Znd. Eng. Chem. Res. 1991,30,745-751 Kander, R. G.;Paulaitis, M. E. Alcohol-Water Separations Using Supercritical Fluid Solvents. Presented a t the AIChE Meeting, San Francisco, CA, November 1984. Kreevoy, M. M.; Kantner, S. S. The Methanol-Trimethoxyboran Azeotrope as a Solvent. Croat. Chem. Acta 1977,49,31-39. Krukonis, V. J.; Kurnik, R. T. Solubility of the Solid Aromatic Isomers in Carbon Dioxide. J. Chem. Eng. Data 1985,30,247-249. Kuk, M. S.; Montagna, J. C. Solubility of Oxygenated Hydrocarbons in Supercritical Carbon Dioxide. In Chemical Engineering at Supercritical Fluid Conditions; Paulaitis, M. E., Penninger, J. M. L., Gray, R. D., Davidson, P., Eds.; Ann Arbor Science: Ann Arbor, MI, 1983; pp 101-112. McHugh, M. A.; Mallett, M. W.; Kohn, J. P. High Pressure Fluid Phase Equilibria of Alcohol-Water-SupercriticalSolvent Mixtures. In Chemical Engineering at Supercritical Fluid Conditions; Paulaitis, M. E., Penninger, J. M. L., Gray, R. D., Davidson, P., Eds.; Ann Arbor Science: Ann Arbor, MI, 1983; pp 113-138. Moses, J. M.; Goklen, K. E.; de Fillipi, R. D. Pilot Plant Critical Fluid Extraction of Organics From Water. Presented at the AIChE Meeting, Los Angeles, November 1982. Munster, N.; Plank, C. A.; Laukhuf, W. L. S.; Christopher, P. M. Vapor-Liquid Equilibria of the Ternary System Methyl BorateMethyl Alcohol-Benzene. J. Chem. Eng. Data 1984,29,178-181. Niswonger, D. C.; Plank, C. A.; Laukhuf, W. L. S. Vapor-Liquid Equilibria of the System Trimethyl Borate (1)-n-Heptane (2). J. Chem. Eng. Data 1985,30, 209-211. Occhiogrosso, R. N.; Igel, J. T.; McHugh, M. A. Phase Behavior of Carbon Dioxide-Aromatic Hydrocarbon Mixtures. Fluid Phase Equilib. 1986, 26, 165-179. Ohgaki, K.; Nishii, H.; Saito, T.; Katayama, T. High Pressure Phase
745
Equilibria for the Methanol-Ethylene System at 25 OC and 40 OC. J. Chem. Eng. Jpn. 1983,16, 263-261. Paulaitis, M. E.; Gilbert, M. L.; Nash, C. A. Separation of Ethanol-Water Mixtures with Supercritical Fluids. Presented at the Second World Congress of Chemical Engineers, Montreal, Canada, October 1981. Paulaitis, M. E.; Kander, R. G.; Diandreth, J. Phase Equilibria Related to Supercritical-Fluid Extraction. Ber. Bumen-Ges. Phys. Chem. 1984,88, 869-875. Peng, D.-Y.; Robinson, D. B. A New Two Constant Equation of State. Znd. Eng. Chem. Fundam. 1976,15,59-64. Plank, C. A.; Christopher, P. M. Vapor-Liquid Equilibria of Methyl Borate-Carbon Tetrachloride and Methyl Borate-Benzene Systems. J. Chem. Eng. Data 1976,21, 211-212. Prausnitz, J. M. Molecular Thermodynamics OJ Fluid-Phase Equilibria; Prentice-Hall: Englewood Cliffs, NJ: 1969. Reid, R. C.; Prausnitz, J. M.; Polling, B. E. The Properties of Gases and Liquids; McGraw-Hill: New York, 1987. Robinson, D. B.; Peng, P.-Y.; Chung. S. Y.-K. Fluid Phase Equilib. 1985,24,25-41. Schmidt, M. B.; Plank, C. A.; Laukhuf, W. L. S. Liquid-Liquid Equilibria for Three Methyl Alcohol-Trimethyl Borate-n-Alkane Systems. J. Chem. Eng. Data 1985,30, 251-253. Seckner, A. J.; McClellan, A. K.; McHugh, M. A. High-pressure Solution Behavior of the Polystyrene-Toluene-EthaneSystem. AZChE J. 1988,34,9-16.
