Stirred Tanks and Mixers for Liquid Extraction ROBERT E. TREYBAL Department of Chemical Engineering, New York University, New York 53, N. Y.
Sound design methods
and
data
rnecha nica lly tanks
are
for
stirred rapidly
being developed. Air agitation
and
line
mixing can be economical and warrant further research
MIXER-SETTLERS
are probably the oldest, and certainly the most obvious, type of equipment for carrying out stagewise contact of two liquids. Despite this, and despite the fact that many tower types of extractors have been developed, they have not diminished in popularity. Application of enough mixing power makes it possible to build the desired number of theoretical stages into an extraction plant, and mixers which generally operate with cocurrent flow of the liquids cannot be flooded. But it is insufficient to know that by mere application of large amounts of power we can get a job done. Rather, we need to know how little power is required and how best to apply it. If mixers cannot be flooded, settlers can, and this represents a limitation with which we must know how to deal. Because the subject is too large other-
wise, this discussion is limited to mixers particularly those for which quantitative data permit useful comparisons and conclusions. Rather than merely setting forth all the available data, which can lead to much confusion, an attempt has been made to interpret them in terms of design methods and particularly to point out the areas where our knowledge is lacking. The available data indicate that the suggested approach to the design of the stirred-tank mixer shows promise. Its limitations with respect to our present knowledge, inconsistencies in data, and areas where research can profitably be done are pointed out. Air agitators and certain line mixers, whose energy requirements may be comparable to or even less than, those for stirred tanks, and which may involve considerably smaller first costs, warrant systematic study.
Stirred Tanks I n 1958. the author suggested a method for estimating the stage efficiency to be expected in a stirred vessel (52), which required for its application a great many approximations owing to a dearth of directly applicable data. Nevertheless the indications were that the general approach could be useful. If this proves ultimately to be true, then all problems of design and scale-up will eventually disappear, since a general method of direct design will be available. I t will be useful to review the situation regarding applicable data now, with emphasis upon what has been accumulated since, and the areas requiring major effort. Briefly the method involves the use of a chart (shown in simplified form as Figure 1) adapted from the work of Grober for heat transfer (72). There are certain assumptions inherent in the application of the chart:
0 Heat and mass transfer are essentially analogous. This seems reasonable, although mass transfer may involve certain complications, as noted below, which are not found in heat transfer.
0 The continuous phase is thoroughly mixed in the vessel. I n the case of agitating granular solids (27), a dye-injection technique has established that this is essentially true, and it seems reasonable to apply the principle to liquid dispersions as well.
0 No interfacial resistance to transfer exists.
mass
0 No chemical reaction is assumed to occur. "Interfacial turbulence," the Marangoni effect, and solvation or dimerization of transferred solute are known to cause deviations from the normal in other situations, and presumably may do so here also. 0""
1.0
'
"
mk,d,
"
lo
'
I
.
.
'
100
-2Db
Figure 1. Use of Murphree dispersed stage efficiency plot for stirred tanks involves basic assumptions
0 Droplet size is assumed to be uniform, without coalescence and re-break-up. I t is a t least capable of expression as an average value.
0 Entrance and exit effects are not included. VOL. 53, NO. 8
AUGUST 1961
597
Dc was found although Dc was varied
Con tin uous Phase Mass-Transf er Coefficients, kc
170-fold and Sc 84-fold. This is shown more clearly in Figure 3, where 1/Dc for Barker's work is proportional to ScO5, so that in Equation 1 kc becomes only a function of R e and T. Actually, the empirical correlation in \\hich DC is excluded describes the data better than Equation 1. This is unexpected. The first attempt to include the diffusivit>-in correlations of kc in stirred vessels was probably that of Hixson and Baum (75), who related kc/Dc to Sc" as suggested by gas-liquid contact in wetted-wall towers and who felt that their own range of Sc was too small to establish the effect firmly. Since then, many workers in this area have assumed this proportionality, while others have used different exponents on Sc. Actually, in vigorously agitated systems. a strong effect of diffusivity is not established. Resnick and White (47) found kc 0: Dcolin beds of granular solids fluidized violently with gas. Lewis ( 2 4 ) found that, in a special stirred transfer cell for measuring liquid-phase mass transfer, DC was without effect. Pratt ( d o ) , in reviewing packed tower liquid-extraction rates, found DC unnecessary to correlate the data. I n working with gas bubbles in agitated vessels. Calderbank (5) assumed no effect of stirring rate on X-C and this resulted in kc a Dc*'~. Later ( 6 ) , he preferred to express the agitator effect as P/v,leaving the kinematic viscosity in Sc, with kc/Dc cc Sc1l3. But Figure 3 shows that with his data the effect actually cancels. Trice ( 5 4 ) , with a form of jet mixer for two-liquid mixtures, and Johnson and Huang (79), in dissolving rings of solid in a stirred vessel. both found kc/Dc = Sco 5, but Figure 3 indicates that again the effect of diffusivity cancels. I t is thus emphasized
For baffled vessels, the most immediately applicable work is that of Barker (7), who worked with suspensions of crystalline solids, to be certain of the interfacial area, in vessels of 6 to 30 inches in diameter. Barker reviewed the available literature on the subject, and this need not be repeated here except as it serves a n immediate purpose. Barker's results are expressed in two ways: a completely empirical expression relating kc to v113 and Re, and another in terms of the customary dimensionless groups. The latter:
Sh = -_ kc T Dc
0.052
(11
Re0.833S~O.5
is more readily compared with other work and is consequently emphasized here. This provides the answer to many problems, but raises several others. Size and Shape of Surface. Barker found no effect. This was assumed as early as 1927 by Murphree (37), and has since been confirmed (Figure 2) by many others who need not all be enumerated here. Johnson and Huang ( 7 9 ) ,whose work was originally used for the stage-efficiency estimates (52), used cast rings ofsoluble solid in the base of the stirred vessel, yet their mass-transfer coefficients are very little different from those for suspended solids. Calderbank ( 5 ) showed larger kc values for large gas bubbles immersed in an agitated tank than for small, but has suggested (6) that this is due to distortion of the bubblcs and possibly a change in interfacial area not likely to be encountered in suspensions of small liquid droplets. Diffusivity, Dc. Although Equation 1 would indicate a n apparent effect of the form kc 0: DCO.6, actually no effect of
that all these correlations for kc will be equally good without a diffusivity and that this is an area which certainly needs further investigation. Reynolds Number or Power/ Volume. Agitator power/volume of the vessel has been used by several in correlating kc data (6, 38). Correlations of the form of Equation 1. obtained from vessels whose diameter and height are nearly equal, can be put in the form:
If P / v is then used as a correlating device. unless n = l (which it is not), then some additional effect of d , / T can be expected. I n Figure 4, data for the dissolution of boric acid crystals in water correlate better in terms of R e than of P/v. Furthermore, Figure 4B will correlate into one line similar data for all values of liquid kinematic viscosity, whereas Figure 4A will not. O n the other hand, R e fails to correlate data from baffled and unbaffled vessels simultaneously, although it will handle different chemical systems (Figure 5 A ) , while Plv seems to handle both baffled and unbaffled vessels for the same chemical system (Figure 5B). These "unbaffled" data are for full vessels with a cover, with no air-liquid interface and no vortex. Figure 5B suggests that under these circumstances at least estimates of kc for unbaffled vessels might be made from data from baffled vessels of the same geometry and same chemical system by computing for equal values of Plv. But these matters obviously need further study. Flow Rate. Equation 1 describes batch operations, but its applicability to cases where liquids flow continuously through the vessel is not established.
