Oil Chemists’ Soc. 38, 470 (1961). (16) Helfferich, Friedrich, ”Ion Exchange,” p. 159, McGraw-Hill, New York, 1962. (17) Higgins, I. R., Ind. En,c. Chem. 53, 635 (1961). (18) Ibid.,p. 999. (19) Higgins, I. R.. U. S.Patent 2,815,322 (Dec. 3. 1957). (20) Hwa, I. C. H . (to Rohm 8L Haas Co.), Ibid., 2,895,925 (July 21, 1959). (21) Juda. Walter, Kirkham. T. A.. Parsi. E. J.. 15th Purdue Industrial’jt‘aste Conference. Mav 3 to 5. 1960 (22) Kerker, Milton, J . Am.’Chem. SOC.79, 3664 (195-). (23) Kraus: K . A . , Moore, G. E., Ibid.,72, 5792 (1950). (24) Kraus, K. A , >Selson, Frederick, Baxter. .J. F.: Ibzd..75, 2768 (15) Hatch, M. J., Smith, H. B., J . A m .
Conclusions
T h e laboratory work on acid retardation has demonstrated its wide applicability Dow Chemical Co., Midland, Mich., private communication. (10) Dow Chemical Go., Midland, Mich., Tech. Service Bull. 164-62. ”Ion Retardation.” (11) Glogau, R. C., Halvorson, D. 0.: Sloan, It’. J., Ind. Eng. Chem. 53, 275 (1961). (12) Hancher, C. \V., .Jury, S. H., Chem. Eng. Progr. Symp. Ser., No. 24: 55, 87 (1959). (13) Hatch, M. J., Abstracts, 138th Meeting, ACS: Sew York, D. 187. 1960. (14) Hatch, M. J., Dillon, J. A , Smith, H. B., Znd. Eng. Chem. 49, 1812 (1957).
~
/ , n C I \ ( 1 7-l J ) .
(25) Leifer. Leslie, Abstracts of Papers. 138th Mecting. ACS New York. D. 39s. 1960. (26) M’Lnalo. G. D.: ‘Turse, Richard, Rieman, It.. R.. .inal. Chim. d c t a 21, 383 (1959). (27) Selson, Frederick, Kraus, K . A . , J . - h i . Chprii. Sac. 77, 329 (1055) \-’--,’
(28) Ibid.,80, 4154 (1958). (29) Newton. R. D., Aries, R. S.,“Chemical Engineerin? Cost Estimates,” p. 5: McGraw-Hill, New York: 1955. (30) Prue, J. E.. Schwarzenback, Gerold. Hrlz~.Chinz. .icta 33, 985 (1950). (31) Reents, A. C.. Kahler, F. H., Ind. Eng. Cheni. 47, -5 (1955). (32) Seamster: .A. H., IVheaton, R . M., Chrm. Eng. 67, No. 17, 119 (1960). (33) Smith, R . S . , Farrell, J. B.! I d . Enq. Chem. 54, No. 6, 29 (1962). Chemical Co.), (34) Taylor, F. C.. Jr., Xamoth. H . L. (to DOLV U. S.Patent 2,868,832 (Jan. 13, 1959). (35) Vromen, B. H.: Ind. Eng. Chem. 54, 20 (1962). (36) Vromen, B. H . , Chamberlin, N. S., Preprint 59, 42nd National Meeting, .Am, Inst. Chem. Engrs., Atlanta. Ga.? Feb. 21 to 24, 1960. (37) Wheaton. R. M., Bauman, \V. C.: Znd. Enq. Chem. 43, 1088 (1951). (38) Ibid.,45, 228 (1953). RECEIVED for review July 19, 1961 . ~ C C E P T E D May 2, 1963
GAS ABSORPTION IN AGITATED GAS-LIQUID CONTACTORS Inteifacial Auea, G a s Holdup, Liquid-Phase M a s s Transfeu CoeJicient, and Reaction Factor F U M I T A K E Y O S H I D A A N D Y O S H I H A R U
M I U R A ’
Departmrnt of Chemical Engineerzn,o, Kpoto Ci2iversity, Kjoto. Japan
Specific interfacial areas in agitated gas-liquid contactors were evaluated by measuring the rate of chemical absorption. Correlations are presented for the specific interfacial area, the gas holdup, and the liquid-phase mass transfer coefficient per unit of interfacial area.
