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Flotation characteristics and flotation kinetics of fine wolframite
Powder Technology 305 (2017) 377–381
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Powder Technology journal homepage: www.elsevier.com/locate/powtec
Flotation characteristics and flotation kinetics of fine wolframite Guanghua Ai, Xiuli Yang ⁎, Xiaobo Li Jiangxi Key Laboratory of Mining Engineering, Jiangxi University of Science and Technology, Jiangxi 341000, China Faculty of Resource and Environmental Engineering, Jiangxi University of Science and Technology, Jiangxi 341000, China
a r t i c l e
i n f o
Article history: Received 17 June 2016 Received in revised form 10 September 2016 Accepted 27 September 2016 Available online 01 October 2016 Keywords: Fine wolframite Flotation characteristics Flotation kinetics Particle size
a b s t r a c t The flotation characteristics and kinetics of fine wolframite from Shizhuyuan Mine, Hunan, China were studied. Coarse and middle particles entered the concentrate easily. However, because of the reduction of middle particles as carriers and the poor collision and attachment between fine particles and air bubbles, it was difficult to float fine particles. A new kinetic model was proposed and compared with four common kinetic models, including a classical first-order model, a modified first-order model, a first-order kinetic model with a rectangular distribution of floatabilities and a second-order kinetic model with a rectangular distribution of floatabilities. The kinetic model evaluation showed that the author's model fitted the experimental data best. The new model was applied to industrial data in a dressing plant to verify its reliability, and a better imitative effect was obtained compared with other models investigated. The modified first-order model agreed well with experimental and industrial data. The optimum flotation kinetic equations of fine wolframite in the laboratory and dressing plant were ε = 87.26 −31.74e−3.446t −55.51e−0.879t and ε =85.76− 44.67e−2.052t −41.09e−0.434t, respectively. © 2016 Elsevier B.V. All rights reserved.
1. Introduction In general, wolframite is recovered by gravity methods as long as the particle size is sufficiently large. However, because wolframite ores are brittle, they are easily over-crushed and over-ground in the crushing and grinding processes. In most cases, wolframite ore exists in a fine state. The recovery of tungsten from fine wolframite as recovered by gravity methods was below 45% [1]. Flotation is an effective and widely used separation method for fine and very fine materials [2]. Flotation as a physical-chemical process is used extensively in mineral processing to separate finely ground valuable minerals from a mixture in a pulp [2–4]. Most flotation developments of fine wolframite focus on the application of reagents and their interactions in flotation and the processing flowsheets [5,6]. Hu et al. (1997) used octyl hydroxamate as a collector to study the interactions with wolframite flotation [7]. Tian et al. (2002) synthesized a new collector with aniline and salicylaldehyde as main materials for wolframite flotation [8]. Fang et al (2007). used a mixture of 731 oxidized paraffinum sodium salts and benzyl hydroxamic acid as collectors for tungsten slime flotation [9]. Deng et al. (2015) proposed a novel surfactant, N-(6(hydroxyamino)-6-oxohexyl) octanamide, for wolframite flotation through hydrogen bonding and electrostatic attraction [10]. Many new flotation technologies have been proposed in recent years. Lu et al. (1994) used polyacrylic acid as a flocculant to study the ⁎ Corresponding author at: Jiangxi Key Laboratory of Mining Engineering, Jiangxi University of Science and Technology, Jiangxi 341000, China. E-mail addresses: [email protected] (G. Ai), [email protected] (X. Yang).
http://dx.doi.org/10.1016/j.powtec.2016.09.068 0032-5910/© 2016 Elsevier B.V. All rights reserved.
flocculation behaviors of fine wolframite; intermediate molecular weight polyacrylic acid showed the best flocculation effect [11]. Qiu et al. (1993) used coarse wolframite particles (N 10 μm) as a carrier to recover fine wolframite particles (b 5 μm) and the tungsten recovery increased from 40.5% to 70.38% [12]. The shear-flocculation flotation process and oil agglomeration flotation process have also been proposed for fine wolframite flotation. A review of this literature indicates that virtually no data were reported on flotation characteristics and kinetics of fine wolframite. This work aims to study the kinetics of fine wolframite on the foundation of flotation characteristics of fine wolframite. 2. Experimental 2.1. Materials Sample were from Shizhuyuan Mine, Hunan, China, and were ground to − 2 mm. Their chemical analysis and mineral composition are shown in Tables 1 and 2. The main gangue minerals in the ore sample are quartz, fluorite, muscovite, anorthose and epidote. 2.2. Flotation tests Flotation tests were conducted on a hanging trough flotation cell. Samples (1000 g) were dispersed with running water. Sodium carbonate (200 g/t), sodium fluorosilicate (20 g/t) and aluminum sulfate (250 g/t) were used as regulators. Lead nitrate (250 g/t) was used as an activator for wolframite. Benzohydroxamic acid (35 g/t) and fatty-
378
G. Ai et al. / Powder Technology 305 (2017) 377–381
Table 1 Chemical analysis of ore sample. Component
WO3
Mo
Bi
Sn
Pb
Zn
S
Fe
Mn
SiO2
Al2O3
CaO
MgO
CaF2
Content/%
0.41
0.08
0.18
0.15
0.014
0.021
1.12
7.21
0.51
36.42
8.58
22.35
0.66
21.24
Table 2 Mineral composition of ore sample. Mineral
Wolframite
Scheelite
Quartz
Fluorite
Muscovite
Anorthose
Epidote
Chlorite
Amphibole
Potassium feldspar
Almandite
Content/%
0.19
0.34
23.06
21.48
7.54
5.88
5.48
4.33
4.22
4.20
3.66
acid collector TAB-3 (18 g/t) were used as collectors for wolframite. Terpenic oil (15 g/t) was used as a foaming agent. The froth layer was removed for a set time using a spatula. The froth product was filtered, dried and weighed, and the recovery was calculated as the weight percentage of wolframite.
