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Effect of Superficial Gas Velocity on Bubble Size Terminal Bubble Rise Velocity and Gas Hold-up in Bubble Columns.

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Effect of Superficial Gas Velocity on
Bubble Size, Terminal Bubble Rise
Velocity and Gas Hold-up in Bubble
Columns
M. Jamialahmadi' and H. MUller-Steinhagen
Deparfment of Chemical and Materials Engineering, The
University of Auckland, Auckland, New Zealand
It is important to have a reliable estimate of bubble size, terminal bubble rise velocity
and gas hold-up in bubble columns, since these parameters are directly related to the
transfer coefficients and the transfer area. Mean bubble diameters have been
measured as a function of the superfwial gas velocity in air-water systems. In the
bubbly flow regime, the bubble size is a strong function of the orifice diameter and
the wettability of the gas distributor and a weak function of superfzcial gas velocity.
In the turbulent churn flow regime this functionality is reversed and the bubble
diameter becomes a strong function of the superfzcial gas velocity. A correlation is
presented which covers both regimes. The terminal bubble rise velocity was measured
as a function of the bubble size and the results were compared with correlations
recommended in the literature. Finally, the gas hold-up was measured over a wide
range of superfzcial gas velocities. The results were compared with a variety of
empirical and theoretical correlations. New equations are presented which predict
gas hold-up of the air-water system with good accuracy.
Introduction
Gas hold-up is one of the most important parameters characterizing the
hydrodynamics of bubble columns. It is defined as the fraction of the total volume
of the system occupied by the gas bubbles. Gas hold-up has two main effects on
the performance of bubble columns: (i) the gas hold-up provides the volume
fraction of the phases present in the system and hence their residence time; (ii) the
gas hold-up in conjunction with the knowledge of the mean bubble diameter
allows the determination of the gas-liquid interfacial area and, therefore, leads to
the mass and heat transfer rates between the two phases.
A large number of correlations for the prediction of gas hold-up can be found
in the literature (see Shah et a1.,1982), this is partly due to the large scatter in the
reported data. These correlations can be classified into two broad categories:
empirical correlations, and theoretical or semi-theoretical correlations. Some of
the well-known empirical correlations which have been developed based on
* To whom correspondence should be addressed
Developments in Chemical Engineering, Vol. 1, No 1, page 16
EfSect of Supeflicial Gas Velocity on Bubbles
17
Table 1 Published empirical gas hold-up correlations.
Reference
Range of Parameters
Correlations
ProDosed
Akita and Yoshida
(1973)
H: 1.26-3.5 m
Hikita et al.
(1980)
UmO: 0.042-0.38
n,. 0.1 m
H: 0.65 m
Mersmann (1987)
Ranges are not
defined
Bach and Pilhofer
(1987)
Ua0:
mfs
(3)
6-0.1 m f s
n,. >o.i m
HI >1.2 m
Table 2 Published theoretical gas hold-up correlations.
Correlations Proposed
Reference
Bridge et a1.(1964)
u, = v, ( 1 - EG
t3-1
(5)
where n-2.39 for air-water
system
Lockett and Kirkpatrick
(1975)
Wallis (1961)
U,=U,, ( 1- E ~ l.''
)
( 1 +2.556:)
(6)
v, = v, ( 1 - Eo) Q - 1
(7)
where n=2 for small bubbles
and n=0 for large bubbles
Marrucci (1965)
V*( 1 - € J
=
5
(8)
1-E2
Turner (1966)
Davidson and Harrison (1966)
=
'b
u , =1u-E0b
(9)
(10)
18
M.Jamialahmadi and H. Muller-Steinhagen
numerous experimental data are summarized in Table 1. The Akita and Yoshida
(1973) correlation is often recommended. Most recently Ogino et al. (1991) used
this correlation with moderate success to predict the gas hold-up in their study of
gas-phase heat transfer coefficients in bubble columns. The correlation proposed
by Mersmann (1980) is similar to that reported by Akita and Yoshida (1973). The
Correlation proposed by Bach and Pilhofer (1987) predicts the hold-up for pure
liquids but is not recommended for mixtures and electrolyte solutions. Only the
analysis of Hikita er al. (1987) includes the physico-chemical properties of the gas
phase. The small exponent of the gas properties in their correlation indicates,
however, that this dependency is weak.
A widely accepted fundamental model for the theoretical treatment of the gas
hold-up in bubble columns based on the slip velocity has been proposed by
Lapidus and Elgin (1957). They showed that the slip velocity is a function of both
the terminal bubble rise velocity of a single bubble, and of the hindering effect of
neighbouring bubbles which can be expressed as a function of the gas hold-up.
