- Email: [email protected]
The difference in flotation kinetics of various size fractions of bituminous coal between rougher and cleaner flotation processes
Powder Technology 292 (2016) 210–216
Contents lists available at ScienceDirect
Powder Technology journal homepage: www.elsevier.com/locate/powtec
The difference in flotation kinetics of various size fractions of bituminous coal between rougher and cleaner flotation processes Chao Ni, Guangyuan Xie ⁎, Mingguo Jin, Yaoli Peng, Wencheng Xia ⁎ 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
Article history: Received 26 February 2015 Received in revised form 15 November 2015 Accepted 2 February 2016 Available online 4 February 2016 Keywords: Rougher flotation Cleaner flotation Flotation kinetics Coal particle size
a b s t r a c t In order to investigate the difference in flotation kinetics of various size fractions of bituminous coal between rougher and cleaner flotation processes, clean coal was collected as a function of time in both rougher and cleaner flotation processes. The size composition of clean coal was then analyzed. Six flotation kinetic models were applied to the modeling of data from the flotation tests by using MATrix LABoratory software. The relationship between flotation rate constant, maximum combustible recovery and particle size was also studied. The results show that the maximum flotation combustible recovery and flotation rate are obtained with an intermediate particle size both in the rougher and cleaner flotation processes. The combustible recovery and flotation rate are higher in the cleaner flotation process than that in the rougher flotation process. Except the classical firstorder flotation kinetic model, the other five kinetic models gave an excellent fit to the flotation data. The rougher flotation process can be described using the first-order and second-order models while the cleaner flotation process can only be described using the first-order model. It is found that the first-order model with rectangular distribution of floatability provides the best fit of the experimental data obtained from both the rougher and cleaner flotation processes among the tested models. © 2016 Elsevier B.V. All rights reserved.
1. Introduction Flotation is a physico-chemical separation process based on the difference in surface properties between valuable minerals and gangues. Flotation kinetics can be described using the mathematical models which incorporate both a recovery and a rate function, since the flotation process is theoretically considered as a time-rate recovery process [1–3]. Furthermore, flotation kinetics models are generally applied to evaluate the flotation tests. The first flotation model was proposed in the 1930s [4]. Subsequently, numerous works about the kinetics of flotation process were reported [3,5–9]. The flotation kinetics models of quite a few flotation processes have been established based on the test data from batch flotation tests or industrial tests under reasonable operating conditions. The effects of flotation parameters including particle size and size distribution, reagents type and dosage, air flow rate, pulp density, and wash water rate on the flotation kinetics in a flotation cell or column were studied [10–14]. A great number of flotation models have been proposed to investigate flotation kinetic behavior [1,6–15]. These models have ⁎ Corresponding authors at: School of Chemical Engineering and Technology, China University of Mining and Technology, Xuzhou 221116, Jiangsu, China. E-mail addresses: [email protected] (C. Ni), [email protected] (G. Xie), [email protected] (W. Xia).
http://dx.doi.org/10.1016/j.powtec.2016.02.004 0032-5910/© 2016 Elsevier B.V. All rights reserved.
conveniently been defined in three categories: (1) empirical models, (2) probability models, and (3) kinetic models [16]. This paper will consider only kinetic models according to the previous studies [1–3]. A single-stage circuit is commonly applied in coal flotation, i.e., rougher flotation process [17]. Therefore, almost all the previous studies on kinetics of coal flotation are based on the single-stage flotation process. However, flotation products that consistently fulfill requirements cannot be obtained using the single-stage flotation process in some cases, e.g. treating poorly floatable coal and producing super-clean coal. In fact, multi-stage coal flotation process is favored in reducing the ash content of clean coal by eliminating the hydraulic entrainment and selectively rejecting lower hydrophobic particles [18–20]. Furthermore, there are a number of multi-stage flotation circuits in the treatment of metallurgical coking coal and production of super-clean coal [17,21–22]. Therefore, the kinetics of multi-stage coal flotation process should also be studied. However, little attention has been devoted to the flotation kinetics of cleaner stages or multi-stage flotation circuits. The difference in the flotation kinetics between rougher and cleaner stages has not been adequately investigated in the past. In this study, the particle size distribution of collected clean coal in various flotation stages both in rougher and cleaner processes was analyzed, and six kinetic flotation models were selected to test their applicability for various size fractions of coal both in rougher and cleaner flotation stages. In addition, a major attempt of the paper was to discuss
C. Ni et al. / Powder Technology 292 (2016) 210–216
the differences in the flotation kinetics of various size fractions between rougher and cleaner flotation process. 2. Experimental 2.1. Materials
2.2. Flotation tests In the flotation experiments, kerosene and DL-2-Octanol (DLO) were used as the collector and frother, respectively. The flotation water used in the experiments was tap water, and the chemical composition was shown in Table 3. The flotation tests were divided into two parts: (1) rougher flotation tests; and (2) cleaner flotation tests. The rougher flotation tests were performed in a 1.5-L Denver flotation cell. In each test, 150 g of coal sample was mixed with 1 L tap water in the cell and was agitated for 2 min at an impeller rotation speed of 1800 rpm. Then, kerosene (1750 g/t) was added to the pulp and conditioned for 2 min. Subsequently, the DLO (300 g/t) was added to the pulp and conditioned for 0.5 min. After the conditioning process, tap water was added to increase the volume of pulp in the cell up to 1.5 L, and the air was introduced into the cell at a flow rate of 4.17 L/min. The pulp was floated for 200 s, and tap water was added to maintain a constant pulp level when it was necessary. The froth was collected by using an automatic froth collector at a rotation speed of 30 r/min. Products were obtained in the rougher flotation tests: clean coal and tailings. The cleaner flotation tests were also performed in a 1.5-L Denver flotation cell, and the feed of which was the froth product of rougher flotation. The operating parameters of cleaner flotation tests were the same to those of rougher flotation tests. In each cleaner flotation test, the rougher flotation concentrate was poured into the cell and was agitated for 1 min at an impeller rotation speed of 1800 rpm. No flotation reagents were added to the pulp. Then, tap water was added to increase the volume of pulp to 1.5 L, and air was introduced into the cell at a flow rate of 4.17 L/min. The flotation time and froth collection time were the same to those of rougher flotation tests. Two products were obtained in the cleaner flotation tests: further clean coal and cleaner tailings. The final froth products from the rougher flotation tests and the cleaner flotation tests were both divided to 5 products according to the collection periods: 0–20 s, 20–40 s, 40–80 s, 80–120 s, and 120– 200 s. All products including flotation concentrate and tailings were filtered, dried, weighed and analyzed for the ash content. In addition, each product was screened into five narrow size fractions: − 500 + 250, − 250 + 125, − 125 + 74, − 74 + 45, and − 45 μm. The ash content Table 1 Particle size distribution of bituminous coal sample.
500–250 250–125 125–74 74–45 −45
Table 2 Proximate and ultimate analyses of bituminous coal sample. Proximate analysis (wt, %, ad)
Ultimate analysis (wt, %, daf)
M
A
V
FC
C
H
O
N
St
1.21
33.57
25.76
39.46
80.85
5.46
10.85
1.12
0.88
LHVad MJ/kg 19.89
ad = Air dry basis; daf = Dry ash-free basis; M = Moisture content; A = Ash content; V = Volatile matter; FC = Fixed carbon; LHV = Low heat value.
A bituminous coal sample obtained from Yunhe Mine of Shangdong province, China, was used in this investigation. The sample was screened to pass 500 μm. The particle size distribution of the coal sample is given in Table 1, and the proximate and ultimate analyses of the coal sample are given in Table 2. The ash content of the coal sample was 33.57% on an air dry basis. The sample had 53.00% fine particles with sizes below 45 μm with an ash content of 43.63%. It indicated that the coal sample had many fine coal particles with high ash content.