3. Results and discussion
The effect of flotation time on concentrate particle size composition was investigated and the results are shown in Fig. 3. As the flotation time increased, the mass of coarse and middle particles that entered the concentrate also increased. However, because of the poor collision and attachment between the fine particles and the air bubbles and the reduction in middle particles as carriers, fine particles that entered the concentrate decreased [3]. The non-selective entrainment of fine gangue particles may have caused the decrease in fine particle concentration in the concentrate.
3.1. Flotation characteristics of fine wolframite 3.2. Flotation kinetics of fine wolframite in the laboratory The rougher, cleaner and scavenging operations included four, seven and seven flotation cells, respectively. The concentrate grade from every flotation cell is shown in Fig. 1. The results indicate that the concentrate grade from the first to the fourth flotation cell was approximately 3%, which is attributed to tungsten particles with good flotability. The concentrate grade increased by 2.4% from the fifth to the eighth flotation cell and increased by 22.3% from the fifth to the eighth flotation cell. This phenomenon shows that the variation in wolframite flotability from bad to good required more time. The tailings grade from every flotation cell is presented in Fig. 2. The trend in grade agrees with the concentrate. The particle size composition of wolframite is presented in Table 3. The results in Table 3 show that the coarse fraction (+0.074 mm), middle fraction (−0.074 + 0.03 mm) and fine fraction (−0.03 mm) yields were 18.81%, 32.77% and 48.42%, respectively. In general, the flotability of the middle fraction is better than that of the coarse and fine fractions. However, the total yield of the coarse and fine fractions was 67.23% and the difficulty in recovering wolframite increased significantly. The results in Table 3 show that the grade of WO3 in the coarse fraction (+0.074 mm), middle fraction (−0.074 + 0.03 mm) and fine fraction (−0.03 mm) were 11.53%, 34.84% and 53.63%, respectively. More than half of the WO3 was distributed in the fine fraction.
32
Kinetic models of flotation have been applied widely based on an analogy with the homogeneous chemical kinetics [13], in which the concentration is modeled by a first-order differential equation as follows: dC ¼ −k∙C dt
ð1Þ
where C is the concentration of valuable minerals, k is the flotation rate constant and t is the time. According to the flotation characteristics of fine wolframite obtained in Section 3.1, the fine wolframite was divided into easy- and difficultfloating minerals. The flotation rate constants of minerals with different flotability are different. Therefore, Eq. (1) can convert to Eq. (2): 2
2 dC d ∑1 C i ¼ − ∑ ki C i ¼ dt dt i¼1
WO3
ð2Þ
WO3
6
28
5 Content of WO3 (%)
Content of WO3 (%)
24 20 16 12
4
3
2
8
1
4
0
0 1
2
3
4
5
6
7
8 9 10 11 12 13 14 15 16 17 18 Flotation cell
Fig. 1. Grade of concentrates from every flotation cell.
1
2
3
4
5
6
7
8 9 10 11 12 13 14 15 16 17 18 Flotation cell
Fig. 2. Grade of tailings from every flotation cell.
G. Ai et al. / Powder Technology 305 (2017) 377–381
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Table 3 The particle size composition of wolframite. Particle range (mm)
Individual yield (%)
Cumulative yield (%)
Grade of WO3 (%)
Distribution rate of WO3 (%)
+0.074 −0.074 + 0.054 −0.054 + 0.041 −0.041 + 0.03 −0.03 + 0.02 −0.02 + 0.01 −0.01 Total
18.81 11.65 9.67 11.45 12.07 15.81 20.54 100.00
18.81 30.46 40.13 51.58 63.65 79.46 100.00
0.35 0.54 0.48 0.77 0.77 0.64 0.54 0.57
11.53 11.07 8.23 15.54 16.42 17.84 19.37 100.00
Fig. 4. Comparison of five kinetic models fitted to the test data.
respectively, and ε2 ∞ and k2 are the maximum recovery and flotation rate constants of difficult-floating wolframite, respectively. Four common first- and second-order flotation kinetics models in Eqs. (5)–(8) were fitted to the experimental data and evaluated: ε ¼ ε∞ 1−e−kt
Fig. 3. Effect of flotation time on particle size composition of concentrate.
