HOLDUP AND MASS TRANSFER IN BUBBLE COLUMNS G. A. H U G H M A R K Ethyl Cor#.,Baton Rouge, La.
A correlation for gas holdup in bubble columns predicts values with an average absolute deviation of about 1 1 % from the experimental holdups. A recent correlation for mass transfer from single gas bubbles in liquids is applicable to the swarm data for bubble columns.
s
Cocurrent superficial liquid velocities u p to 0.3 foot per second
columns often are used as reactors in which the reaction proceeds in the liquid phase with a component or components transferred from the gas phase. T h e gas bubbles upward through a cocurrent or countercurrent flow of liquid so that the liquid phase is continuous. This paper presents correlations for gas holdup and the liquid phase mass transfer coefficient in bubble columns. The holdup can be used to estimate the interfacial area for mass transfer and, with the mass transfer coefficient, provides a method for estimating a mass transfer rate per unit volume for the bubble column system.
Ellis and Jones' data indicate that wall effects increase gas holdup a t diameters up to 3 inches and then for diameters greater than 3 inches, gas holdup is independent of the diameter. Gas holdup was found to be correlated as a function of the superficial gas velocity for the air-water system a t zero liquid flow. The correlation applies to cocurrent liquid systems if the holdup is defined by:
Gas Holdup
T h e Hughmark data were used to evaluate the effect of liquid physical properties. T h e data indicate that holdup for these systems can be correlated with the term
PARGER
Fair, Lambright, and Anderson ( 3 ) , Yoshida and Akita (g), and Towell, Strand, and Ackerman (8) have presented data for gas holdup in bubble columns with diameters in the range of 6 to 42 inches for air-water and air-aqueous solutions. Ellis and Jones ( 2 ) obtained air-water holdup data in the bubble regime with column diameters from 1 to 12 inches and for air with several aqueous solutions in a 2-inch column. Hughmark (5) obtained data in the bubble regime for air with water, a sodium sulfate solution, kerosine, and a light oil in a 1-inch tube. Neusen (6) recently has reported holdup data for steam-water a t 600 p.s.i. in a 2.9-inch pipe; several data points are in the bubble regime. T h e bubbling regime in vertical flow appears to be defined by the conditions:
which reduces to Vsc for the air-water system. Figure 1 shows the correlations for the air-liquid data. Table I shows the average absolute deviation between experimental holdups and holdups calculated from Figure 1. Liquid physical properties cover the range : Density Viscosity Surface tension
48.5 to 106 pounds per cu. foot 0.9 to 152 cp. 25 to 76 dynes per cm.
All data other than those of Neusen are for air a t essentially atmospheric pressure. T h e Neusen data for 600-p.s.i. steam
Superficial gas velocities u p to about 1 foot per second
---
1.07
h 0.1
--
-01 .01
218
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0.1
I&EC PROCESS D E S I G N A N D DEVELOPMENT
I
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I l l 1 1
1.0
I
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10
Table 1.
Ref. (5)
Pipe Diameter, Inches 1
1 2
6
12 16 42
Experimental and Calculated Holdup Data
Superjicial Liquid Velocity, Ft. /Sec. 0.08-0.4 0.07-0.35 0.1-0.2 0.1-0.2
System Air-water Air-NazCOa soln. Air Varsol Air-oil blend 1 Air-water Air-water Air-22-cp. glycerol Air-109-cp. glycerol Air-I 50-cp. glycerol Air-ZnClz soln. Air-water Air-NazSOs soln. Air-3-cp. glycerol Air-7-cp. glycerol Air-water Air-water Air-water
show a n average absolute deviation of 32,5y0 and a positive average deviation of 25y0 from calculated values. Thus, any correction for gas physical properties would be relatively small. Mass Transfer Coefficients
Mass transfer from gas bubbles to a continuous liquid phase can be represented by the two-resistance theory. This will combine the mass transfer coefficient within the bubbles and the coefficient from the bubbles to the liquid phase. This paper considers the liquid phase mass transfer coefficients. Semitheoretical equations of the form
have been used to correlate experimental data for mass transfer from single spherical surfaces to flowing air and liquid streams. These correlations are not applicable to experimental data for mass transfer from single gas bubbles in liquid. A modification of Equation 2 has been proposed (4)to correlate the data for mass transfer for single bubbles in liquid and liquid drops in liquid as well as the data correlated by Equation 2. T h e equation is of the form:
For single gas bubbles, a = 0.061, b = 1.61. Bubble columns operate with swarms of bubbles rather than single bubbles. Figure 2 shows a plot of the data of Towell, Strand, and Ackerman for the COz-water system. T h e gas phase resistance for this system is negligible, so that the mass transfer coefficient can be regarded as applicable to the liquid phase. These data indicate that bubble swarms can be correlated by the equation when a = 0.0187 and b = 1.61 and the velocity in the Reynolds number is represented by the slip velocity between the bubbles and the liquid. Thus, the swarm data have the same slope with respect to the three dimensionless groups as the single bubble data, but the mass transfer coefficients are less than that for the single bubbles. Towell, Strand, and Ackerman report mass transfer coefficients per unit area for their data because interfacial areas were determined experimentally. They observed mean bubble diameters of about 0.25 inch and that the mean bubble diameter was independent of the gas rate. Yoshida and Akita report mass transfer coefficients per unit volume. Their 0 2 -
No. of Data Points 18 14 6 6 14 13 6 11 7 11 15 26 19 12 26 12 5
0 0
0 0 0 0 0 0 0 0 0
0-0.048 0
Av. Abs.