Various researchers have proposed different functions for the dependency of the
slip velocity on the bubble rising velocity and the gas hold-up. Some of these
correlations for the slip velocity are summarized in Table 2.
The aim of the present work was to investigate the effect of superficial gas
velocity on bubble size and terminal bubble rise velocity in a two dimensional
bubble column. These results have then been used to develop a correlation for the
gas hold-up in a cylindrical column. Finally, the effect of the orifice diameter of
the gas distributor plate and its wettability on the stability of the bubbly flow
regime have been investigated.
Apparatus and Experimental Method
Experiments were carried out in two different columns, using air and water at
ambient temperature and atmospheric pressure.
Two-dimensional column
Most of the bubble size and bubble rise velocity measurements were performed in
a two dimensional column ( 5 cm x 30 cm x 150 cm), as this was convenient for
visual and photographic observations. The column was made from perspex and
was open to atmosphere at the top. A wide range of bubble sizes could be obtained
by using a variety of orifices mounted in the base plate of the column.
Aeration was carried out over several hours to ensure that the water was
saturated with air before any measurements were recorded. A microprocessor
controlled camera and video equipment were used to record bubble formation in
the vicinity of the gas distributor, and the bubble rising velocity in the liquid
phase. The mean bubble diameter was calculated from the average bubble volume.
Non-spherical bubbles were assumed to be oblate spheroids.
Three-dimensional column
Additional experimental studies were carried out in a cylindrical bubble column
of 10.5 cm diameter and 180 cm height. Mains water was pumped directly into
the bottom of the column while a controlled air flow passed through a flow
distributor. This consisted of a circular plate in which 1 mm diameter holes were
drilled on a 18 mm triangular pitch. The gas hold-up was measured by the bed
expansion method. Experimental set-up and procedure are described in more
detail elsewhere (Jamialahmadi and Miiller- Steinhagen, 1989).
19
Efect of Superficial Gas Velocity on Bubbles
2.5
(Air-Wated
( A Kataoka et al., 19791
* Koide e t al., 1979
Saxena et al., 1990
E
u 2 rn Deckwer et al., 1978
n
n
-0
W
-
L
$ 1.5
*
E
.-
0
D
-a ,
1
l3
n
3
m
0.5
.......... Akita and Yoshida
correlation, 19 74
Equation (16)
n
U
I
0
2
I
I
6
Gas Velocity
4
I
a
I
10
I
12
14
( uSgI c m / s )
Figure 1 Bubble diameter as a function of the superficial gas velocity.
Comparison between measured data and values calculated according to Akita and
Yoshida (1974) and equation (16).
Results and Discussion
Bubble size distribution
The work of Satterfield and Huff (1981) and Ogino et al. (1991) demonstrates the
importance of precise knowledge of the bubble size which is used to establish the
mass and heat transfer resistances in bubble columns. Saxena el al. (1986)
discussed the conflicting results which can arise i n the absence of such
information.
Based on their experimental data, Akita and Yoshida (1974) proposed the
following correlation for the estimation of bubble size as a function of the gas
velocity and the physical properties of the system:
In Figure 1, measured average bubble diameters are compared with values
predicted from equation (1 I ) and with the experimental results reported by
Kataoka et al. (1979), Koide et al. (1979), Saxena et al. (1990) and Deckwer
20
M. Jamialahmadi and H. Miiller-Steinhagen
et al. (1978). This figure clearly demonstrates that equation (1 1) predicts a
gradual reduction in bubble size with increasing gas velocity which contradicts
almost all experimental observations (Kumar and Kuloor, 1970; Datta and Napier,
1950; Mashelkar, 1970; Schiigerl et al., 1977; Jamialahmadi and
Miiller-Steinhagen, 1989). Therefore, application of the Akita and Yoshida
correlation should be limited to single orifice spargers (Shah e? al., 1982).
Fair (1967) reported data for air-water systems, concluding that the maximum
bubble size was 2.7 cm with the majority of bubbles being between 0.2 cm and
1.6 cm in diameter. Bubble sizes observed in the present study are within this
range.
Correlation for average bubble diameter
The simplest mechanism of bubble formation is when the bubble is formed very
slowly at the open end of an orifice immersed horizontally in water. The bubble
grows until its buoyancy forces exceed the surface tension forces holding it on the
orifice tip. A succession of bubbles break away from the solid-liquid-gas interface
and travel as separate entities in the liquid. If the bubbles are assumed to be
spherical and the orifice is perfectly wetted by the liquid, the following equation
can be derived by equating the two forces:
For air and water at 20°C, CJ = 0.07274 N/m and ( p -~ PG) = 997 kg m-3. Hence:
-
-1
db, 0.036d:
with dbl and do in metres.