1 ε ¼ ε ∞ 1− 1−e−kt kt
ð6Þ
1 ε ¼ ε ∞ 1− ½ ln ð1 þ ktÞ kt
ð7Þ
−t ε ¼ ε ∞ 1−eaþbt
Because εi ¼
ð5Þ
C 0i −C i C 0i
ð3Þ
so Eq. (2) can convert to Eq. (4). ε ¼ ε∞ −ε 1∞ e−k1 t −ε 2∞ e−k2 t
ð4Þ
where ε is the recovery of wolframite at the flotation time t, ε∞ is the maximum recovery of wolframite (t→∞), ε1∞ and k1 are the maximum recovery and flotation rate constants of easy-floating wolframite,
ð8Þ
where a and b are the model constants. The effect of flotation time on cumulative recovery is shown in Table 4. The cumulative recovery at different times was fitted to the five flotation kinetic models (Eqs. (4)–(8)) using MATLAB software. The flotation rate constant, the maximum recovery, the model constants and the multitude correlation coefficient (R2) were also calculated using the software, and the results are given in Table 4 and Fig. 4. Table 4 and Fig. 4 indicate that the model deduced by the author (Model 5), the first-order model with a rectangular distribution of floatabilities (Model 2) and the modified first-order model (Model 4) showed a superior performances compared with the classical first-
Table 4 Non-linear regression results for all models fitting to the experimental data. Eq. (4) (Model 5) Time (min) Experimental CR (%) CR (%) 0.1 0.3 0.6 1 2 3.5 5 Constants DEVS DEVSQ MSD R2
14.5 33.02 50.11 63.89 77.06 85.27 86.31
Deviation
13.92 0.573 33.32 −0.305 50.48 −0.377 63.20 0.685 77.66 −0.603 84.70 0.566 86.57 −0.268 ε∞ = 87.26, ε1∞ = 31.74, ε2∞ = 55.51, k1 = 3.446, k2 = 0.879 0.27 1.79 0.506 0.9996
Eq. (5) (Model 1)
Eq. (6) (Model 2)
Eq. (7) (Model 3)
CR (%)
CR (%)
CR (%)
Deviation
11.77 2.721 30.63 2.383 50.15 −0.047 65.64 −1.752 80.25 −3.194 83.99 1.271 84.39 1.918 ε∞ = 84.43,ε∞ = 84.7487 k = 1.502 3.30 31.66 2.13 0.995
CR: Cumulative recovery, DEVS: Sum of deviance, DEVSQ: Square of deviance, MSD: Mean square deviation.
Deviation
13.07 1.422 32.51 0.507 50.78 −0.670 64.24 −0.355 77.76 −0.7 84.06 1.204 86.59 −0.289 ε∞ = 92.51, k = 3.129 1.12 4.88 0.83 0.9992
Deviation
15.84 −1.347 34.74 −1.729 50.21 −0.104 61.70 2.187 75.52 1.532 84.42 0.85 88.96 −2.650 ε∞ = 96.68, k = 9.291 −1.26 19.70 1.68 0.996
Eq. (8) (Model 4) CR (%))
Deviation
13.71 0.781 33.11 −0.094 50.65 −0.546 63.60 0.284 77.35 −0.299 84.24 1.026 87.01 −0.704 ε∞ = 85.17, a = 0.622, b = 0.309 0.45 2.64 0.61 0.9994
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G. Ai et al. / Powder Technology 305 (2017) 377–381
Table 5 Non-linear regression results for all models fitting to the industrial data. Eq. (4) (Model 5) Time (min) Experimental CR (%) CR (%) 0.6 1.4 2.5 4.0 5.5 7.0 Constants DEVS DEVSQ MSD R2
40.79 61.59 70.56 78.86 82.71 83.21
Deviation
41.04 −0.251 60.84 0.745 71.60 −1.042 78.50 0.359 81.98 0.730 83.79 −0.579 ε∞ = 85.76, ε1∞ = 44.67, ε2∞ = 41.09, k1 = 2.052, k2 = 0.434 −0.037 2.70 0.67 0.998
Eq. (5) (Model 1)
Eq. (6) (Model 2)
Eq. (7) (Model 3)
Eq. (8) (Model 4)
CR (%)
CR (%)
CR (%)
CR (%))
Deviation
37.59 3.202 62.13 −0.541 75.04 −4.484 79.83 −0.966 80.83 1.876 81.05 2.163 ε∞ = 81.10,ε∞ = 84.7487 k = 1.038 1.25 39.79 2.57 0.974
Deviation
39.86 0.931 61.58 0.010 72.86 −2.299 78.75 0.113 81.45 1.262 82.99 0.218 ε∞ = 88.65, k = 2.137 0.235 7.81 1.14 0.994
Deviation
42.14 −1.352 60.06 1.527 70.82 −0.265 78.03 0.826 82.09 0.612 84.75 −1.542 ε∞ = 99.67, k = 2.929 −0.19 7.66 1.13 0.994
Deviation
41.01 −0.220 60.76 0.832 71.83 −1.270 78.46 0.396 81.83 0.884 83.85 −0.640 ε∞ = 118.21, a = 1.009, b = 0.665 −0.019 3.70 0.78 0.997
CR: Cumulative recovery, DEVS: Sum of deviance, DEVSQ: Square of deviance, MSD: Mean square deviation
order model (Model 1) and the second-order kinetic model with rectangular distribution of floatabilities (Model 3). A significant improvement in the model deduced by the author (Model 5) was observed compared with the first-order model with a rectangular distribution of floatabilities (Model 2) and the modified first-order model (Model 4). The square of deviance of the model was smaller than the other applicable kinetic models. The R2 value of model 5 was larger than that of the other models, and the minimum R2 value for model 1 that fitted the flotation results was 0.995. Because the variation was b1 at every time investigated, the values calculated by model 5 agreed well with the experimental values. The fitting results of the model deduced by the author show that the flotation rate constant of easy-floating wolframite (3.446) was much larger than that of easy-floating wolframite (0.879). The maximum recovery of wolframite was 87.26%. The recoveries of easy- and difficult-floating wolframite account for 31.74% and 55.51%, respectively. These results indicate that because of the low flotation rate of difficult-floating wolframite, the maximum recovery of wolframite requires more time. The entrainment of gangue is more serious in the concentrate. Therefore, reasonable control of the flotation time and an increase in the wolframite flotation are important for the concentrate