Size fraction (μm)
211
Mass (%)
14.68 13.44 6.69 12.19 53.00
Ash content (%)
22.85 21.83 20.53 22.82 43.63
of the products and the combustible recovery of the flotation were obtained. The combustible recovery was calculated from Eq. (1): Combustible recovery% ¼ ½WC ð100−AC Þ=½W F 100−A F 100
ð1Þ
where WC is the weight of the concentrate (%), WF is the weight of the feed (%), AC is the ash content of the concentrate by weight (%), and AF is the ash content of the feed by weight (%). 2.3. Flotation kinetic models In this investigation, six flotation kinetic models were selected to study the flotation performance of various size fractions in rougher flotation and cleaner flotation processes, as shown in Table 4. The cumulative combustible recoveries of various size fractions after 20, 40, 80, 120, and 200 s of flotation time were fitted using the six kinetic models. The narrow size fractions included −500 + 250, −250 + 125, − 125 + 74, − 74 + 45, and − 45 μm. The MATrix LABoratory (MATLAB) software (Version 7.0) was used to simulate the flotation rate constant (K), the maximum combustible recovery (ε∞), and the correlation coefficient (R2) based on the nonlinear least square optimization method. MATLAB is one of the most powerful and advanced numerical calculation software. Nonlinear least squares optimization has been widely used in the non-linear regression, curve fitting and optimization of nonlinear model parameters. 3. Results and discussion 3.1. Flotation kinetics of various size fractions in rougher flotation process The flotation time-combustible recovery of various size fractions in rougher flotation process are shown in Fig. 1. The combustible recovery of the flotation increased initially and then decreased with the increase of particle size, and the maximum combustible recovery in the rougher flotation process was obtained with the −250 + 125 μm size fraction. It indicated that the maximum combustible recovery was obtained with an intermediate particle size in the rougher flotation process. Similar findings were also reported by other researchers [23–25]. Flotation is a physic-chemical separation process, in which hydrophobic particles are captured by air bubbles and eventually reported to the froth product. This process is determined by three most critical steps including the particle–bubble collision, attachment, and detachment [3,25–26]. It is well known that particle size is an important parameter in flotation process, and a high process efficiency of froth flotation is typically limited to a relatively narrow particle size range [23–29]. However, outside this range, the recovery drops significantly, whether it is at the fine or the coarse end of the size spectrum [28]. The low combustible recovery of fine particles is mainly because of the poor collision and attachment between the fine particles and air
Cumulative undersize Yield (%)
Ash contend (%)
100.00 85.32 71.88 65.19 53.00
33.57 35.41 37.95 39.74 43.63
Table 3 Conductivity and chemical composition of the tap water (mg/L). Conductivity (mS/cm)
Ca2+
Mg2+
Na+
K+
Cl−
HCO− 3
SO2− 4
0.36
54.7
16.6
15.4
3.4
24.7
13.9
5.4
212
C. Ni et al. / Powder Technology 292 (2016) 210–216
Table 4 Six flotation kinetic models used in this investigation [3,5,6,24]. Series Name of model number 1 2 3
Formula
Classical first-order model First-order model with rectangular distribution of flotabilities Fully mixed reactor model
ε = ε∞[1 − exp (−k1t)] ε ¼ ε ∞ f1− k12 t ½1−expð−k2 tÞg 1 Þ ε ¼ ε∞ ð1− 1þt=k 3
4
Improved gas/solid adsorption model
k4 t ε ¼ ε∞ ð1þk Þ 4t
5
Second-order kinetic model
ε∞ k5 t ε ¼ 1þε ∞ k5 t
6
Second-order model with rectangular distribution of flotabilities
ε ¼ ε ∞ f1− k16 t ½lnð1 þ k6 tÞg
2
Ε = fractional recovery at time t; ε ∞ = fractional ultimate recovery; k n = rate constants (n = 1, …, 6).
bubbles, whereas the poor combustible recovery of coarse particles is primarily due to the high probability of detachment between the coarse particles and air bubbles [25,28–30]. Furthermore, the non-selective entrainment of fine gangue particles maybe also a cause of the low combustible recovery of fine particles, since the fine particles in the feed of rougher flotation tests had a high ash content in this investigation (Table 1). The cumulative combustible recovery at 20, 40, 80, 120, and 200 s with various size fractions in rougher flotation process was fitted to the six flotation kinetic models (Table 4) using the MATLAB software. The flotation rate constant (K), the maximum combustible recovery value (ε∞), and the multitude correlation coefficient (R2) were also calculated using the software, and the results are given in Table 5 and Fig. 2. As shown in Table 5, the maximum ε∞ value of the rougher flotation tests increased initially, reached a maximum and decreased afterwards as the size fraction decreased in all of the models. The maximum ε∞ values were obtained with the −250 + 125 μm size fraction. The results showed an excellent agreement with the change trend of combustible recovery as a function of size fraction in Fig. 1. Furthermore, except the model 3, the K values obtained with all other models exhibited the same change trend as that of the ε∞ values. These results indicated that the maximum flotation rate constant was also obtained with an intermediate particle size. The results were consistent with those of previous studies [3,26,31–35]. The difference in kinetics constants (both K and ε∞) of various size fractions can also be explained by the combined effect of the collision and attachment/detachment sub-processes in flotation process [36,37]. Furthermore, the difference may be related to the
Fig. 1. Effect of the size fractions on the cumulative combustible recovery in the rougher flotation process.
physico-chemical properties of various size particles and hydrodynamic conditions in the flotation cell [26,34–35]. As shown in Table 5, the ε∞ value increased gradually from model 1 to model 6, while the ε∞ values of models 3, 4, and 5 were the same. The term R2 is useful for comparing fitting accuracy of models with different number of independent variables and different degrees of freedom [1]. As shown in Fig. 2, in general, the R2 values for the six kinetic models were greater than 0.9700, which indicated that all kinetic models gave an excellent fit to the experimental data. Zhang et al. [3] also reported similar findings in the lignite reverse flotation process in the presence of sodium chloride. Further, the R2 values of model 2 for the rougher flotation tests with various size fractions were the biggest among the investigated models, which suggested that the model 2 was considered to be more reasonable for fitting the rougher flotation results. This result agreed with the results reported by other researchers [1,3,32,38–39]. This might be due to the fact that model 2 is simple and mathematically stable. We suggested that the rougher flotation can be described with the first-order and second-order models, and the model 2 was considered to be the most reasonable among the tested models. 3.2. Flotation kinetics of various size fractions in cleaner flotation process Fig. 3 shows the flotation time-combustible recovery of various size fractions in the cleaner flotation process. In general, the change trends of combustible recovery of various size fractions in the cleaner flotation process were similar to those in Fig. 1. However, the maximum combustible recovery was obtained with the −125 + 74 μm size fraction and the second was obtained with the − 250 + 125 μm size fraction, which was different from that in Fig. 1. The difference in combustible recovery between various size fractions except the −45 μm size fraction, was smaller during the cleaner flotation, and the combustible recoveries of these size fractions were over 90% after a flotation time of 120 s. The combustible recoveries of all size fractions in the cleaner flotation process were bigger than those in the rougher flotation process. It should be pointed out that the combustible recoveries of all size fractions in cleaner flotation test were calculated on the basis of the clean coal of the rougher flotation process (the feed of cleaner flotation tests was the clean coal from the rougher flotation process), while those in rougher flotation process were calculated on the basis of the feed of the raw coal. The reason for the combustible recoveries of all size fractions in the cleaner flotation process was greater than those in the rougher flotation process may relate to the difference in floatability of the feed used in the rougher and cleaner flotation tests. A large number of difficult-to-float particles were rejected to the tailings in the rougher flotation, and the floatability of the feed in the cleaner flotation was better than that in the rougher flotation since the feed in the rougher flotation was raw coal. Non-linear regression results for six models fitting to the cleaner flotation results are given in Table 6 and Fig. 4. As shown in Table 6, in general, the change trends of both ε∞ values and K values as a function of size fraction in the cleaner flotation process were similar to those in the rougher flotation process. Both the maximum of ε∞ values and K values were obtained with the − 125 + 74 μm size fraction, which were consistent with the experimental results in Fig. 3. The results demonstrated that both the combustible recovery and flotation rate of the intermediate particle size were the maximum among the all size fractions in the cleaner flotation process. It can be observed from the results in Table 6 that all the ε∞ values of models 3, 4, 5, and 6 with various size fractions (except −45 μm size fraction) were greater than 100% in the cleaner flotation process. However, the maximum combustible recovery obtained from the flotation test was 100%, which was a theoretical value. In theory, the maximum ε∞ value calculated by kinetic models was also 100% at most. Therefore, we tentatively put forward that models 3, 4, 5, and 6 were considered to be not reasonable for fitting the results obtained from the cleaner flotation process. The results may be attributed to the low convergence
C. Ni et al. / Powder Technology 292 (2016) 210–216
213
Table 5 Non-linear regression results for all models fitting to the rougher flotation results. Models
Model 1 Model 2 Model 3 Model 4 Model 5 Model 6
−250 + 125 μm
−125 + 74 μm
K (s−1)
−500–250 μm ε∞ (%)
K (s−1)
ε∞ (%)
K (s−1)
ε∞ (%)
K (s−1)
ε∞ (%)
K (s−1)
ε∞ (%)
0.0289 0.0585 29.9957 0.0333 0.0004 0.0702
68.3997 76.3003 81.2828 81.2828 81.2828 88.2564
0.0483 0.1096 14.0813 0.0710 0.0007 0.1709
85.1774 91.7929 94.7489 94.7489 94.7489 99.5352
0.0460 0.1030 15.2098 0.0657 0.0007 0.1557
80.6681 87.2167 90.2697 90.2697 90.2697 95.1161
0.0325 0.0673 25.5527 0.0391 0.0004 0.0843
75.8203 83.8850 88.7817 88.7817 88.7817 95.7151
0.0202 0.0382 50.3097 0.0199 0.0003 0.0387
59.4100 68.0836 75.0017 75.0017 75.0017 83.7661
speeds of these models, i.e., the time for obtaining the maximum yield (ε∞ value) in the fitting curves of these models was much greater than that in the flotation tests.
