- Email: [email protected]
A mass transfer approach to flotation column design
Chemical Enginrning Scienrr. Printed in Great Britain.
Vol.
A MASS
47.
No.
13114.
pp.
360-3612.
1992 0
TRANSFER
APPROACH
TO -TATION
COLUMN
ocm-2509/92 ss.m+o.oo 1992 Pergsmon Press Ltd
DESIGN
Mku T. Ityokumbul Western Research Centre, CANMET 1 Oil Patch Drive P-0. Bag 1280 Devon, Alberta TOC lE0, Canada ABSTRACT
Flotation equipment design is an area of reactor engineering that has not attracted much research interest in chemical engineering. The commercial success of flotation remains a triumph of enlightened know how over inadequate know why as key design and scale-up parameters (e.g. column height) continue to be dictated by such non-process considerations as crane rail and building heights (Ounpuu and Tremblay, 1991). The shortcomings in the present approach to flotation column design and scale-up are discussed. It is shown that the use of first order kinetic expression in flotation column design and scale-up is not correct insofar as the recover-y and order of the process are concentration dependent. By using analogy with interface mass transfer, a new approach to flotation column design is presented, Using literature data, it is shown that only a short recovery zone is required for particles made selectively hydrophobic. Recent experimental data from a 1.2m flotation column (Ounpuu and Tremblay, 1991) and those of others as well (Wheeler, 1984; Bensely et al. 1985; Jameson, 1988; Reddy et al. 1988) confirm this observation. KEYWORDS:
Flotation column, design, scale-up, interface mass transfer
INTRODUCPION The design of flotation equipment is an area of reactor engineering that has not received much research interest in chemical engineering. As reviewed by Harris (1976), the commercial success of flotation remains a triumph of enlightened “know how” over inadequate “knew why”. For these reasons, progress has been made almost exclusively by empericism tempered by engineering judgement subject to the following questions: (i) ‘Does it work?’ (ii) ‘Is it competitive?’ and (iii) ‘What can be changed to make the process more competitive?’ This approach has led to the slow progress in the design and/or application of new flotation cells. In addition, flotation research has been mainly directed at understanding the chemistry without adequate consideration of the physics and mechanics of the process (Flint, 1973). One of the few designs to have achieved commercial success over the last twenty years is the flotation column. A flotation column is a bubble column device in which separation of solid particles is achieved using differences in their affinity for air bubbles. As is common with all bubble column devices, the transport, dispersion and mixing of materials is induced by the motion of gas bubbles in the slurry. The flotation column has three zones: the recovery, washing and froth zones. In the recovery zone, particles suspended in a descending water phase contact a rising swarm of air bubbles introduced at the base of the column. The bubbles are either generated internally using porous media or externally using such devices as the USBM sparger. Floatable solids collide with and adhere to the rising bubbles and are transported to the washing section. Non-floatable solids are removed from the base of the column as tailings. In the CES47:13/14-U:
3605
3606
MKU T.
Cl6
ITYOKIJMBUL
washing section, the mineral ladden air bubbles are subjected to a countercurrent stream of water which removes loosely attached gangue particles and transports them back into the recovery zone, thereby minimising concentrate contamination. The clean froth is recovered at the top of the column as concentrate. In spite of the commercial success of flotation columns, problems exist in their design and scale-up. All present design and scale-up procedures for flotation column are based on the application of the analogy with chemical kinetics (Dobby and Finch, 1986, de1 Villar et al. 1988; Luttrel er al. 1990). According to this procedure, the rate of flotation is considered to be first order in the concentration of floatable solids. By using the sedimentation dispersion model to represent the behaviour of solid particles in the flotation column, the recovery of floatable solids is predicted using Eq. 1. (1 - X) = 4qexp(Pe#2)/{( where
X is the fractional
1 + q)2exp(Pe,q/2)
recovery
and q is defined
- (1 - q)‘exp(-Pe,q/2)) as
q = (1 + 4k”tfle&“’
(2)
where xi, and Per are the particle residence time and Peclet numbers in the collection The particle residence time and Peclet number are predicted using the relationships: $
=
y1
- eJ/(u,
zone respectively.
+ VP)
Eqs. l-4 represent the relationships that are presently used in flotation column design and scale-up. The use of this approach in flotation column design has been questioned recently (Ityokumbul, 1992a). As an example, the use of a sedimentation-dispersion model implies the existence of a constant relative flow between the solid and liquid phases. According to Levenspiel and Fitzgerald (1983), the existence of a constant relative flow is indicative of a Guassian-convection flow. Morever, the application of this model in solid dispersion studies has been found to yield results which show that the solid dispersion ccx@cient increases with particle size (Yiannatos and Bergh, 1992). Since larger particles have a higher inertia, it is unlikely that they will be more mixed than the smaller ones. In addition, the use of first order kinetic expression suggests that the recovew be independent of initial concentration. While this is true for low concentrations of floatable solids, the same is not true at high concentration. At high concentrations, the process changes from being first order to one that is zero order in concentration of floatable solids. In addition, estimates of activation energy for the flotation process give values less than lOKcal/mole (Ityokumbul, 1992a). This is not indicative of chemical reaction control. In agreement with the observations of Jameson et al. (1977), a mass transfer approach to flotation column design is presented.