Received for review May 7, 1990 Revised manuscript received October 15, 1990 Accepted October 31, 1990
Longitudinal Holdup Distribution of Gas and Dispersed Liquid in Bubble Columns with Two Immiscible Liquids Satoru Asai* and Hidekazu Yoshizawa Department of Chemical Engineering, University of Osaka Prefecture, Sakai, Osaka 591, Japan
The longitudinal distribution of the fractional gas holdup and the volume fraction of a dispersed liquid (droplet) was measured in bubble columns with two immiscible liquids. The columns were operated batchwise with respect to both liquids, over a wide range of relevant physical properties and average volume fraction of the dispersed liquid. The average gas holdups could be correlated by a previous empirical expression for a single liquid phase, when it was applied to the individual liquid phases, allowing for their volume fraction. The observed longitudinal distribution of the volume fraction of the dispersed liquid was analyzed by means of the dispersion model, allowing for the slip velocity caused by the density difference between both liquid phases. The data were empirically correlated in terms of the Peclet number based on the slip velocity, as a function of the relevant system parameters. Mass-transfer or chemical reactions for gas-liquid-liquid systems may be encountered in gas absorption, gas-liquid reactions, and fermentation, often with a heterogeneous liquid catalyst or an extracting solvent, liquid-liquid extraction, or liquid-liquid reactions with gas agitation. Some examples can be cited: absorption of SO2 into aqueous emulsion of xylidine in water (Kohl and Riesenfeld, 1985);purification of crude naphthalene with H2S04 accompanied by air sparging (Doraiswamy and Sharma, 1984); air oxidation of hydrocarbon in aqueous emulsion; fermentation of hydrocarbons, in which a substrate, hydrocarbon, is dispersed in an aqueous culture medium with air bubbling; and extractive fermentation of useful species, such as alcohols and steroids, which are produced in the aqueous phase by the metabolism of the relevant microorganisms and are extracted in situ into the coexisting organic phase of an extractant, shifting the reaction fa-
* Author to whom correspondence should be addressed. oaaa-5aa5pi /2~30-0745$02.50/0
vorably. A few examples of more complicated systems containing solid particles are air oxidation of substituted benzyl alcohol catalyzed by palladium catalyst in the presence of aqueous phase, which gives rise to the favorable formation of aldehyde (Ma, King, 1982), and competitive liquid-phase hydrogenation of cyclohexanone and cyclohexene catalyzed by Ru catalyst in the presence of water (Koopman et al., 1981). Over any other conventional gas-liquid or liquid-liquid contactors, bubble columns have many advantages. They are of simple configuration without moving parts and require no seal, need little space and maintenance, can easily and widely adjust the resistance time of the liquid phases, and allow comparatively large liquid-phase volumetric mass-transfer coefficients or interfacial area to be achieved with relatively low energy consumption. Therefore, bubble columns may be expected to be capable of being used successfully also for gas-liquid-liquid systems. However, relatively few studies have been per@ 1991 American Chemical Society
746 Ind. Eng. Chem. Res., Vol. 30, No. 4,1991 Table I. Physical Properties of Liquids Used liquid systems; dispersed-continuous temp, O C kerosine-water 5.4-15.8
phase
D
kerosine-50 w t % sucrose solution
7.8-21.5
C D C
2-ethylhexanol-water
7.6-20.9
D
1,1,2,2-tetrabromoethane-water
8.2-10.0
C D C
water-kerosine
8.8-9.2
D C
formed for this emulsion bubble column. Hatate et al. (1975) measured the average gas holdups, the longitudinal distribution of the volume fraction of a dispersed liquid (droplet), and the longitudinal dispersion coefficients of a dispersed liquid, using two bubble columns (0.066- and 0.122-m i.d.) with a perforated plate as a gas sparger. Their columns were operated batchwise or continuously with respect to liquids. They found less average gas holdups for the air-kerosine (dispersed liquid)-water (continuous liquid) system than for the corresponding ones without kerosine, over a range of superficial gas velocity UG = 0.007-0.09 m/s. They analyzed the longitudinal distribution of the volume fraction of the dispersed liquid, using a dispersion model allowing for the slip velocity. The model assumes that the particles rise or fall with the slip velocity caused by the density difference between the dispersed and continuous phases and explains well the behavior of the solid particles in suspension bubble columns (Suganuma and Yamanishi, 1966; Cova, 1966). The effective slip velocity of the dispersed liquid was also analyzed by using the longitudinal dispersion coefficients of the dispersed liquid measured. However, their study was limited only to the air-kerosine-water system. Using the organic liquids (kerosine, dibutyl phthalate, or groundnut oil) dispersed in water, Bandyopadhyay et al. (1988) measured the average gas holdup of air in a bubble column (0.2 m in diameter) with a multiple nozzle sparger plate, operated batchwise with respect to liquids. They found that the average fractional gas holdup is at a minimum and maximum at the volume fraction of the organic liquid corresponding to the phase inversion point for organic liquids with negative and positive spreading coefficients, respectively. Yoshida and Yamada (1971) measured the mean diameter of kerosine dispersed in the water phase of bubble columns, operated batchwise with respect to both liquids. Hatate et al. (1976) also measured the mean droplet size for a few systems using the two columns described above and correlated it as a function of the superficial gas velocity, interfacial tension, and column diameter. Diaz et al. (1986) examined the dependency of mean droplet size on the superficial gas and liquid velocities, and measured the dispersion coefficients of both liquids, for the airkerosine-water system. Recently, Kato et al. (1984,1985) extended the studies of Hatate et al. (1975, 1976) from a single-stage to the multistage bubble columns of the same diameter. Their study was also limited to the air-kerosine-water system with a few additional ones for the measurement of average gas holdups. The liquid-liquid interfacial area and liquid-phase mass-transfer coefficients in the emulsion bubble columns were measured by Fernandes and Sharma (1968),who took advantage of the alkaline hydrolysis reaction of a few esters for their determination. They assumed complete mixing of both the continuous and dispersed liquids for the analysis. Yoshida et al. (1970) studied the variation of the
kg/m3 803-799 998-996 803-768 1260-1270 843-834 999-998 2970 999 998 801 P9
W p , Pa s 1.92-1.54 1.49-1.12 1.84-1.42 60.1-44.6 15.5-8.38 1.40-1.00 17.2-16.0 1.39-1.32 1.36-1.34 1.79-1.77
lo%, N/m 31.3-30.0 70.5-61.1 30.7-29.9 43.3-35.0 30.5-21.1 42.0-37.9 52.3-51.0 68.2-66.3 67.4-67.1 30.9
T u Figure 1. Experimental apparatus: 1, air compressor; 2, air chamber; 3, rotameter; 4, solenoid valve; 5, thermometer; 6, gas inlet nozzle; 7,manometer with sampling cock; 8,bubble column.
volumetric liquid-phase mass-transfer coefficients for oxygen absorption into water with the addition of kerosine, liquid paraffin, toluene, and oleic acid. In previous studies, the effects of physical properties on the various characteristics of the bubble columns were not clarified. In this work, the longitudinal distribution of fractional gas holdups and the volume fraction of the dispersed liquid was measured over a wide range of relevant physical properties and average volume fraction of the dispersed liquid. The observed average gas holdups and the Peclet numbers based on the slip velocity were empirically correlated as a function of the relevant system parameters.
Experimental Section The experimental apparatus used is illustrated in Figure 1. 'lhobubble columns were used. They were constructed of glass and were 2.0 m in height. Their inside diameters were 0.064 and 0.1 m. For the 0.064-m column, five pressure taps were drilled in the wall at 0.2-m intervals. For the 0.1-m column, on the other hand, four (not shown in Figure 1)and five pressure taps were drilled at 0.32- and 0.25-m intervals in both sides of the wall, 180' apart, respectively. A manometer with a sampling cock was attached in each pressure tap. The gas spargers were of the single-nozzle type, and their inside diameters were 0.005 and 0.007 m for 0.064- and 0.1-m columns, respectively. Each gas nozzle was located 0.05 m above the bottom plate of the column. In order to reduce dead space between the tip of the nozzle and the bottom plate, the space was packed with stainless steel spheres. The bubble columns were operated at room temperature continuously and batchwise with respect to the gas and the two immiscible liquids, respectively. The gas used was always air and was fed from a compressor through two air chambers, rotameter, and nozzle, to the bottom of the column. The superficial gas velocity ranged from 0.051 to 0.43 m/s. The liquid systems used are shown in Table I. The water was deionized. The clear liquid height was mainly 1.08 m, but in some runs it was kept at 0.808 and
Ind. Eng. Chem. Res., Vol. 30, No. 4,1991 747 1.66 m. The average volume fraction of the dispersed liquid was 0.5,0.25, and 0.1 m3 of dispersed liquid/m3 of total liquid. The fractional gas holdups were determined by measuring the axial distribution of the static pressure using manometers, after steady state was attained. The seal liquid in the manometer was the light liquid. Then, small amounts of liquid samples in emulsion (approximately 1.0 x 10" m3) were withdrawn from each sampling cock after reading the manometer to measure the local volume fraction of the dispersed liquid. This sampling was repeated several times, and the measured volume fraction was averaged to ensure reliable values. Analytical Procedure The local fractional gas holdups tG were evaluated from the following expression by using the measured longitudinal distribution of the volume fraction q5 of the dispersed liquid. This expression is an extension of a well-known one for a conventional bubble column with a single liquid operated batchwise (Hills, 1976) to the two-liquid systems. -dP/dz = p'g (1) where
