold was 32.92%. While the yield of the coarse size fraction (−100 + 74 μm) distribution in the feeding was 7.28% and the gold was 7.04%.
Fig. 1. Particle size distributions of the feeding for full-size flotation (a) and the gold in ore sample (b).
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3.2. Flotation tests 3.2.1. Effect of potassium dichromate dosage on the flotation performance The effects of potassium dichromate dosage on the flotation recovery of copper, lead and gold in the separation flotation are investigated, and the Fuerstenau upgrading curves of copper-lead system and goldlead system in the flotation pulp are shown in Fig. 2. The maximum Cu/Au recovery (R∞) and Pb recovery (Ra∞) in the concentrate are assumed to be 100%, then the Eq. (5) can be simplified to Eq. (6) [27]. 2 3 k1 100−Ra k2 5 R ¼ 10041− 100
ð6Þ
The term R2 was used to compare the fitting degree of the predicted results of models with different numbers of independent variables and different degrees of freedom [28]. It can be seen from Fig. 2 that the R2 values are all N0.99, which indicate a good fitting to the test data. The smallest values of the separation selectivity index k of 1.12 and 1.11 and the worst selectivity were observed for the copper-lead system and gold-lead system in the absence of potassium dichromate, respectively. The k values for the copper-lead system and gold-lead system were all present an increasing an initial increase and then a decrease tendency with the increase of potassium dichromate dosage, which indicated that excessive amounts of potassium dichromate will lead to
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low recoveries of copper and gold. The optimal k values (6.85 and 4.27) and the best selectivity in the separation of Cu\\Pb and Au\\Pb were all obtained at the potassium dichromate dosage of 800 g/t. 3.2.2. Effect of sodium diethyldithiocarbamate dosage on the flotation performance Fig. 3 shows the flotation performances of copper, lead and gold in different dosage of DDTC. The R2 values are all N0.99, which indicate a good fitting to the test data. With the increase of the DDTC dosage, the k values for the copper-lead system and gold-lead system were all present an increasing an initial increase and then a decrease tendency. Nevertheless, the collecting ability of DDTC for the impurity minerals (e.g. galena) also increased simultaneously, which led to lower k values and higher entrainment of impurities in the froth product. The maximum k values (6.85 and 4.27) and the best selectivity for the copper-lead system and gold-lead system were all obtained at the DDTC dosage of 30 g/t. In the froth flotation, in addition of flotation reagents, the particle size is another crucial parameter that affects the flotation recovery and separation efficiency. This paper focuses on the specific effects of the particle size on the copper, lead and gold separation flotation. The dosage of K2Cr2O4 and DDTC of 800 and 30 g/t was selected as optimal dosage in the various size fractions flotation study, respectively. It can be seen from the present discussions that gold is mainly enriched in the copper concentrate in the separation flotation. Therefore, the
Fig. 2. The Fuerstenau upgrading curves: relationship between the dosages of potassium dichromate and the separation performances of copper-lead (a) and gold-lead (b) (DDTC 30 g/t).
Fig. 3. The Fuerstenau upgrading curves: relationship between the dosages of DDTC and the separation performances of copper-lead (a) and gold-lead (b) (potassium dichromate 800 g/t).
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Fig. 4. Effects of the size fractions on the cumulative copper, gold and lead recovery in the separation process (K2Cr2O4 600 g/t, DDTC 30 g/t).