MASS
TRANSFER
APPROACH
TO
FLOTATION
COLUMN
DESIGN
As indicated earlier, the use of analogy with chemical kinetics in flotation column design is not correct. In the present work, we consider the flotation process to be analogous to interface mass transfer. For the formulation of the equations describing the process, the following assumptions are made: (1) Particle collection takes place in the recovery zone only. (2) The rate of attachment of particles to air bubbles is proportional to the concentration of floatable solids and uncovered bubble surface. (3) The rate of pat-tide detachment is proportional to the surface concentration of solid particles on the air bubbles (Sastry and Fuerstenau, 1970). 4) The effect of froth height on recovery is small. This is a reasonable assumption unless the froth depth is excessive (Engelbrecht and Woodbum, 1975). 5) The liquid flow rate in the recovery zone is equal to the tailings flow rate. 6) The solid behaviour in the recovery zone may be described using the sedimentation convection model (Ityokumbul, 1986).
Cl6
Mass transfer approach to flotation column design
3607
With assumptions1 and 4, the design of the flotation column reduces to that of the recovery zone. From assumptions 2 and 3, the net bubble loadiig rate may be written aa: dl?/dt= k(l-, - T)C - k’l-
(9
where C is the concentration of floatable solids, r and r, are the bubble and maximum bubble loads, k and k’ are the rate constants for attachment and detachments respectively. From assumption 6, the flux of solids in the recovery zone may be written as: N” = p,
+
V,)U(l - Es)
(6)
The flux of solids in a. 6 is based on the crosssec tional area occupied by the slurry. An overall material balance for the recovery zone (Fig. 1) may be written as:
Qsr
= A(Vp + &.){C
- Cd
(7)
where S is the specific bubble surface area.
r(o) t ------I Feed-i-----I____________:
Q&
z=o
.z=L Air
f
I
lTailings Qt. Ct
Qg
Fig. 1: Material balance for the recovery zone By using analogy with interface mass transfer, the height required for a given recovery is calculated from the expression:
d(Q#=)= vwul
- lT)C - kT]aAdz
or
z = I Qpil-/{[k(l-, J
By definition, a = 6sJd, and S = 6/d,
- lY)C - k’qaA}
i
(8)
3608
MKU
T. ITYOKUMBUL
Cl6
In the presence of frothers. bubble coalescence in the recovery zone is expected to be minimal. Thus Q$/Aa may be taken to be constant. Substituting for a and S in Eq. 9 results in the following dl-/([k(r, - r)C - k’r]} (12) I Solution for the column height requires integration of the RHS of Eq. 12. This is done using the material balance expression (i.e. Eq. 7) which gives the variation of the bubble load with concentration of z =
floatable
U$EI
solids
in the recovery
zone.
DISCUSSION
Determination of Collection Zone LenPth The determination of column height requires a numerical integration of Eq. (12). For this purpose, order of magnitude estimates of the transfer rate constant and hydrodynamic parameters are required. The maximum bubble loading data of King et al. (1975) was rearranged to give (Ityokumbul, 1986): I-,
= 0.0035/d,“-875
(13)
The carrying capacity data of Amelunxen (1991) as well as those of Espionosa-Gomez el al. (1988) indicate that in a large number of applications, the bubbles are lightly loaded (lY’cO.Olkg/m’). For typical flotation size air bubbles (d,cO.O03m), T,,,>>T. The author has shown that under these conditions, what has come to be known as the flotation rate constant is related to the particle transfer rate constant and the vessel hydrodynamic parameters by the expression (Ityokumbul, 1992a): b
= akr,
(14)
For hydrophobic particles and lightly loaded bubbles,
kl-,C>> k'l-
(1%
Investing Eqs. 7, lo-12 and 15, we get z = (U,+V,)/akT,
I
dC/C
(16)
Integration of Eq. 16 gives z = (U,+V,)/akr,
* ln{C(O)/C(L)}
(17a)
* ln(1 - X)
(17b)
or z = - (U,+V,)/akr,
An estimate for k may be made from reported observed rate con&ants using Eq. 14. Typical values for L are in the range 1-3/min. For gas velocities in the range 0.012-O.O17m/s, the maximum interfacial area calculated from the data of Amelunxen (1991) was approximately 9SOm2/m3for a bubble diameter of 0.0012m. Using a value of 16b.of 2/min gives an estimate of approximately 0.000028 m3/kg s for the particle transfer rate constant. Note that this estimate is at least one order of magnitude lower than that reported by King et ~2. (1975). In industrial applications, slurry and gas velocities in the ranges 0.005 O.O2m/sand O-01-O.O3m/srespectively are common. Thus a value of O.Olm/s is assumed for the slurry velocity in the recovery zone. The gas velocity and hold-up data assumed here is that used in the estimation of k above (O.O14m/s and 0.18 respectively). For the bubble size of O.OO12m used above for estimating k, particles with a terminal settling velocity of O.Olm/s and assuming a 90% recovery, the recovery zone height is estimated to be 1.77m. This finding is in apparent contradiction with the current practice of designing flotation columns with recovery zones of over 9m in height. The experimental data of several authors confirm that only a short recovery zone is required for particles made hydrophobic (Wheeler, 1984, Benseley et a/. 1985; Jameson, 1988, Reddy et al. 1988; Ounpuu and Tremblay, 1991).
Cl6
Mass transfer
approach to flotation column
design
360!?