SUSPENDED CRYS (BARKER e TREY
SUSPENLED CRYSTALS lHUMPHREY ET YAN NESS
105 -
Id SON
101
ld
I I
e
1 I
HUANGI
I
104 IMPELLER REYNOLDS Nn.
, I
I
I
O I
1 I06
CONTINUOJS PHASE SCHMIDT NO
Figure 2. Continuous phase mass-transfer coefficients for baffled vessels with flat-blade turbines
Figure 3. Relation between diffusivity and Schmidt number for several studies of continuous phase mass-transfer coefficients
Solid lines are recommended correlations; shaded areas show extreme limits of the data
Diffusivity has no effect on mass-transfer coefficients
598
INDUSTRIAL A N D ENGINEERING CHEMISTRY
LIQUID E X T R A C T I O N
-
lo
0
DATA POINTS FOR KIN. VIS. = 1.0 CS.
@*d
a 1.0 -
$
2L 1 I
P
-
-
%P
-+Vo
A
A
0
-+
a80
DIAMETER IN.
vEssEt.
P
5.45 a 11.2 0 11.2 11.2
BEST LINE FOR
2
*
3 4 6 6
v iza
A I
1
,
I
TJRBNE
0
A 0.1
= c
+
124 124
30.
,
run nm. v i a
% -
cs.
ppn DIAMETER, IN. VESSEL TURSINE
n
9 I2 12
A I
1
a
2
0
3 4 6
5.45 11.2 0 11.2 a 11.2 0 1Z4 A lZ4 A lZ4
,
Figure 4. Dissolution of boric acid crystals in water for baffled vessels with turbine agitator, Data of Barker and Treybal ( I ) Data correlate better in terms of Re (right) than P / v (above)
Figure 2, however, shows the results of Humphrey and Van Ness (78) with continuous liquid flow, and there is evidently little difference. Mattern and others (27) likewise found the same coefficients for batch and continuous dissolving of solids. MacDonald and Piret (25) found that agitator energy could be added to the kinetic energy of the feed streams (both expressed as P / v ) in any ratio to correlate the mixing time of a dye with a homogeneous liquid. It is probably a matter, then, of relative power levels. Liquids entering an extraction vessel are likely to flow a t about 5 feet per second in the piping, so that with the density of water their kinetic energy is about 25 foot pounds per cubic foot of liquid flowing. Typical agitator energies i n extraction, p.articularly with high interfacial tension systems, are likely to be of the order of 1000 foot pounds per cubic foot of liquid flowing. Superficial velocities of liquids through the tank will be of the order of
-1.0
0.1 4
io
0.01 foot per second, whereas velocities induced by the agitator are likely to be of the order of 0.5 to 15 feet per second. I n view of the relative energy and velocity levels, it seems reasonable, therefore, to apply batch mass-transfer data for kc to continuous flow directly. Unbaffled Vessels. T h e most complete recent work is that of Nagata and others (33), who have measured kc for dissolving solids in the presence of an airliquid interface (subject to vortexing). Most industrial liquid-extraction work is done in vessels operated continuously and hence full, with no vortex, so that the direct applicability of these data to extraction problems is unlikely. Their work is evidently very carefully done, however, and will be of great interest in other areas. They also have data where chemical reactions occur (32). O t h e r Questions. For liquid-liquid systems, it is known that R e correlates power data only when a mean viscosity and density are used (23). I t is not
I
I
I
+
I
,30.
6
9 12 ,I2
e
io 5 IMPELLER REYNOLDS
No.
known whether this is required for kc i n such systems. Data from unbaffled vessels with no air-liquid interface (no vortex) are needed, since this is an important condition for extraction (see below). Work is under way to establish these things and also to confirm that kc for solid particles is applicable to liquid droplets. I t is perhaps of theoretical interest that the recent data of Brooks and Su ( 2 ) for heat transfer coefficients to baffled, jacketed vessels agitated with flat blade turbines show values of Nu/ Pr1I3which are substantially higher than the ordinates for mass transfer of Figure 2 , except a t impeller Reynolds numbers greater than about lo5.
Drop Size and Interfacial A r e a Average interfacial area and d r o p size are related through the dispersed phase holdup :
4
= 6 4 a
(3)
Measurements of the interfacial area have been made for a number of situa-
--I
Figure 5. Dissolution of boric acid crystals in 1 1.2-inch-diameter vessel with 4-inch-diameter turbine and no air-liquid interface. Data of Barker and Treybal ( 7 ) Re (left) does not correlate data from both baffled and unbaffled vessels, as does P/v (right)
VOL. 53, NO. 8
0
AUGUST 1961
599
tions by a light-transmittance technique. These are for batch operations, in tanks u p to 18 inches in diameter. The available correlations are outlined very briefly as follows :
unbaffled tanks with or without a vortex. The effect of flow rate is unknown, but it probably at least enters for lois interfacial tension systems at low agitator speeds (see below). \7ermeulen and others (56) indicate that as long as 2 hours may be requirFd for some systems to reach steady-state drop size in batch mixing, flow rate will surely then have influence for continuous operation. \\/e also need to knoiv something about coalescence and redispersion of the droplets.
Six-bladed
flat blade turbines, 0.5 only, baffled vessels [Rodger and others (42, 4 3 ) ] . Two correlations are given of which only one is quoted: =
pD
T h e other correlates the data better, but involves a knowledge of the settling time of the dispersion and is likely not to be so useful practically. I t includes the Weber number to the 0.36 (rather than 0.25) power, although the settling time is probably a function of the agitator speed also.
Dispersed Phase Mass-Transfer
Rates
Pour-bladed flat blade paddles, en = 0.2 to 0.4, baffled vessels IVermeulen and others (56)] : R
=
72p~TYe'O.~/difA 25.4
p p D o . jM T e ' o . F j d ,
(5)
wheref in the first expression depends on pD. Since, in the range of the data, j can be represented reasonably well by 2 . 8 3 ~ , ~ . this ~ , has been substituted to obtain the second expression. Four-bladed flat blade paddles and six-blade turbines, vn = 0 to 0.2, baffled vessels [Calderbank ( 4 )J : a =
100pDWeo.6/diF
60
Io0 PO0 IMPELLER SPEED - R . R M .
