- Email: [email protected]
Effect of froth rheology on froth and flotation performance
Minerals Engineering 115 (2018) 4–12
Contents lists available at ScienceDirect
Minerals Engineering journal homepage: www.elsevier.com/locate/mineng
Effect of froth rheology on froth and flotation performance ⁎
MARK
Chao Li , Kym Runge, Fengnian Shi, Saeed Farrokhpay Julius Kruttschnitt Mineral Research Centre, Sustainable Minerals Institute, University of Queensland, 40 Isles Road, Indooroopilly, 4068 QLD, Australia
A R T I C L E I N F O
A B S T R A C T
Keywords: Froth rheology Consistency index Froth performance Flotation performance
It has been suspected for some time that froth rheology has an impact on froth and flotation performance but little experimental work has been performed to investigate these effects. In this paper, the effect of froth rheology on froth and flotation performance was investigated by performing flotation tests in a 20 L continuous flotation cell using a synthetic ore which was a mixture of pure chalcopyrite and silica. Froth rheology was measured during these tests along with key flotation performance indicators: froth height above the lip, air recovery and silica recovery. It was found that froth rheology was positively correlated to froth height above the lip. Air recovery was also correlated to froth rheology; at low froth viscosity, air recovery increased upon increasing consistency index (a measure of the viscosity of a fluid) while the opposite was found at high froth viscosity. A similar correlation between froth viscosity and silica recovery was also observed. Measurements of froth rheology were also performed in industrial scale flotation cells processing a platinum ore. The investigated industrial scale froth exhibited similar rheological characteristics to that observed in the laboratory work. Both of the froths have a shear-thinning nature with minor yield stress. Froth height above the lip was also found to be positively correlated with froth viscosity, which supports the conclusions drawn from the laboratory work.
1. Introduction Froth flotation consists of pulp and froth phases. The function of the froth phase is to enhance the overall selectivity and recovery of the flotation process. The froth achieves these by reducing the recovery of entrained material to the concentrate stream, while preferentially retaining the attached material. This increases the concentrate grade whilst limiting as far as possible the reduction in recovery of valuables. The importance of the cleaning and recovering actions of the froth in flotation has been well recognised (Feteris et al., 1987; Moys, 1978; Schuhmann, 1942; Subrahmanyam and Forssberg, 1988; Yianatos et al., 1988). The froth efficiency which can be represented by the selectivity and recovery of the process is influenced by froth retention time. A greater froth retention time results in a greater probability of drainage of the water and entrained solids back from the froth phase to the pulp phase through the Plateau borders and vertices within the froth (Wang et al., 2016a). Froth recovery, the fraction of valuable mineral entering the froth phase attached to air bubbles that reports to the concentrate (Finch and Dobby, 1990), is the most commonly used measure of how effectively the froth recovers the valuable mineral. Previous work (Gorain et al., 1998; Mathe et al., 2000) has indicated that froth recovery decreases exponentially with an increase in froth retention time.
⁎
A higher froth retention time results in an increased probability of froth collapse as well as valuable particle drop-back due to detachment and drainage. However, it is difficult to measure froth recovery (Franzidis and Harris, 2010; Runge et al., 2010). Air recovery, the volume fraction of air that is added to the cell which survives and reports to the concentrate, has been used as a measure of froth stability (Hadler et al., 2010; Leiva et al., 2012; Neethling and Cilliers, 2008; Shean et al., 2017). It has been reported that both higher grade and recovery are obtained at the peak air recovery (Hadler and Cilliers, 2009; Hadler et al., 2010; Shean et al., 2017). The valuable minerals are transported from the pulp-froth interface to the launder by attachment to air bubbles in the froth phase. The more air is recovered to the launder, the more valuable minerals are recovered to be concentrate. Hence, froth recovery is likely to be positively correlated with air recovery. It is expected that froth rheology can influence froth and flotation performance through its effect on froth retention time. A more viscous froth resists motion towards the lip, increasing the time the froth remains in the flotation cell. Very little work has been performed to investigate the effect of froth rheology on froth and flotation performance other than the work of Shi and Zheng (2003) who showed that froth rheology had a strong correlation with concentrate grade in an Outokumpu 3-m3 tank cell operated at the Mt Isa Mines (MIM) Copper Concentrator.
Corresponding author. E-mail address: [email protected] (C. Li).
http://dx.doi.org/10.1016/j.mineng.2017.10.003 Received 28 August 2016; Received in revised form 28 September 2017; Accepted 4 October 2017 0892-6875/ © 2017 Elsevier Ltd. All rights reserved.
Minerals Engineering 115 (2018) 4–12
C. Li et al.
Table 1 The conditions in the CCRD flotation tests (Li et al., 2016a). Test
Froth height (cm)
Superficial gas velocity (cm s−1)
Impeller speed (rpm)
Chalcopyrite particle size P80 (µm)
Copper grade (%)
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33
7 6 6 8 6 6 6 6 7 7 8 7 8 8 8 6 8 7 7 8 8 6 7 5 7 7 7 7 7 7 9 7 7
1.4 1.0 1.8 1.8 1.0 1.8 1.0 1.8 1.4 1.4 1.8 1.4 1.0 1.8 1.0 1.8 1.8 1.4 1.4 1.0 1.0 1.0 1.4 1.4 0.6 1.4 1.4 1.4 1.4 2.2 1.4 1.4 1.4
900 750 1050 750 750 750 1050 1050 900 900 750 900 1050 1050 750 750 1050 900 900 750 1050 1050 900 900 900 900 1200 900 600 900 900 900 900
80 50 50 50 110 50 50 110 80 80 110 80 110 110 110 110 50 80 80 50 50 110 140 80 80 80 80 80 80 80 80 80 20
1.0 1.4 1.4 1.4 0.6 0.6 0.6 0.6 1.0 1.0 0.6 1.0 0.6 1.4 1.4 1.4 0.6 1.0 1.0 0.6 1.4 1.4 1.0 1.0 1.0 1.0 1.0 1.8 1.0 1.0 1.0 0.2 1.0
Fig. 1. A pictorial diagram of the experimental set up (Li et al., 2016a).
purchased from Geo Discoveries as bulk rock. The silica was purchased from Sibelco Australia as fine particles (P80 = 73 µm). Before each flotation test, a measured quantity of the chalcopyrite was ground to the targeted particle size distribution, mixed with silica to achieve the desired feed grade, and diluted with Brisbane tap water in a conditioning tank. The volume of water added was that required to achieve 40 wt% solids in the feed to all the tests. Sodium ethyl xanthate (2.0 g/ t) and Dowfroth 250 (14.7 ppm) were used as the collector and the frother, respectively. The flotation tests were operated continuously in a closed circuit by recycling the concentrate and tailing. A pictorial diagram of the experimental set-up is shown in Fig.1. More details of the experiments may be found in previously published work (Li et al., 2016a). After operating the system a sufficient period to achieve process stabilisation, froth rheology was measured, froth vision was recorded and metallurgical samples (feed, concentrate and tailing) were collected for assay (copper and silica). A ruler was then placed at the middle of the cell lip to measure the froth height above the lip as it discharged into the launder. The froth rheology measurement was conducted using a 6-blade vane (22 mm in diameter and 16 mm height) attached to an air-bearing rheometer (Anton Paar DSR301). A tube (74 mm in diameter and 150 mm height) was used to encircle the vane to eliminate the effect of the horizontal froth flow on the rheology measurement as previously discussed by the authors (Li et al., 2015). The vane was positioned in the middle of the cell with its upper edge immersed 2 cm into the froth. During the froth rheology measurement, the torque values were measured by increasing the vane speed from 1 rpm to 15 rpm in equal increments. A total of 5 torque values were measured in each test with a 5 s interval between each measurement. Each series of torque measurements were replicated five times for each test. The vane was only immersed in the froth for the period of the rheology measurements and then moved away to not impede the flotation froth movement. The measured raw data were torque value versus vane speed. The method to convert the raw data to the standard rheological terms (i.e. shear stress versus shear rate) has been developed and presented previously by the authors (Li et al., 2015). A digital video camera (Sony ACC-FV50B) was mounted above the flotation cell to record froth movement and the videos were analysed by a modified SmartFroth machine vision algorithm (Morar, 2010) to determine the froth discharge velocity at the cell launder lip. A single light source was mounted above the froth surface as this results in a single bright light on each bubble – a requirement of the froth analysis algorithm used in the analysis software. The froth velocity was used to calculate air recovery, which will be introduced in Section 4. There was also an attempt to calculate bubble burst rate, the volume of bursting
In previous work published by the authors, the effect of froth properties on froth rheology was investigated using the results of a Central Composite Rotatable Design (CCRD) test program (Li et al., 2016a; Li et al., 2016b). This program consisted of 33 flotation tests performed in a 20 litre flotation rig continuously fed by a synthetically created mixture of silica and chalcopyrite. Tests were performed at a range of different operating conditions while froth rheology, metallurgical samples and various froth parameters were measured. The natural extension of this work, is to use this information to also investigate the effect of froth rheology on the froth and flotation performance, the results of which are presented in this paper. At the end of this paper, a preliminary industrial study of froth rheology conducted in a platinum ore is described. The industrial result was used to validate some findings observed in the laboratory test work. 2. Experimental Table 1 shows the details of the 33 flotation tests that will be analysed in this paper. They involve varying both cell operational parameters (e.g. froth height, superficial gas velocity and impeller speed) as well as the feed properties with the objective of changing the properties of the flotation froth and thus its rheology. They were performed according to a CCRD experimental design which involves testing each variable at five different levels, as described in detail by Napier-Munn (2014). There are seven repeat tests at a central condition (i.e. Test 1, 9, 10, 12, 18, 19, and 26) and it has been shown that the froth rheology data produced from these tests was reasonably repeatable (Li et al., 2016a; Li et al., 2016b). The 33 flotation tests were performed in a bottom driven 20 L flotation cell with cross sectional dimensions of 30 by 30 cm. The flotation feed was a mixture of pure chalcopyrite and silica. The chalcopyrite was 5
Minerals Engineering 115 (2018) 4–12
C. Li et al.
Plastic
Bingham
100.9
Pseudo plastic
Yield stress
1 2 3 4 5 6 7 8 11 13 14 15 16 17 20 21 22 23 24 25 27 28 29 30 31 32 33
100.7
Newtonian
Dilatant Apparent viscosity (pa.s)
100.5
100.3
100.1
10-0.1
Shear rate 10-0.3
Fig. 2. Schematic diagram of shear rate as a function of shear stress for different types of fluid (after Mewis and Wagner, 2012).
10-0.5 10-0.8
bubbles at the froth surface per area per time as this is a measure of the physical changes occurring to the froth structure (Morar et al., 2012). The modified SmartFroth algorithm does this by tracking individual bubbles and counting the number of burst events that occur per set of froth images. However, it was found that extremely small values of bubble burst rate were determined, which were not consistent with the calculated air recovery values. The discrepancy may be due to the vision system not being able to accurately detect and therefore determine the bubble burst rate of very small bubbles. Hence, it was decided not to use the bubble burst rate as it was considered inaccurate. The absence of bubble burst rate in this work is unfortunate and hindered the investigation to a certain extent.
