- Email: [email protected]
Liquid mixing by large gas bubbles in bubble columns
Chemical
Engineering
Science.
1973, Vol. 28, pp. 1437-1445.
Pmgamon Press.
Printed in Gnat
Britain
Liquid mixing by large gas bubbles in bubble columns SHINICHIRO
GONDO, SHINBU TANAKA, KAZUYOSHI KAZIKURI and KOICHIRO KUSUNOKI Department of Chemical Engineering, Kyushu University, Fukuoka 8 12, Japan (Received 16 January 1972)
Abstract- Liquid mixing by large gas bubbles of spherical cup was investigated for co- and countercurrent contact of air-water system with bubble columns of 5 and 10 cm dia. The results obtained are that for the column of 5 cm dia., the longitudinal dispersion coefficient ranges from 5 to 20 cm%ec for superficial gas velocity from 0.07 to 8 cm/set and that for the one of 10 cm in diameter it ranges from 9 to 45 cm*/sec for that from 0.035 to 8 cm/set. Liquid mixing under the coexistence of large and small bubbles was also investigated and it was found that the gas holdup was fairly well explained by an equation derived on the assumption that the mixture of small bubbles and liquid behaves independently of large bubbles. The expansion model was applied to the experimental results on the longitudinal dispersion coefficient and it was observed that there should be the lower limit in the holdup of small bubbles where this model can be applied. INTRODUCTION PLENTY
of work on liquid mixing in the bubble column has been reported. The experimental results have been treated as essentially based on an axial mixing model and the longitudinal dispersion coefficients were presented as a function of superficial gas velocity. As easily observed through the wall of a bubble column, when a superficial gas velocity becomes greater than a critical value, bubbles of moderate diameter coalesce intermittently into a bubble of large diameter which rises up the column much faster than the smaller ones. Large gas bubbles spontaneously generated in this way might have an effect on the liquid mixing of bubble column. Ohki and Inoue [ 11have recently reported properties of coalesced bubbles such as passage frequency and rising velocity. They have also proposed an expansion model for the condition where small bubbles coalesce. In this investigation, large bubbles of spherical cup were generated at the bottom of the column through a single nozzle and the liquid mixing was studied by pulse response of a tracer injected at the inlet of the liquid. Further, large bubbles were generated in the bubble column of small bubbles and an additional effect of large bubbles on the liquid mixing was
studied. The method of making large bubbles reported elsewhere is such that once the gas is kept in the hemispherical cup which opens to the bottom of the column and after the cup is filled with gas it is turned over to release a bubble of spherical cup into liquid. Here a single nozzle of 1.5 mm in hole diameter was used to make large bubbles sequentially, because the former method seems not to be convenient for making large bubbles at arbitrary frequencies. EXPERIMENTAL
APPARATUS
The schematic diagram of the experimental apparatus used in this investigation is shown in Fig. 1. Figures 2a and 2b show the location of the nozzles used for making large bubbles. The left halves of Fig. 2a and 2b show the crosssectional view of the bottom structures of the column used for cocurrent contact of gas and liquid, while the right halves show those for countercurrent contact. Figure 2c shows the assembly of nozzle and sparger ring which was used for the measurements of liquid mixing with small and large bubbles in countercurrent contact. The sparger ring which is connected to the bottom plate with four legs, through which gas is supplied, was used for distributing
1437
SHINICHIRO
/ a-
GONDO
et al.
t Water distributor
Garmster
Bubble column
Water storage
/
Fig. 2c. Assembly of nozzle and sparger ring. E, liquid outlet; IL, air inlet for large bubbles; IS, air inlet for small bubbles; L, supporting legs; N, nozzle with pore of 1.5 mm dia.; S, sparger ring with 3 x 32 pores of 0.4 mm dia.
Fig. 1. Experimental flow diagram: countercurrent contact.
small bubbles. The ring is held above the exit port of liquid as shown in Fig. 2c in order that small bubbles will not be carried over by the accelerated flow of liquid. Through the central nozzle shown in Figs. 2a-2c, the air blows out into the liquid making a large bubble of spherical cup about lo-15 cm above the top of the nozzle. The frequencies of generating large bubbles were adjusted by
changing the time interval between opening and closing the electric solenoid valve, the location of which is shown in Fig. 1. The range of the frequencies tested are presented in Table 1. In the experiments with the column of 5 cm in diameter, deionized water was used. City water was used in case of the column of 16 cm in diameter because of the massive use of water. The solution of the sodium chloride was used as a tracer through the experiments.
(b)
(al
Figs. 2a and 2b. Bottom detail: left halves of (a) and (b) were used for cocurrent contact and right halves for countercurrent. E, liquid outlet; I, liquid inlet; N, nozzle with pore of 1.5 mm dia.; P, perforated plate for distributing water.
