Znd. Eng. C h e m . Res. 1990,29,943-949
943
Conceptual Design of Packed Flotation Columns S c o t t A. Idlas,? Joseph A. FitzPatrick,l and John C. Slattery*it Department of Chemical Engineering and Department of Civil Engineering, Northwestern University, Evans ton, I1linois 60208-3120
A new analysis is presented for packed flotation columns, which have been suggested as being more efficient than open flotation columns. When the column height is fixed, we find that reflux significantly improves the product grade at the expense of decreased recovery. For a given selectivity, recovery can be increased by increasing the excess area available for flotation or by increasing the height of packing below the feed. The recent round-robin test conducted by the Department of Energy (Killmeyer and Hucko, 1989; Hucko and Gala, 1988) suggests that columns have an inherent advantage over standard mechanical/pneumatic flotation machines in cleaning coal. The overall best performer at this point appears to be static tube flotation (a packed flotation column), with columns in general always outperforming cell systems. Three types of columns have been suggested for use in flotation: open, packed, and staged (Kawatara and Eisele, 1987). Open flotation columns with countercurrent washing of the foam generated are currently being used for refining a variety of minerals (Nicol et al., 1988; Subramian et al., 1988; Egan et al., 1988; Moon and Sirois, 1988; Ynchausti et al., 1988; Wheeler, 1988). They are reported to be more efficient than the traditional agitated vessel (Luttrel et al., 1987; Kawatara and Eisele, 1988; Misra and Harris, 1988; Nicol et al., 1988). Backmixing (axial dispersion) can be a problem with these columns. This has been specifically addressed in the analyses of Dobby and Finch (1986), of Luttrel et al. (1987), and of Sastry and Lofftus (1988). The addition of packing reduces the effects of backmixing seen in open columns. Packed flotation columns have been reported by Yang (1988) to achieve the same separation for which eight traditional stages were required. Scale-up of the column diameter to increase throughput was considered to be direct, because residence times could be estimated to be nearly those expected in a plug flow (Yang, 1988). Scale-up of the column height to increase product purity and product recovery has not been previously addressed (Li, 1987; Yang, 1988). A staged flotation column has been proposed (Dell and Jenkins, 1976; Degner and Sabey, 1988). Scale-up of the number of stages to increase product purity and product recovery has been discussed in a companion paper (Idlas et al., 1990). Scale-up of the column diameter to increase throughput has not been addressed. In commercial-scale tests, the WEMCO-Leeds column was reported to be more efficient than standard cells (Degner and Sabey, 1988). Until recently, coal and other minerals were typically ground too coarsely to be used in packed or staged columns without serious plugging problems. Particularly in the case of coal, where there is an increased emphasis on the physical removal of as much of the pyrites as possible, this limitation appears to have been removed. In what follows, we discuss the scale-up of the height of packed flotation columns to increase product purity and product recovery. Since analyses for open flotation col*Current address: Department of Chemical Engineering,Texas A&M University, College Station, TX 77843-3122. Department of Chemical Engineering. Department of Civil Engineering.
0888-5885/90/2629-0943$02.50/0
umns are formally interchangeable with those for packed flotation columns, it is appropriate to compare ours with the somewhat similar analysis presented by Sastry and Lofftus (1988). They assume that the volume fraction of solids being recovered by flotation is small. We have no similar restriction. Following the example common in treatments of distillation, we do not include any effects of backmixing, merging these effects into the expression for the rate of particle attachment. Sastry and Lofftus (1988) include the effects of backmixing (axial dispersion) in their general analysis, but not in their example computations. Finally and most important, we allow for reflux, in which a portion of the overhead product is returned to the top of the column with the washing solution. This appears not to have been previously suggested in the context of flotation, although it is common practice in distillation (Coulson et al., 1978; Geankoplis, 1978; Sherwood et al., 1975; Treybal, 1980). Our approach is similar to that given for staged flotation columns (Idlas et al., 1990). Statement of the Problem Our objective is to outline a design algorithm for the vertical packed flotation column sketched in Figure 1. The packed column is partially filled with a pool of pulp, the level of which is controlled. Gas is introduced at the bottom of the column and rapidly dispersed. Above the pool of pulp, the packed column is filled with a spherical froth that is washed from above by returning a portion of the product pulp, mixed with a make-up stream, as reflux. The operation of the column varies both with the level of the pool of pulp and with the level at which the feed is introduced. The portion of the column above the feed is known as the cleaning section. The fraction of a bubble’s surface covered by species i increases as a bubble rises first through the pulp and then through the froth. The pulp associated with the rising froth is continually replaced by a progressively cleaner pulp washing down from above. The portion of the column below the feed is referred to as the recovery or scavenging section: the concentration in the pulp of the mineral being floated decreases as the pulp descends through this portion of the column, with the tailings leaving from the bottom of the column. The packing has two purposes. First, it prevents backmixing (dispersion) both in the froth and in the pool of pulp, allowing axial concentration gradients to develop in both of these regimes. Backmixing may cause impure pulp to rise, decreasing grade, and it may cause pulp containing the valuable mineral to sink, decreasing recovery (Dobby and Finch, 1985; Laplante et al., 1988). A packed column should give a more efficient separation than an open column having an equal height. Second, because 0 1990 American Chemical Society
944
Ind. Eng. Chem. Res., Vol. 29, No. 6, 1990 GAS
-
SEPARATOR
PRODUCT
I
i
/I
-2-2,
i
i
Ii
PULP
I I
Ii
n GAS
I
SECTION^
I
-z = 0
TAILINGS
Figure 1. Packed flotation column.
