Int. J. Miner. Process. 61 Ž2001. 23–40 www.elsevier.nlrlocaterijminpro
Gas holdup in flotation columns: laboratory measurements F.J. Tavera a,) , R. Escudero a , J.A. Finch b a
Instituto de InÕestigaciones Metalurgicas, UniÕersidad Michoacana, Santiago Tapia 403, 58000 Morelia, ´ Michoacan, Mexico b Department of Mining and Metallurgical Engineering, McGill UniÕersity, Montreal, Canada Received 24 June 1999; accepted 8 June 2000
Abstract The gas holdup in laboratory flotation columns was measured using a conductivity probe. Measurements in a 50-cm-diameter flotation column have shown that gas holdup varies radially depending on the sparging system array, surfactants addition, and spargers malfunctions. The column was run in two modes: unbaffled Žopen., and baffled Žvertically.. Radial differences in gas holdup are enhanced by using baffles if gas is not uniformly injected through the spargers in the flotation column; however, the gas holdup is the same among the quadrants of the baffled column when the gas is evenly injected. Drift flux analysis was applied to estimate bubble size; it was a bubble size radial distribution in the column that was consistent with the gas holdup. q 2001 Elsevier Science B.V. All rights reserved. Keywords: Frother; Bubbles; Column flotation; Surface area flux
1. Introduction The gas holdup is a variable that affects flotation performance. Because of the lack of a reliable technique for measuring gas holdups on-line, in real time in the industrial environment, it had been considered as an unmeasured variable until a new conductivity probe was developed and tested ŽTavera et al., 1996, 1997.. The probe performance principle consists in measuring the electrical conductivity of the gas–liquid Žor gas– )
Corresponding author. Fax: q52-43-167414. E-mail address:
[email protected] ŽF.J. Tavera..
0301-7516r01r$ - see front matter q 2001 Elsevier Science B.V. All rights reserved. PII: S 0 3 0 1 - 7 5 1 6 Ž 0 0 . 0 0 0 2 6 - 0
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slurry. dispersion, and the liquid Žslurry.-only conductivity using flow cells ŽTavera et al., 1998., which are related to the volumetric fraction of the gas phase Žthe nonconducting phase. in the dispersion ŽMaxwell, 1892.. The gas holdup it is a function of a broad group of variables present in flotation: chemical, operational, and machine variables ŽKlimpel et al., 1986., since the gas holdup is related with bubble size Ža function of sparger type, frother characteristics and concentration, solids coverage, and air flowrate., slurry flowrate, solids content, and mixing patterns in the collection zone. Gas holdup defines the bubble-flow density Žor the bubble surface-area flux., which is related to flotation kinetics ŽGorain, 1997.. Therefore, knowledge of the gas holdup should be useful when diagnosing and controlling the operation of a flotation column.
2. Experimental The experiments in the present work were carried out in a 50-cm-diameter Ž4-mheight. laboratory flotation column. Shown in Fig. 1. In this column, air is introduced via eight vertical filter cloth spargers in a ring arrangement Ž40-cm diameter. at the bottom of the column. The column was operated under batch condition. When the system contains no solids, the gas holdup can be accurately measured from pressure difference, which provides a standard to compare against the gas holdup measurement from the conductivity probe. The gas holdup here is estimated from pressure using the equation:
´g s 1 y D Pr Ž rsl gD L . ,
Ž 1.
where D P is the pressure difference between two points separated a vertical distance D L, and rsl is the slurry density ŽFinch and Dobby, 1990.. A differential pressure transmitter ŽBailey, model PTSD. was connected to the second and the third pressure taps in the column, to record the pressure difference. The gas holdup measurement in the flotation column consisted in the simultaneous collection of pressure Ždifferential pressure transmitters., and conductivity Žconductivity probes. at several air flowrates, with the column run with water only Žwith and without surfactant, Dowfroth 250; 20 ppm.. The air flowrate was monitored and controlled using a thermal based mass flow controller ŽMKS, model 1562.. The probe cells, which are described in the literature ŽTavera et al., 1996., were connected to the conductivity meters ŽTacussel models CD810, and CDRV62.. The analog outputs of both conductivity meters and the pressure transmitter were processed in an ArD converter and transmitted to the computer using serial communication. In each experiment, two or three similar conductivity probes were used simultaneously to be able to measure at different positions under the same operating conditions. The conductivity probes were placed in different radial positions between the second and the third pressure taps in the flotation column; at given experimental conditions, a gas holdup from conductivity measurements can be compared with the gas holdup from pressure measurements.
