Oxygen Absorption in Agitated Tanks New Correlution for O p e n flat-Bluded Impellers b Rate of oxygen absorption i s independent of air flow at a given impeller speed over a wide range,of operating conditions. Flat-bladed impellers are superior to vaned disks only at low air rates. T m s preliminary study of oxygen transfer to an aerated copper(I1)catalyzed sodium sulfite solution contained in an agitated tank is an extension of work done by Cooper, Fernstrom, and Miller ( 3 ) . Four-bladed paddle impellers were used in a fully baffled tank. The effect of air rate was much less pronounced than previously reported for other impeller designs, and a modified correlation is suggested. Changes in geometry (particularly impeller shape) are more important than indicated in the literature. Volumetric oxygen absorption rates, K,, have been related to paddle diameter, D,speed of rotation, N , and superficial gas velocity, Jf8, for a single tank diameter, T , over the range: T = 6.0 inches D = 1 19 to3.00inches N = 300 to 2000 r.p.m. V , = 9 . 5 to 86 6 feet per hour
a
Over much of this range K , is independent of V, and is directly proportional to the product of impeller discharge rate and fluid head at the impeller: K&ND3N2D2 or N3D6 Only at very low values of this product does V, affect K,. The power input to the impeller decreased with increased air flow up to a certain point, after which increased gas rates had no effect. The above correlation is more successful and covers a wider range than previous correlations based on power input and V,, for flat-paddle impellers. I t is therefore unnecessary to determine power input-an advantage when power is not an important consideration economically. High-speed photographs have been Present address, E. I. du Pont de Nemours & Co., Inc., Penns Grove, N. J.
used to show the difference in flow patterns produced by flat paddles and vaned disks. As the present study has shown the very rea! effect of changing impeller design, extrapolating the data from one type of impeller to another appears extremely dangerous. The field of gas-liquid reactions in agitated tanks is one of the many research topics in chemical engineering that has not been exhaustively investigated. One of the most important investigations was conducted by Cooper, Fernstrom, and Miller ( 3 ) . Bartholomew and others ( I , 2 ) studied the oxygen uptake of antibiotics, but presented only qualitative results. Hixson ( 6 )and Gaden (7) published more quantitative findings which agreed with those of Cooper over a very limited range. Gas holdup was studied by Foust, Mack, and Rushton (4). _Gally, oxygen absorption carried out in an agitated vessel depends upon both the superficial gas velocity and the power supplied to the liquid by the rotating impeller. The primary purpose of this investigation was to confirm previous work and to extend it to systems of different geometry, as a preliminary to a more fundamental investigation. Experimental Equipment The experimental equipment was modeled after that described by Cooper, Fernstrom, and Miller ( 3 ) . The air for oxidation was taken from a bench line and put through a pressure-reducing valve which maintained the outlet pressure at 28 pounds per square inch gage. Flow was controlled by a needle valve and the stream was metered by a calibrated rotameter. The metered gas was bubbled through a water saturator and an entrainment separator, after which it was passed through a valve and into a constricted pipe sparger. The oxidation took place in a 6-inchdiameter stainless steel beaker which contained cooling coils and baffles, as well as the sparger. The liquid mass was agitated by a laboratory Lightnin mixer, and a series of geometrically similar four-bladed paddle agitators of
design shown in the accompanying figures. In each case blade height was 0.105 times paddle diameter. Power consumption was measured by a torque table dynamometer and impeller speed by a Strobotac. Experimental runs with a vaned disk confirmed the results of Cooper and others for this agitator design and served as a check of experimental techniques. Experimental Results During preliminary work it was deemed advisable to duplicate the results of Cooper, Fernstrom, and Miller ( 3 ) . They proposed a scale-up method for oxygen absorption and worked with two impeller designs : a vaned disk and a flat paddle. More data were taken for the vaned-disk type. Duplication of experiments with a flat paddle did not give the results reported by Cooper; the deviation was not due to experimental error. The equipment used differed only slightly in geometric detail from that employed by Cooper and others. I t was then decided to explore fully the reasons for the variation of results and if possible, present a mere complete correlation. Effect of Air Rate. The most notable result of these investigations is that air rate has little effect on power input and mass transfer when flat-paddle impellers are employed in a fully baffled tank, except at very low impeller speeds or for very small impellers. EFFECTON POWERINPUT.Complete power input data were taken using the largest flat-paddle 'impeller (Figure 1). At low air rates the indicated relationship is
poQN2.' whereas for gas flows above 0.145 cu. foot per minute; or 45 feet per hour, it becomes fi,QN2.4
where p , = power input per unit volume and N = impeller speed. A cross plot of Figure 1, shown in Figure 2, indicates that a limiting gas flow is present, above which no further VOL. 49, NO. 8
AUGUST 1957
1227
I
I
I I I I I I
,
A I
! ri Figure 3. Effect of power’ input on oxygen absorption for largest impeller
t
4
0
AIR FLOW. 0 , CUFT. PER MIN.
