HOLDUP AND MASS TRANSFER IN
BUBBLE COLUMNS G.
A.
HUGHMARK
Ethyl Corp., Baton Rouge, La.
A correlation for gas holdup in bubble columns predicts values with an average absolute deviation of about 11% 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.
columns often are used as reactors in which the proceeds in the liquid phase with a component The gas or components transferred from the gas phase. 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
Downloaded via UNIV OF WINNIPEG on January 23, 2019 at 10:08:42 (UTC). See https://pubs.acs.org/sharingguidelines for options on how to legitimately share published articles.
Sparger reaction
Cocurrent superficial liquid velocities up to 0.3 foot per
second
Ellis and Jones’ data indicate that wall effects increase gas holdup at 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 at zero liquid flow. The correlation applies to cocurrent liquid systems if the holdup is defined by: h
system.
Gas Holdup
Fair, Lambright, and Anderson (3), Yoshida and Akita (9), 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 at 600 p.s.i. in a 2.9-inch pipe; several data in points are in the bubble regime. The bubbling regime conditions: the be defined to flow by vertical appears Superficial gas velocities up to about
218
I
&
E
C
PROCESS
DESIGN
1
AND
foot per second
DEVELOPMENT
=
Vna/Ua
(1)
The Hughmark data were used to evaluate the effect of liquid physical properties. The data indicate that holdup for these systems can be correlated with the term
[(62.4/ )(72/ ) which reduces to Vsg 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 0.9 to 152 cp. 25 to 76 dynes per cm.
cu.
foot
All data other than those of Neusen are for air at essentially The Neusen data for 600-p.s.i. steam
atmospheric pressure.
Experimental and Calculated Holdup Data
Table I.
Superficial
Pipe Diameter,
Liquid Velocity,
Inches
Ref.
(5)
Ft./Sec.
System
Air-water
1
Air Varsol Air-oil blend 1 Air-water Air-water Air-22-cp. glycerol Air-109-cp. glycerol Air-150-cp. glycerol
1
2
Air-ZnCh soln.
Air-water Air-Na2SOs soln. Air-3-cp. glycerol Air-7-cp. glycerol Air-water Air-water Air-water
6
(9)
12 16
(2) (S)
42
(3)
Av. Abs. Dev., %
18 14
5.6 5.6 12.3 10.8 5.6 6.5 11.7
0.08-0.4 0.07-0.35 0.1-0.2 0.1-0.2
Air-Na2CC>3 soln.
(2)
No. of Data Points
6 6
0 0
14
0 0 0 0
6 11 7 11
0 0
26
13
19.1 10.6 12.5 12.6 7.8 21.5 10.8
15
0
19 12 26 12
0 0
0-0.048 0
6.9 15.2 15.6
5
average absolute deviation of 32.5% and a positive of 25% from calculated values. Thus, any deviation average correction for gas physical properties would be relatively small.
show
an
Mass Transfer Coefficients Mass transfer from gas bubbles to a continuous liquid phase 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. Semi theoretical equations of the form can
N8h
=
2
+ edVR.mJV*)1/*
(2)
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. The equation is of the form: Ash
=
2
a
(AV
(3)
For single gas bubbles, a 1.61. 0.061, b 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 CO 2-water system. The 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 in the number is velocity Reynolds 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 O2=
1/3 v.072
Nr,'484 nsc
”9
0
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). water
=
=
Table II compares the experimental and calculated coefficients. Shulman and Molstad (7) report mass transfer data for bubble columns with countercurrent liquid flow. The data
=
Table II.
Experimental and Calculated Mass Transfer Coefficients Pipe
DiamRef.
eter, Inches
(9)
6
(8)
16
No. of Data System
Air-oxygen-water Air-oxygen-3-cp. glycerol Air-oxygen-7-cp. glycerol Air-CC>2-water
VOL.
6
NO.
2
Av. Abs.
Points Dev., % 18 12.1 14 22.0 22 15.4 14 9.3
APRIL
1
967
219
for COi-water at L 5000, 10,000, and 20,000 pounds per hour per sq. foot and H2-water at 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. =
kj^a
=
(40.2) (3.62)/60
2.42 min.
=
1
=
These results compare with experimental values of a = 49 0.052 foot per minute, and kp,a sq. feet per cu. foot, kp 2.56 min.-1 reported by Towell, Strand, and Ackerman for =
=
these conditions.
Nomenclature Example
For C02 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
V SG
0.238 foot per second
(60) (1.4)
h
VsG/ÍVso/h'
=
h
0.145 from Figure 1,
=
Vsl/(1
-
0.238/(0.238/0.145
=
=
g
=
h
=
h'
=
k
=
L
=
A/h
0.0397 foot per second
=
(60) (7.48) (1.4)
Assume h'
=
2D
ArEe Argc
25
Vsl
DP
=
Vs
=
p
0.0397/0.855)
-
From Figure 1, a value of 0.245 is obtained for 0.149. Thus h' is about 0.14. If 0.25-inch bubbles are assumed
v
when
VSg
a
6(0.14)
=
=
=
025/42
Dv
The
mass
A'gh
—
Us
=
iVEe
=
A% Drg11*
=
h
kL
Sq·
2
-j- 0.0187
0.238/0.14
ft pCr
CU·
DP Us/v
r/D
=
1/(28.3) (7) (10-6)
(0.25) [(4,18)(10)8]1/3
=
2
+
0.0187 (835)1·61
S>Nsh/Dj,
=
=
1.65 feet per second
=
=
=
3500
505
gl6Q
=
1080
(7)(10-5)(1080)/(0.25)/12
=
3.62 feet
per hour
220
l&EC
PROCESS
or
sq. ft. per sec.
=
gas phase
foot
(12) [(7) (10-5) ]2/3 =
ft.
Literature Cited
0.0397/0.855
_
cu.
surface tension, dynes per cm. kinematic viscosity, sq. ft. per hour
=
(0.25)(1.65)(3600) (28.3)/12
=
=
liquid density, lb. per
Subscripts L liquid phase
(ATe)0·484^)0·33' -
—
-
=
transfer coefficient is obtained from the equation:
D2/3
A^h
4°·2
= =
0.149
=
G
6 h
=
Us
Greek Letters
')]
-
= =
bubble diameter, ft.
diffusivity, sq. ft. per hour gravitational force, ft. per sq. hour fractional holdup of gas at zero liquid flow fractional holdup of gas mass transfer coefficient, ft. per hour liquid mass velocity, lb. per sq. hour DP Us/v, Reynolds number v/ ), Schmidt number k Dp/S), Sherwood number slip velocity, VSG/h' VSL/{\ h'), ft. per sec. superficial velocity, ft. per sec.
(1) Calderbank, P. H., Trans. Inst. 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. W., Ind. Eng. Chem. Process Design Develop. 1, 33 (1962). (4) Hughmark, G. A., A.I.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., Ind. 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 Accepted August 23, 1966
AIChE meeting, Columbus, Ohio, May 1966.
DESIGN
AND
DEVELOPMENT