+ (1- ~ G ) P M
(2) (1 - ~ P M P M = 4 P D + (1 - 4)PC (3) where p' is the density of the mixture of gas and the two liquids and p M is the density of the mixture of the two liquids. The densities PG, p c , and p D are of the gas, continuous liquid, and dispersed liquid, respectively. dP/dz is the slope of the curve representing the longitudinal distribution of the static pressure P plotted against the distance z from the bottom of the column (tip of nozzle). It was evaluated by using a spline function and central difference of order 3. The dispersed liquid phase created by the sparging of gas from the nozzle has a slip velocity relative to the continuous liquid phase under the influences of buoyant and gravity forces resulting from the difference in densities between the two liquids. The present experimental data on the longitudinal distribution of the volume fraction of the dispersed liquid were analyzed by using the dispersion model, allowing for the slip velocity between two heterogeneous phases (Suganuma and Yamanishi, 1966; Cova, 1966; Hatate et al., 1975). In these dispersion models, the following assumptions are made: (1)The turbulence is uniform in the column and the mixing of the dispersed phase can be described by the longitudinal dispersion coefficient ED of the dispersed liquid phase. (2) Slip velocity u,D of the dispersed liquid is constant everywhere. (3) The volume fraction 4 of the dispersed liquid remains constant over the entire cross section of the column. Based on these assumptions, the flotation dispersion model (the dispersion model with positive slip velocity, i.e., rising velocity of droplets) gives the following mass balance for the dispersed liquid under the steady state and batchwise operation with respect to two liquids. This model can be applied to systems with a dispersed liquid lighter than the continuous liquid. P'
=
~GPG
(4)
The relevant boundary conditions are given by
where
q50
denotes the volume fraction of the dispersed
liquid in the bottom part of the column (z = 0). The solution of (4)and (5) gives rise to
4 = 4 0 exP(
2%) !
The average volume fraction $ of the dispersed liquid over z = 0 (bottom) to z = L (aerated liquid height) is given by
Using (7), (6) may be represented as
where Pe, = u,DDT/ED (9) In (9), the column diameter DT rather than the column height L was used as a characteristic length, since there was no effect of L on u,D/ED, as will be shown later. On the other hand, for systems with dispersed liquid heavier than the continuous liquid, the sedimentation dispersion model (the dispersion model with negative slip velocity) may be expected to be applicable to the analysis of the axial distribution of the dispersed liquid volume fraction. This model has been successfully used in the interpretation of the behavior of solid particles in conventional solid particle suspended bubble columns. The solutions for the steady state and batchwise operation can be easily obtained by replacing uSD in the relevant expressions of the flotation dispersion model with - u a (u,D is always defined as positive). The solution equivalent to (8)is given by
The observed values of $16 were fitted with (8)or (10) by using the Simplex method to evaluate Pe,. The aerated liquid height L was calculated from the relation (11)
using the measured clear liquid heights Lc and average gas holdups 70. The physical properties used in the analysis are shown in Table I. The densities, viscosities, and surface tensions of the liquids were measured by the conventional procedure. Results and Discussion Fractional Gas Holdups. Although the liquids were cloudy, owing to emulsification caused by vigorous mixing of the two immiscible liquids, from observation by light transmission the flow behavior was likely to be in a heterogeneous bubble flow regime. An example of the longitudinal distribution of the static pressure P is illustrated in Figure 2 for a air-kerosine50 w t % aqueous sucrose solution system with a large density difference in both liquids ( A p = pc - p D N 480 kg/m9). It may be seen that no end effect is apparent over the range of z indicated by the data. For the two immiscible liquid systems, the volume fraction of the dispersed and continuous liquids changes along the axial direction. Thus, the distribution of the static pressures is not linear, unlike that of the conventional single-liquid bubble columns. The local fractional gas holdups t~ also may be expected to vary more appreciably than those for single-liquid systems.