IMPELLER SPEED, WM.
01
Figure 1. speed
Power input versus
Figure 2. Effect of air rate on power. Largest impeller
decrease in power input is observed, and that the effect of air rate is less at high impeller speed. The power input to a liquid in turbulent flow is given by
P
=
K’ -N3DSp
so
indicating that power is a function of the speed of rotation. impeller diameter, and fluid density. I t is generally assumed that this expression holds for gas-liquid systems when the bulk density of the mixture is used. For this investigation the measurements suggest that a point is reached above which fractional air holdup becomes constant. EFFECTON MASSTRANSFER. Masstransfer data were obtained using three sizes of paddle a t speeds from 300 to 2000 r.p.m. At the start of the investigation it was decided to develop a correlation of the type presented by Cooper and others, to assure validity of the experimental data. Therefore, complete power and mass-transfer data were taken for the largest flat-paddle impeller. The plot developed from the information found in this study i s shown in Figure 3. U p to this point it was thought that a comparable correlation could be made, even with a different impeller design. However, Cooper’s plot for the vaned disk showed parallel lines for different air rates, whereas a family of curves was obtained in this study. The variation in results is due to the difference in flow pattern and bubble distribution produced by the impellers (Figure 4, A to D). All high-speed photographs of bubble flow generated by the two types of impellers were taken under approximately the same conditions of low impeller speed and low air rate. Figure 4, B, demonstrates the contacting ability of the vaned disk when the impeller is positioned at half the
4 228
30
50
POWER
liquid height. When compared with the flat paddle (Figure 4, A ) a considerable difference is apparent. There is extreme agitation of the bubbles dispersed by the vaned disk in the area below the impeller, whereas above the backing plate there are fewer bubbles. The flat paddle appears to produce a more uniform distribution. The bubbles are not distorted very much until they near the hub of the rotating impeller (Figure 5). Particularly notable are the large bubbles directly below the agitator in Figure 4, A. Generally, the bubbles produced by the vaned disk appear greater in diameter than those created by the paddle. Figure 4, C and D,shows the impellers under the same conditions, but positioned immediately above the sparger and \vith the paddle rotating at a slightly higher speed, Again, the bubbles rising out of the vaned disk are larger than those formed by the paddle. The majority of the experimental runs were conducted with the agitator very close to the sparger opening and directly above it. The distribution of bubbles is very similar when the impellers are compared under severe conditions of air rate and agitation, as shown in Figure 6, B (vaned disk) and A (flat paddle). The bubbles produced by the vaned disk are again greater in size. The power input is very much greater for the vaned disk. Figure 7, A and B, demonstrates the operation of the contactors under high air rate and low impeller speed. The higher air flow produced larger bubbles in both cases, but the distribution is better in the case of the paddle. Smaller bubbles are also present in Figure 7, A. When Figures 4, C, and 7, A , are compared, it can be seen that the population of small bubbles has remained fairly