grade and recovery. The optimum flotation kinetics of fine wolframite in the laboratory is expressed as follows: ε ¼ 87:26−31:74e−3:446t −55:51e−0:879t
ð9Þ
3.3. Flotation kinetics of fine wolframite in the dressing plant Industrial data were obtained from Hunan Shizhuyuan dressing plant, and are presented in Table 5. The data calculated from the five models and the fitting results are shown in Table 5 and Fig. 5. The cumulative recovery increased rapidly to 40.79% in the first 0.6 min and by 20.8% in the subsequent 0.8 min, which indicates that the flotation of easy-floating wolframite was very rapid. Therefore, the corresponding flotation rate constant is bigger than that of the difficult-floating wolframite, which is consistent with the fitting results by model 5, as shown in Table 5. The flotation rate constants of easy-floating wolframite and difficult-floating wolframite are 2.052 and 0.434, respectively. The R2 value of model 5 was larger than that of the other models and thus the imitative effect of the model deduced by the author was best.
Fig. 5. Comparison of five kinetic models fitted to the industrial data.
G. Ai et al. / Powder Technology 305 (2017) 377–381
The deviation at different times was b1 except for that at 2.5 min. The maximum recovery of wolframite was 85.76%. The recoveries of easyfloating wolframite and difficult-floating wolframite account for 44.67% and 41.09%, respectively. The optimum flotation kinetics of fine wolframite in the dressing plant is expressed as: ε ¼ 85:76−44:67e−2:052t −41:09e−0:434t
ð10Þ
Because the modified first-order model (Model 4) assumes that the flotation rate constant changes, it also agrees well with the industrial data, except for model 5. However, it did not allow for the maximum recovery to be fitted. Because of different rate constants for easy- and difficult-floating wolframite, the classical first-order model (Model 1) was inappropriate for fine wolframite flotation. The rectangular distribution of floatabilities (Models 2 and 3) was not suitable for fine wolframite flotation. 4. Conclusions The flotation characteristics of fine wolframite were investigated. Based on this investigation, a new kinetic model was proposed. This model was compared with a classical first-order model, a modified first-order model, a first-order kinetic model with a rectangular distribution of floatabilities and a second-order kinetic model with a rectangular distribution of floatabilities. The main conclusions can be summarized as follows: (1) As the flotation time increased, coarse and middle particles could enter the concentrate easily. However, because of a reduction in middle particles as carriers and the poor collision and attachment between the fine particles and air bubbles, fine particles that entered the concentrate decreased. (2) The new kinetic model was ε = ε∞ − ε1∞ e−k1t − ε2∞ e−k2t. (3) An evaluation of kinetic models showed that the model deduced by the author fitted the experimental and industrial data best. The modified first-order model also agreed well with the experimental and industrial data. (4) The optimum flotation kinetic equations of fine wolframite in the laboratory and dressing plant were ε = 87.26− 31.74e−3.446t − 55.51e−0.879t and ε = 85.76 − 44.67e− 2.052t − 41.09e− 0.434t, respectively.
381
Acknowledgments This work was financially supported by the Project of National Natural Science Foundation of China (No. 51504105), the Project of Natural Science Foundation of Jiangxi Province (No. 20161BAB216127) and the Science and Technology Research Project of Education Department of Jiangxi Province (No. GJJ150656). It was also supported by Program for Excellent Young Talents, JXUST.