occupancy of gold in the copper concentrate was employed to evaluate the separation performance of copper, lead and gold, which was also considered as the recovery of gold in the size fractions flotation study. 3.2.3. Effects of the size fractions on the cumulative copper, gold and lead recovery in the separation flotation process The relationships between recovery of copper, gold and lead and flotation time of different size fractions are showed in Fig. 4. The cumulative recoveries of copper, gold and lead present an initial increase and then a decrease tendency with the increase of particle size, which is consistent with that of some other minerals investigated in previous reports [32–34]. The maximum recovery of gold was obtained with the size fraction −43 + 20 μm, followed by the −58 + 43 μm size fraction. In addition, the gold recovery of 68.14% was obtained with the size fraction of −74 + 58 μm, which indicated that the optimum size fraction of gold in the gold-lead separation flotation was −74 + 20 μm. The excessive coarse size fraction of −100 + 74 μm and the fine size fraction of −20 μm were considered to be detrimental to the recovery of gold in the process of separation flotation. Lower gold recovery of the coarse size fraction may be attributed to insufficient liberation of gold from the sulfide minerals (e.g. galena) and the increased probability of particle/bubble detachment during the flotation. On the one hand, more gold particles may be locked in composite particles with the coarse-grained galena particles and lost in the depressed products in the presence of potassium dichromate. On the other hand, excessive turbulence in the flotation cells and the high weight of gold particles is another important reason for a poor recovery of the coarse gold particles, which increase the gold particles detachment from bubbles [23,35]. For the fine particle
gold, the lower collision efficiency of fine/ultrafine gold particles or gold-carrier minerals with air bubbles are generally caused by its small mass and consequently low momentum in the flotation solution, resulting in a poor gold recovery [36–38]. Furthermore, the associated fine gangue particles and other sulfide mineral impurities coated on the surfaces of the gold particles form hydrophilic “armor” in the presence of potassium dichromate, preventing the adsorption of collector and reducing the capturing ability of gold particles by bubbles [39,40]. The optimum size fraction of copper in the separation flotation process was basically consistent with that of gold. It is worth noting that the maximum recovery of copper was obtained at the size fraction of −74 + 58 μm with a copper recovery of 89.34%, followed by the −43 + 20 μm and − 58 + 43 μm size fractions. Therefore, the optimum size fraction of copper in the Cu\\Au and Pb separation flotation was −74 + 20 μm. For lead, the recoveries present an initial increase and then a decrease tendency with the continuous increase of particle size as an entrainment impurity in the copper-gold concentrate. In particular, the lead flotation performance with various size fractions was consistent with that of copper, and the maximum recovery was obtained at the size fraction of −74 + 58 μm. 3.3. Flotation kinetics analyses 3.3.1. Kinetic analysis of various size fractions based on copper cumulative recovery Flotation kinetic fitting results of cumulative copper recovery of various size fractions as a function of flotation time are shown in Fig. 5 and Table 6. The maximum recovery (R∞) increased gradually from model 1
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Fig. 5. Six kinetic models fitted to the copper cumulative recovery of various size fractions in the separation flotation process.
to model 6, while the R∞ values of models 3–5 are basically equivalent. The R∞ values of −58 μm size fractions obtained from a model is larger than that of +58 μm size fractions. It revealed that fine size fractions (−58 μm) have a high flotation recovery, while coarse size fractions (+58 μm) exhibit poor flotation recovery. Different rate constants (k) obtained from six models fitted presented different changing trends. In addition to the model 3, the k values obtained from the other models decreased with the decreasing of the particle size, which indicates the
fact of that k value of the coarse size fractions is greater than that of the fine size fractions. This suggested that coarse size fraction (−100 + 74 μm) can be stabilized in a relative short time, and a longer flotation time may not increase the recovery of coarse size fractions, while fine size fractions need a longer time to get a higher flotation recovery. It can be seen from Fig. 5 that the R2 values of the six models are all N0.97, which indicate a good fitting of all kinetic models to the test data. Furthermore, the R2 values of model 1 for all of the size fractions
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Table 6 Parameters obtained from six kinetic models fitted to the copper cumulative recovery of various size fractions. Models
Model 1 Model 2 Model 3 Model 4 Model 5 Model 6
−100 + 74 μm
−74 + 58 μm
−58 + 43 μm
−43 + 20 μm
−20 μm
R∞ (%)
k (min−1)
R∞ (%)
k (min−1)
R∞ (%)
k (min−1)
R∞ (%)
k (min−1)
R∞ (%)
k (min−1)
73.8844 82.0640 85.2241 85.2241 85.2241 91.2703
1.4130 2.8387 0.5707 1.7523 0.0206 3.8562
89.6151 100.1128 106.8881 106.8881 106.8881 116.3419
1.1446 2.2853 0.7778 1.2857 0.0120 2.6788
90.9506 106.0254 119.1730 119.1730 119.1730 135.1478
0.6600 2.2853 0.7778 1.2857 0.0120 2.6788
93.3025 110.4564 126.9019 126.9019 126.9019 146.0943
0.5681 1.0071 2.0813 0.4805 0.0038 0.8791
84.7331 100.6023 116.2094 116.2094 116.2094 134.2599
0.5332 0.9406 2.2512 0.4442 0.0038 0.8076
Fig. 6. Six kinetic models fitted to the gold cumulative recovery of various size fractions in the separation flotation process.
