Ind. Eng. Chem. Res. 1992,31, 587-592 Registry No. Caproic acid, 142-62-1; capric acid, 334-48-5; myristic acid, 544-63-8; oleic acid, 112-80-1; erucic acid, 112-86-7; 1,3-butanediol, 584-03-2.
Literature Cited Alexander, P. R.; Callahan, R. W. Liquid-liquid extraction and striming of gold with microporous hollow fibers. J . Membr. Sci. 1987; 35: 57:71. ADDleWhite. T. H. Fats and fattv oils. In Kirk-Othmer EncvcloDedia of Chem;cal Technology; Giayson, M., Ed.; Wiley: New kork, 1980; Vol. 9. Beek, W. J.,; Muttzall, K. M. K. Transport Phenomena; Wiley: London, 1975; p 261. Braae, B. Degummimg and refining practices in Europe. J. Am. Oil Chem. SOC.1976,53, 353-357. Callahan, R. W. Novel uses of microporous membranes: a case study. AZChE Symp. Ser. 1988,84 (No. 261), 54-65. Dahuron, L.; Cussler, E. L. Protein extraction with hollow fibers. AZChE J . 1988,34, 130-136. Dekker, M.; Koenen, P. H. M.; van’t Riet, K. Reversed micellarmembrane-extraction of enzymes. Znt. Chem. Eng. Symp. Ser. - 1
1990, 118, 7.1-7.12.
DElii, N. A.; Dahuron, L.; Cussler, E. L. Liquid-liquid extractions with microporous hollow fibers. J . Membr. Sci. 1986,29,309-319. Faxen, H. Die Bewegung einer starren Kugel langs der Achse eines mit zahrer Flbsigkeit gefiillten Rohres. Ark. Mat. Astron. Fys. 1923, 17, 27.
Keurentjes, J. T. F.; Bosklopper, Th.G.J.; van Dorp, L. J.; van’t Riet, K. The removal of metals from edible oil by a membrane extrac1990,67,28-32. tion procedure. J . Am. Oil Chem. SOC. Keurentjes, J. T. F.; Linders, L. J. M.; Beverloo, W. A.; van’t Riet, K. Membrane cascades for the separation of binary mixtures. Accepted for publication in Chem. Eng. Sci., 1991. Kiani, A.; Bhave, R. R.; Sirkar, K. K. Solvent extraction with immobilized interfaces in a microporous hydrophobic membrane. J. Membr. Sci. 1984,20, 125-145. Kim, B. M. Membrane-based solvent extraction for selective removal and recovery of metals. J. Membr. Sci. 1984,21,5-19. Klein, E.; Holland, F. F.; Eberle, K. Comparison of experimental and calculated permeability and rejection coefficients for hemodialysis membranes. J . Membr. Sci. 1979,5, 173-188. Kloosterman, J.; van Wassenaar, P. D.; Bel, W. J. Membrane bioreactors. Fat Sci. Technol. 1987,89, 592-597.
587
Kreith, F. Principles of Heat Transfer;Harper and Row New York, 1973.
Lo, T. C.; Baird, M. H. I. Liquid-liquid extraction. In Kirk-Othmer Encyclopedia of Chemical Technology; Grayson, M., Ed.; Wiley: New York, 1980; Vol. 9. Mackie, J. S.; Meares, P. The diffusion of electrolytes in a cation exchange resin membrane. R o c . R. SOC.London 1955, A232, 498-509.
Norris, F. A. Refining and bleaching. In Bailey’s Industrial Oil and Fats Products, Vol. 2,4th ed.; Swern, D., Ed.; Wiley: New York, 1982.