−74 + 45 μm
−45 μm
In the cleaner flotation tests, the feed owned a good floatability, and a high combustible recovery can be obtained after a short flotation time. As shown in Fig. 3, the combustible recoveries of all size fractions
Fig. 2. Comparison of six kinetic models fitted to the test data of various size fractions in the rougher flotation process.
214
C. Ni et al. / Powder Technology 292 (2016) 210–216
3.3. Comparison of flotation kinetics between the rougher and cleaner flotation process
Fig. 3. Effect of the size fractions on the cumulative combustible recovery in the cleaner flotation process.
(except −45 μm size fraction) at 200 s were over 90%. After this period, the combustible recoveries of these size fractions showed a very little increase with the increasing flotation time. However, there was a significant difference between the trend of test data and all the fitting curves of models 3, 4, 5, and 6 when the flotation time was more than 200 s. As shown in Fig. 4, the fitting curves of the various size fractions with the models 3, 4, 5, and 6 were already higher than the test data at the flotation time of 200 s, and they presented a gradual rising trend with the continued increase of flotation time. Therefore, the difference between the experimental value obtained from flotation tests and the fitting values calculated by models 3, 4, 5, and 6 was increased with the increase of flotation time. As a result, when the flotation time gradually approached to the infinite time, the ε∞ values of these models fitted to the data of the clearer flotation tests may be more than 100%. It also can be seen in Fig. 4, there was a significant deviation between the test data and the fitting curves of the model 1. This curve showed no change when the flotation time was greater than 100 s due to a rapid convergence velocity of the model 1. Therefore, the combustible recovery calculated by the model 1 was significantly smaller than the test value at the flotation time of over 120 s. Furthermore, the R2 values of the model 1 with −250 + 125 μm and −125 + 74 μm size fractions were only 0.9354 and 0.9442, respectively. These results indicated that the model 1 does not give an excellent fit to the experimental data. In contrast, the fitting curves of the model 2 exhibited a good agreement with the test data of various size fractions. Moreover, the R2 values of model 2 for various size fractions were distinctly bigger than those of model 1, and the minimum R2 value for model 2 fitting to the cleaner flotation results was 0.9845. Therefore, we concluded that the cleaner flotation process can only be described with the first-order models, and the model 2 provided the best fit of the experimental data obtained from the cleaner flotation tests among the six models.
As shown in Figs. 1 and 3, the slopes of the curves for various size fractions in the cleaner flotation process were steeper than those in the rougher flotation process. Furthermore, the cumulative combustible recovery of various size fractions showed little change after 120 s in the rougher flotation process but the corresponding time was 80 s in the cleaner flotation process. These results demonstrated that the flotation rates of the various size fractions were increased in the cleaner flotation process compared with those in the rougher flotation process. This conclusion can also be supported from a comparison of the results obtained in Tables 5 and 6. It can be observed that the K values of all size fractions in the cleaner flotation tests were greater than those in the rougher flotation tests. Take the calculations of model 2 as an example, the K values of −500 + 250 μm, −250 + 125 μm, −125 + 74 μm, −74 + 45 μm, and − 45 μm size fractions showed the increases by 58.97%, 15.97%, 38.16%, 63.60%, and 114.14%, respectively, in the cleaner flotation tests compared with those in the rougher flotation tests. The results suggested that the increases in flotation rates of coarse and fine particle size fractions were especially more obvious than those of the intermediate particle size fractions. It also indicated that the floatability and flotation of coal particles were determined by many factors, such as coal surface properties, particle size, pulp density, and agent concentration [2,10,18,40–45]. 4. Conclusions In this investigation, the difference in flotation rates of various size fractions of bituminous coal between rougher and cleaner flotation processes was studied. Six flotation kinetic models were applied in the fitting process of the flotation data from the rougher and cleaner flotation tests. The MATLAB software was used to estimate the relationship between the flotation rate constant (K), the maximum combustible recovery (ε∞), and the particle size based on the nonlinear least square optimization method. The results obtained from this study lead to the following conclusions: (1) Both in the rougher and cleaner flotation processes, the maximum flotation combustible recoveries and flotation rates were obtained with an intermediate particle size. Besides, the combustible recoveries and flotation rates of various size fractions were improved in the cleaner flotation process. In this investigation, the maximum recovery of 87.15% was obtained with the −250 + 125 μm size fraction in the rougher flotation process, and the maximum recovery of 95.65% was obtained with −125 + 74 μm size fraction in the cleaner flotation process. The maximum flotation rate constants were also obtained with the same size fraction in both rougher and cleaner flotation processes. (2) Compared with the rougher flotation process, the flotation rates of various size fractions were increased in the cleaner flotation process, and the increases of coarse and fine particle size fractions were especially more obvious than those of the intermediate particle size fractions.
Table 6 Non-linear regression results for all models fitting to the cleaner flotation results. Models Model 1 Model 2 Model 3 Model 4 Model 5 Model 6
−250 + 125 μm
−125 + 74 μm
K (s−1)
−500–250 μm ε∞ (%)
K (s−1)
ε∞ (%)
K (s−1)
ε∞ (%)
−74 + 45 μm K (s−1)
ε∞ (%)
−45 μm K (s−1)
ε∞ (%)
0.0423 0.0930 17.0902 0.0585 0.0006 0.1359
90.3028 98.0776 101.8248 101.8248 101.8248 107.7265
0.0538 0.1271 11.7729 0.0849 0.0008 0.2119
92.4214 98.8355 101.4833 101.4833 101.4833 105.9295
0.0588 0.1423 10.2185 0.0979 0.0010 0.2517
93.3283 99.3559 101.5881 101.5881 101.5881 105.5377
0.0480 0.1101 13.954 0.0717 0.0007 0.1731
91.0161 97.9459 101.0216 101.0216 101.0216 106.0453
0.0383 0.0818 20.0813 0.0498 0.0005 0.1120
82.8381 90.6534 94.8061 94.8061 94.8061 101.0434
C. Ni et al. / Powder Technology 292 (2016) 210–216
215
Fig. 4. Comparison of six kinetic models fitted to the test data of various size fractions in the cleaner flotation process.
(3) The flotation kinetic of the rougher flotation process can be described using the first-order and second-order models while that of the cleaner flotation process can only be described using the first-order models. The first-order model with rectangular distribution of floatability was considered to be the most reasonable to fit the results from both rougher and cleaner flotation processes among the tested models.
Acknowledgments This work was supported by the National Natural Science Foundation of China (NSFC, Grant No. 51474213 and No. 51374205) and A Priority Academic Program Development of Jiangsu Higher Education Institutions. We also want to thank the support of the Postdoctoral Science Foundation of China (2015M580497).