1438
Liquid mixing by large gas bubbles in bubble columns Table 1. Experimental conditions
4 (cm)
h (cm)
contacting
5
100 200 157 227 100 200 100 200 200 200 200 200
counter counter co co counter counter co co counter co counter co
5 5 5 10 10 10 10 10 10 10 10
temperature:
f
l/S l/5 l/5 l/5 l/2 l/2 l/2 l/2 l/2 l/2 l/2 l/2
l/2.5 1 s/3 l/2.5 1 5/3 l/2.5 1 5/3 l/2.5 15/3 3/10 l/5 l/l0 3/10 l/5 l/10 3110 l/5 l/l0 3/10 l/5 l/l0 l/5 l/IO l/5 l/10 l/5 l/l0 l/5 l/l0
UI
km3
(cmlsec)
7-16 5-7 7-9 10-11 46-76 35-49 47-54 50-53 26-29 27-29 119-132 121-131
OG-1.0 OG-0.7 0.1-1.0 0.1-1.0 0.09-10.6 0.09-0.4 0.0!%0.5 0~09-10.5 t 0.09-0.4 0.1-0.5 I O%-0.4 0.1-0.5 I
Fig. 6
(4)
(1)
(2) (3)
12-22°C
The tracer was injected into the water distributor installed at the top of the column for countercurrent contact or into the bottom, just above the perforated plate, through the four holes located on the concentric circle. The concentration of sodium chloride was measured by a platinum electrode and recorded. LIQUID
VB
Wsec)
MIXING BY LARGE BUBBLES SPHERICAL CUP
OF
The measurements of liquid mixing by large gas bubbles of spherical cup were measured for the columns of 5 and 10 cm dia for co- and countercurrent contact of gas and water. The
frequency of generating large bubbles f tested and the range of bubble volume V, measured are presented in Table 1 for each of columns used. The photographic studies of large bubbles could not correctly reproduce the bubble shape because of the deformation from an ideal shape of spherical cup. Table 2 illustrates the examples of bubble dimensions determined photographically, the bubble volume, VBP, calculated with the dimensions thus obtained under the assumption of completely spherical cup and also the one determined by the volumetric method, V,, where the bubble volume was determined by dividing the volume of gas throughput by
Table 2. Examples of bubble dimensions
4 (cm)
h (cm)
Contacting
5 5 5 5 *5 10 10 10 10 10 10 10
100 200 157 227 100 200 100 200 200 200 200 200
counter counter co co counter counter co co counter co counter co
f
a
b
V BP
Wsec)
(cm)
(cm)
(cm3
l/5 l/5 l/5 l/5 l/l0 l/l0 l/l0 l/10 l/l0 l/l0 l/l0 l/l0
3.0 3.4 3.3 3.3 6.3 5.7 6.0 6.0 4.9 5.2 7.7 6.8
1.9 1.2 1.4 1.6 2.5 2.4 2.0 1.9 1.7 1.5 3.4 3.5
11.0 6.4 7-5 9.1 47.0 38.0 32 31 19 18 loo 86
vs
(cmS) 15.1 6.9 8.4 11.4 46 35 45 50 25 25 124 119
SHINICHIRO
GONDO
the number of bubbles generated. It should be noted that VB thus obtained did not always represent the real volume of a bubble correctly because each bubble was almost always accompanied by smaller bubbles by which a part of gas throughput was consumed. An axial mixing model was used to investigate the liquid mixing by large bubbles. A tracer was injected within a time interval short enough compared to the average residence time of liquid to have an impulse response, and a time of miximum response where an outlet concentration of a tracer injected reaches its maximum was measured. A partial differential material balance equation has been solved analytically by Yagi and Miyauchi[3] for a tracer response. This analytical solution gives the theoretical relation of the time of miximum response and the Peclet number. Therefore, with an observed time of maximum response the Peclet number can be estimated. Figure 3 shows the examples of the response curve observed and the ones calculated with an estimated value of Peclet number. Most of the response curves observed
et al.
were as close to the theoretical ones as those shown in Fig. 3. The coincidence of the experimental and calculated curve seems practical for an axial mixing model to be applied through this investigation since the discrepancies between theories and experiments were almost the same as those observed for the column of small bubbles where an axial mixing model is usually applied. 8,, time of maximum response divided by average residence time of liquid, was correlated almost linearly with flul on a semi-log diagram as shown in Fig. 4, for instance, for the case of
0.6 -
d,=5
2
0.4-
h =200 f
=1/2.5
lJi =0.3
0.2 -
Fig. 4. Dimensionless time of maximum response. h = 200 cm, countercurrent. Countwcurrenf
Fig.
3.
Theoretical and experimental pulse Theory, ------ Experiment.
response.
dT = 5 cm,
countercurrent contact in the column of 5 cm dia. and 200 cm in height. The term flur dessignates the average number of gas bubbles which are encountered by an element of liquid during its movement of unit length along the axis, say 1 cm. When we plot 8, given theoretically for an axial dispersion model as an 1440
Liquid mixing by large gas bubbles in bubble columns
ordinate and natural logarithmic value of the term E,( 1 - QJ/UJI as an abscissa, we can obtain the curve whose slope is almost equal to those of the correlation lines appearing in Fig. 4. Therefore, the following proportionality will hold. flUl m &( 1 -EL) l&h.
O
0 f-l/2 a
3110
0
0
30 e
l/5
0
l/IO
(1) -0
The right side of Eq. (1) can be approximately replaced by EljuJz because lL is much less than unity in the columns of large bubbles. Therefore, when f and h are fixed, EL must be constant for Eq. (1) to hold. Thus EL may not depend on uz. Figures 5a and 5b represent EL against flul for the countercurrent contact in the column of 5 cm dia. and 200 cm in height, and in the
-0-o 20 EL
e e
0
-a-
0
/__1
20 0
0. I
0
0
0 0
-‘to
Fig. 5b. Longitudinal dispersion coefficients of liquid. dT = 10 cm, h = 200 cm, countercurrent.
