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Effect of slimes on the flotation recovery and kinetics of coal particles
Fuel 220 (2018) 159–166
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Full Length Article
Effect of slimes on the flotation recovery and kinetics of coal particles ⁎
Chao Ni , Xiangning Bu, Wencheng Xia, Yaoli Peng, Guangyuan Xie
⁎
T
Key Laboratory of Coal Processing and Efficient Utilization (Ministry of Education), School of Chemical Engineering and Technology, China University of Mining and Technology, Xuzhou 221116, Jiangsu, China
A R T I C L E I N F O
A B S T R A C T
Keywords: Slimes Coal Flotation Recovery Kinetics
To investigate the effect of slimes on the flotation recovery and kinetics of coal particles, batch flotation and flotation rate tests were carried out using flotation mixtures including slime particles and coal particles within 0.5–0.25 mm, 0.25–0.125 mm and 0.125–0.074 mm size ranges, respectively. Six flotation kinetic models were applied to fit all the flotation test results. It was found that both the flotation recovery and rate of coal particles decreased with the increase in the mass proportion of slime particles under the mixed flotation conditions, especially coarse coal particles. Compared with the flotation performance of coal particles in the individual flotation, slimes enhanced the flotation recovery of coal particles at a low mass proportion of slime particles. In contrast, slimes decreased the flotation recovery of coal particles at a high mass proportion of slime particles. Furthermore, for the coal particles in 0.5–0.25 mm size range, slimes increased its flotation rate at a low mass proportion of slime particles, otherwise slimes decreased its flotation rate. Slimes mainly improved the flotation rate of coal particles in 0.25–0.125 mm size range, while it primarily reduced flotation rate of coal particles in 0.125–0.074 mm size range.
1. Introduction With the unprecedented demand for resources and the rapid depletion of high quality mineral resources, there is increasing need to process low-grade and hard-to-handle ores [1–2]. For the coal mine, it is also facing the same dilemma [3]. Flotation is the most effective method for beneficiating fine coal [4–5]. However, fine coal usually contains excessive levels of ultrafine gangue particles and other materials such as clays, known as slimes, as the quality of fine coal deteriorates. The slimes in turn leads to a major problem for handling fine coal, i.e., the slimes enter into the froth product and contaminate the clean coal during the flotation process, resulting in the high ash content of clean coal [6–8]. The contamination of slimes on clean coal is also the most serious problem in fine coal flotation to date. Although there are few studies on the contamination behavior of slimes in coal flotation, the contamination behavior of fine gangue particles in mineral flotation process has been widely studied [6–11]. Since sufficient dissociation of valuable minerals and gangue minerals needs a much smaller dissociation particle size than that in the dissociation process between coal and gangues. The mechanism of gangue particles contaminating the flotation concentrates includes mechanical entrainment, entrapment, composite particles, and slime coating [11]. Among them, the mechanical entrainment is considered to be the most dominant mechanism for gangue particles entering into the clean coal
⁎
[11–13]. Furthermore, there are numerous factors that affect the recovery behavior of gangue particles during flotation process including water recovery, froth characters, particle size, bubbles size, flotation agent types and dosage, etc [8,11,14,15]. Numerous studies have further proposed the method to reduce the contamination of fine gangue particles to concentrate during the flotation process from the angle of flotation flowsheet, flotation equipment, and flotation agents [16–20]. These results can provide reference for the study of slimes contamination in coal flotation. However, little attention has been devoted to the effect of slime on coal flotation behavior, especially coal flotation kinetics. An actual flotation process is a highly complex separation process involving three phases (air bubbles, water, and solids) and a large number of sub-processes, such as particle-bubble collision and attachment, transport of particle-bubble aggregate to the froth phase, and recovery of particle from the froth phase to concentrate launder [21,22]. From a macroscopic view, the flotation process is also considered as a time-rate recovery process, since the cumulative recovery of floatable minerals is undoubtedly proportional to the flotation time [23,24]. Therefore, the flotation time-recovery profiles are widely used to describe the kinetics of flotation, which can also be completely described using mathematical models [25]. Numerous flotation models have been proposed to investigate flotation kinetic behavior [24,26]. It is also a widely adopted method for studying the flotation kinetics.
Corresponding authors. E-mail addresses: [email protected] (C. Ni), [email protected] (G. Xie).
https://doi.org/10.1016/j.fuel.2018.02.003 Received 8 November 2017; Received in revised form 18 January 2018; Accepted 1 February 2018 0016-2361/ © 2018 Elsevier Ltd. All rights reserved.
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Table 1 Proximate and ultimate analysis results of the coal particles. Proximate analysis (wt%)
Ultimate analysis (wt%)
Mad
Ad
Vdaf
FCd
Std
Odaf
Cdaf
Hdaf
Ndaf
1.00
8.81
41.36
53.47
0.37
16.13
76.79
5.16
1.51
d = Dry basis; ad = Air dry basis; daf = Dry ash-free basis; M = Moisture content; A = Ash content; V = Volatile matter; FC = Fixed carbon.
In this study, six flotation kinetic models were selected to test their applicability for various size fractions of coal particles under the mixed flotation condition of coal and slimes, and a major attempt was to completely discuss the effect of slimes on the flotation recovery and kinetics of different particle size coal. Fig. 2. X-ray diffraction patterns of the slime particles.
2. Experimental
2.2. Flotation tests
2.1. Materials
The flotation tests were performed in a 1.5-L RK/FD-11 flotation cell at an impeller speed of 1800 rpm and a constant air flow-rate of 0.24 m3/h. No collector was added to the flotation tests, and an analytical grade 2-octanol (purity greater than 98.0%) was used as the frother. The dosage of the 2-octanol for a ton of coal was 100 g, and the amount of coal used for each flotation test was also 100 g. Tap water was used to maintain the flotation pulp level. The detailed operating method of the flotation tests can be found elsewhere [27]. The test sample was a mixed sample of the coal particles and slime particles, and the mixing ratio was 80:20%, 65:35%, 50:50%, 35:65% and 20:80% by weight. In order to facilitate the separation of coal particles and slime particles, the size range of the coal particles was 0.5–0.25 mm, 0.25–0.125 mm and 0.125–0.074 mm, respectively, while that of the slime particles was below 0.045 mm in size. During the flotation speed tests, the froth products collected from the flotation tests were divided to 5 products according to the collection periods: 0–5 s, 5–10 s, 10–30 s, 30–60 s and 60–180 s. However, in the conventional flotation test, the collection time for the only one froth product was 180 s. After the flotation tests, both the collected froth products and tailings were wet sieved at a size of 0.045 mm. Then the sieved samples were filtered, dried and weighed. Therefore, the flotation yield of the coal particles and slime particles can be calculated respectively. In these flotation tests, the flotation yield was also the flotation recovery.