References [1] X.M. Yuan, B.I. Palsson, K.S.E. Forssberg, Statistical interpretation of flotation kinetics for a complex sulphide ore, Miner. Eng. 9 (4) (1996) 429–442. [2] R. Sripriya, P.V.T. Rao, B.R. Choudhury, Optimisation of operating variables of fine coal flotation using a combination of modified flotation parameters and statistical techniques, Int. J. Miner. Process. 68 (1) (2003) 109–127. [3] H. Zhang, J. Liu, Y. Cao, Y. Wang, Effects of particle size on lignite reverse flotation kinetics in the presence of sodium chloride, Powder Technol. 246 (2013) 658–663. [4] H.G. Zuniga, Flotation recovery is an exponential function of its rate, Boln. Soc. Nac. Min. 47 (1935) 83–86 (Santiago). [5] E.C. Dowling, R.R. Klimpel, F.F. Aplan, Model discrimination in the flotation of a porphyry copper ore, Miner. Metall. Process. 2 (2) (1985) 87–101. [6] G.J. Jameson, S. Nam, M.M. Young, Physical factors affecting recovery rates in flotation, Miner. Sci. Eng. 9 (3) (1977) 103–118. [7] G.E. Agar, J. Chia, L.C. Requis, Flotation rate measurements to optimize an operating circuit, Miner. Eng. 11 (4) (1998) 347–360. [8] J.F. Oliveira, S.M. Saraiva, J.S. Pimenta, A.P.A. Oliveira, Kinetics of pyrochlore flotation from Araxá mineral deposits, Miner. Eng. 14 (1) (2001) 99–105. [9] E.C. Çilek, Estimation of flotation kinetic parameters by considering interactions of the operating variables, Miner. Eng. 17 (1) (2004) 81–85.
216
C. Ni et al. / Powder Technology 292 (2016) 210–216
[10] R.B. Read, L.R. Camp, M.S. Summers, D.M. Rapp, The influence of reagent type on the kinetics of ultrafine coal flotation, Powder Technol. 59 (3) (1989) 153–162. [11] A.J. Niemi, Role of kinetics in modelling and control of flotation plants, Powder Technol. 82 (1) (1995) 69–77. [12] J. Labidi, M.A. Pelach, X. Turon, P. Mutjé, Predicting flotation efficiency using neural networks, Chem. Eng. Process. Process Intensif. 46 (4) (2007) 314–322. [13] M. Uçurum, O. Bayat, Effects of operating variables on modified flotation parameters in the mineral separation, Sep. Purif. Technol. 55 (2) (2007) 173–181. [14] M. Uçurum, Influences of Jameson flotation operation variables on the kinetics and recovery of unburned carbon, Powder Technol. 191 (3) (2009) 240–246. [15] L. Mao, R.H. Yoon, Predicting flotation rates using a rate equation derived from first principles, Int. J. Miner. Process. 51 (1) (1997) 171–181. [16] A.J. Lynch, N.W. Johnson, E.V. Manlapig, C.G. Thome, Mineral and coal flotation circuits. Chapter 3, mathematical models of flotation(advisory editor) in: D.W. Fuerstenau (Ed.), Development in Mineral Processing, Elsevier, Amsterdam, 1981 (3, 57). [17] J.W. Leonard, D.R. Mitchell, Coal Preparation, The American Institute of Mining. Metallurgical, and Petroleum Engineers, Inc., New York, NY, 1979 10–75. [18] B.A. Firth, A.R. Swanson, S.K. Nicol, Flotation circuits for poorly floating coals, Int. J. Miner. Process. 5 (4) (1979) 321–334. [19] R.Q. Honaker, M.K. Mohanty, Enhanced column flotation performance for fine coal cleaning, Miner. Eng. 9 (9) (1996) 931–945. [20] D. Tao, G.H. Luttrell, R.H. Yoon, An experimental investigation on column flotation circuit configuration, Int. J. Miner. Process. 60 (1) (2000) 37–56. [21] K.J. Miller, Coal-pyrite flotation, Trans. Soc. Min. Eng. AIME 258 (1975) 30–33. [22] G.H. Luttrell, Hydrodynamic Studies and Mathematical Modeling of Fine Coal Flotation(PhD dissertation) Department of Mining and Minerals Engineering, Virginia Polytechnic Institute and State University, Blacksburgh, Virginia, 1986. [23] A.M. Gaudin, J.O. Groh, H.B. Henderson, Effect of Particle Size on Flotation, Tech. Publ., 414, American Institute of Mining and Metallurgical Engineering, 1931 3–23. [24] W.J. Trahar, L.J. Warren, The floatability of very fine particles—a review, Int. J. Miner. Process. 3 (1976) 103–131. [25] D. Tao, Role of bubble size in flotation of coarse and fine particles—a review, Sep. Sci. Technol. 39 (4) (2005) 741–760. [26] S. Muganda, M. Zanin, S.R. Grano, Benchmarking flotation performance: single minerals, Int. J. Miner. Process. 98 (3–4) (2011) 182–194. [27] G.J. Jameson, A.V. Nguyen, S. Ata, The flotation of fine and coarse particles, in: M.C. Fuerstenau (Ed.), Centenary of Flotation Commemorative, Society for Mining, 5, Metallurgy and Exploration, Inc. (SME), USA 2008, pp. 339–372. [28] G.J. Jameson, Advances in fine and coarse particle flotation, Can. Metall. Q. 49 (4) (2010) 325–330.
[29] B. Shahbazi, B. Rezai, S.M. Javad Koleini, Bubble–particle collision and attachment probability on fine particles flotation, Chem. Eng. Process. Process Intensif. 49 (6) (2010) 622–627. [30] H. Schubert, On the optimization of hydrodynamics in fine particle flotation, Miner. Eng. 21 (12–14) (2008) 930–936. [31] D. Feng, C. Aldrich, Effect of particle size on flotation performance of complex sulphide ores, Miner. Eng. 12 (7) (1999) 721–731 (11). [32] O. Bayat, M. Ucurum, C. Poole, Effects of size distribution on flotation kinetics of Turkish sphalerite, Min. Process. & Extrac. Metallurgy Imm Trans. 113 (1) (2004) 53–59. [33] S.P. Mehrotra, P.C. Kapur, The effects of aeration rate, particle size and pulp density on the flotation rate distributions, Powder Technol. 9 (74) (1974) 213–219. [34] G.J. Jameson, The effect of surface liberation and particle size on flotation rate constants, Miner. Eng. 36-38 (10) (2012) 132–137. [35] S.D.D. Welsby, S.M.S.M. Vianna, J.P. Franzidis, Assigning physical significance to floatability components, Int. J. Miner. Process. 97 (1–4) (2010) 59–67. [36] E. Abkhoshka, M. Kor, B. Rezai, A study on the effect of particle size on coal flotation kinetics using fuzzy logic, Expert Systems with Applications 37 (7) (2010) 5201–5207. [37] Y. Li, W. Zhao, X. Gui, X. Zhang, Flotation kinetics and separation selectivity of coal size fractions, Physicochem. Probl. Min. Process. 49 (2) (2013) 387–395. [38] A.P. Chaves, A.S. Ruiz, Considerations on the kinetics of froth flotation of ultrafine coal contained in tailings, Int. J. Coal Prep. Util. 29 (6) (2009) 289–297. [39] X. GUI, J. LIU, X. TAO, Y. WANG, Y. CAO, Studies on flotation rate of a hard-to-float fine coal, J. China Coal Soc. 2011 (1895-1900) 36(11) (In Chinese). [40] W. Xia, G. Xie, C. Liang, J. Yang, Flotation behavior of different size fractions of fresh and oxidized coals, Powder Technol. 267 (2014) 80–85. [41] W. Xia, G. Xie, Y. Peng, Recent advances in beneficiation for low rank coals, Powder Technol. 277 (2015) 206–221. [42] W. Xia, C. Ren, Y. Peng, D. Pan, Comparison of traditional and zero-conditioning flotation performances of oxidized anthracite coal, Powder Technol. 275 (2015) 280–283. [43] W. Xia, G. Xie, Changes in the hydrophobicity of anthracite coals before and after high temperature heating process, Powder Technol. 264 (2014) 31–35. [44] W. Xia, C. Ni, G. Xie, The influence of surface roughness on wettability of natural/ gold-coated ultra-low ash coal particles, Powder Technol. 288 (2016) 286–290. [45] W. Xia, G. Xie, D. Pan, J. Yang, Effects of cooling conditions on surface properties of heated coals, Ind. Eng. Chem. Res. 53 (26) (2014) 10810–10813.