For example, Ounpuu and Tremblay (1991) have shown that a recovery zone height of 05m was sufficient to attain 65% recovery of sphalerite (ZnS) in their 1.2m diameter flotation column, thus confirming that only a short recovery zone is required. Similarily, Reddy et al. (1989) and Luttrel et al. (1988) have shown that recovery zone heights of l.Om were sufficient to yield 90% and 96% recovery of -500~ and -5~ coal in their O.lOm and 0.05m flotation columns respectively. From Eq. 17, the term (U,+VJ/akF, is equivalent to the height of a transfer unit, HTU, while the integral represents the number of transfer units, NTU. Since the FFfU is a measure of the difficulty of the separation, it follows from Eq. 17 that increasing the particle size results in an in increase in the height required for a given recovery. Since King et al. (1975) did not find any dependence of k on particle size, this finding is indeed a valid one insofar as the particle residence time is also reduced. This may partly explain the difficulty the flotation of gelena (PbS), a mineral with a density greater than 5,000kg/m3. Eq. 17 also indicates that the column height required for a given performance is inversely related to the quality of the air dispersion in the recovery zone (air interficial area, a). Since flotation is an interficial phenomenon, this finding is a reasonable one. For a given gas velocity, increasing the bubble interficial area will therefore be expected to increase the rate of flotation thus reducing the HTU. It should be noted that the quality of the air dispersion (measured by the bubble size) also affects the maximum bubble load. Since the maximum bubble load per unit surface area increases with decreasing bubble size (King et UC. 1975), this will also contribute to the reduction in the HTU. Since most new flotation column installations are equipped with external spargers, control of the bubble size represents a useful operational tool. The fundamental work of McKay et al. (1988) show how the bubble size may be controlled with the external sparging system. Aunlication to Other Studies With the mass transfer approach to flotation column, Eq. 17 becomes a useful tool for the comparison of column performance and also for the determination of rate data. As an example, if the recovery height is fixed and the slurry velocity varied, a plot of z/-ln(l-X) vs U, should yield a straight line with the following parameters (Ityokumbul, 1992b): slope = l/akFm intercept = VJakF, From these, the rate constant and particle settling velocities may be determined. This procedure was applied to the recent experimental data of Reis and Peres (1991) for gold-bearing chalcopyrite ore. These authors reported that the ore was ground to a d, of 12Om (i.e. 80% passing the indicated particle size). The use of this procedure gave an observed rate constant of 0.0103/s and an average particle size of 90,fun (Ityokumbul, 1992b). The fact that the particle size is within the d, range reported by these authors is an indication of the validity of this approach in flotation column design. Ynchausti et al. (1988) presented recovery data for flourite (CaFa and pyrolusite (MnOa as a function of recovery zone height. The recovery data exhibited a maxima. From Eq. 17, a plot of z vs ln(1 - X) was made as shown in Fig. 2. According to this theory, the slope of the plot of z vs -ln(l-X) should equal the HTU. The transition heights in this plot is clearly marked on the figure. The following were determined for flourite flotation: = 0.68m HTU = 1.36m HTU = 1.96m
HTU
zsl.Sm 1.9m 5 z s 3.4m z 2 3.4m
Since U, and V, are not affected by height, it follows that the increase in resistance to flotation is due to either hydrodynamic changes (e.g. reduction in a and l?a or changes in the rate constant k. At the present time, the exact factor responsible for the increase in the HTU is not known, but it is noted that the recovery data for coal as a function of recovery zone height (see Fig. 3) did not exhibit the trend
3610
MKU
Cl6
T. ITYOKUMBUL
shown in Fig. 2.
- In(l - X) Fig. 2:. Variation of flourite recovery with recovery zone height (Ynchausti et al. 1988) Since coal is naturally hydrophobic, this would appear to suggest that the changes in HTU for flourite fi otation are related to k. One possible explaination for this would be oxidation of the collector molecules adsorbed on the particle surfaces and/or oxidation of the mineral surface itself. This will be expected to alter the hydrophobicity of the mineral surface, thus reducing k. This would partly explain the poor recovery data of gelena in tall flotation columns (Kennedy, 1990). While oxidation of the gelena was cited as a possible reason for the poor recovery, this could not be backed with theory. The theory and procedure reported here remains the first to predict this behaviour. 4
3
I q
E d-
P
2 0
1
o-
0.0
I
0.5
1.0
1.5
2.0
- In (1 - X)
Fig. 3: Variation of coal recovery with recovery zone height (Bensley ef al. 1985) The data of Ounpuu and Tremblay (1991) mentioned earlier gives a value of 0.48m for the HTU for spharelite flotation. The reported particle size was -38~. For coal flotation, the data of Larttrei ef al. (1988) and Reddy et al. (1989) give values of 0.31m and 0.43m for the HTU. In general, the HTU for coal flotation was lower than that for mineral flotation (Ityokumbul, 1992b). ‘This is attributed to the fact that coal is naturally hydrophobic and has a lower density (hence lower settling velocity) compared to mineral particles with the same size.
Cl6
Mass transfer
approach
to flotationcolumn design
3611
CONCLUSION A mass transfer approach, to flotation column design has been presented. It reveals that the difficulty in particle collection as measured by the height of a transfer unit, HTU, is a function of the process variables (quality of air dispersion, particle settling velocity, slurry velocity in the recovery zone). Using literature data, it is shown that only a short recovery zone (of the order of lm) is required for particles made selectively hydrophobic. The current practice of sizing columns purely on such extrenous factors such as building and crane rail heights is an indication of the poor state of understanding of the factors affecting the particle collection process. This indicates that present day flotation columns may not be optimally designed and/or scaled. The procedure has also been used to partially explain the observed poor recovery data for readily oxidized minerals (e.g. gelena) in tall flotation columns.