The coal sample was collected from a coal preparation plant in Shandong province, China. It was the bituminous coal. From this coal sample, the lump coal with a size range of 25–13 mm and a density of less than 1400 kg/m3 was obtained via the screening test and float-andsink test. Then, the lump coal was crushed to a size below 0.5 mm by a jaw crusher. The obtained coal particles having unique characteristics were used in this study. The proximate and ultimate analysis results of the coal particles are given in Table 1. The coal particles were pressured into a flat surface and measured the static contact angle using the dropping method. As illustrated Fig. 1 (a), the static contact angle of the coal particles was 97°. The slime particles were prepared using lump gangue, which was also collected from the same coal preparation plant. The density of the lump gangue was heavier than 2000 kg/m3, and its ash content was 85.16%. The lump gangue was first crushed to a size below 3 mm with a jaw crusher, and then it was ground to below 0.045 mm using a laboratory ball mill. The grinding product was the slime particles. The mineral compositions of the slime particles were determined using an x-ray diffractometer, and the results are presented in Fig. 2. The principal mineral matters of the slime particles were quartz, kaolinite, dickite and nakrite. Furthermore, there were small amounts of calcite and pyrite in the slime particles. The static contact angle of slime particles was also measured using the dropping method. As described in Fig. 1 (b), the static contact angle of slime particles was 23°.
(a) Coal particles
(b) Slime particles
Fig. 1. The static contact angle of coal particles (a) and slime particles (b).
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Table 2 Six flotation kinetic models used in this investigation. No.
Model
Formula
Remarks [24,25]
1 2
ε = ε∞ [1−exp(−k1 t)]
3
Classical first-order model First-order model with rectangular distribution of flotabilities Fully mixed reactor model
4
Improved gas/solid adsorption model
5
Second-order kinetic model
6
Second-order model with rectangular distribution of flotabilities
This model has been reported to predict values best when the recovery is especially low. This model has been reported to be the best of all models tested to fit experimental data because the rectangular distribution of flotabilities gives an added flexibility. This model assumes that flotation components are exponentially distributed which gives an added flexibility over the classical first-order model and enables it to fit the observed values very well. This mathematical form of model 4 is similar to model 3, which can be derived from model 3 by assuming k3 = 1/k4. Two-parameter expression describing the flotation of a monodisperse feed with particles having a constant floatability. Similar to model 2, this model assumes that flotation components are rectangular distribution. The fit to the experimental data and the confidence intervals become increasingly worse as the fractional recovery approaches 1.0.
ε=
ε = ε∞
ε = ε∞ ε=
{ (1−
}
1 ε∞ 1− [1−exp(−k2 t)] k2 t
(
1 1 + t/k3
k4 t 1 + k4 t
)
)
2k t ε∞ 5 1 + ε∞ k5 t
{
ε = ε∞ 1−
1 [ln(1 k6 t
}
+ k 6 t)]
ε = fractional recovery at time t, %; ε∞ = fractional ultimate recovery, %; kn = rate constants (n = 1, …, 6), s−1.
2.3. Models and modeling methods of flotation kinetics
were calculated again. The predicted recovery value at time t = t2 by the model was referred to as Y2∗∗, and the e2 = Y2 − Y2∗∗. The calculation process was repeated n times resulting n prediction errors, so the ei = Yi − Yi∗∗. The sum of the squares of the n predictions was referred to as the PRESS residuals. Generally, the model having the smallest RMSE value and the biggest R2 value maybe considered the one has the best model fit, and the model having the smallest PRESS value maybe considered the one has the best model stability [28].
In this investigation, six flotation kinetic models were selected to study the effect of slimes particles on the flotation kinetics of coal particles within different size fractions, as shown in Table 2. The parameters of all the model were calculated using the MATrix LABoratory software (Version 7.0) based on the nonlinear least square optimization method. Both the root mean square error (RMSE) and correlation coefficient (R2) were used for measuring the goodness of model fit, and the predictive error sum of squares (PRESS) residuals was used to measure the model stability. To calculate these parameters, consider the test data set consists of n pairs of observations (t1, Y1), (t2, Y2), …, (tn, Yn) were obtained from the time-recovery curve of a flotation test, where ti (the unit of seconds) refers to the flotation time at which ith time interval was taken, and Yn (the unit of%) refers to the corresponding cumulative recovery from the begin to this time point. Therefore, the n was the number of time intervals for the froth products collected during the flotation test. The RMSE was defined by the following expression:
1 n
RMSE =
3. Results and discussions 3.1. Effect of slime particles on the flotation recovery of coal particles Fig. 3 shows the relationship between the flotation recovery of coal particles within different size fractions and the mass ratio of coal particles and slime particles. It can be seen that both in the individual flotation of coal particles and in the mixed flotation of coal particles and slime particles, in general, the recovery of coal particles in the size range of 0.125–0.074 mm was the largest, and that of the 0.25–0.125 mm size range was the second, and the recovery of the 0.5–0.25 mm size range was the smallest. However, the difference in the recovery for the 0.125–0.074 mm and 0.25–0.125 mm size range was relatively small. In this investigation, the ash content of coal particles within various size ranges was between 8.5 and 9.0%, which indicates that difference in the surface hydrophobicity of coal particles within different size range was very small. Therefore, the difference in
n
∑
(Yi−Y ∗i )2
(1)
i= 1
∗
where, Yi was the calculated cumulative recovery of the froth product from the begin to the ith time interval by the models, %. The R2 was defined by the following expression: n
n
∑ R2 =
(Y ∗i −Y)2
i= 1 n
∑
∑ = 1−
∑
(Yi−Y)2
(Yi−Y ∗i )2
i= 1 n
(Yi−Y)2
i= 1
i= 1
(2)
where, Y was the average of the cumulative recoveries of froth products obtained from all the time intervals, %. The PRESS was defined by the following expression: n
PRESS =
∑ i= 1
n
e2i =
∑ i= 1
2 (Yi−Y ∗∗ i )
(3)
To generate this measure, firstly, the data point (t1, Y1) was deleted from the n pairs of data set and the remaining (n-1) pairs of data were used to calculate the parameters for all the candidate models. The calculated values of the model parameters were inserted into the model to predict the cumulative recovery at time t = t1, and the predictive value was referred to as Y1∗∗ (%). Then, the prediction error e1 can also be calculated, e1 = Y1-Y1∗∗. Second, the first data point (t1, Y1) was replaced into the data set and the second data point (t2, Y2) was removed from the data set. Then, the parameters of the candidate model
Fig. 3. Relationship between the flotation recovery of coal particles within different size fractions and the mass ratio of coal particles and slime particles.
