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Entrainment in froth flotation: The degree of entrainment and its contributing factors
Entrainment in froth flotation: The degree of entrainment and its contributing factors L. Wang, Y. Peng, K. Runge PII: DOI: Reference:
S0032-5910(15)30137-6 doi: 10.1016/j.powtec.2015.10.049 PTEC 11315
To appear in:
Powder Technology
Received date: Revised date: Accepted date:
31 July 2015 19 October 2015 30 October 2015
Please cite this article as: L. Wang, Y. Peng, K. Runge, Entrainment in froth flotation: The degree of entrainment and its contributing factors, Powder Technology (2015), doi: 10.1016/j.powtec.2015.10.049
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ACCEPTED MANUSCRIPT Entrainment in froth flotation:
Julius Kruttschnitt Mineral Research Centre, University of Queensland, Australia b
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a
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L. Wang a,*, Y. Peng b,*, K. Runge a, c
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The degree of entrainment and its contributing factors
School of Chemical Engineering, University of Queensland, Australia Metso Process Technology and Innovation, Australia
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c
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ABSTRACT
In froth flotation, the degree of entrainment affects the concentrate grade and it is often assumed to be only a function of particle size in models. Literature suggests that other variables might also have a
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significant impact on the degree of entrainment. In this study, a factorial batch flotation experiment
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using a mixture of liberated chalcopyrite and two liberated gangue minerals, quartz and hematite, was
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performed to investigate the effects of these other variables (including impeller speed, gas flowrate, froth height and the specific gravity of gangue mineral) on the degree of entrainment. Results show that the degree of entrainment varied significantly as the flotation test conditions changed. Particle
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density and the interaction between gas flowrate and froth height had a statistically significant effect on the average degree of entrainment measured for the entire test. The degree of entrainment also significantly changed with flotation time throughout each experiment. It is hypothesised that these effects are a consequence of the degree of entrainment being affected by the weight of particles (not just their size) because of its effect on particle settling as well as the froth structure which provides varying resistance to particle drainage. It is concluded that models for the degree of entrainment that incorporate only particle size are not sufficient to predict gangue recovery and concentrate grade in an industrial application. Keywords: entrainment; degree of entrainment; water recovery; froth flotation
1 *Corresponding author. Tel: +61 7 3346 5983 E-mail address: [email protected] (L. Wang) [email protected] (Y. Peng)
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1. Introduction
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Entrainment is a mechanical transfer process by which mineral particles suspended in water enter the
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flotation froth, move upwards, and finally leave the flotation cell with the mineral particles recovered
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by true flotation. It plays a critical role especially in the processing of ores with a large proportion of fine gangue particles (Fuerstenau, 1980; Kirjavainen, 1996). The quality of final products in mineral
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flotation is often greatly influenced by entrained gangue materials.
Entrainment is generally taken as a two-step process: in step 1, mineral particles ascend upwards into
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the froth phase from the region just below the pulp/froth interface, and in step 2, the entrained particles in the froth are transferred to the concentrate launder with water. These two steps are
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strongly dependent on the processes occurring within both the pulp and froth phases (Neethling and
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Cilliers, 2002). As a result, the recovery by entrainment is related to the state of solids suspension in the pulp, the drainage in the froth phase as well as the recovered water.
(1)
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CFif=
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A classification function has been proposed to describe the drainage in the froth (Johnson, 1972):
where CFi f is the classification function representing the drainage in the froth phase, subscript i represents the particle size and superscript f represents the froth phase. Similarly, a classification function has been proposed to describe the state of solids suspension in the pulp (Zheng et al., 2005): CFip=
(2)
where superscript p represents the pulp phase. Taking the classification effects in both the pulp and the froth into account, the overall classification effect can be determined by:
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ACCEPTED MANUSCRIPT ENTi CFi p CFi f
(3)
where ENTi is the degree of entrainment representing the overall classification effect in both the pulp
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and the froth (for particle size i). ENTi can be used directly for the estimation of gangue recovery by entrainment by the combination of
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these two classification effects. The recovery by entrainment is virtually the water recovered corrected by the degree of entrainment. There are two models of gangue recovery by entrainment that are
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commonly seen in the literature (see Eqs. (4) and (5)) (Jowett, 1966; Engelbrecht and Woodburn; Laplante et al., 1989):
ENTi Rw 1 Rw ( ENTi 1)
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R e nt ,i
(5)
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R e nt ,i ENTi Rw
(4)
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where Rent,i is the recovery by entrainment and Rw is the water recovery. However, the boundary conditions for applying these models in industrial applications are not specified in the literature. Eq. (4) was derived from the definition of gangue recovery (based on the
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mass of the gangue in the concentrate and the feed), water recovery (based on the mass of the water in the concentrate and the feed) and ENT (based on the mass of solids and water in both the concentrate and the tailing). Hence, it can deliver a very precise value of gangue recovery by entrainment. Eq. (5) is a simplified form of Eq. (4) that can be used either when water recovery is below 30 % or for ultrafine particles regardless of the water recovery. This is demonstrated in Fig. 1 which shows the gangue recovery calculated using these two equations for different water recovery and degree of entrainment values. There is a debate whether a minor change in the degree of entrainment will change the gangue recovery and the concentrate grade significantly in industrial applications, and hence whether it is necessary to pay special attention to the degree of entrainment. Despite this, some research has been carried out on the degree of entrainment and its influencing factors. In froth flotation, particle 3
ACCEPTED MANUSCRIPT properties and operating conditions are always of great importance in the mechanical entrainment process. These factors change the processes occurring in the pulp and the froth which result in a change either in the water recovery or in the degree of entrainment. Among these factors, the degree
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of entrainment is always size dependent with coarse particles exhibiting a low degree of entrainment (ENTi→0) and the fine particles exhibiting a high degree of entrainment (ENTi→1). Particles smaller
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than 50 μm are generally known to be recovered more easily by entrainment (Savassi et al., 1998). Many studies have also shown that the degree of entrainment is influenced by the particle density
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(Johnson, 1972; Bisshop, 1974; Thorne et al., 1976; Maachar and Dobby, 1992; Drzymala, 1994). However, the extent to which it affects the degree of entrainment is unresolved. Bisshop (1974), for
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example, who measured the degree of entrainment of different gangue minerals found that particle density significantly affected the degree of entrainment. However, the work of Johnson (1972)
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showed that the degree of entrainment of different gangue minerals in an industrial rougher flotation
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cell was similar, which suggested that the effect of particle density was less significant than that of other factors. This latter conclusion was supported by Savassi (1998). It should be noted that the
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effect of particle density is often influenced by the effect of particle size, and requires further investigation where the influence of particle size is specifically excluded.
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Gangue recovery by entrainment is significantly affected by gas flowrate and froth height, although the importance of these two factors compared with other influencing factors is still poorly understood. It is often thought that these two parameters affect the recovery by entrainment by changing the residence time and therefore the time available for water and particle drainage (Zheng et al., 2006). Recent studies have also demonstrated a change in the recovery of gangue minerals by entrainment with changes in the impeller speed (Cilek, 2009; Akdemir and Sönmez, 2003). Impeller speed can greatly change water recovery which in turn affects the gangue entrainment, but it is still not clear whether the degree of entrainment is affected by the impeller speed and its interaction with other variables.
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ACCEPTED MANUSCRIPT The literature contains several models which can be used to evaluate and predict the degree of entrainment. However, these models which incorporate different influencing factors cannot predict entrainment for industrial applications (Wang et al., 2015). One main reason is that little work has
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been done on the identification of the key drivers of the degree of entrainment. It should be noted that, whatever model is developed, one requirement for a good model is that it should describe the basic
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phenomena and account for all factors affecting the response significantly (Bisshop, 1974). In this study, therefore, batch flotation tests were performed to identify the key drivers of the degree
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of entrainment using a mixture of liberated chalcopyrite as a valuable mineral and two liberated gangue minerals, quartz and hematite. The aim was to develop fundamental knowledge that is
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currently lacking to enable modelling of the degree of entrainment in industrial flotation applications.
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2.1 Materials and reagents
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2. Experimental
The flotation feeds to the experiments were created artificially by mixing pure chalcopyrite with pure
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gangue minerals. Quartz (SG=2.65) and hematite (SG=5.26) purchased from Geodiscoveries were used to investigate the effect of specific density of gangue minerals on the degree of entrainment. Sodium hydroxide (NaOH) was used to adjust the pH of the slurry to 9.5. Sodium ethyl xanthate
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(SEX), used as the collector, was supplied by Qingdao Lnt Chemical LTD. The collector dosage used in the flotation tests was 50 g/t of the feed. The frother used in the flotation experiments was Dowfroth 250 that was supplied by Chemical Dictionary Online. The concentration of the frother was kept at 10 mg/L. These reagents were prepared daily prior to the flotation tests using Brisbane tap water. 2.2 Flotation tests Pure chalcopyrite, quartz and hematite samples were crushed to below 3.35 mm using a laboratory jaw crusher and then split to create numerous samples of 53 g, 1530 g and 1530 g, respectively. These weights were chosen so that, when combined, they resulted in a 1 wt.% copper feed grade and 37 wt.% solids in the flotation cell. Chalcopyrite samples were stored in a freezer to avoid oxidation. 5
ACCEPTED MANUSCRIPT Prior to each flotation test, a sample of chalcopyrite and one of the gangue minerals were ground separately to produce the appropriate feed particle size distribution. The chalcopyrite sample was ground with water (35 wt.% solids) in a rod mill operated at a speed of 76 rpm to obtain 80 %
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particles passing 106 μm.
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The gangue minerals were ground to a particle size of P80=70-80 μm, a size similar to that in typical flotation plants. This resulted in a substantial quantity of -50 μm particles which typically are recovered by entrainment. To compare the overall degree of entrainment (ENToverall) values without
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sizing the samples, a similar particle size distribution of the quartz and hematite as shown in Fig. 2 was achieved by grinding the gangue minerals in a Bond ball mill for different grinding times. The
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mill is 0.305 m by 0.305 m, with rounded corners, a smooth lining, and was operated at 70 rpm. The charge consisted of 285 balls, weighing about 20 kg in total.