Peppas, N. A.; Reinhart, C. T. Solute diffusion in swollen membranes. Part I. A new theory. J . Membr. Sci. 1983,15,275-287. Pons, W. A.; Eaves, P. H. Aqueous acetone extraction of cottonseed. J. Am. Oil Chem. SOC.1967,44,460-464. Prasad, R.; Sirkar, K. K. Solvent extraction with hydrophilic and composite membranes. AZChE J. 1987,33, 1057-1066. Prasad, R.; Sirkar, K. K. Dispersion-free solvent extraction with microporous hollow fiber modules. AZChE J . 1988,34,177-188. Sakai, K.; Takesawa, S.; Mimura, R.; Ohashi, H. Structural analysis of hollow fiber dialysis membranes for clinical use. J. Chem. Eng. Jpn. 1987,20,351-356. Sandell, E. B. Meaning of the term separation factor. Anal. Chem. 1968,4,834-835.
Satterfield, C. N.; Colton, C. K.; Pitcher, W. H. Restricted diffusion in liquids with fine pores. AZChE J . 1973,19,62&635. Shah, K. J.; Venkatesan, T. K. Aqueous isopropyl alcohol for extraction of free fatty acids from oils. J . Am. Oil Chem. SOC.1989, 66, 783-787.
Stein, W. The hydrophilization process for the separation of fatty materials. J. Am. Oil Chem. SOC.1968,45,471-474. Torrey, S., Ed. Edible oils and fate, developments since 1978. Food Technology, Rev. 57; Noyes Data Corp.: Park Ridge, 1983. Uksila, E.; Varesmaa, M.; Lehtinen, I. Separation of unsaturated fatty acids of soybean and linseed oils by crystallization and subsequent liquid-liquid extraction. Acta Chim. Scand. 1966,20, 1651-1657.
Wilke, C. R.; Chang, P. Correlation of diffusion coefficients in dilute solutions. AZChE J . 1955, I, 264-270. Yang, M. C.; Cussler, E. L. Designing hollow fiber contactors. AZChE J . 1986,32, 1910-1916. Zilch, K. T. Separation of fatty acids. J. Am. Oil Chem. SOC.1979, 56,739A-742A.
Received for review March 1, 1991 Accepted October 18, 1991
Individual Longitudinal Dispersion Coefficients of Two Immiscible Liquids in Bubble Columns Satoru Ami* and Hidekazu Yoshizawa Department of Chemical Engineering, University of Osaka Prefecture, Sakai, Osaka 591, Japan
The individual longitudinal dispersion coefficients of continuous and dispersed liquid phases were measured in bubble columns with two immiscible liquids, by means of a transient-state measurement technique. The columna were operated batchwise with respect to both liquids, over a wide range of the relevant physical properties and average volume fraction of the dispersed liquid. The observed individual dispersion coefficients were empirically correlated in terms of the Peclet number based on the superficial gas velocity, as a function of the relevant system parameters. Bubble columns may be used for operations of gas-liquid-liquid systems in diverse areas (Asai and Yoshizawa, 1991). Limited studies are available for some characteristics in such bubble columns, including the longitudinal holdup distribution of the gas and dispersed liquid and the mean drop size and drop size distribution (Asai and
* T o whom correspondence should be addressed.
Yoshizawa, 1991; Hatzikiriakos et al., 1990a,b,). Information concerning the mixing of fluids in bubble columns with immiscible liquids is important for predicting the concentration profiles of relevant species, or temperature profile, in the design or analysis of mass- and heat-transfer equipment, and reactors. Hatate et al. (1975) measured the longitudinal dispersion coefficients of dispersed liquid for an +kerosine (dispersed liquid)-water
0888-5885/92/2631-0587$03.00/00 1992 American Chemical Society
588 Ind. Eng. Chem. Res., Vol. 31, No. 2, 1992 Table I. Physical ProDerties of Liauids Used liquid systems dispersed-continuous temp/OC kerosine-water 11.8-26.0
kerosine-50 wt 9'0 sucrose solution
10.0-12.8
2-ethylhexanol-water
12.0-17.8
1,1,2,2-tetrabromoethane-water
12.0-16.1
phase" D C D C D C D C
p/(kg/m3) 800-795 997 798-791 1270 840-836 998 2970 998
103/(Pa s) 1.68-1.29 1.24-0.863 1.76-1.67 42.9-38.9 12.6-9.62 1.25-1.07 14.7-12.5 1.24-1.10 X
u
x 103/(N/m) 30.5-28.8 64.5-51.8 30.6-30.4 74.7-71.9 27.4-23.3 40.6-38.8 49.6-46.6 64.2-59.8
"D = dispersed liquid; C = continuous liquid.