NOMENCLATURE interficial area, m2 bubble surface/m3 reactor volume column cross sectional area, m2 solid concentration in the feed stream, kg/m3 slurry c, solid concentration, kg/m3 slurry solid concentration in the tailing stream, kg/m3 slurry : C(0) sotid concentration in the column at the feed point, kg/m3 C(L) solid concentration in the column at the tailings withdrawal point, kg/m’ bubble diameter, m d, particle dispersion coefficient, m*/s E, solid transfer rate constant, m3/kg s k k’ rate of particle detachment, l/s c k” first order rate constant, l/s L recovery zone height, m N” solid flux, kg/m* s Pe particle Peclet number defined by Eq. 3. Qt slurry feed rate, m’/s Qs gas flow rate, m3/s particle Reynolds number, d,Vpp& Re, specific bubble surface area, m bubble surface/m3 bubble volume S t time, s superficial gas velocity, m/s U, slurry velocity in the recovery zone, m/s Ux particle settling velocity in the presence of gas bubbles, m/s V, fractional recovery X Z axial length, m
:
Greek Symbols
Ei3 gas hold-up
l-
l-m
bubble load, kg/m’ bubble surface maximum bubble load, kg/m* bubble
surface
REFERENCES Lip loading considerations in, flotation columns. &-cc. Infer. Conf: on Ontario, June 2-6, 1991,& 661-672. Bensley, C.N., Roberts, T. and Nicol, S.K. (1985). Column flotation for the treatment of fine coal. Proc. 3rd. Australian Coal Prep. Conf. Wollong, NSW 18-21 Nov. (C.N.Bensley, ed.) 87103. de1 Villar, R., Finch, J.A., Yiannatos, J.B. and Laplante, A.R. (1988). Column flotation simulation. Iu
Amelunxen,
R.L.
(1991).
column flotation, Sudbury,
3612
MKU
T. ITYOKUMBUL
Cl6
Computer Applications in the Mineral Industry. (K. Fytas, J. Collins and R.J. Singhal, eds.), 233-239. A.A. Balkema, Rotterdam. Bobby, G.S. and Finch, J.A. (1986). Flotation column scale-up and modelling. CfMBuCC. 7& 89-96. Engelbrecht, J.A. and E.T. Woodburn (1975). The effects of froth height, aeration rate and gas precipitation on flotation. J. South African Inst. Min. Metall. 75, 125-132. Espinosa-Gomez, R., J.B. Yiannatos, J.A. Finch and N.W. Johnson. (1988). Carrying capacity limitations in flotation column. In Column Fcotation 4@& (KVS. Sastry, ed.), Chap_ 15, 143 148. Society of Mining Engineers, Inc. Littleton, Colorado. Flint, L.R. (1973). Factors influencing the design of flotation equipment. Min. Sci. Eng. 5 232-241. Harris, C.C. (1976). Flotation machines. In Flotation: A.M. Gaudin Memorial Volume, (MC Fuerstenau, ed.), Chap. 27, 753-815. AIME, New York. Ityokumbul, M.T. (1986). Hydrodynamic study of bubble column flotation for the recovery of heavy minerals from oil sand tailings. Ph.D. The& The University of Western Ontario, London, Canada (October 1986). Ityokumbul, M.T. (1992-a). A new modelling approach to flotation column design. Minerals Engineering, & 58.5-593. Ityokumbul, M.T. (1992b). Selection of recovery zone height in flotation column design. Submitted to Chem. Eng. Proc. Jameson, G.J., Nam, S. and Moo-Young, M. (1977). Physical factors affecting recovery rates in flotation. Miner. Eng. Sci. 3 103-118. Jameson, G.J. (1988). New concept in flotation column design. Miner. and Me&f. Process. s 44-47. Kennedy, A. (1990). The Jameson flotation cell. Mining Magazine, 163. 281-285. King, R-P., Hatton, T.A. and Hulbert, D.G. (1975). Bubble loading during flotation. Trans. Inst. Min. Metrill. 8& Cl12-115. Levenspiel, 0. and Fitzgerald, T.J. (1983). A warning on the misuse of the dispersion model. Chem.
Eng. Sci. 38, 489-492. Luttrell, G.H., Yan, S., Adel, G.T. and Yoon, R.H. (1990). A computer-aided design package for column flotation. Paper presented at SME Annual Meeting, Salt Lake City, Utah, February 26 - March 1, 1990. Luttrell, G.H., Weber, A.T., Adel, G.T. and Yoon, R.H. (1988). Microbubble flotation of fine coal. In Column Flotation 88, (K.V.S. Sastry, ed.), Chap. 21, 205211. Society of Mining Engineers, Inc. Littleton, Colorado. McKay, J.D., D.G. Foot, Jr. and M.B. Shirts (1988). Column flotation and bubble generation studies at the Bureau of Mines. In Column Flotation 88, (K.V.S. Sastry, ed.), Chap. 18, 173-186. Society of Mining Engineers, Inc. Littleton, Colorado. Ounpuu, M. and Tremblay, R. (1991). Investigation into the effect of column height on the 12OOmm diameter column at Matagami. Proc. Inter. Conf on column frotation, Sudbury, Ontario, June 2-6, 1991, L 303-316. Reddy, P.S.R., Kumar, S.G., Bhattacharyya, K.K., Sastri, S.R.S and Narasimhan, KS. (1988). Flotation column for fine coal beneficiation. Int. J. Miner. Process. 24. 161-172. Reis, Jr. J.B. and Peres, A.E.S., Industrial application of flotation columns in the concentration of a sulfide ore at Mineracao Manati Ltda. - Brazil, Proc. International Conference on column flotation, Sudbury, Ontario, June 2-6, 1991, Vol. 2, ~~525-537. Sastry, K.V.S. and D.W. Fuerstenau (1970). Theoretical analysis of a countercurrent flotation column. Trans. AIME 247, 46-52. Wheeler, D.A. (1984). Private communication. Yiannatos, J.B. and Bergh, L.G. (1991). RTD studies in an industrial flotation column: Use of radioactive tracer techniques. Proc. Inter. Conf: on column flotation, Sudbury, Ontario, June 2-6, 1991, L 221-232. Ynchausi, R.A., McKay, J.D. and Foot Jr., D.G., Column flotation parameters - their effects. in Column Flotation ‘88 (K.V.S. Sastry, ed.), Society of Mining Engineers, Inc. Littleton, GO, 1988, Chap. 18, ~~157-172.