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After grinding, the mill discharges were transferred to a 3.5 L conventional Agitair flotation cell with
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a movable lip to enable the froth height to be changed without altering the pulp volume, as shown in
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Fig. 3. The cell was then started with the impeller set-point adjusted to 1200 rpm. The pH of the pulp slurry was adjusted to 9.5 by adding 5 wt.% sodium hydroxide solution. 50 g/t of collector was added to the slurry and conditioned for 1 min. Frother was then added to achieve a frother concentration of
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10 mg/L followed by another 1 min conditioning time. After conditioning, the froth height, gas flowrate and impeller speed were then set to those required for the particular experiment. Once air was introduced into the flotation cell, four flotation concentrates were collected from 0 to 0.5 min, 0.5 to 2 min, 2 to 5 min and 5 to 10 min. The froth was scraped every 10 s. The froth scraper was designed to only remove the froth above and 1mm below the cell launder lip to minimise any disturbance to the underlying froth structure. Tap water was added to the test periodically to maintain the pulp level. This added water was dosed with frother at the same concentration to that established at the beginning of the test (i.e. 10 mg/L) with the aim of achieving a relatively constant concentration of frother in the cell throughout the experiment. After 10 min of flotation, all concentrates and the tailings were filtered, dried, weighed, sampled and assayed.
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ACCEPTED MANUSCRIPT 2.3 Factorial design and analysis A four-factor, two-level, factorial experimental design was used. This design was chosen as it allows
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one to examine multiple factors simultaneously and quantify the effect of these variables and their
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interactions. The experimental results were analysed using Minitab 17 Statistical Software.
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In the factorial experimental design, each variable for testing had a maximum, minimum and centroid value (see Table 1). The difference between the maximum and minimum values represents the range over which each variable was studied. Four central point repeat experiments were used to calculate
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the experimental error and determine whether the effects observed in experiments were significant or
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not. All of the runs were conducted under relatively homogeneous conditions. To reduce the program to a feasible number of experiments, only four variables were chosen to
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investigate the key drivers of the degree of entrainment. However, the degree of entrainment is not
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restricted to these influencing factors. Therefore, future work should involve investigating other influencing variables such as viscosity and frother type in a separate experimental program.
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The levels of the variables shown in Table 1 were determined using exploratory laboratory flotation tests. Experimentation was performed to determine the range of froth heights, impeller speeds and gas
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flowrates that resulted in reasonable changes in flotation recovery but not poor flotation behaviour. In flotation, superficial gas velocity (Jg) is the parameter usually used to represent the air flowrate as it is considered relatively independent of cell size. In industrial applications, Jg usually ranges from 0.6 to 1.5 cm/s. In this study, the minimum, centroid and maximum Jg values chosen were 0.6, 0.8 and 1.0 cm/s, respectively. The corresponding air flowrates were 8.5, 11.5 and 14.5 L/min, respectively. The impeller speeds selected were based on the need to keep the majority of particles in suspension without an overly turbulent pulp-froth interface. The maximum impeller speed chosen was 1200 rpm at which some turbulent effects were visually observed to affect the froth phase. The minimum impeller speed was chosen to be 800 rpm because at this speed there was a small amount of solids observed to be settling in the flotation cell. All froth depths selected were reasonably shallow (i.e. 1.0,
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ACCEPTED MANUSCRIPT 1.5 and 2.0 cm) because deeper froth heights could not be maintained throughout the whole period of the flotation test.
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3. Results
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3.1 Flotation reproducibility
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In flotation, the overall error is a consequence of minor variations in the grinding, flotation, sampling and assaying as well as operator and random errors. The total error associated with the experimental procedure was assessed using the four replicates of the central point experiment. Fig. 4 shows the
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reproducibility of the flotation recovery of quartz. For the 10 min concentrate, a 95% confidence
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interval of 3.26% relative error was obtained. This degree of error is considered acceptable and sufficiently low to enable the effect of different variables on the entrainment parameters to be
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determined with statistical confidence.
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3.2 Flotation results
The experimental results for the factorial experiments are shown in Table 2. Copper recovery was
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high in all the tests. There were large variations in the gangue recovery, which resulted in large variations in concentrate grade. It should be noted that the gangue minerals used in these tests were
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fully liberated, and presumably it can therefore be assumed that they were recovered into the concentrate only by entrainment. Therefore, the variation in the concentrate grade was caused by changes in entrainment recovery. Gangue recovery in the different tests is a strong function of water recovery which varied significantly in the different tests (refer to Fig. 5). However, it also changes as a consequence of variation in the degree of entrainment, which according to Eq. (5), can be approximated by the slope of the gangue versus water recovery relationships shown in Fig. 5. ENT values were calculated for each experimental condition using Eq. (4). The overall ENT values ranged from approximately 0.1 to 0.2. However, the ENT values in the first concentrates of all the
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ACCEPTED MANUSCRIPT tests ranged from about 0.1 to 0.5. This implies that the degree of entrainment changes significantly at different conditions.
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Fig. 6 shows the ENT values for quartz and hematite plotted separately against water recovery. There
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was no correlation between the degree of entrainment and water recovery for either gangue mineral,
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which indicates that the variables that affected water recovery were not the same as those that affected the degree of entrainment.
In addition, the degree of entrainment was found to vary with flotation time. In each of the twenty
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batch flotation tests, the ENT values dramatically decreased as the experiment progressed.
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3.3 The importance of the degree of entrainment
As mentioned previously, the overall ENT values ranged from approximately 0.1 to 0.2 under the
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various experimental conditions. It is questionable whether such a change in the ENT value will have
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a significant impact on the concentrate grade. To test this, concentrate grades at different ENT values and water recoveries were estimated. In these calculations, copper recovery was set to a constant
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value. Copper recoveries in the rougher flotation tests performed in this study were generally high, so a copper recovery of 90% was selected. Gangue recovery for each water recovery and degree of
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entrainment value was simulated using Eq. (4). Using these copper and gangue recoveries, weighted according to the copper feed grade of 1% used in the test, concentrate grade was then calculated. Fig. 7 shows the concentrate grade as a function of water recovery and the degree of entrainment determined from these simulations. At each water recovery, the concentrate grade decreases with increasing degree of entrainment. The reduction is fairly obvious at relatively low water recovery, but even at high water recoveries, there is a discernible change in the concentrate grade when the degree of entrainment increases from 0.1 to 0.3. Indeed, examining the experimental results of the present study, a dramatic decrease in the concentrate grade can be seen when the overall degree of entrainment increased from approximately 0.1 to 0.2 (Table 2). Therefore, the degree of entrainment can be critical in terms of influencing the concentrate grade and should not be ignored. 9
ACCEPTED MANUSCRIPT 3.4 Statistical significance of variables and interactions The effects and interactions of the four variables on the degree of entrainment at a 95 % confidence
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level were analysed using Minitab 17 Statistical Software. The results are summarized in Table 3.
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Note that the P values in the table indicate the significance of a factor; a relatively small P value,
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smaller than the selected significance level of 0.05, implies that a factor has a significant effect on a response. As can be seen from Table 3, the degree of entrainment was significantly affected by the particle density and the interaction between gas flowrate and froth height, while other variables and
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interactions did not affect the degree of entrainment significantly. It should be noted that the “not significant” factors and interactions do not imply no effect or interaction, but rather that the effect or
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interaction cannot be determined with confidence based on error in the data. In addition, the P value of 0.007 for “curvature” in Table 3 also indicates that the relationship between the examined
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significant factors and their interactions and the degree of entrainment is non-linear.
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The significant variables and variable interactions in a two-level factorial design can also be
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determined from a normal probability plot. The fitted line of this plot indicates where you would expect the points to fall if the effects were zero and the variation observed was random and normally distributed. The greater the distance from the line, the more significant the effect of a tested variable.
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Points that fall to the left of the line have a negative effect and the points to the right have a positive effect. Fig. 8 shows the normal probability plot created by Minitab when evaluating the effects of the experimental conditions on the measured overall degree of entrainment. Two effects, particle density and the interaction between gas flowrate and froth height stand out and have a much more significant effect than the other variables. Both have a negative correlation with the overall degree of entrainment. The effect of particle density is more significant than the interaction between gas flowrate and froth height. 4. Discussion 4.1 Particle density
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ACCEPTED MANUSCRIPT The results have shown that particle density has a significant effect on the degree of entrainment. Quartz with a specific gravity of 2.65 results in a higher degree of entrainment than hematite with a specific gravity of 5.26. This can be observed in Fig. 6 with the overall degree of entrainment values
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measured for quartz being clearly higher than those measured for haematite. Fig. 9 shows the average ENT value measured in the different concentrates of the batch flotation test for those tests performed
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using quartz to those performed using hematite. The ENT values of the quartz were always larger than those of hematite. This difference can be interpreted as the effect of particle density (as the particle
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size distributions were similar).
Fig. 10 shows the average overall degree of entrainment plotted against particle density for all the
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tests performed under the different operating conditions. The correlation is negative and the average changes from 0.180 for quartz to 0.125 for hematite. As shown in Fig. 7, a decrease of the degree of
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entrainment from 0.2 to 0.1 can lead to a large change in concentrate grade, regardless of the water
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recovery, which indicates that the effect of particle density on the degree of entrainment is significant and should not be ignored when the degree of entrainment is modelled. No conclusion can be drawn
design.
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as to whether this correlation is linear as only two particle densities were used in the experimental
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The decrease in the degree of entrainment with increasing particle density is in line with that observed in many other studies (Johnson, 1972; Bisshop, 1974; Thorne et al., 1976; Maachar and Dobby, 1992; Drzymala, 1994). The higher entrainment of low-density particles is presumably associated with the fact that they tend to move with water due to their lower sedimentation velocities. As a result, the degree of solids suspension in the pulp phase may be poorer for higher density minerals, resulting in less carry over from the pulp into the froth. In addition, high density minerals have a greater chance of settling and draining through the plateau borders within the froth phase than the lower density minerals. Therefore, the degree of entrainment decreases when the particle density is increased.
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ACCEPTED MANUSCRIPT Traditionally entrainment recovery has been modelled based on particle size alone. These results would suggest that it would be better to model entrainment based on particle mass which will be a
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consequence of both particle size and density.
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4.2 Impeller speed
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The impeller speed and its interactions with other variables did not have a great impact on the degree of entrainment according to the statistical analysis. Fig. 11 shows the average degree of entrainment for quartz and hematite measured in the different batch flotation concentrates at different impeller
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speeds. There was no significant variation in the ENT values except for hematite in the first
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concentrates. This difference might be because of a change in froth structure caused by variation in the flotation of copper in this first concentrate.