References [1] G.Q. Fu, Study on flotation process and reagent of fine wolframite, Central South University, Changsha, 2010. [2] A. Azizi, A. Hassanzadeh, B. Fadaei, Investigating the first-order flotation kinetics models for Sarcheshmeh copper sulfide ore, Int. J. Min. Sci. Technol. 25 (2015) 849–854. [3] C. Ni, G.Y. Xie, M.G. Jin, Y.L. Peng, W.C. Xia, The difference in flotation kinetics of various size fractions of bituminous coal between rougher and cleaner flotation processes, Powder Technol. 292 (2016) 210–216. [4] E. Yalcin, S. Kelebek, Flotation kinetics of a pyritic gold ore, Int. J. Miner. Process. 98 (2011) 48–54. [5] G.C. He, C.H. Xiao, Experimental study on flotation of wolframite tailings in a Jiangxi tungsten mine, Nonferrous Met. Sci. Eng. 6 (2015) 82–87. [6] Y. Zhou, W.Y. Hu, Combined floatation-gravity-floatation flowsheet of a low grade wolframite slime, Nonferrous Met. Sci. Eng. 5 (2013) 58–63. [7] Y. Hu, D. Wang, Z. Xu, A study of interactions and flotation of wolframite with octyl hydroxamate, Miner. Eng. 10 (1997) 623–633. [8] X.D. Tian, Y.Q. Yang, X.Y. Zhang, D.Z. Wang, L.F. Li, J.G. Zhu, A new collector for wolframite slime flotation, Trans. Nonferrous Metals Soc. China 12 (2002) 310–312. [9] X.H. Fang, C.M. Zhong, Imporing tungsten recovery rate by applying combination collectors in tungsten-slime flotation, China Tungsten Ind. 22 (2007) 26–28. [10] L.Q. Deng, H. Zhong, S. Wang, G.Y. Liu, A novel surfactant N-(6-(hydroxyamino)-6oxohexyl)octanamide: synthesis and flotation mechanisms to wolframite, Sep. Purif. Technol. 145 (2015) 8–16. [11] Y.P. Lu, H. Zhong, X.H. Huang, Flotation of fine wolframite flocs using polyacrylic acid as flocculant, Min. Metall. Eng. 14 (1994) 30–33. [12] G.Z. Qiu, Interaction Between Particles and Fine Particle Flotation, Central South University Press, Changsha, 1993. [13] L. Vinnett, M. Alvarez-Silva, A. Jaques, F. Hinojosa, J. Yianatos, Batch flotation kinetics: fractional calculus approach, Miner. Eng. 77 (2015) 167–171.
Contents lists available at ScienceDirect
Powder Technology journal homepage: www.elsevier.com/locate/powtec
Flotation characteristics and flotation kinetics of fine wolframite Guanghua Ai, Xiuli Yang ⁎, Xiaobo Li Jiangxi Key Laboratory of Mining Engineering, Jiangxi University of Science and Technology, Jiangxi 341000, China Faculty of Resource and Environmental Engineering, Jiangxi University of Science and Technology, Jiangxi 341000, China
a r t i c l e
i n f o
Article history: Received 17 June 2016 Received in revised form 10 September 2016 Accepted 27 September 2016 Available online 01 October 2016 Keywords: Fine wolframite Flotation characteristics Flotation kinetics Particle size
a b s t r a c t The flotation characteristics and kinetics of fine wolframite from Shizhuyuan Mine, Hunan, China were studied. Coarse and middle particles entered the concentrate easily. However, because of the reduction of middle particles as carriers and the poor collision and attachment between fine particles and air bubbles, it was difficult to float fine particles. A new kinetic model was proposed and compared with four common kinetic models, including a classical first-order model, a modified first-order model, a first-order kinetic model with a rectangular distribution of floatabilities and a second-order kinetic model with a rectangular distribution of floatabilities. The kinetic model evaluation showed that the author's model fitted the experimental data best. The new model was applied to industrial data in a dressing plant to verify its reliability, and a better imitative effect was obtained compared with other models investigated. The modified first-order model agreed well with experimental and industrial data. The optimum flotation kinetic equations of fine wolframite in the laboratory and dressing plant were ε = 87.26 −31.74e−3.446t −55.51e−0.879t and ε =85.76− 44.67e−2.052t −41.09e−0.434t, respectively. © 2016 Elsevier B.V. All rights reserved.
1. Introduction In general, wolframite is recovered by gravity methods as long as the particle size is sufficiently large. However, because wolframite ores are brittle, they are easily over-crushed and over-ground in the crushing and grinding processes. In most cases, wolframite ore exists in a fine state. The recovery of tungsten from fine wolframite as recovered by gravity methods was below 45% [1]. Flotation is an effective and widely used separation method for fine and very fine materials [2]. Flotation as a physical-chemical process is used extensively in mineral processing to separate finely ground valuable minerals from a mixture in a pulp [2–4]. Most flotation developments of fine wolframite focus on the application of reagents and their interactions in flotation and the processing flowsheets [5,6]. Hu et al. (1997) used octyl hydroxamate as a collector to study the interactions with wolframite flotation [7]. Tian et al. (2002) synthesized a new collector with aniline and salicylaldehyde as main materials for wolframite flotation [8]. Fang et al (2007). used a mixture of 731 oxidized paraffinum sodium salts and benzyl hydroxamic acid as collectors for tungsten slime flotation [9]. Deng et al. (2015) proposed a novel surfactant, N-(6(hydroxyamino)-6-oxohexyl) octanamide, for wolframite flotation through hydrogen bonding and electrostatic attraction [10]. Many new flotation technologies have been proposed in recent years. Lu et al. (1994) used polyacrylic acid as a flocculant to study the ⁎ Corresponding author at: Jiangxi Key Laboratory of Mining Engineering, Jiangxi University of Science and Technology, Jiangxi 341000, China. E-mail addresses: [email protected] (G. Ai), [email protected] (X. Yang).
http://dx.doi.org/10.1016/j.powtec.2016.09.068 0032-5910/© 2016 Elsevier B.V. All rights reserved.