For a 1 mm diameter orifice, a bubble diameter of 3.6 mm is predicted. This
value is in good agreement with most experimental results reported by different
researchers for the bubbly flow regime as well as with the results observed in this
investigation.
Bubble size measurements reported by various investigators (Jamialahmadi
and Miiller-Steinhagen, 1989; Fair, 1967.; Leibson et a1.,1956; Smith et al., 1986)
indicate that at higher gas velocities larger bubbles are formed at the orifice or in
the vicinity of the distributor, and equation (12) is no longer valid. In the turbulent
churn flow regime, the bubble diameter is mainly influenced by the superficial gas
velocity and by the gas hold-up, as given by:
21
EfSect of Superjicial Gas Velocity on Bubbles
Values of the constant K and exponents a and b are calculated from regression
analysis of the experimental data obtained for the turbulent churn regime. For a
water/air mixture at 20°C:
Therefore, the bubble size for superficial gas velocities ranging from
0-12 cm s-' can be calculated for the air-water system, by combining
equations (13) and (15) to give the following expression:
The values predicted from equation (16) are also plotted in Figure 1 showing
the reliability of this equation for air-water systems at 20°C.
Terminal rise velocity of single bubbles
Shah ef al. (1982), and Godbole and Shah (1986) in their review paper on the
estimation of design parameters for bubble column reactors, recommended that
the bubble rise velocity is calculated from the Clift et al. (1978) correlation:
Uh-
M-0*140(J-0.857)
f' Ldb
where:
J-0.94h0-747
for
2qhi59.3
J- 3.42 h0Su1
for
h > 69.3
and
where
(19)
M. Jamialahmadi and H. Miiller-Steinhagen
22
70
n
v)
\
U 60
E
I
I
W
h
.-w
2: 50
Q,
>
g
.-
40
CSI Bryn, 1933
CK
0 Datta et al, 1950
-
*
o 30
.-C
Gorodetskaya, 1949
0 Haberman and Morton, 1956
E
b
-
-I
..........................................
20
4) O'Erien and Gosline, 1935
Q,
23
10
a3
Rosenberg, 1950
A
0
2
0
4
a
6
Bubble Diameter ( d b , c m )
Figure 2 Measured and predicted values of the terminal bubble rise velocity as
function of the bubble diameter.
0.25
0.2
a
3
1 0.15
22
0
I
0
0.1
c3
0.05
0
1
2
6
4
8
10
12
Gas Velocity ( u s g c m / s )
f
Figure 3 Gas hold-up as a function o the superjkial gas velocity (for
experimental values, lJ
=,
0.05
, cm s- ).
14
23
EfSect of Superficial Gas Velocity on Bubbles
v)
2300
-
E
V
-
z250
C
a,
.-
U
+
200
-
150
-
100
-
a,
0
t
.-0
2
b,
Q
.-v)
n 50I
0
I
I
I
4
6
8
I
12
10
Figure 4 Dispersion coeflcient as a function of the superjkial gas velocity.
0.25
lUsl = 0.05 crn/sl
0.2
-
1 0.15
-
Q
3
U
0
I
0
0.1
-
c3
Orifice d i a m e t e r
A
0.05 c m
o 0.10 cm
17 0.15 cm
I
0
2
I
4
I
6
I
I
8
Gas Velocity ( Usg
Figure 5 Effect of orifice diameter on gas hold-up.
I
12
10
I
cm/s
)
14
24
M.Jamialahmadi and H. Miiller-Steinhagen
and
Jamialahmadi et al. (1991) developed the following correlation for the
terminal bubble rise velocity, based on the wave analogy:
where
and
In Figure 2, measured terminal bubble rise velocities of air bubbles in water
as reported in the literature (Rosenberg, 1950; Bryn, 1933; Gorodetskaya, 1949;
Datta, 1950; Habermann, 1956; O'Brien, 1935; Peebles and Garber, 1953) are
compared with values calculated according to Clift et al. (1978) and Jamialahmadi
etal. (1991). Small bubbles behave like rigid spheres and follow Stokes law,
while large bubbles are prone to surface oscillations. Between these two regions
is a transition regime, where the shape of the bubble changes from sphere to cap.
Figure 2 clearly shows that most reported bubble rise velocities are larger than
the values predicted by the Clift et al. model (1978), and it is fair to conclude that
equation (23) predicts the observed trends considerably better. This conclusion is
especially true for bubble sizes ranging from 0.5 cm to 3 cm which are commonly
observed in bubble columns. The Clift correlation may be applied with good
accuracy for bubble diameters below 0.5 cm.