of imperfect separation of the minerals during the crushing and grinding preceding flotation, the surfaces of some particles will be heterogeneous, preventing even the best reagent systems from providing perfect selectivity. The packed column may facilitate more intimate contact between the rising bubbles and descending pulp, giving the sorting process further opportunities to operate. We will make the following assumptions in our analysis. (1)The column will be considered to operate at steady state, although in reality the flow of the froth through the packing may be episodic. (2) We will assume that the feed is introduced below the top of the pool of pulp. The case where the feed is introduced above the pool of pulp can easily be developed by analogy. This means that the column can be divided into three sections: section 1 is the scavenging section below the feed, section 2 is that portion of the cleaning section between the pool of pulp and the feed, and section 3 is that portion of the cleaning section between the top of the column and the pool of the pulp. (3) The character of the rising bubbles is both constant and the same in the three sections of the column. This means that we are neglecting both coalescence and splitting of the bubbles as they rise through the packing. This assumption can be eliminated. (4) The feed is a pulp or suspension rather than a froth. It contains the surfactant system. (5) Any make-up solution added to the reflux (see Figure 1) contains sufficient surfactant to avoid dilution of the reagent system. (6) Both the cross section at which the feed is introduced as well as the top of the pool of pulp are represented as singular surfaces. (7) We will not include the effects of backmixing of the gas and pulp. One can say either that the model is limited to the case where the gas and pulp move countercurrently in a one-dimensional flow or that the effects of any backmixing are included in the empirical description of the rate of flotation of particles. This is analogous to the standard description of distillation, gas adsorption, etc., in packed columns. This assumption could be eliminated by including the effects of backmixing, possibly following the example of Dobby and Finch (1986) and Sastry and Lofftus (19881, who discussed open columns.
I I G, Y3(Il
I
t
LB, X,(I)
Figure 2. Cleaning section of column above ZL.
(8) Sedimentation in the pulp phase is neglected. This assumption can be eliminated.
Mass Balances With reference to Figure 2, the mass balance for solid species i in section 3 (that portion of the cleaning section consisting of froth between the top of the column and the pool of pulp) requires
-d f-l )--- L,
dXf) (1) dz G dz This can also be referred to as the operating line for solid species i in section 3 of the column. Here yl" is the mass of solid species i attached to the rising bubbles per unit mass of gas at some arbitrary cross section in section j , Xf) is the mass of solid species i per unit mass of the continuous liquid phase in the pulp in section j , G is the mass rate of flow of gas per unit cross-sectional area which is assumed to be a constant, and Lj is the mass rate of flow of the continuous liquid phase in section j per unit cross-sectional area. The mass balance for the continuous liquid phase in this section of the column requires
where R is the reflux ratio (fraction of the pulp stream exiting from the separator that is diverted to reflux), the subscript P denotes the overhead product stream from the separator, and the subscript R denotes the reflux stream returned to the top of the column. It is important to recognize that the product stream exiting overhead from the column is a froth, the quality of which is
and that different amounts of solids are carried by the bubbles and pulp in this froth (4)
Ind. Eng. Chem. Res., Vol. 29, No. 6,1990 945 G, Y,(i)
L,, X(')
7-7 -2 =
G
0
LT, X,()i
Figure 4. Scavenging section of column below Zp
The mass balances at the cross section ZLcorresponding to the top of the pool of pulp are satisfied identically once we recognize that at z = 2,
I I I
t
G,Y,(i)
L., X,(i)
k3') = yp
(11)
X f ) = xp,
(12)
Figure 3. Cleaning section of column above ZFincluding a portion of section 2.