(continuous liquid) system, using a bubble column with a perforated plate as a gas sparger. The observed dispersion coefficients were correlated in terms of the Peclet numbers based on the superficial gas velocity, as a function of the Froude number. They also correlated the longitudinal dispersion coefficients of a continuous liquid using the limited data of Murakami et al. (1972).These correlations were of a type similar to that of the liquid mixing characteristics in a conventional gas-single liquid bubble column. Kat0 et al. (1984)confirmed that the correlation of Hatate et al. for the dispersion coefficientsof a dispersed liquid in single-stage bubble columns can also be applied to multistage bubble columns. Diaz et al. (1986)measured the Peclet numbers of a dispersed liquid (kerosine) and continuous liquid (water) in a liquid-liquid countercurrent extraction column agitated by an upflow of air. The Peclet numbers for continuous liquid obtained in the range of 0.1-1.2 was found to decrease with water flow rates and with increases in air and kerosine flow rates. The observed Peclet numbers for the dispersed liquid were 0.1-0.4,decreasing with increases in superficial air flow rates. In these previous studies, the systems used were limited to air-kerosine-water. Hikita and Kikukawa (1974,1975) demonstrated the profound effect of the physical properties of liquids on the liquid-phase dispersion coefficients in conventional gas-single liquid bubble columns. Therefore, a similar substantial effect of the physical properties may be expected on the individual longitudinal dispersion coefficients of continuous and dispersed liquids in bubble columns with immiscible liquids. In this work, the individual dispersion coefficients of both liquids were measured in two bubble columns with a single nozzle gas sparger, over a wide range of relevant physical properties. The observed dispersion coefficients were correlated in the form of empirical expressions.
Experimental Section The experimental apparatus was similar to that in a previous work (Asai and Yoshizawa, 1991). The two bubble columns used were constructed of glass and were 0.064and 0.1 m in diameter and 2.0 m in height. The gas spargers were of the single-nozzle type of 0.005- and 0.007-m i.d. for the 0.064-and 0.1-m columns, respectively. Each gas nozzle was located 0.05m 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, batchwise with respect to two immiscible liquids and continuously with respect to gas. The gas used was always air and was fed from the gas nozzle to the bottom of the column after being metered with rotameters. The superficial gas velocity ranged from 0.05 to 0.48 m/s. The liquid systems used are shown in Table I. [For the systems of kerosine-sucrose solution and 1,1,2,2-tetrabromoethane-water with $ = 0.5,phase
inversion was likely to occur in the regions near the top and bottom of the column, respectively, which were outside the measurement section of the dispersion coefficients, at the low superficial gas velocities. However, here the organic liquid with less surface tension is defined as the dispersed phase for convenience.] The water used was deionized. The clear liquid height was mainly 1.12m, but in some runs it was kept at 0.528m. The average volume fraction of the dispersed liquid varied from 0.1 to 0.5 m3 of dispersed liquid/(m3 of total liquid). The longitudinal dispersion coefficients of the continuous and dispersed liquid were determined by means of a transient-state measurement technique (Siemes and Weiss, 1957;Ohki and Inoue, 1970;Loffler and Merchuk, 1973; Hikita and Kikukawa, 1974). The tracers used were soluble only for either of the dispersed liquids (organic liquids) or continuous liquids (water or aqueous sucrose solution). Oil red dye was used as a tracer for the dispersed liquids, and methylene blue or KC1 was used for the continuous liquids. The amount of both dyes (oil red dye and methylene blue) injected was 2.0 X 104-1.2 X lo* m3. The amount of the KC1 injected was adjusted to give the equilibrium concentration (the finally attainable uniform concentration over the entire column) less than 0.05 kmol/m3, in which the effect of the electrolyte on the size and coalescence of bubbles is negligible. The tracers for both the liquids were injected in the column simultaneously and instantaneously. For the small column, the tracers were injected at a point of 0.862 m from the bottom for the run with a clear liquid height of 1.12m and at a point of 0.462 or 0.662 m for the run with a clear liquid height of 0.528 m. In the run with an injection point of 0.662m above the bottom, which is higher than the clear liquid height of 0.528m, also the injection point was always below the free surface owing to the existence of gas holdup. The liquid samples were taken through a sampling cock on the column wall, which was located 0.265 m above the bottom plate. For the large column, on the other hand, the points of tracer injection and sampling were 0.97and 0.33 m above the bottom plate, respectively. The liquid samples were taken into a fraction collector at time intervals of 5-10 s, after injection of the tracers. The liquid samples were separated into two liquid phases by settling, and the concentration of the relevant tracer in each liquid was measured by a spectrophotometer and an electric conductivity meter for the dyes and KC1, respectively. The equilibrium concentrations of both tracers were also measured by sampling the liquids after sufficiently long operations.