0
l 0
velocity, uBL,is equivalent to the bubble volume V, multiplied by the frequency f divided by the column cross-sectional area. Figure 6 shows
-..-1 IO -
0
EL
0
f=5/3
0
I
a a
0
"'I
I6
f/U,
0
OP
I
e
l/2.5
0
l/5 I
I I 11111l
__
II
IO f/U1
Fig. Sa. Longitudinal dispersion coefficients of liquid. dT = 5 cm, h = 200 cm, countercurrent. IO EL
one of 10 cm dia and 200 cm in height, respectively. Through the inspections of Fig. 5a, 5b and also the other figures corresponding to these for other experimental conditions which are contained in Table 1, any systematical dependencies of, EL on flu*, that is, on uz for a given value off could not be observed. Thus the average value of EL at a given f was plotted against the superficial gas velocity of large bubbles, ugL, in Fig. 6 for all the experimental conditions investigated. The superficial gas
E 0
IO 2ooco
Fig. 6. Correlations at longitudinal dispersion coefficient of liquid. cu, countercurrent; co, cocurrent. As for the details of V, and other conditions, refer to Table 1.
1441
SHINICHIRO
that EL increases proportionally to the square root of ugL, that is, the square root of V, multiplied by f, and that there is apparent difference in EL between the columns of 5 and 10 cm dia while the column height does not affect EL. It is also shown that the bubble volume V, has no appreciable effect on EL in the correlations presented in Fig. 6 and that differences between co- and countercurrent contact do not exist.
GONDO et al.
were generated, against uIIs. The experiments for the coexistence of small and large bubbles were carried out for the flow rate ratios, ug,Jufl, as shown in Fig. 8 where uBTis the sum of uI and ugs. I
LIQUID MIXING UNDER THE COEXISTENCE OF LARGE AND SMALL BUBBLES.
As described previously, it was one of our interests to study how much the existence of large bubbles effects liquid mixing in the bubble column of small bubbles. The measurements of liquid mixing in countercurrent contact with both small and large bubbles were performed for the column of 10 cm dia at such a superficial gas velocity where the spontaneous coalescence of small bubbles does not take place. ET was estimated by measuring 8, in a similar way to that in the studies on large gas bubbles. Figure 7 represents ls, the void fraction of the bubble observed only when small bubbles
00 0
a
O
o
0 0 0
0 0
0 0
001
0. I
I
I I111111
I I
I I11111 IO
4T
Fig. 8. Feed fraction of large bubbles. dT = 10 cm, h = 200 cm, countercurrent.
The rising velocities of large bubbles of spherical cup VL were measured by photographic examination and ranged from 35 to 48 cmlsec in the case of large bubbles only. These values of VL deviated within f 20 per cent from those calculated by the equation, V, = 20*8V%, reported by Davis er al. [2] where R is the radius of sphere a part of which makes a spherical cup to be treated. Under the condition of coexistence of large and small bubbles, the I’, is found to be accelerated by the rising of small bubbles as shown in Fig. 9, although the experimental points were rather scattered and a clear conclusion could not be reached Ohki and Inoue [ll reported an increase of rising velocity of coalesced bubbles with an increase of superficial gas velocity. As it is the sum of the void fraction of small bubbles and that of large ones, Ed can be represented as follows.
Fig. 7. Gas holdup of small bubbles column. dT= lOcm, h = 200 cm, u1= 0.3 cm/set, countercurrent.
1442
Liquid mixing by large gas bubbles in bubble columns
1:
IO
I
I
I
IllIll
I I
0. I
II 5
4s
Fig. 9. Rising velocity of large bubbles. dT= 10 cm, h = 200 cm, ur= O-3cmlsec, countercurrent. For marks used, refer to Fig. 8.
In Eq. (2), EL and es. are the fractional holdup of the small bubbles and that of the large ones, respectively, which are to be observed in the condition of coexistence of small and large bubbles. ELis equal to udl’, where V,, is the one shown in Fig. 9. In this investigation, ugSwas so low that the spontaneous coalescences of small bubbles did not take place. Therefore, the mixture of small bubbles and liquid behaved almost independently of large bubbles so that the effect of large bubbles on l h may not be large. Therefore, we assumed that l ;1could be replaced by eS(uaS) which is a fractional gas holdup of small bubbles at u,, given by Fig. 7. Then, Eq. (2) can be rewritten to give an estimation equation for lTas follows. (+)ca1=
d%S)
+z.
a
215
e
I
Fig. 10. Predictions of er by Eq. (3). dT = 10 cm, h = 200 cm, uI = O-3cm/set, countercurrent, (e&r: er given by Eq. (3), (Gobs: er observed.
equal to ugs in the former case. In the experiments with small bubbles only, the spontaneous coalescence of bubbles was observed at ugS greater than about 3 cmlsec. Therefore, in the experiments with large and small bubbles, ugT was kept under the critical velocity of 3 cmlsec because an additional effect of the artificial large bubbles on the liquid mixing could not be distinguished from that of the
/O” (3)
Small
bubbles,
o 0 “&$Po bW 1 .9/“p “a. 0 0”” 0 y @ / w ++’ /a - . ,MGLarge bubbles, EL IO 01
I
I
I111111
I I
EL.