Contents lists available at ScienceDirect
Powder Technology journal homepage: www.elsevier.com/locate/powtec
The difference in flotation kinetics of various size fractions of bituminous coal between rougher and cleaner flotation processes Chao Ni, Guangyuan Xie ⁎, Mingguo Jin, Yaoli Peng, Wencheng Xia ⁎ 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
Article history: Received 26 February 2015 Received in revised form 15 November 2015 Accepted 2 February 2016 Available online 4 February 2016 Keywords: Rougher flotation Cleaner flotation Flotation kinetics Coal particle size
a b s t r a c t In order to investigate the difference in flotation kinetics of various size fractions of bituminous coal between rougher and cleaner flotation processes, clean coal was collected as a function of time in both rougher and cleaner flotation processes. The size composition of clean coal was then analyzed. Six flotation kinetic models were applied to the modeling of data from the flotation tests by using MATrix LABoratory software. The relationship between flotation rate constant, maximum combustible recovery and particle size was also studied. The results show that the maximum flotation combustible recovery and flotation rate are obtained with an intermediate particle size both in the rougher and cleaner flotation processes. The combustible recovery and flotation rate are higher in the cleaner flotation process than that in the rougher flotation process. Except the classical firstorder flotation kinetic model, the other five kinetic models gave an excellent fit to the flotation data. The rougher flotation process can be described using the first-order and second-order models while the cleaner flotation process can only be described using the first-order model. It is found that the first-order model with rectangular distribution of floatability provides the best fit of the experimental data obtained from both the rougher and cleaner flotation processes among the tested models. © 2016 Elsevier B.V. All rights reserved.
1. Introduction Flotation is a physico-chemical separation process based on the difference in surface properties between valuable minerals and gangues. Flotation kinetics can be described using the mathematical models which incorporate both a recovery and a rate function, since the flotation process is theoretically considered as a time-rate recovery process [1–3]. Furthermore, flotation kinetics models are generally applied to evaluate the flotation tests. The first flotation model was proposed in the 1930s [4]. Subsequently, numerous works about the kinetics of flotation process were reported [3,5–9]. The flotation kinetics models of quite a few flotation processes have been established based on the test data from batch flotation tests or industrial tests under reasonable operating conditions. The effects of flotation parameters including particle size and size distribution, reagents type and dosage, air flow rate, pulp density, and wash water rate on the flotation kinetics in a flotation cell or column were studied [10–14]. A great number of flotation models have been proposed to investigate flotation kinetic behavior [1,6–15]. These models have ⁎ Corresponding authors at: School of Chemical Engineering and Technology, China University of Mining and Technology, Xuzhou 221116, Jiangsu, China. E-mail addresses: [email protected] (C. Ni), [email protected] (G. Xie), [email protected] (W. Xia).
http://dx.doi.org/10.1016/j.powtec.2016.02.004 0032-5910/© 2016 Elsevier B.V. All rights reserved.
conveniently been defined in three categories: (1) empirical models, (2) probability models, and (3) kinetic models [16]. This paper will consider only kinetic models according to the previous studies [1–3]. A single-stage circuit is commonly applied in coal flotation, i.e., rougher flotation process [17]. Therefore, almost all the previous studies on kinetics of coal flotation are based on the single-stage flotation process. However, flotation products that consistently fulfill requirements cannot be obtained using the single-stage flotation process in some cases, e.g. treating poorly floatable coal and producing super-clean coal. In fact, multi-stage coal flotation process is favored in reducing the ash content of clean coal by eliminating the hydraulic entrainment and selectively rejecting lower hydrophobic particles [18–20]. Furthermore, there are a number of multi-stage flotation circuits in the treatment of metallurgical coking coal and production of super-clean coal [17,21–22]. Therefore, the kinetics of multi-stage coal flotation process should also be studied. However, little attention has been devoted to the flotation kinetics of cleaner stages or multi-stage flotation circuits. The difference in the flotation kinetics between rougher and cleaner stages has not been adequately investigated in the past. In this study, the particle size distribution of collected clean coal in various flotation stages both in rougher and cleaner processes was analyzed, and six kinetic flotation models were selected to test their applicability for various size fractions of coal both in rougher and cleaner flotation stages. In addition, a major attempt of the paper was to discuss
C. Ni et al. / Powder Technology 292 (2016) 210–216
the differences in the flotation kinetics of various size fractions between rougher and cleaner flotation process. 2. Experimental 2.1. Materials
2.2. Flotation tests In the flotation experiments, kerosene and DL-2-Octanol (DLO) were used as the collector and frother, respectively. The flotation water used in the experiments was tap water, and the chemical composition was shown in Table 3. The flotation tests were divided into two parts: (1) rougher flotation tests; and (2) cleaner flotation tests. The rougher flotation tests were performed in a 1.5-L Denver flotation cell. In each test, 150 g of coal sample was mixed with 1 L tap water in the cell and was agitated for 2 min at an impeller rotation speed of 1800 rpm. Then, kerosene (1750 g/t) was added to the pulp and conditioned for 2 min. Subsequently, the DLO (300 g/t) was added to the pulp and conditioned for 0.5 min. After the conditioning process, tap water was added to increase the volume of pulp in the cell up to 1.5 L, and the air was introduced into the cell at a flow rate of 4.17 L/min. The pulp was floated for 200 s, and tap water was added to maintain a constant pulp level when it was necessary. The froth was collected by using an automatic froth collector at a rotation speed of 30 r/min. Products were obtained in the rougher flotation tests: clean coal and tailings. The cleaner flotation tests were also performed in a 1.5-L Denver flotation cell, and the feed of which was the froth product of rougher flotation. The operating parameters of cleaner flotation tests were the same to those of rougher flotation tests. In each cleaner flotation test, the rougher flotation concentrate was poured into the cell and was agitated for 1 min at an impeller rotation speed of 1800 rpm. No flotation reagents were added to the pulp. Then, tap water was added to increase the volume of pulp to 1.5 L, and air was introduced into the cell at a flow rate of 4.17 L/min. The flotation time and froth collection time were the same to those of rougher flotation tests. Two products were obtained in the cleaner flotation tests: further clean coal and cleaner tailings. The final froth products from the rougher flotation tests and the cleaner flotation tests were both divided to 5 products according to the collection periods: 0–20 s, 20–40 s, 40–80 s, 80–120 s, and 120– 200 s. All products including flotation concentrate and tailings were filtered, dried, weighed and analyzed for the ash content. In addition, each product was screened into five narrow size fractions: − 500 + 250, − 250 + 125, − 125 + 74, − 74 + 45, and − 45 μm. The ash content Table 1 Particle size distribution of bituminous coal sample.
500–250 250–125 125–74 74–45 −45
Table 2 Proximate and ultimate analyses of bituminous coal sample. Proximate analysis (wt, %, ad)
Ultimate analysis (wt, %, daf)
M
A
V
FC
C
H
O
N
St
1.21
33.57
25.76
39.46
80.85
5.46
10.85
1.12
0.88
LHVad MJ/kg 19.89
ad = Air dry basis; daf = Dry ash-free basis; M = Moisture content; A = Ash content; V = Volatile matter; FC = Fixed carbon; LHV = Low heat value.
A bituminous coal sample obtained from Yunhe Mine of Shangdong province, China, was used in this investigation. The sample was screened to pass 500 μm. The particle size distribution of the coal sample is given in Table 1, and the proximate and ultimate analyses of the coal sample are given in Table 2. The ash content of the coal sample was 33.57% on an air dry basis. The sample had 53.00% fine particles with sizes below 45 μm with an ash content of 43.63%. It indicated that the coal sample had many fine coal particles with high ash content.