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the recovery of coal particles within different size fractions was mainly due to the particle size. There is an optimum particle size range for a particular mineral flotation system, and the recovery of both coarse and fine particles beyond this size range reduces [29]. For the coal particles used in this study, the size range of 0.25–0.074 mm might be within its optimum particle size range for flotation, while the 0.5–0.25 mm size range may be beyond this size range. Hence, the recovery of 0.5–0.25 mm size range was significantly lower than that of the other two size ranges. Furthermore, the recovery of coal particles within different size ranges in the mixed flotation was greater than that of coal particles in the individual flotation when the mass proportion of slime particles was less than 20%. On the contrary, the former was smaller than the latter when the mass proportion of slime particles was more than 20%, and the recovery of coal particles within various size ranges decreased with the increase of mass proportion of slime particles. In addition, the decreasing trend in the recovery of coal particles was more obvious as the particle size increased. These results indicate that the effect of slime particles on the recovery of coal particles varied with the change of the proportion of slime particles. When the mass of slime particles was less than a certain percentage, the slime particles promoted the flotation of coal particles; conversely, the slime particles inhibited the flotation of coal particles when its mass was greater than this certain percentage. And, the inhibition effect of slime particles on the coal particles was more obvious as the particle size of coal particles increased. In a flotation system, the solid particles have an important effect on the stability of flotation froth, especially fine particles [30,31]. The froth and its stability in flotation are also recognized as an important factor which affects recovery and grade [32,33]. Therefore, the increase in recovery of coal particles when the mass proportion of slime particles was less than 20% was mainly due to the increase of froth stability by adding the slime particles. Because the particle size of the slime particles was significantly smaller than that of the coal particles used in this investigation. However, when the mass proportion of slime particles was more than 20%, the slime particles may cover on the surface of the coal particles or bubbles because of the increase in the concentration of slime particles in the pulp. As a result, the collision probability between the coal particles and bubbles decreased, while the detachment probability between both increased. Besides, the disturbance effect of slime particles on the flotation recovery of coal particles also enhanced with the increase of the mass proportion of slime particles in the pulp. Therefore, the recovery of coal particles within different size ranges decreased as the mass proportion of slime particles increased, and the coal particles having a bigger size presented a more pronounced reduction in flotation recovery.
(a) 0.5-0.25 mm size range
(b) 0.25-0.125 mm size range
3.2. Effect of slime particles on the flotation kinetics of coal particles Fig. 4 shows the time-recovery graphs of coal particles within different size ranges under various mass ratios between coal particles and slime particles. These results were obtained with the flotation tests. In order to explore the effect of slime particles on the flotation kinetics of coal particles within different size fractions from the quantitative point of view, the model parameters of the six flotation kinetic models (Table 2), including the flotation rate constant (K) and the maximum theoretical combustible recovery (ε∞), were calculated based on the flotation test results using the MATLAB software. The results are provided in Tables 3–5. Furthermore, the evaluation indexes of all the investigated models, including the RMSE, R2 and PRESS, were also calculated using the software, and the results are shown in the Figs. 5–7. It should be noted that the ε∞ values of models 3, 4, and 5 were the same. The results were consistent with those of previous studies [25,26]. Furthermore, the calculation values of the evaluation indexes, including the RMSE, R2 and PRESS of the models 3, 4, and 5, were also the same. Therefore, there were only four curves that can be observed in Figs. 5–7.
(c) 0.125-0.074 mm size range Fig. 4. Time-recovery graphs of coal particles within different size ranges under various mass ratios of coal particles and slime particles.
As shown in Tables 3–5, the ε∞ value continued to increase from the model 1 to model 6, since the convergence rate of the first-order model was faster than that of the second-order model. When the flotation time (t) tended to infinity, the ε∞ value calculated by the first-order model was smaller than that of the second-order model. Secondly, the ε∞ values of some models were greater than 100%. This might be due to the fact that the floatability of coal particles was very good in this 162
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Table 3 Model parameters of six flotation kinetic models fitting the flotation results of coal particles within 0.5–0.25 mm size fraction. Model No.
Model 1 Model 2 Model 3 Model 4 Model 5 Model 6
Parameter
ε∞ (%) K (s−1) ε∞ (%) K (s−1) ε∞ (%) K (s−1) ε∞ (%) K (s−1) ε∞ (%) K (s−1) ε∞ (%) K (s−1)
Mass ratio of coal particles and slime particles (coal:slimes) Pure coal
80:20%
65:35%
50:50%
35:65%
20:80%
87.6834 0.0394 94.9659 0.0865 100.7065 20.4902 100.7065 0.0488 100.7065 0.0005 108.9186 0.1020
84.6880 0.0659 91.9151 0.1398 97.0105 12.7664 97.0105 0.0783 97.0105 0.0008 103.8052 0.1679
85.0145 0.0577 92.0404 0.1250 97.2552 14.2458 97.2552 0.0702 97.2552 0.0007 104.3117 0.1496
80.5735 0.0516 87.3216 0.1120 92.4224 15.9022 92.4224 0.0629 92.4224 0.0007 99.3787 0.1332
78.4106 0.0385 84.5819 0.0862 89.8039 20.6088 89.8039 0.0485 89.8039 0.0005 97.1233 0.1016
68.9802 0.0378 74.7625 0.0826 79.2544 21.3854 79.2544 0.0468 79.2544 0.0006 85.7875 0.0976
Table 4 Model parameters of six flotation kinetic models fitting the flotation results of coal particles within 0.25–0.125 mm size fraction. Model No.
Model 1 Model 2 Model 3 Model 4 Model 5 Model 6
Parameter
ε∞ (%) K (s−1) ε∞ (%) K (s−1) ε∞ (%) K (s−1) ε∞ (%) K (s−1) ε∞ (%) K (s−1) ε∞ (%) K (s−1)
Mass ratio of coal particles and slime particles (coal:slimes) Pure coal
80:20%
65:35%
50:50%
35:65%
20:80%
92.6304 0.0567 100.4551 0.1212 105.7919 14.5080 105.7919 0.0689 105.7919 0.0007 113.3876 0.1471
95.0319 0.0850 102.2821 0.1815 106.3860 9.3370 106.3860 0.1071 106.3860 0.0010 112.4793 0.2392
95.3712 0.0747 102.8051 0.1605 107.2832 10.6640 107.2832 0.0938 107.2832 0.0009 113.8338 0.2068
93.3353 0.0747 100.7539 0.1595 105.2687 10.7938 105.2687 0.0926 105.2687 0.0009 111.8038 0.2035
92.5409 0.0733 99.9789 0.1557 104.4365 11.0454 104.4365 0.0905 104.4365 0.0009 110.9680 0.1985
82.0769 0.0637 88.7826 0.1370 93.2221 12.7315 93.2221 0.0785 93.2221 0.0008 99.4988 0.1700
Table 5 Model parameters of six flotation kinetic models fitting the flotation results of coal particles within 0.125–0.074 mm size fraction. Model No.