Figure 11 shows experimental results on the dispersion coefficient for the existence of small bubbles only, Es, and for the coexistence of large and small bubbles, ET. uor is of course
I/ a’
/o
Iu” 100 -
The observed values of lT are shown against (&al in Fig. 10. The values of (uJV,)/er ranged from 0.007 to O-91. Although (E&~ is slightly larger than the observed values, Eq. (3) appears to be appropriate in predicting lT. The effect of f on Ed does not appear in Fig. 10, which supports the previous discussions on
E, 0/----+-~~~
I
I
I lllll IO
uor Fig. 11. Longitudinal dispersion coefficients of liquid for the coexistence of large and small bubbles. dT = 10 cm, h = 200 cm, ur = 0.3 cmlsec, countercurrent. For marks used, refer to Fii. 8.
1443
SHINICHIRO
GONDO
60
spontaneous ones probably in the region of ugTgreater than 3 cmlsec. As shown in Fig. 11, an addition of large bubbles clearly lowers the value of ET ‘even to the correlation line of large bubbles when ugT is low. Recently Ohki and Inoue [l] proposed an expansion model to explain the dispersion coefficient at high gas flow rate at which bubbles coalesce into large ones. It is quite interesting to apply their model to our experimental results shown in Fig. 11. They separated the bubble column into two sections, the liquid and the gas section, and introduced an actual dispersion coefficient, ETO, which represents the mixing properties of the turbulent motion of the liquid section, the mixture of small bubbles and liquid, caused by the gas section, that is, the large bubbles. According to their theories, Em is related to the apparent dispersion coefficient ET by the following equation. Em=
(~-ET)~ET.
et al.
(a)
f=
l/IO
60 , ,' .'o ,'
40-
20 60
/ I'*'o ,
w
,
, , ,,,,I
(b) 60-
40 -
I
II
/ ,/ l I' ,I' /' *'
F' *' ,M'O 0,' l.s' I
1111111
(4)
They also showed that Em is given empirically by ET0 = 14 dT.
II
0
f-1/5
20
I
--0*0y 0
(5)
Em was calculated by Eq. (4) and plotted against u,, in Figs. 12a-12e. Ohki and Inoue plotted Em against urrr and showed that ET0 becomes constant independently of uBT,As we thought that l k might be one of the important factors which affect the fluid dynamical characterictics of the liquid section, we used u,, as an abscissa in place of uBTbecause l h depends on uQs. Figures 12a-12e show that ET0 is constant for ugs greater than 1 cm/set and that the values of ET0 decrease as ugS decreases from 1 cmlsec and finally reach that of a liquid free of small bubbles, EL. Here, we will tentatively call the liquid section at EL greater than 0.04 the dispersed liquid section distinguishing from the one at EL less than 0.04 which may adequately be called the liquid-like liquid section. An expansion model appears to be effective for the dispersed liquid section. The average values
-”
(df
, I
e
60
t_
e_------
__---
___--e
--
/
0. I
&s
Fig. 12. Em vs. ugs. dT = 10 cm, h = 200 cm, uI = 0.3 cm/set, countercurrent.
of Em for the dispersed liquid section ranged from 63 to 75 cm2/sec for f from l/10 to 1. The systematic dependencies of ET,, on f were not observed which means that the disturbances caused by the large bubbles already reach a maximum within the range of f used in this investigation. There should be a lower limit inf which can keep Em for the dispersed liquid section unchanged. The values of Em from 63 to 75 cm2/sec are about a half of that estimated
1444
Liquid mixing by large gas bubbles in bubble columns
ET
by Eq. (5). This discrepancy probably comes from the differences in shapes and so in volumes of large bubbles.
En, dT
CONCLUSIONS
Liquid mixing with large gas bubbles was investigated and it was found that the longitudinal dispersion coefficient of liquid phase depends on the column diameter, it is proportional to the square root of the superficial gas velocity, that is, to the square root of the product of jVB and it does not depend on factors such as column height and contacting method of co- or countercurrent. Experiments on liquid mixing with large and small bubbles gave the results that the gas holdup is fairly well explained by the prediction equation which was introduced on the assumption of the additivities of the holdup of small bubbles and that of large ones. The expansion model was applied to the longitudinal dispersion coefficients observed and it was found that the model appears to be effective for the bubble column where the holdup of small bubbles is greater than about 0.04.
f h Pe
ugL uBs ugT u1 V, V Bp V,
Greek symbols E fractional gas holdup
NOTATION a
b E EL Es
E for the large and small bubbles column, cm2/sec actual dispersion coefficient defined by Eq. (4), cmYsec column diameter, cm generating frequency of large bubbles, l/set column height, cm Peclet number, superficial velocity of large bubbles, cmlsec superficial velocity of small bubbles, cmlsec superficial velocity of large and small bubbles, cm/set superficial liquid velocity, cm/set volume of a large bubble measured by volumetric method, cm3 volume of a large bubble measured by photographic method, cm3 rising velocity of large bubbles, cmlsec
diameter of a base of spherical cup, cm maximum thickness of spherical cup, cm longitudinal dispersion coefficient of liquid, cm+ec E for the large bubble column, cm2/sec E for the small bubble column, cm2/sec
eL E for the large bubbles column & E of the large bubbles for the large and small bubbles column E for the small bubbles column 69 d E of the small bubbles for the large and small bubbles column Ed E for the large and small bubbles column 8, dimensionless time of maximum pulse response
REFERENCES [l] OHKI Y. and INOUE H., Chem. Engng Sci. 1970 25 1. [2] DAVIS R. M. andTAYLOR G., hoc. R. Sot. London 1950 200 375. [3] YAGI S. and MIYAUCHI T.,Kagaku Kogaku (Chem. EngngJupan) 1953 17 382.