flocculation behaviors of fine wolframite; intermediate molecular weight polyacrylic acid showed the best flocculation effect [11]. Qiu et al. (1993) used coarse wolframite particles (N 10 μm) as a carrier to recover fine wolframite particles (b 5 μm) and the tungsten recovery increased from 40.5% to 70.38% [12]. The shear-flocculation flotation process and oil agglomeration flotation process have also been proposed for fine wolframite flotation. A review of this literature indicates that virtually no data were reported on flotation characteristics and kinetics of fine wolframite. This work aims to study the kinetics of fine wolframite on the foundation of flotation characteristics of fine wolframite. 2. Experimental 2.1. Materials Sample were from Shizhuyuan Mine, Hunan, China, and were ground to − 2 mm. Their chemical analysis and mineral composition are shown in Tables 1 and 2. The main gangue minerals in the ore sample are quartz, fluorite, muscovite, anorthose and epidote. 2.2. Flotation tests Flotation tests were conducted on a hanging trough flotation cell. Samples (1000 g) were dispersed with running water. Sodium carbonate (200 g/t), sodium fluorosilicate (20 g/t) and aluminum sulfate (250 g/t) were used as regulators. Lead nitrate (250 g/t) was used as an activator for wolframite. Benzohydroxamic acid (35 g/t) and fatty-
378
G. Ai et al. / Powder Technology 305 (2017) 377–381
Table 1 Chemical analysis of ore sample. Component
WO3
Mo
Bi
Sn
Pb
Zn
S
Fe
Mn
SiO2
Al2O3
CaO
MgO
CaF2
Content/%
0.41
0.08
0.18
0.15
0.014
0.021
1.12
7.21
0.51
36.42
8.58
22.35
0.66
21.24
Table 2 Mineral composition of ore sample. Mineral
Wolframite
Scheelite
Quartz
Fluorite
Muscovite
Anorthose
Epidote
Chlorite
Amphibole
Potassium feldspar
Almandite
Content/%
0.19
0.34
23.06
21.48
7.54
5.88
5.48
4.33
4.22
4.20
3.66
acid collector TAB-3 (18 g/t) were used as collectors for wolframite. Terpenic oil (15 g/t) was used as a foaming agent. The froth layer was removed for a set time using a spatula. The froth product was filtered, dried and weighed, and the recovery was calculated as the weight percentage of wolframite.
3. Results and discussion
The effect of flotation time on concentrate particle size composition was investigated and the results are shown in Fig. 3. As the flotation time increased, the mass of coarse and middle particles that entered the concentrate also increased. However, because of the poor collision and attachment between the fine particles and the air bubbles and the reduction in middle particles as carriers, fine particles that entered the concentrate decreased [3]. The non-selective entrainment of fine gangue particles may have caused the decrease in fine particle concentration in the concentrate.
3.1. Flotation characteristics of fine wolframite 3.2. Flotation kinetics of fine wolframite in the laboratory The rougher, cleaner and scavenging operations included four, seven and seven flotation cells, respectively. The concentrate grade from every flotation cell is shown in Fig. 1. The results indicate that the concentrate grade from the first to the fourth flotation cell was approximately 3%, which is attributed to tungsten particles with good flotability. The concentrate grade increased by 2.4% from the fifth to the eighth flotation cell and increased by 22.3% from the fifth to the eighth flotation cell. This phenomenon shows that the variation in wolframite flotability from bad to good required more time. The tailings grade from every flotation cell is presented in Fig. 2. The trend in grade agrees with the concentrate. The particle size composition of wolframite is presented in Table 3. The results in Table 3 show that the coarse fraction (+0.074 mm), middle fraction (−0.074 + 0.03 mm) and fine fraction (−0.03 mm) yields were 18.81%, 32.77% and 48.42%, respectively. In general, the flotability of the middle fraction is better than that of the coarse and fine fractions. However, the total yield of the coarse and fine fractions was 67.23% and the difficulty in recovering wolframite increased significantly. The results in Table 3 show that the grade of WO3 in the coarse fraction (+0.074 mm), middle fraction (−0.074 + 0.03 mm) and fine fraction (−0.03 mm) were 11.53%, 34.84% and 53.63%, respectively. More than half of the WO3 was distributed in the fine fraction.
32
Kinetic models of flotation have been applied widely based on an analogy with the homogeneous chemical kinetics [13], in which the concentration is modeled by a first-order differential equation as follows: dC ¼ −k∙C dt
ð1Þ
where C is the concentration of valuable minerals, k is the flotation rate constant and t is the time. According to the flotation characteristics of fine wolframite obtained in Section 3.1, the fine wolframite was divided into easy- and difficultfloating minerals. The flotation rate constants of minerals with different flotability are different. Therefore, Eq. (1) can convert to Eq. (2): 2
2 dC d ∑1 C i ¼ − ∑ ki C i ¼ dt dt i¼1
WO3
ð2Þ
WO3
6
28
5 Content of WO3 (%)
Content of WO3 (%)
24 20 16 12
4
3
2
8
1
4
0
0 1
2
3
4
5
6
7
8 9 10 11 12 13 14 15 16 17 18 Flotation cell
Fig. 1. Grade of concentrates from every flotation cell.
1
2
3
4
5
6
7
8 9 10 11 12 13 14 15 16 17 18 Flotation cell
Fig. 2. Grade of tailings from every flotation cell.
