Gas Holdup and Volumetric Mass Transfer Coefficient in Bubble Columns Effects of Liquid Properties Kiyomi Akita Tokushima University, Tokushima, Japan
Fumitake Yoshidal Kyoto University, Kyoto, Japan
Experimental data for the fractional gas holdup and the volumetric liquid phase mass transfer coefficient kLa in gas bubble columns with various systems were correlated by dimensionless equations. The gas holdup varies with density and viscosity of liquid, surface tension, and the superficial gas velocity. In addition to these factors, liquid phase diffusivity and the column diameter affect kLa, which is proportional to the gas holdup to the 1.1 power.
T h e gas bubble column is used more and more widely as the gas-liquid reactor or as the fermentor. The main objective of the present work is to study the effects of the liquid physical properties on the gas holdup and the volumetric coefficient for liquid phase mass transfer kLa. Studies on the bubble size distribution, resulting in the separation of kLa into k L and the specific interfacial area a, will be reported in a subsequent paper. Table I lists ranges of the variables in the gas holdup experiments and Table I1 is a similar table for the mass transfer experiments. Experimental
The bubble column used for most of the experiments was 15.2 cm in inside diameter and 400 em in height. I t was constructed of transparent vinyl chloride resin, 5 nim thick, to facilitate observation of the motion of the swarm of bubbles. T o minimize the fluctuation of gas pressure, a gas chamber, 10 em in height and of the same diameter as the column, was attached to the column bottom. The gas sparger was a single hole, 5.0 m m in diameter, drilled a t the center of the vinyl chloride resin plate, 5 m m thick, partitioning the column and the gas chamber. The column was operated continuously with respect to the gas flow. Ex:cept for the sulfite oxidation and gas holdup experiments that were performed to study the effects of the liquid flow, operation v a s batch-to-batch with respect to liquids. -1liquid was charged into the column after its temperature was controlled a t a desired temperature in a separate reservoir. The gas holdup was measured by measuring level of the aerated liquid during operat'ion Z F and that of clear liquid ZL.Thus, the a.verage fractional gas holdup t G is given as ZIi. - ZL fG
~
Z F
To whom correspondence should be addressed. 76 Ind.
Eng. Chem. Process Des. Develop., Vol. 1 2 , No. 1 ,
1973
The height of the aerated liquid Z F ranged from 200 cni to 300 em. Values of the volumetric coefficient for liquid phase mass transfer kLa with respect to the unit volume of aerated liquid was obtained from experiments of absorption of oxygen into various liquids. Oxygen from a cylinder was supplied to the gas chamber a t the column bottom through a surge tank, 25 liters in volume and packed with 9-mm Berl saddles for the purpose of minimizing the fluctuation of the reading of the orifice flow meter located between the tank and the column. Before a n absorption experiment, oxygen was desorbed from the liquid in the column by sparging nitrogen for 5-10 min a t a superficial gas velocity of about 100 meters per hour. .After the clear liquid height was measured, a n absorption run was started. It lasted 1-5 min, depending on the gas rat'e and ot'her factors. The concentration of dissolved oxygen in the liquid sample was analyzed chemically by the Winkler method (Treadwell and Hall, 1942). Two liquid samples each before and after a run were withdrawn through the sample cock a t the middle of the liquid height, using 100-ml stoppered Erlenmeyer flasks with caution not to leave any gas above the liquid in the flasks. Since the gas phase resistance for mass transfer was negligible, the values of kLa for the batch experiments on the physical absorpt,ion of oxygen were obtained by the following relationship :
kLa =
1t ~
EG
In
c* - ci c* - c, ~
which can be derived from the oxygen balance, on the assumption of complete liquid mixing. The dissolved oxygen concentration in a liquid a t saturation. C*, was determined by sparging pure oxygen through the liquid in the column for a sufficient length of time, in case published data were not available.