At cross section ZF where the feed is introduced, the mass balance for solid species i requires
By p(G) we mean the density of the gas, p(L)the density of the continuous liquid phase, p ( j ) ( j = 1,..., C)the density of solid phase j , and Zc is the height of the column. Referring to Figure 3, the mass balance for solid species i in section 2 (that portion of the cleaning section consisting of the pool of pulp above the feed) demands
and the mass balance for the continuous liquid phase demands Lz - L1+ LF = 0 (14)
dk3f) L3 dX&? -=-(5) dz G dz This is the operating line for solid species i in section 2 of the column. The mass balance for the continuous liquid phase in this section of the column is satisfied by recognizing
Lz = L3
(6)
Referring to Figure 4, the mass balance for solid species i over the bottom portion of section 1 (the scavenging section) takes the form (7) This is also known as the operating line for solid species i in the scavenging section of the column. The mass balance for the continuous liquid phase in this section of the column simply requires
L 1 = LT (8) where the subscript T refers to the tailings removed from the bottom of the column. The mass balance for solid species i over the mixer shown in Figure 1 gives
The mass balance for the continuous liquid phase requires
LR = l - RLp+M
(10)
in which we have introduced M as the mass rate of flow of make-up solution added per unit cross-sectional area.
The subscript z > ZF denotes that the quantity is defined in section 2 as the feed cross section is approached; the subscript z < ZF indicates that it is defined in section 1 in the limit as this cross section is approached. In arriving at eq 13, we have assumed that at z = ZF
yy = yp
(15)
So far we have developed the equations that ensure that mass is conserved. Next we must describe the attachment process. These equations, unlike the preceding, will be very dependent on the column packing and operating conditions. Rate of Attachment In order to describe the transfer of particles from the pulp to the gas, we must describe the functional form of the attachment/detachment rate expression. The kinetics of flotation processes have been reviewed by Jameson et al. (1977) and Mori et al. (1986). We will assume the following, consistent with standard flotation practice: (9) The rate of collisions between the particles and bubbles is proportional to the concentration of particles in the pulp. (10) The probability of a successful collision is proportional to the uncovered area on a bubble. A slightly more complicated relationship has been proposed by Szatkowski and Freyberger (1985); however, a simple linear relationship is adequate for our purposes. (11)The rate of particle detachment is proportional to the surface concentration of particles on the bubbles. Little work has been done on detachment rates in flotation; this is one of the simplest choices. Equations that describe the net rate of attachment at each axial position of section j and that are consistent with assumptions 7-11 and the operating lines, eqs 1 , 5 , and 7, are ( j = 1-3)
946 Ind. Eng. Chem. Res., Vol. 29, No. 6, 1990
Here K,') and k!) are the rate constants that take into account the hydrodynamics and surface chemistry of the attachment/detachment procesaes, respectively, in section j , ai is the interfacial area per unit volume of column in section j , and "
is the mass of species i in the pulp per unit volume of pulp in section j . The quantity
characterizes the difference between the interfacial area b per unit mass of gas and the interfacial area per unit mass of gas currently occupied by all of the various species present; VCk)is the volume of species i per unit area occupied by species i. This must be greater than zero for attachment to continue. In view of assumption 3, b is assumed to be a constant throughout the column. Both forms of eq 16, applied successively to each of the C species of solid in each of the three sections of the column, must be integrated, consistent with the conditions for section 3 at z = Zc
yy = yyZC
(18)
that the height of the column Zc, the top of the pool of pulp ZL,and the location of the feed ZF are given; that the gas flow rate G,the reflux ratio R, and the make-up solution flow rate M are known; that the quality QP of the froth exiting overhead from the column is known; and that we have previously determined the rate constants for each section J as well as the interfacial area b per unit mass of gas and the volume V") of species i per unit area of interface occupied by species i. In order to determine Lp and Xg),we must solve 9C + 6 equations for each of the C solid species [eq 4, eq 9, eq 14, both forms of eq 16 (subject to eqs 18-29 with eq 17 substituted to eliminate c!)) in each of the three sections of the column, in addition to eqs 2, 3,6,8,10, and 131 in 9C + 6 unknowns for each of the C solid species y':!zL, eizF,Xg), Xg), X!Lz , X$.+ X!izF, and X I ) as well as L,, L2, L,, Lp, LT, and kR].