Model 1 Model 2 Model 3 Model 4 Model 5 Model 6
Parameter
ε∞ (%) K (s−1) ε∞ (%) K (s−1) ε∞ (%) K (s−1) ε∞ (%) K (s−1) ε∞ (%) K (s−1) ε∞ (%) K (s−1)
Mass ratio of coal particles and slime particles (coal:slimes) Pure coal
80:20%
65:35%
50:50%
35:65%
20:80%
95.0280 0.0681 102.8850 0.1440 107.7079 12.0242 107.7079 0.0832 107.7079 0.0008 114.7549 0.1805
97.7096 0.0613 105.8244 0.1305 110.9633 13.3095 110.9632 0.0751 110.9632 0.0007 118.5296 0.1618
96.7689 0.0596 104.8198 0.1273 110.0450 13.6944 110.0450 0.0730 110.0450 0.0007 117.6731 0.1568
95.6755 0.0612 103.6748 0.1300 108.7824 13.3946 108.7824 0.0747 108.7825 0.0007 116.2474 0.1606
94.6768 0.0576 102.6123 0.1232 107.9297 14.2163 107.9297 0.0703 107.9297 0.0007 115.5787 0.1504
95.2327 0.0522 103.4195 0.1111 109.0086 15.8423 109.0086 0.0631 109.0086 0.0006 117.1002 0.1337
ratios of 0.5–0.25 mm size range coal particles and slime particles, and the R2 value of this model was the largest at the same time. It indicates that the model 6 gave the best fit goodness for the flotation results of coal particles within 0.5–0.25 mm size range among the investigated models. Furthermore, the PRESS value of the model 6 was also the minimum among the six models, which shows that this model had the best stability for fitting the flotation results of 0.5–0.25 mm size range coal particles. Hence, the model 6, i.e., secondary matrix distribution model was considered as the most reasonable model for fitting the flotation results of 0.5–0.25 mm size range coal particles among the six models based on the comprehensive evaluation of the model's goodness of fit and stability. Similarly, the model 2, i.e., first-order matrix distribution model was determined to be the best model to fit the flotation
study. As evident in Fig. 4, the accumulated recovery of coal particles obtained by the flotation tests can reach more than 90% when the flotation time was only 180 s, and the recoveries of 0.25–0.125 mm and 0.125–0.074 mm size range were even close to 100%. Therefore, if the convergence rate of the flotation kinetic model was slow, the ε∞ value calculated by this model may be greater than 100%. However, the flotation time in the actual flotation test usually lasts only a few minutes, and it cannot be sustained for infinite time. As long as the fitting accuracy of the kinetic model meets the requirements, it is still reliable to apply the flotation kinetic model to fit the mineral flotation process with a finite flotation time. It can be seen from Fig. 5 that the RMSE value of the model 6 was the minimum among all the investigated models under different mass 163
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(a) PRESS
(a) PRESS
(b) RMSE (b) RMSE
(c) R2
(c) R2 Fig. 5. Model evaluation indexes of six flotation kinetic models fitting the flotation results of coal particles within 0.5–0.25 mm size fraction.
Fig. 6. Model evaluation indexes of six flotation kinetic models fitting the flotation results of coal particles within 0.25–0.125 mm size fraction.
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results obtained with both 0.25–0.125 mm and 0.125–0.074 mm size range coal particles among the six models by analyzing the evaluation indexes showed in Figs. 6 and 7. Since the expression of the flotation rate constant (K) in different flotation kinetic models was different, the K value obtained by different models was not comparable. In order to ensure the comparability of the K values under different test conditions, the K values of coal particles within different size fractions calculated by the first-order matrix distribution model was selected to analyze the effect of slime particles on the flotation kinetics of coal particles, and the results are shown in the Fig. 8. As illustrated in Fig. 8, in general, the K values of coal particles within different size fractions decreased with the increase of the mass proportion of slime particles under the condition of mixed flotation. The results prove that the increase in the concentration of slime particles in the flotation pulp did reduce the flotation rate of coal particles. It should be noted that this finding was applicable to the mixed flotation conditions of slime particles and coal particles. However, the K value of coal particles within different size fractions exhibited the different relative magnitude relationships when it compared with that of the individual flotation of coal particles. For the 0.5–0.25 mm size range coal particles, when the mass proportion of slime particles was less than 50% in the mixed flotation, the K value of coal particles was larger than that of coal particles in the individual flotation. However, the former was less than the latter when the mass proportion of slime particles was bigger than 50%. For the 0.25–0.125 mm size range coal particles, the K value of coal particles in the mixed flotation at the different mass proportions of slime particles was greater than that of coal particles in the individual flotation. In contrast, for the 0.125–0.074 mm size range coal particles, the K values of coal particles in the mixed flotation were smaller than that in the individual flotation. The above results indicate that the effect of slime particles on the flotation rate of coal particles was related to both the particle size of coal particles and the content of slime particles. For the coarse coal particles, slime particles increased its flotation rate when the amount of slime particles was small in the flotation pulp. In contrast, the slime particles decreased its flotation rate at a high content of slime particles in the flotation pulp. For the medium size coal particles, slime particles mainly improved its flotation rate. However, for the fine coal particles, slime particles primarily reduced its flotation rate. In addition, the increase in the concentration of slime particles in the flotation pulp decreased the flotation rate of coal particles with different particle size under the mixed flotation condition.
(a) PRESS
(b) RMSE
4. Conclusions In this investigation, the effect of slimes on the flotation kinetics and recovery of coal particles within different size fractions was thoroughly explored. Six flotation kinetic models were applied to fit the flotation data that obtained from flotation tests under various mixing ratios of coal particles and slime particles. The MATLAB software was used to estimate calculate the model parameters (K and ε∞) and model evaluation indexes (RMSE, R2 and PRESS) based on the nonlinear least square optimization method. The results obtained from this study lead to the following conclusions:
(c) R
(1) The effect of slime particles on the flotation recovery of coal was depended on the content of slime particles and the particle size of the coal. When the mass proportion of the slime particles below 20%, the flotation recovery of coal particles within all size fractions in the mixed flotation was greater than that of coal particles in the individual flotation. However, the former was lower than the latter when the mass proportion of the slime particles over 20%. Furthermore, the flotation recovery of coal particles within all size fractions decreased with the increase in the content of slime
2
Fig. 7. Model evaluation indexes of six flotation kinetic models fitting the flotation results of coal particles within 0.125–0.074 mm size fraction.
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Fig. 8. The flotation rate constant (K) value of coal particles within different size fractions under various mass ratios of coal particles and slime particles.