Table I. Ranges of Variables in Gas Holdup Experiments Systems
JTa ter-air
Wa ter-oxygen Glycol-air iO-Vol % glycol-air 30 Methanol-air 40 Vol % methanol-air 25 CU-air 0 l 5 X S a 2 S 0 3soln-air 0 03 XXaC1 soln-air 0.O i J l 0.15.1I 0 6JI 1Jf R a t er-helium Kater-air Wa ter-oxygen Water-COn a Square cross section.
Temp, OC
Column diam, cm
G a s velocity M /hr
Fractional gas holdup
N Fx ~ 103
N Bx ~ 10-3
10 10 20 30 40 20
15.2 60.0 15.2 15.2 15. 15.2
26.2- 540 44.2-1510 47.5- 894 62.6- 407 26.1- 105 33.7- 821 29.4- 891 30.4- 904 30.5- 690 34 0- 770 30.4- 607 21.5- 471 32.7- 593 30.6- 415 41.9-1450 58.1- 515 58.4- 519 58.4- 519 58.6- 519 57.1- 518 20.7- 605 23.8- 227 31.8- 217 19.1- 411
0.022-0.238 0.038-0.231 0.038-0.285 0.044-0.171 0.017-0.050 0.016-0.192 0,018-0,214 0.026-0.239 0.030-0.268 0.025-0.231 0.022-0.236 0.016-0.189 0.030-0.230 0.020-0.209 0.034-0.335 0.053-0.240 0.053-0.248 0,051-0.248 0,055-0.273 0 , O W O ,232 0.014-0.161 0.014-0.111 0.024-0.101 0.011-0.173
6.0-123 5.1-173 IO.8-204 14.3- 92.6 5.9- 23.9 7.7-187 6.7-203 6.9-206 6.9-157 7.7-175 6.9-138 4,9-107 7 .4-135 4.9-167 4.8-167 13.2-117 13.3-118 13.3-118 13.3-118 13.0-1 18 4.7-139 5.5- 5 2 . 0 7.3- 4 9 . 7 4.4- 9 4 . 2
3 05 47 6 3 I1 3 17 3 23 5 48 4 57 3 94 8 00 5 75 5 04 13 4 3 11 12 2 48 5 3 09 3 10 3 10 3 15 3 22 3 02 3 02 3 02 3 02
20 22 22 20 15.2 30.1 60.0 15.2
152 15* 20
15*
Table Temp, Systems
Kater-oxygen
a
2.01 124 3.39 5.32 7.87 0.00968 0,0618 0.633 6.42 1.20 1.59 9.26 2.91 22.6 179 3.39 3.37 2.99 3.10 2.91 3.26 3.26 3.26 3.26
II. Ranges of Variables in M a s s Transfer Experiments
'C
Column diam, cm
G a s velocity M/hr
Fractional gas holdup
10 20 20 30 30 40 20
15.2 15.2 30.1 15.2 30.1 15' 15.2
20
15.2 30.1 60.0
65.6- 286 14.5- 319 19.2- 102 17.9- 421 14.9- 211 26.1- 105 72.3- 289 76.6.- 271 22.7- 237 32.1- 216 35.3- 226 34.6- 159 23.8- 363 33.8- 311 48.4-1180
0.035-0.129 0.006-0.159 0.026-0.086 0.014-0.161 0.012-0.108 0.017-0.050 0.056-0.180 0.048-0.174 0.013-0.105 0.025-0.098 0.021-0.082 0.029-0.113 0.016-0.210 0.021-0.189 0,040-0.284
3 c P glycerol soh-oxygen 7 30 Vol % glycol soln-oxygen 70 100 20 Methanol-oxygen 22 0 . 1 5 N Na2S03soh-air 20
Nc. X
Npr
x
N G X~ 103
14.9- 65.1 3.3- 7 2 . 6 3.1- 1 6 . 5 4.1- 9 5 8 2.4- 3 4 . 1 6.0- 24.1 16.5- 6 5 . 8 17.4- 6 1 . 7 5.2- 5 3 . 9 7.3- 4 9 . 2 8.0- 5 1 . 4 7.9- 3 6 . 2 5.4- 8 2 . 6 5.5- 5 0 . 3 5.5-135
N
~ 10-3 ~ X
3.05 3.11 12.1 3.17 12.4 3.14 3.48 3.92 3.94 4.57 5.48 8.02 3.11 12.2 48.5
10-10
~s~
2.01 3.39 26.4 5.32 41.3 7.57 0.511 0.0908 0.636 0.0618 0.00968 6.44 2.91 22.6 179
x
10-3
C ,833 0.480 0.480 0.295 0,295 0.192 2.92 12.6 2.20 11.1 72.5 0.173 0,570
0 . 570
Square cross section.