7
Figure 6. Calculated interfacial area for kerosine dispersed in water; 1 foot-diameter baffled vessel, impeller diameter = '/3 foot. The correlations generally agree very well Rodger, Trice, and Rushton (C$ D = (2.5) Vermeulen, Williams, and Langlois (+o = 0.3) 3. Calderbank (C$ D = 0.3) 4. Kafarov and Babanov ( 4 =~ 0.3) 5. Pavlushenko and Yanishevskii (C$D = 0.3) 1.
2.
(6)
cvhere F F
+ 3 . 7 5 ~for~ four-blade paddles ( d i / T = 2/3) = 1 + 9 p D for six-blade turbines
=
1
(dt/T
=
1/31
Calderbank has also given another general expression in terms of P/v. Various impellers, baffled vessels, dilute dispersions [Kafarov and Babanov
(20)I : =
C ~~e0.6Re0.1p 0.81/di
(7)
where C = 13.65 to 25.9, depending upon the impeller type. Screw-type impellers, turbines, 1foot-diameter, round-bottomed, baffled vessel, ppD= 0.075 to 0.4 [Pavlushenko and Yanishevskii ( 3 9 ) l :
These correlations all appear to be distinctly different, especially in the effect of impeller speed, as betlveen concentrated ( p D = 0.5) and dilute (pD < 0.4) dispersions. Shinnar and Church (49) pointed out, however, that for dilute dispersions, \vhere the average particle size is determined by break-up of drops, a should vary as N to a poiver greater than unity; while for concentrated dispersions, where coalescence is more likely to play an important role, the power should be less than unity.
600
To compare them further, a typical situation was chosen: dispersion of kerosine ( p D = 50.5 pounds per cubic foot; pn = 3.38 pounds per foot-hour) into water ( p c = 62.3; p c = 2.18); interfacial tension 35 dynes per cm., in a 1-foot-diameter baffled vessel ; impeller diameter = 1,/3 foot. For all correlations but the first, pD was taken as 0.3, and for the first correlation as 0.5 (since it is only applicable a t that value). The results are shown in Figure 6. With the exception of the correlation for the roundbottomed vessels, the results are remarkably similar for dilute dispersions. However, the second, third, and fourth correlations do not involve tank diameter, yet it would seem that if di/ T were quite small this would have to enter in some fashion. The less steep line for the first correlation (pn = 0.5) results from Equation 4; the steeper line was drawn (corresponding to the better using We0,3G correlation) by arbitrarily assuming a settling time, in turn unaffected by agitator speed. The variation of the speed effect with pn is striking; evidently a t high speeds interfacial area passes through a maximum with increasing pD. The problems which clearly require further investigation include the effects of tank diameter; pD, particularly in what is evidently a transition range, from 0.4 to 0.5 and higher; viscosity and density differences. We have no data from
INDUSTRIAL A N D ENGINEERING CHEMISTRY
I t was suggested (52) that these be characterized by D D ' , a dispersed phasc diffusivity larger. as necessary: than the true molecular diffusivity to account for circulation within: and osdlation of, the droplets. I n studies of single drops and in spray towers. the values ranged from about 1.5 to very- large multiples of the molecular diffusivit).. but as yet without well established pattern. For stirred vessels there are no data, but the matter is bzing pursued actively. For the time being, DD' = 2Do to 2 . 5 D ~ is suggested. Uniformity of Mixing
I n the case of batch operation, hlillcr and M a n n (28) used unbaffled vessels and measured uniformity of mixing throughout thc vcsscl. A vortcx was present. A power application of 250 to 500 foot pounds per minute-cubic foot \vas sufficient to give essential uniformity for several types of impellers. Nagata and others (35) found the minimum speed for the separate liquid layers to disappear in unbaffled vessels Lsith fourblade paddles (d, = T 3) to be:
I n a 1-foot-diameter tank, with kerosine and water, this bsould indicate approximately 30 foot pounds per minute-cubic foot: so that substantial additional power is evidently required for spreading the dispersion uniformly throughout thc tank. I t would seem from what follows that interfacial tension probably should enter into these criteria. Nagata also experimented (34) to find the best geometry for batch dispersion of t l v o liquids. The preferred arrangement involved baffles of ividth equal to 0.1T submerged to a depth d,:2 and set out from the wall, Tvitli paddle diameter equal to 0 . 4 T . I t is shoivn later that a fixed ratio of d , / T is not likely to be profitable for extraction. I n a batch operation, the fraction of the vessel volume occupied by the dispersed phase is the same as that in the charged liquids, but this is not true for continuous operation unless the level of power is sufficiently high. A felt, data ivere available in 1958 taken incidentally
LIQUID E X T R A C T I O N io other measurements, and these were “correlated” by plotiing ( o D / ( Q ~ / Q ~ ) against P/QT (52). Since then, some new measurements have been made (48)over a very limited range of conditions (baffled vessel, T = 1 foot; flat-blade turbine, di = 0.5 foot; operated without an air-liquid interface). Figure 7 shows that power/ flow rate is not the correlating device, since on this basis results at different flow rates are segregated. When plotted against power alone (or P/v,since only one tank size was used) or Re, the segregation caused by flow rate disappears except for systems of low interfacial tension (see Figure 8). I n the case of the latter, the kinetic energy of the inflowing mixture is only about 0.5 foot pound per minute, so that merely adding this to the agitator power is of no help. The use of the Weber number for the abscissa tends to bring the curves for different systems together, but not really well. To decide between Weber number or power as the correlating device will require study of different impeller sizes. I t is noteworthy that for a system such as kerosine-water, the Nagata criterion for initial dispersion (in terms of P/v) and the Miller-Mann criterion for complete uniformity in unbaffled vessels very roughly correspond to the points of initial rise and final leveling off, respectively, of curve C of Figure 8 (which is for a baffled vessel). There is also an implication that the interfacial area correlations of the sort discussed earlier may require a flow-rate term a t low power levels for systems of low interfacial tensions, when they are applied to continuous flow conditions. I n continuous extraction, Overcashier (37) found that the stage efficiency
0.8
-
0.G
-
0.4
-
0“P O W S LB.
cum%
7RA 8 C
D E I
I
2
,
I
,
10
I
KEROSINE -AQ. KEROSINE -Aq.Caa2
KEROSINE -WATER 39.6 11.9 KERO. ISOHJO~-WA7u?13.85 I12 ISOBUOH -WATER 4 6.4
-
I
I
1
,
3&3 33.2 36.8 22.8
,
100 IMPELLER POWER = F%LB./MIN.
,
6
4
8
,
roo00
1000
Figure 8. Dispersed phase hold-up in 12-inch-diameter baffled vessel with 6-inch-diameter flat blade turbine, cocurrently upward flow, light phase dispersed. Data of Seewald ( 4 8 ) Power or P/v eliminates segregation of data caused by different flow rates
varied markedly with time u p to 20 residence times, although the fluctuation was about a fairly steady average after 10 times. This is undoubtedly due to nonuniformity of dispersion, and, while important in experimental work, is less so in commercial extraction. Power for Agitation
Baffled Vessels, with or without AirLiquid Interface. These are not subject to vortexing. The available data (23, 36) are well correlated by the curves of Figure 9. I t is noteworthy that these curves for baffled vessels correlate both single- and two-liquid-phase mixtures equally well, provided that, for two-phase mixtures, the density and viscosity are computed from:
The data for single liquids are plentiful and have been summarized by Rushton and others (44). Data for twoliquid-phase mixtures are very scarce.