of the gas-liquid contactor in which gas is bubbled through a mechanically agitated liquid has usually been expressed in terms of the volumetric coefficient such as k,a Recently, Calderbank ( I ) separated k , from the interfacial area per unit volume, a, measured by the light-reflection or the light-transmission technique. The latter method was first adopted by Vermeulen and coworkers ASS T R A N S F E R PERFORMANCE
Present address, Hirneji Technical College, Himeji, Japan
(5) for the measurement of the liquid-liquid and the gas-liquid interfacial areas in a closed agitated tank. In the present work, the interfacial area around gas bubbles was measured by a method utilizing the rate of chemical absorption, ar?d the average bubble diameter was calculated from the interfacial area a n d the observed values of the gas holdup, resulting in a correlation which involves the bubble diameter, agitator speed, a n d physical properties of liquid. VOL. 2
NO.
4 OCTOBER 1 9 6 3
263
Principles
T h e principle of the method for the evaluation of the interfacial area is the same as that adopted by the authors (3, 7, 8) for the evaluation of the effective interfacial area in packed columns for chemical absorption. Recently, Westerterp ( 6 ) also applied this technique to the agitated gas-liquid contactor. Either the film model or the penetration theory (4, 8 ) can be used to show that the coefficient for absorption with a moderately fast first order to pseudo-first order reaction is given as
k ~ '= (kCBDa)'!2
(1 1
provided that
The coefficient k , ' in Equation 1 is defined by XA
=
kL'(C.d% - C A L )
(3)
Equation 1 implies that, under conditions such that inequality of Equation 2 holds, the coefficient kL' is independent of the mass transfer coefficient k , and accordingly of hydrodynamic conditions. Under such conditions, the whole gas-liquid interface is considered uniformly effective for absorption, and the values of k,' can be readily calculated by Equation 1, with the knowledge of the reaction rate constant k , the concentration ,, and diffusivity of the solute of the reactive liquid component C gas in the liquid phase D,. Thus, it is possible to evaluate the interfacial area per unit liquid volume a from the values of kL', calculated by Equation 1, and the values of the volumetric coefficient kL'a obtained from experimental data, given values ,, can be assumed zero for a n irreversible of CALand CAS. C reaction if enough quantity of the reactive liquid component exists as is usually the case. C,i can be estimated from the Henry's law constant with necessary correction for the presence of electrolytes. The fractional gas holdup can be determined by measuring the bulk density of aerated liquid as will be mentioned later. The average diameter of gas bubbles can be obtained from calculated values of the interfacial area and observed values of the gas holdup. Thus, if bubbles are assumed to be spheres n
Hu =
5
di3
(4)
i=l
a =
*di2
(5)
i=l
The average bubble diameter is defined as
diameter of the agitator was equal to four tenths of the tank diameter. Two types of agitators (9)were tested: the vaneddisk type with 16 radial vanes, one tenth of the agitator diameter in height, on the bottom surface of the disk, and the turbine type with 12 radial vanes, two tenths of the agitator diameter in height. With each type, the length of the vanes was 0.35 times the agitator diameter. Gas was blown into the liquid through a single nozzle a t the bottom center. The nozzle diameter was 4 mm. for the 25-cm. tank and was made proportional to the tank size for most of the runs. Experiments on the absorption of carbon dioxide contained in air by aqueous solutions of