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Table 7 Parameters obtained from six kinetic models fitted to the gold cumulative recovery of various size fractions. Models
Model 1 Model 2 Model 3 Model 4 Model 5 Model 6
−100 + 74 μm
−74 + 58 μm
−58 + 43 μm
−43 + 20 μm
−20 μm
R∞ (%)
k (min−1)
R∞ (%)
k (min−1)
R∞ (%)
k (min−1)
R∞ (%)
k (min−1)
R∞ (%)
k (min−1)
48.7544 53.6514 56.3138 56.3138 56.3138 60.3490
1.4016 2.8998 0.5781 1.7300 0.0307 3.7974
68.3633 76.4245 82.4776 82.4776 82.4776 88.9457
1.1340 2.2608 0.8138 1.2287 0.0149 2.6382
76.8659 89.4671 100.4119 100.4119 100.4119 113.7526
0.6827 1.2509 1.6016 0.6244 0.0062 1.1789
80.4492 95.4671 110.0264 110.0264 110.0264 126.9389
0.5471 0.9647 2.1867 0.4573 0.0042 0.8333
69.9873 93.2567 97.4084 96.4440 96.4440 111.6311
0.5216 0.9166 2.3733 0.4307 0.0045 0.7803
flotation tests were basically the largest among the six investigated models, which showed that the model 1 exhibited more reasonable for fitting the flotation separation test results. 3.3.2. Kinetic analysis of various size fractions based on gold cumulative recovery The cumulative gold recovery at different time with various size fractions in separation flotation was fitted to the six kinetic models, and the results are shown in Fig. 6 and Table 7. In general, the R∞ values increased gradually from model 1 to model 6, which showed a same changing trend with that of copper. The greatest R∞ values were obtained from the −43 + 20 μm size fractions for all six kinetic models, which presented the difference from the gold recovery as a function of flotation time with various size fractions that have been shown in Fig. 4. The coarse size fractions (+74 μm) exhibited the poorest recovery for whichever model was fitted, which was consistent with that of the copper recovery (Fig. 6). The changing trends of k values of gold with various size fractions in the separation flotation process were similar to those of copper (Table 6). Except for model 3, the order of the k values of each size fraction is −100 + 74 μm N −74 + 58 μm N −58 + 43 μm N −43 + 20 μm N −20 μm for all the kinetic models. It indicated that a similar flotation rate difference between copper and gold with various size fractions may be used to illustrate the concomitant of copper and gold in the separation flotation. As is shown in Fig. 6, the R2 values of all six models are N 0.97, which indicated that all models gave an excellent fit to the test data. Furthermore, the maximum R2 values of five size fractions all appeared in model 1, which meant that model 1 was more reasonable than others for fitting the gold recovery as a function of flotation time in the separation flotation process. Particularly, the R∞ values of the six kinetic models with some size fractions were N100% for fitting the copper or gold recovery as a function of flotation time in the separation flotation process. However, the theoretical maximum recovery of flotation, as well as the R∞ values calculated from all six kinetic models, was 100%. Nevertheless, it did not suggest that the six models are not reasonable for fitting the data obtained from the separation flotation tests. A larger data would be obtained by fitting from the kinetic models for its larger original test data and lower convergence speed. Therefore, the R2 values of the kinetic models with various size fractions were considered to be the criterion for the fitting correlation, which present an excellent agreement with the changing trend of the cumulative recovery when the R2 value is close to 1. 3.3.3. Kinetic analysis of various size fractions based on lead cumulative recovery In the separation flotation process, lead was enriched in the coppergold concentrate as an entrainment impurity. The kinetic studies of lead were conducted by fitting to the six kinetic models to investigate the entrainment cumulative recovery at different time with various size fractions in the froth products, and the results are shown in Fig. 7 and Table 8. The R∞ values of fine size fraction (−58 μm) were greater compared with the coarse size fraction (−100 + 58 μm), which exhibited a