%
5.6 5.6 12.3 10.8 5.6 6.5 11.7 19.1 10.6 12.5 12.6 7.8 21.5 10.8 6.9 15.2 15.6
I
1000
-
Figure 2.
Bubble swarm data
water data were converted to a unit area basis by assuming that the gas holdups could be converted to interfacial areas for 0.25-inch spherical bubbles. Bubble diameters for the air-3-cp. aqueous glycerol and air-7-cp. aqueous glycerol were estimated by correcting a 0.25-inch bubble for liquid physical properties as indicated by Calderbank (7).
Table I1 compares the experimental and calculated coefficients. Shulman and Molstad (7) report mass transfer data for bubble columns with countercurrent liquid flow. T h e data
Table II. Experimental and Calculated M a s s Transfer Coefficients
(9)
Pipe Diameter, Inches 6
(8)
16
Ref.
System Air-oxygen-water Air-oxygen-3-cp. glycerol Air-oxygen-7-cp. glycerol Air-COz-water
VOL. 6
NO. 2
No. of Av. Data Abs. Points Deu., yo 18 12.1 14 22.0 22 15.4 14 9.3
APRIL 1967
219
for COQ-water a t L = 5000, 10,000, and 20,000 pounds per hour per sq. foot and H2-water a t L = 20,000 were used to estimate values of kL. Experimental gas holdups were converted to interfacial areas for the observed 0.4-cm. bubbles. The average absolute deviation between experimental and calculated coefficients per unit area is 15% for the 15 data points.
kLa = (40.2)(3.62)/60 = 2.42 min.-l These results compare with experimental values of a = 49 sq. feet per C U . foot, k~ = 0.052 foot per minute, and kLa = 2.56 min.-’ reported by Towell, Strand, and Ackerman for these conditions. Nomenclature
Example
D,
For COa desorption from water in a 16-inch column with rates of 20 standard cu. feet per minute for air and 25 gallons per minute for water 20 VSG = ___ - 0.238 foot per second (60) (1.4) 25 VSL =
(60) (7.48) (1.4)
=
0.0397 foot per second
bubble diameter, ft. diffusivity, sq. ft. per hour g gravitational force, ft. per sq. hour h fractional holdup of gas a t zero liquid flow h‘ = fractional holdup of gas k = mass transfer coefficient, ft. per hour L = liquid mass velocity, lb. per sq. hour N R ~= D , LfS/v, Reynolds number A’sc = V/D, Schmidt number I f S h = k D,/D, Sherwood number Us = slip velocity, Vso/h‘ - V s L / ( l - h‘), ft. per sec. Va = superficial velocity, ft. per sec. D
= = = =
Assume h’ = 0.145 from Figure 1,
- V S L / (-~ h ’ ) ]
h = V,,/[V,w/h’
h = 0.238/(0.238/0.145
- 0.0397/0.855)
=
0.149
From Figure 1, a value of 0.245 is obtained for VSGwhen h = 0.149. Thus h’ is about 0.14. If 0.25-inch bubbles are assumed 6h a=-=-D,
6(0.14) - 40.2 sq. ft. per cu. foot 0.25112
T h e mass transfer coefficient is obtained from the equation:
Us
=
Nx,
= Dp
Ng, =
DPg1I3 - -
-
D2’3
- 0.0397/0.855
0.238/0.14 C’,/v
v/D
=
=
=
1.65 feet per second
(0.25)(1.65)(3600)(28.3)/12 = 3500
1/(28.3)(7)(10-5)
=
505
(0.25) [(4.18)(10)8]1’3 = 9160 (12) [(7)(10-j)]2/3
nrsh
= 2
kL
=
+ 0.0187 (835)l.G’ = 1080
DNSh/D,
=
(7)(10-5)(1080)/(0.25)/12
=
3.62 feet
per hour
220
I & E C PROCESS D E S I G N A N D D E V E L O P M E N T
GREEKLETTERS = liquid density, Ib. per cu. ft. = surface tension, dynes per cm. = kinematic viscosity, sq. ft. per hour or sq. ft. per sec. Y
p c
SUBSCRIPTS = liquid phase = gas phase
L G
literature Cited
(1) Calderbank, P. H., Trans. Znst. Chem. Engrs. 36, 443 (1955). ( 2 ) Ellis, J. E., Jones, E. L., Two Phase Flow Symposium, Exeter, England, June 1965. (3) Fair, J. R., Lambright, A. J., Anderson, J. LV., IND.END. CHEY.PROCESS DESIGN DEVELOP. 1, 33 (1962). (4) Hughmark, G. A., A.Z.Ch. E. J., in press. ( 5 ) Hughmark, G. A , , Ph.D. dissertation, Louisiana State University, Baton Rouge, La., 1959. ( 6 ) Neusen, K. F., ASME-AIChE Heat Transfer Conference, Los Angeles, August 1965. (7) Shulman, H. L., Molstad, M. C., Znd. Eng. Chem. 42, 1058 (1950). (8) Towell, G. D., Strand, C. P., Ackerman, G. H., AIChE-Inst. Chem. Engrs. Joint Meeting, London, England, June 1965. ( 9 ) Yoshida, F., Akita, K., A.I.Ch.E. J . 11, 9 (1965).
RECEIVED for review May 16, 1966 ACCEPTEDAugust 23, 1966 AIChE meeting, Columbus, Ohio, May 1966.