particles. Besides, the effect of slime particles on the flotation recovery of coarse coal particles was more obvious. (2) The secondary matrix distribution model was considered to be the most reasonable for fitting the flotation results obtained with the coal particles in 0.5–0.25 mm among the tested models, while the first-order matrix distribution model was the best model for the coal particles both within 0.25–0.125 mm and 0.125–0.074 mm size ranges. (3) The effect of slime particles on the flotation kinetics of coal was also depended on the particle size of the coal and the content of slime particles. In the mixed flotation, the flotation rate of coal particles within all size ranges was reduced as the content of slime particles increased. However, compared with flotation rate of coal particles in the individual flotation, the flotation rate of coal particles within 0.25–0.125 mm size range in the mixed flotation increased, while that of coal particles within 0.125–0.074 mm size range decreased. The flotation rate of coal particles within 0.5–0.25 mm size range increased initially decreased afterwards as the content of slime particles increased. Acknowledgements This work was funded by the China Postdoctoral Science Foundation (No. 2017M621879), the National Natural Science Foundation of China (NSFC, Grant No. 51474213) and A Priority Academic Program Development of Jiangsu Higher Education Institutions. The authors wish to express their thanks to Ma Guangxi, Zhang Tuantuan and He wenzhen for their contributions to this work. References [1] Galvin KP, Zhou J, Dickinson JE, Ramadhani H. Desliming of dense minerals in fluidized beds. Miner Eng 2012;39:9–18. [2] Wang B, Peng Y. The behaviour of mineral matter in fine coal flotation using saline
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Full Length Article
Effect of slimes on the flotation recovery and kinetics of coal particles ⁎
Chao Ni , Xiangning Bu, Wencheng Xia, Yaoli Peng, Guangyuan Xie
⁎
T
Key Laboratory of Coal Processing and Efficient Utilization (Ministry of Education), School of Chemical Engineering and Technology, China University of Mining and Technology, Xuzhou 221116, Jiangsu, China
A R T I C L E I N F O
A B S T R A C T
Keywords: Slimes Coal Flotation Recovery Kinetics
To investigate the effect of slimes on the flotation recovery and kinetics of coal particles, batch flotation and flotation rate tests were carried out using flotation mixtures including slime particles and coal particles within 0.5–0.25 mm, 0.25–0.125 mm and 0.125–0.074 mm size ranges, respectively. Six flotation kinetic models were applied to fit all the flotation test results. It was found that both the flotation recovery and rate of coal particles decreased with the increase in the mass proportion of slime particles under the mixed flotation conditions, especially coarse coal particles. Compared with the flotation performance of coal particles in the individual flotation, slimes enhanced the flotation recovery of coal particles at a low mass proportion of slime particles. In contrast, slimes decreased the flotation recovery of coal particles at a high mass proportion of slime particles. Furthermore, for the coal particles in 0.5–0.25 mm size range, slimes increased its flotation rate at a low mass proportion of slime particles, otherwise slimes decreased its flotation rate. Slimes mainly improved the flotation rate of coal particles in 0.25–0.125 mm size range, while it primarily reduced flotation rate of coal particles in 0.125–0.074 mm size range.
1. Introduction With the unprecedented demand for resources and the rapid depletion of high quality mineral resources, there is increasing need to process low-grade and hard-to-handle ores [1–2]. For the coal mine, it is also facing the same dilemma [3]. Flotation is the most effective method for beneficiating fine coal [4–5]. However, fine coal usually contains excessive levels of ultrafine gangue particles and other materials such as clays, known as slimes, as the quality of fine coal deteriorates. The slimes in turn leads to a major problem for handling fine coal, i.e., the slimes enter into the froth product and contaminate the clean coal during the flotation process, resulting in the high ash content of clean coal [6–8]. The contamination of slimes on clean coal is also the most serious problem in fine coal flotation to date. Although there are few studies on the contamination behavior of slimes in coal flotation, the contamination behavior of fine gangue particles in mineral flotation process has been widely studied [6–11]. Since sufficient dissociation of valuable minerals and gangue minerals needs a much smaller dissociation particle size than that in the dissociation process between coal and gangues. The mechanism of gangue particles contaminating the flotation concentrates includes mechanical entrainment, entrapment, composite particles, and slime coating [11]. Among them, the mechanical entrainment is considered to be the most dominant mechanism for gangue particles entering into the clean coal
⁎
[11–13]. Furthermore, there are numerous factors that affect the recovery behavior of gangue particles during flotation process including water recovery, froth characters, particle size, bubbles size, flotation agent types and dosage, etc [8,11,14,15]. Numerous studies have further proposed the method to reduce the contamination of fine gangue particles to concentrate during the flotation process from the angle of flotation flowsheet, flotation equipment, and flotation agents [16–20]. These results can provide reference for the study of slimes contamination in coal flotation. However, little attention has been devoted to the effect of slime on coal flotation behavior, especially coal flotation kinetics. An actual flotation process is a highly complex separation process involving three phases (air bubbles, water, and solids) and a large number of sub-processes, such as particle-bubble collision and attachment, transport of particle-bubble aggregate to the froth phase, and recovery of particle from the froth phase to concentrate launder [21,22]. From a macroscopic view, the flotation process is also considered as a time-rate recovery process, since the cumulative recovery of floatable minerals is undoubtedly proportional to the flotation time [23,24]. Therefore, the flotation time-recovery profiles are widely used to describe the kinetics of flotation, which can also be completely described using mathematical models [25]. Numerous flotation models have been proposed to investigate flotation kinetic behavior [24,26]. It is also a widely adopted method for studying the flotation kinetics.
Corresponding authors. E-mail addresses: [email protected] (C. Ni), [email protected] (G. Xie).
https://doi.org/10.1016/j.fuel.2018.02.003 Received 8 November 2017; Received in revised form 18 January 2018; Accepted 1 February 2018 0016-2361/ © 2018 Elsevier Ltd. All rights reserved.
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Table 1 Proximate and ultimate analysis results of the coal particles. Proximate analysis (wt%)
Ultimate analysis (wt%)
Mad
Ad
Vdaf
FCd
Std
Odaf
Cdaf
Hdaf
Ndaf
1.00
8.81
41.36
53.47
0.37
16.13
76.79
5.16
1.51
d = Dry basis; ad = Air dry basis; daf = Dry ash-free basis; M = Moisture content; A = Ash content; V = Volatile matter; FC = Fixed carbon.
In this study, six flotation kinetic models were selected to test their applicability for various size fractions of coal particles under the mixed flotation condition of coal and slimes, and a major attempt was to completely discuss the effect of slimes on the flotation recovery and kinetics of different particle size coal. Fig. 2. X-ray diffraction patterns of the slime particles.
2. Experimental
2.2. Flotation tests
2.1. Materials
The flotation tests were performed in a 1.5-L RK/FD-11 flotation cell at an impeller speed of 1800 rpm and a constant air flow-rate of 0.24 m3/h. No collector was added to the flotation tests, and an analytical grade 2-octanol (purity greater than 98.0%) was used as the frother. The dosage of the 2-octanol for a ton of coal was 100 g, and the amount of coal used for each flotation test was also 100 g. Tap water was used to maintain the flotation pulp level. The detailed operating method of the flotation tests can be found elsewhere [27]. The test sample was a mixed sample of the coal particles and slime particles, and the mixing ratio was 80:20%, 65:35%, 50:50%, 35:65% and 20:80% by weight. In order to facilitate the separation of coal particles and slime particles, the size range of the coal particles was 0.5–0.25 mm, 0.25–0.125 mm and 0.125–0.074 mm, respectively, while that of the slime particles was below 0.045 mm in size. During the flotation speed tests, the froth products collected from the flotation tests were divided to 5 products according to the collection periods: 0–5 s, 5–10 s, 10–30 s, 30–60 s and 60–180 s. However, in the conventional flotation test, the collection time for the only one froth product was 180 s. After the flotation tests, both the collected froth products and tailings were wet sieved at a size of 0.045 mm. Then the sieved samples were filtered, dried and weighed. Therefore, the flotation yield of the coal particles and slime particles can be calculated respectively. In these flotation tests, the flotation yield was also the flotation recovery.
