Axial dispersion coefficients in bubble columns

The Chemical Engineering

Journal,

I I (1976)

15 3-l 56

Short Communication

Axial dispersion coefficients

in bubble columns

Experimental apparatus and procedure The experiments for the axial dispersion measurements were carried out in three columns. The details of the columns and the gas and tracer distributors used in the experiments are shown in Table 1. The flow diagram for the experimental set-up is shown in Fig. 1. The liquid height was determined by filling the column until the aerated liquid ran out of an overflow line. At the start of each run, a sulfuric acid tracer was injected at the top of the column at the liquidgas interface using a rotating disc which ensured an instantaneous and uniform distribution of the tracer. The concentration of tracer at the bottom of the column was measured as a function of time with a probe SOLU conductivity meter. The experiments for evaluating the effects of liquid properties on the axial dispersion coefficient were carried out in the smallest circular column (i.d. 2jf in). The surface tension and the viscosity of the liquid were varied by, respectively, adding a surfactant (Triton DF-12) and using various glycerol-water mixtures (see Table 2). The measured tracer concentration versus time curve was used to calculate the axial dispersion coefficient using the method described by Ohki and Inoue’.

B. F. ALEXANDER Gulf Research and Development Pa. 15230 (U.S.A.)

Company, Harmarsville,

Y. T. SHAH

of Chemical Engineering, University of Pittdugh,

Department

Pittsburgh, Pa. 15261

(Received

29 July

(U.S.A.)

1975; in final form 23 December

1975)

Introduction There is a large amount of literature on axial dispersion in a bubble column’-20. This brief communication evaluates experimentally: (a) the effects of column diameter and the gas velocity on the dispersion coefficient in the bubble flow regime in cylindrical bubble columns; (b) the effects of the fluid properties, surface tension and viscosity on the dispersion coefficient; and (c) the effect of the gas flow rate on the dispersion coefficient in a rectangular bubble column. Since it has been shown9 that the liquid flow rate has an insignificant effect on the dispersion coefficient in a bubble column, all the data reported in this study were taken in a batch system.

TABLE 1 Details of the bubble

columns Gas distributor

Tracer distributor

1.22 (48)

Single orifice, 6.4 mm diameter

25.4 mm rotating perforated disc

3.08 (121.25)

3.03 (119.25)

Porous plate thirteen 0.79 mm holes

76 mm rotating perforated disc

1.12 (44.25)

0.82 (32.25)

Porous plate, ten 6.35 ($ in) holes

25.4 mm rotating perforated disc

Cross section

L*

Z*

(mm (in))

Cm (in))

On (in))

60.3 (2;) diameter, circular

1.24 (49)

152.4 (6) diameter, circular 76.2 x 229 (3 x 9) rectangUhI

* As shown

Results and discussion All the data in the present study were obtained in the bubble flow regime (i.e. in the superficial gas velocity

in Fig. 1.

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TABLE 2 Properties of the liquids used in the present study .__ Liquid

Surface tension

Dynamic viscosity

(mN m-’ (dyn cm-’ j)

(mPa P’ (cP)j

12* Water 0.001% Triton DF-12? 44* 0.01% Triton DF-12 * 45% glycerol-55% water ZZ.L** 6.5%glycerol-35% water 67.5**

0.86*

0.90* 0.90* 5.21** 14.45**

* 27 “C (80 “F). ** 20 “C (68 OF). t Obtained from Kohn and Haas Company, Philadelphia, Pa., U.S.A. range O-7 cm s-’ ). Previous investigators have shown that the axial dispersion coefficient in bubble columns is dependent mainly upon the gas velocity and column diameter. The present data for the dispersion coefficient 0(&V,> in two cylindrical columns (i.d. 23 in and 6 in) were found to be considerably smaller (by more than 100%) than the data predicted by the semi-theoretical relation of Ohki and moue (i.e. eqn. (24) of ref. 9).