ce&,,
Illustration In order to illustrate how a packed column may work, let us restrict ourselves to the following idealizations. (a) Thinking in terms of an application in which we wish to remove ash and pyrite from coal, we will assume that there are only two solid species present, coal and gangue. (b) With respect to eq 16, we will assume that detachment does not occur: =0 (30) J
J
Under these conditions, we have 24 equations to solve in 24 unknowns. In presenting the results, it will be convenient to define the dimensionless rate constants for each section of the column as
We recognize that these dimensionless rate constants are a product of the dimensional rate constants and a gasphase residence time rjG)in section j . The following ratios will also be useful
as well as the s e l e c t i v i t y in section j of the column 8, z KP)*/KP)*
of the system. Perfect selectivity corresponds to Sj By g r a d e atz=O
(36)
-
m.
C
yp = 0
(28)
9
I
x p (;=1C X p ' j ) ) - '
(37)
we mean the ratio of the mass of coal to the total mass of solids in the overhead product. By recovery
Summary of Equations Let us assume that there are C species of solid in the system; that the properties of the feed (LF,Xb))are given;
Ind. Eng. Chem. Res., Vol. 29, No. 6, 1990 947 1.0
1.0
O
R=0.8
s = 100 q
f
0.Q
G
w
0.8
G
0.8
0.6
0
1
2
3
4
5
K?* Figure 5. Product grade 9 as a function of @* for various values of the selectivity 8,the reflux ratio R = 0, @A = 1, @?= 5,and the excess interfacial area 34 = 1.
Figure 7. Product grade 9 as a function of 'I* for various values of the reflux ratio R, the selectivity 8 = lo,%$ = 1, I@\) = 5,and the excess interfacial area 34 = 1.
On' 0.6 "
I
o
i
2
I
,
3
4
t 0
5
K:c'* Figure 6. Recovery R as a function of @)* for various valuea of the selectivity 8,the reflux ratio R = 0, K# = 1, @i = 5,and the excess interfacial area 34 = 1.
1
2
3
4
5
K:c'* Figure 8. Product grade 9 as a function of I@)* for various values of the reflux ratio R,the selectivity 8 = 10, @A = 3, @i = 5,and the excess interfacial area 34 = 1. 1.07
we mean the ratio of the mass of coal in the product to the mass of coal in the feed. By C
A
E
bGICXF'J'LF/(p'''V'J~)]-l- 1 j=l
(39)
we denote the excess interfacial area required to float all of the solids in the feed, both coal and gangue. Except where noted otherwise, the standard parameters used in these example computations are as follows: (i) mass percent solids in feed = 6.9%, mass percent coal in feed solids = 60%, mass percent gangue in feed solids = 40%, bubble radius Rb = 1 mm, particle radius R , = 10 pm, V ( ' )= 4/3Rp = 13.3 pm, QP = 0.74, pfc)= 1.5 g/cm3, pk) = 2.5 g/cm3, p@) = 1.225 X g/cm3, p(L)= 1g/cm3, b = ~ / ( R G ( ~=) )2.45 X lo4 cm2/g, and 8 Sj for all sections j . (ii) The volumetric flow rate of gas is s twice the volumetric flow rate of the feed slurry:
(iii) The volumetric flow rate of make-up solution is
0.6 0
1
3
4
K?*
Figure 9. Product grade 9 as a function of K(E)* for various values of the reflux ratio R,the selectivity 8 = IO,& = 10,K&i = 5,and the excess interfacial area 34 = 1.
0.4v 0.2
0 4 : 0
This means that, as R is varied, the volume rate of flow of the slurry returning to the top of the column remains constant and equal to twice the volume rate of flow of the pulp exiting the top of the column as foam. In the absence of reflux, Figure 5 shows that the product grade increases as the selectivity increases. Figure 6 indicates that, at least for the conditions chosen, the recovery is relatively independent of 8, although it does increase as @* increases.
2
1
:
:
:
2
3
4
lO,2$
Figure 10. Recovery R as a function of the reflux ratio R,the selectivity 8 = excess interfacial area 34 = 1.