1445
Engineering
Science.
1973, Vol. 28, pp. 1437-1445.
Pmgamon Press.
Printed in Gnat
Britain
Liquid mixing by large gas bubbles in bubble columns SHINICHIRO
GONDO, SHINBU TANAKA, KAZUYOSHI KAZIKURI and KOICHIRO KUSUNOKI Department of Chemical Engineering, Kyushu University, Fukuoka 8 12, Japan (Received 16 January 1972)
Abstract- Liquid mixing by large gas bubbles of spherical cup was investigated for co- and countercurrent contact of air-water system with bubble columns of 5 and 10 cm dia. The results obtained are that for the column of 5 cm dia., the longitudinal dispersion coefficient ranges from 5 to 20 cm%ec for superficial gas velocity from 0.07 to 8 cm/set and that for the one of 10 cm in diameter it ranges from 9 to 45 cm*/sec for that from 0.035 to 8 cm/set. Liquid mixing under the coexistence of large and small bubbles was also investigated and it was found that the gas holdup was fairly well explained by an equation derived on the assumption that the mixture of small bubbles and liquid behaves independently of large bubbles. The expansion model was applied to the experimental results on the longitudinal dispersion coefficient and it was observed that there should be the lower limit in the holdup of small bubbles where this model can be applied. INTRODUCTION PLENTY
of work on liquid mixing in the bubble column has been reported. The experimental results have been treated as essentially based on an axial mixing model and the longitudinal dispersion coefficients were presented as a function of superficial gas velocity. As easily observed through the wall of a bubble column, when a superficial gas velocity becomes greater than a critical value, bubbles of moderate diameter coalesce intermittently into a bubble of large diameter which rises up the column much faster than the smaller ones. Large gas bubbles spontaneously generated in this way might have an effect on the liquid mixing of bubble column. Ohki and Inoue [ 11have recently reported properties of coalesced bubbles such as passage frequency and rising velocity. They have also proposed an expansion model for the condition where small bubbles coalesce. In this investigation, large bubbles of spherical cup were generated at the bottom of the column through a single nozzle and the liquid mixing was studied by pulse response of a tracer injected at the inlet of the liquid. Further, large bubbles were generated in the bubble column of small bubbles and an additional effect of large bubbles on the liquid mixing was
studied. The method of making large bubbles reported elsewhere is such that once the gas is kept in the hemispherical cup which opens to the bottom of the column and after the cup is filled with gas it is turned over to release a bubble of spherical cup into liquid. Here a single nozzle of 1.5 mm in hole diameter was used to make large bubbles sequentially, because the former method seems not to be convenient for making large bubbles at arbitrary frequencies. EXPERIMENTAL
APPARATUS
The schematic diagram of the experimental apparatus used in this investigation is shown in Fig. 1. Figures 2a and 2b show the location of the nozzles used for making large bubbles. The left halves of Fig. 2a and 2b show the crosssectional view of the bottom structures of the column used for cocurrent contact of gas and liquid, while the right halves show those for countercurrent contact. Figure 2c shows the assembly of nozzle and sparger ring which was used for the measurements of liquid mixing with small and large bubbles in countercurrent contact. The sparger ring which is connected to the bottom plate with four legs, through which gas is supplied, was used for distributing
1437
SHINICHIRO
/ a-
GONDO
et al.
t Water distributor
Garmster
Bubble column
Water storage
/
Fig. 2c. Assembly of nozzle and sparger ring. E, liquid outlet; IL, air inlet for large bubbles; IS, air inlet for small bubbles; L, supporting legs; N, nozzle with pore of 1.5 mm dia.; S, sparger ring with 3 x 32 pores of 0.4 mm dia.
Fig. 1. Experimental flow diagram: countercurrent contact.
small bubbles. The ring is held above the exit port of liquid as shown in Fig. 2c in order that small bubbles will not be carried over by the accelerated flow of liquid. Through the central nozzle shown in Figs. 2a-2c, the air blows out into the liquid making a large bubble of spherical cup about lo-15 cm above the top of the nozzle. The frequencies of generating large bubbles were adjusted by
changing the time interval between opening and closing the electric solenoid valve, the location of which is shown in Fig. 1. The range of the frequencies tested are presented in Table 1. In the experiments with the column of 5 cm in diameter, deionized water was used. City water was used in case of the column of 16 cm in diameter because of the massive use of water. The solution of the sodium chloride was used as a tracer through the experiments.
(b)
(al
Figs. 2a and 2b. Bottom detail: left halves of (a) and (b) were used for cocurrent contact and right halves for countercurrent. E, liquid outlet; I, liquid inlet; N, nozzle with pore of 1.5 mm dia.; P, perforated plate for distributing water.