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Fig. 1. Schematic representation of the experimental apparatus. Ža. Open column. Žb. Baffled column. Ž1. Flotation column. Ž2. Filter cloth spargers. Ž3. Pressure transmitters ŽPT.. Ž4. Serial IrO communication interface. Ž5. 486 IBM compatible computer. Ž6. Vertical Baffles. Ž7. Mass flow controller.
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In groups of experiments, vertical cruciform baffles were installed in the column; the baffles divided the column in four quadrants. Under this scheme, the conductivity probes were placed in two quadrants at the same depth during the experiment. Fig. 1 represents schematically the general setup for laboratory tests. In some tests, the effect of sparger malfunction on gas distribution in the column was simulated by switching off selected spargers in both open and baffled column modes.
3. Results and discussion 3.1. Open flotation column The gas holdup estimates from conductivity compared well with those from pressure ŽFig. 2Ža... The figure shows some scatter. One source of scatter is related to the fact that the gas holdup estimated from pressure is an average value over the volume contained between the two tapping points, while the measurement with the conductivity probe is more localised. Therefore, differences can be expected if the gas holdup is not evenly distributed radially in the column. The radial distribution of the gas holdup was checked by placing probes at three radial positions in the column, i.e. in the centre, midway between the centre and the wall, and at the wall of the column, along a line midway between the position of the two tapping points. Because the spargers arrangement in the column, air enters as an annular Acurtain.B The results ŽFig. 2Žb.. show the gas holdup is higher at the centre of the column than at the wall. In the test, the gas holdup determined from pressure fell in between the values determined from conductivity. Tests were also conducted in systems containing no surfactant. The results are also presented in Fig. 2Žb.. These data consistently show that the gas holdup is highest in the centre of the column. The gas holdup is higher with surfactant, as expected since the bubbles are smaller and the rise velocity is lower. The differences in the radial gas holdups appear to be lower when the surfactant is present. This implies that the hydrodynamic behaviour of the system is modified by the bubble size ŽFinch and Dobby, 1990.. To observe the effect of the sparger malfunction on the distribution of air in the column, the system is simulated by switching off selected spargers. Fig. 3Ža. shows the gas holdup estimates with one sparger switched off. Measurements were made along the column diameter passing through the switched-off sparger. It can be seen that there is a decrease in gas holdup in the region above the switched-off sparger, while the highest gas holdup occurs in the position opposed to the switched-off sparger. Fig. 3Žb. shows the column operation with two switched-off neighbouring spargers. In this case, there is a notable change in the distribution of gas holdup when surfactant is added as compared with that presented in the system without surfactant; without surfactant, the highest gas holdup is above the switched-off spargers as a result of the mixing, which brings small bubbles to that region. However, when the surfactant is
F.J. TaÕera et al.r Int. J. Miner. Process. 61 (2001) 23–40 Fig. 2. Experimental results in two-phase waterrair systems. Ža. Comparison of the gas holdup measurements between pressure and conductivity. Žb. Gas holdups as a function of the superficial gas velocity; white symbols represent the system with 20 ppm of frother ŽDowfroth 250., and black symbols represent the system without frother. 27
28 F.J. TaÕera et al.r Int. J. Miner. Process. 61 (2001) 23–40 Fig. 3. Gas holdup as a function of the superficial gas velocity at radial positions with respect to failed spargers. Simulation of spargers malfunction: Ža. one sparger is switched off in the system Žwithout frother.; Žb. two neighbouring spargers are switched off, the white symbols represent the system with frother Ž20 ppm Dowfroth 250., and the black symbols represent the system without surfactant. Ao.s.B means opposite side to failed sparger.