10-0.4
10-0.2
100
100.2
100.4
100.6
Shear rate (s-1) Fig. 3. Froth rheograms determined for each test (Li et al., 2016b).
froth was calculated to be less than 4 s−1 in all the tests (Li et al., 2016a), Fig. 3 only shows the froth rheograms for shear rate less than 4 s−1. Apparent viscosity changes significantly with shear rate, confirming that the flotation froths were shear thinning fluids. Eq. (1) shows that the shape of the modified froth rheogram is defined by the consistency index and the flow index. If the flow index can be considered constant, the variation of froth rheology in these tests can be represented by the differences in the consistency indices (μ). In order to validate this hypothesis, the authors (Li et al., 2016b) statistically analysed and proved that the flow index could be treated as a constant in this work, and the froth rheology could be evaluated by using only the consistency index. Therefore, in the following sections, the froth viscosity will be represented by the consistency index calculated for the froth of each test.
3. Characterisation of froth rheology Rheology is the science related to the deformation and flow of matter. The rheological behaviour of a substance is often presented as a plot of the shear stress against the shear rate (the ‘flow curve’ or ‘rheogram’) measured by a rheometer. Various types of rheogram are illustrated in Fig. 2. In general, a substance can exhibit either Newtonian or non-Newtonian behaviour, with the latter including dilatant, plastic, pseudo-plastic and Bingham behaviours. A Newtonian fluid exhibits a linear increase of the shear stress as a function of the shear rate. Two important rheological terms which are often associated with rheology studies are ‘yield stress’, which is the intercept of the flow curve on the shear stress axis at zero shear rate, and ‘apparent viscosity’, which is the slope of the line connecting the origin and a point on the flow curve at a particular shear rate. As shown in Fig. 2, the viscosity is constant throughout the entire shear rate range for Newtonian fluids. However, it changes as a function of shear rate for non-Newtonian fluids. Therefore, the viscosity of a non-Newtonian fluid at a specified point is referred to as ‘apparent viscosity’. The froth produced in the test program has been shown to exhibit shear-thinning behaviour with a minor yield stress (i.e. pseudo-plastic in nature) (Li et al., 2016a). Viscosity in a shear-thinning froth is dependent on the shear rate which changes throughout the froth which makes it difficult to directly correlate froth viscosity to froth performance indicators. To overcome this problem, the authors (Li et al., 2016b) have used a modification of the Herschel-Bulkley model to fit modified froth rheograms as shown in Eq. (1):
η = μ·γ ṅ − 1
10-0.6
4. Determination of flotation and froth performance indicators Flotation performance typically refers to flotation recovery and concentrate grade. The former is determined by froth and pulp recoveries. The latter is affected by pulp and froth conditions as well as feed grade. Pulp and froth recoveries as well as feed grade all are changing significantly as the operating variables of the system are varied in the different tests. Therefore, it would be difficult to study the direct effect of froth rheology on concentrate grade and flotation recovery. Instead, this study investigated the effects of rheology on other key flotation performance indicators. Given that there are only liberated chalcopyrite and silica particles in the flotation system, upgrading in the froth is achieved by maximising the drainage of entrained silica. Hence, the recovery of silica will be a measure of entrainment recovery which is known to significantly affect the final concentrate grade. It was therefore decided to investigate the effect of froth rheology on silica recovery. The silica recovery was calculated based on the mass flow rates of silica in the concentrate and tailings. Froth recovery is an ideal indicator of froth performance. However, it is difficult to measure as mentioned previously. As the valuable minerals are recovered by attachment to bubble surfaces, air recovery is used as an indicator for froth recovery in this study. Air recovery was calculated using Eq. (2) developed by Cilliers et al. (1998):
(1)
where η is the apparent viscosity (Pa ·s ) calculated at each shear rate value, μ is the consistency index (Pa ·sn ), γ̇ is the shear rate (s−1) and n is the flow index (dimensionless). The rheograms of apparent viscosity versus shear rate for all tests are plotted on a log-log scale as shown in Fig. 3. As shear rate in the
αa = 100· 6
Qoverflow Qin
1 vf ·L·hf ·εf = 100· · 2 Jg ·A
(2)
Minerals Engineering 115 (2018) 4–12
C. Li et al.
where αa is air recovery (%), Qoverflow is the volumetric flow rate of air overflowing the lip (ml/s), Qin is the volumetric flow rate of air added to the flotation cell (ml/s), vf is the froth discharging velocity at the lip (cm/s) which in this study was measured by analysing froth vision, L is the lip length (cm), hf is the height above the lip (cm), εf is the gas holdup in the overflowing froth which was calculated using Eq. (3) by assuming gas hold-up is constant in the froth (Li et al., 2016b), Jg is the superficial gas rate (cm/s) and A is the cross-sectional area of the cell (cm3). The term “1/2” accounts for the fact that the average discharge velocity of the froth is half of the discharge velocity at the surface (Cilliers et al., 1998).
εf = 100∗
QA Q A + Qcs
Table 2 Data used for the regression of froth height above the lip.
(3)
where QA is the volumetric flowrate of air added into the cell and QCS is the volumetric flowrate of slurry to the concentrate. Froth height above the lip determines the froth transportation volume and consequently affects the froth transportation velocity, which influences the froth retention time. Hence, the froth height above the lip can indirectly affect the flotation performance. Harris (2013) recognised that the height to which the froth rises above the launder lip will vary with froth properties and operating conditions, rather than being constant. The effect of froth rheology on froth height above the lip is also investigated in this study. 5. Results and discussions 5.1. Effect of froth rheology on froth height above the lip The froth height above the lip is expected to be determined by the froth properties as well as the flotation operating conditions. In a situation where a variable is being affected by multiple variables, regression analysis is the best method for determining whether an influencing parameter is of significance. The flotation operating condition which was changed in the test program and would be expected to affect froth height above the lip is superficial gas velocity. The greater the volume of gas moving through the transportation zone of a froth (i.e. that above the lip), the greater the tendency for the froth to rise before it overflows into the launder. The froth properties that are expected to affect froth height significantly are froth rheology and bubble burst rate (Harris, 2013). Froth rheology is providing a resistance to flow whereas bubble burst rate affects the amount of gas moving through the froth volume as it is a measure of how much gas is escaping at the froth surface. As outlined in Section 2, bubble burst rate was not able to be measured in the experimental program. Hence, the froth height above the lip was regressed only against the froth consistency index and the superficial gas velocity using the data shown in Table 2. Minitab 17 was used to perform the regression analysis. The resulting model is shown in Eq. (4):
hf = −2.61 + 2.77Jg + 2.79μ−0.75J2g−0.74μ2 + 0.003Jg ·μ
R2 = 0.68
Test order
Superficial gas velocity (cm s−1)
Consistency index (Pa ·sn )
Froth height above lip (cm)
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33
1.4 1.0 1.8 1.8 1.0 1.8 1.0 1.8 1.4 1.4 1.8 1.4 1.0 1.8 1.0 1.8 1.8 1.4 1.4 1.0 1.0 1.0 1.4 1.4 0.6 1.4 1.4 1.4 1.4 2.2 1.4 1.4 1.4
1.43 1.97 1.72 1.80 1.00 1.98 1.40 1.06 1.33 1.35 1.32 1.20 1.71 1.09 1.71 1.20 1.26 1.43 1.45 1.54 1.72 0.63 0.56 1.01 1.61 1.22 0.96 1.58 1.34 1.37 1.26 0.85 1.55
2.3 2.4 2.8 2.5 1.4 2.2 1.9 2.1 2.0 2.0 1.9 1.9 2.1 2.3 1.8 2.1 2.6 2.0 2.1 1.8 2.9 1.3 0.8 2.1 1.2 2.3 1.9 3.1 2.1 2.5 2.2 1.5 2.9
that the missing predictor in the regression is bubble burst rate. This may explain why the correlation coefficient (R2) is only 0.68. The regression result may have been significantly improved (with a higher R2) if bubble burst rate had been able to be included in the regression. The model presented above was not developed with the intention of predicting froth performance, but rather to investigate how various operational variables and the froth rheology affect the flotation performance. This is also the aim of the models presented in the following sections. Minitab 17 was used to calculate the significance of the linear, quadratic and interaction effects of each factor on the froth height above the lip, as shown in Table 3. Conventionally a factor is considered to be statistically significant if its P-value ≤ .05. Table 3 shows that the consistency index significantly affects the froth height above the lip in a linear way, with a P-value of .001. The P-value of its square term ( μ2 ) which indicates curvature is .059, which is barely significant. The superficial gas velocity also significantly affects the froth height above the lip in a non-linear way, with a P-value of .002. The P-value of its square term (Jg2) is .043. The interaction between the froth rheology and the superficial gas velocity on the froth height above the lip is not a concern as the P-value is .995. Fig. 4 shows the surface plot of froth height
(4)
where hf is the froth height above lip (cm), Jg is the superficial gas velocity (cm s−1) and μ is the consistency index (Pa ·sn ). Eq. (4) is a conventional response surface model with linear, quadratic and cross-product terms (Napier-Munn, 2014). The standard error of the model which is a measure of the prediction uncertainty is 0.30. As discussed above, there are seven repeat tests in the CCRD program and these repeat tests were used to calculate the standard error of the froth height above the lip as a consequence of experimental error. This calculated experimental standard error is 0.16. Thus, the model error is almost double the experimental error, which indicates that the model is deficient in predicting the froth height above the lip owing to a missing predictor (s). As bubble burst rate is also expected to have a significant effect on the froth height above the lip in flotation, it is likely
Table 3 Significance of variables in predicting the froth height above the lip. Terms
P-value
μ
.001 .059
μ2 Jg Jg2 μ * Jg
7
.002 .043 .995
Minerals Engineering 115 (2018) 4–12
C. Li et al.
Fig. 4. Surface plot of froth height above the lip versus superficial gas velocity and consistency index.
Froth height above lip (cm)
Superficial gas velocity (cm/s) Consistency index (Pa s )
Based on the discussion above, air recovery in the flotation tests is expected to be a function of superficial gas velocity, froth rheology and bubble burst rate. In the absence of any bubble burst rate data, a regression model for air recovery was developed as a function of superficial gas velocity and the froth rheology. The data used for the regression of air recovery is summarised in Table 4. The resulting model is given in Eq. (6).
above the lip versus superficial gas velocity and consistency index. Fig. 4 shows that the froth height above the lip increases as the froth becomes more viscous or with an increase in superficial gas rate. Harris (2013) proposed that the equilibrium height at which the cell operates will be the point at which the energy of the system is minimised; the energy components consist of the kinetic energy of the concentrate discharge (Ek ), the gravitational energy of the froth zone above the concentrate launder level (Eg ), and the resistance to flow (Eμ ) which is defined by the froth rheology. Harris (2013) developed a model to predict the froth height above the lip which incorporated froth rheology effects. As this model has not yet been released publically, and is subject to an IP confidentiality agreement, no additional model details can be presented here. The general structure of the model, representing the energy balance between the three energy components, is shown in Eq. (5).
Ek = Eg−Eμ
αa = −34.0 + 31.87Jg + 32.96μ−11.57Jg 2−10.62μ2 + 0.91μ·Jg
R2 = 0.77 (6)
where αa is the air recovery (%), Jg is the superficial gas velocity (cm/s) and μ is the consistency index (Pa ·sn ). Similar to Eq. (4), Eq. (6) is a conventional response surface model with linear, quadratic and cross-product terms (Napier-Munn, 2014). The standard error of the model is 1.88 while the experimental error
(5) Table 4 Data used for the regression of air recovery.