1438
Liquid mixing by large gas bubbles in bubble columns Table 1. Experimental conditions
4 (cm)
h (cm)
contacting
5
100 200 157 227 100 200 100 200 200 200 200 200
counter counter co co counter counter co co counter co counter co
5 5 5 10 10 10 10 10 10 10 10
temperature:
f
l/S l/5 l/5 l/5 l/2 l/2 l/2 l/2 l/2 l/2 l/2 l/2
l/2.5 1 s/3 l/2.5 1 5/3 l/2.5 1 5/3 l/2.5 15/3 3/10 l/5 l/l0 3/10 l/5 l/10 3110 l/5 l/l0 3/10 l/5 l/l0 l/5 l/IO l/5 l/10 l/5 l/l0 l/5 l/l0
UI
km3
(cmlsec)
7-16 5-7 7-9 10-11 46-76 35-49 47-54 50-53 26-29 27-29 119-132 121-131
OG-1.0 OG-0.7 0.1-1.0 0.1-1.0 0.09-10.6 0.09-0.4 0.0!%0.5 0~09-10.5 t 0.09-0.4 0.1-0.5 I O%-0.4 0.1-0.5 I
Fig. 6
(4)
(1)
(2) (3)
12-22°C
The tracer was injected into the water distributor installed at the top of the column for countercurrent contact or into the bottom, just above the perforated plate, through the four holes located on the concentric circle. The concentration of sodium chloride was measured by a platinum electrode and recorded. LIQUID
VB
Wsec)
MIXING BY LARGE BUBBLES SPHERICAL CUP
OF
The measurements of liquid mixing by large gas bubbles of spherical cup were measured for the columns of 5 and 10 cm dia for co- and countercurrent contact of gas and water. The
frequency of generating large bubbles f tested and the range of bubble volume V, measured are presented in Table 1 for each of columns used. The photographic studies of large bubbles could not correctly reproduce the bubble shape because of the deformation from an ideal shape of spherical cup. Table 2 illustrates the examples of bubble dimensions determined photographically, the bubble volume, VBP, calculated with the dimensions thus obtained under the assumption of completely spherical cup and also the one determined by the volumetric method, V,, where the bubble volume was determined by dividing the volume of gas throughput by
Table 2. Examples of bubble dimensions
4 (cm)
h (cm)
Contacting
5 5 5 5 *5 10 10 10 10 10 10 10
100 200 157 227 100 200 100 200 200 200 200 200
counter counter co co counter counter co co counter co counter co
f
a
b
V BP
Wsec)
(cm)
(cm)
(cm3
l/5 l/5 l/5 l/5 l/l0 l/l0 l/l0 l/10 l/l0 l/l0 l/l0 l/l0
3.0 3.4 3.3 3.3 6.3 5.7 6.0 6.0 4.9 5.2 7.7 6.8
1.9 1.2 1.4 1.6 2.5 2.4 2.0 1.9 1.7 1.5 3.4 3.5
11.0 6.4 7-5 9.1 47.0 38.0 32 31 19 18 loo 86
vs
(cmS) 15.1 6.9 8.4 11.4 46 35 45 50 25 25 124 119
SHINICHIRO
GONDO
the number of bubbles generated. It should be noted that VB thus obtained did not always represent the real volume of a bubble correctly because each bubble was almost always accompanied by smaller bubbles by which a part of gas throughput was consumed. An axial mixing model was used to investigate the liquid mixing by large bubbles. A tracer was injected within a time interval short enough compared to the average residence time of liquid to have an impulse response, and a time of miximum response where an outlet concentration of a tracer injected reaches its maximum was measured. A partial differential material balance equation has been solved analytically by Yagi and Miyauchi[3] for a tracer response. This analytical solution gives the theoretical relation of the time of miximum response and the Peclet number. Therefore, with an observed time of maximum response the Peclet number can be estimated. Figure 3 shows the examples of the response curve observed and the ones calculated with an estimated value of Peclet number. Most of the response curves observed
et al.
were as close to the theoretical ones as those shown in Fig. 3. The coincidence of the experimental and calculated curve seems practical for an axial mixing model to be applied through this investigation since the discrepancies between theories and experiments were almost the same as those observed for the column of small bubbles where an axial mixing model is usually applied. 8,, time of maximum response divided by average residence time of liquid, was correlated almost linearly with flul on a semi-log diagram as shown in Fig. 4, for instance, for the case of
0.6 -
d,=5
2
0.4-
h =200 f
=1/2.5
lJi =0.3
0.2 -
Fig. 4. Dimensionless time of maximum response. h = 200 cm, countercurrent. Countwcurrenf
Fig.
3.
Theoretical and experimental pulse Theory, ------ Experiment.
response.
dT = 5 cm,
countercurrent contact in the column of 5 cm dia. and 200 cm in height. The term flur dessignates the average number of gas bubbles which are encountered by an element of liquid during its movement of unit length along the axis, say 1 cm. When we plot 8, given theoretically for an axial dispersion model as an 1440
Liquid mixing by large gas bubbles in bubble columns
ordinate and natural logarithmic value of the term E,( 1 - QJ/UJI as an abscissa, we can obtain the curve whose slope is almost equal to those of the correlation lines appearing in Fig. 4. Therefore, the following proportionality will hold. flUl m &( 1 -EL) l&h.
O
0 f-l/2 a
3110
0
0
30 e
l/5
0
l/IO
(1) -0
The right side of Eq. (1) can be approximately replaced by EljuJz because lL is much less than unity in the columns of large bubbles. Therefore, when f and h are fixed, EL must be constant for Eq. (1) to hold. Thus EL may not depend on uz. Figures 5a and 5b represent EL against flul for the countercurrent contact in the column of 5 cm dia. and 200 cm in height, and in the
-0-o 20 EL
e e
0
-a-
0
/__1
20 0
0. I
0
0
0 0
-‘to
Fig. 5b. Longitudinal dispersion coefficients of liquid. dT = 10 cm, h = 200 cm, countercurrent.