sodium hydroxide were performed under the following conditions : concentration of sodium hydroxide, 0.005 to IN; concentration of total alkalies, 0.1 to 1N; temperature, 10' to 30' C.; agitator speed, 60 to 400 r.p.m.; and superficial gas velocity with respect to the total cross section of the tanks, 20 to 90 feet per hour. Gas was preheated to the temperature of liquid in the tank. Content of carbon dioxide in the air was varied from 1 to 14%. This variation was made possible by passing air through a packed column, in which carbon dioxide was stripped from water, and by varying the gas-liquid ratio. T h e rate of absorption was determined by analyzing the solution for sodium hydroxide before and after each run. In calculating the values of kL'a, the mass transfer resistance in the gas phase was assumed negligible a t least for this particular system, which seems justifiable in view of the results on the same system with a bead column (8). For the evaluation of the interfacial area per unit liquid volume, a, on the aforementioned principle some runs were made a t 20' C. under conditions such that the observed values of kL'a varied in proportion to the square roots of the average concentrations of sodium hydroxide, CB, other factors such as liquid viscosity, density, surface tension, gas rate, and agitator speed being kept constant. Such conditions were found by trial experiments. Physical properties of the solution were practically constant a t a given temperature, since the concentration of the total alkalies did not vary in the course of a series of runs. Thus, from the data of those runs the interfacial area was calculated by
The gas holdup is defined here as the volume occupied by gas bubbles as a fraction of the clear liquid volume. Since the density of gas is usually negligible compared with that of liquid, the gas holdup, Hu,is related to the bulk density of aerated liquid p B as follows: HU =
Experimental
Two agitated gas-liquid contactors used in a previous work (Q), 25 and 37.5 cm. in diameter, and a larger one, 58.5 cm. in diameter, were employed in the present work. They were all constructed to be geometricall>- similar. 'The clear liquid depth in each tank was made equal to the tank diameter. Four equally spaced vertical baffles? one tenth of the tank diameter in width, were attached to the shell. Each agitator was mounted a t the axis of the tank with a clearance from the bottom equal to three tenths of the tank diameter. T h e 264
l&EC PROCESS DESIGN A N D DEVELOPMENT
(PL
-
PB)/PB
(8)
The bulk density of aerated liquid was measured by means of two pressure taps fastened to the inside of the tank wall a t about midway between two adjacent baffles, one near the tank bottom and the other near the free liquid surface. Each of the pressure taps consisted of two concentric tubes closed a t one end and with small holes drilled through the tube wall, which transmitted only the pressure, being unaffected by the flowing stream. From the difference in the readings of the two separate inclined manometers connected to the pressure taps and open to the atmosphere a t the other ends, the bulk density of aerated liquid was calculated by the following relationship:
L(PL-
PB)/PL =
h
(9)
where L is the vertical distance betxveen the t\vo pressure taps,
10
VANED DISK TANK D I A M . = 2 5 c r n
2 n
E
\ . I
E
100
8
0
6 I
4
20
0
I14
V
92
~
4 1
2
I
8
6
(k (CBla". O n ) ' ,
IO
m/ hr
Figure 1 . Plot of kL'a vs. [ & ( C B ) ~ ~ D for A ] 'runs ' ~ for evaluating interfacial area, normality of solution =
0.4 100
R.P.M.
e
TANK D I A M . = ' 2 5 c m Vs = i 2.2 m / h r
6 m
I
E
I
I
-I
I
.4
.e
I
I
.e
I
'T-i 1 IO 0.06 8 0.1
.2 TOTAL SODIUM
Figure 2. area
.