similar trend with the fitting results of the copper and gold as a function of flotation in the separation flotation. It should be noted that the changing trends of k and R∞ values (Table 8) from model 1 to model 6 were all consistent with the copper and gold although potassium dichromate existed in the pulp as the lead depressant, the only difference was that the k and R∞ values (Table 6 and Table 7) obtained from all the six kinetic models were much smaller than the fitting results of copper and gold. The lead fitting results of the six kinetic models with various size fractions were shown in the Fig. 7. In general, the R2 values obtained from the calculated using all the six kinetic models were N0.97, which indicated that a good fit to the test data. Model 1 presents a more excellent fit to the lead recovery as a function of flotation time in the separation flotation process, and the R2 values obtained from the model 1 with various size fractions were all N0.99, which were the biggest among the investigated models. Therefore, the model 1 was considered to be the most reasonable model for fitting the lead recovery in the separation flotation process. 3.3.4. Separation efficiency of various size fractions After the comparisons of R2 values obtained from the six kinetic models of copper, gold and lead with various size fractions, model 1 was concluded to be the most reasonable model for fitting the separation flotation process. Therefore, the separation efficiency (SE) among copper, gold and lead was calculated on basis of the classical firstorder model (model 1). Furthermore, the sum content of galena and chalcopyrite dispersed in the ore are up to 94.061% (Table 2), which means that the separation flotation of the ore can be considered as the separation between chalcopyrite, gold and galena. The separation efficiency (SE) was used to assess the flotation separation performance of one mineral from another mineral. The SE of copper-lead and gold-lead as a function of flotation time with various size fractions of the ore sample in separation flotation process are shown in Fig. 8 (a) and (b), respectively. As can be seen from Fig. 8 (a), in the copper-lead separation flotation, the values of SE present an initial increase and then a decreasing tendency with the continuous increase of particle size, and the maximum value of SE was obtained with the size fraction −74 + 58 μm, followed by the −43 + 20 μm size fraction and − 58 + 43 μm size fraction, which meant that the optimum separation flotation size fraction of copper-lead was −74 + 20 μm. The poor copper recovery of the fine particle size was contributed to a lower SE value of −20 μm size fraction as the slight changing trend of lead recovery with the particle size increased, which has been shown in the Fig. 4. Furthermore, the lowest value of SE was obtained from the size fraction of −100 + 74 μm, which suggested that excessive coarse size fraction and the ultra-fine size fraction depressed the separation of copper and gold in the froth flotation. The similar changing trend was also presented on the curves of goldlead separation efficiency with various size fractions as a function of flotation time, and the results are shown in Fig. 8 (b). In view of the values of SE, the favorable particle size fractions for gold-lead separation flotation are −43 + 20 μm and − 58 + 43 μm, while the negative particle size fractions are −20 μm and − 100 + 74 μm. Therefore, in all the
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Fig. 7. Six kinetic models fitted to the lead cumulative recovery of various size fractions in the separation flotation process.