When the froth does not exhibit a significant yield stress, like the froth in this study, the energy required to overcome the flow resistance is directly proportional to the froth viscosity. As the froth becomes more viscous, the energy required to overcome the flow resistance increases. As a result, the froth above the concentrate lip increases in height to the level at which the resistance to flow is overcome by the increased gravitational energy and the resulting kinetic energy of the froth discharge. This potentially provides more residence time in the froth for froth drainage but also more time for bubble coalescence which will affect air and silica recoveries. The extent to which this occurs will be evaluated in the following sections. 5.2. Effect of froth rheology on air recovery Air recovery is expected to be correlated to the froth retention time above the lip and bubble burst rate. Zheng et al. (2004) divided the froth into two zones: the froth below and above the discharging lip. The froth below the lip rises vertically whereas the froth above the lip moves horizontally, prior to discharging over the launder lip. The loss of air only occurs at the froth surface while no air is lost as the air moves through the transportation zone below the lip. Froth retention time above the lip is expected to be affected by the superficial gas velocity, bubble burst rate and froth viscosity. Superficial gas velocity provides the driving force for froth movement, and consequently significantly influences froth retention time. In addition, the bubbles bursting at the froth surface drag neighbouring bubbles to fill their vacuum and, therefore, slow the froth velocity towards the lip and increase froth retention time. Froth viscosity is a measure of the resistance to froth flow which results in a greater froth height above the lip (as discussed in Section 5.1) which increases the volume through which the gas must flow prior to discharge and consequently results in longer froth retention times. 8
Test order
Superficial gas velocity (cm s−1)
Consistency index (Pa ·sn )
Air recovery (%)
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33
1.4 1.0 1.8 1.8 1.0 1.8 1.0 1.8 1.4 1.4 1.8 1.4 1.0 1.8 1.0 1.8 1.8 1.4 1.4 1.0 1.0 1.0 1.4 1.4 0.6 1.4 1.4 1.4 1.4 2.2 1.4 1.4 1.4
c 1.97 1.72 1.80 1.00 1.98 1.40 1.06 1.33 1.35 1.32 1.20 1.71 1.09 1.71 1.20 1.26 1.43 1.45 1.54 1.72 0.63 0.56 1.01 1.61 1.22 0.96 1.58 1.34 1.37 1.26 0.85 1.55
14.44 11.98 12.11 11.14 8.79 10.45 12.15 10.63 12.47 12.13 8.72 12.22 13.16 11.12 10.93 10.09 10.44 13.57 14.65 5.88 14.24 4.60 2.77 14.78 5.07 15.53 12.92 19.93 13.75 12.12 15.05 8.19 17.30
Minerals Engineering 115 (2018) 4–12
C. Li et al.
properties change and result in higher viscosity and therefore hindered froth movement, these effects outweigh any decrease in bubble burst rate that may result. Froth rheology has therefore been shown to significantly affect air recovery (which is expected to be closely related to froth recovery), and it is therefore speculated that froth rheology can also significantly affect froth recovery. It is recommended that this be verified when a reliable approach to measure froth recovery is developed in future. More importantly, a peak air recovery with consistency index is observed in Fig. 5. Peak air recovery is desirable in terms of flotation cell control as the optimal flotation performance (i.e. mineral recovery and concentrate grade) has been observed at the peak air recovery (Hadler and Cilliers, 2009; Hadler et al., 2010; Shean et al., 2017). Hence, it should be recognised that it is important to take into account froth rheology in the flotation bank control strategy as it clearly affects the magnitude of the air recovery at the peak air rate condition. It also has a marginal effect on the value of the optimal air rate.
Table 5 Significance of variables in predicting the air recovery. Terms
P-value
μ
.001 .001
μ2 Jg Jg2 μ* Jg
.605 .001 .792
calculated from the seven repeat tests is 1.35; i.e. the prediction uncertainty of the model is greater than the experimental error. Again, it implies that the regression data is not fully sufficient to predict air recovery and probably some important variable(s) is missing. It is still expected that the important missing variable in the regression is bubble burst rate. The regression result might be improved if bubble burst rate were to be taken into account. The significance of the terms in the model used to predict air recovery is presented in Table 5. Table 5 shows that the froth rheology and the superficial gas velocity have significant non-linear effects on air recovery with the P-values of both square terms being .001. The interaction between the froth rheology and the superficial gas velocity on the froth height above the lip is not a concern as the P-value is .792. Fig. 5 shows the surface plot of air recovery versus superficial gas velocity and consistency index. Fig. 5 shows that when the consistency index is low, air recovery increases as the froth becomes more viscous (i.e. as the consistency index increases) but when at higher froth viscosities the opposite is observed. This type of relationship is an indication that competing mechanisms are involved. As demonstrated in previous work by the authors (Li et al., 2016b), smaller bubble size and greater particle surface coverage on a bubble will result in greater froth viscosity but these conditions are those which will also decrease bubble burst rate (Ali et al., 2000). In other words, the consistency index may be negatively correlated with bubble burst rate. As discussed above, increasing froth viscosity is expected to increase froth retention times above the lip by resisting froth motion, while a decrease in bubble burst rate should enhance froth transportation and decrease froth retention time. These two effects oppose each other. The resulting froth performance (as measured by the air recovery) depends on which effect dominates the froth transportation process. Fig.5 implies that in this study the variation of air recovery was dominated by bubble burst rate at low froth viscosity, and by froth rheology at high froth viscosity. At low froth viscosity, changes in the froth which result in less bursting of bubbles outweigh any adverse effects associated with higher viscosity. However, at high froth viscosity, as the froth
5.3. Effect of froth rheology on silica recovery Silica recovery is also expected to be affected by froth rheology because of its effect on froth retention time. In addition to froth rheology, other parameters that affect water recovery should also be taken into account to model silica recovery. It has been found previously that the amount of gangue entrained is proportional to the water recovery (Neethling and Cilliers, 2009; Zheng et al., 2006). Silica recovery will be a function of the amount of silica entering the froth phase and the amount of silica draining back to the pulp. The former can be significantly influenced by superficial gas velocity as it has been experimentally found that superficial gas velocity affects the amount of water entering the froth zone (Neethling and Cilliers, 2009; Zheng et al., 2006). In addition, turbulence also influences the amount of entrained particles entering the froth phase by affecting the turbulence in the pulp phase and subsequent suspension of solids into the upper pulp zone just below the froth-pulp interface (Wang et al., 2016b). Turbulence is mainly determined by the impeller speed. Superficial gas velocity and impeller speed were varied systematically in the CCRD program (Table 1). Hence, the two parameters were taken into account in the regression process. Froth retention time determines the drainage of silica from the froth phase. Froth depth affects the froth retention time and the amount of water reporting to the concentrate (Vazirizadeh et al., 2014). The froth retention time below the concentrate lip is determined by the superficial gas velocity and the froth depth (Zheng et al., 2004) while the froth retention time above the lip (as discussed in Section 5.2) is likely determined by the superficial gas velocity, the bubble burst rate and the froth height above the lip. Froth height above the lip has been shown to Fig. 5. Surface plot of air recovery versus superficial gas velocity and consistency index.
9
Minerals Engineering 115 (2018) 4–12
C. Li et al.
Table 6 Data used for the regression of silica recovery.
Table 7 Significance of variables in predicting the silica recovery.
Test order
Superficial gas velocity (cm s−1)
Impeller speed (rpm)
Froth depth (cm)
Consistency index (Pa ·sn )
Silica recovery (%)
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33
1.4 1.0 1.8 1.8 1.0 1.8 1.0 1.8 1.4 1.4 1.8 1.4 1.0 1.8 1.0 1.8 1.8 1.4 1.4 1.0 1.0 1.0 1.4 1.4 0.6 1.4 1.4 1.4 1.4 2.2 1.4 1.4 1.4
900 750 1050 750 750 750 1050 1050 900 900 750 900 1050 1050 750 750 1050 900 900 750 1050 1050 900 900 900 900 1200 900 600 900 900 900 900
7 6 6 8 6 6 6 6 7 7 8 7 8 8 8 6 8 7 7 8 8 6 7 5 7 7 7 7 7 7 9 7 7
1.43 1.97 1.72 1.8 1 1.98 1.4 1.06 1.33 1.35 1.32 1.2 1.71 1.09 1.71 1.2 1.26 1.43 1.45 1.54 1.72 0.63 0.56 1.01 1.61 1.22 0.96 1.58 1.34 1.37 1.26 0.85 1.55
28.0 12.4 40.8 20.1 21.5 30.3 24.6 29.3 25.7 32.4 29.2 30.6 21.7 20.4 17.1 15.0 7.7 32.2 34.6 3.3 6.3 4.5 8.4 35.4 7.5 33.4 31.0 28.0 19.8 35.0 20.7 16.0 22.3
= 0.79
P-value
Hf Jg
.001 .001
IS μ Jg 2
.100 .002 .022
2
.001
μ
the consistency index all have a statistically significant effect on the silica recovery, while the impeller speed does not. In addition, the superficial gas velocity and the consistency index have non-linear correlations with the silica recovery, with the P-values of their square terms being .022 and .001, respectively. No significant interaction effects between the factors on silica recovery are observed. Fig. 6 shows the surface plot of silica recovery versus consistency index and superficial gas velocity at the mean value of froth depth and impeller speed. Similar to the correlation between air recovery and consistency index shown in Fig.5, Fig.6 shows that at low froth viscosity the silica recovery increases as the froth becomes more viscous (increasing consistency index) while the opposite is observed at high froth viscosity. Silica recovery is determined by drainage, which in turn depends on the time that particles stay in the froth (Wang et al., 2016a). It is expected that increasing froth viscosity would slow down the froth transportation and increase the froth retention time. However, as mentioned above, bubble burst rate also decreases when the froth becomes more viscous and this speeds up the froth transportation process. A froth with a lower bubble burst rate will also be associated with smaller bubble sizes and longer plateau border lengths which is known to impede liquid drainage (Wang et al., 2016a) and therefore increase silica recovery. Hence, it is deduced that in this study, at low froth viscosity the variation of silica recovery was dominated by the bubble burst rate effects, thereby increasing silica recovery. At high froth viscosity, the effects of higher froth viscosity outweighed the effects caused by reduced bubble burst rate, and consequently froth retention time increased with increasing froth viscosity, thereby decreasing silica recovery.
be correlated with froth rheology and superficial gas velocity (Fig. 4). Hence, a multi-regression analysis for silica recovery was performed as a function of the superficial gas velocity, the impeller speed, the froth depth and the froth rheology. The data used for the regression of silica recovery are shown in Table 6. As a large number of terms were present in the response surface regression model, a stepwise procedure was used to remove the insignificant terms in the prediction of silica recovery. Stepwise regression is an approach to selecting a subset of effects for a regression model based on the significance of the coefficients for each term in the model. The Fcriterion for entering a term in the model or removing a term from the model was set at 0.15. The resulting model is shown in Eq. (7).