N
Effect of electrolyte concentration on interfacial
and h is the difference in the readings of the two manometers in terms of the clear liquid head. Interfacial Area Figure 1 shows a n example of the plot of kL'a against the square roots of [k(C,),,, D A ] for the C02-NaOH runs for the evaluation of the inte:rfacial area. Each line in this figure represents a series of consecutive runs with a fixed concentration of the total alkalies. Each data point is for a n average value of the sodium hydroxide concentrations before and after each run. Slope of unity of the straight lines in Figure 1 indicates that Equation 1 holds for these runs, and the interfacial area can be ca.lculated by the aforementioned method. Thus, the interfacial a.rea in the 25-cm. tank a t a gas rate of
400
6
8
1000
2
N D ,
4
6000
m/hr
Figure 3. Interfacial areas as function of peripheral speed of agitator with vaned-disk (above) and turbine (below) agitators
40 feet (12.2 meters) per hour and five agitator speeds were obtained by dividing the values of the ordinate in Figure 1 by those of the abscissa. With all the runs shown in Figure 1, the concentration of the total aIkalies was approximately 0.45. Plots similar to Figure 1 were made for several total alkali concentrations, various gas rates, and for three sizes of tanks with two types of agitators. Figure 2 was prepared from four figures similar to and including Figure 1 and shows the effect of the concentration of the total alkalies on the interfacial area in the 25-cm. tank a t a gas rate of 40 feet per hour. At low agitator speeds, the interfacial area is independent of alkali concentrations, but a t agitator speeds higher than about 200 r.p.m., the interfacial area increases slightly with increasing alkali concentrations. VOL. 2
NO. 4
OCTOBER 1963
265
Occurrence of bubbles in the electrolytic solution which are smaller than in pure water a t higher stirring speeds was observed in a previous study (9) and can be explained by the electrostatic potential a t the interface. Figure 2 indicates that even a t higher stirring speeds the interfacial area approaches asymptotically to the values for pure water a t concentration around 0.1S. Thus, it can be assumed that the interfacial areas obtained from experiments with 0.1 N solutions are equal to those in pure water, dilute electrolytic solutions, and in nonelectrolytic solutions with physical properties not considerably different from those of water. Interfacial areas in the three contactors-25, 37.5, and 58.5 cm. in diameter-with the vaned-disk and the turbine agitators were evaluated for three superficial gas velocities, 20, 40, and 90 feet per hour. T h e results shown in Figure 3 for the vaned-disk and the turbine agitatcrs indicate that the interfacial area for a given gas rate varies with the product N D , which is proportional to the peripheral speed of the agitator. T h e interfacial area with the turbine agitator is proportional to the 0.74 power of the gas rate and to the 1.1 power of the peripheral agitator speed. With the vaneddisk agitator, the exponential effect of the agitator speed decreases with increasing gas velocity. The effect of the diameter of the gas inlet nozzle on the interfacial area was studied by experimenting with the nozzles, 4, 8, and 12 mm. in diameter and the 25-cm. tank equipped with a vaned-disk agitator. The 12-mm. nozzle gave slightly smaller interfacial areas than the other two nozzles, apparently because of the increase of the bubble size. T h e difference between the results with the 4- and 8-mm. nozzles were negligible. T h e effect of liquid viscosity on the interfacial area \vas investigated by performing experiments on the absorption of carbon dioxide into sodium hydroxide solutions in waterglycerol mixtures of various compositions a t 20' C. in the 25-cm. tank with the vaned-disk agitator a t agitatcr speeds of 110 and 200 r.p.rn. and a gas rate of 40 feet per hour. Values of the reaction rate constant k necessary for the calculation of y were measured by experimenting with a liquid laminar jet absorption apparatus. T h e values of k at 28" C. are given below,: 0 12.3 Glycerol, wt. % k , cubic meter/(kg.-mole)(sec.) 8400 11,000
26.0 14,800
I .c E
1
E 4
2
'E
0.1 E
a \
a
I
c 1
01.02
I.C
a E L
9 5
€
2
-
N
0.1 \
X
a 6 4
0.02 )
1
I
I
2
4
I I
6 8 100 R . t? M .
I
I
I
2
4
600
Correlations for gas holdup in contactors with Figure 4. vaned-disk (above) and turbine (below) agitators
32.5 15,000
k increases slightly with increasing glycerol-water ratioLe., increasing viscosity. Values of y calculated using these k values were always greater than 5! making possible the evaluation of the interfacial area by the aforementioned method. T h e results showed that the interfacial area is independent of liquid viscosity a t least over the range etudied-i.e., approximately 1 to 4 cp. No conclusion was obtained on the effect of surface tension on the interfacial area, since surface tension of waterglycerol mixtures used was practically equal to that of water.