Surface tensions of aqueous solutions unavailable in the literature were nieasured using the stalagmometer. Gas Holdup Correlation
Conceivable factor.. affecting the gas holdup are the column diameter D , the diameter of gas inlet orifice do, superficial gas velocity I'c, kinematic riscosity v L and density p L of liquid, surface tension y , and gravity g. By dimensional analysis, one obtains
whew
.yFr =
~ Y ~ / v ' ~ D Froude number
16)
do ' D
(7)
diameter ratio
The effect of the diameter of the single gas inlet orifice d, was considered negligible (Yoshida and Akita, 1965). D a t a of Fair et al. (1962) and of Yoshida and -1kita (1965) using sewral columns of various diameters showed that the effect of the column diameter o n the gas holdup was negligible for columns larger than 15 cni in diameter. Thus, d,iD in Equation 3 can be ruled out. Xnother factor which might possibly affect the gas holdup is the gas density. Data of the esperiments with water and four gases of different densities, helium, air, oxygen, and carbon diosjde, in a column with a 15 X 15 em square cross sectioii shorr that the effect of the gas density on the gas holdup could be neglected, although the gas Ind. Eng. Chem. Process Des. Develop., Vol. 1 2 , No. 1,
1973 77
0.1 -
I
0 Cy
i
1 5 - c m s q u a r e column orifice diameter = 4 . 5 m m c water-air. 2 0 ° C A water-COp.
0.01-
a water-He,
I
3
$
1
watrr-O2. 1
IO
1000
100
Figure 1. Effect of gas density on gas holdup
0.01' IO
I
100
I
IO00
UO , rn.hr-'
D = ZFdo= UO'
0.06/ 0 04
0.02
"
"
-100
"
"
'
0
'
"
'
15.2 crn 302 crn 0 . 5 crn 118 r n h i ' ,
100
,
'
11
Figure 3. Gas holdup correlation for methanol-air, waterair, and glycol-air
following procedure. Equation 8 was expanded into
,
UL , rnh?
(9)
Figure 2. Effect of liquid rate on gas holdup
holdup with helium appears slightly lower at, higher gas velocities (Figure 1). The effect of the liquid rate on the gas holdup, studied with the sodium sulfite solution-air syst'em in the column 15.2 cm in diameter, was negligible for superficial liquid velocities up to 160 m / h r either in gas-liquid countercurrent or cocurrent operation as shown in Figure 2 , in which minus values of C-L indicate countercurrent operation. Since the conditions in the vicinity of the gas inlet, orifice are different from the ot'her parts in the column, there should be some end effects. However, as shown by our previous experiments (Yoshida and Akita, 1965) with the clear liquid heights ranging from 126 to 350 cm, the end effects in a column with a clear liquid height over 100 cm, if any, should be within experimental errors. Data of Fair e t aI. (1962), Yoshida and Akita (1968), and Towell et al. (1965) indicat'e t h a t the fractional gas holdup cG increases linearly with the superficial gas velocity LTG for velocities lom-er than 100 meters per hour, but the slope of a log-log plot of eG vs. LTG decreases gradually a t higher gas rates. However, an empirical plot of the values of cG(l E ~ ) -against ~ CGon a log-log paper gives straight lines with a slope of unity. Figure 3 shows such plots for the holdup of air in three liquids, methanol, water, and glycol. Thus, one can assume that
Since P L , y, and p z are properties of individual liquids, it is difficult to vary either 'YH,, or - Y G iiidependently. ~ Values of exponents a and b were determined by the 7 8 Ind.