Vol.
A MASS
47.
No.
13114.
pp.
360-3612.
1992 0
TRANSFER
APPROACH
TO -TATION
COLUMN
ocm-2509/92 ss.m+o.oo 1992 Pergsmon Press Ltd
DESIGN
Mku T. Ityokumbul Western Research Centre, CANMET 1 Oil Patch Drive P-0. Bag 1280 Devon, Alberta TOC lE0, Canada ABSTRACT
Flotation equipment design is an area of reactor engineering that has not attracted much research interest in chemical engineering. The commercial success of flotation remains a triumph of enlightened know how over inadequate know why as key design and scale-up parameters (e.g. column height) continue to be dictated by such non-process considerations as crane rail and building heights (Ounpuu and Tremblay, 1991). The shortcomings in the present approach to flotation column design and scale-up are discussed. It is shown that the use of first order kinetic expression in flotation column design and scale-up is not correct insofar as the recover-y and order of the process are concentration dependent. By using analogy with interface mass transfer, a new approach to flotation column design is presented, Using literature data, it is shown that only a short recovery zone is required for particles made selectively hydrophobic. Recent experimental data from a 1.2m flotation column (Ounpuu and Tremblay, 1991) and those of others as well (Wheeler, 1984; Bensely et al. 1985; Jameson, 1988; Reddy et al. 1988) confirm this observation. KEYWORDS:
Flotation column, design, scale-up, interface mass transfer
INTRODUCPION The design of flotation equipment is an area of reactor engineering that has not received much research interest in chemical engineering. As reviewed by Harris (1976), the commercial success of flotation remains a triumph of enlightened “know how” over inadequate “knew why”. For these reasons, progress has been made almost exclusively by empericism tempered by engineering judgement subject to the following questions: (i) ‘Does it work?’ (ii) ‘Is it competitive?’ and (iii) ‘What can be changed to make the process more competitive?’ This approach has led to the slow progress in the design and/or application of new flotation cells. In addition, flotation research has been mainly directed at understanding the chemistry without adequate consideration of the physics and mechanics of the process (Flint, 1973). One of the few designs to have achieved commercial success over the last twenty years is the flotation column. A flotation column is a bubble column device in which separation of solid particles is achieved using differences in their affinity for air bubbles. As is common with all bubble column devices, the transport, dispersion and mixing of materials is induced by the motion of gas bubbles in the slurry. The flotation column has three zones: the recovery, washing and froth zones. In the recovery zone, particles suspended in a descending water phase contact a rising swarm of air bubbles introduced at the base of the column. The bubbles are either generated internally using porous media or externally using such devices as the USBM sparger. Floatable solids collide with and adhere to the rising bubbles and are transported to the washing section. Non-floatable solids are removed from the base of the column as tailings. In the CES47:13/14-U:
3605
3606
MKU T.
Cl6
ITYOKIJMBUL
washing section, the mineral ladden air bubbles are subjected to a countercurrent stream of water which removes loosely attached gangue particles and transports them back into the recovery zone, thereby minimising concentrate contamination. The clean froth is recovered at the top of the column as concentrate. In spite of the commercial success of flotation columns, problems exist in their design and scale-up. All present design and scale-up procedures for flotation column are based on the application of the analogy with chemical kinetics (Dobby and Finch, 1986, de1 Villar et al. 1988; Luttrel er al. 1990). According to this procedure, the rate of flotation is considered to be first order in the concentration of floatable solids. By using the sedimentation dispersion model to represent the behaviour of solid particles in the flotation column, the recovery of floatable solids is predicted using Eq. 1. (1 - X) = 4qexp(Pe#2)/{( where
X is the fractional
1 + q)2exp(Pe,q/2)
recovery
and q is defined
- (1 - q)‘exp(-Pe,q/2)) as
q = (1 + 4k”tfle&“’
(2)
where xi, and Per are the particle residence time and Peclet numbers in the collection The particle residence time and Peclet number are predicted using the relationships: $
=
y1
- eJ/(u,
zone respectively.
+ VP)
Eqs. l-4 represent the relationships that are presently used in flotation column design and scale-up. The use of this approach in flotation column design has been questioned recently (Ityokumbul, 1992a). As an example, the use of a sedimentation-dispersion model implies the existence of a constant relative flow between the solid and liquid phases. According to Levenspiel and Fitzgerald (1983), the existence of a constant relative flow is indicative of a Guassian-convection flow. Morever, the application of this model in solid dispersion studies has been found to yield results which show that the solid dispersion ccx@cient increases with particle size (Yiannatos and Bergh, 1992). Since larger particles have a higher inertia, it is unlikely that they will be more mixed than the smaller ones. In addition, the use of first order kinetic expression suggests that the recovew be independent of initial concentration. While this is true for low concentrations of floatable solids, the same is not true at high concentration. At high concentrations, the process changes from being first order to one that is zero order in concentration of floatable solids. In addition, estimates of activation energy for the flotation process give values less than lOKcal/mole (Ityokumbul, 1992a). This is not indicative of chemical reaction control. In agreement with the observations of Jameson et al. (1977), a mass transfer approach to flotation column design is presented.
MASS
TRANSFER
APPROACH
TO
FLOTATION
COLUMN
DESIGN
As indicated earlier, the use of analogy with chemical kinetics in flotation column design is not correct. In the present work, we consider the flotation process to be analogous to interface mass transfer. For the formulation of the equations describing the process, the following assumptions are made: (1) Particle collection takes place in the recovery zone only. (2) The rate of attachment of particles to air bubbles is proportional to the concentration of floatable solids and uncovered bubble surface. (3) The rate of pat-tide detachment is proportional to the surface concentration of solid particles on the air bubbles (Sastry and Fuerstenau, 1970). 4) The effect of froth height on recovery is small. This is a reasonable assumption unless the froth depth is excessive (Engelbrecht and Woodbum, 1975). 5) The liquid flow rate in the recovery zone is equal to the tailings flow rate. 6) The solid behaviour in the recovery zone may be described using the sedimentation convection model (Ityokumbul, 1986).