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The effect of impeller speed on the average degree of entrainment is shown in Fig. 12 for all the tests
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as well as those only performed using quartz and hematite, respectively. A slight increase in the mean ENT value was found with increasing impeller speed but it is not statistically significant and would
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not be expected to result in an appreciable change in concentrate grade. It is interesting to note, however, that there were observable increases in gangue recovery (and thus
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decreases in concentrate grade) with an increase in impeller speed in the test results. This was a consequence of an increase in water recovery. The increase in gangue recovery by entrainment is in agreement with observations made in other studies in the literature (Cilek, 2009; Akdemir and Sönmez, 2003). 4.3 The interaction between gas flowrate and froth height Table 3 shows that the degree of entrainment was significantly affected by the interaction between gas flowrate and froth height. This is illustrated in Fig. 13 and Fig. 14 which show the average overall entrainment value as a function of gas rate at different froth depths in all the tests and subsets of tests. In all these graphs, at a shallow froth depth, the degree of entrainment increases as gas flowrate
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ACCEPTED MANUSCRIPT increases. Conversely, at the deeper froth depths, the degree of entrainment decreases as gas flowrate increases.
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This is a relatively unexpected result as intuitively one would expect that either an increase in froth
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height or an increase in gas flowrate would result in less time for drainage and therefore a decrease in
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both the degree of entrainment and water recovery and subsequently the gangue recovery. In this paper there are examples where an increase in gas flowrate can decrease the degree of entrainment (deep froths) and examples where increasing froth depth (at low gas flowrates) increases the degree of
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entrainment. Increasing degrees of entrainment with froth height (at a low gas flowrate) have previously been observed by Zheng et al. (2006) who collected data from an Outokumpu 3 m3 pilot
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tank cell operating under various operating conditions (four different gas flowrates and four different froth heights) using ore diverted from the feed of a rougher bank of the Xstrata Mt. Isa Mines copper
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concentrator. Fig. 15 shows the degree of entrainment of quartz for different particle sizes at two froth
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heights at the lowest gas flowrate of 1085 L/min (Jg = 0.91 cm/s) measured in this study. The degree
height of 19.0 cm.
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of entrainment of the finer particle sizes is greater at the froth height of 23.2 cm than that at the froth
At a low gas flowrate, water content in the froth phase is known to decrease rapidly with increasing
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froth height (Cutting et al., 1981). The low water content might result in a narrowing of the plateau borders providing resistance and therefore less drainage of solids (per unit volume of water). At the lower froth depths, this thinning may not occur and a greater amount of solid drainage may result, decreasing the degree of entrainment of the gangue minerals. At the higher gas rates, a “wetter froth” which may not lead to sufficient thinning of the plateau borders to impede solid drainage. Solids suspended in water may move more freely and this causes a reversal in the trends observed. Now as froth depth increases, there may be more time for drainage and therefore the degree of entrainment decreases. In addition, a decrease of solids in unit water in the upper froth may be associated with a greater amount of bubble bursting in the froth. Ekmekçi et al.
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ACCEPTED MANUSCRIPT (2003) observed a low froth stability and brittle froth structure in deep froths. This may result in an increase in the solid drainage within the froth phase.
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The above explanations are purely speculative at this stage and more research is required to determine
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definitively the reason for the observed results. It is likely, however, to be due to froth structural
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changes. 4.4 Froth residence time
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Froth residence time, or the time particles and bubbles exist within the froth phase, plays a critical role in determining froth mineral recovery (Mathe et al., 2000). Intuitively, froth residence time may also
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affect entrainment (water recovery and the degree of entrainment) as longer times would result in more water drainage and potentially more solids to drain preferentially to the water (Zheng, et al.,
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2006). In the literature, froth residence time is commonly calculated by either of the following
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equations based on the air and the slurry in the froth (Gorain et al., 1998; Lynch et al., 1981; Schwarz
Hf Jg
slurry
(6)
(1 g ) V f Qs
(7)
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air
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and Grana, 2005; Szatkowski, 1987):
where λair is the froth residence time of air, λslurry is the froth residence time of slurry, Hf is froth height; Jg is the superficial gas velocity which is the ratio between the volumetric gas flowrate and cross-sectional area of the flotation cell, εg is the mean air hold-up in the froth, Qs is the volumetric flowrate of the concentrate, incorporating both solids and liquid flowrates and Vf is the volume of the froth. Fig. 16 shows the effect of froth residence time of gas (0.98 s, 1.86 s and 3.35 s) (calculated by Eq. (6)) on the mean of the degree of entrainment measured in this experimental study. Little change was observed in the degree of entrainment when the froth residence time increased from 0.98 s to 3.35 s.
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ACCEPTED MANUSCRIPT The froth residence time of the slurry may be better correlated with entrainment than the residence time of the air. In this study, froth residence time of slurry was calculated by dividing the froth volume by the volumetric flow of water and solids in the concentrate, corrected for an estimate of the
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air holdup in the froth (see Eq. (7)). The mean air holdup in the froth phase will be high (>95%), and in this work was estimated by dividing the air volumetric flowrate by the combined volumetric
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flowrate of concentrate and air as performed by Zheng et al. (2004). Froth residence time calculated in this alternative way also did not exhibit a relationship with the measured degree of entrainment (see
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Fig. 17).
This is contrast to the water recovery results. Water recovery varied significantly in the experiments
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of this test and was found to be strongly correlated with froth residence time. An increase in froth residence time resulted in less water recovery and therefore less gangue recovery which thus
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increased concentrate grade.
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Therefore, it can be concluded that froth residence time affects gangue recovery by entrainment
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through an effect on water recovery, but does not affect the relative drainage of solids to water (i.e. the degree of entrainment).
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4.5 Change of ENT with flotation time Interestingly, the degree of entrainment was found to decrease throughout the batch flotation experiment with the first concentrate of all 20 tests having a much higher degree of entrainment value than that measured in the later concentrates (see Table 2). The change is significant with entrainment averaging about 0.3 to 0.4 in the first concentrate and 0.1 in the last (see Fig 9). This effect is more significant than that caused by any of the other variables tested in this study. Potentially this variation could have been caused by a change in particle size. The particle size feeding all experiments is the same but the particle size feeding the later stages of the test could be coarser (and therefore results in lower ENT values) because of the preferential removal of fines by entrainment. Calculations performed, however, show that the amount of gangue removed by entrainment in the test is insufficient to result in an appreciable change in the particle size distribution 15
ACCEPTED MANUSCRIPT in the cell throughout the experiments. This is corroborated by Runs 5 and 16 where gangue recovery is very low but the degree of entrainment still decreases significantly throughout the test.
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During the experiment, the copper feed grade (and therefore the copper loading) will be decreasing
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and potentially the frother concentration may also be decreasing. Although there is frother added to
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the water added during the flotation experiment, the frother concentration in the concentrates is often higher than in the pulp and this will result in a general decrease in frother concentration during the test. To assess whether the change in copper feed grade is the primary driver for the result, flotation tests
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were conducted using quartz or hematite without the addition of copper or collector to the feed. These
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tests were performed using a frother dosage of 10 mg/L, impeller speed of 1000 rpm, gas flowrate of 11.5 L/min and a froth height of 1cm. Fig. 18 shows the degree of entrainment of quartz and hematite in the concentrates produced during these experiments. The ENT values for both gangue minerals
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decrease dramatically, with a similar trend to that observed in the factorial test results. It is therefore
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concluded that frother concentration is decreasing during the experiment. It is hypothesized that a
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higher frother concentration increases the drag force (liquid velocity) within the froth, resulting in less settling of particles and therefore a higher degree of entrainment. More work is being conducted to identify the mechanism by which ENT is changing during the flotation test which will be reported in a
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5. Conclusions
A factorial batch flotation experiment was performed using a mixture of liberated chalcopyrite as the valuable mineral and two liberated gangue minerals, quartz and hematite, to identify the primary factors affecting the degree of entrainment. The obtained experimental results and data analysis performed allow the following conclusions to be drawn:
Experimental results show that the degree of entrainment varied significantly as the flotation test conditions changed, which suggests that models for the degree of entrainment that incorporate only particle size are not sufficient to predict gangue recovery and concentrate grade in an industrial application. 16
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There was no correlation between the measured water recovery and the degree of entrainment, which indicates that the key drivers of water recovery were not the same as those that affected the degree of entrainment.
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Particle density and the interaction between gas flowrate and froth height had a statistically
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significant effect on the degree of entrainment. The degree of entrainment also changed
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significantly with flotation time throughout each experiment.
Hypothetically, these identified effects are a consequence of the degree of entrainment being
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affected by the weight of particles (not just their size) because of its effect on particle settling as well as the froth structure which provides varying resistance to particle drainage. Froth residence time showed no relationship with the degree of entrainment. It implies that
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the drainage of gangue solids relative to the water in the froth phase is not time dependent.
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Acknowledgements
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effect on water recovery.
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Froth residence time did, however, have a significant effect on entrainment because of its
The authors would like to thank the sponsors of the AMIRA P9 project for the funding which made this work possible. The authors also wish to thank Prof. Tim Napier-Munn of the Julius Kruttschnitt
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Mineral Research Centre for providing help with the experimental design and Prof. J.P. Franzidis for providing advice regarding the write up of this paper. The first author would also like to thank the University of Queensland and Julius Kruttschnitt Mineral Research Centre for providing his scholarship. References Akdemir, Ü., Sönmez, İ., 2003. Investigation of coal and ash recovery and entrainment in flotation. Fuel Processing Technology 82, 1–9. Bisshop, J.P., 1974. A study of particle entrainment in flotation froths, B.Sc thesis. The University of Queensland, Brisbane, Australia.
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ACCEPTED MANUSCRIPT Cilek, E.C., 2009. The effect of hydrodynamic conditions on true flotation and entrainment in flotation of a complex sulphide ore. International Journal of Mineral Processing 90, 35–44.
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Cutting, G.W., Watson, D, Whitehead, A., Barber, S.P, 1981. Froth structure in continuous flotation
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cells: relation to the prediction of plant performance from laboratory data using process models.
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International Journal of Mineral Processing 7, 347–369.
Drzymala, J., 1994. Characterization of materials by Hallimond tube flotation. Part 1: maximum size
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of entrained particles. International Journal of Mineral Processing 42, 139–152. Ekmekçi, Z., Bradshaw, D.J., Allison, S.A., Harris, P.J., 2003. Effects of frother type and froth height
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on the flotation behaviour of chromite in UG2 ore. Minerals Engineering 16, 941–949. Engelbrecht, J., Woodburn, E., 1975. The effects of froth height, aeration rate and gas precipitation on
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flotation. J. South Afr. Inst. Min. Metall. 76, 125–132.
Fuerstenau, D., 1980. Fine particle flotation. Fine Particles Processing 1, 669–705.