Eng. Chem. Process Des. Develop., Vol. 12, No. 1 , 1973
When we assumed a value of a/2b, experimental values of ~ ~ -( ec)-4 1 for a gas velocity of 100 m/hr were plotted on a log-log paper against the values of ~ ~ ( ~ / p ~ calculated ) a ' ~ b for various systems. From the slope of the plot, -2b was evaluated, and a was obtained from the assumed value of a/2b. These values of a and b should satisfy the relationship, = 0, which is required by the experimental 2a 3b result that the gas holdup is independent of the column diameter, D. By trial-and-error, values of a and b which satisfy the above requirements were determined t o be l,'* and 1/12, respectively. Hence, from Equation 9
+
Values of the esponents in Equation 10 are somewhat different from those in the gas holdup correlation by Hughmark (1967). The value of c1 in Equations 8-10, determined from '~ the log-log plot of t G ( 1 - t G ) - 4 against ~ L - l ' e ( y / ~ L ) . - l CG with all the esprimental data, is 0.20. Thus, Equation 8 becomes ~€0 - 0.20 (1 - € G I 4
( g ~ 2 p L / ~ ) 1 ' 8 ( g ~ 3 / Y L 2 ) 1 ' 1 2 ( ~ aG / ~ ~ ) 1
(11) I n Figure 4 all the eyperimental data for eG for the systems used in the present work are plotted on log-log coordinates ~ ~ 'SF^. ~ Equation 10 or 11, or against the product S B LY~,1'12 the curve in Figure 4 may be useful for the prediction of gas holdup iii bubble columns, if used with caution. Yoshida and Akita (1965) observed that the gas holdup in aqueous solutions of electrolytes, such sodium sulfite and sodium sulfate, was slightly larger than in nonelectrolyte solutions or liquids due to the electrostatic potential at the gas-liquid interface. For
I
1.0
0.15M NaZSO, soln.- a i r 20oc
.
a &'
&@
0.1
e,
&y"
W
*%
o water 30% gl!,COl
A 70%
100%
A
"
column dlom. 0.0
30.1 cm 60 cm IO 0.01
Figure 4. General correlation for gas holdup
1.0
0.I EG
7 ' 1 -
IL
'
t
'
'
'
'
'
'
'
400
Figure 6. kLa vs. gas holdup for sodium sulfite solutionair
200.
5
2
'
.--,-.5-.Ae-.-.---
10001
100-
0
80-
D = 1 5 . 2 cm 2 ~ - 3 0 2c m
60-
40t I
.
.
.
.
.
.
,
.
. 0
-100 UL
.
.
,
.
.
.
I
,
Water- 01
.
3OoC
'
I
.
100
, mhr-'
Figure 5. Effect of liquid rate on kLa for sulfite oxidation column diom. 7.7 crn 15.2 crn 321 cm
0
electrolj te solutions, it is suggested t h a t 0.25 instead of 0.20 be taken as the value of c1 in Equations 10 and 11, or the T alues of cG obtained from Figuie 4 be increased b y 25%.