Analytical Procedure Nishiwaki and Kato (1972)clarified that in solid particle suspended bubble columns the residence time distribution of the solid particles, which is evaluated on the basis of the dispersion model with a slip velocity, is nearly equal to that based on the conventional mixing diffusion model,
Ind. Eng. Chem. Res., Vol. 31, No. 2 , 1992 589 notwithstanding that the behavior of the solid particles in the column obeys the former dispersion model. Hatate et al. (1975) used this approximate procedure successfully in their analysis of the longitudinal dispersion coefficients of the dispersed liquid for bubble columns with two immiscible liquids. Also in the present study, a similar procedure is used for evaluation of the individual longitudinal dispersion coefficients of the continuous and dispersed liquids. The partial differential equation of the dispersion concerned with a transient-state measurement technique in a batch system was solved analytically by Siemes and Weiss (1957). The tracer concentration C is given as a function of time t and the height z above the bottom of the column:
c - co --
c, - co
- 1 + - x2L 7rx[ in=l {sin(
n7r(l + A)
)-
o0v
I
10
1
I
I
I
20
30
40
50
t
Lc(rn) 1.12 0.528
c. - Cn
0.00ll 0.02
I
I
l
4
6
8 0.1 UG
using the clear liquid height Lc and the average fractional gas holdup zG The values of zG for the liquid mixture with the average volume fraction 4 of the dispersed liquid on a gas-free basis were evaluated according to the following procedure (Asai and Yoshizawa, 1991) yielding reasonable accuracy: ZG
= ZGD$
+ zGC(1 - 4)
(4)
The average gas holdups zm and QD of the continuous and dispersed liquids, respectively, were calculated using the physical properties of the respective liquids, according to the following expression (Hikita et al., 1980) ZG
= 0.672(Cao.578)(Mo -''131)(pc/p~)o'062(c1~/c1~)o'107 (5)
where
Ca = u G ~ L / u , Mo = pL4g/pLa3 (6) The physical properties used in the analysis are shown in Table I. The densities, viscosities, and surface tensions of the liquids were measured by conventional techniques. Results and Discussion The agreement of the experimental tracer response curves for both the continuous and dispersed liquids with eq 2 was satisfactory, as illustrated in Figure 1,where the response curve for the &kerosine-water system is shown
I
I
80
90
100
Figure 1. Tracer response of continuous liquid (water)phase for the air-kerosine-water system: UG = 0.34 m/s; 4 = 0.1; D, = 0.064 m; 18.0 O C . (-) Fit according to eq 2 with Ec = 0.012 mz/s.