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Gorain, B.K., Harris, M.C., Franzidis, J.P., Manlapig, E.V., 1998. The effect of froth residence time on the kinetics of flotation. Miner. Eng. 11, 627–638.
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Johnson, N.W., 1972. The flotation behaviour of some chalcopyrite ores, PhD thesis, The University of Queensland, Brisbane, Australia. Jowett, A., 1966. Gangue mineral contamination of froth. Br. Chem. Eng. 11, 330–333. Kirjavainen, V.M., 1996. Review and analysis of factors controlling the mechanical flotation of gangue minerals. International Journal of Mineral Processing 46, 21–34. Laplante, A., Kaya, M., Smith, H., 1989. The effect of froth on flotation kinetics – a mass transfer approach. Miner. Process. Extract. Metall. Rev. 5, 147–168. Lynch, A., Johnson, N., Manlapig, E., Thorne, C., 1981. Mineral and Coal Flotation Circuits. Elsevier, Amsterdam.
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ACCEPTED MANUSCRIPT Maachar, A., Dobby, G.S., 1992. Measurement of Feed Water Recovery and Entrainment Solids Recovery in Flotation Columns. Canadian Metallurgical Quarterly 31, 167–172.
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Mathe, Z., Harris, M., O’Connor, C., 2000. A review of methods to model the froth phase in non-
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steady state flotation systems. Minerals Engineering 13, 127–140.
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Neethling, S.J., Cilliers, J.J., 2002. The entrainment of gangue into a flotation froth. International Journal of Mineral Processing 64, 123–134.
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Savassi, O. N., 1998. Direct estimation of the degree of entrainment and the froth recovery of attached particles in industrial cells, PhD thesis. The University of Queensland, Brisbane, Australia.
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Szatkowski, M., 1987. Factors influencing behaviour of flotation froth. Inst. Min. Metall. Trans. (Sect. C. Miner. Process. Extract. Metall.) 96, 115–122.
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Schwarz, S., Grano, S., 2005. Effect of particle hydrophobicity on particle and water transport across a flotation froth. Colloids and Surfaces A: Physicochemical and Engineering Aspects 256, 157–164.
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Thorne, G., Manlapig, E., Hall, J., Lynch, A., 1976. Modelling of industrial sulfide flotation circuits. Flotation, AM Gaudin Memorial Volume 2, 725–752.
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Wang, L., Peng, Y., Runge, K., Bradshaw, D., 2015. A review of entrainment: Mechanisms, contributing factors and modelling in flotation. Minerals Engineering 70, 77–91. Zheng, X., Knopjes, L., 2004. Modelling of froth transportation in industrial flotation cells Part II. Modelling of froth transportation in an Outokumpu tank flotation cell at the Anglo Platinum Bafokeng–Rasimone Platinum Mine (BRPM) concentrator. Minerals Engineering 17, 989–1000. Zheng, X., Franzidis, J.P., Johnson, N.W., Manlapig, E.V., 2005. Modelling of entrainment in industrial flotation cells: the effect of solids suspension. Minerals Engineering 18, 51–58. Zheng, X., Johnson, N.W., Franzidis, J.P., 2006. Modelling of entrainment in industrial flotation cells: Water recovery and degree of entrainment. Minerals Engineering 19, 1191–120.
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ACCEPTED MANUSCRIPT Figures: Fig. 1. Gangue recovery at different water recoveries and ENT values.
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Fig. 2. Particle size distributions of the quartz and hematite after grinding.
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Fig. 3. Side view of the plastic flotation cell with a movable concentrate lip.
Fig. 4. The reproducibility of the flotation recovery of quartz in four central point experiments.
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Fig. 5 The cumulative gangue recovery versus cumulative water recovery: (a) quartz and (b) hematite.
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Fig. 6. The overall ENT values versus overall water recovery for quartz and hematite. Fig. 7. The simulated concentrate grade at different water recoveries and ENT values.
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Fig. 8. Normal probability plot created by Minitab when analysing the effect of the variables of the
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experiment and their interactions on the degree of entrainment.
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Fig. 9. The mean of the ENT of four concentrates (Con 1: 0-0.5 min; Con 2: 0.5-2 min; Con 3: 2-5 min; Con 4: 5-10 min) as a function of particle density.
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Fig. 10. The effect of particle density on the mean degree of entrainment. Fig. 11. The effect of impeller speed on the degree of entrainment of four concentrates (Con 1: 0-0.5 min; Con 2: 0.5-2 min; Con 3: 2-5 min; Con 4: 5-10 min): (a) quartz and (b) hematite. Fig.12. The effect of impeller speed on the degree of entrainment. Fig. 13. The interaction of gas flowrate and froth height on the degree of entrainment. Fig. 14. The degree of entrainment of quartz and hematite under various operating conditions. Fig. 15. The degree of entrainment of quartz as a function of particle size at the froth height of 19.0 and 23.2 cm at the gas flowrate of 1085 L/min (after Zheng et al., 2006). Fig.16. The degree of entrainment as a function of froth residence time of gas. 20
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Tables:
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Table 1 Levels of each factor used in the factorial experimental design. Table 2 Summary of two-level factorial experimental results.
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Table 3 Results of a statistical evaluation of the effect of four variables and their interactions on the degree of entrainment.
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Fig.7
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Normal Plot of the Standardized Effects
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Effect Type Not Significant Significant
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70 60 50 40 30 20
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Name Impeller speed, rpm Particle density Gas flowrate, L/min Froth height, cm
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Fig. 14
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Fig. 18
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ACCEPTED MANUSCRIPT Table 1 Levels of each factor used in the factorial experimental design. Levels
Impeller speed, rpm
800
1000
Froth height, cm
1.0
1.5
Air flowrate, L/min
8.5
Particle density
2.65
Maximum
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Minimum
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1200 2.0
11.5
14.5
2.65
5.26
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CR % 96.08 94.22 95.32 94.88
GR % 4.41 10.63 1.42 3.27
WRoverall % 23.81 38.97 6.54 17.28
1 13 15 7
2.65 2.65 2.65 2.65
1200 1200 1200 1200
8.5 14.5 8.5 14.5
1 1 2 2
98.48 99.01 96.60 96.63
6.01 11.26 1.74 3.32
25.82 37.90 9.44 16.79
9 10 19 20
2.65 2.65 2.65 2.65
1000 1000 1000 1000
11.5 11.5 11.5 11.5
1.5 1.5 1.5 1.5
95.11 95.97 89.03 97.69
3.95 3.88 4.08 3.93
21.18 20.70 21.99 20.30
2 14 16 8
5.26 5.26 5.26 5.26
800 800 800 800
8.5 14.5 8.5 14.5
1 1 2 2
97.03 95.96 95.01 91.69
2.33 4.43 0.95 1.64
12 4 6 18
5.26 5.26 5.26 5.26
1200 1200 1200 1200
8.5 14.5 8.5 14.5
1 1 2 2
91.72 93.87 94.53 94.20
4.78 9.56 1.56 3.55
0.148 0.186 0.206 0.162
Con Grade, % 12.12 5.93 21.56 14.63
ENT1
ENT2
ENT3
ENT4
0.316 0.342 0.423 0.283
0.145 0.161 0.204 0.121
0.102 0.113 0.115 0.079
0.100 0.099 0.077 0.066
10.09 6.44 20.18 14.57
0.376 0.354 0.367 0.318
0.176 0.178 0.188 0.140
0.126 0.104 0.106 0.086
0.128 0.103 0.073 0.070
0.153 0.155 0.151 0.161
12.84 13.43 12.81 13.35
0.293 0.290 0.319 0.310
0.127 0.129 0.135 0.132
0.083 0.091 0.087 0.076
0.075 0.083 0.074 0.068
21.58 32.16 5.86 13.77
0.087 0.098 0.155 0.105
17.59 12.06 24.70 20.12
0.087 0.207 0.371 0.261
0.162 0.089 0.193 0.106
0.078 0.060 0.083 0.055
0.056 0.052 0.059 0.041
28.24 42.47 9.83 19.77
0.127 0.143 0.145 0.149
10.93 6.87 20.74 13.68
0.283 0.276 0.477 0.267
0.113 0.131 0.144 0.083
0.084 0.058 0.077 0.048
0.065 0.046 0.051 0.043
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0.184 0.208 0.170 0.170
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11 3 5 17
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AR, L/min 8.5 14.5 8.5 14.5
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2.65 2.65 2.65 2.65
IS, rpm 800 800 800 800
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Table 2 Summary of two-level factorial experimental results.
Note: SG is the specific gravity, IS is the impeller speed, AR is the air flowrate, FH is the froth height, CR and GR are the assayed copper recovery and gangue recovery, respectively, WRoverall is the overall water recovery representing a fraction of water in the cell recovered into the concentrate, Con grade is the concentrate grade, ENToverall, ENT 1, 2, 3 and 4 are the overall degree of entrainment (total mass gangue in total mass water in concentrate divided by that in tailings) and the degree of entrainment for the four concentrates in a batch flotation test (mass gangue in mass water in each concentrate divided by that in the tailings)
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0.000
Gas flowrate
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Froth height
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Impeller speed* Particle density
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Impeller speed* Gas flowrate
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Impeller speed* Froth height
0.072
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Graphical abstract
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ACCEPTED MANUSCRIPT Hgihlights Particle density is of great importance in affecting the degree of entrainment.
The relative drainage of solids to water is not residence time dependent in froth.
Frother dosage significantly affects entrained solids to water ratio.