Size fraction (μm)
211
Mass (%)
14.68 13.44 6.69 12.19 53.00
Ash content (%)
22.85 21.83 20.53 22.82 43.63
of the products and the combustible recovery of the flotation were obtained. The combustible recovery was calculated from Eq. (1): Combustible recovery% ¼ ½WC ð100−AC Þ=½W F 100−A F 100
ð1Þ
where WC is the weight of the concentrate (%), WF is the weight of the feed (%), AC is the ash content of the concentrate by weight (%), and AF is the ash content of the feed by weight (%). 2.3. Flotation kinetic models In this investigation, six flotation kinetic models were selected to study the flotation performance of various size fractions in rougher flotation and cleaner flotation processes, as shown in Table 4. The cumulative combustible recoveries of various size fractions after 20, 40, 80, 120, and 200 s of flotation time were fitted using the six kinetic models. The narrow size fractions included −500 + 250, −250 + 125, − 125 + 74, − 74 + 45, and − 45 μm. The MATrix LABoratory (MATLAB) software (Version 7.0) was used to simulate the flotation rate constant (K), the maximum combustible recovery (ε∞), and the correlation coefficient (R2) based on the nonlinear least square optimization method. MATLAB is one of the most powerful and advanced numerical calculation software. Nonlinear least squares optimization has been widely used in the non-linear regression, curve fitting and optimization of nonlinear model parameters. 3. Results and discussion 3.1. Flotation kinetics of various size fractions in rougher flotation process The flotation time-combustible recovery of various size fractions in rougher flotation process are shown in Fig. 1. The combustible recovery of the flotation increased initially and then decreased with the increase of particle size, and the maximum combustible recovery in the rougher flotation process was obtained with the −250 + 125 μm size fraction. It indicated that the maximum combustible recovery was obtained with an intermediate particle size in the rougher flotation process. Similar findings were also reported by other researchers [23–25]. Flotation is a physic-chemical separation process, in which hydrophobic particles are captured by air bubbles and eventually reported to the froth product. This process is determined by three most critical steps including the particle–bubble collision, attachment, and detachment [3,25–26]. It is well known that particle size is an important parameter in flotation process, and a high process efficiency of froth flotation is typically limited to a relatively narrow particle size range [23–29]. However, outside this range, the recovery drops significantly, whether it is at the fine or the coarse end of the size spectrum [28]. The low combustible recovery of fine particles is mainly because of the poor collision and attachment between the fine particles and air
Cumulative undersize Yield (%)
Ash contend (%)
100.00 85.32 71.88 65.19 53.00
33.57 35.41 37.95 39.74 43.63
Table 3 Conductivity and chemical composition of the tap water (mg/L). Conductivity (mS/cm)
Ca2+
Mg2+
Na+
K+
Cl−
HCO− 3
SO2− 4
0.36
54.7
16.6
15.4
3.4
24.7
13.9
5.4
212
C. Ni et al. / Powder Technology 292 (2016) 210–216
Table 4 Six flotation kinetic models used in this investigation [3,5,6,24]. Series Name of model number 1 2 3
Formula
Classical first-order model First-order model with rectangular distribution of flotabilities Fully mixed reactor model
ε = ε∞[1 − exp (−k1t)] ε ¼ ε ∞ f1− k12 t ½1−expð−k2 tÞg 1 Þ ε ¼ ε∞ ð1− 1þt=k 3
4
Improved gas/solid adsorption model
k4 t ε ¼ ε∞ ð1þk Þ 4t
5
Second-order kinetic model
ε∞ k5 t ε ¼ 1þε ∞ k5 t
6
Second-order model with rectangular distribution of flotabilities
ε ¼ ε ∞ f1− k16 t ½lnð1 þ k6 tÞg
2
Ε = fractional recovery at time t; ε ∞ = fractional ultimate recovery; k n = rate constants (n = 1, …, 6).
bubbles, whereas the poor combustible recovery of coarse particles is primarily due to the high probability of detachment between the coarse particles and air bubbles [25,28–30]. Furthermore, the non-selective entrainment of fine gangue particles maybe also a cause of the low combustible recovery of fine particles, since the fine particles in the feed of rougher flotation tests had a high ash content in this investigation (Table 1). The cumulative combustible recovery at 20, 40, 80, 120, and 200 s with various size fractions in rougher flotation process was fitted to the six flotation kinetic models (Table 4) using the MATLAB software. The flotation rate constant (K), the maximum combustible recovery value (ε∞), and the multitude correlation coefficient (R2) were also calculated using the software, and the results are given in Table 5 and Fig. 2. As shown in Table 5, the maximum ε∞ value of the rougher flotation tests increased initially, reached a maximum and decreased afterwards as the size fraction decreased in all of the models. The maximum ε∞ values were obtained with the −250 + 125 μm size fraction. The results showed an excellent agreement with the change trend of combustible recovery as a function of size fraction in Fig. 1. Furthermore, except the model 3, the K values obtained with all other models exhibited the same change trend as that of the ε∞ values. These results indicated that the maximum flotation rate constant was also obtained with an intermediate particle size. The results were consistent with those of previous studies [3,26,31–35]. The difference in kinetics constants (both K and ε∞) of various size fractions can also be explained by the combined effect of the collision and attachment/detachment sub-processes in flotation process [36,37]. Furthermore, the difference may be related to the
Fig. 1. Effect of the size fractions on the cumulative combustible recovery in the rougher flotation process.
physico-chemical properties of various size particles and hydrodynamic conditions in the flotation cell [26,34–35]. As shown in Table 5, the ε∞ value increased gradually from model 1 to model 6, while the ε∞ values of models 3, 4, and 5 were the same. The term R2 is useful for comparing fitting accuracy of models with different number of independent variables and different degrees of freedom [1]. As shown in Fig. 2, in general, the R2 values for the six kinetic models were greater than 0.9700, which indicated that all kinetic models gave an excellent fit to the experimental data. Zhang et al. [3] also reported similar findings in the lignite reverse flotation process in the presence of sodium chloride. Further, the R2 values of model 2 for the rougher flotation tests with various size fractions were the biggest among the investigated models, which suggested that the model 2 was considered to be more reasonable for fitting the rougher flotation results. This result agreed with the results reported by other researchers [1,3,32,38–39]. This might be due to the fact that model 2 is simple and mathematically stable. We suggested that the rougher flotation can be described with the first-order and second-order models, and the model 2 was considered to be the most reasonable among the tested models. 3.2. Flotation kinetics of various size fractions in cleaner flotation process Fig. 3 shows the flotation time-combustible recovery of various size fractions in the cleaner flotation process. In general, the change trends of combustible recovery of various size fractions in the cleaner flotation process were similar to those in Fig. 1. However, the maximum combustible recovery was obtained with the −125 + 74 μm size fraction and the second was obtained with the − 250 + 125 μm size fraction, which was different from that in Fig. 1. The difference in combustible recovery between various size fractions except the −45 μm size fraction, was smaller during the cleaner flotation, and the combustible recoveries of these size fractions were over 90% after a flotation time of 120 s. The combustible recoveries of all size fractions in the cleaner flotation process were bigger than those in the rougher flotation process. It should be pointed out that the combustible recoveries of all size fractions in cleaner flotation test were calculated on the basis of the clean coal of the rougher flotation process (the feed of cleaner flotation tests was the clean coal from the rougher flotation process), while those in rougher flotation process were calculated on the basis of the feed of the raw coal. The reason for the combustible recoveries of all size fractions in the cleaner flotation process was greater than those in the rougher flotation process may relate to the difference in floatability of the feed used in the rougher and cleaner flotation tests. A large number of difficult-to-float particles were rejected to the tailings in the rougher flotation, and the floatability of the feed in the cleaner flotation was better than that in the rougher flotation since the feed in the rougher flotation was raw coal. Non-linear regression results for six models fitting to the cleaner flotation results are given in Table 6 and Fig. 4. As shown in Table 6, in general, the change trends of both ε∞ values and K values as a function of size fraction in the cleaner flotation process were similar to those in the rougher flotation process. Both the maximum of ε∞ values and K values were obtained with the − 125 + 74 μm size fraction, which were consistent with the experimental results in Fig. 3. The results demonstrated that both the combustible recovery and flotation rate of the intermediate particle size were the maximum among the all size fractions in the cleaner flotation process. It can be observed from the results in Table 6 that all the ε∞ values of models 3, 4, 5, and 6 with various size fractions (except −45 μm size fraction) were greater than 100% in the cleaner flotation process. However, the maximum combustible recovery obtained from the flotation test was 100%, which was a theoretical value. In theory, the maximum ε∞ value calculated by kinetic models was also 100% at most. Therefore, we tentatively put forward that models 3, 4, 5, and 6 were considered to be not reasonable for fitting the results obtained from the cleaner flotation process. The results may be attributed to the low convergence
C. Ni et al. / Powder Technology 292 (2016) 210–216
213
Table 5 Non-linear regression results for all models fitting to the rougher flotation results. Models
Model 1 Model 2 Model 3 Model 4 Model 5 Model 6
−250 + 125 μm
−125 + 74 μm
K (s−1)
−500–250 μm ε∞ (%)
K (s−1)
ε∞ (%)
K (s−1)
ε∞ (%)
K (s−1)
ε∞ (%)
K (s−1)
ε∞ (%)
0.0289 0.0585 29.9957 0.0333 0.0004 0.0702
68.3997 76.3003 81.2828 81.2828 81.2828 88.2564
0.0483 0.1096 14.0813 0.0710 0.0007 0.1709
85.1774 91.7929 94.7489 94.7489 94.7489 99.5352
0.0460 0.1030 15.2098 0.0657 0.0007 0.1557
80.6681 87.2167 90.2697 90.2697 90.2697 95.1161
0.0325 0.0673 25.5527 0.0391 0.0004 0.0843
75.8203 83.8850 88.7817 88.7817 88.7817 95.7151
0.0202 0.0382 50.3097 0.0199 0.0003 0.0387
59.4100 68.0836 75.0017 75.0017 75.0017 83.7661
speeds of these models, i.e., the time for obtaining the maximum yield (ε∞ value) in the fitting curves of these models was much greater than that in the flotation tests.