0
l 0
velocity, uBL,is equivalent to the bubble volume V, multiplied by the frequency f divided by the column cross-sectional area. Figure 6 shows
-..-1 IO -
0
EL
0
f=5/3
0
I
a a
0
"'I
I6
f/U,
0
OP
I
e
l/2.5
0
l/5 I
I I 11111l
__
II
IO f/U1
Fig. Sa. Longitudinal dispersion coefficients of liquid. dT = 5 cm, h = 200 cm, countercurrent. IO EL
one of 10 cm dia and 200 cm in height, respectively. Through the inspections of Fig. 5a, 5b and also the other figures corresponding to these for other experimental conditions which are contained in Table 1, any systematical dependencies of, EL on flu*, that is, on uz for a given value off could not be observed. Thus the average value of EL at a given f was plotted against the superficial gas velocity of large bubbles, ugL, in Fig. 6 for all the experimental conditions investigated. The superficial gas
E 0
IO 2ooco
Fig. 6. Correlations at longitudinal dispersion coefficient of liquid. cu, countercurrent; co, cocurrent. As for the details of V, and other conditions, refer to Table 1.
1441
SHINICHIRO
that EL increases proportionally to the square root of ugL, that is, the square root of V, multiplied by f, and that there is apparent difference in EL between the columns of 5 and 10 cm dia while the column height does not affect EL. It is also shown that the bubble volume V, has no appreciable effect on EL in the correlations presented in Fig. 6 and that differences between co- and countercurrent contact do not exist.
GONDO et al.
were generated, against uIIs. The experiments for the coexistence of small and large bubbles were carried out for the flow rate ratios, ug,Jufl, as shown in Fig. 8 where uBTis the sum of uI and ugs. I
LIQUID MIXING UNDER THE COEXISTENCE OF LARGE AND SMALL BUBBLES.
As described previously, it was one of our interests to study how much the existence of large bubbles effects liquid mixing in the bubble column of small bubbles. The measurements of liquid mixing in countercurrent contact with both small and large bubbles were performed for the column of 10 cm dia at such a superficial gas velocity where the spontaneous coalescence of small bubbles does not take place. ET was estimated by measuring 8, in a similar way to that in the studies on large gas bubbles. Figure 7 represents ls, the void fraction of the bubble observed only when small bubbles
00 0
a
O
o
0 0 0
0 0
0 0
001
0. I
I
I I111111
I I
I I11111 IO
4T
Fig. 8. Feed fraction of large bubbles. dT = 10 cm, h = 200 cm, countercurrent.
The rising velocities of large bubbles of spherical cup VL were measured by photographic examination and ranged from 35 to 48 cmlsec in the case of large bubbles only. These values of VL deviated within f 20 per cent from those calculated by the equation, V, = 20*8V%, reported by Davis er al. [2] where R is the radius of sphere a part of which makes a spherical cup to be treated. Under the condition of coexistence of large and small bubbles, the I’, is found to be accelerated by the rising of small bubbles as shown in Fig. 9, although the experimental points were rather scattered and a clear conclusion could not be reached Ohki and Inoue [ll reported an increase of rising velocity of coalesced bubbles with an increase of superficial gas velocity. As it is the sum of the void fraction of small bubbles and that of large ones, Ed can be represented as follows.
Fig. 7. Gas holdup of small bubbles column. dT= lOcm, h = 200 cm, u1= 0.3 cm/set, countercurrent.
1442
Liquid mixing by large gas bubbles in bubble columns
1:
IO
I
I
I
IllIll
I I
0. I
II 5
4s
Fig. 9. Rising velocity of large bubbles. dT= 10 cm, h = 200 cm, ur= O-3cmlsec, countercurrent. For marks used, refer to Fig. 8.
In Eq. (2), EL and es. are the fractional holdup of the small bubbles and that of the large ones, respectively, which are to be observed in the condition of coexistence of small and large bubbles. ELis equal to udl’, where V,, is the one shown in Fig. 9. In this investigation, ugSwas so low that the spontaneous coalescences of small bubbles did not take place. Therefore, the mixture of small bubbles and liquid behaved almost independently of large bubbles so that the effect of large bubbles on l h may not be large. Therefore, we assumed that l ;1could be replaced by eS(uaS) which is a fractional gas holdup of small bubbles at u,, given by Fig. 7. Then, Eq. (2) can be rewritten to give an estimation equation for lTas follows. (+)ca1=
d%S)
+z.
a
215
e
I
Fig. 10. Predictions of er by Eq. (3). dT = 10 cm, h = 200 cm, uI = O-3cm/set, countercurrent, (e&r: er given by Eq. (3), (Gobs: er observed.
equal to ugs in the former case. In the experiments with small bubbles only, the spontaneous coalescence of bubbles was observed at ugS greater than about 3 cmlsec. Therefore, in the experiments with large and small bubbles, ugT was kept under the critical velocity of 3 cmlsec because an additional effect of the artificial large bubbles on the liquid mixing could not be distinguished from that of the
/O” (3)
Small
bubbles,
o 0 “&$Po bW 1 .9/“p “a. 0 0”” 0 y @ / w ++’ /a - . ,MGLarge bubbles, EL IO 01
I
I
I111111
I I
EL.