The coal sample was collected from a coal preparation plant in Shandong province, China. It was the bituminous coal. From this coal sample, the lump coal with a size range of 25–13 mm and a density of less than 1400 kg/m3 was obtained via the screening test and float-andsink test. Then, the lump coal was crushed to a size below 0.5 mm by a jaw crusher. The obtained coal particles having unique characteristics were used in this study. The proximate and ultimate analysis results of the coal particles are given in Table 1. The coal particles were pressured into a flat surface and measured the static contact angle using the dropping method. As illustrated Fig. 1 (a), the static contact angle of the coal particles was 97°. The slime particles were prepared using lump gangue, which was also collected from the same coal preparation plant. The density of the lump gangue was heavier than 2000 kg/m3, and its ash content was 85.16%. The lump gangue was first crushed to a size below 3 mm with a jaw crusher, and then it was ground to below 0.045 mm using a laboratory ball mill. The grinding product was the slime particles. The mineral compositions of the slime particles were determined using an x-ray diffractometer, and the results are presented in Fig. 2. The principal mineral matters of the slime particles were quartz, kaolinite, dickite and nakrite. Furthermore, there were small amounts of calcite and pyrite in the slime particles. The static contact angle of slime particles was also measured using the dropping method. As described in Fig. 1 (b), the static contact angle of slime particles was 23°.
(a) Coal particles
(b) Slime particles
Fig. 1. The static contact angle of coal particles (a) and slime particles (b).
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Table 2 Six flotation kinetic models used in this investigation. No.
Model
Formula
Remarks [24,25]
1 2
ε = ε∞ [1−exp(−k1 t)]
3
Classical first-order model First-order model with rectangular distribution of flotabilities Fully mixed reactor model
4
Improved gas/solid adsorption model
5
Second-order kinetic model
6
Second-order model with rectangular distribution of flotabilities
This model has been reported to predict values best when the recovery is especially low. This model has been reported to be the best of all models tested to fit experimental data because the rectangular distribution of flotabilities gives an added flexibility. This model assumes that flotation components are exponentially distributed which gives an added flexibility over the classical first-order model and enables it to fit the observed values very well. This mathematical form of model 4 is similar to model 3, which can be derived from model 3 by assuming k3 = 1/k4. Two-parameter expression describing the flotation of a monodisperse feed with particles having a constant floatability. Similar to model 2, this model assumes that flotation components are rectangular distribution. The fit to the experimental data and the confidence intervals become increasingly worse as the fractional recovery approaches 1.0.
ε=
ε = ε∞
ε = ε∞ ε=
{ (1−
}
1 ε∞ 1− [1−exp(−k2 t)] k2 t
(
1 1 + t/k3
k4 t 1 + k4 t
)
)
2k t ε∞ 5 1 + ε∞ k5 t
{
ε = ε∞ 1−
1 [ln(1 k6 t
}
+ k 6 t)]
ε = fractional recovery at time t, %; ε∞ = fractional ultimate recovery, %; kn = rate constants (n = 1, …, 6), s−1.
2.3. Models and modeling methods of flotation kinetics
were calculated again. The predicted recovery value at time t = t2 by the model was referred to as Y2∗∗, and the e2 = Y2 − Y2∗∗. The calculation process was repeated n times resulting n prediction errors, so the ei = Yi − Yi∗∗. The sum of the squares of the n predictions was referred to as the PRESS residuals. Generally, the model having the smallest RMSE value and the biggest R2 value maybe considered the one has the best model fit, and the model having the smallest PRESS value maybe considered the one has the best model stability [28].
In this investigation, six flotation kinetic models were selected to study the effect of slimes particles on the flotation kinetics of coal particles within different size fractions, as shown in Table 2. The parameters of all the model were calculated using the MATrix LABoratory software (Version 7.0) based on the nonlinear least square optimization method. Both the root mean square error (RMSE) and correlation coefficient (R2) were used for measuring the goodness of model fit, and the predictive error sum of squares (PRESS) residuals was used to measure the model stability. To calculate these parameters, consider the test data set consists of n pairs of observations (t1, Y1), (t2, Y2), …, (tn, Yn) were obtained from the time-recovery curve of a flotation test, where ti (the unit of seconds) refers to the flotation time at which ith time interval was taken, and Yn (the unit of%) refers to the corresponding cumulative recovery from the begin to this time point. Therefore, the n was the number of time intervals for the froth products collected during the flotation test. The RMSE was defined by the following expression:
1 n
RMSE =
3. Results and discussions 3.1. Effect of slime particles on the flotation recovery of coal particles Fig. 3 shows the relationship between the flotation recovery of coal particles within different size fractions and the mass ratio of coal particles and slime particles. It can be seen that both in the individual flotation of coal particles and in the mixed flotation of coal particles and slime particles, in general, the recovery of coal particles in the size range of 0.125–0.074 mm was the largest, and that of the 0.25–0.125 mm size range was the second, and the recovery of the 0.5–0.25 mm size range was the smallest. However, the difference in the recovery for the 0.125–0.074 mm and 0.25–0.125 mm size range was relatively small. In this investigation, the ash content of coal particles within various size ranges was between 8.5 and 9.0%, which indicates that difference in the surface hydrophobicity of coal particles within different size range was very small. Therefore, the difference in
n
∑
(Yi−Y ∗i )2
(1)
i= 1
∗
where, Yi was the calculated cumulative recovery of the froth product from the begin to the ith time interval by the models, %. The R2 was defined by the following expression: n
n
∑ R2 =
(Y ∗i −Y)2
i= 1 n
∑
∑ = 1−
∑
(Yi−Y)2
(Yi−Y ∗i )2
i= 1 n
(Yi−Y)2
i= 1
i= 1
(2)
where, Y was the average of the cumulative recoveries of froth products obtained from all the time intervals, %. The PRESS was defined by the following expression: n
PRESS =
∑ i= 1
n
e2i =
∑ i= 1
2 (Yi−Y ∗∗ i )
(3)
To generate this measure, firstly, the data point (t1, Y1) was deleted from the n pairs of data set and the remaining (n-1) pairs of data were used to calculate the parameters for all the candidate models. The calculated values of the model parameters were inserted into the model to predict the cumulative recovery at time t = t1, and the predictive value was referred to as Y1∗∗ (%). Then, the prediction error e1 can also be calculated, e1 = Y1-Y1∗∗. Second, the first data point (t1, Y1) was replaced into the data set and the second data point (t2, Y2) was removed from the data set. Then, the parameters of the candidate model
Fig. 3. Relationship between the flotation recovery of coal particles within different size fractions and the mass ratio of coal particles and slime particles.