c - co --
(3)
I
70
(SI
The relation of L >> nX was always satisfied under the present experimental conditions. Then, eq 1 can be simplified and reduced to the Carslaw and Jaeger solution (1959):
Therefore, one can obtain the individual longitudinal dispersion coefficients E by fitting the observed time variation of the tracer concentration C at a fixed position z with eq 2. Such fitting was performed by using the simplex method. The aerated liquid height L was calculated from
I 60
l
EC ED 0 . A A
I
I
l
2
4
6 0.8
l
(mk)
Figure 2. Longitudinal dispersion coefficients Ec and E , for the air-kerosine-water system: 4 = 0.5; DT = 0.064 m;22.4 f 3.6 O C . Key: (- -) Baird and Rice (1975); (-.-) air-water, Hikita and Kikukawa (1975); (---) air-kerosine, Hikita and Kikukawa (1975).
for the continuous liquid (water). This verifies the applicability of the dispersion model. Figure 2 shows the effect of the clear liquid height Lc on the longitudinal dispersion coefficients Ec and ED of the continuous and dispersed liquids, respectively, for the air-kerosine-water system. At a superficial gas velocity of less than 0.1 m/s, the turbulence was not large enough to allow the tracer to disperse sufficiently over the short section of the column between the injection point of the tracer and the sampling point. Consequently, part of the mass of the tracer carried by the fluctuating downflow of the heterogeneous liquid reached the sampling point irregularly. Thus, the reproducible data of the dispersion coefficients were difficult to measure at such low superficial gas velocities in the run with Lc = 0.528 m. From the results for the higher superficial gas velocity, however, the dispersion coefficients Ec and ED of both liquids may be regarded as independent of the clear liquid height Lc. Therefore, all other experiments were performed at a clear liquid height of 1.12 m. In this figure are also shown the values of the liquid-phase dispersion coefficient predicted from the correlations of Baird and Rice (1975) and of Hikita and Kikukawa (1975) for a gasaingle liquid system. The latter correlation allows for the effect of the physical properties of the liquid, so that the dispersion coefficients were calculated by using the individual physical properties of kerosine and water. The correlation of Baird and Rice does not allow for the effect of the physical properties. Thus, it deviates slightly more from the experimental data than that of Hikita and Kikukawa, but all the correlations may be regarded as being satisfactory. Figure 3 shows the effect of the average volume fraction 4 of the dispersed liquid on Ec and ED for the airkero-
590 Ind. Eng. Chem. Res., Vol. 31, No. 2, 1992
0.1
0.002 Wt
I
6
I
I
8 0.1 UG
0
I
I
2
4
a mW
6
8 0.1
(mls 1
2 UG
Figure 3. Longitudinal dispersion coefficients Ec and ED for the air-keroeinewater system: DT = 0.064 m; 22.4 f 3.6 "C. Key: (--) Ec,eq 7, Hatate et al. (1975); (-*-) ED,eq 8,Hatate et al. (1975).
4
0.6
(mk)
Figure 5. Longitudinal dispersion coefficients Ec and ED for the air-kerosine-50 w t % sucrose solution system: DT = 0.064 m; 11.4 f 1.4 "C. Key: the same as that in Figure 3.
0.04
m
0.004
-
u al
QW
6
2
8
4
0.004 0.04
0.6
(mls 1 Figure 4. Longitudinal dispersioncoefficientsEc and ED for the air -1,1,2,2-tetrabromoethanewater system: DT = 0.064 m; 14.1 f 2.1 "C. Key: the same as that in Figure 3.
+
PeD = u&T/ED,
Fr = U ~ / ( ~ D , ) ~ / ~ (9)
The present findings, that Ec and ED are independent of $, are in line with eq 7 and 8. These expressions also give nearly equal values of Ec and ED, but they yield values higher than the present data by about 30-60 % on the average. This difference may be due to the difference in the gas spargers used: a perforated plate in their experiments against a single nozzle in this study. Figure 4 represents the dispersion coefficients of both the liquids for the air-1,1,2,2-tetrabromoethane-water system. The dispersion coefficients ED of the dispersed liquid greatly decrease with an increase in the volume fraction $ of the dispersed liquid, while a substantial effect of $ on Ec cannot be found. This system is characterized by a significantly large density and the viscosity of the dispersed liquid. As will be stated later in connection with Figure 6 for the air-2-ethylhexanol-watersystem, the increase in the viscosity of the dispersed liquid appears to rather improve the dispersion of both liquids. Thus, the
2
4
c i
(rnls)
Figure 6. Longitudinal dispersion coefficients Ec and ED for the air-2-ethylhexanol-water system: DT = 0.064 m; 14.9 f 2.9 "C. Key the same as that in Figure 3.