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S0032-5910(15)30137-6 doi: 10.1016/j.powtec.2015.10.049 PTEC 11315
To appear in:
Powder Technology
Received date: Revised date: Accepted date:
31 July 2015 19 October 2015 30 October 2015
Please cite this article as: L. Wang, Y. Peng, K. Runge, Entrainment in froth flotation: The degree of entrainment and its contributing factors, Powder Technology (2015), doi: 10.1016/j.powtec.2015.10.049
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ACCEPTED MANUSCRIPT Entrainment in froth flotation:
Julius Kruttschnitt Mineral Research Centre, University of Queensland, Australia b
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L. Wang a,*, Y. Peng b,*, K. Runge a, c
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The degree of entrainment and its contributing factors
School of Chemical Engineering, University of Queensland, Australia Metso Process Technology and Innovation, Australia
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c
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ABSTRACT
In froth flotation, the degree of entrainment affects the concentrate grade and it is often assumed to be only a function of particle size in models. Literature suggests that other variables might also have a
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significant impact on the degree of entrainment. In this study, a factorial batch flotation experiment
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using a mixture of liberated chalcopyrite and two liberated gangue minerals, quartz and hematite, was
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performed to investigate the effects of these other variables (including impeller speed, gas flowrate, froth height and the specific gravity of gangue mineral) on the degree of entrainment. Results show that the degree of entrainment varied significantly as the flotation test conditions changed. Particle
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density and the interaction between gas flowrate and froth height had a statistically significant effect on the average degree of entrainment measured for the entire test. The degree of entrainment also significantly changed with flotation time throughout each experiment. It is hypothesised that these effects are a consequence of the degree of entrainment being affected by the weight of particles (not just their size) because of its effect on particle settling as well as the froth structure which provides varying resistance to particle drainage. It is concluded that models for the degree of entrainment that incorporate only particle size are not sufficient to predict gangue recovery and concentrate grade in an industrial application. Keywords: entrainment; degree of entrainment; water recovery; froth flotation
1 *Corresponding author. Tel: +61 7 3346 5983 E-mail address: [email protected] (L. Wang) [email protected] (Y. Peng)
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1. Introduction
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Entrainment is a mechanical transfer process by which mineral particles suspended in water enter the
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flotation froth, move upwards, and finally leave the flotation cell with the mineral particles recovered
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by true flotation. It plays a critical role especially in the processing of ores with a large proportion of fine gangue particles (Fuerstenau, 1980; Kirjavainen, 1996). The quality of final products in mineral
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flotation is often greatly influenced by entrained gangue materials.
Entrainment is generally taken as a two-step process: in step 1, mineral particles ascend upwards into
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the froth phase from the region just below the pulp/froth interface, and in step 2, the entrained particles in the froth are transferred to the concentrate launder with water. These two steps are
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strongly dependent on the processes occurring within both the pulp and froth phases (Neethling and
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Cilliers, 2002). As a result, the recovery by entrainment is related to the state of solids suspension in the pulp, the drainage in the froth phase as well as the recovered water.
(1)
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CFif=
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A classification function has been proposed to describe the drainage in the froth (Johnson, 1972):
where CFi f is the classification function representing the drainage in the froth phase, subscript i represents the particle size and superscript f represents the froth phase. Similarly, a classification function has been proposed to describe the state of solids suspension in the pulp (Zheng et al., 2005): CFip=
(2)
where superscript p represents the pulp phase. Taking the classification effects in both the pulp and the froth into account, the overall classification effect can be determined by:
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(3)
where ENTi is the degree of entrainment representing the overall classification effect in both the pulp
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and the froth (for particle size i). ENTi can be used directly for the estimation of gangue recovery by entrainment by the combination of
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these two classification effects. The recovery by entrainment is virtually the water recovered corrected by the degree of entrainment. There are two models of gangue recovery by entrainment that are
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commonly seen in the literature (see Eqs. (4) and (5)) (Jowett, 1966; Engelbrecht and Woodburn; Laplante et al., 1989):
ENTi Rw 1 Rw ( ENTi 1)
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R e nt ,i
(5)
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(4)
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where Rent,i is the recovery by entrainment and Rw is the water recovery. However, the boundary conditions for applying these models in industrial applications are not specified in the literature. Eq. (4) was derived from the definition of gangue recovery (based on the
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mass of the gangue in the concentrate and the feed), water recovery (based on the mass of the water in the concentrate and the feed) and ENT (based on the mass of solids and water in both the concentrate and the tailing). Hence, it can deliver a very precise value of gangue recovery by entrainment. Eq. (5) is a simplified form of Eq. (4) that can be used either when water recovery is below 30 % or for ultrafine particles regardless of the water recovery. This is demonstrated in Fig. 1 which shows the gangue recovery calculated using these two equations for different water recovery and degree of entrainment values. There is a debate whether a minor change in the degree of entrainment will change the gangue recovery and the concentrate grade significantly in industrial applications, and hence whether it is necessary to pay special attention to the degree of entrainment. Despite this, some research has been carried out on the degree of entrainment and its influencing factors. In froth flotation, particle 3
ACCEPTED MANUSCRIPT properties and operating conditions are always of great importance in the mechanical entrainment process. These factors change the processes occurring in the pulp and the froth which result in a change either in the water recovery or in the degree of entrainment. Among these factors, the degree
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of entrainment is always size dependent with coarse particles exhibiting a low degree of entrainment (ENTi→0) and the fine particles exhibiting a high degree of entrainment (ENTi→1). Particles smaller
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than 50 μm are generally known to be recovered more easily by entrainment (Savassi et al., 1998). Many studies have also shown that the degree of entrainment is influenced by the particle density
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(Johnson, 1972; Bisshop, 1974; Thorne et al., 1976; Maachar and Dobby, 1992; Drzymala, 1994). However, the extent to which it affects the degree of entrainment is unresolved. Bisshop (1974), for
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example, who measured the degree of entrainment of different gangue minerals found that particle density significantly affected the degree of entrainment. However, the work of Johnson (1972)
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showed that the degree of entrainment of different gangue minerals in an industrial rougher flotation
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cell was similar, which suggested that the effect of particle density was less significant than that of other factors. This latter conclusion was supported by Savassi (1998). It should be noted that the
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effect of particle density is often influenced by the effect of particle size, and requires further investigation where the influence of particle size is specifically excluded.
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Gangue recovery by entrainment is significantly affected by gas flowrate and froth height, although the importance of these two factors compared with other influencing factors is still poorly understood. It is often thought that these two parameters affect the recovery by entrainment by changing the residence time and therefore the time available for water and particle drainage (Zheng et al., 2006). Recent studies have also demonstrated a change in the recovery of gangue minerals by entrainment with changes in the impeller speed (Cilek, 2009; Akdemir and Sönmez, 2003). Impeller speed can greatly change water recovery which in turn affects the gangue entrainment, but it is still not clear whether the degree of entrainment is affected by the impeller speed and its interaction with other variables.
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been done on the identification of the key drivers of the degree of entrainment. It should be noted that, whatever model is developed, one requirement for a good model is that it should describe the basic
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phenomena and account for all factors affecting the response significantly (Bisshop, 1974). In this study, therefore, batch flotation tests were performed to identify the key drivers of the degree
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of entrainment using a mixture of liberated chalcopyrite as a valuable mineral and two liberated gangue minerals, quartz and hematite. The aim was to develop fundamental knowledge that is
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currently lacking to enable modelling of the degree of entrainment in industrial flotation applications.
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2. Experimental
The flotation feeds to the experiments were created artificially by mixing pure chalcopyrite with pure
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gangue minerals. Quartz (SG=2.65) and hematite (SG=5.26) purchased from Geodiscoveries were used to investigate the effect of specific density of gangue minerals on the degree of entrainment. Sodium hydroxide (NaOH) was used to adjust the pH of the slurry to 9.5. Sodium ethyl xanthate
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(SEX), used as the collector, was supplied by Qingdao Lnt Chemical LTD. The collector dosage used in the flotation tests was 50 g/t of the feed. The frother used in the flotation experiments was Dowfroth 250 that was supplied by Chemical Dictionary Online. The concentration of the frother was kept at 10 mg/L. These reagents were prepared daily prior to the flotation tests using Brisbane tap water. 2.2 Flotation tests Pure chalcopyrite, quartz and hematite samples were crushed to below 3.35 mm using a laboratory jaw crusher and then split to create numerous samples of 53 g, 1530 g and 1530 g, respectively. These weights were chosen so that, when combined, they resulted in a 1 wt.% copper feed grade and 37 wt.% solids in the flotation cell. Chalcopyrite samples were stored in a freezer to avoid oxidation. 5
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particles passing 106 μm.
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The gangue minerals were ground to a particle size of P80=70-80 μm, a size similar to that in typical flotation plants. This resulted in a substantial quantity of -50 μm particles which typically are recovered by entrainment. To compare the overall degree of entrainment (ENToverall) values without
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sizing the samples, a similar particle size distribution of the quartz and hematite as shown in Fig. 2 was achieved by grinding the gangue minerals in a Bond ball mill for different grinding times. The
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mill is 0.305 m by 0.305 m, with rounded corners, a smooth lining, and was operated at 70 rpm. The charge consisted of 285 balls, weighing about 20 kg in total.
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After grinding, the mill discharges were transferred to a 3.5 L conventional Agitair flotation cell with
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a movable lip to enable the froth height to be changed without altering the pulp volume, as shown in
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Fig. 3. The cell was then started with the impeller set-point adjusted to 1200 rpm. The pH of the pulp slurry was adjusted to 9.5 by adding 5 wt.% sodium hydroxide solution. 50 g/t of collector was added to the slurry and conditioned for 1 min. Frother was then added to achieve a frother concentration of
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10 mg/L followed by another 1 min conditioning time. After conditioning, the froth height, gas flowrate and impeller speed were then set to those required for the particular experiment. Once air was introduced into the flotation cell, four flotation concentrates were collected from 0 to 0.5 min, 0.5 to 2 min, 2 to 5 min and 5 to 10 min. The froth was scraped every 10 s. The froth scraper was designed to only remove the froth above and 1mm below the cell launder lip to minimise any disturbance to the underlying froth structure. Tap water was added to the test periodically to maintain the pulp level. This added water was dosed with frother at the same concentration to that established at the beginning of the test (i.e. 10 mg/L) with the aim of achieving a relatively constant concentration of frother in the cell throughout the experiment. After 10 min of flotation, all concentrates and the tailings were filtered, dried, weighed, sampled and assayed.
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ACCEPTED MANUSCRIPT 2.3 Factorial design and analysis A four-factor, two-level, factorial experimental design was used. This design was chosen as it allows
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one to examine multiple factors simultaneously and quantify the effect of these variables and their
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interactions. The experimental results were analysed using Minitab 17 Statistical Software.
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In the factorial experimental design, each variable for testing had a maximum, minimum and centroid value (see Table 1). The difference between the maximum and minimum values represents the range over which each variable was studied. Four central point repeat experiments were used to calculate
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the experimental error and determine whether the effects observed in experiments were significant or
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not. All of the runs were conducted under relatively homogeneous conditions. To reduce the program to a feasible number of experiments, only four variables were chosen to
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investigate the key drivers of the degree of entrainment. However, the degree of entrainment is not
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restricted to these influencing factors. Therefore, future work should involve investigating other influencing variables such as viscosity and frother type in a separate experimental program.