25
EfSect of Superficial Gas Velocity on Bubbles
0.25
0.2
LUsl = 0.05 cm/sl
.
Q
3
1 0.15
E
0
I
0
0.1
'
c3
0
0
0
0 Nylon gas distributor plate
0 Teflon gas distributor plate
I
I
I
2
4
6
I
Gas Velocity
Flguk-e 6 E'ect
I
I
a
10
( usglcm/s)
12
14
of orrfice plute material on the gas hold-up.
0.7
pFwzZ
: Experiment
( 1 ) : Bridge et al., 1964
0.6 ( 2 ) : Lockett ,and
Kirkpatrick, 1975
( 3 ) :Wallis, 1961
(4
) . . I . .
(3)
0.5
Q
(5 ). ...-"'
3
I 0.4
/-
0
I
*.--'
,/*
,.*-
@>...-
_.-.___.-.
,_.-.-._.-.
m 0.3
0
c3
0.2
0
. o
0
0.1
0
I
1
I
I
I
2
4
6
8
10
Gas Velocity ( Usg , c m / s )
Figure 7 Measured and calculated eflect of supe@cial gas velocity on the gas
hold-up: semi-theoretical correlations.
12
26
M.Jamialahmadi and H. Miiller-Steinhagen
Gas hold-up and liquid phase back-mixing
Figures 3 and 4 show the effect of superficial gas velocity on the gas hold-up and
on the liquid-phase dispersion coefficient measured at the side of the column. The
observations are in good agreement with the results of other investigations (Argo
and Cova, 1965; Siemes and Weiss, 1957; Habil, 1972; Kunugita et al., 1970;
Ostergaard, 1978; Aoyama et al., 1968). Three regions can be clearly identified,
namely bubbly flow (Us < 0-4 cm s-I), a transition region (Us < 4-6 cm s-I),
and the churn turbulent #ow regime (Usg > 6 cm s-'). In the bubby flow regime,
the bubbles detaching from the gas distributor are uniform in size and ascend
through the liquid phase without significant collision or coalescence. Since the
bubbles do not transport a large volume of liquid upwards, the extent of liquid
back-mixing is low in this regime.
In the churn turbulent flow regime, bubbles coalesce within a few centimetres
of the gas distributor and form large bubbles. These bubbles ascend at the centre
of the column along a wave-like path and carry a considerable amount of liquid
in their wakes. When the large bubbles leave the system, the liquid in their wake
moves downwards at the sides of the column, forming "multiple mixing cells"
(Chen et al., 1989), intensifying the liquid phase back-mixing.
Wide discrepancies have been reported between the experimental results and
some empirical correlations for gas hold-up as indicated in Figure 3. The
deviations in the bubbly flow regime occur mainly because this regime is unstable
(Hills, 1976; Lockett and Kirkpatrick, 1975).
The bubbly flow regime is created by ensuring a uniform dispersion of small
equi-sized bubbles from the gas distributor into the liquid phase. According to
Figure 1 and equation (12), the bubble diameter in the bubbly flow regime is a
strong function of the gas distributor orifice diameter, the interfacial tension
between the gas and the liquid phase, and the wettability of the gas distributor.
Figure 5 shows the effect of gas distributor orifice diameter on the gas hold-up.
In the bubbly flow regime, decreasing the hole diameter of the gas distributor
reduced the bubble size and therefore, increased the gas hold-up. It has been
reported that a decrease in surface tension reduces the bubble size and therefore,
increases the gas hold-up (Schiigerl et al., 1977; Jamialahmadi and
MUller-Steinhagen, 1990).
While a considerable amount of work has been done on the effect of surface
wettability on the bubble size under pool boiling conditions (see
Miiller-Steinhagen and Jamialahmadi, 1990) hardly any information can be found
for bubble columns. Figure 6 shows the effect of the gas distributor material for
plates made from nylon and teflon. In the bubbly flow regime, a bubble size of
about 4.0 mm was observed on the teflon gas distributor which is known to be
non-wettable. With the highly wettable nylon distributor, bubbles of about 3.4 mm
diameter were observed. Therefore, a higher gas hold-up would be expected for
nylon plates.
The stability of the bubbly flow regime can also be improved by either
increasing the operational pressure (Oyevaar et al., 1989), by filling the column
with a few centimetres of packing (Abraham and Sawant, 1990), or by using radial
baffling (Fair et al., 1962; Jamialahmadi and MUller-Steinhagen, 1991).