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added in the system, changes occur in such way that the highest gas holdup is localised in the region opposed to the switched-off spargers. The experimental data on the simulated sparger malfunction implies that the radial differences in the gas holdup may be due to differences in bubble size Žamong the points of measurement.. By comparing Fig. 3Ža. with the data presented in Fig. 3Žb. for the system without surfactant, it can be noticed that the radial distribution of gas across the column is different when two neighbouring spargers are switched off from what occurs in the system when only one sparger is not working. This implies that the mixing conditions are different in these two cases, affecting in a different way the distribution of gas in the column. Bubble size is estimated from drift-flux analysis, applying the technique presented by Finch and Dobby Ž1990.. Drift-flux analysis relates the relative or slip velocity of the gasrslurry phases ŽUsb . to the properties of the system. The general relationship is: Usb s Ž Jgr´g . " Jslr Ž 1 y ´g . ,
Ž 2.
where Jg is the superficial gas velocity, ´g is the gas holdup, Jsl is the superficial liquid Žor slurry. velocity, q refers to countercurrent flow Žas in most operations of flotation columns., and y to cocurrent flow. The Usb is related to the bubble terminal velocity ŽUbt . and the gas holdup by: Usb s Ubt Ž 1 y ´g .
my 1
.
Ž 3.
By equating Eqs. Ž2. and Ž3., Ubt is determined, which, in turn, is related to bubble size Ž D b .. There are several models relating Ubt and D b . One used here is the Schiller and Naumann Ž1933. model: Usb s gD 2b Ž rsl y r b . Ž 1 y ´g .
my 1
.1 m s 4.45 q 18 Ž D brDc . Rey0 b
Re b s D b Ubt rslrmsl ,
0.687 r 18 msl Ž 1 q 0.15Re bs . ,
1 - Re b - 200,
Ž 4. Ž 5. Ž 6.
where Re b , rsl , r b , and msl are the bubble’s Reynolds number, the liquid Žor slurry. density, the bubble density, and the liquid Žor slurry. viscosity, respectively. In two-phase Žgasrwater. systems, the bubble density becomes negligible. In mineral flotation systems, the bubble density becomes important and its value depends of the fraction of bubble surface covered with solids Ž K ., the solids specific gravity Ž rp ., and particle size Ž Dp . ŽFinch and Dobby, 1990.:
r b s Kp Dp rpr D b q Ž Kp Dp . .
Ž 7.
The method of calculation to determine bubble size is described in the literature ŽFinch and Dobby, 1990; Banisi and Finch, 1994..
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Recently, drift-flux analysis to estimate bubble size was validated in two-phase systems against an independent photographic method ŽEscudero-Garcıa, ´ 1998; Escudero-Garcıa ´ et al., 1998.. Image-analysis results and the drift-flux analysis predictions were in good agreement; therefore, these experiences show the technique to be a reliable method to predict bubble size in two-phase systems. As first approximation, in the application of the drift flux model, Jg can be assumed to be constant across the column Ž Jg is defined as the ratio: volumetric gas flowrate Žcm3rs.rcross-sectional area of the column Žcm2 ... Fig. 4Ža. presents the bubble-size estimates, when one and two spargers are switched off, respectively. Fig. 4Ža. corresponds to the system that contains no surfactant and, in this case, the column has one and two spargers switched off. It can be seen that in the system with one sparger switched off, it is a radial variation in bubble size such that the smaller bubble size is presented in the region opposed to that of the switched-off sparger; this implies that in that region, gas holdup must be higher, as presented in Fig. 3Ža.. The differences in bubble size can be produced by bubbles coalescence in the system as a result of mixing. Also, Fig. 4Ža. represents the experimental data generated when the column was operated with two neighbouring spargers switched off, without surfactant. In the system without surfactant, the smaller bubbles are distributed mainly in