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The levels of the variables shown in Table 1 were determined using exploratory laboratory flotation tests. Experimentation was performed to determine the range of froth heights, impeller speeds and gas
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flowrates that resulted in reasonable changes in flotation recovery but not poor flotation behaviour. In flotation, superficial gas velocity (Jg) is the parameter usually used to represent the air flowrate as it is considered relatively independent of cell size. In industrial applications, Jg usually ranges from 0.6 to 1.5 cm/s. In this study, the minimum, centroid and maximum Jg values chosen were 0.6, 0.8 and 1.0 cm/s, respectively. The corresponding air flowrates were 8.5, 11.5 and 14.5 L/min, respectively. The impeller speeds selected were based on the need to keep the majority of particles in suspension without an overly turbulent pulp-froth interface. The maximum impeller speed chosen was 1200 rpm at which some turbulent effects were visually observed to affect the froth phase. The minimum impeller speed was chosen to be 800 rpm because at this speed there was a small amount of solids observed to be settling in the flotation cell. All froth depths selected were reasonably shallow (i.e. 1.0,
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3. Results
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3.1 Flotation reproducibility
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In flotation, the overall error is a consequence of minor variations in the grinding, flotation, sampling and assaying as well as operator and random errors. The total error associated with the experimental procedure was assessed using the four replicates of the central point experiment. Fig. 4 shows the
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reproducibility of the flotation recovery of quartz. For the 10 min concentrate, a 95% confidence
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interval of 3.26% relative error was obtained. This degree of error is considered acceptable and sufficiently low to enable the effect of different variables on the entrainment parameters to be
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determined with statistical confidence.
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3.2 Flotation results
The experimental results for the factorial experiments are shown in Table 2. Copper recovery was
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high in all the tests. There were large variations in the gangue recovery, which resulted in large variations in concentrate grade. It should be noted that the gangue minerals used in these tests were
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fully liberated, and presumably it can therefore be assumed that they were recovered into the concentrate only by entrainment. Therefore, the variation in the concentrate grade was caused by changes in entrainment recovery. Gangue recovery in the different tests is a strong function of water recovery which varied significantly in the different tests (refer to Fig. 5). However, it also changes as a consequence of variation in the degree of entrainment, which according to Eq. (5), can be approximated by the slope of the gangue versus water recovery relationships shown in Fig. 5. ENT values were calculated for each experimental condition using Eq. (4). The overall ENT values ranged from approximately 0.1 to 0.2. However, the ENT values in the first concentrates of all the
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Fig. 6 shows the ENT values for quartz and hematite plotted separately against water recovery. There
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was no correlation between the degree of entrainment and water recovery for either gangue mineral,
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which indicates that the variables that affected water recovery were not the same as those that affected the degree of entrainment.
In addition, the degree of entrainment was found to vary with flotation time. In each of the twenty
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batch flotation tests, the ENT values dramatically decreased as the experiment progressed.
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3.3 The importance of the degree of entrainment
As mentioned previously, the overall ENT values ranged from approximately 0.1 to 0.2 under the
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various experimental conditions. It is questionable whether such a change in the ENT value will have
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a significant impact on the concentrate grade. To test this, concentrate grades at different ENT values and water recoveries were estimated. In these calculations, copper recovery was set to a constant
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value. Copper recoveries in the rougher flotation tests performed in this study were generally high, so a copper recovery of 90% was selected. Gangue recovery for each water recovery and degree of
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entrainment value was simulated using Eq. (4). Using these copper and gangue recoveries, weighted according to the copper feed grade of 1% used in the test, concentrate grade was then calculated. Fig. 7 shows the concentrate grade as a function of water recovery and the degree of entrainment determined from these simulations. At each water recovery, the concentrate grade decreases with increasing degree of entrainment. The reduction is fairly obvious at relatively low water recovery, but even at high water recoveries, there is a discernible change in the concentrate grade when the degree of entrainment increases from 0.1 to 0.3. Indeed, examining the experimental results of the present study, a dramatic decrease in the concentrate grade can be seen when the overall degree of entrainment increased from approximately 0.1 to 0.2 (Table 2). Therefore, the degree of entrainment can be critical in terms of influencing the concentrate grade and should not be ignored. 9
ACCEPTED MANUSCRIPT 3.4 Statistical significance of variables and interactions The effects and interactions of the four variables on the degree of entrainment at a 95 % confidence
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level were analysed using Minitab 17 Statistical Software. The results are summarized in Table 3.
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Note that the P values in the table indicate the significance of a factor; a relatively small P value,
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smaller than the selected significance level of 0.05, implies that a factor has a significant effect on a response. As can be seen from Table 3, the degree of entrainment was significantly affected by the particle density and the interaction between gas flowrate and froth height, while other variables and
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interactions did not affect the degree of entrainment significantly. It should be noted that the “not significant” factors and interactions do not imply no effect or interaction, but rather that the effect or
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interaction cannot be determined with confidence based on error in the data. In addition, the P value of 0.007 for “curvature” in Table 3 also indicates that the relationship between the examined
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significant factors and their interactions and the degree of entrainment is non-linear.
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The significant variables and variable interactions in a two-level factorial design can also be
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determined from a normal probability plot. The fitted line of this plot indicates where you would expect the points to fall if the effects were zero and the variation observed was random and normally distributed. The greater the distance from the line, the more significant the effect of a tested variable.
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Points that fall to the left of the line have a negative effect and the points to the right have a positive effect. Fig. 8 shows the normal probability plot created by Minitab when evaluating the effects of the experimental conditions on the measured overall degree of entrainment. Two effects, particle density and the interaction between gas flowrate and froth height stand out and have a much more significant effect than the other variables. Both have a negative correlation with the overall degree of entrainment. The effect of particle density is more significant than the interaction between gas flowrate and froth height. 4. Discussion 4.1 Particle density
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ACCEPTED MANUSCRIPT The results have shown that particle density has a significant effect on the degree of entrainment. Quartz with a specific gravity of 2.65 results in a higher degree of entrainment than hematite with a specific gravity of 5.26. This can be observed in Fig. 6 with the overall degree of entrainment values
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measured for quartz being clearly higher than those measured for haematite. Fig. 9 shows the average ENT value measured in the different concentrates of the batch flotation test for those tests performed
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using quartz to those performed using hematite. The ENT values of the quartz were always larger than those of hematite. This difference can be interpreted as the effect of particle density (as the particle
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size distributions were similar).
Fig. 10 shows the average overall degree of entrainment plotted against particle density for all the
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tests performed under the different operating conditions. The correlation is negative and the average changes from 0.180 for quartz to 0.125 for hematite. As shown in Fig. 7, a decrease of the degree of
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entrainment from 0.2 to 0.1 can lead to a large change in concentrate grade, regardless of the water
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recovery, which indicates that the effect of particle density on the degree of entrainment is significant and should not be ignored when the degree of entrainment is modelled. No conclusion can be drawn
design.
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as to whether this correlation is linear as only two particle densities were used in the experimental
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The decrease in the degree of entrainment with increasing particle density is in line with that observed in many other studies (Johnson, 1972; Bisshop, 1974; Thorne et al., 1976; Maachar and Dobby, 1992; Drzymala, 1994). The higher entrainment of low-density particles is presumably associated with the fact that they tend to move with water due to their lower sedimentation velocities. As a result, the degree of solids suspension in the pulp phase may be poorer for higher density minerals, resulting in less carry over from the pulp into the froth. In addition, high density minerals have a greater chance of settling and draining through the plateau borders within the froth phase than the lower density minerals. Therefore, the degree of entrainment decreases when the particle density is increased.
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ACCEPTED MANUSCRIPT Traditionally entrainment recovery has been modelled based on particle size alone. These results would suggest that it would be better to model entrainment based on particle mass which will be a
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consequence of both particle size and density.
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4.2 Impeller speed
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The impeller speed and its interactions with other variables did not have a great impact on the degree of entrainment according to the statistical analysis. Fig. 11 shows the average degree of entrainment for quartz and hematite measured in the different batch flotation concentrates at different impeller
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speeds. There was no significant variation in the ENT values except for hematite in the first
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concentrates. This difference might be because of a change in froth structure caused by variation in the flotation of copper in this first concentrate.
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The effect of impeller speed on the average degree of entrainment is shown in Fig. 12 for all the tests
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as well as those only performed using quartz and hematite, respectively. A slight increase in the mean ENT value was found with increasing impeller speed but it is not statistically significant and would
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not be expected to result in an appreciable change in concentrate grade. It is interesting to note, however, that there were observable increases in gangue recovery (and thus
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decreases in concentrate grade) with an increase in impeller speed in the test results. This was a consequence of an increase in water recovery. The increase in gangue recovery by entrainment is in agreement with observations made in other studies in the literature (Cilek, 2009; Akdemir and Sönmez, 2003). 4.3 The interaction between gas flowrate and froth height Table 3 shows that the degree of entrainment was significantly affected by the interaction between gas flowrate and froth height. This is illustrated in Fig. 13 and Fig. 14 which show the average overall entrainment value as a function of gas rate at different froth depths in all the tests and subsets of tests. In all these graphs, at a shallow froth depth, the degree of entrainment increases as gas flowrate
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ACCEPTED MANUSCRIPT increases. Conversely, at the deeper froth depths, the degree of entrainment decreases as gas flowrate increases.
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This is a relatively unexpected result as intuitively one would expect that either an increase in froth
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height or an increase in gas flowrate would result in less time for drainage and therefore a decrease in
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both the degree of entrainment and water recovery and subsequently the gangue recovery. In this paper there are examples where an increase in gas flowrate can decrease the degree of entrainment (deep froths) and examples where increasing froth depth (at low gas flowrates) increases the degree of
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entrainment. Increasing degrees of entrainment with froth height (at a low gas flowrate) have previously been observed by Zheng et al. (2006) who collected data from an Outokumpu 3 m3 pilot
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tank cell operating under various operating conditions (four different gas flowrates and four different froth heights) using ore diverted from the feed of a rougher bank of the Xstrata Mt. Isa Mines copper
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concentrator. Fig. 15 shows the degree of entrainment of quartz for different particle sizes at two froth
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heights at the lowest gas flowrate of 1085 L/min (Jg = 0.91 cm/s) measured in this study. The degree
height of 19.0 cm.