sine-water system. It may be noted that the difference between Ec and ED is not substantial, and the effect of 4 cannot be observed for both the dispersion coefficients in the present system. This suggests that the slip velocity between the two liquid phases is not so large owing to a small density difference. The broken and dot-dash lines represent the correlations of Hatate et al. (1975) for Ec and ED, respectively, which were proposed for the present system: 11.5(FrI . , Pec = (7) 1 + 8(Fr0.85) lO(Fr) PeD = 1 6.5(Fr".8) where Pec = u$,/Ec,
6 8 0.1 UG
UG
Y
Ind. Eng. Chem. Res., Vol. 31, No. 2, 1992 591
2-
-I h
8 ' 8" -
A
-
64/
0.2
'
0.2
I
I
I
4
6
8 1.0
(Pe,
I
1
1
2
L
lccrl. (-1
Figure 8. Comparison of the present data with the proposed correlation for the Peclet number of continuous liquid Pec. Key: (0) kerosine-water (DT= 0.064 m); (V)2-ethylhexanol-water; (A)kerwine50 w t % sucrose solution; (0) 1,1,2,2-tetrabromoethane-water; ( 0 )kerosine-water (DT= 0.1 m).
equal. The increase in these dispersion coefficients with the increase in the average volume fraction 4may possibly be attributed to the promotion of the turbulence of both liquids due to the increase in the diameter and/or number of viscous droplets. The effects of the column diameter DT on Ec and E D are shown in Figure 7 for the air-kerosine-water system. As can be seen, the values of Ec and E D , which are equal to each other, increase with the column diameter DT.The dependency on the column diameter is about 0.8 power. This is less than that in the previous correlations, which showed powers of 1.0-1.5 and mostly 1.33 for the conventional bubble column with the single liquid (Baird and Rice, 1975; Joshi and Shah, 1981; Shah et al., 1982; Deckwer and Schumpe, 1987; Kawase and Moo-Young, 1990). However, the effect of the superficial gas velocity uG on the dispersion coefficients, giving a slope of about 1/3, is similar to that in the previous correlations. At the present stage, it is difficult to give a qualitative explanation about the lesser dependency on the column diameter for a bubble column with two immiscible liquids. All the observed values of the longitudinal dispersion coefficients of both liquids were correlated in terms of the relevant dimensionless numbers, by allowing for the form of the expressions proposed previously for conventional single liquid or two immiscible liquid system bubble columns (Kato et al., 1972; Hatate et al., 1975; Hikita and Kikukawa, 1974, 1975). The following correlations are proposed:
L
(MoCo.O3)(Fr)(1 - 4)/1.83] 0.037
PeD =
1
1/1.83
+ 0.188(Fr0.72)
pee (11) 36.7(lAp/p~1)~.~m~,~~(1 - 2$)3.6(Fr-0.69)
where MOC = PC4g/PCQC3, MOD= WD4g/pDaD3 (12) In the correlation of eq 11,it is assumed that the mixing characteristics of the dispersed liquid are influenced by that of the continuous liquid. Furthermore, the dispersed liquid is assumed to move together with the continuous liquid (Pec = PeD) in the limiting case of 4 0. This
-
_. 0.I
2
L
6
81I)
2
L
( PeD led. (-
1 Figure 9. Comparison of the present data with the proposed correlation for the Peclet number of dispersed liquid PeD. Key: the same as that in Figure 8.