the region of the switched-off spargers, which is consistent with the gas holdup data presented in Fig. 3Žb.. However, the addition of surfactant in the system Ž20 ppm Dowfroth 250. originates a more homogeneous bubble size across the column, as expected, thereby decreasing the radial differences in the gas holdup. The effect of the surfactant on the bubble size is schematically represented in Fig. 4Žb.. The so-called buoyancy velocity of a bubble swarm ŽNicklin, 1962. was also measured using the principles of the technique of Shen et al. Ž1995.. As anticipated, the buoyancy velocity decreased as the gas holdup increased. It was also found that there was a radial profile in the buoyancy velocity, which reflects the radial distribution of the gas holdup and that of bubble size; these distributions on the bubble-swarm buoyancy velocity are presented in Fig. 5Ža. and Žb. with and without surfactant additions, respectively. The data on the gas holdup and the buoyancy velocity measurements are consistent with the bubble-size estimates from drift-flux analysis. These parameters, in turn, reflect the effect of the sparger performance. 3.2. Measurements in a baffled column Large-diameter open Žunbaffled.-flotation columns are well mixed ŽGomez et al., 1995.. It has been recommended that columns greater than 1-m diameter be baffled to reduce axial mixing. However, some researchers have found that baffles enhanced rather than dampened mixing. The reason was a ApumpingB action between the baffled section if slurry and gas are not well distributed and differences in bulk density are generated. In a laboratory, column mixing was only reliably reduced when the baffle was raised so that its top was above the level of the froth–slurry interface, which stopped the ApumpingB action ŽMoys et al., 1991..
F.J. TaÕera et al.r Int. J. Miner. Process. 61 (2001) 23–40 Fig. 4. Bubble diameter calculated by drift flux analysis as a function of the superficial gas velocity. Ža. The system is without surfactant; white symbols are for one sparger switched off, and black symbols are for two spargers switched off. Žb. The system contains frother Ž20 ppm Dowfroth 250. and two spargers are switched off. Ao.s.B means opposite side from failed spargerŽs.. 31
32 F.J. TaÕera et al.r Int. J. Miner. Process. 61 (2001) 23–40 Fig. 5. Radial profile of bubble swarm buoyancy velocity as a function of the superficial gas velocity. Ža. The system does not contain surfactant. Žb. The system contains frother Ž20 ppm Dowfroth 250.. Measurements are at five radial positions. Two neighbouring spargers are switched off to simulate sparger malfunction; the term Ao.s.B means opposite side of failed spargers.
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In the present work, a number of tests were conducted to detect differences in the gas holdup between sections of the 50-cm-diameter laboratory column after introducing vertical baffles. Three-meter-long cruciform baffles were installed vertically in the column and held 50 cm above the spargers and 50 cm below the column lip. In this manner, the column was divided into four quadrants in such manner that below each quadrant there were two vertical filter cloth spargers. Fig. 6Ža. shows the data collected without surfactant, and with the presence of surfactant Ž20 ppm Dowfroth 250. when all spargers are working. This shows consistent, but minor, differences in the gas holdup between sections. The small differences in gas holdup among the quadrants suggest that the installation of baffles reduces axial mixing as compared with the gas holdup in the unbaffled column Ži.e. Fig. 2Žb.., if gas is evenly introduced in the column. Every effort was made to ensure an even injection of gas among the spargers. In practice, this may not always be the case. To test, a malfunction of spargers was simulated by switching off selected spargers in the 50-cm column. Fig. 6Žb. shows the gas holdup estimates with two neighbouring spargers switched off in the fourth quadrant. It