Rs = −61.6−5.21Hf + 58.2Jg + 0.01IS + 87.7μ−14.78Jg2−30.54μ2
Terms
5.4. Industrial measurement The opportunity was taken to carry out a preliminary study of froth rheology in a platinum plant in South Africa, using the same rheometer (Anton Paar DSR 301) which was used to perform the froth rheology measurement in the CCRD tests in the laboratory. The flotation circuit of the plant consisted of rougher, scavenger, primary cleaner and secondary cleaner sections. The measurements were performed in the third and fifth rougher cells and the first primary cleaner cell. The rheometer head was fixed on a holder which was attached to the handrail and the rheometer head was moved vertically to adjust the position of the vane in the froth, based on the froth height. The set-up of the rheometer is shown in Fig.7. During each froth rheology measurement in each flotation cell, four or five torque values were acquired at different vane speeds. The vane speed and torque values were converted to shear rate and shear stress using the method developed by the authors (Li et al., 2015). The rheograms of the flotation froths in the three flotation cells are shown in Fig.8. Each flow curve was fitted to the power-law model (Eq. (1)). The following conclusions can be drawn from Fig.8:
R2 (7)
where Rs is the silica recovery (%), Hf is the froth depth (cm), IS is the impeller speed (rpm), Jg is the superficial gas velocity (cm s−1) and μ is the consistency index (Pa ·sn ). As mentioned before, this is the conventional response surface model with linear, quadratic and cross-product terms generated to explore the effects of the variables on silica recovery. The standard error of the model is 5.11 while the experimental error calculated from the seven repeat tests is 3.15. Again, the prediction uncertainty of the model is much greater than the experimental error, which implies that the regression data is not fully sufficient to predict silica recovery and that some important variable(s) is probably missing. It is still expected that the important missing variable in the regression is bubble burst rate. The regression result might be improved with a high R2 if bubble burst rate were to be taken into account. The significant terms influencing silica recovery are shown in Table 7. Table 7 shows that the froth height, the superficial gas velocity and
I. The platinum ore froth exhibited non-Newtonian flow characteristics similar to those observed in the laboratory work using the synthetic copper ore. The froth appeared to be shear-thinning with minimal yield stress, which is in agreement with the flow behaviour of the froth generated in the laboratory. 10
Minerals Engineering 115 (2018) 4–12
C. Li et al.
Fig. 6. Surface plot of silica recovery versus consistency index and superficial gas velocity.
Silica recovery (%)
Superficial gas velocity (cm/s) Consistency index (P s )
II. The effect of froth rheology on the froth height above the lip followed the same trend as that found in the laboratory work. To compare the froth in the different cells on the basis of apparent viscosity, Fig. 7 shows that the froth flow curve of the third rougher cell is above that of the fifth. The flow curve of the first primary cleaner is below the other two. In other words, the froth in the third rougher cell has the highest viscosity, followed by the fifth rougher cell and then the first primary cleaner cell. Table 8 shows the froth height above the lip measured in each of the three flotation cells. Each froth height was measured three times at different positions along the concentrate lip. A t-test was performed using these repeat values to evaluate whether the froth heights measured for the three cells can be considered statistically different. It was found that the froth height of the third rougher is statistically lower than that of the fifth rougher cell with 95.5% confidence; and the froth height of the fifth rougher cell is lower than that of the first primary cleaner cell with 99.99 confidence. Hence, the average of the measured froth heights decreased from the third rougher to the fifth rougher, and then to the first primary cleaner. The froth height above the lip is positively correlated with froth viscosity, which agrees with the finding of the laboratory work (as shown in Fig. 4).
Fig. 7. Set-up of the Anton Paar DSR 301 rheometer in an industrial cell.
16 y = 22.30x0.51 R² = 0.999
14
Shear stress (Pa)
12
y = 16.43x0.46 R² = 0.995
10 8
5th rougher
y = 15.94x0.50 R² = 0.999
6
The effect of froth rheology on the froth cleaning action was not investigated in the industrial study, as the ore consisted mainly of complex clay minerals. The minerals attached to the bubble surfaces were dominated by various hydrophobic clay minerals (e.g. floatable talc) rather than the valuable minerals. Hence, the variation of froth rheology did not necessarily affect the upgrading of the valuable minerals.
3rd rougher
1st primary cleaner
4 2 0 0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
6. Conclusions
Shear rate (s-1) Fig. 8. Rheograms of flotation froth acquired in three flotation cells in a platinum concentrator.
The effects of froth rheology on froth and flotation performance were studied in this work. The froth rheology was positively related to the froth height above the lip, which in turn was determined by the equilibrium of energy in the froth. The froth height above the lip provides the potential energy to overcome the flow resistance (i.e. froth viscosity) and the kinetic energy for froth flow. When the froth becomes more viscous, the froth height increases to generate more potential energy to overcome the resistance. The effects of froth rheology on air recovery and silica recovery were also investigated in this work. It was found that air recovery was significantly affected by froth rheology; at low froth viscosity, air recovery increased upon increasing consistency index while the opposite was found at high froth viscosity. As the valuable minerals are recovered by attachment to bubble surfaces, it is expected that froth rheology also has a significant impact on froth recovery. A similar
Table 8 Froth heights above the lip in the three flotation cells. Cell Position
3rd rougher (mm)
5 th rougher (mm)
1 st cleaner (mm)
1 2 3 Mean STDEV
104 108 107 106 2.08
103 104 99 102 2.65
65 65 70 67 2.89
11
Minerals Engineering 115 (2018) 4–12
C. Li et al.
Leiva, J., Vinnett, L., Yianatos, J., 2012. Estimation of air recovery by measuring froth transport over the lip in a bi-dimensional flotation cell. Miner. Eng. 36–38, 303–308. Li, C., Farrokhpay, S., Runge, K., Shi, F.N., 2016a. Determining the significance of flotation variables on froth rheology using a central composite rotatable design. Powder Technol. 287, 216–225. Li, C., Farrokhpay, S., Shi, F., Runge, K., 2015. A novel approach to measure froth rheology in flotation. Miner. Eng. 71, 89–96. Li, C., Runge, K., Shi, F.N., Farrokhpay, S., 2016b. Effect of flotation froth properties on froth rheology. Powder Technol. 294, 55–65. Mathe, Z.T., Harris, M., C., O'Connor, C.T, 2000. A review of methods to model the froth phase in non-steady state flotation systems. Miner. Eng. 13, 127–140. Mewis, J., Wagner, N.J., 2012. Colloidal Suspension Rheology. Cambridge University Press, Cambridge, New York. Morar, S.H., 2010. The Use of Machine Vision to Describe and Evaluate Froth Phase Behaviour and Performance in Mineral Flotation Systems, University of Cape Town. Morar, S.H., Bradshaw, D.J., Harris, M.C., 2012. The use of the froth surface lamellae burst rate as a flotation froth stability measurement. Miner. Eng. 36–38, 152–159. Moys, M.H., 1978. A study of a plug-flow model for flotation froth behaviour. Int. J. Miner. Process. 5, 21–38. Napier-Munn, T.J., 2014. Statistical methods for mineral engineers-how to design experiments and analyse data, second ed. Julius Kruttschnitt Mineral Research Centre, Brisbane, Australia. Neethling, S.J., Cilliers, J.J., 2008. Predicting air recovery in flotation cells. Miner. Eng. 21, 937–943. Neethling, S.J., Cilliers, J.J., 2009. The entrainment factor in froth flotation: Model for particle size and other operating parameter effects. Int. J. Miner. Process. 93, 141–148. Runge, K., Crosbie, R., Rivett, T., MaMaster, J., 2010. An evaluation of froth recovery measurement techniques, XXV International Mineral Processing Congress (IMPC) 2010. Brisbane, Australia. Schuhmann, R., 1942. Flotation Kinetics I. Methods for steady-state study of flotation problems. J. Phys. Chem. 46, 891–902. Shean, B., Hadler, K., Cilliers, J.J., 2017. A flotation control system to optimise performance using peak air recovery. Chem. Eng. Res. Des. 117, 57–65. Shi, F.N., Zheng, X.F., 2003. The rheology of flotation froths. Int. J. Miner. Process. 69, 115–128. Subrahmanyam, T.V., Forssberg, E., 1988. Froth stability, particle entrainment and drainage in flotation – a review. Int. J. Miner. Process. 23, 33–53. Vazirizadeh, A., Bouchard, J., Del Villar, R., 2014. The effect of gas dispersion properties on water recovery in flotation columns, IMPC 2014–27th International Mineral Processing Congress. Santiago, Chine. Wang, J., Nguyen, A.V., Farrokhpay, S., 2016a. A critical review of the growth, drainage and collapse of foams. Adv. Coll. Interface. Sci. 228, 55–70. Wang, L., Runge, K., Peng, Y., 2016b. The observed effect of flotation operating conditions and particle properties on water recovery at laboratory scale. Miner. Eng. 94, 83–93. Yianatos, J., Finch, J.A., Laplante, A.R., 1988. Selectivity in column flotation froths. Int. J. Miner. Process. 23, 279–292. Zheng, X., Franzidis, J.P., Manlapig, E., 2004. Modelling of froth transportation in industrial flotation cells: Part I. Development of froth transportation models for attached particles. Miner. Eng. 17, 981–988. Zheng, X., Johnson, N.W., Franzidis, J.P., 2006. Modelling of entrainment in industrial flotation cells: water recovery and degree of entrainment. Miner. Eng. 19, 1191–1203.
correlation between froth viscosity and silica recovery was also observed. A preliminary industrial study of froth rheology was performed for a platinum ore. It was found that the froth exhibited similar rheological characteristics to the froth generated in the laboratory work using a synthetic copper ore. Both of the froths have a shear-thinning nature with minor yield stress. The industrial data supported the correlation between froth viscosity and the froth height above the lip observed from the laboratory work. The interactions between froth rheology and bubble burst rate in a froth phase are still poorly understood. It is recommended that the correlation between froth rheology and bubble burst rate be further investigated with a view to improving the understanding of the effect of froth rheology on froth and flotation performance. Acknowledgments The authors would like to thank the AMIRA P9P (013908) sponsors for the project funding. The authors also gratefully acknowledge the valuable help provided by Professor Tim Napier-Munn of the JKMRC who assisted with the statistical analysis of the results, Dr Sam Morar for analysing the froth images produced in this work., Mr. Stefan Geldenhuys and Dr. Belinda McFadzean from the University of Cape Town for organising the survey in South Africa and providing assistance in setting up the survey device. References Ali, S.A., Gauglitz, P.A., Rossen, W.R., 2000. Stability of solids-coated liquid layers between bubbles. Ind. Eng. Chem. Res. 39, 2742–2745. Cilliers, J.J., Asplin, R.A., Woodburn, E.T., 1998. Kinetic flotation modelling using froth imaging data. In: Laskowski, J.A., Woodburn, E.T. (Eds.), Frothing in Flotation II. Gordon and Breach Science Publishers, The Netherlands. Feteris, S.M., Frew, J.A., Jowett, A., 1987. Modelling the effect of froth depth in flotation. Int. J. Miner. Process. 20, 121–135. Finch, J.A., Dobby, G.S., 1990. Column Flotation. Pergamon Press, London, UK. Franzidis, J.P., Harris, M.C., 2010. Froth recovery factor – What is it and why is it so difficult to measure? Can. Metall. Q. 49, 337–344. 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. Hadler, K., Cilliers, J.J., 2009. The relationship between the peak in air recovery and flotation bank performance. Miner. Eng. 22, 451–455. Hadler, K., Smith, C.D., Cilliers, J.J., 2010. Recovery vs. mass pull: the link to air recovery. Miner. Eng. 23, 994–1002. Harris, M.C., 2013. Modelling the Froth Transport Zone in a Flotation Cell. AMIRA P9P Discussion Document (unpublished).