Average diameters of gas bubbles calculated by Equation 6 from the interfacial area and the gas holdup range from 1.5 to 4 . 5 mm., in agreement with photographic observations in the previous work ( 9 ) . Variarion of the interfacial area, the gas holdup, and the average bubble diameter can be summarized as folloivs: \l'ith the turbine agitator a
Hu
(n;O)l.lV,O.i6 0: L ~ ~ 0 . 8 ~ 1 . 2 V , 0 . 7 6
dB a
;V-O.3DO.l
LYith the vaned-disk agitator : Gas Holdup and Bubble Diameter
Common correlations for the gas holdup in the three tanks of different sizes were obtained for the vaned-disk and the turbine agitators as shown in Figure 4. The gas holdup a t a given gas rate and a n agitator speed varies with the tank size raised to the powers of unity and 1.2 with the vaned-disk and the turbine, respectively, The steep slopes of the lines at higher agitator speeds may indicate that in this range the extent to which the gas is entrapped from the free aurface increases with increasing agitator speed. 266
l&EC PROCESS DESIGN AND DEVELOPMENT
V,, Ft./Hr. 20 a
0:
(.VD)O,Q
Hu a 5 0 . 8 0 ds ;V-O.lDO.L
40
go
( AvD )O.i .Y0.6D
('VD)0.8 iy0.7D
L\--O,lDO
.2
Av-0.1 DO
.3
For the gas holdup and the average bubble diameter, the above table does not apply to the range where gas entrapping from the free surface occurs. It is considered chat the interfacial area measured by the aforementioned method is negligibly affected by gas entrapping, even if it does occur.
Figure 5. General correlation
for k~ in agitated gas-liquid contactors
Correlation for liquid Phase Mass Transfer Coeff icient
I n a previous study (g), a correlation was proposed for the volumetric liquid-phase mass transfer coefficient k,a for the absorption of oxygen into water in the agitated tanks identical to those used in the present work. T h e volumetric coefficient a t a given gas rate was shown to be a function of the power consumed by the agitator per unit liquid volume. Although such a correlation is convenient in practice, it seems sounder to obtain a direct correlation for k , separated from the specific interfacial area, a. Thus, values of k , were obtained from the previous data on k,a and the present correlations for a, shown in Figure 3. T h e previous data included oxygen-water runs a t 5 O , 20°, and 30" C. and oxygen-aqueous glycerol solution runs a t 15" C. with a range of viscosity from 1.9 to 3.6 cp. and 20-fold variation in the Schmidt number. Effects of liquid viscosity and surface tension on the interfacial area were assumed negligible for the ranges studied. Figure 5 is a log-log plot for all the runs with three sizes of tanks and two types of agitators. T h e straight line through the data points is expressed by the equation:
Agreement of data for the two types of agitators might be a coincidence, because the value of the constant in the above equation should vary with the geometry of equipment. I n a recent paper, Calderbank (7) proposed a correlation in which k L is proportional to thel/d power of the agitator power consumed per unit liquid volume. Since the power required for agitation is proportional approximately to the cube of agitator speed, his results imply that k, varies with the 3/4 power of the agitator speed in slight disagreement with the
present correlation. H e also states that the type of agitator used may have a minor influence on k, for a given value of the agitator power dissipation per unit volume. Values of k , obtained in the present work range from 0.6 to 3.4 meters per hour and are somewhat higher than values calculated by the Calderbank correlation. Reaction Factor in Agitated Gas-liquid Contactors
To estimate the coefficient for chemica! absorption k,' for a new system, it is necessary to know the values of the reaction factor-Le., the ratio of k,' to k,, and those of k, for a liquid with corresponding physical properties. T h e current authors (8) have shown experimentally that the reaction factor for a moderately fast first order or pseudo-first order reaction in bead columns-i.e., a column of spheres connected in a vertical row over which liquid flows down in countercurrent to a gas stream-can be represented by the following theoretical equation, which was derived from the penetration model but practically agrees with the equation of Hatta ( 2 ) derived from the film model:
Besides the runs for the evaluation of the interfacial area, a number of runs were made on the absorption of carbon dioxide into aqueous solutions of sodium hydroxide in the 25-cm. tank with the vaned-disk agitator under the following conditions: N a O H concentrations, 0.006 to 0.75A'; agitator speeds, 80 to 300 r.p.m.; temperatures, 15" to 22" C., and superficial gas velocities, 20 to 90 feet per hour. Values of the reaction factor were obtained as the ratio of the experimental values of k,'a to the values of k,a estimated from EquaVOL. 2
NO. 4
OCTOBER 1 9 6 3
267
IO 8
e Figure 6. Reaction factor in agitated gas-liquid contactors, absorption of COZ in NaOH aqueous solutions
CQ
4
2
I
0.6
8
1.0
2
4
6
8
10
20
= difference in manometer readings in clear liquid
tion 10 and Figure 3. Figure 6 shows values of /3 plotted against y and the curve representing Equation 11. The figure indicates that the reaction factor in bubbling agitated gasliquid contactors can also be estimated by Equation 11.