Table 8 Parameters obtained from six kinetic models fitted to the lead cumulative recovery of various size fractions in the separation flotation process. Models
Model 1 Model 2 Model 3 Model 4 Model 5 Model 6
−100 + 74 μm
−74 + 58 μm
−58 + 43 μm
−43 + 20 μm
−20 μm
R∞ (%)
k (min−1)
R∞ (%)
k (min−1)
R∞ (%)
k (min−1)
R∞ (%)
k (min−1)
R∞ (%)
k (min−1)
19.5860 21.5389 22.5920 22.5920 22.5920 24.1948
1.4131 2.9293 0.5707 1.7524 0.0776 3.8564
26.4999 29.6012 31.6022 31.6022 31.6022 34.7386
1.1453 2.2876 0.7768 1.2873 0.0407 2.5950
27.2613 31.6817 35.4877 35.4877 35.4877 40.1446
0.6943 1.2765 1.5632 0.6397 0.0180 1.2116
28.2890 33.1649 38.1002 38.4812 38.1002 43.8629
0.5479 0.9925 2.1126 0.4628 0.0124 0.8660
25.7034 30.2714 35.0670 35.0670 35.0670 40.5893
0.5103 0.9171 2.3210 0.4309 0.0123 0.7806
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Fig. 8. Separation efficiency as a function of flotation time: (a) copper-lead; (b) gold-lead.
experiments of copper-lead separation flotation and gold-lead separation flotation, the separation efficiency of the intermediate size fractions is the highest. A lower SE value of gold-lead for the coarse size fraction may be due to insufficient liberation of gold from galena or other gangue minerals. Furthermore, the low SE value of coarse size fractions may be explained by the lower collector DDTC dosage of 30 g/t, which was used to reduce the entrainment of impurity minerals (e.g. galena) in the separation flotation. While for the ultra-fine particle size minerals, the low SE value of gold-lead separation flotation may without relation to insufficient liberation. The main reason is due to low bubble collision efficiency or insufficient kinetic energy to collide and initiate the attachment process for the native gold and gold-carrier minerals under multi-phase flotation solution system [41,42]. In particular, the values of SE of gold-lead separation flotation for the same size fractions are all smaller than those of copper-lead separation flotation. In addition, the SE values of coarse size fractions can be stabilized in a relative short time despite the minimum separation efficiency (SEmin) values were obtained from the maximum size fraction of −100 + 74 μm, while fine size fractions need a longer time to obtain a higher SE values.
rates of the associated Au in the flotation separation of Cu\\Pb for investigating mineral flotation separation and performances. The distribution index (D.I.) was introduced in this investigation to study the distribution rates of gold with various size fractions in the separation flotation, and the results are provided in Fig. 9. The lower the D.I. value was, the easier the gold was enriched in froth produce (copper concentrate). Considering all the size fractions, the lowest D.I. value appeared with the size fraction of −43 + 20 μm, followed by −58 + 43 μm size fraction, which meant that the favorable particle size fraction for gold enriched in the copper concentrate was −58 + 20 μm. In contrast to the cumulative recovery of gold with various size fractions, the greatest D.I. value was appeared with the coarse size fraction of −100 + 74 μm, which indicated that the worse selective enrichment of gold in the copper concentrate was of the −100 + 74 μm size fraction during the separation flotation process, possibly since the insufficient liberation of gold from the lead minerals. While the fine size fraction (−20 μm) presented a relative high selectivity enrichment although the recovery was lower than that of the size fraction of −74 + 58 μm (Fig. 4). 4. Conclusions
3.3.5. Distribution indexes of various size fractions The selectivity enrichment of associated elements in the flotation separation of two host minerals is very important for mineral processing, especially when the associated minerals are priced only in foam products. Therefore, it is of great significance to analyze the distribution
Fig. 9. Distribution indexes of gold with various size fractions during the separation flotation as a function of flotation time.