12
Contents lists available at ScienceDirect
Minerals Engineering journal homepage: www.elsevier.com/locate/mineng
Effect of froth rheology on froth and flotation performance ⁎
MARK
Chao Li , Kym Runge, Fengnian Shi, Saeed Farrokhpay Julius Kruttschnitt Mineral Research Centre, Sustainable Minerals Institute, University of Queensland, 40 Isles Road, Indooroopilly, 4068 QLD, Australia
A R T I C L E I N F O
A B S T R A C T
Keywords: Froth rheology Consistency index Froth performance Flotation performance
It has been suspected for some time that froth rheology has an impact on froth and flotation performance but little experimental work has been performed to investigate these effects. In this paper, the effect of froth rheology on froth and flotation performance was investigated by performing flotation tests in a 20 L continuous flotation cell using a synthetic ore which was a mixture of pure chalcopyrite and silica. Froth rheology was measured during these tests along with key flotation performance indicators: froth height above the lip, air recovery and silica recovery. It was found that froth rheology was positively correlated to froth height above the lip. Air recovery was also correlated to froth rheology; at low froth viscosity, air recovery increased upon increasing consistency index (a measure of the viscosity of a fluid) while the opposite was found at high froth viscosity. A similar correlation between froth viscosity and silica recovery was also observed. Measurements of froth rheology were also performed in industrial scale flotation cells processing a platinum ore. The investigated industrial scale froth exhibited similar rheological characteristics to that observed in the laboratory work. Both of the froths have a shear-thinning nature with minor yield stress. Froth height above the lip was also found to be positively correlated with froth viscosity, which supports the conclusions drawn from the laboratory work.
1. Introduction Froth flotation consists of pulp and froth phases. The function of the froth phase is to enhance the overall selectivity and recovery of the flotation process. The froth achieves these by reducing the recovery of entrained material to the concentrate stream, while preferentially retaining the attached material. This increases the concentrate grade whilst limiting as far as possible the reduction in recovery of valuables. The importance of the cleaning and recovering actions of the froth in flotation has been well recognised (Feteris et al., 1987; Moys, 1978; Schuhmann, 1942; Subrahmanyam and Forssberg, 1988; Yianatos et al., 1988). The froth efficiency which can be represented by the selectivity and recovery of the process is influenced by froth retention time. A greater froth retention time results in a greater probability of drainage of the water and entrained solids back from the froth phase to the pulp phase through the Plateau borders and vertices within the froth (Wang et al., 2016a). Froth recovery, the fraction of valuable mineral entering the froth phase attached to air bubbles that reports to the concentrate (Finch and Dobby, 1990), is the most commonly used measure of how effectively the froth recovers the valuable mineral. Previous work (Gorain et al., 1998; Mathe et al., 2000) has indicated that froth recovery decreases exponentially with an increase in froth retention time.
⁎
A higher froth retention time results in an increased probability of froth collapse as well as valuable particle drop-back due to detachment and drainage. However, it is difficult to measure froth recovery (Franzidis and Harris, 2010; Runge et al., 2010). Air recovery, the volume fraction of air that is added to the cell which survives and reports to the concentrate, has been used as a measure of froth stability (Hadler et al., 2010; Leiva et al., 2012; Neethling and Cilliers, 2008; Shean et al., 2017). It has been reported that both higher grade and recovery are obtained at the peak air recovery (Hadler and Cilliers, 2009; Hadler et al., 2010; Shean et al., 2017). The valuable minerals are transported from the pulp-froth interface to the launder by attachment to air bubbles in the froth phase. The more air is recovered to the launder, the more valuable minerals are recovered to be concentrate. Hence, froth recovery is likely to be positively correlated with air recovery. It is expected that froth rheology can influence froth and flotation performance through its effect on froth retention time. A more viscous froth resists motion towards the lip, increasing the time the froth remains in the flotation cell. Very little work has been performed to investigate the effect of froth rheology on froth and flotation performance other than the work of Shi and Zheng (2003) who showed that froth rheology had a strong correlation with concentrate grade in an Outokumpu 3-m3 tank cell operated at the Mt Isa Mines (MIM) Copper Concentrator.
Corresponding author. E-mail address: [email protected] (C. Li).
http://dx.doi.org/10.1016/j.mineng.2017.10.003 Received 28 August 2016; Received in revised form 28 September 2017; Accepted 4 October 2017 0892-6875/ © 2017 Elsevier Ltd. All rights reserved.
Minerals Engineering 115 (2018) 4–12
C. Li et al.
Table 1 The conditions in the CCRD flotation tests (Li et al., 2016a). Test
Froth height (cm)
Superficial gas velocity (cm s−1)
Impeller speed (rpm)
Chalcopyrite particle size P80 (µm)
Copper grade (%)
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33
7 6 6 8 6 6 6 6 7 7 8 7 8 8 8 6 8 7 7 8 8 6 7 5 7 7 7 7 7 7 9 7 7
1.4 1.0 1.8 1.8 1.0 1.8 1.0 1.8 1.4 1.4 1.8 1.4 1.0 1.8 1.0 1.8 1.8 1.4 1.4 1.0 1.0 1.0 1.4 1.4 0.6 1.4 1.4 1.4 1.4 2.2 1.4 1.4 1.4
900 750 1050 750 750 750 1050 1050 900 900 750 900 1050 1050 750 750 1050 900 900 750 1050 1050 900 900 900 900 1200 900 600 900 900 900 900
80 50 50 50 110 50 50 110 80 80 110 80 110 110 110 110 50 80 80 50 50 110 140 80 80 80 80 80 80 80 80 80 20
1.0 1.4 1.4 1.4 0.6 0.6 0.6 0.6 1.0 1.0 0.6 1.0 0.6 1.4 1.4 1.4 0.6 1.0 1.0 0.6 1.4 1.4 1.0 1.0 1.0 1.0 1.0 1.8 1.0 1.0 1.0 0.2 1.0
Fig. 1. A pictorial diagram of the experimental set up (Li et al., 2016a).
purchased from Geo Discoveries as bulk rock. The silica was purchased from Sibelco Australia as fine particles (P80 = 73 µm). Before each flotation test, a measured quantity of the chalcopyrite was ground to the targeted particle size distribution, mixed with silica to achieve the desired feed grade, and diluted with Brisbane tap water in a conditioning tank. The volume of water added was that required to achieve 40 wt% solids in the feed to all the tests. Sodium ethyl xanthate (2.0 g/ t) and Dowfroth 250 (14.7 ppm) were used as the collector and the frother, respectively. The flotation tests were operated continuously in a closed circuit by recycling the concentrate and tailing. A pictorial diagram of the experimental set-up is shown in Fig.1. More details of the experiments may be found in previously published work (Li et al., 2016a). After operating the system a sufficient period to achieve process stabilisation, froth rheology was measured, froth vision was recorded and metallurgical samples (feed, concentrate and tailing) were collected for assay (copper and silica). A ruler was then placed at the middle of the cell lip to measure the froth height above the lip as it discharged into the launder. The froth rheology measurement was conducted using a 6-blade vane (22 mm in diameter and 16 mm height) attached to an air-bearing rheometer (Anton Paar DSR301). A tube (74 mm in diameter and 150 mm height) was used to encircle the vane to eliminate the effect of the horizontal froth flow on the rheology measurement as previously discussed by the authors (Li et al., 2015). The vane was positioned in the middle of the cell with its upper edge immersed 2 cm into the froth. During the froth rheology measurement, the torque values were measured by increasing the vane speed from 1 rpm to 15 rpm in equal increments. A total of 5 torque values were measured in each test with a 5 s interval between each measurement. Each series of torque measurements were replicated five times for each test. The vane was only immersed in the froth for the period of the rheology measurements and then moved away to not impede the flotation froth movement. The measured raw data were torque value versus vane speed. The method to convert the raw data to the standard rheological terms (i.e. shear stress versus shear rate) has been developed and presented previously by the authors (Li et al., 2015). A digital video camera (Sony ACC-FV50B) was mounted above the flotation cell to record froth movement and the videos were analysed by a modified SmartFroth machine vision algorithm (Morar, 2010) to determine the froth discharge velocity at the cell launder lip. A single light source was mounted above the froth surface as this results in a single bright light on each bubble – a requirement of the froth analysis algorithm used in the analysis software. The froth velocity was used to calculate air recovery, which will be introduced in Section 4. There was also an attempt to calculate bubble burst rate, the volume of bursting
In previous work published by the authors, the effect of froth properties on froth rheology was investigated using the results of a Central Composite Rotatable Design (CCRD) test program (Li et al., 2016a; Li et al., 2016b). This program consisted of 33 flotation tests performed in a 20 litre flotation rig continuously fed by a synthetically created mixture of silica and chalcopyrite. Tests were performed at a range of different operating conditions while froth rheology, metallurgical samples and various froth parameters were measured. The natural extension of this work, is to use this information to also investigate the effect of froth rheology on the froth and flotation performance, the results of which are presented in this paper. At the end of this paper, a preliminary industrial study of froth rheology conducted in a platinum ore is described. The industrial result was used to validate some findings observed in the laboratory test work. 2. Experimental Table 1 shows the details of the 33 flotation tests that will be analysed in this paper. They involve varying both cell operational parameters (e.g. froth height, superficial gas velocity and impeller speed) as well as the feed properties with the objective of changing the properties of the flotation froth and thus its rheology. They were performed according to a CCRD experimental design which involves testing each variable at five different levels, as described in detail by Napier-Munn (2014). There are seven repeat tests at a central condition (i.e. Test 1, 9, 10, 12, 18, 19, and 26) and it has been shown that the froth rheology data produced from these tests was reasonably repeatable (Li et al., 2016a; Li et al., 2016b). The 33 flotation tests were performed in a bottom driven 20 L flotation cell with cross sectional dimensions of 30 by 30 cm. The flotation feed was a mixture of pure chalcopyrite and silica. The chalcopyrite was 5
Minerals Engineering 115 (2018) 4–12
C. Li et al.
Plastic
Bingham
100.9
Pseudo plastic
Yield stress
1 2 3 4 5 6 7 8 11 13 14 15 16 17 20 21 22 23 24 25 27 28 29 30 31 32 33
100.7
Newtonian
Dilatant Apparent viscosity (pa.s)
100.5
100.3
100.1
10-0.1
Shear rate 10-0.3
Fig. 2. Schematic diagram of shear rate as a function of shear stress for different types of fluid (after Mewis and Wagner, 2012).
10-0.5 10-0.8
bubbles at the froth surface per area per time as this is a measure of the physical changes occurring to the froth structure (Morar et al., 2012). The modified SmartFroth algorithm does this by tracking individual bubbles and counting the number of burst events that occur per set of froth images. However, it was found that extremely small values of bubble burst rate were determined, which were not consistent with the calculated air recovery values. The discrepancy may be due to the vision system not being able to accurately detect and therefore determine the bubble burst rate of very small bubbles. Hence, it was decided not to use the bubble burst rate as it was considered inaccurate. The absence of bubble burst rate in this work is unfortunate and hindered the investigation to a certain extent.