748 Ind. Eng. Chem. Res., Vol. 30, No. 4, 1991
Y
0.06 0.04
1
6
1
1
8 0.1 UG
I
I
2
4
l
l
6 8
0
(mk)
Figure 4. Average gas holdups for air-kerosine-water and air-water systems: 6 = 0.5; DT = 0.064m; 9.7 f 1.9 "C; -, (13) and (15); - - -, (16).
Z (m) Figure 2. Longitudinal distribution of static pressure for air-kerosine50 w t 9i aqueous sucrose solution system: 6 = 0.50; DT = 0.064 m; 8.8 f 0.2 O C . 1
0,61 0
.
0
0 LI
%(mk) - 0.35 0.27 , 0.16 0.10 0.054
U
1
2
I
Y
w"
A 0
A
01
-8
0.06
I-
'
0.2
r\
0 I
I
I
I
I
I
0.4
0.6
0.8
1.0
1.2
1.4
Z (m) Figure 3. Longitudinal gas holdup distribution for air-kerosine50 wt % aqueous sucrose solution system: 6 = 0.5; DT = 0.064 m; 8.8 0.2 "C; -, (12) and (13). Some of the data for the air-kerosine-50 wt % aqueous sucrose solution system are shown in Figure 3 for $ = 0.5. The solid lines represent the predictions of fractional gas holdups calculated from t G = zGD4 + b c ( 1 - 4) (12) The average gas holdups zGD and zwfor the dispersed and continuous liquids, respectively, were estimated by using the physical properties of the corresponding phases, from the previous empirical correlation for a single liquid phase (Hikita et al., 1980):
where UGPL
PL4g
U
PLU3
Ca = -, Mo=-
(14)
The predictions may be seen to be in reasonable agreement with the experimental data. Figure 4 presents the comparisons of the measured average gas holdups ZG for the air-kerosine-water system with 4 = 0.50with those for the conventional air-water system.
As a check on the present static pressure measurements, the values of ZG for the former system were also determined by measuring the difference in total liquid height between sparged and unsparged conditions. Although in this technique the measurements of the liquid level under the sparged conditions were not so easy owing to violent fluctuation, the average values of several measurements agreed with the values obtained from the static pressure measurements within an error of about 10%. The solid line in Figure 4 shows the average gas holdups ZG calculated from
which is derivable from (12). Both systems give the same observed values and are in good agreement with the predictions, (15). This is not in line with the findings of Hatate et al. (1975), Kato et al. (1984) and Bandyopadhyay et al. (1988), who found lower average gas holdups for the air-kerosine-water system. However, their experiments were performed with a perforated plate or a multiple nozzle, in the region of lower superficialgas velocity, where the flow mechanism is known to vary with the configuration of the gas sparger. Therefore, possibly this different observation may be attributed to the different effect of the liquid physical properties on the fractional gas holdups in the different flow regimes. In fact, the data of Bandyopadhyay et al. reveal a reduction of the difference in the gas holdups between both systems with an increase of gas flow rate. In Figure 4 are also shown the predicted values from an empirical correlation of zG for the air-kerosinewater system proposed by Bandyopadhyay et al. (1988):
Bandyopadhyay et al. claimed that this expression correlates their data for the air-kerosine-water system lower than those for the air-water systems, but still it gives rise to larger values than our data for both systems. In Figure 5, all the observed average gas holdups for the systems used in this work are compared with the empirical predictions, (15), by using (13). The observed values are in reasonable agreement with the calculated ones, with a maximum deviation of 30%. Such a comparatively large deviation may be primarily attributed to the difficulty of exact determination of the local fractional gas holdup by the numerical differentiation from the nonlinear axial distribution of static pressures. Longitudinal Distribution of Dispersed Liquid. As examples of the axial distribution of the volume fraction 4 of the dispersed liquid, Figures 6 and 7 show the experimental data for the systems of air-kerosine-water and
Ind. Eng. Chem. Res., Vol. 30, No. 4,1991 149
1.o
6 t /
/
h
/
4
8
c
I 6 e 4
/
Y
/ h
I
Y
ui
8 - 2
-
0.1
I$
0.08
Y
0
4
I
I
0.2
0.4
-
0.10
F I
I
0.6
0.8
I
I
1.0
1.2
Z (m) 0.1
Figure 7. Longitudinal distribution of dispersed liquid for airkerosine-50 wt % sucrose solution system: UG = 0.10 m/s; D T = 0.064 m; 8.4 0.6 "C.