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the recovery of coal particles within different size fractions was mainly due to the particle size. There is an optimum particle size range for a particular mineral flotation system, and the recovery of both coarse and fine particles beyond this size range reduces [29]. For the coal particles used in this study, the size range of 0.25–0.074 mm might be within its optimum particle size range for flotation, while the 0.5–0.25 mm size range may be beyond this size range. Hence, the recovery of 0.5–0.25 mm size range was significantly lower than that of the other two size ranges. Furthermore, the recovery of coal particles within different size ranges in the mixed flotation was greater than that of coal particles in the individual flotation when the mass proportion of slime particles was less than 20%. On the contrary, the former was smaller than the latter when the mass proportion of slime particles was more than 20%, and the recovery of coal particles within various size ranges decreased with the increase of mass proportion of slime particles. In addition, the decreasing trend in the recovery of coal particles was more obvious as the particle size increased. These results indicate that the effect of slime particles on the recovery of coal particles varied with the change of the proportion of slime particles. When the mass of slime particles was less than a certain percentage, the slime particles promoted the flotation of coal particles; conversely, the slime particles inhibited the flotation of coal particles when its mass was greater than this certain percentage. And, the inhibition effect of slime particles on the coal particles was more obvious as the particle size of coal particles increased. In a flotation system, the solid particles have an important effect on the stability of flotation froth, especially fine particles [30,31]. The froth and its stability in flotation are also recognized as an important factor which affects recovery and grade [32,33]. Therefore, the increase in recovery of coal particles when the mass proportion of slime particles was less than 20% was mainly due to the increase of froth stability by adding the slime particles. Because the particle size of the slime particles was significantly smaller than that of the coal particles used in this investigation. However, when the mass proportion of slime particles was more than 20%, the slime particles may cover on the surface of the coal particles or bubbles because of the increase in the concentration of slime particles in the pulp. As a result, the collision probability between the coal particles and bubbles decreased, while the detachment probability between both increased. Besides, the disturbance effect of slime particles on the flotation recovery of coal particles also enhanced with the increase of the mass proportion of slime particles in the pulp. Therefore, the recovery of coal particles within different size ranges decreased as the mass proportion of slime particles increased, and the coal particles having a bigger size presented a more pronounced reduction in flotation recovery.
(a) 0.5-0.25 mm size range
(b) 0.25-0.125 mm size range
3.2. Effect of slime particles on the flotation kinetics of coal particles Fig. 4 shows the time-recovery graphs of coal particles within different size ranges under various mass ratios between coal particles and slime particles. These results were obtained with the flotation tests. In order to explore the effect of slime particles on the flotation kinetics of coal particles within different size fractions from the quantitative point of view, the model parameters of the six flotation kinetic models (Table 2), including the flotation rate constant (K) and the maximum theoretical combustible recovery (ε∞), were calculated based on the flotation test results using the MATLAB software. The results are provided in Tables 3–5. Furthermore, the evaluation indexes of all the investigated models, including the RMSE, R2 and PRESS, were also calculated using the software, and the results are shown in the Figs. 5–7. It should be noted that the ε∞ values of models 3, 4, and 5 were the same. The results were consistent with those of previous studies [25,26]. Furthermore, the calculation values of the evaluation indexes, including the RMSE, R2 and PRESS of the models 3, 4, and 5, were also the same. Therefore, there were only four curves that can be observed in Figs. 5–7.
(c) 0.125-0.074 mm size range Fig. 4. Time-recovery graphs of coal particles within different size ranges under various mass ratios of coal particles and slime particles.
As shown in Tables 3–5, the ε∞ value continued to increase from the model 1 to model 6, since the convergence rate of the first-order model was faster than that of the second-order model. When the flotation time (t) tended to infinity, the ε∞ value calculated by the first-order model was smaller than that of the second-order model. Secondly, the ε∞ values of some models were greater than 100%. This might be due to the fact that the floatability of coal particles was very good in this 162
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Table 3 Model parameters of six flotation kinetic models fitting the flotation results of coal particles within 0.5–0.25 mm size fraction. Model No.
Model 1 Model 2 Model 3 Model 4 Model 5 Model 6
Parameter
ε∞ (%) K (s−1) ε∞ (%) K (s−1) ε∞ (%) K (s−1) ε∞ (%) K (s−1) ε∞ (%) K (s−1) ε∞ (%) K (s−1)
Mass ratio of coal particles and slime particles (coal:slimes) Pure coal
80:20%
65:35%
50:50%
35:65%
20:80%
87.6834 0.0394 94.9659 0.0865 100.7065 20.4902 100.7065 0.0488 100.7065 0.0005 108.9186 0.1020
84.6880 0.0659 91.9151 0.1398 97.0105 12.7664 97.0105 0.0783 97.0105 0.0008 103.8052 0.1679
85.0145 0.0577 92.0404 0.1250 97.2552 14.2458 97.2552 0.0702 97.2552 0.0007 104.3117 0.1496
80.5735 0.0516 87.3216 0.1120 92.4224 15.9022 92.4224 0.0629 92.4224 0.0007 99.3787 0.1332
78.4106 0.0385 84.5819 0.0862 89.8039 20.6088 89.8039 0.0485 89.8039 0.0005 97.1233 0.1016
68.9802 0.0378 74.7625 0.0826 79.2544 21.3854 79.2544 0.0468 79.2544 0.0006 85.7875 0.0976
Table 4 Model parameters of six flotation kinetic models fitting the flotation results of coal particles within 0.25–0.125 mm size fraction. Model No.
Model 1 Model 2 Model 3 Model 4 Model 5 Model 6
Parameter
ε∞ (%) K (s−1) ε∞ (%) K (s−1) ε∞ (%) K (s−1) ε∞ (%) K (s−1) ε∞ (%) K (s−1) ε∞ (%) K (s−1)
Mass ratio of coal particles and slime particles (coal:slimes) Pure coal
80:20%
65:35%
50:50%
35:65%
20:80%
92.6304 0.0567 100.4551 0.1212 105.7919 14.5080 105.7919 0.0689 105.7919 0.0007 113.3876 0.1471
95.0319 0.0850 102.2821 0.1815 106.3860 9.3370 106.3860 0.1071 106.3860 0.0010 112.4793 0.2392
95.3712 0.0747 102.8051 0.1605 107.2832 10.6640 107.2832 0.0938 107.2832 0.0009 113.8338 0.2068
93.3353 0.0747 100.7539 0.1595 105.2687 10.7938 105.2687 0.0926 105.2687 0.0009 111.8038 0.2035
92.5409 0.0733 99.9789 0.1557 104.4365 11.0454 104.4365 0.0905 104.4365 0.0009 110.9680 0.1985
82.0769 0.0637 88.7826 0.1370 93.2221 12.7315 93.2221 0.0785 93.2221 0.0008 99.4988 0.1700
Table 5 Model parameters of six flotation kinetic models fitting the flotation results of coal particles within 0.125–0.074 mm size fraction. Model No.