can be seen that differences in the gas holdup Žamong the sections of the column. are enhanced by the presence of baffles when gas is not evenly injected among the spargers. From the experimental data presented in Fig. 6Žb., bubble size was estimated by drift-flux analysis. It was found that there is a bubble-size distribution among the quadrants of the baffled section in the column. Fig. 7 presents the bubble-size estimates in the system Žwithout surfactant, and with surfactant additions.. It can be seen that the data presented in Fig. 7Ža. Žin the system without surfactant. are consistent with the gas holdup measurements presented in Fig. 6Žb., i.e. the fourth quadrant contains the larger bubbles and lower gas holdups, while the second quadrant presents the smaller bubble size and higher gas holdups, as it should be anticipated. This feature of the gas holdup-and-bubble size is also present when the system contains surfactant ŽFig. 7Žb.., where the bubble-size estimates are plotted as a function of the superficial gas velocity; this representation corresponds to the data presented in Fig. 6Žb.. Interestingly, the experimental data under the presence of surfactant ŽFig. 7Žb.. show that the bubble size increases slightly with the increase in the superficial gas velocity. This may be due to the fact that the small gas bubbles remain long enough in the column to coalesce and this being more notable as the gas holdup increases Žor increasing the superficial gas velocity.. On the other hand, the system containing no surfactant ŽFig. 7Ža.. shows that the bubble size remains almost constant with increasing the superficial gas velocity Žwith exception of the smaller bubble size that increases slightly with the gas rate.. 3.3. Bubble surface-area flux Bubble surface-area flux Ž S b , with units of timey1 . is defined as the bubble surface moving through a unit of area normal to the direction of the bubble motion Žthe last, in
34 F.J. TaÕera et al.r Int. J. Miner. Process. 61 (2001) 23–40 Fig. 6. Gas holdup as a function of the superficial gas velocity in a baffled 50-cm laboratory flotation column; vertical cruciform baffled divide the column into four quadrants. There are two spargers in each quadrant: Ža. The spargers are working properly; Žb. Two spargers are switched off in the 4th quadrant. Black symbols are for the system without surfactant; white symbols are for the system with frother Ž20 ppm Dowfroth 250..
F.J. TaÕera et al.r Int. J. Miner. Process. 61 (2001) 23–40 Fig. 7. Bubble size estimates by drift flux analysis as a function of the superficial gas velocity. Vertical baffled flotation column; simulation of sparger malfunction by switching off two neighbouring spargers Žfourth quadrant.. Ža. The system is without surfactant. Žb. The system contain frother Ž20 ppm Dowfroth 250..
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the case of a flotation column, would be the column cross-sectional area. in m2rsrm2 . This parameter takes into account the effect of the bubble size Žwhich depends on the chemical, hydrodynamics and the bubble generation characteristics., and the superficial gas velocity Žwhich depends on the machine characteristics and the operating conditions.. Therefore, S b should be related to the operation performance better than the bubble size, the superficial gas velocity and the gas holdup individually. S b is a proper measure of hydrodynamic conditions in a flotation process. It has been found in mechanical flotation cells ŽGorain, 1997. that the bubble surface-area flux has a strong correlation with the flotation rate constant, k. Also, it has been presented that in flotation columns ŽGorain et al., 1996., a clear relationship exists between k and S b , irrespective of the ore type and chemical conditions. S b can be derived by the above definition as ŽFinch and Dobby, 1990.: S b s n = SrA, S s p D 2b , n s 6 Qgr Ž p D 3b . ,
Ž where Qg is the volumetric gas flowrate. ,
S b s 6Qgr Ž D b A . , Jg s QgrA, [ S b s 6 JgrD b .
Ž 8.