'
8 '
0.2
0.06
a06
e
0.1
2
6
4
0.8 0.1
(b)col.(-) Liquid system Kerosine Kerosine
-
5 water (DT = 0.064 I) 50 ut a Sucrose Soln.
-
2-Ethylhexanol Water 1,1,2,2-Tetrabrorwthane Water Xerosine
-
Xerosine
-
Water (DT
-
-
Water
-
0.50
0.25
0
0
A
A
0.10
.
0
0
v
v
+
0.1 B)
A
v
+ X
A
I
-&- .
1
4
0
A
0
0.01
8 6
2
1.66
T
0.5
8
A
I i
0.001 0
Or = 0.064 m
01= 0.1 m
Key
i
8
0.10
0
0.10
A 0
0.25 0.50
A
0.25 0.50
Key
0.808 1.08
*
0
2
2 Key
A 0
4
Lc(m)
.
m
4 Y
.
o
A
h
Figure 5. Comparison of present data with proposed correlation for average gas holdups.
h
0
8 6
Key
4
6
0
6 8 0.1 UG
2
4
6
(m)
Figure 8. Effects of column diameter and average volume fraction of dispersed liquid on Peclet number Pe,: air-kerosine-water system; 7.6 f 2.2 O C .
proaches being flat with an increase in the average volume fraction 4 of the dispersed liquid. This is probably due to the decrease in the slip velocity caused by the enhanced interaction among the droplets with an increase in 4,as suggested by Hatate et al. (1975). As shown in Figure 7, however, the reverse effect of 4 on the distribution of 6 is observed for the air-kerosine50 wt % aqueous sucrose solution system, the liquids being dispersed more uniformly with a decrease in 3. This reduction of the axial distribution of 4 may be attributed to the fact that when 4is small, even the highly viscous continuous liquid embodies relatively easily the dispersed liquid. That is, the distribution of 4 is likely to be determined by the compromise of the two reverse effects, the enhanced hindrance for the motion of the droplet and the reduced bulk mixing, with an increase of the average volume fraction 4. Figure 8 shows the effects of the column diameter DT and the average volume fraction 4 of the dispersed liquid on the observed Peclet number Pe, for the air-kerosinewater system. It may be seen that the values of Pe, for the small column decrease more significantly with an increase in the superficial gas velocity UG than those for the large column. The values of Pe, are larger for the large column. This indicates that the increase in axial dispersion coefficient ED of the dispersed liquid with the column diameter is smaller than that of us&., as apparent from the definition of Pe,. The effect of the superficial gas
750 Ind. Eng. Chem. Res., Vol. 30, No. 4, 1991
velocity uG on Pe, is approximately independent of the average volume fraction 4 of the dispersed liquid. However, Pe, decreases with an increase in 4 for the small column, as suggested in Figure 6, while it increases with 4 for the large column. This different effect of 4 on Pe, for the two columns may reflect the difference in flow behavior of the dispersed liquids and relevant variation in the slip velocity. At the present stage, we cannot give a consistent explanation for this different effect. For the ail-kerosine50 wt 90aqueous sucrose solution system,Pe, increases with 4 even for the small column, as expected from Figure 7. Figure 9 represents the data of the systems of the air2-ethylhexanol-water ( A p = pc - PD = 160 kg/m3) and air-l,l,2,2-tetrabromoethane-water ( A p = -1971 kg/m3) to demonstrate the effects of the density difference on Pe,. Although the viscosities and surface tensions of the dispersed liquids and interfacial tensions differ from each other by about 15, 76, and 25%, respectively, for both systems, the absolute values of the density difference differ by 12.3 times. Thus, the density difference may be primarily responsible for the difference in the data for both systems. Naturally, Pe, increases with the density difference, because of the increased slip velocity of the dispersed liquid. Furthermore, it may be seen that the dependency of Pe, on uc (Pe, = u G - ” . ~ ~ ) for both systems, which have almost the same viscosity, is weaker than the ) the air-kerosinedependency (roughly Pe, = U G - ~ . ~for water system, which is shown in Figure 8. The much larger viscosities of the present dispersed liquids may be responsible for this weaker dependency, since the shear supplied by the sparged gas is not large enough for substantial improvement in the dispersion. Using all the experimental data for Pe, > 0.006,in which Pe, can be evaluated with reasonable accuracy, the observed peclet numbers Pe, were correlated as a function of the dimensionless parameten. The relevant phenomena are too complicated to be able to express Pe, by a simple correlation, but the following expression may be proposed Pe, =
(
4 . 6 1 B 0 ~ - ” * ~ F r -”.~~~
E)”’“(n)’”
- Tetrabromoethone-Water 2-Ethylhexanol -Water 1.1,2,2
A
0
0.1 8-
6-
I
L-
Y
d
2 -
-
0.01 8-
*
60.004 0.02
4
2
6 8 0.1
6 8
4
(mls 1 Figure 9. Effect of density difference on Peclet number Pe,: 0.5; DT = 0.064 m;8.4 f 0.8 O C . UG
’
0.004’ 0.00L 6 8QO1
I
2
I
I
4
6 8 0.1
l
l
I
I
2
4 0.6
4=
(PevIcai. (-1 X
Key
Liquid system
0 0 A
Kerosine Water (DT = 0.061 m) Kerosine 50 ut a Sucrose Soln. 2-Ethylhexanol Water 1,1,2,2-Tetrabromoethane Water Water - Kerosine Kerosine water ( D =~ 0.1 m)
V 8 0
-
-
-
-
Figure 10. Comparison of present data with proposed correlation for Peclet number Pe,.