−74 + 45 μm
−45 μm
In the cleaner flotation tests, the feed owned a good floatability, and a high combustible recovery can be obtained after a short flotation time. As shown in Fig. 3, the combustible recoveries of all size fractions
Fig. 2. Comparison of six kinetic models fitted to the test data of various size fractions in the rougher flotation process.
214
C. Ni et al. / Powder Technology 292 (2016) 210–216
3.3. Comparison of flotation kinetics between the rougher and cleaner flotation process
Fig. 3. Effect of the size fractions on the cumulative combustible recovery in the cleaner flotation process.
(except −45 μm size fraction) at 200 s were over 90%. After this period, the combustible recoveries of these size fractions showed a very little increase with the increasing flotation time. However, there was a significant difference between the trend of test data and all the fitting curves of models 3, 4, 5, and 6 when the flotation time was more than 200 s. As shown in Fig. 4, the fitting curves of the various size fractions with the models 3, 4, 5, and 6 were already higher than the test data at the flotation time of 200 s, and they presented a gradual rising trend with the continued increase of flotation time. Therefore, the difference between the experimental value obtained from flotation tests and the fitting values calculated by models 3, 4, 5, and 6 was increased with the increase of flotation time. As a result, when the flotation time gradually approached to the infinite time, the ε∞ values of these models fitted to the data of the clearer flotation tests may be more than 100%. It also can be seen in Fig. 4, there was a significant deviation between the test data and the fitting curves of the model 1. This curve showed no change when the flotation time was greater than 100 s due to a rapid convergence velocity of the model 1. Therefore, the combustible recovery calculated by the model 1 was significantly smaller than the test value at the flotation time of over 120 s. Furthermore, the R2 values of the model 1 with −250 + 125 μm and −125 + 74 μm size fractions were only 0.9354 and 0.9442, respectively. These results indicated that the model 1 does not give an excellent fit to the experimental data. In contrast, the fitting curves of the model 2 exhibited a good agreement with the test data of various size fractions. Moreover, the R2 values of model 2 for various size fractions were distinctly bigger than those of model 1, and the minimum R2 value for model 2 fitting to the cleaner flotation results was 0.9845. Therefore, we concluded that the cleaner flotation process can only be described with the first-order models, and the model 2 provided the best fit of the experimental data obtained from the cleaner flotation tests among the six models.
As shown in Figs. 1 and 3, the slopes of the curves for various size fractions in the cleaner flotation process were steeper than those in the rougher flotation process. Furthermore, the cumulative combustible recovery of various size fractions showed little change after 120 s in the rougher flotation process but the corresponding time was 80 s in the cleaner flotation process. These results demonstrated that the flotation rates of the various size fractions were increased in the cleaner flotation process compared with those in the rougher flotation process. This conclusion can also be supported from a comparison of the results obtained in Tables 5 and 6. It can be observed that the K values of all size fractions in the cleaner flotation tests were greater than those in the rougher flotation tests. Take the calculations of model 2 as an example, the K values of −500 + 250 μm, −250 + 125 μm, −125 + 74 μm, −74 + 45 μm, and − 45 μm size fractions showed the increases by 58.97%, 15.97%, 38.16%, 63.60%, and 114.14%, respectively, in the cleaner flotation tests compared with those in the rougher flotation tests. The results suggested that the increases in flotation rates of coarse and fine particle size fractions were especially more obvious than those of the intermediate particle size fractions. It also indicated that the floatability and flotation of coal particles were determined by many factors, such as coal surface properties, particle size, pulp density, and agent concentration [2,10,18,40–45]. 4. Conclusions In this investigation, the difference in flotation rates of various size fractions of bituminous coal between rougher and cleaner flotation processes was studied. Six flotation kinetic models were applied in the fitting process of the flotation data from the rougher and cleaner flotation tests. The MATLAB software was used to estimate the relationship between the flotation rate constant (K), the maximum combustible recovery (ε∞), and the particle size based on the nonlinear least square optimization method. The results obtained from this study lead to the following conclusions: (1) Both in the rougher and cleaner flotation processes, the maximum flotation combustible recoveries and flotation rates were obtained with an intermediate particle size. Besides, the combustible recoveries and flotation rates of various size fractions were improved in the cleaner flotation process. In this investigation, the maximum recovery of 87.15% was obtained with the −250 + 125 μm size fraction in the rougher flotation process, and the maximum recovery of 95.65% was obtained with −125 + 74 μm size fraction in the cleaner flotation process. The maximum flotation rate constants were also obtained with the same size fraction in both rougher and cleaner flotation processes. (2) Compared with the rougher flotation process, the flotation rates of various size fractions were increased in the cleaner flotation process, and the increases of coarse and fine particle size fractions were especially more obvious than those of the intermediate particle size fractions.
Table 6 Non-linear regression results for all models fitting to the cleaner flotation results. Models Model 1 Model 2 Model 3 Model 4 Model 5 Model 6
−250 + 125 μm
−125 + 74 μm
K (s−1)
−500–250 μm ε∞ (%)
K (s−1)
ε∞ (%)
K (s−1)
ε∞ (%)
−74 + 45 μm K (s−1)
ε∞ (%)
−45 μm K (s−1)
ε∞ (%)
0.0423 0.0930 17.0902 0.0585 0.0006 0.1359
90.3028 98.0776 101.8248 101.8248 101.8248 107.7265
0.0538 0.1271 11.7729 0.0849 0.0008 0.2119
92.4214 98.8355 101.4833 101.4833 101.4833 105.9295
0.0588 0.1423 10.2185 0.0979 0.0010 0.2517
93.3283 99.3559 101.5881 101.5881 101.5881 105.5377
0.0480 0.1101 13.954 0.0717 0.0007 0.1731
91.0161 97.9459 101.0216 101.0216 101.0216 106.0453
0.0383 0.0818 20.0813 0.0498 0.0005 0.1120
82.8381 90.6534 94.8061 94.8061 94.8061 101.0434
C. Ni et al. / Powder Technology 292 (2016) 210–216
215
Fig. 4. Comparison of six kinetic models fitted to the test data of various size fractions in the cleaner flotation process.
(3) The flotation kinetic of the rougher flotation process can be described using the first-order and second-order models while that of the cleaner flotation process can only be described using the first-order models. The first-order model with rectangular distribution of floatability was considered to be the most reasonable to fit the results from both rougher and cleaner flotation processes among the tested models.
Acknowledgments This work was supported by the National Natural Science Foundation of China (NSFC, Grant No. 51474213 and No. 51374205) and A Priority Academic Program Development of Jiangsu Higher Education Institutions. We also want to thank the support of the Postdoctoral Science Foundation of China (2015M580497).