situation means that a very small amount of existing tiny liquid drops move without any interference among them and with no slip velocity from the continuous liquid. On the other hand, the correlation of eq 10 makes allowance for the fact that Pec should reduce to that for the liquidphase longitudinal dispersion in conventional gas-single liquid bubble columns (Hikita and Kikukawa, 1975) (Moo.O3)(Fr) . . 0.037 + 0.188(Fr0.72) when dispersed liquid is absent (4 0). The coefficients and powers in eq 10 and 11were determined by the simplex method. The range of the relevant dimensionless numbers covered in this experiment is 0.1 I4 I0.5,0.053 IFr 50.53, 3.9 X IMOC5 4 . 5 X 1.4 X I MOD I1.4 X 0.19 I I A p l / p ~5 0.66. Comparisons between the observed Peclet numbers, Pec and PeD,and the calculated ones from eq 10 and 11are shown in Figures 8 and 9 for the continuous and dispersed liquids, respectively. Most of the data can be correlated within an error of 50%. A substantial error reflects the difficulty of correlating the data over an extremely wide range of physical properties, due to complicated phenomena prevailing, as well as the difficulty of measuring precisely the small values of Pe in some cases. -
Pee =
-
Conclusion The longitudinal dispersion coefficients of continuous and dispersed liquids were measured in bubble columns operated batchwise with respect to two immiscible liquids. The dispersion of both liquids could be represented by the dispersion model of Siemes and Weiss (1957). The longitudinal dispersion coefficients Ec and ED of the continuous and dispersed liquids were independent of the clear liquid height. For both systems of air-kerosine-water and air-2ethylhexanol-water, which are characterized by a small density difference between the continuous and dispersed liquids, the difference between Ec and E D was not substantial, indicating that the two liquids move together. The effect of the average volume fraction 4of the dispersed liquid on the dispersion coefficients was not observed for the former system, which has a relatively small viscosity difference between two liquids, but Ec and EDincreased with 4 for the latter system, which has a highly viscous dispersed liquid.
592 Ind. Eng. Chem. Res., Vol. 31, No. 2, 1992
For the ai1-1,1,2,2-tetrabromoethane-watersystem with a large density of dispersed liquid, ED decreased with an increase in $, but a substantial effect of $ was not observed on Ec. For the ail-kerosine-50 w t 90aqueous sucrose solution system with a highly viscous continuous liquid, Ec increased and ED decreased with an increase in $. Both dispersion coefficients were found to be proportional to a column diameter with a power of 0.8, in contrast to a conventional bubble column with a single liquid having the power of 1.33. All observed longitudinal dispersion coefficients of both liquids could be correlated empirically by eq 10 and 11. Further studies are required for extension to a continuous operation with respect to both immiscible liquids.
Acknowledgment We express our gratitude to Honjyo Chemicals Co. Ltd., Osaka, Japan, for providing 1,1,2,2-tetrabromoethane.
Nomenclature C = concentration of tracer, kmol/m3 Ca = capillary number, uGktL/a D T = column diameter, m E = longitudinal dispersion coefficient, m2/s Fr = Froude number, U G / ( 9 D T ) 1 / 2 g = gravitational acceleration, m/s2 L = height of aerated liquid, m Lc = height of clear liquid, m 1 = height of tracer injection point above bottom plate, m Mo = Morton (or capillary-buoyancy) number, pL4g/p~63 n = parameter Pe = Peclet number, U $ T / E t = time, s u = superficial velocity, m/s z = longitudinal distance measured from bottom plate, m Greek Letters Ap = density difference, PC - P D , kg/m3 t G = gas holdup, m3 of gas/(m3 0.f column) X = height of column corresponding to volume of tracer injected, m p = viscosity, Pa s p = density, kg/m3 u = surface tension, N/m 4 = volume fraction of dispersed liquid, m3of dispersed liquid/(m3 of liquid mixture) Subscripts C = continuous liquid