Furthermore, the Ohki and moue relation predicted a much stronger dependence of the dispersion coefficient on both the column diameter and the gas velocity than that measured in our experiments. The empirical relations of Deckwer et al. I1 and Hikita and Kikukawa (i.e. eqn. (6) and ref. 19), on the other hand, correlated our data very well. The parity plots between the measured D values and the values calculated from their relations are shown in Fig. 2. Unfortunately, none of the previous investigators has studied the effects of fluid properties on the dispersion coefficient by varying only one fluid property at a time. We evaluated the effects of variations of the surface tension and viscosity of the liquid on the dispersion coefficient by varying only one fluid property at a time. The effect of a variation in surface tension on the dispersion coefficient is illustrated in Fig. 3(aj. As shown by previous investigatorss”8’19, these results indicate that the surface tension of the liquid has an insignificant effect on the axial dispersion coefficient. Similarly, Fig. 3(b) indicates that the fluid viscosity has an insignificant effect on the axial dispersion coefficient-a conclusion suggested by Aoyama et al.’ and Cova” but not by Hikata and Kikukawa”. In the present study, pressure drops across the columns were not measured. The gas holdups measured under a few typical conditions agreed well with the ones predicted from the correlation of Akita and Yoshida*l. Two different types of gas distributors were used in two cylindrical columns. However, no reliable and noticeable effect of the distributor hole diameter on the dispersion coefficient was obtained. Ohki and moue’ explained their data in the bubble flow region using a velocity distribution model, which assumes a homogeneous bubble column with a uniform velocity independent of the column diameter. More recently, Baird and Rice*’ proposed an isotropic turbulence model based on the Kolmogoroff theory of isotropic turbulence in a homogeneous medium. Both these models also assume that large scale interactions (i.e. large eddies or diffusion on a large scale compared with the size of gas bubbles) play an important role on the magnitude of the dispersion coefficient. Therefore, fluid viscosity which partly determines the minimum eddy size, and fluid surface tension, which determines the shape and size of the small bubbles, should have little effect on the magnitude of the dispersion coefficient. This was verified in the present study. Both the velocity distribution model and the isotropic turbulence model predict strong effects of gas velocity and column diameter on the dispersion coefficient because the size of a large eddy

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D

measured-

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Fig. 2. Experimental data vs. predictions from the correlations of Deckwer er al. l5 and Hikita and Kikukawa”: A column i.d. 22 in, DC& from Deckwer et Ql.15; Acolumn i.d. 2: in, &al from Hikita and Kikukawa”; 0 column i.d. 6 in, &a~ from Deckwer ef al. Is; @column i.d. 6 in, &at from Hikita and KikukawaL9; n rectangular column 3 in x 9 in, Deal from Deckwer ef al. I5

should be dependent upon these parameters. Once again, this was found to be the case. The quantitative relationship between the dispersion coefficient, gas velocity and the column diameter, however, was better correlated by the isotropic turbulence model than the velocity distribution model. In a dimensionless form, the present data were well correlated (within approximately 5%) by the relation of Kato and Nishiwaki r7 : Pe =

13 Fr 1 + 6.5 Fro.*

where the Peclet and Froude numbers are defined as Pe = V,D,/D and Fr = V,/G Since the dispersion coefficient was found to be independent of fluid properties, the dimenstbnless numbers which include the fluid properties were not used in the present correlation of the data, Effect of column shape Since fermentation vats are often rectangular in shape, axial dispersion coefficients in a rectangular column

were also measured in this study. These data are shown in Fig. 2. It can be seen from these data that, for this column, measured dispersion coefficients were significantly higher (approximately 24 times) than the ones calculated using the correlation of either Deckwer et al. *’ or Hikita and,Kikukawarg. For this case the value of Dt used in the correlations was the diameter of a circular tube which would have the same cross sectional area as that of the rectangular column. Figure 2 also indicates that the axial dispersion coefficient for a rectangular column has the same dependence on the gas velocity as the ones given by the relation of Deckwer et ~1.” The large dispersion coefficients obtained in the rectangular column are probably due to secondary flow effects. In a recent paper, Akita and Yoshida’r indicated that the same liquid phase mass transfer coefficient can be obtained in a square column and a cylindrical column with a diameter equal to the side of a square. The present data, however, indicate that owing to secondary flow the velocity distribution within the column is not parabolic and this non-uniform