'I*
I
5
for various values of = 1,J@ = 5,and the
The effect of reflux ratio on 0 is presented in Figures 7-9 for K@ = 1,3, and 10, respectively. In each case, B increases with increasing R. The recovery decreases as R increases in Figures 10-12. The large decrease in recovery
948 Ind, Eng. Chem. Res., Vol. 29, No. 6, 1990
r------m
0
I!;, 0
1
2
,
I
3
4
Figure 11. Recovery 5-7 as a function of the reflux ratio R,the selectivity S = 10, excess interfacial area A 1.
;i 5
Sherwood et al., 1975; Treybal, 1980). However, there is a penalty. If all other operating variables are held fixed, product recovery decreases as the reflux ratio and product grade are increased. In order to maintain the product recovery constant as the product grade increases, one must solve an optimization problem in which both the excess interfacial area available for flotation and the packing height below the feed may be increased. As one would expect, both operating costs and capital costs must be increased, in order to improve the product grade while maintaining the product recovery constant. Acknowledgment
= 5, and the
Y.01
K:C'* Figure 12. Recovery R as a function of fie)* for various values of the reflux ratio R,the selectivity S = 10, K E = 10, K$i = 5, and the excess interfacial area A = 1.
for R = 0.8 can be attributed to a limitation in the interfacial area available to float the solids. Only 20% of the interfacial area is used to remove product. Discussion In order to implement this analysis for scale-up, experimental studies are required to determine the rate constants K,(i)ajfor attachment and ky)ajfor detachment of each species i in each section j of the column, as well as the interfacial area per unit mass of gas and the volume of species i per unit area of interface occupied by species i. All of these parameters can be expected to be functions of a variety of variables affecting local column conditions as well as the chemistry of the system. Once these parameters are known, scale-up is, in principle, straightforward. For the illustrative computation presented above, eqs 31-36 permit one to determine the heights of the three sections of the column and consequently the height of the column as functions of the reflux ratio and of the excess interfacial area. With given objectives for product grade and recovery, the column height as well as R and A would be chosen to be consistent with minimization of capital and operating expenses. This, of course, assumes that the rate constants K,")aiare independent of the operating parameters. The range of validity of such an assumption can be determined only experimentally. The primary conclusion here is that product grade can be improved by using reflux. This provides additional opportunities for filling the liquid-gas interface with the desired product and for displacing any undesired species by competition. This does not appear to have been previously suggested in the context of flotation, although it is common practice in distillation, liquid-liquid extraction, and gas adsorption (Coulson et al., 1978; Geankoplis, 1978
We are grateful for the financial support received from the Center for Research on Sulfur in Coal, Carterville, IL 62918-0008. Nomenclature a, = interfacial area per unit volume of column in section j A = excess interfacial area, defined by eq 39 b = interfacial area per unit mass of gas cj') = mass of solid species i in the pulp per unit volume of pulp within section j , defined by eq 17 G = mass rate of flow of gas per unit cross-sectional area 9 = grade, defined by eq 37 k!' = rate constants that take into account the hydrodynamics and surface chemistry of the detachment processes for section j , introduced in eq 16 Kj" = rate constants that take into account the hydrodynamics and surface chemistry of the attachment processes for section j , introduced in eq 16 K("* = defined by eqs 31-33 Kfd = defined by eqs 34 and 35 L, = mass rate of flow of the continuousliquid phase in section 1