Unbaffled Vessels, Air-Liquid Interface. These are subject to vortexing and, consequently, scale-up difficulties and are not likely to find extensive use in liquid extraction. Miller and Mann (28) have done the most complete work.
0.2 -
paw = p c q c
+
(10)
PDVD
I n the case of the Olney-Carlson data, the originals were recomputed on this basis in preparing Figure 9. Overcashier and others (37) provided additional power data, but the information on dispersed phase hold-up is too fragmentary to put them on the same basis. Until more data are available, it is suggested that the extensive single-liquid data (44) be used for power estimates, with the help of Equations IO and 11. Unbaffled Vessels, No Air-Liquid Interface. These are not subject to vortexing and can be scaled u p without difficulty. The available data (23) correlate with those for single liquids, without the need for including the Froude number, by the curve of Figure 9, provided that for two liquids the density is computed by Equation 10 and viscosity by:
-A0’ 4
’
I
”
IO
lo0
-P
O,=
IO00
FTLB./HR. CU.FT/HR.
Figure 7. Dispersed phase hold-up in 12-inch-diameter baffled vessel with 6-inch-diameter flat blade turbine, cocurrently upward flow. System kerosine (dispersed)-isobutyl alcohol-water (continuous); Ap = 1 1.2 pounds per cubic foot; cr = 13.9 dynes per cm. Data of Seewald ( 4 8 ) Power/flow rote is not the correlating device
PM
= ” ‘Po
[1
- %]; P + w
< 0.4
pqn
(13)
These viscosities d o not seem very satisfactory for the long term and are likely to be revised as more data are accumulated. The case is important, since VOL. 53, NO. 8
AUGUST 1961
601
~~~
The stage efficiency clearly always increases with increased P, but if one maximizes E ~ r u i Pby obtaining:
~~
&BLADED FLAT BLADE TURBINE, WALL BRFRES (LAITY 4 TREYBAL) ARROWHEAD TURBINE, WALL BAFFLES (OLNEY t) CARLSON) C W J I SPIRAL TURBINE (TURBO-MIXERI. STATOR-RING BAFFLE ONLY (CiNEY 4 CARLSON) 4: 6 - 8 6 m E D FLATBADE mmM, NO BAFFLLS,NO AIR-LJQ. INTERFACF (LAITY a T m B A L )
I: CUWEP:
IO.
, ,
I I , I
I
I
I
I
I l l 1
I
I
I
I
I
I
, , I ,
,
I
then the maximum E M D I Pis given at = 0, di = a (which is of little help); but the impeller diameter which maximizes E,, at any power level P i s :
P
where
IMPELLER REYNOLDS No.
Figure 9. Power for agitating two-phase liquid mixtures in the absence o f vortex These curves correlate single- and two-liquid-phase mixtures equally well
Vermeulen (55) suggested that, as an approximation :
evidently very favorable extraction conditions prevail in such vessels (37).
Describing d, through Equation 3 and holding time in terms of rate of flow and vessel volume, there results:
The question of what impeller diameter to use for a given situation is an interesting one, particularly since the meager data available are, on the surface, confusing. I t is well known (45) that for a given type of impeller a t a given power input, the ratio of energy in the flowing liquid from the impeller to that in the small scale turbulence of the eddies varies with impeller size. High speed, small diameter impellers produce more turbulence and less flow; the reverse fcr slow speed, large diameter impellers. Presumably we want to maximize the ratio of stage efficiency to power for a given situation, but the requirements for the dispersed and continuous phases are different. Figure 1 can be used to achieve this, but it requires rather tedious trial and error. I t may be possible to proceed as follows. T h e over-all resistances are :
-~ QD (16)
I---NO BAfKES
For baffled vessels, Equation 1 can be used for kc. The area a depends on the level of pD, as shown earlier. For pD = 0.5, Equation 4 can be used. One may substitute for impeller speed in We and Re the value obtained from a constant power number N p , , and obtain:
ivhere H1 and H s are complicated expressions involving physical properties.
(14)
-
~
For example, Overcashier and others (37) extracted butylamine between kerosine and water in a baffled vessel 1.23 feet in diameter, using flat blade turbines of diameters 6, 8, and 10 inches. Holdup of dispersed phase was about 0.50. At low power input (say, 0.004 hp.), the kerosine was dispersed and the 6-inch turbine was found to be the best (Figure 10). Equations 1 9 and 20 yield (H2/HJ?,n = 0.677 for this case: and d: = 0.07 foot, which implies that even better results might havc been found had smaller impellers been tried. At higher power inputs (say, 0.02 hp.), the authors indicate a strong likelihood that the water was dispersed (this sort of emulsion inversion is common), and the 10-inch turbine was the best of the three. For this case, (H2/HL)2.ii
mkcawD
1 - EMD
..-
(15)
k n a = 4 T’DL/di
Impeller Diameter
1 1 ____ =- 1 1 kDa0 -I- rnkcae In ____
Equations 19 and 20 show that the physical properties and which phase is dispersed can be most important. Specifically, the lower the interfacial tension u (which influences interfacial area) and the lower the distribution ratio rn (which controls the relative importance of the continuous and dispersed phase masstransfer resistances), the bigger the impeller should be; for a given sysrem. the higher the power level, the smaller should be the impeller. I t is interesting to apply this to a specific case.
#
-- ---I
ID
/
_ - - - - --- -
-- - NORAFFLES -~ -TURBlM// IN.FLAITBL.,)/’,/~
- / - -
0.8
I
-6 - I N . PROI?--d/
B-It
0.6 - 6 - N
SPIRAL4
0.6
0.4 0.002
10- IN, I
0-004
1
aoi
-4 I
0.02
0.04
0.IO
04 0.002
Continuous extraction of butylamine between water and kerosine. T = 1.23 feet; impeller centered;
602
OPTIMUM IMPELLER SIZE 4 WALL /+-IN. FLAT BL. TURBINE I , I I I BAFFLG I 0.m 0.01 002 0.04 IMPELLER HORSEPOWER
-
WALL BAFFLI
IMPELLER HORSEPOWER
Figure 10.
8-/N.PROPELLER ‘8.9-1N. SPIRAL TUREINE
INDUSTRIAL AND ENGINEERING CHEMISTRY
holding time, 1.08 minutes.