A 0
0.01
€0
Factors that conceivably affect the volumetric mass transfer coefficient kLa are liquid phase diffusir-ity DL, liquid kiiiematic viscosity vL, surface tension y , liquid densitj pL, gravity g, column diameter D, and the surerficial gas velocity, CG.The effect of the diameter of the single gas inlet orifice can be neglected in vien- of the data of Yoshida and Akita (1965). The effect of the liquid rate of kLa, studied by coiitiiiuou\ countercurrent aiid cocurren t sulfite oxidatioii experiments, \\as found to be negligible as shown in Figure 5 In sulfite oxidation experiments, since the back pressure of oxjgeii iii the bulk of liquid is zero throughout the column, the degree of longitudinal mixing in the liquid phase does not affect the distribution of the driving potential and the calculated \alue5 of kLa. Thus, dimensional analyhis gives -ySh
(aD)= f 2 ( - y S c r
- y B o , - y G a , -\*Fr)
(12)
1%here
.vSh =
il-sc
kLD/DL
= YL/DL
Sherwood number Schmidt number
Elimination of SF^ froni Equations 8 and 12 gires
(aD) = . f o ( S S c ,
(13) Since on logarithmic cooidinate>the kLa vs. CGplot is curved but the kLa vs. CG plot is straight, as nil1 be shonn later, it I C conaeiiient to use Equation 13 rather than Equation 12. 1TSh
1.0
0.I
Correlation for kLa
S B o , .lTGa,
Cc)
Figure 7. kLa vs. gas holdup for water-oxygen
.-lssuiiie that
ss h (0)= y s 8 *sB C
c1
0 ' s
G
'€e'
(14)
Assuming a value of for the exponent on the Schmidt number seems reasonable, siiice the penetration or the random surface renewal model is considered to hold for the liquid phase mass transfer a t the gas-liquid interface, we can show that kLa varies with eG to the 1.1 power except for very small columns. In Figure 6 previous data of Yoshida and .Ikita (1965) on kLa and ec for the sodium sulfite solutioii-air system in four columns, 60, 30.1, 15.2, and 7.7 cm in diameter, are replotted on the log-log coordinates, giving straight lines with a slope of 1.1except for the smallest column. Figure 7 is a similar for the water-oxygen system with three plot of kl,a vs, columns, 30.1, 15.2, aiid 7.7 cm in diameter. -1gain the slope is 1.1 except, for the 7.7-cni column. This seems to imply that the mean bubble diameter decreases aiid the specific interfacial area a inc.reases with increasing gas holdup, or with increasing gas velocity. Values of p arid q in Equation 14 were determined by a procedure similar to that used for a a i d b in Equation 8. Thus, froni Equation 14
kLa
= C , D L 1 ~ 2 , G l . l u L l ! 2 - 2 Q ( '~p L ) - P D 2 P - 3 q - 2
gp+Q
(15a)
Ind. Eng. Chem. Process Des. Develop., Vol. 1 2 , No. 1 , 1973
79
I
'
"
10
I
1
I
I
able that the trend levels off for columns of larger diameter. For design purposes, it might be safer to use the kLa values for the 60-em column for the columns of larger diameter. Before using Equation 18, one must calculate eG by Equation 11. To avoid this, it is possible to espress kLaD2/DL as a direct function of S s c , M G ~SB,,, , and .VF~.However, such a correlation cannot be expressed by a simple equation, since F ~ with the magnitude of Xpr. the exponent on ~ V varies
100
D. cm
Figure
8.
Effect
Conclusions
of column diameter on kLa
-
The fractional gas holdup in the bubble column can be predicted by Equation 10 or 11 or by Figure 4.The volumetric coefficient of liquid phase mass transfer kLa in the bubble column varies with the gas holdup to the 1.1 power, except for very small columns, and can be predicted by Equation 17 or 18. These correlations seem to be generally applicable to various systems, if used with due caution.
-.I;
Acknowledgment
I
I
I
/
n
, &
3 c p glycerol, D7cp o ,, 0 methanol. 22'C owater, 20°C 30.1
The authors wish to express their gratitude to those undergraduate students a t Kyoto and Tokushima Universities who assisted in the experimental work.