G. Ai et al. / Powder Technology 305 (2017) 377–381
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Table 3 The particle size composition of wolframite. Particle range (mm)
Individual yield (%)
Cumulative yield (%)
Grade of WO3 (%)
Distribution rate of WO3 (%)
+0.074 −0.074 + 0.054 −0.054 + 0.041 −0.041 + 0.03 −0.03 + 0.02 −0.02 + 0.01 −0.01 Total
18.81 11.65 9.67 11.45 12.07 15.81 20.54 100.00
18.81 30.46 40.13 51.58 63.65 79.46 100.00
0.35 0.54 0.48 0.77 0.77 0.64 0.54 0.57
11.53 11.07 8.23 15.54 16.42 17.84 19.37 100.00
Fig. 4. Comparison of five kinetic models fitted to the test data.
respectively, and ε2 ∞ and k2 are the maximum recovery and flotation rate constants of difficult-floating wolframite, respectively. Four common first- and second-order flotation kinetics models in Eqs. (5)–(8) were fitted to the experimental data and evaluated: ε ¼ ε∞ 1−e−kt
Fig. 3. Effect of flotation time on particle size composition of concentrate.
1 ε ¼ ε ∞ 1− 1−e−kt kt
ð6Þ
1 ε ¼ ε ∞ 1− ½ ln ð1 þ ktÞ kt
ð7Þ
−t ε ¼ ε ∞ 1−eaþbt
Because εi ¼
ð5Þ
C 0i −C i C 0i
ð3Þ
so Eq. (2) can convert to Eq. (4). ε ¼ ε∞ −ε 1∞ e−k1 t −ε 2∞ e−k2 t
ð4Þ
where ε is the recovery of wolframite at the flotation time t, ε∞ is the maximum recovery of wolframite (t→∞), ε1∞ and k1 are the maximum recovery and flotation rate constants of easy-floating wolframite,
ð8Þ
where a and b are the model constants. The effect of flotation time on cumulative recovery is shown in Table 4. The cumulative recovery at different times was fitted to the five flotation kinetic models (Eqs. (4)–(8)) using MATLAB software. The flotation rate constant, the maximum recovery, the model constants and the multitude correlation coefficient (R2) were also calculated using the software, and the results are given in Table 4 and Fig. 4. Table 4 and Fig. 4 indicate that the model deduced by the author (Model 5), the first-order model with a rectangular distribution of floatabilities (Model 2) and the modified first-order model (Model 4) showed a superior performances compared with the classical first-
Table 4 Non-linear regression results for all models fitting to the experimental data. Eq. (4) (Model 5) Time (min) Experimental CR (%) CR (%) 0.1 0.3 0.6 1 2 3.5 5 Constants DEVS DEVSQ MSD R2
14.5 33.02 50.11 63.89 77.06 85.27 86.31
Deviation
13.92 0.573 33.32 −0.305 50.48 −0.377 63.20 0.685 77.66 −0.603 84.70 0.566 86.57 −0.268 ε∞ = 87.26, ε1∞ = 31.74, ε2∞ = 55.51, k1 = 3.446, k2 = 0.879 0.27 1.79 0.506 0.9996
Eq. (5) (Model 1)
Eq. (6) (Model 2)
Eq. (7) (Model 3)
CR (%)
CR (%)
CR (%)
Deviation
11.77 2.721 30.63 2.383 50.15 −0.047 65.64 −1.752 80.25 −3.194 83.99 1.271 84.39 1.918 ε∞ = 84.43,ε∞ = 84.7487 k = 1.502 3.30 31.66 2.13 0.995
CR: Cumulative recovery, DEVS: Sum of deviance, DEVSQ: Square of deviance, MSD: Mean square deviation.
Deviation
13.07 1.422 32.51 0.507 50.78 −0.670 64.24 −0.355 77.76 −0.7 84.06 1.204 86.59 −0.289 ε∞ = 92.51, k = 3.129 1.12 4.88 0.83 0.9992
Deviation
15.84 −1.347 34.74 −1.729 50.21 −0.104 61.70 2.187 75.52 1.532 84.42 0.85 88.96 −2.650 ε∞ = 96.68, k = 9.291 −1.26 19.70 1.68 0.996
Eq. (8) (Model 4) CR (%))
Deviation
13.71 0.781 33.11 −0.094 50.65 −0.546 63.60 0.284 77.35 −0.299 84.24 1.026 87.01 −0.704 ε∞ = 85.17, a = 0.622, b = 0.309 0.45 2.64 0.61 0.9994
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G. Ai et al. / Powder Technology 305 (2017) 377–381
Table 5 Non-linear regression results for all models fitting to the industrial data. Eq. (4) (Model 5) Time (min) Experimental CR (%) CR (%) 0.6 1.4 2.5 4.0 5.5 7.0 Constants DEVS DEVSQ MSD R2
40.79 61.59 70.56 78.86 82.71 83.21
Deviation
41.04 −0.251 60.84 0.745 71.60 −1.042 78.50 0.359 81.98 0.730 83.79 −0.579 ε∞ = 85.76, ε1∞ = 44.67, ε2∞ = 41.09, k1 = 2.052, k2 = 0.434 −0.037 2.70 0.67 0.998
Eq. (5) (Model 1)
Eq. (6) (Model 2)
Eq. (7) (Model 3)
Eq. (8) (Model 4)
CR (%)
CR (%)
CR (%)
CR (%))
Deviation
37.59 3.202 62.13 −0.541 75.04 −4.484 79.83 −0.966 80.83 1.876 81.05 2.163 ε∞ = 81.10,ε∞ = 84.7487 k = 1.038 1.25 39.79 2.57 0.974
Deviation
39.86 0.931 61.58 0.010 72.86 −2.299 78.75 0.113 81.45 1.262 82.99 0.218 ε∞ = 88.65, k = 2.137 0.235 7.81 1.14 0.994
Deviation
42.14 −1.352 60.06 1.527 70.82 −0.265 78.03 0.826 82.09 0.612 84.75 −1.542 ε∞ = 99.67, k = 2.929 −0.19 7.66 1.13 0.994
Deviation
41.01 −0.220 60.76 0.832 71.83 −1.270 78.46 0.396 81.83 0.884 83.85 −0.640 ε∞ = 118.21, a = 1.009, b = 0.665 −0.019 3.70 0.78 0.997
CR: Cumulative recovery, DEVS: Sum of deviance, DEVSQ: Square of deviance, MSD: Mean square deviation