References [1] X.M. Yuan, B.I. Palsson, K.S.E. Forssberg, Statistical interpretation of flotation kinetics for a complex sulphide ore, Miner. Eng. 9 (4) (1996) 429–442. [2] R. Sripriya, P.V.T. Rao, B.R. Choudhury, Optimisation of operating variables of fine coal flotation using a combination of modified flotation parameters and statistical techniques, Int. J. Miner. Process. 68 (1) (2003) 109–127. [3] H. Zhang, J. Liu, Y. Cao, Y. Wang, Effects of particle size on lignite reverse flotation kinetics in the presence of sodium chloride, Powder Technol. 246 (2013) 658–663. [4] H.G. Zuniga, Flotation recovery is an exponential function of its rate, Boln. Soc. Nac. Min. 47 (1935) 83–86 (Santiago). [5] E.C. Dowling, R.R. Klimpel, F.F. Aplan, Model discrimination in the flotation of a porphyry copper ore, Miner. Metall. Process. 2 (2) (1985) 87–101. [6] G.J. Jameson, S. Nam, M.M. Young, Physical factors affecting recovery rates in flotation, Miner. Sci. Eng. 9 (3) (1977) 103–118. [7] G.E. Agar, J. Chia, L.C. Requis, Flotation rate measurements to optimize an operating circuit, Miner. Eng. 11 (4) (1998) 347–360. [8] J.F. Oliveira, S.M. Saraiva, J.S. Pimenta, A.P.A. Oliveira, Kinetics of pyrochlore flotation from Araxá mineral deposits, Miner. Eng. 14 (1) (2001) 99–105. [9] E.C. Çilek, Estimation of flotation kinetic parameters by considering interactions of the operating variables, Miner. Eng. 17 (1) (2004) 81–85.
216
C. Ni et al. / Powder Technology 292 (2016) 210–216
[10] R.B. Read, L.R. Camp, M.S. Summers, D.M. Rapp, The influence of reagent type on the kinetics of ultrafine coal flotation, Powder Technol. 59 (3) (1989) 153–162. [11] A.J. Niemi, Role of kinetics in modelling and control of flotation plants, Powder Technol. 82 (1) (1995) 69–77. [12] J. Labidi, M.A. Pelach, X. Turon, P. Mutjé, Predicting flotation efficiency using neural networks, Chem. Eng. Process. Process Intensif. 46 (4) (2007) 314–322. [13] M. Uçurum, O. Bayat, Effects of operating variables on modified flotation parameters in the mineral separation, Sep. Purif. Technol. 55 (2) (2007) 173–181. [14] M. Uçurum, Influences of Jameson flotation operation variables on the kinetics and recovery of unburned carbon, Powder Technol. 191 (3) (2009) 240–246. [15] L. Mao, R.H. Yoon, Predicting flotation rates using a rate equation derived from first principles, Int. J. Miner. Process. 51 (1) (1997) 171–181. [16] A.J. Lynch, N.W. Johnson, E.V. Manlapig, C.G. Thome, Mineral and coal flotation circuits. Chapter 3, mathematical models of flotation(advisory editor) in: D.W. Fuerstenau (Ed.), Development in Mineral Processing, Elsevier, Amsterdam, 1981 (3, 57). [17] J.W. Leonard, D.R. Mitchell, Coal Preparation, The American Institute of Mining. Metallurgical, and Petroleum Engineers, Inc., New York, NY, 1979 10–75. [18] B.A. Firth, A.R. Swanson, S.K. Nicol, Flotation circuits for poorly floating coals, Int. J. Miner. Process. 5 (4) (1979) 321–334. [19] R.Q. Honaker, M.K. Mohanty, Enhanced column flotation performance for fine coal cleaning, Miner. Eng. 9 (9) (1996) 931–945. [20] D. Tao, G.H. Luttrell, R.H. Yoon, An experimental investigation on column flotation circuit configuration, Int. J. Miner. Process. 60 (1) (2000) 37–56. [21] K.J. Miller, Coal-pyrite flotation, Trans. Soc. Min. Eng. AIME 258 (1975) 30–33. [22] G.H. Luttrell, Hydrodynamic Studies and Mathematical Modeling of Fine Coal Flotation(PhD dissertation) Department of Mining and Minerals Engineering, Virginia Polytechnic Institute and State University, Blacksburgh, Virginia, 1986. [23] A.M. Gaudin, J.O. Groh, H.B. Henderson, Effect of Particle Size on Flotation, Tech. Publ., 414, American Institute of Mining and Metallurgical Engineering, 1931 3–23. [24] W.J. Trahar, L.J. Warren, The floatability of very fine particles—a review, Int. J. Miner. Process. 3 (1976) 103–131. [25] D. Tao, Role of bubble size in flotation of coarse and fine particles—a review, Sep. Sci. Technol. 39 (4) (2005) 741–760. [26] S. Muganda, M. Zanin, S.R. Grano, Benchmarking flotation performance: single minerals, Int. J. Miner. Process. 98 (3–4) (2011) 182–194. [27] G.J. Jameson, A.V. Nguyen, S. Ata, The flotation of fine and coarse particles, in: M.C. Fuerstenau (Ed.), Centenary of Flotation Commemorative, Society for Mining, 5, Metallurgy and Exploration, Inc. (SME), USA 2008, pp. 339–372. [28] G.J. Jameson, Advances in fine and coarse particle flotation, Can. Metall. Q. 49 (4) (2010) 325–330.
[29] B. Shahbazi, B. Rezai, S.M. Javad Koleini, Bubble–particle collision and attachment probability on fine particles flotation, Chem. Eng. Process. Process Intensif. 49 (6) (2010) 622–627. [30] H. Schubert, On the optimization of hydrodynamics in fine particle flotation, Miner. Eng. 21 (12–14) (2008) 930–936. [31] D. Feng, C. Aldrich, Effect of particle size on flotation performance of complex sulphide ores, Miner. Eng. 12 (7) (1999) 721–731 (11). [32] O. Bayat, M. Ucurum, C. Poole, Effects of size distribution on flotation kinetics of Turkish sphalerite, Min. Process. & Extrac. Metallurgy Imm Trans. 113 (1) (2004) 53–59. [33] S.P. Mehrotra, P.C. Kapur, The effects of aeration rate, particle size and pulp density on the flotation rate distributions, Powder Technol. 9 (74) (1974) 213–219. [34] G.J. Jameson, The effect of surface liberation and particle size on flotation rate constants, Miner. Eng. 36-38 (10) (2012) 132–137. [35] S.D.D. Welsby, S.M.S.M. Vianna, J.P. Franzidis, Assigning physical significance to floatability components, Int. J. Miner. Process. 97 (1–4) (2010) 59–67. [36] E. Abkhoshka, M. Kor, B. Rezai, A study on the effect of particle size on coal flotation kinetics using fuzzy logic, Expert Systems with Applications 37 (7) (2010) 5201–5207. [37] Y. Li, W. Zhao, X. Gui, X. Zhang, Flotation kinetics and separation selectivity of coal size fractions, Physicochem. Probl. Min. Process. 49 (2) (2013) 387–395. [38] A.P. Chaves, A.S. Ruiz, Considerations on the kinetics of froth flotation of ultrafine coal contained in tailings, Int. J. Coal Prep. Util. 29 (6) (2009) 289–297. [39] X. GUI, J. LIU, X. TAO, Y. WANG, Y. CAO, Studies on flotation rate of a hard-to-float fine coal, J. China Coal Soc. 2011 (1895-1900) 36(11) (In Chinese). [40] W. Xia, G. Xie, C. Liang, J. Yang, Flotation behavior of different size fractions of fresh and oxidized coals, Powder Technol. 267 (2014) 80–85. [41] W. Xia, G. Xie, Y. Peng, Recent advances in beneficiation for low rank coals, Powder Technol. 277 (2015) 206–221. [42] W. Xia, C. Ren, Y. Peng, D. Pan, Comparison of traditional and zero-conditioning flotation performances of oxidized anthracite coal, Powder Technol. 275 (2015) 280–283. [43] W. Xia, G. Xie, Changes in the hydrophobicity of anthracite coals before and after high temperature heating process, Powder Technol. 264 (2014) 31–35. [44] W. Xia, C. Ni, G. Xie, The influence of surface roughness on wettability of natural/ gold-coated ultra-low ash coal particles, Powder Technol. 288 (2016) 286–290. [45] W. Xia, G. Xie, D. Pan, J. Yang, Effects of cooling conditions on surface properties of heated coals, Ind. Eng. Chem. Res. 53 (26) (2014) 10810–10813.