Figure 11 shows experimental results on the dispersion coefficient for the existence of small bubbles only, Es, and for the coexistence of large and small bubbles, ET. uor is of course
I/ a’
/o
Iu” 100 -
The observed values of lT are shown against (&al in Fig. 10. The values of (uJV,)/er ranged from 0.007 to O-91. Although (E&~ is slightly larger than the observed values, Eq. (3) appears to be appropriate in predicting lT. The effect of f on Ed does not appear in Fig. 10, which supports the previous discussions on
E, 0/----+-~~~
I
I
I lllll IO
uor Fig. 11. Longitudinal dispersion coefficients of liquid for the coexistence of large and small bubbles. dT = 10 cm, h = 200 cm, ur = 0.3 cmlsec, countercurrent. For marks used, refer to Fii. 8.
1443
SHINICHIRO
GONDO
60
spontaneous ones probably in the region of ugTgreater than 3 cmlsec. As shown in Fig. 11, an addition of large bubbles clearly lowers the value of ET ‘even to the correlation line of large bubbles when ugT is low. Recently Ohki and Inoue [l] proposed an expansion model to explain the dispersion coefficient at high gas flow rate at which bubbles coalesce into large ones. It is quite interesting to apply their model to our experimental results shown in Fig. 11. They separated the bubble column into two sections, the liquid and the gas section, and introduced an actual dispersion coefficient, ETO, which represents the mixing properties of the turbulent motion of the liquid section, the mixture of small bubbles and liquid, caused by the gas section, that is, the large bubbles. According to their theories, Em is related to the apparent dispersion coefficient ET by the following equation. Em=
(~-ET)~ET.
et al.
(a)
f=
l/IO
60 , ,' .'o ,'
40-
20 60
/ I'*'o ,
w
,
, , ,,,,I
(b) 60-
40 -
I
II
/ ,/ l I' ,I' /' *'
F' *' ,M'O 0,' l.s' I
1111111
(4)
They also showed that Em is given empirically by ET0 = 14 dT.
II
0
f-1/5
20
I
--0*0y 0
(5)
Em was calculated by Eq. (4) and plotted against u,, in Figs. 12a-12e. Ohki and Inoue plotted Em against urrr and showed that ET0 becomes constant independently of uBT,As we thought that l k might be one of the important factors which affect the fluid dynamical characterictics of the liquid section, we used u,, as an abscissa in place of uBTbecause l h depends on uQs. Figures 12a-12e show that ET0 is constant for ugs greater than 1 cm/set and that the values of ET0 decrease as ugS decreases from 1 cmlsec and finally reach that of a liquid free of small bubbles, EL. Here, we will tentatively call the liquid section at EL greater than 0.04 the dispersed liquid section distinguishing from the one at EL less than 0.04 which may adequately be called the liquid-like liquid section. An expansion model appears to be effective for the dispersed liquid section. The average values
-”
(df
, I
e
60
t_
e_------
__---
___--e
--
/
0. I
&s
Fig. 12. Em vs. ugs. dT = 10 cm, h = 200 cm, uI = 0.3 cm/set, countercurrent.
of Em for the dispersed liquid section ranged from 63 to 75 cm2/sec for f from l/10 to 1. The systematic dependencies of ET,, on f were not observed which means that the disturbances caused by the large bubbles already reach a maximum within the range of f used in this investigation. There should be a lower limit inf which can keep Em for the dispersed liquid section unchanged. The values of Em from 63 to 75 cm2/sec are about a half of that estimated
1444
Liquid mixing by large gas bubbles in bubble columns
ET
by Eq. (5). This discrepancy probably comes from the differences in shapes and so in volumes of large bubbles.
En, dT
CONCLUSIONS
Liquid mixing with large gas bubbles was investigated and it was found that the longitudinal dispersion coefficient of liquid phase depends on the column diameter, it is proportional to the square root of the superficial gas velocity, that is, to the square root of the product of jVB and it does not depend on factors such as column height and contacting method of co- or countercurrent. Experiments on liquid mixing with large and small bubbles gave the results that the gas holdup is fairly well explained by the prediction equation which was introduced on the assumption of the additivities of the holdup of small bubbles and that of large ones. The expansion model was applied to the longitudinal dispersion coefficients observed and it was found that the model appears to be effective for the bubble column where the holdup of small bubbles is greater than about 0.04.
f h Pe
ugL uBs ugT u1 V, V Bp V,
Greek symbols E fractional gas holdup
NOTATION a
b E EL Es
E for the large and small bubbles column, cm2/sec actual dispersion coefficient defined by Eq. (4), cmYsec column diameter, cm generating frequency of large bubbles, l/set column height, cm Peclet number, superficial velocity of large bubbles, cmlsec superficial velocity of small bubbles, cmlsec superficial velocity of large and small bubbles, cm/set superficial liquid velocity, cm/set volume of a large bubble measured by volumetric method, cm3 volume of a large bubble measured by photographic method, cm3 rising velocity of large bubbles, cmlsec
diameter of a base of spherical cup, cm maximum thickness of spherical cup, cm longitudinal dispersion coefficient of liquid, cm+ec E for the large bubble column, cm2/sec E for the small bubble column, cm2/sec
eL E for the large bubbles column & E of the large bubbles for the large and small bubbles column E for the small bubbles column 69 d E of the small bubbles for the large and small bubbles column Ed E for the large and small bubbles column 8, dimensionless time of maximum pulse response
REFERENCES [l] OHKI Y. and INOUE H., Chem. Engng Sci. 1970 25 1. [2] DAVIS R. M. andTAYLOR G., hoc. R. Sot. London 1950 200 375. [3] YAGI S. and MIYAUCHI T.,Kagaku Kogaku (Chem. EngngJupan) 1953 17 382.
1445