D = dispersed liquid e = equilibrium G = gas L = liquid 0 = initial condition
Superscript
- = average value Literature Cited As&, S.; Yoshizawa, H. Longitudinal Holdup Distribution of Gas and Dispersed Liquid in Bubble Columns with Two Immiscible Liquids. Ind. Eng. Chem. Res. 1991,30, 745-751. Baird, M. H. I.; Rice, R. G. Axial dispersion in large unbaffled columns. Chem. Eng. J. 1975,9,171-174. Carslaw, H. S.;Jaeger, J. C. Conduction of Heat in Solids, 2nd ed.; Clarendon Press: Oxford, U.K., 1959; p 361. Deckwer, W.-D.; Schumpe, A. Bubble Columns-the State of the Art and Current Trends. Int. Chem. Eng. 1987,27,405-422. Dim, M.; Aguayo, A. T.; Alvarez, R. Hydrodynamics of a LiquidLiquid Countercurrent Extraction Column with Upflow Gas Agitation. Chem.-Ing.-Tech. 1986,58, 74-75. Hatate, Y.; Okuma, S.; Kato, Y. Longitudinal Dispersion Coefficient and Holdup Distribution of Droplets in Bubble Columns. Kugaku Kogaku Ronbunsyu 1975,1,577-582. Hatzikiriakos, S. G.; Gaikwad, R. P.; Nelson, P. R.; Shaw, J. M. Hydrodynamics of Gas-Agitated Liquid-Liquid Dispersions. AIChE J. 1990a,36,677-684. Hatzikiriakos, S.G.; Gaikwad, R. P.; Shaw, J. M. Transitional Drop Size Distributions in Gas Agitated Liquid-Liquid Dispersions. Chem. Eng. Sci. 1990b,45,2349-2356. Hikita, H.; Kikukawa, H. Liquid-Phase Mixing in Bubble Columns: Effect of Liquid Properties. Chem. Eng. J. 1974,8,191-197. Hikita, H.; Kikukawa, H. Dimensionless Correlation of Liquid-Phase Dispersion Coefficient in Bubble Columns. J. Chem. Eng. Jpn. 1975,8,412-413. Hikita, H.; Asai, S.; Tanigawa, K.; Segawa, K.; Kitao, M. Gas HoldUp in Bubble Columns. Chem. Eng. J. 1980,20,59-67. Joshi, J. B.; Shah, Y. T. Hydrodynamics and Mixing Models for Bubble Column Reactors. Chem. Eng. Commun. 1981, 11, 165-199. Kato, Y.; Nishiwaki, A.; Fukuda, T.; Tanaka, S. The Behavior of Suspended Solid Particles and Liquid in Bubble Columns. J. Chem. Eng. Jpn. 1972,5,112-118. Kato, Y.; Kago, T.; Morooka, S. Longitudinal Concentration Distribution of Droplets in Multi-Stage Bubble Columns for GasLiquid-Liquid Systems. J. Chem. Eng. Jpn. 1984,17,429-435. Kawase, Y.; Moo-Young, M. Mathematical Models for Design of Bioreactors: Applications of Kolmogoroff s Theory of Isotropic Turbulence. Chem. Eng. J. 1990,43,B19-B41. Loffler, D. G.; Merchuk, J. C. Distribucion de Tiempos de Residencia en una Columna de Burbujeo de Orificio Unico. Lat. Am. J. Chem. Eng. Appl. Chem. 1973,3,107-120. Murakami, N.; Kato, Y.; Morooka, S.; Nishiwaki, A. The 37th Annual Meeting of the Society of Chemical Engineers, Nagoya, Japan; Society of Chemical Engineers: Tokyo, 1972;No. E207,pp 122-124. Nishiwaki, A.; Kato, Y. Age Distributions of Suspended Solid Particles in Bubble Columns. Kugaku Kogaku 1972,36,1147-1150. Ohki, Y.;Inoue, H. Longitudinal Mixing of the Liquid Phase in Bubble Columns. Chem. Eng. Sci. 1970,25,1-16. Shah, Y.T.; Kelkar, B. G.; Godbole, S. P.; Deckwer, W.-D. Design Parameters Estimations for Bubble Column Reactors. AIChE J. 1982,28,353-379. Siemes, W.; Weiss, W. Flussigkeitsdurchmischungin engen Blasensaulen. Chem.-Zng.-Tech. 1957,29,727-732. Received for review December 4, 1990 Revised manuscript received May 29, 1991 Accepted November 10,1991