The unbaffled vessel performed best
Data of Overcashier and others
(37)
a IO
LIQUID E X T R A C T I O N = 6.92 and d: = 3.30 feet. This is too large to fit in the tank, but the indication is that the largest possible turbine would have given the best results. The direction of the observations is predicted. T h e above example is a case where extraction is “difficult,” owing to the high interfacial tension (39 dynes per cm.). If one computes the case for the “easy” system, methyl isobutyl ketoneacetic acid-water (approximately 10 dynes per cm.) in the same tank, one finds dr = 1.2 feet for ketone dispersed, dT = 5.75 feet for water dispersed, a t 0.04 hp. Both of these are too large for the tank but indicate that the largest possible diameter would be best. There are no data with which to check this. The same analysis for p D less than 0.5 indicates quite different results. If Equation 5 is used for the interfacial area, one obtains :
from which it follows that the slope of the E,$fD/Pus. di curve is always negative at real values of d, and the smaller the di the better for any power level and for any set of circumstances. Obviously all of the above is speculative to a certain extent, but it does indicate clearly that there is likely no one best &/T for all situations and that there is much room for additional work. Scale-up
As indicated earlier, if a direct method of design is fully established, then scale-up is no problem because small scale experiments need not be done. But in view of the uncertainties still remaining in the suggested approach, small scale experiments for new processes are still required, I t has been customary to scale u p stirred vessel extractors by making the large vessel geometrically similar to the small, allowing for equal holding time for large and small and applying equal agitator power/volume in both cases. The suggested design procedure discussed above indicates that this will always result in considerable increase in stage efficiency on scale-up (53) and is therefore a safe procedure. I t can also be expensive. Scale-up to give precisely the same performance on both large and small scale. or insistence on nearly 1 0 0 ~ o stage efficiency. may be uneconomical. What is needed is a set of conditions for the large scale which results in the most economical plant. A large number of smaller, less efficient stages may be less costly than a small number of large, very efficient stages. But this cannot be decided unless the characteristics of the entire extraction process, including the solvent-recovery operations, are also taken into consideration.
the authors observed that the wire-mesh packing which formed the upper and lower boundaries produced a flow pattern similar to that found in baffled vessels. Three chemical systems were studied, and Karr and Scheibel were able to correlate the data for these empirically in terms of an over-all mass-transfer coefficient based on activity. It is perhaps noteworthy that diffusivity did not enter their correlation. Figure 11 shows the data of their Table 8A for the 11.5-inch-diameter section, and these are very typical. The curves shown were calculated by the methods described above, using Equation 6 10 estimate the interfacial area and allowing DA = 2.2500. The reported hold-up data were used, since for countercurrent flow these are considerably lower than would be expected for the cocurrent flow normally used for mixer-settler extractors. No correction is included for extraction a t zeio agitator speed, although this can be appreciable. Presumably a t high agitator speeds the “entrance effect” becomes unimportant. At any rate, the calculated stage efficiencies compare very favorably with the observed. However, the direction of extraction-whether to or from the dispersed phase-was observed to have a significant effect on the extraction rates, and the methods of calculation cannot take this into account. Flynn and Treybal (70) extracted benzoic acid from water into toluene and kerosine in two sizes of geometrically similar, baffled vessels, operated continuously and agitated with flat-blade turbines. Curves were obtained which resemble in form those of Figure 11. I t has already been shown ( 5 2 ) that their data can be reasonably well described by the methods of calculation proposed. Nevertheless, for each system and flow ratio, the stage efficiency corrected for that a t zero agitator speed, when plotted against agitator work per volume of
Methods for doing this have been presented (53) for any extractor, including the establishment of the most economical scaled-up stage efficiency for stirred vessels if they are used. The details are somewhat lengthy to summarize here, but it is perhaps worthwhile to emphasize the following regarding the computation of the optimum stage efficiency for large stirred vessels from small-scale measurements. Only the form of the relationships required in the suggested design procedure, but not necessarily the specific coefficients for the various relations, need be agreed upon. Most of the uncertainties cancel out when ratios of large-to-small scale are taken. Extraction Data
Probably the earliest quantitative data are those of Hixson and Smith (76), who batch-extracted iodine from water into CC14 in geometrically similar, unbaffled vessels of three different diameters, with axially arranged three-bladed propellers (subject to vortexing) . Their data cannot be used to test the previously described computation method for lack of information on interfacial area. I t is sufficient to point out that a plot of log (1 - E ) against time produces a good straight line a t any one agitator speed for any one geometrical arrangement, as might be anticipated, and that the data for the three vessel sizes cannot be correlated in simple fashion owing to lack of dynamic similarity among them as a result of vortexing. Holm and Terjesen (77) showed that very small amounts of a surface-active agent have profound effects on the rate of extraction in this chemical system. Karr and Scheibel ( 2 2 ) operated two sizes of one section of the familiar earlymodel Scheibel extractor countercurrently. These were unbaffled mixing sections with four-blade flat paddles, but MURPHREE OKP. PHASE EFNCIFNCY * E”0
Oa:aLcaf1.0
Ob
0.4
-
b
-.*
0 s0Bm.i
V,c y = 81.7
>
0
100
IMPELLER
wo SPEED
3lw
,
R.P.M.
Figure 11. Continuous extraction of acetic acid from water into methyl isobutyl ketone (dispersed). Calculation methods do not account for effect of direction of extraction on extraction V u / V c = 1 ; T = 0.957; Z = 0.25; d i = 0.333 foot.