10-0.4
10-0.2
100
100.2
100.4
100.6
Shear rate (s-1) Fig. 3. Froth rheograms determined for each test (Li et al., 2016b).
froth was calculated to be less than 4 s−1 in all the tests (Li et al., 2016a), Fig. 3 only shows the froth rheograms for shear rate less than 4 s−1. Apparent viscosity changes significantly with shear rate, confirming that the flotation froths were shear thinning fluids. Eq. (1) shows that the shape of the modified froth rheogram is defined by the consistency index and the flow index. If the flow index can be considered constant, the variation of froth rheology in these tests can be represented by the differences in the consistency indices (μ). In order to validate this hypothesis, the authors (Li et al., 2016b) statistically analysed and proved that the flow index could be treated as a constant in this work, and the froth rheology could be evaluated by using only the consistency index. Therefore, in the following sections, the froth viscosity will be represented by the consistency index calculated for the froth of each test.
3. Characterisation of froth rheology Rheology is the science related to the deformation and flow of matter. The rheological behaviour of a substance is often presented as a plot of the shear stress against the shear rate (the ‘flow curve’ or ‘rheogram’) measured by a rheometer. Various types of rheogram are illustrated in Fig. 2. In general, a substance can exhibit either Newtonian or non-Newtonian behaviour, with the latter including dilatant, plastic, pseudo-plastic and Bingham behaviours. A Newtonian fluid exhibits a linear increase of the shear stress as a function of the shear rate. Two important rheological terms which are often associated with rheology studies are ‘yield stress’, which is the intercept of the flow curve on the shear stress axis at zero shear rate, and ‘apparent viscosity’, which is the slope of the line connecting the origin and a point on the flow curve at a particular shear rate. As shown in Fig. 2, the viscosity is constant throughout the entire shear rate range for Newtonian fluids. However, it changes as a function of shear rate for non-Newtonian fluids. Therefore, the viscosity of a non-Newtonian fluid at a specified point is referred to as ‘apparent viscosity’. The froth produced in the test program has been shown to exhibit shear-thinning behaviour with a minor yield stress (i.e. pseudo-plastic in nature) (Li et al., 2016a). Viscosity in a shear-thinning froth is dependent on the shear rate which changes throughout the froth which makes it difficult to directly correlate froth viscosity to froth performance indicators. To overcome this problem, the authors (Li et al., 2016b) have used a modification of the Herschel-Bulkley model to fit modified froth rheograms as shown in Eq. (1):
η = μ·γ ṅ − 1
10-0.6
4. Determination of flotation and froth performance indicators Flotation performance typically refers to flotation recovery and concentrate grade. The former is determined by froth and pulp recoveries. The latter is affected by pulp and froth conditions as well as feed grade. Pulp and froth recoveries as well as feed grade all are changing significantly as the operating variables of the system are varied in the different tests. Therefore, it would be difficult to study the direct effect of froth rheology on concentrate grade and flotation recovery. Instead, this study investigated the effects of rheology on other key flotation performance indicators. Given that there are only liberated chalcopyrite and silica particles in the flotation system, upgrading in the froth is achieved by maximising the drainage of entrained silica. Hence, the recovery of silica will be a measure of entrainment recovery which is known to significantly affect the final concentrate grade. It was therefore decided to investigate the effect of froth rheology on silica recovery. The silica recovery was calculated based on the mass flow rates of silica in the concentrate and tailings. Froth recovery is an ideal indicator of froth performance. However, it is difficult to measure as mentioned previously. As the valuable minerals are recovered by attachment to bubble surfaces, air recovery is used as an indicator for froth recovery in this study. Air recovery was calculated using Eq. (2) developed by Cilliers et al. (1998):
(1)
where η is the apparent viscosity (Pa ·s ) calculated at each shear rate value, μ is the consistency index (Pa ·sn ), γ̇ is the shear rate (s−1) and n is the flow index (dimensionless). The rheograms of apparent viscosity versus shear rate for all tests are plotted on a log-log scale as shown in Fig. 3. As shear rate in the
αa = 100· 6
Qoverflow Qin
1 vf ·L·hf ·εf = 100· · 2 Jg ·A
(2)
Minerals Engineering 115 (2018) 4–12
C. Li et al.
where αa is air recovery (%), Qoverflow is the volumetric flow rate of air overflowing the lip (ml/s), Qin is the volumetric flow rate of air added to the flotation cell (ml/s), vf is the froth discharging velocity at the lip (cm/s) which in this study was measured by analysing froth vision, L is the lip length (cm), hf is the height above the lip (cm), εf is the gas holdup in the overflowing froth which was calculated using Eq. (3) by assuming gas hold-up is constant in the froth (Li et al., 2016b), Jg is the superficial gas rate (cm/s) and A is the cross-sectional area of the cell (cm3). The term “1/2” accounts for the fact that the average discharge velocity of the froth is half of the discharge velocity at the surface (Cilliers et al., 1998).
εf = 100∗
QA Q A + Qcs
Table 2 Data used for the regression of froth height above the lip.
(3)
where QA is the volumetric flowrate of air added into the cell and QCS is the volumetric flowrate of slurry to the concentrate. Froth height above the lip determines the froth transportation volume and consequently affects the froth transportation velocity, which influences the froth retention time. Hence, the froth height above the lip can indirectly affect the flotation performance. Harris (2013) recognised that the height to which the froth rises above the launder lip will vary with froth properties and operating conditions, rather than being constant. The effect of froth rheology on froth height above the lip is also investigated in this study. 5. Results and discussions 5.1. Effect of froth rheology on froth height above the lip The froth height above the lip is expected to be determined by the froth properties as well as the flotation operating conditions. In a situation where a variable is being affected by multiple variables, regression analysis is the best method for determining whether an influencing parameter is of significance. The flotation operating condition which was changed in the test program and would be expected to affect froth height above the lip is superficial gas velocity. The greater the volume of gas moving through the transportation zone of a froth (i.e. that above the lip), the greater the tendency for the froth to rise before it overflows into the launder. The froth properties that are expected to affect froth height significantly are froth rheology and bubble burst rate (Harris, 2013). Froth rheology is providing a resistance to flow whereas bubble burst rate affects the amount of gas moving through the froth volume as it is a measure of how much gas is escaping at the froth surface. As outlined in Section 2, bubble burst rate was not able to be measured in the experimental program. Hence, the froth height above the lip was regressed only against the froth consistency index and the superficial gas velocity using the data shown in Table 2. Minitab 17 was used to perform the regression analysis. The resulting model is shown in Eq. (4):
hf = −2.61 + 2.77Jg + 2.79μ−0.75J2g−0.74μ2 + 0.003Jg ·μ
R2 = 0.68
Test order
Superficial gas velocity (cm s−1)
Consistency index (Pa ·sn )
Froth height above lip (cm)
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33
1.4 1.0 1.8 1.8 1.0 1.8 1.0 1.8 1.4 1.4 1.8 1.4 1.0 1.8 1.0 1.8 1.8 1.4 1.4 1.0 1.0 1.0 1.4 1.4 0.6 1.4 1.4 1.4 1.4 2.2 1.4 1.4 1.4
1.43 1.97 1.72 1.80 1.00 1.98 1.40 1.06 1.33 1.35 1.32 1.20 1.71 1.09 1.71 1.20 1.26 1.43 1.45 1.54 1.72 0.63 0.56 1.01 1.61 1.22 0.96 1.58 1.34 1.37 1.26 0.85 1.55
2.3 2.4 2.8 2.5 1.4 2.2 1.9 2.1 2.0 2.0 1.9 1.9 2.1 2.3 1.8 2.1 2.6 2.0 2.1 1.8 2.9 1.3 0.8 2.1 1.2 2.3 1.9 3.1 2.1 2.5 2.2 1.5 2.9
that the missing predictor in the regression is bubble burst rate. This may explain why the correlation coefficient (R2) is only 0.68. The regression result may have been significantly improved (with a higher R2) if bubble burst rate had been able to be included in the regression. The model presented above was not developed with the intention of predicting froth performance, but rather to investigate how various operational variables and the froth rheology affect the flotation performance. This is also the aim of the models presented in the following sections. Minitab 17 was used to calculate the significance of the linear, quadratic and interaction effects of each factor on the froth height above the lip, as shown in Table 3. Conventionally a factor is considered to be statistically significant if its P-value ≤ .05. Table 3 shows that the consistency index significantly affects the froth height above the lip in a linear way, with a P-value of .001. The P-value of its square term ( μ2 ) which indicates curvature is .059, which is barely significant. The superficial gas velocity also significantly affects the froth height above the lip in a non-linear way, with a P-value of .002. The P-value of its square term (Jg2) is .043. The interaction between the froth rheology and the superficial gas velocity on the froth height above the lip is not a concern as the P-value is .995. Fig. 4 shows the surface plot of froth height
(4)
where hf is the froth height above lip (cm), Jg is the superficial gas velocity (cm s−1) and μ is the consistency index (Pa ·sn ). Eq. (4) is a conventional response surface model with linear, quadratic and cross-product terms (Napier-Munn, 2014). The standard error of the model which is a measure of the prediction uncertainty is 0.30. As discussed above, there are seven repeat tests in the CCRD program and these repeat tests were used to calculate the standard error of the froth height above the lip as a consequence of experimental error. This calculated experimental standard error is 0.16. Thus, the model error is almost double the experimental error, which indicates that the model is deficient in predicting the froth height above the lip owing to a missing predictor (s). As bubble burst rate is also expected to have a significant effect on the froth height above the lip in flotation, it is likely
Table 3 Significance of variables in predicting the froth height above the lip. Terms
P-value
μ
.001 .059
μ2 Jg Jg2 μ * Jg
7
.002 .043 .995
Minerals Engineering 115 (2018) 4–12
C. Li et al.
Fig. 4. Surface plot of froth height above the lip versus superficial gas velocity and consistency index.
Froth height above lip (cm)
Superficial gas velocity (cm/s) Consistency index (Pa s )
Based on the discussion above, air recovery in the flotation tests is expected to be a function of superficial gas velocity, froth rheology and bubble burst rate. In the absence of any bubble burst rate data, a regression model for air recovery was developed as a function of superficial gas velocity and the froth rheology. The data used for the regression of air recovery is summarised in Table 4. The resulting model is given in Eq. (6).
above the lip versus superficial gas velocity and consistency index. Fig. 4 shows that the froth height above the lip increases as the froth becomes more viscous or with an increase in superficial gas rate. Harris (2013) proposed that the equilibrium height at which the cell operates will be the point at which the energy of the system is minimised; the energy components consist of the kinetic energy of the concentrate discharge (Ek ), the gravitational energy of the froth zone above the concentrate launder level (Eg ), and the resistance to flow (Eμ ) which is defined by the froth rheology. Harris (2013) developed a model to predict the froth height above the lip which incorporated froth rheology effects. As this model has not yet been released publically, and is subject to an IP confidentiality agreement, no additional model details can be presented here. The general structure of the model, representing the energy balance between the three energy components, is shown in Eq. (5).
Ek = Eg−Eμ
αa = −34.0 + 31.87Jg + 32.96μ−11.57Jg 2−10.62μ2 + 0.91μ·Jg
R2 = 0.77 (6)
where αa is the air recovery (%), Jg is the superficial gas velocity (cm/s) and μ is the consistency index (Pa ·sn ). Similar to Eq. (4), Eq. (6) is a conventional response surface model with linear, quadratic and cross-product terms (Napier-Munn, 2014). The standard error of the model is 1.88 while the experimental error
(5) Table 4 Data used for the regression of air recovery.