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of entrainment of the finer particle sizes is greater at the froth height of 23.2 cm than that at the froth
At a low gas flowrate, water content in the froth phase is known to decrease rapidly with increasing
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froth height (Cutting et al., 1981). The low water content might result in a narrowing of the plateau borders providing resistance and therefore less drainage of solids (per unit volume of water). At the lower froth depths, this thinning may not occur and a greater amount of solid drainage may result, decreasing the degree of entrainment of the gangue minerals. At the higher gas rates, a “wetter froth” which may not lead to sufficient thinning of the plateau borders to impede solid drainage. Solids suspended in water may move more freely and this causes a reversal in the trends observed. Now as froth depth increases, there may be more time for drainage and therefore the degree of entrainment decreases. In addition, a decrease of solids in unit water in the upper froth may be associated with a greater amount of bubble bursting in the froth. Ekmekçi et al.
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ACCEPTED MANUSCRIPT (2003) observed a low froth stability and brittle froth structure in deep froths. This may result in an increase in the solid drainage within the froth phase.
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The above explanations are purely speculative at this stage and more research is required to determine
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definitively the reason for the observed results. It is likely, however, to be due to froth structural
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changes. 4.4 Froth residence time
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Froth residence time, or the time particles and bubbles exist within the froth phase, plays a critical role in determining froth mineral recovery (Mathe et al., 2000). Intuitively, froth residence time may also
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affect entrainment (water recovery and the degree of entrainment) as longer times would result in more water drainage and potentially more solids to drain preferentially to the water (Zheng, et al.,
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2006). In the literature, froth residence time is commonly calculated by either of the following
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equations based on the air and the slurry in the froth (Gorain et al., 1998; Lynch et al., 1981; Schwarz
Hf Jg
slurry
(6)
(1 g ) V f Qs
(7)
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air
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and Grana, 2005; Szatkowski, 1987):
where λair is the froth residence time of air, λslurry is the froth residence time of slurry, Hf is froth height; Jg is the superficial gas velocity which is the ratio between the volumetric gas flowrate and cross-sectional area of the flotation cell, εg is the mean air hold-up in the froth, Qs is the volumetric flowrate of the concentrate, incorporating both solids and liquid flowrates and Vf is the volume of the froth. Fig. 16 shows the effect of froth residence time of gas (0.98 s, 1.86 s and 3.35 s) (calculated by Eq. (6)) on the mean of the degree of entrainment measured in this experimental study. Little change was observed in the degree of entrainment when the froth residence time increased from 0.98 s to 3.35 s.
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ACCEPTED MANUSCRIPT The froth residence time of the slurry may be better correlated with entrainment than the residence time of the air. In this study, froth residence time of slurry was calculated by dividing the froth volume by the volumetric flow of water and solids in the concentrate, corrected for an estimate of the
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air holdup in the froth (see Eq. (7)). The mean air holdup in the froth phase will be high (>95%), and in this work was estimated by dividing the air volumetric flowrate by the combined volumetric
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flowrate of concentrate and air as performed by Zheng et al. (2004). Froth residence time calculated in this alternative way also did not exhibit a relationship with the measured degree of entrainment (see
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Fig. 17).
This is contrast to the water recovery results. Water recovery varied significantly in the experiments
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of this test and was found to be strongly correlated with froth residence time. An increase in froth residence time resulted in less water recovery and therefore less gangue recovery which thus
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increased concentrate grade.
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Therefore, it can be concluded that froth residence time affects gangue recovery by entrainment
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through an effect on water recovery, but does not affect the relative drainage of solids to water (i.e. the degree of entrainment).
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4.5 Change of ENT with flotation time Interestingly, the degree of entrainment was found to decrease throughout the batch flotation experiment with the first concentrate of all 20 tests having a much higher degree of entrainment value than that measured in the later concentrates (see Table 2). The change is significant with entrainment averaging about 0.3 to 0.4 in the first concentrate and 0.1 in the last (see Fig 9). This effect is more significant than that caused by any of the other variables tested in this study. Potentially this variation could have been caused by a change in particle size. The particle size feeding all experiments is the same but the particle size feeding the later stages of the test could be coarser (and therefore results in lower ENT values) because of the preferential removal of fines by entrainment. Calculations performed, however, show that the amount of gangue removed by entrainment in the test is insufficient to result in an appreciable change in the particle size distribution 15
ACCEPTED MANUSCRIPT in the cell throughout the experiments. This is corroborated by Runs 5 and 16 where gangue recovery is very low but the degree of entrainment still decreases significantly throughout the test.
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During the experiment, the copper feed grade (and therefore the copper loading) will be decreasing
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and potentially the frother concentration may also be decreasing. Although there is frother added to
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the water added during the flotation experiment, the frother concentration in the concentrates is often higher than in the pulp and this will result in a general decrease in frother concentration during the test. To assess whether the change in copper feed grade is the primary driver for the result, flotation tests
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were conducted using quartz or hematite without the addition of copper or collector to the feed. These
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tests were performed using a frother dosage of 10 mg/L, impeller speed of 1000 rpm, gas flowrate of 11.5 L/min and a froth height of 1cm. Fig. 18 shows the degree of entrainment of quartz and hematite in the concentrates produced during these experiments. The ENT values for both gangue minerals
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decrease dramatically, with a similar trend to that observed in the factorial test results. It is therefore
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concluded that frother concentration is decreasing during the experiment. It is hypothesized that a
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higher frother concentration increases the drag force (liquid velocity) within the froth, resulting in less settling of particles and therefore a higher degree of entrainment. More work is being conducted to identify the mechanism by which ENT is changing during the flotation test which will be reported in a
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separate paper.
5. Conclusions
A factorial batch flotation experiment was performed using a mixture of liberated chalcopyrite as the valuable mineral and two liberated gangue minerals, quartz and hematite, to identify the primary factors affecting the degree of entrainment. The obtained experimental results and data analysis performed allow the following conclusions to be drawn:
Experimental results show that the degree of entrainment varied significantly as the flotation test conditions changed, which suggests that models for the degree of entrainment that incorporate only particle size are not sufficient to predict gangue recovery and concentrate grade in an industrial application. 16
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There was no correlation between the measured water recovery and the degree of entrainment, which indicates that the key drivers of water recovery were not the same as those that affected the degree of entrainment.
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Particle density and the interaction between gas flowrate and froth height had a statistically
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significant effect on the degree of entrainment. The degree of entrainment also changed
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significantly with flotation time throughout each experiment.
Hypothetically, these identified effects are a consequence of the degree of entrainment being
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affected by the weight of particles (not just their size) because of its effect on particle settling as well as the froth structure which provides varying resistance to particle drainage. Froth residence time showed no relationship with the degree of entrainment. It implies that
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the drainage of gangue solids relative to the water in the froth phase is not time dependent.
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Acknowledgements
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effect on water recovery.
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Froth residence time did, however, have a significant effect on entrainment because of its
The authors would like to thank the sponsors of the AMIRA P9 project for the funding which made this work possible. The authors also wish to thank Prof. Tim Napier-Munn of the Julius Kruttschnitt
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Mineral Research Centre for providing help with the experimental design and Prof. J.P. Franzidis for providing advice regarding the write up of this paper. The first author would also like to thank the University of Queensland and Julius Kruttschnitt Mineral Research Centre for providing his scholarship. References Akdemir, Ü., Sönmez, İ., 2003. Investigation of coal and ash recovery and entrainment in flotation. Fuel Processing Technology 82, 1–9. Bisshop, J.P., 1974. A study of particle entrainment in flotation froths, B.Sc thesis. The University of Queensland, Brisbane, Australia.
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ACCEPTED MANUSCRIPT Cilek, E.C., 2009. The effect of hydrodynamic conditions on true flotation and entrainment in flotation of a complex sulphide ore. International Journal of Mineral Processing 90, 35–44.
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Cutting, G.W., Watson, D, Whitehead, A., Barber, S.P, 1981. Froth structure in continuous flotation
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cells: relation to the prediction of plant performance from laboratory data using process models.
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International Journal of Mineral Processing 7, 347–369.
Drzymala, J., 1994. Characterization of materials by Hallimond tube flotation. Part 1: maximum size
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of entrained particles. International Journal of Mineral Processing 42, 139–152. Ekmekçi, Z., Bradshaw, D.J., Allison, S.A., Harris, P.J., 2003. Effects of frother type and froth height
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on the flotation behaviour of chromite in UG2 ore. Minerals Engineering 16, 941–949. Engelbrecht, J., Woodburn, E., 1975. The effects of froth height, aeration rate and gas precipitation on
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flotation. J. South Afr. Inst. Min. Metall. 76, 125–132.
Fuerstenau, D., 1980. Fine particle flotation. Fine Particles Processing 1, 669–705.
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Gorain, B.K., Harris, M.C., Franzidis, J.P., Manlapig, E.V., 1998. The effect of froth residence time on the kinetics of flotation. Miner. Eng. 11, 627–638.
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Johnson, N.W., 1972. The flotation behaviour of some chalcopyrite ores, PhD thesis, The University of Queensland, Brisbane, Australia. Jowett, A., 1966. Gangue mineral contamination of froth. Br. Chem. Eng. 11, 330–333. Kirjavainen, V.M., 1996. Review and analysis of factors controlling the mechanical flotation of gangue minerals. International Journal of Mineral Processing 46, 21–34. Laplante, A., Kaya, M., Smith, H., 1989. The effect of froth on flotation kinetics – a mass transfer approach. Miner. Process. Extract. Metall. Rev. 5, 147–168. Lynch, A., Johnson, N., Manlapig, E., Thorne, C., 1981. Mineral and Coal Flotation Circuits. Elsevier, Amsterdam.
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ACCEPTED MANUSCRIPT Maachar, A., Dobby, G.S., 1992. Measurement of Feed Water Recovery and Entrainment Solids Recovery in Flotation Columns. Canadian Metallurgical Quarterly 31, 167–172.
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Mathe, Z., Harris, M., O’Connor, C., 2000. A review of methods to model the froth phase in non-
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steady state flotation systems. Minerals Engineering 13, 127–140.
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Neethling, S.J., Cilliers, J.J., 2002. The entrainment of gangue into a flotation froth. International Journal of Mineral Processing 64, 123–134.
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Savassi, O. N., 1998. Direct estimation of the degree of entrainment and the froth recovery of attached particles in industrial cells, PhD thesis. The University of Queensland, Brisbane, Australia.
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Szatkowski, M., 1987. Factors influencing behaviour of flotation froth. Inst. Min. Metall. Trans. (Sect. C. Miner. Process. Extract. Metall.) 96, 115–122.
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Schwarz, S., Grano, S., 2005. Effect of particle hydrophobicity on particle and water transport across a flotation froth. Colloids and Surfaces A: Physicochemical and Engineering Aspects 256, 157–164.
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Thorne, G., Manlapig, E., Hall, J., Lynch, A., 1976. Modelling of industrial sulfide flotation circuits. Flotation, AM Gaudin Memorial Volume 2, 725–752.