M = mass rate of flow of make-up solution added per unit cross-sectional area QP = quality of froth exiting overhead from column, volume of gas per unit volume of froth as defined by eq 3 R = reflux ratio (fraction of the pulp stream exiting from the separator that is diverted to reflux) R = recovery, defined by eq 38 S = 8,for all sections j S = selectivity in section j of the column, defined by eq 36 = volume of species i per unit area of interface occupied by species i Xy' = mass of solid species i per unit mass of the continuous liquid phase in pulp within section j = mass of solid species i attached to rising bubbles per unit mass of gas within section j z = axial position measured between the stages Zc = height of packed column 2, = location of top of pool of pulp with respect to the bottom of the column ZF = location of feed with respect to the bottom of the column
do)
q)
Greek L e t t e r s p(') = 71")
mass density of phase i
= gas residence time in section j , defined by eqs 31-33
Others j = subscript denotes section of column, =1-3
F = subscript denotes feed stream P = subscript denotes overhead product stream from separator R = subscript denotes reflux stream returned to the top of the column T = subscript denotes tailings stream I = superscript denotes species i G = superscript denotes the gas phase I' = superscript denotes the continuous liquid phase
Ind. Eng. Chem. R e s . 1990,29,949-955
Literature Cited Coulson, J. M.; Richardson, J. F.; Backhurst, J. R.; Harker, J. H. Chemical Engineering, 3rd ed.; Pergamon Press: Oxford 1978; VOl. 2. Degner, V. R.; Sabey, J. B. WEMCO/Leeds Flotation Column Development. In Column Flotation ‘88,Society of Mining Engineers Annual Meeting, Phoenix, AZ, Jan 2528,1988; Sastry, K. V. S., Ed.; Society of Mining Engineers: New York, 1988; p 267. Dell, C. C.; Jenkins, B. W. The Leeds Flotation Column. Seventh International Coal Preparation Congress, Sydney, 1976. Dobby, G. S.; Finch, J. A. Mixing Characteristics of Industrial Flotation Columns. Chem. Eng. Sci. 1985,40, 1061. Dobby, G. S.; Finch, J. A. Flotation Column Scale-up and Modeling. CZM Bull. 1986, 79, 89. Egan, J. R.; Fairweather, M. J.; Meekel, W. A. Application of Column Flotation to Lead and Zinc Beneficiation at Cominco. In Column Flotation ‘88, Society of Mining Engineers Annual Meeting, Phoenix, AZ, Jan 25-28, 1988; Sastry, K. V. S., Ed.; Society of Mining Engineers: New York, 1988; p 19. Geankoplis, C. J. Transport Processes and Unit Operations, Allyn and Bacon: Boston, 1978. Hucko, R. E.; Gala, H. B. Promising Advanced Coal Preparation Technologies for Reducing SO2 Emissions. Prepr. Pap.-Am. Chem. Soc., Diu. Enuiron. Chem. 1988,28 (No. l), 211-215. Idlas, S. A.; FitzPatrick, J. A.; Slattery, J. C. Conceptual Design of Staged Flotation Columns. Znd. Eng. Chem. Res. 1990, following pap& in this issue. Jameson, G. J.; Nam, S.; Young, M. M. Physical Factors Affecting Recovery Rates in Flotation. Miner. Sei. Eng. 1977, 9, 103. Kawatara,-S. K.; Eisele, T. C. Column Flotation of Fine Coal. In Fine Coal Processing; Mishra, S. K., Klimpel, R. R., Eds.; Noyes Publications: Park Ridge, NJ, 1987; p 414. Kawatara, S. K.; Eisele, T. C. Studies Relating to Removal of Pyritic Sulfur from Coal by Column Flotation. In Column Flotation ‘88, Society of Mining Engineers Annual Meeting, Phoenix, AZ, Jan 25-28, 1988; Sastry, K. V. S., Ed.; Society of Mining Engineers: New York, 1988; p 213. Killmeyer, R. P.; Hucko, R. E. Interlaboratory Comparison of Advanced Froth Flotation Processes. Preprint, Society of Mining Engineers Annual Meeting, Las Vegas, NV, Feb 27-March 2, 1989; Society of Mining Engineers: New York, 1989;No. 89-137. Laplante, A. R.; Yianatos, J.; Finch, J. A. On the Mixing Characteristics of the Collection Zone in Flotation Columns. In Column Flotation ‘88, Society of Mining Engineers Annual Meeting, Phoenix, AZ, Jan 25-28, 1988; Sastry, K. V. S., Ed.; Society of Mining Engineers: New York, 1988; p 69. Li, C. Process Analysis of a Static Tube Flotation System for Fine Coal Cleaning. M.S. Thesis, Michigan Technological University, Houghton, 1987. Luttrel, G. H.; Adel, G. T.; Yoon, R. H. Modeling of Column Flotation. Preprint, AIME Annual Meeting, Denver, CO, Feb 24-27,