In this investigation, the effects of particle size on flotation parameters of copper-gold and lead were studied by flotation kinetic analysis using the determinate reagent dosages. Flotation conditional tests were carried out to find out the optimum dosage for flotation kinetic study with various size fractions. Six flotation kinetic models were adopted for fitting the test data of copper, lead and gold recovery. The origin 8.0 software was employed for calculation of the flotation rate constant (k), the maximum recoveries values (R∞), and the multitude correlation coefficient (R2) of each model, as well as the separation efficiency (SE) and the distribution index (D.I.) of each size fraction. The major conclusions of this investigation are as follows: (1) Whichever for copper, gold or lead, the minimum flotation recoveries were obtained with the coarse size fraction (−100 + 74 μm). The maximum gold recovery of 73.88% was obtained with the size fraction of −43 + 20 μm, and the maximum copper recovery of 89.34% and the maximum entrainment lead recovery of 26.43% were obtained with the −74 + 58 μm size fraction. Considering the flotation performances of copper and gold, the optimum size fraction in the flotation separation of Cu\\Au minerals from Pb components was −74 + 20 μm. (2) The classical first-order model (Model 1) was considered to be most reasonable for fitting the recoveries of copper, gold and lead as a function of flotation time during the separation flotation process. For the copper, gold and lead, the maximum fitting
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recoveries were all obtained with the size fraction of −43 + 20 μm, and the flotation rates of the coarse size fraction (−100 + 74 μm) were all greater than those of the fine size fraction (−20 μm). The recovery of coarse size fractions can be stabilized in a relative short time, while longer flotation time may improve the recovery of the fine size fraction. (3) In all the experiments of copper-lead separation flotation and gold-lead separation flotation, the separation efficiency of the intermediate size fractions is greater than that of the coarse or ultra-fine size fractions. Based on the SE of copper-lead, the maximum value of SE was obtained with the size fraction of −74 + 58 μm (62.91%), followed by −43 + 20 μm size fraction (61.08%). While based on the SE of gold-lead, the SEmax appeared with the size of −43 + 20 μm (48.00%), followed by the size of −58 + 43 μm (47.48%). (4) The distribution index also exhibits a fact that the most reasonable size fraction for gold enriched in the copper concentrate was −58 + 20 μm, and a relative lower value of D.I. was obtained with the intermediate particle size fraction (−58 + 20 μm). While the greatest D.I. value was obtained with the coarse size fraction of −100 + 74 μm, which indicated that the worst selective enrichment of gold in the copper concentrate was of the coarse size fraction of −100 + 74 μm. Acknowledgements The authors would like to acknowledge the financial funded by the Research Fund Program of Guangdong Provincial Key Laboratory of Development and Comprehensive Utilization of Mineral Resources (Grant No. 2017B030314046). References [1] S. Sen, A. Seyrankaya, Y. Cilingir, Coal-oil assisted flotation for the gold recovery, Miner. Eng. 18 (2005) 1086–1092. [2] L. Valderrama, J. Rubio, High intensity conditioning and the carrier flotation of gold fine particles, Int. J. Miner. Process. 52 (1998) 273–285. [3] A. Rabieh, B. Albijanic, J.J. Eksteen, A review of the effects of grinding media and chemical conditions on the flotation of pyrite in refractory gold operations, Miner. Eng. 94 (2016) 21–28. [4] P.B. Kowalczuk, O. Sahbaz, J. Drzymala, Maximum size of floating particles in different flotation cells, Miner. Eng. 24 (2011) 766–771. [5] J. Drzymala, Characterization of materials by Hallimond tube flotation, part 3. Maximum size of floating and interacting particles, Int. J. Miner. Process. 55 (1999) 203–218. [6] S. Farrokhpay, H.R. Manouchehri, S. Grano, Effect of feed classification by hydrocycloning on copper recovery in flotation, Can. Metall. Q. 49 (2010) 107–112. [7] D. Dziki, The crushing of wheat kernels and its consequence on the grinding process, Powder Technol. 185 (2008) 181–186. [8] N.-N. Zhang, C.-C. Zhou, J.-H. Pan, W.-C. Xia, C. Liu, M.-C. Tang, S.-S. Cao, The response of diasporic-bauxite flotation to particle size based on flotation kinetic study and neural network simulation, Powder Technol. 318 (2017) 272–281. [9] S. Farrokhpay, D. Fornasiero, Flotation of coarse composite particles: effect of mineral liberation and phase distribution, Adv. Powder Technol. 28 (2017) 1849–1854. [10] G.J. Jameson, Advances in fine and coarse particle flotation, Can. Metall. Q. 49 (2013) 325–330. [11] H.J. Schulze, B. Radoev, Th. Geidel, H. Stechemesser, E. Töpfer, Investigations of the collision process between particles and gas bubbles in flotation - a theoretical analysis, Int. J. Miner. Process. 27 (1989) 263–278.
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