0
+
)I
+
30T
I
0.001''0101
n
I
Nomenclature
1
1.0
0.I €0
Figure
9. General
correlation for kLa
or kLa(h:Sc)112 =
eo. t G1.1[ u L ( y / p L ) P / ( 2 9 - - I )
1 I -2Y x gP
+YDZP+3P-2
(15b) Data of Yoshida and Akita (1965) using four columns, 7.7, 15.2, 30.1, and 60.0 em in diameter, showed that kLa increased with increasing column diameter a t least for the range of diameter they studied. Figure 8 shows kLa values a t eG of 0.1 for the two systems, sodium sulfite solution-air and waterosygen, cross-plotted from Figures 6 and 7 against' the column diameter. The curves are not straight, but except for the data with the 7.7-em column, the relationship between kLa and the column diameter can be represented by straight lines with a slope of 0.17. Then, from Equation 15, 2p
+ 39 - 2 = 0.17
(16) Using the data for yarious systems listed in Table I1 and by the procedure described before, one obtains from Equation 15b and 16
p
=
0.62
q = 0.31
Equation 15a then becomes kLa = c2DL0.jVL-0. 1 2 ( T / p L )
-0.62D0.17g0.93,G1,
1
(17)
01'
Xsh(aD)
=
kLaD2:/DL =
~ ~ r s ~ 0 . 5 . ~ ; ~ ~ 0 . 6 2 S ~ ~ o . 3 118) 12G1.1
Figure 9 shows log-log plots of the group ( k L a D 2 / D L ) / ( S s C o J N ; B ~ ~ , ~ against ~ S G eG, ~ ~both , ~ obtained ~ ) from the esperimeiits with the systems listed in Table 11. The value of c2 determined from the figure is 0.6. I n determiriiiig the values of the exponents in Equation 18, it was assumed that the kLa increased with the column diameter to the 0.17 power. HoJyever, this assumption was verified by experiments only up to a diameter of 60 em. I t is conceiv80
Ind. Eng. Chern. Process Des. Develop., Vol. 1 2 , No. 1 , 1973
-4ny consistent unit can be used a = specific gas-liquid interfacial area, L z / L 3or L-1 a , b = constants, dimensionless C,, C, = initial and final concentrations of dissolved oxygen in liquid, respect'ively, C* = dissolved oxygen concent'ration a t saturation, el, c2 = constants, dimensionless D = column diameter, L DL = liquid phase diffusivity, L2T-' do = diameter of gas inlet orifice, L g = gravitational constant, LTP2 k L = liquid phase mass transfer coefficient, LT-l kLa = volumetric liquid phase mass transfer coefficient,
T-' S;B~ =
Bond number = g D 2 p L / y ,dimensionless Froude number L-,Jd&, dimensionless .VG& Galileo number = gD3/uL2,dimensionless NsC Schmidt number = uL/DL, dimensionless Arsh Sherwood number = kLD/DL, dimensionless p , q = constants, dimensionless t = time, T VG = superficial gas velocity with respect' to the total cross section of column, LT-' LTL = superficial liquid velocit'y with respect to the total cross section of column, LT-l ZF = height of aerated liquid, L 2, = height of clear liquid, L *\'Fr
= = = =
GREEKLETTERS y = surface tension, eG = gas holdup, fraction of total volume of aerated liquid, dimensionless uL = kinematic viscosity of liquid, L2T-' pL = liquid density, JfL-3 Literature Cited Fair, J. R., Lanibright, il. J., Anderson, J. W., Ind. Enq. Chern. Prorpss 1.D33 . . 11962). ..... Des. I > P ~ J o ~ o Hughniark, G. A,, ibid., 6, 218 (1967). Tou-ell, G. D., Strand, C. P., Ackerman, G . H., A.I.Ch.E.-Inst. Chem. Eng. Symp. Serz'rs (London), No. 10, 1 0 ~ 9 7 (1965). Treadwell, F. P., Hall, W. T., "Analytical Chemlstry," Vol. 11, p 700, Wilrv, h'ew York, S.Y., 1942. Yoshida, F., Akita, K., A.I.Ch.E. J., 11, 9 (1963). ~
~1~
2
-
1
~~
>
~
RECEIVED for review Bpril 13, 1972 A C C E P T E D A4UgUSt 11, 1972