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Wang, L., Peng, Y., Runge, K., Bradshaw, D., 2015. A review of entrainment: Mechanisms, contributing factors and modelling in flotation. Minerals Engineering 70, 77–91. Zheng, X., Knopjes, L., 2004. Modelling of froth transportation in industrial flotation cells Part II. Modelling of froth transportation in an Outokumpu tank flotation cell at the Anglo Platinum Bafokeng–Rasimone Platinum Mine (BRPM) concentrator. Minerals Engineering 17, 989–1000. Zheng, X., Franzidis, J.P., Johnson, N.W., Manlapig, E.V., 2005. Modelling of entrainment in industrial flotation cells: the effect of solids suspension. Minerals Engineering 18, 51–58. Zheng, X., Johnson, N.W., Franzidis, J.P., 2006. Modelling of entrainment in industrial flotation cells: Water recovery and degree of entrainment. Minerals Engineering 19, 1191–120.
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ACCEPTED MANUSCRIPT Figures: Fig. 1. Gangue recovery at different water recoveries and ENT values.
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Fig. 2. Particle size distributions of the quartz and hematite after grinding.
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Fig. 3. Side view of the plastic flotation cell with a movable concentrate lip.
Fig. 4. The reproducibility of the flotation recovery of quartz in four central point experiments.
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Fig. 5 The cumulative gangue recovery versus cumulative water recovery: (a) quartz and (b) hematite.
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Fig. 6. The overall ENT values versus overall water recovery for quartz and hematite. Fig. 7. The simulated concentrate grade at different water recoveries and ENT values.
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Fig. 8. Normal probability plot created by Minitab when analysing the effect of the variables of the
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experiment and their interactions on the degree of entrainment.
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Fig. 9. The mean of the ENT of four concentrates (Con 1: 0-0.5 min; Con 2: 0.5-2 min; Con 3: 2-5 min; Con 4: 5-10 min) as a function of particle density.
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Fig. 10. The effect of particle density on the mean degree of entrainment. Fig. 11. The effect of impeller speed on the degree of entrainment of four concentrates (Con 1: 0-0.5 min; Con 2: 0.5-2 min; Con 3: 2-5 min; Con 4: 5-10 min): (a) quartz and (b) hematite. Fig.12. The effect of impeller speed on the degree of entrainment. Fig. 13. The interaction of gas flowrate and froth height on the degree of entrainment. Fig. 14. The degree of entrainment of quartz and hematite under various operating conditions. Fig. 15. The degree of entrainment of quartz as a function of particle size at the froth height of 19.0 and 23.2 cm at the gas flowrate of 1085 L/min (after Zheng et al., 2006). Fig.16. The degree of entrainment as a function of froth residence time of gas. 20
ACCEPTED MANUSCRIPT Fig. 17. The degree of entrainment as a function of froth residence time of slurry. Fig. 18. The degree of entrainment of quartz and hematite at the froth concentration of 10 mg/L (Con
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1: 0-0.5 min; Con 2: 0.5-2 min; Con 3: 2-5 min; Con 4: 5-10 min).
Tables:
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Table 1 Levels of each factor used in the factorial experimental design. Table 2 Summary of two-level factorial experimental results.
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Table 3 Results of a statistical evaluation of the effect of four variables and their interactions on the degree of entrainment.
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ACCEPTED MANUSCRIPT
25
Fig. 5
AC
CE P
TE
D
MA
NU
SC R
IP
T
ACCEPTED MANUSCRIPT
26
MA
NU
SC R
IP
T
ACCEPTED MANUSCRIPT
AC
CE P
TE
D
Fig. 6
27
Fig.7
AC
CE P
TE
D
MA
NU
SC R
IP
T
ACCEPTED MANUSCRIPT
28
ACCEPTED MANUSCRIPT
T
Normal Plot of the Standardized Effects
IP
(response is ENT, A lpha = 0.05) 99
Effect Type Not Significant Significant
SC R
95 90
70 60 50 40 30 20
NU
CD
10
B
5 1
-4
-3 -2 -1 0 Standardized Effect
MA
-5
Fig. 8
CE P
TE
D
-6
AC
Percent
80
29
1
2
3
Factor A B C D
Name Impeller speed, rpm Particle density Gas flowrate, L/min Froth height, cm
MA
NU
SC R
IP
T
ACCEPTED MANUSCRIPT
AC
CE P
TE
D
Fig. 9
30
Fig. 10
AC
CE P
TE
D
MA
NU
SC R
IP
T
ACCEPTED MANUSCRIPT
31
MA
NU
SC R
IP
T
ACCEPTED MANUSCRIPT
AC
CE P
TE
D
Fig. 11
32
Fig.12
AC
CE P
TE
D
MA
NU
SC R
IP
T
ACCEPTED MANUSCRIPT
33
NU
SC R
IP
T
ACCEPTED MANUSCRIPT
AC
CE P
TE
D
MA
Fig. 13
34
Fig. 14
AC
CE P
TE
D
MA
NU
SC R
IP
T
ACCEPTED MANUSCRIPT
35
MA
NU
SC R
IP
T
ACCEPTED MANUSCRIPT
AC
CE P
TE
D
Fig. 15
36
NU
SC R
IP
T
ACCEPTED MANUSCRIPT
AC
CE P
TE
D
MA
Fig.16
37
MA
NU
SC R
IP
T
ACCEPTED MANUSCRIPT
AC
CE P
TE
D
Fig. 17
38
Fig. 18
AC
CE P
TE
D
MA
NU
SC R
IP
T
ACCEPTED MANUSCRIPT
39
ACCEPTED MANUSCRIPT Table 1 Levels of each factor used in the factorial experimental design. Levels
Impeller speed, rpm
800
1000
Froth height, cm
1.0
1.5
Air flowrate, L/min
8.5
Particle density
2.65
Maximum
T
Central
AC
CE P
TE
D
MA
NU
SC R
Minimum
IP
Factors
40
1200 2.0
11.5
14.5
2.65
5.26
ACCEPTED MANUSCRIPT
CR % 96.08 94.22 95.32 94.88
GR % 4.41 10.63 1.42 3.27
WRoverall % 23.81 38.97 6.54 17.28
1 13 15 7
2.65 2.65 2.65 2.65
1200 1200 1200 1200
8.5 14.5 8.5 14.5
1 1 2 2
98.48 99.01 96.60 96.63
6.01 11.26 1.74 3.32
25.82 37.90 9.44 16.79
9 10 19 20
2.65 2.65 2.65 2.65
1000 1000 1000 1000
11.5 11.5 11.5 11.5
1.5 1.5 1.5 1.5
95.11 95.97 89.03 97.69
3.95 3.88 4.08 3.93
21.18 20.70 21.99 20.30
2 14 16 8
5.26 5.26 5.26 5.26
800 800 800 800
8.5 14.5 8.5 14.5
1 1 2 2
97.03 95.96 95.01 91.69
2.33 4.43 0.95 1.64
12 4 6 18
5.26 5.26 5.26 5.26
1200 1200 1200 1200
8.5 14.5 8.5 14.5
1 1 2 2
91.72 93.87 94.53 94.20
4.78 9.56 1.56 3.55
0.148 0.186 0.206 0.162
Con Grade, % 12.12 5.93 21.56 14.63
ENT1
ENT2
ENT3
ENT4
0.316 0.342 0.423 0.283
0.145 0.161 0.204 0.121
0.102 0.113 0.115 0.079
0.100 0.099 0.077 0.066
10.09 6.44 20.18 14.57
0.376 0.354 0.367 0.318
0.176 0.178 0.188 0.140
0.126 0.104 0.106 0.086
0.128 0.103 0.073 0.070
0.153 0.155 0.151 0.161
12.84 13.43 12.81 13.35
0.293 0.290 0.319 0.310
0.127 0.129 0.135 0.132
0.083 0.091 0.087 0.076
0.075 0.083 0.074 0.068
21.58 32.16 5.86 13.77
0.087 0.098 0.155 0.105
17.59 12.06 24.70 20.12
0.087 0.207 0.371 0.261
0.162 0.089 0.193 0.106
0.078 0.060 0.083 0.055
0.056 0.052 0.059 0.041
28.24 42.47 9.83 19.77
0.127 0.143 0.145 0.149
10.93 6.87 20.74 13.68
0.283 0.276 0.477 0.267
0.113 0.131 0.144 0.083
0.084 0.058 0.077 0.048
0.065 0.046 0.051 0.043
MA N
0.184 0.208 0.170 0.170
TE D
11 3 5 17
ENToverall
IP
FH, cm 1 1 2 2
CR
AR, L/min 8.5 14.5 8.5 14.5
US
2.65 2.65 2.65 2.65
IS, rpm 800 800 800 800
CE P
SG
AC
Run
T
Table 2 Summary of two-level factorial experimental results.
Note: SG is the specific gravity, IS is the impeller speed, AR is the air flowrate, FH is the froth height, CR and GR are the assayed copper recovery and gangue recovery, respectively, WRoverall is the overall water recovery representing a fraction of water in the cell recovered into the concentrate, Con grade is the concentrate grade, ENToverall, ENT 1, 2, 3 and 4 are the overall degree of entrainment (total mass gangue in total mass water in concentrate divided by that in tailings) and the degree of entrainment for the four concentrates in a batch flotation test (mass gangue in mass water in each concentrate divided by that in the tailings)
41
ACCEPTED MANUSCRIPT Table 3 Results of a statistical evaluation of the effect of four variables and their interactions on the degree of entrainment.
0.000
Gas flowrate
0.988
Froth height
0.259
Impeller speed* Particle density
0.218
Impeller speed* Gas flowrate
0.218
Impeller speed* Froth height
0.072
Negative (exhibits maximum)
MA
Particle density* Gas flowrate
0.595 0.116
D
Particle density *Froth height
TE
Gas flowrate* Froth height
0.026 0.007
AC
CE P
Curvature
T
Particle density
IP
0.054
NU
Impeller speed
Effect on response
SC R
P value
Term
42
Negative (exhibits minimum)
ACCEPTED MANUSCRIPT
AC
CE P
TE
D
MA
NU
SC R
IP
T
Graphical abstract
43
ACCEPTED MANUSCRIPT Hgihlights Particle density is of great importance in affecting the degree of entrainment.
The relative drainage of solids to water is not residence time dependent in froth.
Frother dosage significantly affects entrained solids to water ratio.
AC
CE P
TE
D
MA
NU
SC R
IP
T
44