When the froth does not exhibit a significant yield stress, like the froth in this study, the energy required to overcome the flow resistance is directly proportional to the froth viscosity. As the froth becomes more viscous, the energy required to overcome the flow resistance increases. As a result, the froth above the concentrate lip increases in height to the level at which the resistance to flow is overcome by the increased gravitational energy and the resulting kinetic energy of the froth discharge. This potentially provides more residence time in the froth for froth drainage but also more time for bubble coalescence which will affect air and silica recoveries. The extent to which this occurs will be evaluated in the following sections. 5.2. Effect of froth rheology on air recovery Air recovery is expected to be correlated to the froth retention time above the lip and bubble burst rate. Zheng et al. (2004) divided the froth into two zones: the froth below and above the discharging lip. The froth below the lip rises vertically whereas the froth above the lip moves horizontally, prior to discharging over the launder lip. The loss of air only occurs at the froth surface while no air is lost as the air moves through the transportation zone below the lip. Froth retention time above the lip is expected to be affected by the superficial gas velocity, bubble burst rate and froth viscosity. Superficial gas velocity provides the driving force for froth movement, and consequently significantly influences froth retention time. In addition, the bubbles bursting at the froth surface drag neighbouring bubbles to fill their vacuum and, therefore, slow the froth velocity towards the lip and increase froth retention time. Froth viscosity is a measure of the resistance to froth flow which results in a greater froth height above the lip (as discussed in Section 5.1) which increases the volume through which the gas must flow prior to discharge and consequently results in longer froth retention times. 8
Test order
Superficial gas velocity (cm s−1)
Consistency index (Pa ·sn )
Air recovery (%)
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33
1.4 1.0 1.8 1.8 1.0 1.8 1.0 1.8 1.4 1.4 1.8 1.4 1.0 1.8 1.0 1.8 1.8 1.4 1.4 1.0 1.0 1.0 1.4 1.4 0.6 1.4 1.4 1.4 1.4 2.2 1.4 1.4 1.4
c 1.97 1.72 1.80 1.00 1.98 1.40 1.06 1.33 1.35 1.32 1.20 1.71 1.09 1.71 1.20 1.26 1.43 1.45 1.54 1.72 0.63 0.56 1.01 1.61 1.22 0.96 1.58 1.34 1.37 1.26 0.85 1.55
14.44 11.98 12.11 11.14 8.79 10.45 12.15 10.63 12.47 12.13 8.72 12.22 13.16 11.12 10.93 10.09 10.44 13.57 14.65 5.88 14.24 4.60 2.77 14.78 5.07 15.53 12.92 19.93 13.75 12.12 15.05 8.19 17.30
Minerals Engineering 115 (2018) 4–12
C. Li et al.
properties change and result in higher viscosity and therefore hindered froth movement, these effects outweigh any decrease in bubble burst rate that may result. Froth rheology has therefore been shown to significantly affect air recovery (which is expected to be closely related to froth recovery), and it is therefore speculated that froth rheology can also significantly affect froth recovery. It is recommended that this be verified when a reliable approach to measure froth recovery is developed in future. More importantly, a peak air recovery with consistency index is observed in Fig. 5. Peak air recovery is desirable in terms of flotation cell control as the optimal flotation performance (i.e. mineral recovery and concentrate grade) has been observed at the peak air recovery (Hadler and Cilliers, 2009; Hadler et al., 2010; Shean et al., 2017). Hence, it should be recognised that it is important to take into account froth rheology in the flotation bank control strategy as it clearly affects the magnitude of the air recovery at the peak air rate condition. It also has a marginal effect on the value of the optimal air rate.
Table 5 Significance of variables in predicting the air recovery. Terms
P-value
μ
.001 .001
μ2 Jg Jg2 μ* Jg
.605 .001 .792
calculated from the seven repeat tests is 1.35; i.e. the prediction uncertainty of the model is greater than the experimental error. Again, it implies that the regression data is not fully sufficient to predict air recovery and probably some important variable(s) is missing. It is still expected that the important missing variable in the regression is bubble burst rate. The regression result might be improved if bubble burst rate were to be taken into account. The significance of the terms in the model used to predict air recovery is presented in Table 5. Table 5 shows that the froth rheology and the superficial gas velocity have significant non-linear effects on air recovery with the P-values of both square terms being .001. The interaction between the froth rheology and the superficial gas velocity on the froth height above the lip is not a concern as the P-value is .792. Fig. 5 shows the surface plot of air recovery versus superficial gas velocity and consistency index. Fig. 5 shows that when the consistency index is low, air recovery increases as the froth becomes more viscous (i.e. as the consistency index increases) but when at higher froth viscosities the opposite is observed. This type of relationship is an indication that competing mechanisms are involved. As demonstrated in previous work by the authors (Li et al., 2016b), smaller bubble size and greater particle surface coverage on a bubble will result in greater froth viscosity but these conditions are those which will also decrease bubble burst rate (Ali et al., 2000). In other words, the consistency index may be negatively correlated with bubble burst rate. As discussed above, increasing froth viscosity is expected to increase froth retention times above the lip by resisting froth motion, while a decrease in bubble burst rate should enhance froth transportation and decrease froth retention time. These two effects oppose each other. The resulting froth performance (as measured by the air recovery) depends on which effect dominates the froth transportation process. Fig.5 implies that in this study the variation of air recovery was dominated by bubble burst rate at low froth viscosity, and by froth rheology at high froth viscosity. At low froth viscosity, changes in the froth which result in less bursting of bubbles outweigh any adverse effects associated with higher viscosity. However, at high froth viscosity, as the froth
5.3. Effect of froth rheology on silica recovery Silica recovery is also expected to be affected by froth rheology because of its effect on froth retention time. In addition to froth rheology, other parameters that affect water recovery should also be taken into account to model silica recovery. It has been found previously that the amount of gangue entrained is proportional to the water recovery (Neethling and Cilliers, 2009; Zheng et al., 2006). Silica recovery will be a function of the amount of silica entering the froth phase and the amount of silica draining back to the pulp. The former can be significantly influenced by superficial gas velocity as it has been experimentally found that superficial gas velocity affects the amount of water entering the froth zone (Neethling and Cilliers, 2009; Zheng et al., 2006). In addition, turbulence also influences the amount of entrained particles entering the froth phase by affecting the turbulence in the pulp phase and subsequent suspension of solids into the upper pulp zone just below the froth-pulp interface (Wang et al., 2016b). Turbulence is mainly determined by the impeller speed. Superficial gas velocity and impeller speed were varied systematically in the CCRD program (Table 1). Hence, the two parameters were taken into account in the regression process. Froth retention time determines the drainage of silica from the froth phase. Froth depth affects the froth retention time and the amount of water reporting to the concentrate (Vazirizadeh et al., 2014). The froth retention time below the concentrate lip is determined by the superficial gas velocity and the froth depth (Zheng et al., 2004) while the froth retention time above the lip (as discussed in Section 5.2) is likely determined by the superficial gas velocity, the bubble burst rate and the froth height above the lip. Froth height above the lip has been shown to Fig. 5. Surface plot of air recovery versus superficial gas velocity and consistency index.
9
Minerals Engineering 115 (2018) 4–12
C. Li et al.
Table 6 Data used for the regression of silica recovery.
Table 7 Significance of variables in predicting the silica recovery.
Test order
Superficial gas velocity (cm s−1)
Impeller speed (rpm)
Froth depth (cm)
Consistency index (Pa ·sn )
Silica recovery (%)
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33
1.4 1.0 1.8 1.8 1.0 1.8 1.0 1.8 1.4 1.4 1.8 1.4 1.0 1.8 1.0 1.8 1.8 1.4 1.4 1.0 1.0 1.0 1.4 1.4 0.6 1.4 1.4 1.4 1.4 2.2 1.4 1.4 1.4
900 750 1050 750 750 750 1050 1050 900 900 750 900 1050 1050 750 750 1050 900 900 750 1050 1050 900 900 900 900 1200 900 600 900 900 900 900
7 6 6 8 6 6 6 6 7 7 8 7 8 8 8 6 8 7 7 8 8 6 7 5 7 7 7 7 7 7 9 7 7
1.43 1.97 1.72 1.8 1 1.98 1.4 1.06 1.33 1.35 1.32 1.2 1.71 1.09 1.71 1.2 1.26 1.43 1.45 1.54 1.72 0.63 0.56 1.01 1.61 1.22 0.96 1.58 1.34 1.37 1.26 0.85 1.55
28.0 12.4 40.8 20.1 21.5 30.3 24.6 29.3 25.7 32.4 29.2 30.6 21.7 20.4 17.1 15.0 7.7 32.2 34.6 3.3 6.3 4.5 8.4 35.4 7.5 33.4 31.0 28.0 19.8 35.0 20.7 16.0 22.3
= 0.79
P-value
Hf Jg
.001 .001
IS μ Jg 2
.100 .002 .022
2
.001
μ
the consistency index all have a statistically significant effect on the silica recovery, while the impeller speed does not. In addition, the superficial gas velocity and the consistency index have non-linear correlations with the silica recovery, with the P-values of their square terms being .022 and .001, respectively. No significant interaction effects between the factors on silica recovery are observed. Fig. 6 shows the surface plot of silica recovery versus consistency index and superficial gas velocity at the mean value of froth depth and impeller speed. Similar to the correlation between air recovery and consistency index shown in Fig.5, Fig.6 shows that at low froth viscosity the silica recovery increases as the froth becomes more viscous (increasing consistency index) while the opposite is observed at high froth viscosity. Silica recovery is determined by drainage, which in turn depends on the time that particles stay in the froth (Wang et al., 2016a). It is expected that increasing froth viscosity would slow down the froth transportation and increase the froth retention time. However, as mentioned above, bubble burst rate also decreases when the froth becomes more viscous and this speeds up the froth transportation process. A froth with a lower bubble burst rate will also be associated with smaller bubble sizes and longer plateau border lengths which is known to impede liquid drainage (Wang et al., 2016a) and therefore increase silica recovery. Hence, it is deduced that in this study, at low froth viscosity the variation of silica recovery was dominated by the bubble burst rate effects, thereby increasing silica recovery. At high froth viscosity, the effects of higher froth viscosity outweighed the effects caused by reduced bubble burst rate, and consequently froth retention time increased with increasing froth viscosity, thereby decreasing silica recovery.
be correlated with froth rheology and superficial gas velocity (Fig. 4). Hence, a multi-regression analysis for silica recovery was performed as a function of the superficial gas velocity, the impeller speed, the froth depth and the froth rheology. The data used for the regression of silica recovery are shown in Table 6. As a large number of terms were present in the response surface regression model, a stepwise procedure was used to remove the insignificant terms in the prediction of silica recovery. Stepwise regression is an approach to selecting a subset of effects for a regression model based on the significance of the coefficients for each term in the model. The Fcriterion for entering a term in the model or removing a term from the model was set at 0.15. The resulting model is shown in Eq. (7).