where
The coefficients and powers of (17) were determined by the Simplex method. The ranges of the dimensionless number, over which the use of (17) seems justified, are as follows: 600 < BOD < 2500, 0.053 < Fr < 0.53, 1.4 X 10-lo < Mob < 8.2 X lo-’, 0.19 < J A p l / p < ~ 0.66, 0.17 < [AU(/CD< 1.3, 0.081 < p c / ~ ~33, < 0.34 < p ~ / p D< 1.7, 0.46 < UC/UD < 2.3, 0.1 < 4 < 0.5 The comparison of the values of Pe, obtained in the present work with those calculated from (17) are shown in Figure 10. Most of the data are in reasonable agree-
ment with the calculated ones within an error of 50%. Although the observed values of Pe, are considerably scattered, the axial distribution of the volume fraction of the dispersed liquid, which is calculated from (8) or (10) by using the values of Pe, predicted from (171, represents the experimental data satisfactorily. This is due to the weak sensitivity of Pe, to the local volume fraction -$I of the dispersed liquid. Figure 11 compares the present data with the correlation proposed by Hatate et al. (1975): lOFr U,D Pe, = 1 + 6.5Ffl.8 where
Ind. Eng. Chem. Res., Vol. 30, No. 4, 1991 751
v v
I
- 1
e *V
A A
e o
__-,I
.
6
"O
h
6 8 IO-&
1
A
O
I
I
e*
u
A
4t I
9 1
V
-1
21
e
V
lo: 6
-7
I
0
V
v
2 t
I
2
I
4
I
l
I/
l
/ I
2
6 8 ( Pev
/
(-
4
I
l
l
6 8 IO-'
I
2
4
1
Figure 11. Comparison of present data with correlation of Hatate et al., (19);symbols are the same as those in Figure 10.
This correlation,which was made on the basis of their data for only the &kerosine-water system, gives considerably lower values of Pe, than the observed ones and displays great scattering, not reflecting the effect of the physical properties. Of course, the data for the air-1,1,2,2-tetrabromoethanewater system with a large density difference in the two liquids, and for the air-kerosine-50 wt % aqueous sucrose solution system with highly viscous continuous liquid, deviate more greatly from the correlation than those for the air-kerosine-water system.