INDUSTRIAL AND ENGINEERING CHEMISTRY
low
100 INPUT, P v ,
( F T L 6 /Y,H
2000
cu ~ 7 )
uniform although the gas flow has increased. The outstanding difference between the two photographs appears to be the presence of the large, greatly deformed bubbles. This would account to some extent for the small effect of air rate on mass transfer. The large bubbles rise quickly, and, because of their low surface area contribute little to the gas absorption. The actual gas holdup did not increase substantially with increased flow of air. At high air rates it is possible that the vaned disk forces even the larger bubbles to break up, thereby increasing the holdup. As a correlation using the power input per unit volume fi, was not convenient; it was decided to see if correlation was better when impeller speed \vas a variable, Plots of Kv us. izi are shown in Figure 8, with impeller size and air rate as parameters. I t is clear that gas flow has very little effect when flatpaddle impellers of large diameter are employed and small diameter agitators are used at high speeds. IVhen very small paddles are employed poor distribution of the bubbles results. (Figure 3: ,4 and B ) , In Figure 9, A , the operation termed “flooding” is observed-bubbles of gas are rising along the shaft of the agitator without great deformation and are unhindered in their motion. Effect of Impeller Height on Mass Transfer. To determine the effect of the height of the impeller above the sparger on mass transfer: the base of the paddle was put in three positions: 1S/l6, 2l,;I6, and the usual “run” position, 3/32 inch, above the sparger. The data taken for the medium height were not significantly different from those obtained under normal conditions, but those at the greatest height lay above the aforementioned data-i.e. higher K,. ~
A B C 0 Figure 4. Variation in results is due to difference in fiow pattern and bubble distribution produced by impellers A. Flat-paddle N. 378 r.p.m. H. 1 3 / 1 ~ inches D. 3.00 inches V,. 13.5 feet per hoLr
B. Vaned-disk H. 1.18 inches D. 2.38 inches
N. 483 r.p.m.
C. Flat-paddle
N.
H.
344 r.p.m. D. 3 inches
'/lo
inch
V, 13.5 feet per hour
D. Vaned-disk N. 221 r.p.m. H. a/ D. 2.38 inches
inch
Modified Correlation. In Figure 8, which shows the effect of impeller speed on mass transfer, the lines through the data points for the larger diameter impellers are parallel. To get an approximate trend, a third parallel line was passed through the experimental points obtained for the smallest paddle. These lines were then cross-plotted (Figure 10). These graphs indicate the relationship Kv = cNW8D4.94
Figure 5. High-speed photograph of bubble formatron
N.
508 r.p.m.
D.
1.1 9 inches 1a/l6 inches 13.5 feet per hour
H. V..
Figure 6. Impellers in operation under severe conditions of air rate and agitation A. Flat-paddle N. 915 r.p.m. H. 3/le inch D. 3.00 inches V,. 86 feet per hour
Figure 8.
B. Vaned-disk
N. 910 r.p.m.
D. 2.38 inches
H.
*/a inch
Effect of agitator speed on oxygen absorption
v
40
Figure 7. speed
Operation under high air rate and low impeller
A. Flat-paddle N. 335 r.p.m. H. 3/~6inch D. 3.00 inches
Figure
Va. 86 feet per hour
B. Vaned-disk N. 224 r.p.m. H. 3/sinch D. 2.38 inches
9. Smallest paddle in operation, flooding
A. N. 493 r.p.m. D. 1.19inches
H.
3/16 inch Vs. 13.5 feet per hour
B. N.
509 r.p.m. D. 1.19 inches
H. 3/36 inch Vs. 86 feet per hour
AGITATOR
SPEED, N,
VOL. 49, NO. 8
R.RM.
AUGUST 1957
1229
VOLUMETRIC ABSORPTION COEFFICIENT,
Figure 10.