Experimental scatter due to flow instability is usually reduced at higher gas
velocities where uniform bubbling can not occur.
27
Ejyrect of Superficial Gas Velocity on Bubbles
0.25
0.2
(1
3
I 0.15
-0
r
.o
0
0.1
c3
0.05
0
0
2
4
6
Gas Velocity
a
( usg '
cm/s)
10
12
14
Figure 8 Measured and calculated effecr of supeficial gas velociry on the gas
hold-up: equations (28) and (30).
Correlation for gas hold-up
The theoretical approach of correlating gas hold-up as a function of superficial gas
and liquid velocities assumes that the gas bubbles are rising, relative to the liquid
surrounding them, at a velocity called the slip velocity (Lapidus and Elgin, 1957).
where:
It is usually assumed that:
where Ub is the terminal rise velocity of single bubbles, and f(&G) is the hindering
effect of neighbouring bubbles expressed as a function of the voidage.
Functions for the dependence of the slip velocity on the gas hold-up and the
bubble rise velocity are summarized in Table 2. Gas hold-up predicted from these
M. Jamialahmadi and H. Miiller-Steinhagen
28
functions is compared with experimental results in Figure 7. Obviously, the
correlations suggested by Bridge er al. (1964), Lockett and Kirkpatrick (1975),
Wallis, (1961), Marrucci (1965) and Turner (1966) redict gas hold-up
satisfactorily only up to gas velocities of about 2 cm s- . The Davidson and
Harrison (1966) equation is valid up to a gas velocity of 5 cm s-'. None of these
functions predict the gas hold-up for the churn turbulent flow regime
satisfactorily. This result may be expected because the theoretical derivation of
these equations generally assumed that bubble size and bubble terminal rise
velocity remain constant as the gas velocity increases. A better correlation may be
obtained if the variations of bubble size and terminal bubble rise velocity with gas
velocity are also taken into account. This is accomplished by fitting the
experimental results to the general form of the Davidson and Harrison (1966)
correlation:
P
It is assumed that db and Ub vary according to equations (16) and (23),
respectively. Non-linear regression analysis of the experimental results
determined n = 2.184 to fit the experimental results.
A more practical correlation is obtained by assuming that the slip velocity
changes with bubble rise velocity and gas hold-up according to:
Regression analysis yields:
-
Us 0.23+ 4eY2
The terminal bubble rise velocity is 0.23 m s-' for a bubble with a diameter of
about 0.4 cm, which is the average bubble size observed for the bubbly flow
regime in this study. Equation (30) is similar to the empirical correlation
developed by Hill (1976) for looped bubble column reactors with liquid velocities
below 30 cm s-'. Experimental data are compared with the values predicted from
equations (28) and (30) in Figure 8, both correlations predict the gas hold-up for
air and water at 2OoC satisfactorily. However, the variations of bubble size and
terminal bubble rise velocity with superficial gas velocity are required in order to
obtain the gas hold-up from equation (28), while no such information is needed if
equation (30) is used.
Conclusions
Measurements of bubble rise velocity, bubble diameter and gas hold-up in bubble
columns have been presented for the aidwater system at 2OOC. The measured data
Effect of Superjiicial Gas Velocity on Bubbles
29
have been compared with appropriate correlations from the literature,
demonstrating a poor understanding of the effect of process conditions on average
bubble diameter and gas hold-up. Correlations presented reproduce the measured
trends well, but need to be extended to apply for other process liquids.
Nomenclature
dbl
dbt
db
do
Dc
Eo
g
h
H
J
K
M
b'
US
mean bubble diameter at low gas velocities (m)
mean bubble diameter in churn turbulent regime (m)
mean bubble diameter calculated from equation (16) (m)
orifice diameter (m)
column diameter (m)
Eotvos number, defined in equation (22)
gravitational constant (m s - ~ )
variable defined in equation (21)
column height (m)
variable defined in equations (1 9) and (20)
constant of equation (14)
variable defined in equation (1 8)
terminal bubble rising velocity (m s-l)
slip velocity (m s-')
superficial gas velocity (m s-1)
superficial liquid velocity (m s-')
Greek Symbols
pG
pL
vL
.sG
pG
PL
(3
viscosity of the gas phase (kg m-' s-')
viscosity of the liquid phase (kg m-' s-')
kinematic viscosity of the liquid phase (m2 s-I)
gas hold up
density of the gas phase (kg mP3)
density of the liquid phase (kg w3)
surface tension (N m-*)
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Received: 4 October; Accepted: 5 February 1992
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