Model 1 Model 2 Model 3 Model 4 Model 5 Model 6
Parameter
ε∞ (%) K (s−1) ε∞ (%) K (s−1) ε∞ (%) K (s−1) ε∞ (%) K (s−1) ε∞ (%) K (s−1) ε∞ (%) K (s−1)
Mass ratio of coal particles and slime particles (coal:slimes) Pure coal
80:20%
65:35%
50:50%
35:65%
20:80%
95.0280 0.0681 102.8850 0.1440 107.7079 12.0242 107.7079 0.0832 107.7079 0.0008 114.7549 0.1805
97.7096 0.0613 105.8244 0.1305 110.9633 13.3095 110.9632 0.0751 110.9632 0.0007 118.5296 0.1618
96.7689 0.0596 104.8198 0.1273 110.0450 13.6944 110.0450 0.0730 110.0450 0.0007 117.6731 0.1568
95.6755 0.0612 103.6748 0.1300 108.7824 13.3946 108.7824 0.0747 108.7825 0.0007 116.2474 0.1606
94.6768 0.0576 102.6123 0.1232 107.9297 14.2163 107.9297 0.0703 107.9297 0.0007 115.5787 0.1504
95.2327 0.0522 103.4195 0.1111 109.0086 15.8423 109.0086 0.0631 109.0086 0.0006 117.1002 0.1337
ratios of 0.5–0.25 mm size range coal particles and slime particles, and the R2 value of this model was the largest at the same time. It indicates that the model 6 gave the best fit goodness for the flotation results of coal particles within 0.5–0.25 mm size range among the investigated models. Furthermore, the PRESS value of the model 6 was also the minimum among the six models, which shows that this model had the best stability for fitting the flotation results of 0.5–0.25 mm size range coal particles. Hence, the model 6, i.e., secondary matrix distribution model was considered as the most reasonable model for fitting the flotation results of 0.5–0.25 mm size range coal particles among the six models based on the comprehensive evaluation of the model's goodness of fit and stability. Similarly, the model 2, i.e., first-order matrix distribution model was determined to be the best model to fit the flotation
study. As evident in Fig. 4, the accumulated recovery of coal particles obtained by the flotation tests can reach more than 90% when the flotation time was only 180 s, and the recoveries of 0.25–0.125 mm and 0.125–0.074 mm size range were even close to 100%. Therefore, if the convergence rate of the flotation kinetic model was slow, the ε∞ value calculated by this model may be greater than 100%. However, the flotation time in the actual flotation test usually lasts only a few minutes, and it cannot be sustained for infinite time. As long as the fitting accuracy of the kinetic model meets the requirements, it is still reliable to apply the flotation kinetic model to fit the mineral flotation process with a finite flotation time. It can be seen from Fig. 5 that the RMSE value of the model 6 was the minimum among all the investigated models under different mass 163
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(a) PRESS
(a) PRESS
(b) RMSE (b) RMSE
(c) R2
(c) R2 Fig. 5. Model evaluation indexes of six flotation kinetic models fitting the flotation results of coal particles within 0.5–0.25 mm size fraction.
Fig. 6. Model evaluation indexes of six flotation kinetic models fitting the flotation results of coal particles within 0.25–0.125 mm size fraction.
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results obtained with both 0.25–0.125 mm and 0.125–0.074 mm size range coal particles among the six models by analyzing the evaluation indexes showed in Figs. 6 and 7. Since the expression of the flotation rate constant (K) in different flotation kinetic models was different, the K value obtained by different models was not comparable. In order to ensure the comparability of the K values under different test conditions, the K values of coal particles within different size fractions calculated by the first-order matrix distribution model was selected to analyze the effect of slime particles on the flotation kinetics of coal particles, and the results are shown in the Fig. 8. As illustrated in Fig. 8, in general, the K values of coal particles within different size fractions decreased with the increase of the mass proportion of slime particles under the condition of mixed flotation. The results prove that the increase in the concentration of slime particles in the flotation pulp did reduce the flotation rate of coal particles. It should be noted that this finding was applicable to the mixed flotation conditions of slime particles and coal particles. However, the K value of coal particles within different size fractions exhibited the different relative magnitude relationships when it compared with that of the individual flotation of coal particles. For the 0.5–0.25 mm size range coal particles, when the mass proportion of slime particles was less than 50% in the mixed flotation, the K value of coal particles was larger than that of coal particles in the individual flotation. However, the former was less than the latter when the mass proportion of slime particles was bigger than 50%. For the 0.25–0.125 mm size range coal particles, the K value of coal particles in the mixed flotation at the different mass proportions of slime particles was greater than that of coal particles in the individual flotation. In contrast, for the 0.125–0.074 mm size range coal particles, the K values of coal particles in the mixed flotation were smaller than that in the individual flotation. The above results indicate that the effect of slime particles on the flotation rate of coal particles was related to both the particle size of coal particles and the content of slime particles. For the coarse coal particles, slime particles increased its flotation rate when the amount of slime particles was small in the flotation pulp. In contrast, the slime particles decreased its flotation rate at a high content of slime particles in the flotation pulp. For the medium size coal particles, slime particles mainly improved its flotation rate. However, for the fine coal particles, slime particles primarily reduced its flotation rate. In addition, the increase in the concentration of slime particles in the flotation pulp decreased the flotation rate of coal particles with different particle size under the mixed flotation condition.
(a) PRESS
(b) RMSE
4. Conclusions In this investigation, the effect of slimes on the flotation kinetics and recovery of coal particles within different size fractions was thoroughly explored. Six flotation kinetic models were applied to fit the flotation data that obtained from flotation tests under various mixing ratios of coal particles and slime particles. The MATLAB software was used to estimate calculate the model parameters (K and ε∞) and model evaluation indexes (RMSE, R2 and PRESS) based on the nonlinear least square optimization method. The results obtained from this study lead to the following conclusions:
(c) R
(1) The effect of slime particles on the flotation recovery of coal was depended on the content of slime particles and the particle size of the coal. When the mass proportion of the slime particles below 20%, the flotation recovery of coal particles within all size fractions in the mixed flotation was greater than that of coal particles in the individual flotation. However, the former was lower than the latter when the mass proportion of the slime particles over 20%. Furthermore, the flotation recovery of coal particles within all size fractions decreased with the increase in the content of slime
2
Fig. 7. Model evaluation indexes of six flotation kinetic models fitting the flotation results of coal particles within 0.125–0.074 mm size fraction.
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Fig. 8. The flotation rate constant (K) value of coal particles within different size fractions under various mass ratios of coal particles and slime particles.
particles. Besides, the effect of slime particles on the flotation recovery of coarse coal particles was more obvious. (2) The secondary matrix distribution model was considered to be the most reasonable for fitting the flotation results obtained with the coal particles in 0.5–0.25 mm among the tested models, while the first-order matrix distribution model was the best model for the coal particles both within 0.25–0.125 mm and 0.125–0.074 mm size ranges. (3) The effect of slime particles on the flotation kinetics of coal was also depended on the particle size of the coal and the content of slime particles. In the mixed flotation, the flotation rate of coal particles within all size ranges was reduced as the content of slime particles increased. However, compared with flotation rate of coal particles in the individual flotation, the flotation rate of coal particles within 0.25–0.125 mm size range in the mixed flotation increased, while that of coal particles within 0.125–0.074 mm size range decreased. The flotation rate of coal particles within 0.5–0.25 mm size range increased initially decreased afterwards as the content of slime particles increased. Acknowledgements This work was funded by the China Postdoctoral Science Foundation (No. 2017M621879), the National Natural Science Foundation of China (NSFC, Grant No. 51474213) and A Priority Academic Program Development of Jiangsu Higher Education Institutions. The authors wish to express their thanks to Ma Guangxi, Zhang Tuantuan and He wenzhen for their contributions to this work. References [1] Galvin KP, Zhou J, Dickinson JE, Ramadhani H. Desliming of dense minerals in fluidized beds. Miner Eng 2012;39:9–18. [2] Wang B, Peng Y. The behaviour of mineral matter in fine coal flotation using saline
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