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1987; AIME: New York, 1987; No. 87-130. Misra, M.; Harris, R. Column Flotation of Fine Coal from Waste Coal Refuse. In Column Flotation ‘88, Society of Mining Engineers Annual Meeting, Phoenix, AZ, Jan 25-28,1988, Sastry, K. V. S., Ed.; Society of Mining Engineers: New York, 1988, p 235. Moon, K. S.; Sirois, L. L. Theory and Industrial Application of Column Flotation in Canada. In Column Flotation ‘88, Society of Mining Engineers Annual Meeting, Phoenix, AZ, Jan 25-28, New 1988: Sastry, K. V. S., Ed.; Society of Mining- Engineers: York, 1988; p 91. Mori. S.: Okamoto. H.: Hara. T.: Aso. K. Kinetics Studies of Fluorite Flotation. Proc. 15th Znt. A h.hocess. Cong., Cannes 1986,3, 155-162. Nicol, S. K.; Roberts, T.; Bensley, C. N.; Kidd, G. W.; Lamb, R. Column Flotation of Ultrafine Coal: Experience at BHP-Utah Coal Limited’s Riverside Mine. In Column Flotation ‘88,Society of Mining Engineers Annual Meeting, Phoenix, AZ, Jan 25-28, 1988; Sastry, K. V. S., Ed.; Society of Mining Engineers: New York, 1988; p 7. Sastry, K. V. S.; Lofftus, K. Mathematical Modeling and Computer Simulation of Column Flotation. In Column Flotation ‘88, Society of Mining Engineers Annual Meeting, Phoenix, AZ, Jan 25-28, 1988; Sastry, K. V. S., Ed.; Society of Mining Engineers: New York, 1988; p 57. Sherwood, T. K.; Pigford, R. L.; Wilke, C. R. Mass Transfer; McGraw-Hill: New York, 1975. Subramian, K. N.; Connelly, D. E. G.; Wong, K. Y. Commercialization of a Column Flotation Circuit for Gold Sulfide Ore. In Column Flotation ‘88, Society of Mining Engineers Annual Meeting, Phoenix, AZ, Jan 25-28, 1988; Sastry, K. V. S., Ed.; Society of Mining Engineers: New York, 1988; p 13. Szatkowski, M.; Freyberger, W. L. Model Describing Mechanism of the Flotation Process. Trans. Znst. Min. Metall. 1985,94, C61C70. Treybal, R. E. Mass-Transfer Operations, 3rd ed.; McGraw-Hill: New York, 1980. Wheeler, D. A. Historical View of Column Flotation Development. In Column Flotation ‘88, Society of Mining Engineers Annual Meeting, Phoenix, AZ, Jan 25-28, 1988; Sastry, K. V. S., Ed.; Society of Mining Engineers: New York, 1988; p 3. Yang, D. C. Development and Demonstration of a Static Tube Flotation System for Producing Superclean Coal. Eleventh Quarterly Progress Report to USDOE under Contract De-AC22-85PC87210, July 13, 1988. Ynchausti, R. A.; McKay, J. D.; Foot, D. G. Column Flotation Parameters-Their Effects. In Column Flotation ‘88, Society of Mining Engineers Annual Meeting, Phoenix, AZ,Jan 25-28,1988, Society of Mining Engineers: New York, 1988; p 157.
Received for reuiew September 18, 1989 Revised manuscript received February 23, 1990 Accepted March 6, 1990
Conceptual Design of Staged Flotation Columns Scott A. Idlas,?Joseph A. FitzPatrick,*and John C. Slattery*pt Department of Chemical Engineering and Department of Civil Engineering, Northwestern University, Evanston, Illinois 60208-3120
A new analysis is presented for staged flotation columns, of which the WEMCO-Leeds flotation column, which is staged above the feed, appears to be the only current example. When the column height is fixed, we find that reflux significantly improves the product grade at the expense of decreased recovery. Increasing the number of stages while maintaining the height of the column constant can help, only if there is a mechanism for scouring gangue particles from the froth as it passes from one stage to the next. More generally, one must solve an optimization problem in which both the excess interfacial area available for flotation and the height of the column below the feed may be increased. The recent round-robin test conducted by the Department of Energy (Killmeyer and Hucko, 1989; Hucko and *Current address: Department of Chemical Engineering, Texas A&M University, College Station, T X 77843-3122. t Department of Chemical Engineering. t Department of Civil Engineering.
Gala, 1988) suggests that columns have an inherent advantage over standard mechanical/pneumatic flotation machines in cleaning coal. Three types of columns have been suggested for use in flotation: open, packed, and staged (Kawatara and Eiele, 1987). In a companion paper, Idlas et al. (1990) give a brief summary of the literature concerned with open columns as well as an in-depth dis-
0888-5885/ 90 / 2629-0949$02.50/ 0 0 1990 American Chemical Society