Cl6
Mass transfer approach to flotation column design
3607
With assumptions1 and 4, the design of the flotation column reduces to that of the recovery zone. From assumptions 2 and 3, the net bubble loadiig rate may be written aa: dl?/dt= k(l-, - T)C - k’l-
(9
where C is the concentration of floatable solids, r and r, are the bubble and maximum bubble loads, k and k’ are the rate constants for attachment and detachments respectively. From assumption 6, the flux of solids in the recovery zone may be written as: N” = p,
+
V,)U(l - Es)
(6)
The flux of solids in a. 6 is based on the crosssec tional area occupied by the slurry. An overall material balance for the recovery zone (Fig. 1) may be written as:
Qsr
= A(Vp + &.){C
- Cd
(7)
where S is the specific bubble surface area.
r(o) t ------I Feed-i-----I____________:
Q&
z=o
.z=L Air
f
I
lTailings Qt. Ct
Qg
Fig. 1: Material balance for the recovery zone By using analogy with interface mass transfer, the height required for a given recovery is calculated from the expression:
d(Q#=)= vwul
- lT)C - kT]aAdz
or
z = I Qpil-/{[k(l-, J
By definition, a = 6sJd, and S = 6/d,
- lY)C - k’qaA}
i
(8)
3608
MKU
T. ITYOKUMBUL
Cl6
In the presence of frothers. bubble coalescence in the recovery zone is expected to be minimal. Thus Q$/Aa may be taken to be constant. Substituting for a and S in Eq. 9 results in the following dl-/([k(r, - r)C - k’r]} (12) I Solution for the column height requires integration of the RHS of Eq. 12. This is done using the material balance expression (i.e. Eq. 7) which gives the variation of the bubble load with concentration of z =
floatable
U$EI
solids
in the recovery
zone.
DISCUSSION
Determination of Collection Zone LenPth The determination of column height requires a numerical integration of Eq. (12). For this purpose, order of magnitude estimates of the transfer rate constant and hydrodynamic parameters are required. The maximum bubble loading data of King et al. (1975) was rearranged to give (Ityokumbul, 1986): I-,
= 0.0035/d,“-875
(13)
The carrying capacity data of Amelunxen (1991) as well as those of Espionosa-Gomez el al. (1988) indicate that in a large number of applications, the bubbles are lightly loaded (lY’cO.Olkg/m’). For typical flotation size air bubbles (d,cO.O03m), T,,,>>T. The author has shown that under these conditions, what has come to be known as the flotation rate constant is related to the particle transfer rate constant and the vessel hydrodynamic parameters by the expression (Ityokumbul, 1992a): b
= akr,
(14)
For hydrophobic particles and lightly loaded bubbles,
kl-,C>> k'l-
(1%
Investing Eqs. 7, lo-12 and 15, we get z = (U,+V,)/akT,
I
dC/C
(16)
Integration of Eq. 16 gives z = (U,+V,)/akr,
* ln{C(O)/C(L)}
(17a)
* ln(1 - X)
(17b)
or z = - (U,+V,)/akr,
An estimate for k may be made from reported observed rate con&ants using Eq. 14. Typical values for L are in the range 1-3/min. For gas velocities in the range 0.012-O.O17m/s, the maximum interfacial area calculated from the data of Amelunxen (1991) was approximately 9SOm2/m3for a bubble diameter of 0.0012m. Using a value of 16b.of 2/min gives an estimate of approximately 0.000028 m3/kg s for the particle transfer rate constant. Note that this estimate is at least one order of magnitude lower than that reported by King et ~2. (1975). In industrial applications, slurry and gas velocities in the ranges 0.005 O.O2m/sand O-01-O.O3m/srespectively are common. Thus a value of O.Olm/s is assumed for the slurry velocity in the recovery zone. The gas velocity and hold-up data assumed here is that used in the estimation of k above (O.O14m/s and 0.18 respectively). For the bubble size of O.OO12m used above for estimating k, particles with a terminal settling velocity of O.Olm/s and assuming a 90% recovery, the recovery zone height is estimated to be 1.77m. This finding is in apparent contradiction with the current practice of designing flotation columns with recovery zones of over 9m in height. The experimental data of several authors confirm that only a short recovery zone is required for particles made hydrophobic (Wheeler, 1984, Benseley et a/. 1985; Jameson, 1988, Reddy et al. 1988; Ounpuu and Tremblay, 1991).
Cl6
Mass transfer
approach to flotation column
design
360!?