Rs = −61.6−5.21Hf + 58.2Jg + 0.01IS + 87.7μ−14.78Jg2−30.54μ2
Terms
5.4. Industrial measurement The opportunity was taken to carry out a preliminary study of froth rheology in a platinum plant in South Africa, using the same rheometer (Anton Paar DSR 301) which was used to perform the froth rheology measurement in the CCRD tests in the laboratory. The flotation circuit of the plant consisted of rougher, scavenger, primary cleaner and secondary cleaner sections. The measurements were performed in the third and fifth rougher cells and the first primary cleaner cell. The rheometer head was fixed on a holder which was attached to the handrail and the rheometer head was moved vertically to adjust the position of the vane in the froth, based on the froth height. The set-up of the rheometer is shown in Fig.7. During each froth rheology measurement in each flotation cell, four or five torque values were acquired at different vane speeds. The vane speed and torque values were converted to shear rate and shear stress using the method developed by the authors (Li et al., 2015). The rheograms of the flotation froths in the three flotation cells are shown in Fig.8. Each flow curve was fitted to the power-law model (Eq. (1)). The following conclusions can be drawn from Fig.8:
R2 (7)
where Rs is the silica recovery (%), Hf is the froth depth (cm), IS is the impeller speed (rpm), Jg is the superficial gas velocity (cm s−1) and μ is the consistency index (Pa ·sn ). As mentioned before, this is the conventional response surface model with linear, quadratic and cross-product terms generated to explore the effects of the variables on silica recovery. The standard error of the model is 5.11 while the experimental error calculated from the seven repeat tests is 3.15. Again, the prediction uncertainty of the model is much greater than the experimental error, which implies that the regression data is not fully sufficient to predict silica recovery and that some important variable(s) is probably missing. It is still expected that the important missing variable in the regression is bubble burst rate. The regression result might be improved with a high R2 if bubble burst rate were to be taken into account. The significant terms influencing silica recovery are shown in Table 7. Table 7 shows that the froth height, the superficial gas velocity and
I. The platinum ore froth exhibited non-Newtonian flow characteristics similar to those observed in the laboratory work using the synthetic copper ore. The froth appeared to be shear-thinning with minimal yield stress, which is in agreement with the flow behaviour of the froth generated in the laboratory. 10
Minerals Engineering 115 (2018) 4–12
C. Li et al.
Fig. 6. Surface plot of silica recovery versus consistency index and superficial gas velocity.
Silica recovery (%)
Superficial gas velocity (cm/s) Consistency index (P s )
II. The effect of froth rheology on the froth height above the lip followed the same trend as that found in the laboratory work. To compare the froth in the different cells on the basis of apparent viscosity, Fig. 7 shows that the froth flow curve of the third rougher cell is above that of the fifth. The flow curve of the first primary cleaner is below the other two. In other words, the froth in the third rougher cell has the highest viscosity, followed by the fifth rougher cell and then the first primary cleaner cell. Table 8 shows the froth height above the lip measured in each of the three flotation cells. Each froth height was measured three times at different positions along the concentrate lip. A t-test was performed using these repeat values to evaluate whether the froth heights measured for the three cells can be considered statistically different. It was found that the froth height of the third rougher is statistically lower than that of the fifth rougher cell with 95.5% confidence; and the froth height of the fifth rougher cell is lower than that of the first primary cleaner cell with 99.99 confidence. Hence, the average of the measured froth heights decreased from the third rougher to the fifth rougher, and then to the first primary cleaner. The froth height above the lip is positively correlated with froth viscosity, which agrees with the finding of the laboratory work (as shown in Fig. 4).
Fig. 7. Set-up of the Anton Paar DSR 301 rheometer in an industrial cell.
16 y = 22.30x0.51 R² = 0.999
14
Shear stress (Pa)
12
y = 16.43x0.46 R² = 0.995
10 8
5th rougher
y = 15.94x0.50 R² = 0.999
6
The effect of froth rheology on the froth cleaning action was not investigated in the industrial study, as the ore consisted mainly of complex clay minerals. The minerals attached to the bubble surfaces were dominated by various hydrophobic clay minerals (e.g. floatable talc) rather than the valuable minerals. Hence, the variation of froth rheology did not necessarily affect the upgrading of the valuable minerals.
3rd rougher
1st primary cleaner
4 2 0 0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
6. Conclusions
Shear rate (s-1) Fig. 8. Rheograms of flotation froth acquired in three flotation cells in a platinum concentrator.
The effects of froth rheology on froth and flotation performance were studied in this work. The froth rheology was positively related to the froth height above the lip, which in turn was determined by the equilibrium of energy in the froth. The froth height above the lip provides the potential energy to overcome the flow resistance (i.e. froth viscosity) and the kinetic energy for froth flow. When the froth becomes more viscous, the froth height increases to generate more potential energy to overcome the resistance. The effects of froth rheology on air recovery and silica recovery were also investigated in this work. It was found that air recovery was significantly affected by froth rheology; at low froth viscosity, air recovery increased upon increasing consistency index while the opposite was found at high froth viscosity. As the valuable minerals are recovered by attachment to bubble surfaces, it is expected that froth rheology also has a significant impact on froth recovery. A similar
Table 8 Froth heights above the lip in the three flotation cells. Cell Position
3rd rougher (mm)
5 th rougher (mm)
1 st cleaner (mm)
1 2 3 Mean STDEV
104 108 107 106 2.08
103 104 99 102 2.65
65 65 70 67 2.89
11
Minerals Engineering 115 (2018) 4–12
C. Li et al.
Leiva, J., Vinnett, L., Yianatos, J., 2012. Estimation of air recovery by measuring froth transport over the lip in a bi-dimensional flotation cell. Miner. Eng. 36–38, 303–308. Li, C., Farrokhpay, S., Runge, K., Shi, F.N., 2016a. Determining the significance of flotation variables on froth rheology using a central composite rotatable design. Powder Technol. 287, 216–225. Li, C., Farrokhpay, S., Shi, F., Runge, K., 2015. A novel approach to measure froth rheology in flotation. Miner. Eng. 71, 89–96. Li, C., Runge, K., Shi, F.N., Farrokhpay, S., 2016b. Effect of flotation froth properties on froth rheology. Powder Technol. 294, 55–65. Mathe, Z.T., Harris, M., C., O'Connor, C.T, 2000. A review of methods to model the froth phase in non-steady state flotation systems. Miner. Eng. 13, 127–140. Mewis, J., Wagner, N.J., 2012. Colloidal Suspension Rheology. Cambridge University Press, Cambridge, New York. Morar, S.H., 2010. The Use of Machine Vision to Describe and Evaluate Froth Phase Behaviour and Performance in Mineral Flotation Systems, University of Cape Town. Morar, S.H., Bradshaw, D.J., Harris, M.C., 2012. The use of the froth surface lamellae burst rate as a flotation froth stability measurement. Miner. Eng. 36–38, 152–159. Moys, M.H., 1978. A study of a plug-flow model for flotation froth behaviour. Int. J. Miner. Process. 5, 21–38. Napier-Munn, T.J., 2014. Statistical methods for mineral engineers-how to design experiments and analyse data, second ed. Julius Kruttschnitt Mineral Research Centre, Brisbane, Australia. Neethling, S.J., Cilliers, J.J., 2008. Predicting air recovery in flotation cells. Miner. Eng. 21, 937–943. Neethling, S.J., Cilliers, J.J., 2009. The entrainment factor in froth flotation: Model for particle size and other operating parameter effects. Int. J. Miner. Process. 93, 141–148. Runge, K., Crosbie, R., Rivett, T., MaMaster, J., 2010. An evaluation of froth recovery measurement techniques, XXV International Mineral Processing Congress (IMPC) 2010. Brisbane, Australia. Schuhmann, R., 1942. Flotation Kinetics I. Methods for steady-state study of flotation problems. J. Phys. Chem. 46, 891–902. Shean, B., Hadler, K., Cilliers, J.J., 2017. A flotation control system to optimise performance using peak air recovery. Chem. Eng. Res. Des. 117, 57–65. Shi, F.N., Zheng, X.F., 2003. The rheology of flotation froths. Int. J. Miner. Process. 69, 115–128. Subrahmanyam, T.V., Forssberg, E., 1988. Froth stability, particle entrainment and drainage in flotation – a review. Int. J. Miner. Process. 23, 33–53. Vazirizadeh, A., Bouchard, J., Del Villar, R., 2014. The effect of gas dispersion properties on water recovery in flotation columns, IMPC 2014–27th International Mineral Processing Congress. Santiago, Chine. Wang, J., Nguyen, A.V., Farrokhpay, S., 2016a. A critical review of the growth, drainage and collapse of foams. Adv. Coll. Interface. Sci. 228, 55–70. Wang, L., Runge, K., Peng, Y., 2016b. The observed effect of flotation operating conditions and particle properties on water recovery at laboratory scale. Miner. Eng. 94, 83–93. Yianatos, J., Finch, J.A., Laplante, A.R., 1988. Selectivity in column flotation froths. Int. J. Miner. Process. 23, 279–292. Zheng, X., Franzidis, J.P., Manlapig, E., 2004. Modelling of froth transportation in industrial flotation cells: Part I. Development of froth transportation models for attached particles. Miner. Eng. 17, 981–988. Zheng, X., Johnson, N.W., Franzidis, J.P., 2006. Modelling of entrainment in industrial flotation cells: water recovery and degree of entrainment. Miner. Eng. 19, 1191–1203.
correlation between froth viscosity and silica recovery was also observed. A preliminary industrial study of froth rheology was performed for a platinum ore. It was found that the froth exhibited similar rheological characteristics to the froth generated in the laboratory work using a synthetic copper ore. Both of the froths have a shear-thinning nature with minor yield stress. The industrial data supported the correlation between froth viscosity and the froth height above the lip observed from the laboratory work. The interactions between froth rheology and bubble burst rate in a froth phase are still poorly understood. It is recommended that the correlation between froth rheology and bubble burst rate be further investigated with a view to improving the understanding of the effect of froth rheology on froth and flotation performance. Acknowledgments The authors would like to thank the AMIRA P9P (013908) sponsors for the project funding. The authors also gratefully acknowledge the valuable help provided by Professor Tim Napier-Munn of the JKMRC who assisted with the statistical analysis of the results, Dr Sam Morar for analysing the froth images produced in this work., Mr. Stefan Geldenhuys and Dr. Belinda McFadzean from the University of Cape Town for organising the survey in South Africa and providing assistance in setting up the survey device. References Ali, S.A., Gauglitz, P.A., Rossen, W.R., 2000. Stability of solids-coated liquid layers between bubbles. Ind. Eng. Chem. Res. 39, 2742–2745. Cilliers, J.J., Asplin, R.A., Woodburn, E.T., 1998. Kinetic flotation modelling using froth imaging data. In: Laskowski, J.A., Woodburn, E.T. (Eds.), Frothing in Flotation II. Gordon and Breach Science Publishers, The Netherlands. Feteris, S.M., Frew, J.A., Jowett, A., 1987. Modelling the effect of froth depth in flotation. Int. J. Miner. Process. 20, 121–135. Finch, J.A., Dobby, G.S., 1990. Column Flotation. Pergamon Press, London, UK. Franzidis, J.P., Harris, M.C., 2010. Froth recovery factor – What is it and why is it so difficult to measure? Can. Metall. Q. 49, 337–344. 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. Hadler, K., Cilliers, J.J., 2009. The relationship between the peak in air recovery and flotation bank performance. Miner. Eng. 22, 451–455. Hadler, K., Smith, C.D., Cilliers, J.J., 2010. Recovery vs. mass pull: the link to air recovery. Miner. Eng. 23, 994–1002. Harris, M.C., 2013. Modelling the Froth Transport Zone in a Flotation Cell. AMIRA P9P Discussion Document (unpublished).
12