Data of Karr and Scheibel(22)
VOL. 53, NO. 8
0
AUGUST 1961
603
liquid treated ( P i Q r ) ,produced a single curve for both 6- and 12-inch-diameter vessels and total flows of from 500 to 4000 pounds per hour. If Pi'v is used the different vessel sizes and flow rates produce separate curves. I t seems reasonable that this should be so, but nevertheless it was shown above that P'QT is not a correlating device for hold-up of dispersed phase, whereas P l v is (at least €or one vessel size). The reason for this anomaly is not known. The answer may lie in the somewhat arbitrary method used for correcting efficiencies for zero agitator speed, which then produced the correlation accidentally. More work is clearly needed. Felix and Holder (9) operated a singlestage device for extracting lubricating oil with phenol; the stage was apparently not mechanically agitated. The nature of the system precludes the application of the calculation methods proposed, but the conclusions of the authors would be anticipated, qualitatively a t least: stage efficiency was greater for longer mixing time, for higher temperature (which reduced oil viscosity), and for systems of lower interfacial tension. They showed also that modest amounts of interstage entrainment do not greatly influence stage efficiency. Overcashier and others (37) continuously extracted butylamine between kerosine and water. Their data are most valuable because a variety of impellers was used in both baffled and unbaffled tanks (in rhe case of the latter, the vessels were opzrated without an airliquid interface and hence no vortex). Data for flat-blade turbines are shown in the left half of Figure 10, and it has already k e n shown (52) that, for baffled vessels, the methods of calculation proposed above handle these data reasonably well. Comment has been made above about the influence of impeller size. The point of special significance is the improved efficiency a t a given power which results when wall baffles are omitted. This is probably the result of the combination of reduced axial mixing of the continuous phase and reduced power a t a given impeller speed for this arrangement. I n the right portion of Figure 10, the
performance of the best impeller sizes (best efficiencyjpower) for each impeller type is shown. Evidently the flat-blade turbine and absence of baffles make the best combination. Space does not permit detailed consideration of all the findings, but an empirical correlation of the data is offered which relates stage efficiency to P/QT and not Pjv. In the absence of baffles, vertical location of the impeller is relatively immaterial; with baffles, best results are obtained with the impeller placed one-third the liquid depth down from the top. Ryon and others (46) provided many data for the extraction of uranium from acidic sulfate ore leach liquors into kerosine containing a combination of tributyl phosphate and di(2-ethylhexy1)phosphoric acid. They used baffled vessels from 6 to 36 inches in diameter and flat-blade turbines, operated batch and continuously. The organic phase was dispersed. Their results are correlated in terms of an over-all rate coefficient K'a, defined as follows: Batch: K'a =
-
(1
- pD)ln(l
- E)
e (22)
Continuous: K'a
=
(1 - Po)E
e(i
-
E)
(23)
These assume completely uniform mixing throughout the vessel for both phases. O n this basis. the coefficients for continuous operation were about two thirds those for batch; K'a for d , / T = 0.333 varied as ( P / ' v ) ' , ~for both batch and continuous and was larger for smaller values of d,/ T . Unfortunately, it is not possible to analyze these data in terms ol anything as yet known to us. The distribution coefficient m is only about 0.03 for this case, and it might be thought that the major mass-transfer resistance would therefore lie within the continuous phase. However, attempts to calculate stage efficiencies on this basis lead to values which are far higher than those observed, indicating the presence of appreciable additional resistance. The system is a chemically reacting one, either in the organic (dispersed) phase or a t the interface, the kinetics of which are not well established particularly in view of the two competing
reagents in the organic phase. Diffusivities of the uranium complexes are practically impossible to estimate. That there are extraordinarily large resistances to t r a d e r may be perhaps appreciated by considering the following : The 36-inch diameter mixers were operated with a combined flow of 110 gallons per minute and with agitator power of 30 hp. per 1000 gallons of tank volume, corresponding to an expended energy of 9000 foot pounds per cubic foot of liquid treated, which is extremely high. Yet the stage efficiency achieved was only 78.97,. The same level of power intensity for the 6-inch diameter mixer produced only about 60% efficiency. Much less energy expenditure will ordinarily produce essentially complete equilibrium in simple extraction systems. For example, the highest abscissa on Figure 10 corresponds to only 7.5 hp. per 1000 gallons of tank volume or 1720 foot pounds per cubic foot of liquid treated. I n Figure 11. 1007, stage efficiency is achieved a t 300 r.p.m. which corresponds to a conservatively estimated 0.15 hp. per 1000 gallons or 125 foot pounds per cubic foot of liquid treated. It has been noted (7) that diluting the alkyl phosphate reagents with the less viscous hexane, rather than kerosine, has brought about considerable improvement in industrial operation of this uranium extraction, as expected. Mottel and others (29, 30) have used heat transfer between kerosine and water to test the performance of a box-type mixer-settler. This is an interesting development and, if successful, would certainly simplify the problem of gathering performance data. However, the indications are that heat transfer will not substitute for mass transfer to complete our understanding of these devices. For example, the relative importance of dispersed and continuous phase masstransfer resistances are clearly very dependent upon the distribution coefficient, and, for the same physical properties of a pair of liquids, the major resistance (and hence the entire performance characteristics) can be shifted from one phase to the other by choice of transferred solute. This is not true in the case of heat transfer.
Gas Agitation Although gas agitation has generally been considered a n uneconomical method of applying mixing power, there is actually relatively little in the way of quantitative data with which to judge its effectiveness in contacting two liquids. Thornton (51)described an air-mixed mixer-settler, and Mathers and TVinter ( 2 6 ) provided some data. I n the case of the latter, an air-lift
604
type of mixer is used in a box-type mixer-settler. The air is introduced at the bottom of the mixer through a nozzle surmounted by a vertical pipe which rises through roughly two thirds of the liquid depth. I n a mixer of 5liter volume, acetic acid was extracted from water (3.48 liters per minute) into methyl isobutyl ketone (6.9 liters per minute), using 0.3 cubic foot of air
INDUSTRIAL AND ENGINEERING CHEMISTRY
per minute. The power for air \VdS 0.001 hp., corresponding to 90 foot pounds of energy per cubic foot of liquid treated. The Murphree aqueous phase stage efficiency was 937, (including the effect of the 10-liter settler; total holdins time was 1.45 minutes). and the extraction factor was such that this corresponds to a Murphree extract efficiency also of 93%.
LIQUID E X T R A C T I O N Referring to Figure 11 for the same system in a mechanically stirred vessel, the same holding time corresponds to VD Vc = 10.4, and the same stage efficiency would be produced a t an impeller speed of about 225 r.p.m.
+
This is estimated to represent an energy expenditure of 415 foot pounds per cubic foot of liquid treated. Of course, Figure 11 also indicates that a t higher flow rates, the job might be done with only 53 foot pounds per cubic foot.
The point is merely that gas agitation need not necessarily be considered uneconomical. We have no data for more “difficult” extraction systems, and there are, of course, limitations on the use of gas agitation for volatile liquids.
Other Mixing Devices “In-line” or “line” mixers, wherein the liquids to be contacted are pumped cocurrently through a device of relatively small volume, usually without moving parts, have been used for years. These may be jets, injectors, orifices, mixing nozzles, and the like. In these devices the pressure drop is representative of the energy spent in causing the mixing. Alternately, the liquids may both be introduced into the suction side of the same pump, which then both mixes and pumps. If holding time for extraction is required, it may be obtained in the pipe leading to the settler, which may be of large diameter to provide the necessary volume, and sometimes fitted with simple baffles to maintain the dispersion. Sometimes the time for settling in a gravity settler is sufficient for this purpose. Relatively little is known concerning the mass-transfer characteristics of these devices, and they are mentioned only in cases where we have a few data. Jets
Trice (54) used a form of jet mixer in which two liquids impinged upon a plate contained within a cylindrical vessel. Measurements were made of interfacial area, drop size, and kc for two systems and two vessel diameters (4 and 6 inches). T h e data were correlated by:
The similarity of this to Equation 1 is striking. Comment has already been made about the cancellation of 1/Dc and ScO.6 from this equation. injectors
Kafarov (27) used several very small injector mixers to extract benzoic and acetic acids from CC14 with water, the stage efficiency ranging from 85 to 100%. The largest of the devices was only approximately 3 inches from throat to outlet, with a throat diameter of approximately 0.1 inch. Nevertheless, flow rates of roughly 2.1 to 3.5 cubic feet per hour were used. Pressure-drop data and induced flow rates were correlated in terms of flow rates of the working fluid.