For example, Ounpuu and Tremblay (1991) have shown that a recovery zone height of 05m was sufficient to attain 65% recovery of sphalerite (ZnS) in their 1.2m diameter flotation column, thus confirming that only a short recovery zone is required. Similarily, Reddy et al. (1989) and Luttrel et al. (1988) have shown that recovery zone heights of l.Om were sufficient to yield 90% and 96% recovery of -500~ and -5~ coal in their O.lOm and 0.05m flotation columns respectively. From Eq. 17, the term (U,+VJ/akF, is equivalent to the height of a transfer unit, HTU, while the integral represents the number of transfer units, NTU. Since the FFfU is a measure of the difficulty of the separation, it follows from Eq. 17 that increasing the particle size results in an in increase in the height required for a given recovery. Since King et al. (1975) did not find any dependence of k on particle size, this finding is indeed a valid one insofar as the particle residence time is also reduced. This may partly explain the difficulty the flotation of gelena (PbS), a mineral with a density greater than 5,000kg/m3. Eq. 17 also indicates that the column height required for a given performance is inversely related to the quality of the air dispersion in the recovery zone (air interficial area, a). Since flotation is an interficial phenomenon, this finding is a reasonable one. For a given gas velocity, increasing the bubble interficial area will therefore be expected to increase the rate of flotation thus reducing the HTU. It should be noted that the quality of the air dispersion (measured by the bubble size) also affects the maximum bubble load. Since the maximum bubble load per unit surface area increases with decreasing bubble size (King et UC. 1975), this will also contribute to the reduction in the HTU. Since most new flotation column installations are equipped with external spargers, control of the bubble size represents a useful operational tool. The fundamental work of McKay et al. (1988) show how the bubble size may be controlled with the external sparging system. Aunlication to Other Studies With the mass transfer approach to flotation column, Eq. 17 becomes a useful tool for the comparison of column performance and also for the determination of rate data. As an example, if the recovery height is fixed and the slurry velocity varied, a plot of z/-ln(l-X) vs U, should yield a straight line with the following parameters (Ityokumbul, 1992b): slope = l/akFm intercept = VJakF, From these, the rate constant and particle settling velocities may be determined. This procedure was applied to the recent experimental data of Reis and Peres (1991) for gold-bearing chalcopyrite ore. These authors reported that the ore was ground to a d, of 12Om (i.e. 80% passing the indicated particle size). The use of this procedure gave an observed rate constant of 0.0103/s and an average particle size of 90,fun (Ityokumbul, 1992b). The fact that the particle size is within the d, range reported by these authors is an indication of the validity of this approach in flotation column design. Ynchausti et al. (1988) presented recovery data for flourite (CaFa and pyrolusite (MnOa as a function of recovery zone height. The recovery data exhibited a maxima. From Eq. 17, a plot of z vs ln(1 - X) was made as shown in Fig. 2. According to this theory, the slope of the plot of z vs -ln(l-X) should equal the HTU. The transition heights in this plot is clearly marked on the figure. The following were determined for flourite flotation: = 0.68m HTU = 1.36m HTU = 1.96m
HTU
zsl.Sm 1.9m 5 z s 3.4m z 2 3.4m
Since U, and V, are not affected by height, it follows that the increase in resistance to flotation is due to either hydrodynamic changes (e.g. reduction in a and l?a or changes in the rate constant k. At the present time, the exact factor responsible for the increase in the HTU is not known, but it is noted that the recovery data for coal as a function of recovery zone height (see Fig. 3) did not exhibit the trend
3610
MKU
Cl6
T. ITYOKUMBUL
shown in Fig. 2.
- In(l - X) Fig. 2:. Variation of flourite recovery with recovery zone height (Ynchausti et al. 1988) Since coal is naturally hydrophobic, this would appear to suggest that the changes in HTU for flourite fi otation are related to k. One possible explaination for this would be oxidation of the collector molecules adsorbed on the particle surfaces and/or oxidation of the mineral surface itself. This will be expected to alter the hydrophobicity of the mineral surface, thus reducing k. This would partly explain the poor recovery data of gelena in tall flotation columns (Kennedy, 1990). While oxidation of the gelena was cited as a possible reason for the poor recovery, this could not be backed with theory. The theory and procedure reported here remains the first to predict this behaviour. 4
3
I q
E d-
P
2 0
1
o-
0.0
I
0.5
1.0
1.5
2.0
- In (1 - X)
Fig. 3: Variation of coal recovery with recovery zone height (Bensley ef al. 1985) The data of Ounpuu and Tremblay (1991) mentioned earlier gives a value of 0.48m for the HTU for spharelite flotation. The reported particle size was -38~. For coal flotation, the data of Larttrei ef al. (1988) and Reddy et al. (1989) give values of 0.31m and 0.43m for the HTU. In general, the HTU for coal flotation was lower than that for mineral flotation (Ityokumbul, 1992b). ‘This is attributed to the fact that coal is naturally hydrophobic and has a lower density (hence lower settling velocity) compared to mineral particles with the same size.
Cl6
Mass transfer
approach
to flotationcolumn design
3611
CONCLUSION A mass transfer approach, to flotation column design has been presented. It reveals that the difficulty in particle collection as measured by the height of a transfer unit, HTU, is a function of the process variables (quality of air dispersion, particle settling velocity, slurry velocity in the recovery zone). Using literature data, it is shown that only a short recovery zone (of the order of lm) is required for particles made selectively hydrophobic. The current practice of sizing columns purely on such extrenous factors such as building and crane rail heights is an indication of the poor state of understanding of the factors affecting the particle collection process. This indicates that present day flotation columns may not be optimally designed and/or scaled. The procedure has also been used to partially explain the observed poor recovery data for readily oxidized minerals (e.g. gelena) in tall flotation columns.