head, meter = reaction rate constant. cubic meter/’(kg. mole)
(sec.) = liquid-phase mass transfer coefficient, meter, hr. = liquid-phase coefficient for chemical absorption,
Conclusions
meter/hr.
The liquid-phase mass transfer coefficient in agitated gasliquid contactors, as separated from the interfacial area per unit liquid volume, can be correlated as a function of the Reynolds number for the agitator with the average bubble diameter as the principal dimension and the liquid phase Schmidt number. When absorption is accompanied by a moderately fast first order or pseudo-first order reaction, the reaction factor, which should be multiplied to the liquid phase mass transfer coefficient to obtain the coefficient for chemical absorption, can be estimated by theoretical equations when values of the reaction rate constant, diffusivity, the liquid phase mass transfer coefficient, and other factors are available. Further experimental work is desired on the effect of liquid viscosity and surface tension on the interfacial area. Nomenclature = gas-liquid interfacial area per unit liquid volume,
square meter/cubic meter
C A L = concentrations of the component absorbed, a t the = = =
= =
=
Hu
interface and in the bulk of liquid, respectively, kg.-moles/cubic meter concentration of the reactive component in the bulk of liquid, kg.-moles/’cubic meter agitator diameter, meter diffusivity of the component absorbed through the liquid phase, square meter/hr., square meter/ sec. bubble diameter, meter average bubble diameter, meter Gauss error function defined as
= gas holdup as fraction of clear liquid volume,
dimensionless 268
l & E C PROCESS D E S I G N A N D D E V E L O P M E N T
= vertical distance between two pressure taps, meter
= number of revolutions =
= = =
= = p , p~
=
per unit time, hr,-l; normality rate of absorption, kg.-moles, (sq. meter) (hr.) superficial gas velocity with respect to the total cross section of tank, meterjhr., ft./hr. reaction factor defined as k ~ ’k ~ dimensionless , ratio defined bv Equation 2 liquid viscosity’kg.)(meter) (hr.) bulk density of aerated liquid, kg.,’cubic meter density of liquid, kg./cubic meter
literature Cited
(1) Calderbank, P. H., Moo-Young, M. B., Chem. Enz. Sci. 16, 39 (1961). (2) Hatta, S., J . Sac. Chem. 2nd. Jupun 35, 1389 (1932). (3) Miura, Y., Dissertation, Kyoto University, Kyoto, Japan, 1961. (4) Van Krevelen, D. W., Hoftyzer, P. J., Rer. Trau. C h h . 6 7 , 563 (1948) ; Chem. Eng. Sci. 2, 145 (1953). (5) Vermeulen, T., Williams, G. M.: Langlois, G. E., Chem. Eng. Progr. 51, 85 (1953). ( 6 ) Westerterp, K. R., Dissertation, Technische Hogeschool, Delft, Holland. 1962. (7) Yoshida, F., Preprint, 25th Anniversary Congress, SOC.Chem. Engrs., Japan, November 1961. (8) Yoshida, F., Miura, Y., A.2.Ch.E. J . 9, 331 (1963). (9) Yoshida, F., Ikeda, A,, Imakawa, S., Miura. Y., 2nd. Enz. Chem. 52, 435 (1960). RECEIVED for review July 24. 1962 ACCEPTED May 15, 1963 Experimental data of this study have been deposited as Document No. 7570 with the AD1 Auxiliary Publications Project, Photoduplication Service, Library of Congress, Washington 25, D. C. A copy may be secured by citing the document number and by remitting $10.00 for photoprints or $3.50 for 35-mm. microfilm. Advance payment is required. Make checks or money orders payable to Chief, Photoduplication Service. Library of Congress.