The correlations are not discussed in detail here because the small size of the devices makes the general applicability perhaps somewhat doubtful. But from the data, energy expenditures are estimated to be in the range 30 to 900 foot pounds per cubic foot of liquids treated for the above flow rates which, for the “difficult” extractions done and the stage efficiencies obtained, are quite low.
a good opportunity to compare mixing valves and stirred vessels. Butylamine was extracted from kerosine into water, using a 1-inch gate valve line mixer. Phase separation was done in cyclones, and indeed it was the characteristics of these which were evidently the major objectives of the work. In general, phase separation was poor, and became worse the more intense the mixing (and the better the mass transfer). But 10 gallons per minute of the liquids gave a Orifices, Nozzles, and Valves mass-transfer stage efficiency of 95.5% Orifices. Scott and others (47) used with an energy expenditure in the mixing orifices in a 1-inch pipe to disperse water valve of 147 foot pounds per cubic foot, into kerosine and measured the interand 20 gallons per minute produced an facial area produced by a light- ransefficiency of 63.3% at 29.4 foot pounds mittance technique. At 7 inches downper cubic foot. stream from the orifice : Figure 10, for essentially the same u = 282 ( ~ D ~ ~ ~ ~(25) ~ ( system, C ~ ~ indicates A ~ ) roughly ~ ~ ~ 1700 ~ ~ foot pounds per cubic foot for stage effiThe area decayed, owing to coalescence ciencies approaching 100% and 80 to in the pipe downstream, to about one 260 at the 63y0 level. The line mixer tenth its original value a t 18 feet and then energies compare favorably, and it is seemed to remain constant at least to useful to keep in mind that high stage about 30 feet. The constant 282 is efficiencies do not necessarily make an believed to be inversely proportional to economical plant. Respecting the poor interfacial tension. From their data, a phase separation, Hitchon (74) has mixture of water ( p D = 0.1) and kerosine pointed out that two cyclones operated a t 12 gallons per minute, with an orifice with a recycle stream can be used and, of 0.4375 inch in diameter, produced an course, ordinary gravity settlers also. interfacial area of 105 square feet per cubic foot initially, which decayed to Ultrasonic Energy about 11. T h e estimated energy conWoodle and Vilbrandt (57) have sumption was roughly 385 foot pounds reviewed the meager literature on the per cubic foot, or about 0.02 hp. If we use of ultrasonic vibration to enhance used a stirred vessel of the same volume extraction. Among other things, they as the 30 feet of pipe (T = 2 = 0.61 extracted methanol from toluene into foot, di = 0.2 foot) Equation 6 and water in a very simple line mixer (feed Figure 9 indicate that the 105 square liquids entering from the branches of a Y feet per cubic foot could be generated and flowing into the I-inch diameter by as little as 10-5 hp. stem), surrounded for a distance of 4 Yet this type of device is evidently inches by an 800-kc. transducer. The very effective. For example, in the effluent liquids were led to a settler. Dualayer process of treating gasoline Pressure drop for flow must have been (71), mixing nozzles effectively do the negligible. At flow rates corresponding job at 1440 foot pounds per cubic foot of to 5.9 to 18 seconds of contact time Xvith liquid mixture. the transducer, stage efficiencies without Valves. These are essentially adjustinsonation were 10 to 1270. T h e able orifices. In desalting crude oil with greatest incremental improvement in water, from 2880 (73) to 4300 (3) foot efficiency occurred a t about 20 watts pounds per cubic foot and in caustic insonation power (efficiencies = 15 to treating and water washing of naphtha 45%). At 60 watts and 18 seconds’ ( 8 ) ,1152 and 576 foot pounds per cubic contact time, the stage efficiency was foot are the energy consumptions with valves. These are all “difficult” systems 59%. This last corresponds to an energy expenditure of 800,000 foot pounds per and the energies listed are small. cubic foot of liquid treated. Simken and Olney (50) have provided VOL. 53. NO. 8
AUGUST 1961
605
Other Devices
Space does not permit detailed review of the phase-separation devices, which include gravity settlers, cyclones, and mechanically operated centrifuges, nor the auxiliaries such as mechanical and electrostatic coalescers and separating membranes. Gravity settlers are of course the simplest, yet there is no adequate method available for their design. We know little about the rate of settling of swarms of liquid droplets and the time for coalescence, or the best geometrical arrangement to be used. These matters are important, since too large a settler can cost considerably more than the mixing vessel. I n the field of extractive metallurgy, it is desirable to be able to subject ore slurries to liquid extraaion directly, eliminating the costly clarification steps, but this leads to difficult settling problems. I n the past several years, there have been considerable changes in the arrangements of mixer-settlers to make them more compact and to reduce their cost. T h e box-type, tandem-like arrangement, really a modification of the older HolleyMort extractors, eliminates interstage pumps; some use gravity flow, while others use the mixing impeller to do the pumping. Piping and space requirements have been Ieduced by placing the mixing vessel inside the settler and even carrying out the mixing and settling continuously in the same vessel. These are welcome developments. especially since economic considerations dictate that in most circumstances much larger number of extraction stages should be used in extraction operations than have been in customary practice. Nomenclature
a c
= interfacial surface, sq. ft./cu. ft. = concentration of solute, lb. moles/cu ft.
C,
=
d, d;
= impeller diameter, ft.
orifice coefficient, dimensionless
impeller diameter for largest stage efficiency for a given power, ft. d, = mean droplet diameter, ft. D = molecular diffusivity, sq. ft./hr. D ’ = effective molecular diffusivity, sq. ft./hr. E = stage efficiency, approach to equilibrium of effluent phases, as a fraction E I I D = Murphree dispersed phase stage efficiency, as a fraction g, = conversion factor, 4.18(10*) Ib. mass (ft.)/lb. force (sq. hr.) H I , H2, HI’, H2’ = defined by Eq. 1721 k = individual phase mass-transfer coefficient, lb. moles/hr. (sq. ft.) (lb. moles/cu. ft.) = ft./ hr. K = over-all mass-transfer coefficient. Ib. moler/hr. (sq. ft.) (lb. mole/cu. ft.) K’a = a n over-all mass-transfer coefficient, l/hr.