K, = mass-transfer coefficient, as before constant of proportionality impeller speed impeller diameter
= = =
:V
D
which is very close to the product N3D6 which occurs in the expression for power input, 7,-
’
I
Because a correlation with the power product ( 5 ) , 1V3D5, was indicated, the data were assembled to permit evaluation. The final correlation of this study is presented in Figure 11. I n the upper region of the curve the data give a fairly good trend, indicating reasonably accurate correlation. The lower region represents the area where data were taken for the impeller of smallest diameter. Here, there is a definite effect of air flow
2 t: 3
103, (LO. N*LEYcu.m,nd
at low values of .V305. As the power product increases, however, the deviation from the indicated trend line decreases. The additional scatter of data in the lower region is due to flooding of the impeller blades and analytical inaccuracies, as only very small quantities of oxygen were transferred. The great advantage of this type of correlation is that the variables involved are easily measured. The unusual effect of air rate encountered in this investigation is of considerable value where the cost of gas is an economic factor in the feasibility of a project. Summary The results of this investigation indicate, convincingly, that gas flow has no effect on the mass transfer of oxygen when flat-paddle impellers of diameters greater than 40y0 of the tank diameter are employed in a fully baffled vessel. This would exclude the smallest agitator used in this study.
Figure 1 1 . Effect of power product N3D5 on oxygen absorption
5
I
Effect of impeller size on mass transfer
where
c
K~
The vertical positioning of the impeller is of some importance and an optimum position of the blades is indicated. This positioning must be determined experimentally. Extreme caution is required in extending the results obtained from one impeller design to another. The correlations and high-speed photographs show a considerable difference in performance between flat-paddle and vaned-disk agitator% The best correlation for a paddle impeller involves the use of the power product 5305. This group is easilv evaluated and no further information is necessary. The applicability of this type of correlation to vessels of different sizes and for very small impellers remains to be demonstrated. Small impellers are used in a number of industrial applications and some effect of air rate should be noted. There are also applications of importance a t air rates greater than those investigated. Nomenclature
constant of proportionality impeller diameter, feet g, = gravitational conversion factor H = distance between impeller and sparger, inches K , = volumetric oxygen absorption coIb. moles efficient __ cu. ft. x hr. x atm. k” = constant of uroportionalitv dl =’impeller speed, r.p.m. P , = power input per unit volume of ft. -1b. agitated liquid, min. X cu. ft. P = power input Q = inlet gas flow, cu. feet per minute T = tank diameter, inches V , = superficial gas velocity based on inlet gas volume and cross section of tank, feet per hour G
D
= =
GREEKLETTER p = liquid density, pounds per cu. foot
10
2
Literature Cited
1
(1) Bartholomew, W.H., Karow, E. 0. Sfat, M. F., Wilhelm, R. H.: IND. ENG.CHEM.42, 1801 (1950). (2) Ibid.,p. 1810. (3) Cooper, C. M., Fernstrom, G. A , , Miller. S.A , . Zbid..36. 504 11944). ( 4 ) Foust, H . C., ’Mack, D: E., Rushton, J. H., Zbid.: 36, 517 (1944). (5) Friedman, A. M., M.S. thesis, [Jniversity of Wisconsin, 1956. ( 6 ) Hixson, A. hr,,IND.END.CIIEM.36, 488 (1944). ( 7 ) Hixson, A. W., Gaden, E. L., Ibid.,42, 1972 (1950).
LD Y
n0x
>
x
i
w
Y 0
I
W
0
E
t
8 P
RECEIVED for review November 20, 1956 ACCEPTED June 4. 1957
I
3 p
0.1
POWER
1230
PRODUCT,
N3D:
x
18, (fish?)
INDUSTRIAL AND ENGINEERING CHEMISTRY
Division of Agricultural and Food Chemistry, Symposium on Fermentation Process and Equipment Design, 130th Meeting, ACS, Atlantic City, N. J., September 1956.