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Dt

Fr z Pe v, z !J Y

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bubble column diameter, or column diameter having the same cross sectional area as that of a rectangular column, cm Froude number V,/fi gravitational constant, cm2 s-r height of the aerated liquid, cm Peclet number V,D,/D superficial gas velocity, cm s -’ distance between the probe and the top of the aerated liquid, cm viscosity of liquid, g cm -r s-r surface tension of liquid, dyn cm-r

REFERENCES

Fig. 3. Effect of liquid viscosity axial dispersion coefficient.

and surface

tension

on the

velocity distribution results in a net increase in the dispersion coefficient. It is likely that, because of the secondary flow pattern, the velocity at the center of the rectangular column may be larger than that at the center of a cylindrical column having the same cross section. According to the velocity distribution model, this could cause an increase in the dispersion coefficient. The secondary flow can also give rise to larger and stronger eddies which in turn can increase the dispersion coefficient as predicted by the isotropic turbulence model of Baird and Ricem. Further experimental work is needed to evaluate the effect of velocity distribution and the breadth-to-width ratio of a rectangular column on the dispersion coefficient. Acknowledgment Many valuable comments of Dr. J. A. Paraskos on this paper are gratefully acknowledged. NOMENCLATURE

D

axial dispersion coefficient,

cm2 s-l

1 W. Siemes and W. Weiss. Chem. Ina. Tech., 29 (1957) 727. 2 T. Tadaki and S. Maeda, Kagaku Kogaku, 28 (1964) 270. 3 Y. Kato, Dr. Engng. thesis, University of Tokyo, Japan, 1961. 4 K. Akita, F. Yoshida and T. Hirotaki, Mtg. Chem. Erzg. Sot. of Japan, Osaka, 1966. 5 W. B. Argo and D. R. Cova, Ind. Eng. Chem. Process Des. Dev., 4 (1965) 352. 6 T. Reith, S. Renken and B. A. Israel, Chem. Eng. Sci., 23 (1968) 619. 7 K. B. Bishoff and J. B. Phillips, Ind. Eng. Chem., 5 (1966) 416. 8 Y. Aoyama, K. Ogushi, K. Koide and H. J. Kubota, J. Chem. Eng. Jpn, I (1968) 158. 9 Y. Ohki and H. Inoue, Chem. Eng. Sci., 25 (1960) 1. 10 R. Badura, W. D. Deckwer, H. J. Warnecke and H. Langemann, Chem. Ing. Tech., 46 (1974) 399. 11 W. D. Deckwer, U. Graeser, Y. Serpemen and H. Langemann, Chem. Eng. Sci., 28 (1973) 1223. 12 E. Kunugita, M. fkura and T. Otake, .I. Chem. Eng. Jpn, 3 (1970) 24. 13 P. Gohler, Doctoral thesis, Technische Universitat Berlin, 1972. Proc. 5th Europ., 2nd 14 C. D. ToweU and G. H. Ackermann, Int. Symp. on Chemical Reaction Engineering, Amsterdam, 1972. 15 W. D. Deckwer, R. Burckhart and G. Zoll, Chem. Eng. Sci., 29 (1974) 2177. 16 R. A. Mashelkar,Br. Chem. Eng., 15 (1970) 1297. 17 Y. Kato and A. Nishiwaki, Int. Chem. Eng., I2 (1972) 182. 18 D. R. Cova, Ind. Eng. Chem. Process Des. Dev.. 13 (1974) 292. 19 H. Hikita and H. Kikukawa,Chem. Eng. J., 8 (1974) 191. 20 M. H. I. Baird and R. G. Rice, Chem. Eng. J., 9 (1975) 171. 21 K. Akita and F. Yoshida, Ind. Eng. Chem. Process Des. ,i Dev., 12 (1973) 76. 22 K. Akita and F. Yoshida, Ind. Eng. Chem. Process Des. Dev., 13 (1974) 84.