NOMENCLATURE interficial area, m2 bubble surface/m3 reactor volume column cross sectional area, m2 solid concentration in the feed stream, kg/m3 slurry c, solid concentration, kg/m3 slurry solid concentration in the tailing stream, kg/m3 slurry : C(0) sotid concentration in the column at the feed point, kg/m3 C(L) solid concentration in the column at the tailings withdrawal point, kg/m’ bubble diameter, m d, particle dispersion coefficient, m*/s E, solid transfer rate constant, m3/kg s k k’ rate of particle detachment, l/s c k” first order rate constant, l/s L recovery zone height, m N” solid flux, kg/m* s Pe particle Peclet number defined by Eq. 3. Qt slurry feed rate, m’/s Qs gas flow rate, m3/s particle Reynolds number, d,Vpp& Re, specific bubble surface area, m bubble surface/m3 bubble volume S t time, s superficial gas velocity, m/s U, slurry velocity in the recovery zone, m/s Ux particle settling velocity in the presence of gas bubbles, m/s V, fractional recovery X Z axial length, m
:
Greek Symbols
Ei3 gas hold-up
l-
l-m
bubble load, kg/m’ bubble surface maximum bubble load, kg/m* bubble
surface
REFERENCES Lip loading considerations in, flotation columns. &-cc. Infer. Conf: on Ontario, June 2-6, 1991,& 661-672. Bensley, C.N., Roberts, T. and Nicol, S.K. (1985). Column flotation for the treatment of fine coal. Proc. 3rd. Australian Coal Prep. Conf. Wollong, NSW 18-21 Nov. (C.N.Bensley, ed.) 87103. de1 Villar, R., Finch, J.A., Yiannatos, J.B. and Laplante, A.R. (1988). Column flotation simulation. Iu
Amelunxen,
R.L.
(1991).
column flotation, Sudbury,
3612
MKU
T. ITYOKUMBUL
Cl6
Computer Applications in the Mineral Industry. (K. Fytas, J. Collins and R.J. Singhal, eds.), 233-239. A.A. Balkema, Rotterdam. Bobby, G.S. and Finch, J.A. (1986). Flotation column scale-up and modelling. CfMBuCC. 7& 89-96. Engelbrecht, J.A. and E.T. Woodburn (1975). The effects of froth height, aeration rate and gas precipitation on flotation. J. South African Inst. Min. Metall. 75, 125-132. Espinosa-Gomez, R., J.B. Yiannatos, J.A. Finch and N.W. Johnson. (1988). Carrying capacity limitations in flotation column. In Column Fcotation 4@& (KVS. Sastry, ed.), Chap_ 15, 143 148. Society of Mining Engineers, Inc. Littleton, Colorado. Flint, L.R. (1973). Factors influencing the design of flotation equipment. Min. Sci. Eng. 5 232-241. Harris, C.C. (1976). Flotation machines. In Flotation: A.M. Gaudin Memorial Volume, (MC Fuerstenau, ed.), Chap. 27, 753-815. AIME, New York. Ityokumbul, M.T. (1986). Hydrodynamic study of bubble column flotation for the recovery of heavy minerals from oil sand tailings. Ph.D. The& The University of Western Ontario, London, Canada (October 1986). Ityokumbul, M.T. (1992-a). A new modelling approach to flotation column design. Minerals Engineering, & 58.5-593. Ityokumbul, M.T. (1992b). Selection of recovery zone height in flotation column design. Submitted to Chem. Eng. Proc. Jameson, G.J., Nam, S. and Moo-Young, M. (1977). Physical factors affecting recovery rates in flotation. Miner. Eng. Sci. 3 103-118. Jameson, G.J. (1988). New concept in flotation column design. Miner. and Me&f. Process. s 44-47. Kennedy, A. (1990). The Jameson flotation cell. Mining Magazine, 163. 281-285. King, R-P., Hatton, T.A. and Hulbert, D.G. (1975). Bubble loading during flotation. Trans. Inst. Min. Metrill. 8& Cl12-115. Levenspiel, 0. and Fitzgerald, T.J. (1983). A warning on the misuse of the dispersion model. Chem.
Eng. Sci. 38, 489-492. Luttrell, G.H., Yan, S., Adel, G.T. and Yoon, R.H. (1990). A computer-aided design package for column flotation. Paper presented at SME Annual Meeting, Salt Lake City, Utah, February 26 - March 1, 1990. Luttrell, G.H., Weber, A.T., Adel, G.T. and Yoon, R.H. (1988). Microbubble flotation of fine coal. In Column Flotation 88, (K.V.S. Sastry, ed.), Chap. 21, 205211. Society of Mining Engineers, Inc. Littleton, Colorado. McKay, J.D., D.G. Foot, Jr. and M.B. Shirts (1988). Column flotation and bubble generation studies at the Bureau of Mines. In Column Flotation 88, (K.V.S. Sastry, ed.), Chap. 18, 173-186. Society of Mining Engineers, Inc. Littleton, Colorado. Ounpuu, M. and Tremblay, R. (1991). Investigation into the effect of column height on the 12OOmm diameter column at Matagami. Proc. Inter. Conf on column frotation, Sudbury, Ontario, June 2-6, 1991, L 303-316. Reddy, P.S.R., Kumar, S.G., Bhattacharyya, K.K., Sastri, S.R.S and Narasimhan, KS. (1988). Flotation column for fine coal beneficiation. Int. J. Miner. Process. 24. 161-172. Reis, Jr. J.B. and Peres, A.E.S., Industrial application of flotation columns in the concentration of a sulfide ore at Mineracao Manati Ltda. - Brazil, Proc. International Conference on column flotation, Sudbury, Ontario, June 2-6, 1991, Vol. 2, ~~525-537. Sastry, K.V.S. and D.W. Fuerstenau (1970). Theoretical analysis of a countercurrent flotation column. Trans. AIME 247, 46-52. Wheeler, D.A. (1984). Private communication. Yiannatos, J.B. and Bergh, L.G. (1991). RTD studies in an industrial flotation column: Use of radioactive tracer techniques. Proc. Inter. Conf: on column flotation, Sudbury, Ontario, June 2-6, 1991, L 221-232. Ynchausi, R.A., McKay, J.D. and Foot Jr., D.G., Column flotation parameters - their effects. in Column Flotation ‘88 (K.V.S. Sastry, ed.), Society of Mining Engineers, Inc. Littleton, GO, 1988, Chap. 18, ~~157-172.