From the experimental data presented in Fig. 7, the bubble surface-area flux is calculated using Eq. Ž8.. Fig. 8 represents the S b values as a function of Jg . It can be seen that because of the differences in the distribution of gas among the quadrants of the baffled column, the bubble surface-area flux is different among the quadrants; these differences in S b are more noticeable when the system does not contain frother additions ŽFig. 8Ža.., i.e. in the second quadrant the bubble surface-area flux presents the higher values as a result of the smaller size of the bubbles, which are present there. The presence of surfactant ŽFig. 8Žb.. produces smaller differences in bubble size among the quadrants in the baffled section of the column as compared to those when the system does not contain surfactant. If there are differences in S b among the quadrants of a baffled column, this may imply that the efficiency of the column would decrease in a mineral flotation performance, since the carrying rate, Cr , is related directly to S b ŽFinch and Dobby, 1990., Cr s S b Ž Kp Dp rpr6. where K, Dp , and rp are the fraction of the bubble surface covered with solids, the particle size, and the particle density, respectively. Fig. 9 shows the experimental data on ´g in terms of the calculated S b ; it can be seen that this relationship presents no differences among the quadrants of the baffled section of the column, which denotes that ´g is equivalent to S b Ž ´g s S b d br 6 L c 4 where Lc is the height of the collection zone of the column., being the equivalence between these two parameters, the mechanical, chemical, and hydrodynamic characteristics of the flotation process.
F.J. TaÕera et al.r Int. J. Miner. Process. 61 (2001) 23–40 Fig. 8. Bubble surface area flux, Sb, as a function of superficial gas velocity. Effect of sparger malfunction on the distribution of Sb Žtwo spargers are switched off in the fourth quadrant.. The column is vertically baffled. Ža. The system is without surfactant. Žb. The system contains frother Ž20 ppm Dowfroth 250..
37
38 F.J. TaÕera et al.r Int. J. Miner. Process. 61 (2001) 23–40 Fig. 9. Relationship between the gas holdup and the bubble surface area flux in a vertically baffled flotation column. The column has two spargers switched off in the fourth quadrant. Ža. The system is without surfactant. Žb. The system contains frother Ž20 ppm Dowfroth 250..
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4. Conclusions Localised measurements of gas holdups were carried out in a 50-cm-diameter laboratory flotation column by using conductivity probes. The experiments were done in two-phase water–air systems with and without surfactant additions ŽDowfroth 250.. It was found that there are radial differences in gas holdup, which depend on the sparger system arrangement and the sparger performance. The tests showed that if gas is evenly distributed in the column, the use of vertical baffles reduces such differences in the gas holdup and lowers the mixing effect. The addition of frother reduces the radial differences of the gas holdup in the column, and increases the gas holdup value, as compared with those presented in the absence of the surfactant. The addition of frother reduces the bubble size and, as a consequence, increases the bubble surface-area flux. In these experiments, it was shown that the bubble surface-area flux varied between 12 and 120 sy1 , which are typical for two-phase water–air systems. From the experimental data collected in the baffled column, it was found that the relation S brJg is different among the quadrants of the baffled section of the column, which appears that each section behaves as an independent column; however, when S b is related to ´g , the column operation data is unified, showing the operation of the column as a whole. This information suggests that both parameters, S b and ´g , could be useful to describe the performance of a flotation column.
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Nicklin, D.J., 1962. Two-phase bubble flow. Chem. Eng. Sci. 17, 693–702. Schiller, L., Naumann, A., 1933. Ver. Dtsch. Ing. 77, As reported by Banisi, S., Finch, J.A., 1994. Shen, G., Nawfal, H., Watson, J., Banisi, S., Finch, J.A., 1995. Measurement of bubble swarm buoyancy velocity in three-phase system. CAMI’95. 3rd Canadian Conference on Computer Applications in the Mineral Industry, Montreal, Quebec, Oct. 22–25. pp. 1–8. Tavera, F.J., Gomez, C.O., Finch, J.A., 1996. Novel gas hold-up probe and application in flotation columns. Trans. Inst. Min. Metall. 105, C99–C104. Tavera, F.J., Escudero, R., Gomez, C.O., Finch, J.A., 1997. Gas holdup and slurry conductivity as process diagnostics in column flotation. In: Finch, J.A., Rao, S.R., Holubec, I. ŽEds.., Processing of Complex Ores. pp. 3–20, TMS of CIM. Tavera, F.J., Gomez, C.O., Finch, J.A., 1998. Conductivity flow cells for measurements on dispersions. Can. Metall. Q. 37 Ž1., 19–25.