us = mean slip velocity, m/s z = longitudinal distance measured from bottom plate, m
Greek Letters Ap = density difference, pc - P D , kg/m3 Au = surface tension difference, uc - UD, N/m cG = gas holdup, m3 of gas/m3 of column p = viscosity, Pa s p = density, kg/m3 p' = density of aerated liquid mixture, kg/m3 u = surface tension, N/m ui = interfacial tension, N/m = volume fraction of dispersed liquid, m3 of dispersed liquid/m3 of liquid mixture Subscripts C = continuous liquid D = dispersed liquid G = gas L = liquid M = liquid mixture O=atz=O Superscript - = average
Literature Cited
Bandyopadhyay, N.; Ray, P.; Dutta, B. K. Gas Holdup in a Bubble Column with Immiscible Liquid Mixtures. Can. J. Chem. Eng. 1988,66,995-999. Cova, D. R.Catalyst Suspension in Gas-Agitated Tubular Reactors. Ind. Eng. Chem. Process Des. Dev. 1966,5,20-25. Dim, M.; Aguayo, A. T.; Alvarez, R. Hydrodynamics of a LiquidLiquid Countercurrent Extraction Column with Upflow Gas Agitation. Chem.-hg.-Tech. 1986,58,74-75. Doraiswamy, L. K.; Sharma, M. M. Heterogeneous Reactions; Wiley: Conclusions New York, 1984;Vol. 2. Fernandes, J. B.; Sharma, M. M. Air-Agitated Liquid-Liquid ConThe local and average fractional gas holdups and the tactors. Chem. Eng. Sci. 1968,23,9-16. longitudinal distribution of the dispersed liquid were Hatate, Y.; Okuma, S.; Kato, Y. Longitudinal Dispersion Coefficient measured in two bubble columns with inside diameters of and Holdup Distribution of Droplets in Bubble Columna. Kagaku 0.066 and 0.122 m, for the systems of air sparging into Kogaku Ronbunsyu 1975,1,577-582. kerosine (dispersed phase)-water (continuous phase), Hatate, Y.; Mori, S.; Okuma, S.; Kato, Y. Drop Size in Gas-Liquidkerosine-50 w t % aqueous sucrose solution, 2-ethylLiquid System Bubble Columns. Kagaku Kogaku Ronbunsyu 1976,2,133-137. hexanol-water, 1,1,2,2-tetrabromoethane-water, and Hikita, H.; As&, S.; Tanigawa, K.; Segawa, K.; Kitao, M. Gas Holdwater-kerosine. The o b s e ~ e dfractional gas holdups could up in Bubble Columns. Chem. Eng. J . 1980,20,59-67. be correlated by (12) and (15) for the local and average Hills, J. H. The Operation of a Bubble Column at High Throughputa values, respectively. The Peclet numbers, which were I. Gas Holdup Measurements. Chem. Eng. J . 1976,12,89-99. evaluated from the measured axial distribution of the Kato, Y.; Kago, T.; Morooka, S. Longitudinal Concentration Disvolume fraction of the dispersed liquid, could be correlated tribution of Droplets in Multi-Stage Bubble Columns for GasLiquid-Liquid Systems. J . Chem. Eng. Jpn. 1984,17,429-435. by (17). Kato, Y.; Kago, T.; Morooka, S.; Nishiwaki, A. Logitudinal Dispersion of Droplet Phase in Single- and Multi-Stage Bubble Columna Acknowledgment for Gas-Liquid-Liquid Systems. J. Chem. Eng. Jpn. 1985,18, 154-159. We express our gratitude to Honjyo Chemicals Co. Ltd., Kohl, A. L.: Riesenfeld, F. C. Gas Purification, 4th ed.; Gulf: Japan, for providing 1,1,2,24etrabromoethane. Houston, '1985. Koopman, P. G. J.; Buurmans, H. M. A.; Kieboom, A. P. G.; Van Nomenclature Bekkum. H. Solvent-Reactant-SuDDortInteractions in Liauid Phase Hydrogenation. Red. Tra;.'Chim. Pays-Bas 1981, jO0, Bo = Bond number, gDT2p/u 156-161. Ca = capillary number, u G ~ L / u Ma, King, W. Multiphase oxidation of an alcohol to an aldehyde. DT = column diameter, m US. Pat. 4306083,Dow Chemical Co. 1981;Chem. Abstr. 1982,%3, E = longitudinal dispersion coefficient, m2/s 68598P. Fr = Froude number, uG/(gDT)1/2 Suganuma, T.; Yamanishi, T. Behaviors of Solid Particles in Bubble Columns. Kagaku Kogaku 1966,30,1136-1140. g = gravitational acceleration, m/s2 Yoshida, F.; Yamada, T. Average Size of Oil Drops in Hydrocarbon L = height of aerated liquid, m Fermentors. J . Ferment. TechnoZ. 1971,49,235-244. L, = height of clear liquid, m F.; Yamane, T.; Miyamoto, Y. Oxygen Absorption into Mo = Morton (or capillary-buoyancy) number, p ~ ~ g / p ~ a 3 Yoshida, Oil-in-Water Emulsions. A Study on Hydrocarbon Fermentors. Mor= modified Morton number, p4glApl/p2$ Ind. Eng. Chem. Process Des. Dev. 1970,9,570-577.
P = static pressure, Pa Pe, ='Peclet number, v&T/ED u = superficial velocity, m/s
Receiued for review May 1, 1990 Accepted October 22, 1990