606
=
m
= equilibrium distribution coeffi-
cient, dcc/dcD, dimensionless .V = impeller speed, rev./hr. Nu = Nusselt number, dimensionless AVpo = power number, Pg,/pN3d:, dimensionless Pr = Prandtl number, dimensionless = Reynolds number for an imRe peller, N d : p , / p , , dimensionless Sc = Schmidt number for the continuous phase, p c / p c D c , dimensionless Sh = Sherwood number, k T / D , dimensionless = number of over-all dispersed phase transfer units, dimensionless \Ve = Weber number for an impeller, d;.V*pC/u, dimensionless LVe’ = Weber number for an impeller, calculated with p w , dimensionless Ap = pressure drop for orifice, lb./sq. in. P = agitator power, ft. lb./hr. Q = rate of flow, cu. ft./hr. T = vessel diameter, ft. u = vessel volume, cu. ft. V = superficial velocity, cu. ft./hr. (sq ft.) = ft./hr. 2 = height of liquid in a vessrl, ft. e = time of contact, hr. I/. = viscosity, lb./ft. hr. p = density, lb./cu. ft. = interfacial tension, lb./(sq. hr.) u = (dynes/cm.) (28.7) (lo3) = volume fraction of a phase in a 9 vessel Subscripts C = continuous
D M
=
dispersed
T
= mean = organic = total for both phases
w
=
o
aqueous
Literature Cited (1) Barker, J. J., Treybal, R. E., A.Z.Ch.E. Journal 6. 289 (1960). (2) Brooks,’G., Sa, G.’J., Chem. Eng. Progr. 55, No. 10, 54 (1959). (3) Burtis, T. .4.,Kirkbride, C. G., Trans. A m . Znst. Chem. En,crs. 42, 413 ( 1946) . (4) Calderbank, P. H., Trans. Znst. Chem. Engrs. (London) 36, 443 (1958). (5) Ibid.,37, 173 (1959). (6) Calderbank, P. H., Univ. of Edinburgh, personal communication, 1960. (7) Cronan, C. S., Chem. Eng. 66, 66 (May 4, 1959). (8) Ibid.,p. 26 (Nov. 2, 1959). (9) Felix, J. R., Holder, C. H., A.Z.Ch.E. Journal 1. 296 (1955). (10) Flynn; A. h.,Treybal, R. E., Zbid., 1, 324 (1955). (11) Greek, B. F., Duval, C. A., Kalichevsky, V. A,, T N D . ENG. CHEM.49, 1938 (1957). (12) Grober, Heinrich, Z. Ver. deut. Zngr. 69, 705 (1925). (13) Hayes, J. G., Hays, L. A , , Wood, H. S., Chem. Eng. Progr. 45, 235 (1949). (14) Hitchon, J. W.: At. Energy Research Estab. (Gt. Brit.), CEIR-2777, 1959. (15) Hixson, A. W.,Baum, S. J., IND. ENG.CHEM.33, 478 (1941). (16) Hixson, -4.W., Smith, M. I., Zbid., 41, 973 (1949). (17) Holm, A., Terjesen, S. G., Chem. Eng. Sci. 4, 265 (1955). (18) Humphrey, D. W., Van Xess, H. C., A.Z.Ch.E. Journal 3, 283 (1957).
INDUSTRIAL AND ENGINEERING CHEMISTRY
(19) Johnson, A. I., Huang, Chen-Jung, Zbid.,2, 412 (1956). (20) Kafarov, V. V., Babanov, B. M., Zhur. Priklad. Khim. 32, 789 (1959). (21) ,Kafarov, V. V., Zhukovskaya, S. A , Zbzd., 31, 376 (1958). (22) Karr, A. E., Scheibel, E. G., Chem. Eng. Progr. Symposium Ser. 50, No. 10, 73 (1954). (23) Laity, D. S., Treybal, R. E., A.1. Ch.E. Journal 3, 176 (1957). (24) Lewis, J. B., Chem. Eng. Sci. 3, 248, 260 (1952). (25) MacDonald, R. W., Piret, E. L., Chem. Eng. Progr. 47, 363 (1951). (26) Mathers, W. G., Winter, E. E., Can. J . Chem. Eng. 37, 99 (1959). (27) Mattern, R. V., Bilous, O., Piret, E. L., A.Z.CIi.E. Journal 3,497 (1957). (28) Miller, S. A, Mann, C. A., Trans. Am. Znst. Chem. Engrs. 40, 709 (1944). (29) Mottel, W. J., U. S. At. Energy Comm. DE’-130, 1955. (30) Mottel, W. J., Colven, T. J., Zbid., DP-254, 1957. (31) Murphree, E. V., IND.ENG. CHEM. 15, 148 (1923). (32) Nagata, S., Yamaguchi, I., Yabuta, S., Harada, M., Mem. Fac. Eng., Kyoto Univ.21, Pt. 3, 275 (1959). (33) Zbid.,22, Pt. 1, 86 (1960). (34) Nagata, S., Yokoyama, T., Hanjyo, M., Chem. Eng. (Japun) 15,.49 (1951). (35) Nagata, S., Yoshioka, N., Yokoyama, T., Teramoto, D., Trans. SOL. Chern. Engrs. (Japan) 8, 43 (1950). (36) Olney, R. B., Carlson, G. J., Chem. Eng. Progr. 43, 473 (1947). (37) Overcashier, R. H., Kingsley, H. A., Olney, R . B., A.Z.Ch.E. Journal 2, 529 (1956). (38) Oyama, Y., Endoh, K., Trans. SOC. Chem. Engrs. (Japan) 20, 575 (1956). (39) Pavlushenko, I. S., Yanishevskii, A. V., Zhur. Priklad. Khim. 31, 1348 (1958). (40) Pratt, H. R. C., Znd. Chemist 31, 552 (1955). (41) Resnick, W., White, R. R., Chem. Eng. Progr. 45, 377 (1949). (42) Rodger, W. A., U. S. At. Energy Comm. ANL-5575, 1956. (43) Rodger, LV. A., Trice, V. G., Rushton, J. H., Chem. Eng. Progr. 52, 515 (1956). (44) Rushton, J. H., Costich, E. W., Everett, H. J., Zbid., 46, 395, 467 (1950). (45) Rushton, J. H., Oldshue, J. Y., Zbid., 49, 161, 267 (1953). (46) Ryon, A . D., Daley, F. L., Lowrie, R. S., Zbid., 5 5 , No. 10, 70 (1959). (47) Scott, L. S., Hayes, W. B., Holland, C. D., A.Z.Ch.E. Journal 4, 346 (1958). (48) Seewald, M., M.Ch.E. thesis, New York Univ., 1960. (49) Shinnar, R., Church, J. M., IND. ENG.CHEM.52, 253 (1960). (50) Simken, D. J., Olney, R . B., A.Z. Ch.E. Journal 2, 545 (1956). (51) Thornton, J. D., Nuclear Eng. 1, 156, 204 (1956). (52) Treybal, R. E., A.Z.Ch.E. Journal 4, 202 (1958); 6, 5M (1760). (53) Zbid., 5, 474 (1959). (54) Trice, V. G., L.S. At. Energy Comm. ANL-5741, 1957. (55) ,--, Vermeulen, T., IND.END.CHEW45, 1664 (1953). (56) Vermeulen, T., Williams, G. M., Langlois, G. E., Chem. Eng. Progr. 51, 85F (1955). (57) ‘Cl‘oodle, H. A., Vilbrandt, F. C., A.Z.Ch.E. Journal 6, 296 (1960). RECEIVED for review March 9, 1961 ACCEPTED May 31, 1961 Symposium on Liquid-Liquid Extraction, 44th National Meeting, A. I. Ch. E., New Orleans, La., February 1961.