order model (Model 1) and the second-order kinetic model with rectangular distribution of floatabilities (Model 3). A significant improvement in the model deduced by the author (Model 5) was observed compared with the first-order model with a rectangular distribution of floatabilities (Model 2) and the modified first-order model (Model 4). The square of deviance of the model was smaller than the other applicable kinetic models. The R2 value of model 5 was larger than that of the other models, and the minimum R2 value for model 1 that fitted the flotation results was 0.995. Because the variation was b1 at every time investigated, the values calculated by model 5 agreed well with the experimental values. The fitting results of the model deduced by the author show that the flotation rate constant of easy-floating wolframite (3.446) was much larger than that of easy-floating wolframite (0.879). The maximum recovery of wolframite was 87.26%. The recoveries of easy- and difficult-floating wolframite account for 31.74% and 55.51%, respectively. These results indicate that because of the low flotation rate of difficult-floating wolframite, the maximum recovery of wolframite requires more time. The entrainment of gangue is more serious in the concentrate. Therefore, reasonable control of the flotation time and an increase in the wolframite flotation are important for the concentrate
grade and recovery. The optimum flotation kinetics of fine wolframite in the laboratory is expressed as follows: ε ¼ 87:26−31:74e−3:446t −55:51e−0:879t
ð9Þ
3.3. Flotation kinetics of fine wolframite in the dressing plant Industrial data were obtained from Hunan Shizhuyuan dressing plant, and are presented in Table 5. The data calculated from the five models and the fitting results are shown in Table 5 and Fig. 5. The cumulative recovery increased rapidly to 40.79% in the first 0.6 min and by 20.8% in the subsequent 0.8 min, which indicates that the flotation of easy-floating wolframite was very rapid. Therefore, the corresponding flotation rate constant is bigger than that of the difficult-floating wolframite, which is consistent with the fitting results by model 5, as shown in Table 5. The flotation rate constants of easy-floating wolframite and difficult-floating wolframite are 2.052 and 0.434, respectively. The R2 value of model 5 was larger than that of the other models and thus the imitative effect of the model deduced by the author was best.
Fig. 5. Comparison of five kinetic models fitted to the industrial data.
G. Ai et al. / Powder Technology 305 (2017) 377–381
The deviation at different times was b1 except for that at 2.5 min. The maximum recovery of wolframite was 85.76%. The recoveries of easyfloating wolframite and difficult-floating wolframite account for 44.67% and 41.09%, respectively. The optimum flotation kinetics of fine wolframite in the dressing plant is expressed as: ε ¼ 85:76−44:67e−2:052t −41:09e−0:434t
ð10Þ
Because the modified first-order model (Model 4) assumes that the flotation rate constant changes, it also agrees well with the industrial data, except for model 5. However, it did not allow for the maximum recovery to be fitted. Because of different rate constants for easy- and difficult-floating wolframite, the classical first-order model (Model 1) was inappropriate for fine wolframite flotation. The rectangular distribution of floatabilities (Models 2 and 3) was not suitable for fine wolframite flotation. 4. Conclusions The flotation characteristics of fine wolframite were investigated. Based on this investigation, a new kinetic model was proposed. This model was compared with a classical first-order model, a modified first-order model, a first-order kinetic model with a rectangular distribution of floatabilities and a second-order kinetic model with a rectangular distribution of floatabilities. The main conclusions can be summarized as follows: (1) As the flotation time increased, coarse and middle particles could enter the concentrate easily. However, because of a reduction in middle particles as carriers and the poor collision and attachment between the fine particles and air bubbles, fine particles that entered the concentrate decreased. (2) The new kinetic model was ε = ε∞ − ε1∞ e−k1t − ε2∞ e−k2t. (3) An evaluation of kinetic models showed that the model deduced by the author fitted the experimental and industrial data best. The modified first-order model also agreed well with the experimental and industrial data. (4) The optimum flotation kinetic equations of fine wolframite in the laboratory and dressing plant were ε = 87.26− 31.74e−3.446t − 55.51e−0.879t and ε = 85.76 − 44.67e− 2.052t − 41.09e− 0.434t, respectively.
381
Acknowledgments This work was financially supported by the Project of National Natural Science Foundation of China (No. 51504105), the Project of Natural Science Foundation of Jiangxi Province (No. 20161BAB216127) and the Science and Technology Research Project of Education Department of Jiangxi Province (No. GJJ150656). It was also supported by Program for Excellent Young Talents, JXUST.
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