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Efficiency of non-reactive isothermal bubble column based on mass transfer.

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ASIA-PACIFIC JOURNAL OF CHEMICAL ENGINEERING
Asia-Pac. J. Chem. Eng. 2008; 3: 440–451
Published online 23 July 2008 in Wiley InterScience
(www.interscience.wiley.com) DOI:10.1002/apj.164
Research Article
Efficiency of non-reactive isothermal bubble column based
on mass transfer
Subrata Kumar Majumder*
Assistant Professor, Department of Chemical Engineering, Indian Institute of Technology Guwahati, Guwahati, India
Received 19 April 2008; Revised 3 June 2008; Accepted 5 June 2008
ABSTRACT: Bubble column reactor as a gas–liquid contactor is extensively used in the chemical and biochemical
industries. Mass transfer coefficients governing the transport processes in bubble contactors are a growing concern in
chemical and biotechnological processes whose rates are often limited by the mass transfer rate. The influences of
different physical, dynamic and geometric variables affect the efficiency characterization of the equipment which are
involved in gas/liquid mass transfer processes. This characterization has great importance to optimize the process plant
design. In this article, efficiency of two-phase mass transfer in bubble column reactors has been analyzed based on
dynamic, geometric and physical variables of the system. An empirical correlation for mass transfer efficiency has also
been developed in terms of those variables. The present analysis on the gas–liquid mass transfer efficiency of bubble
column may give insight into a further understanding and modeling of multiphase reactors in industrial applications.
 2008 Curtin University of Technology and John Wiley & Sons, Ltd.
KEYWORDS: bubble column; mass transfer efficiency; transfer coefficient; mixing intensity; interfacial area;
gas–liquid flow
INTRODUCTION
Bubble columns are intensively used as multiphase
contactors and reactors in chemical, biochemical and
petrochemical industries. In biochemical industries bubble columns are used as bioreactors in which microorganisms are utilized in order to produce industrially
valuable products such as enzymes, proteins, antibiotics
etc. Bubble column reactors owe their wide application area to a number of advantages they provide both
in design and operation as compared to other reactors.
They have excellent heat and mass transfer characteristics, meaning high heat and mass transfer coefficients.
Little maintenance and low operating costs are required
due to lack of moving parts and compactness. Owing
to their industrial importance and wide application area,
the design and scale-up of bubble column reactors and
investigation of important hydrodynamic and operational parameters characterizing their operation have
gained considerable attention during the past 20 years.
Recent research with bubble columns frequently focuses
on the following topics: gas holdup studies,[1 – 7] bubble characteristics,[8 – 11] flow regime investigations and
*Correspondence to: Subrata Kumar Majumder, Assistant Professor, Department of Chemical Engineering, Indian Institute of Technology Guwahati, Guwahati 781039, India.
E-mail: skmaju@iitg.ernet.in
 2008 Curtin University of Technology and John Wiley & Sons, Ltd.
computational fluid dynamics studies,[12 – 14] and mass
transfer studies.[15 – 17] The effects of column dimensions, column internal design, operating conditions, i.e.
pressure and temperature,[18,19] the effect of superficial
gas velocity, solid type, and concentration are commonly investigated in these studies. Many experimental
studies have been directed towards the quantification of
the effects that operating conditions, physical properties and column dimensions have on the performance
of bubble columns. Although a tremendous number of
studies exist in the literature, bubble columns are still
not well understood due to the fact that most of these
studies are often oriented on only one phase, i.e. either
liquid or gas.Research is still being conducted on the
hydrodynamics of the bubble column due to its wide
application in chemical, biochemical and petrochemical
industries. Bubble columns are preferred for gas–liquid
processes that take place in the absorption regime with
slow reaction, although they may be used for fast reactions too, especially if they offer special features such
as good heat removal rates or simplicity of construction. To determine the efficiency of a bubble column
based on mass transfer, the knowledge of the extent of
mass transfer is required. Literature provides information on the mass transfer coefficient for a large number
of material systems. The definition of concentration difference within the reactor becomes very important when
calculating mass transfer coefficient from the measured
Asia-Pacific Journal of Chemical Engineering
EFFICIENCY OF NON-REACTIVE ISOTHERMAL BUBBLE COLUMN
absorption rates or from the values characterizing the
concentration of components passing through the reactor. This is because of concentration difference which is
a function of various hydrodynamic factors. However,
the studies of efficiency of bubble column based on
mass transfer are meager. The objective of this work
is to analyze the mass transfer efficiency of a bubble
column with 18 different systems in terms of dynamic,
geometric and physical variables of the system. A general correlation has also been developed with different
variables within the range of minimum to maximum
operating variables available in the literature.
THEORETICAL BACKGROUND
Consider a bubble column operating with a gas and
a liquid where the gas is flowing homogeneously and
concurrently in the flow of continuous liquid without
reaction as a dispersed phase of bubble. The schematic
flow diagram is illustrated in Fig. 1. The effective
volume of the bubble column reactor for mass transfer
having a gas–liquid mixture height of hm is divided
axially into a series of segments at h1 , h2 , h3 , . . . , hi
from the distribution source of the gas. Assume that the
gas leaving from each axial segment hi is in equilibrium
with the liquid with respect to both heat and mass
transfer. Consider the liquid flows at the rate Ql m3 /s.
The interfacial surface area between gas and liquid is
a m2 per unit volume of the gas–liquid mixture. As
the gas–liquid mixture rises to a differential height dh,
the area of contact is adh per unit active area of the
column. If the solute undergoes a concentration change
dCl at this gas–liquid mixture height (dhi ), the solute
balance can be represented as:
∗
Ql dCl,hi = Ac kl adhi (Cl,h
− Cl,hi )
i
(1)
Then,
cl,hi
cl,hi −1
Ac kl a
dCl,hi
=
∗
Cl,hi − Cl,hi
Ql
hi
dhi
Pt = Patm + ρl ghi + 4σ/db
Cl,hi − Cl,hi −1
kl a(hi − hi −1 )
= 1 − exp −
∗
Cl,h
− Cl,hi −1
usl
i
where Patm is the atmospheric pressure above the liquid
and σ is the surface tension.
The dimensionless distance, hR,i represents hi /hm .
ρl g(1 − εg )hm
(1 − εg )
=
Pt
PR + hR,i + Pb,R
(7)
where, PR = Patm /(ρl ghm ), Pb,R = 4σ/(ρl ghm db )
If the gas phase molar fraction is constant, Eqn (4)
becomes
(3)
The saturation concentration in liquid phase, Cl∗ , a
function of height in tall bubble columns:
(4)
∗
=
Cl,h
i
yPt [1 + α(1 − hR,i )]
H
(5)
 2008 Curtin University of Technology and John Wiley & Sons, Ltd.
(8)
Since the saturation concentration and the solute
concentration in the liquid at various axial locations
of the column may differ, the local efficiency of mass
transfer at a particular axial distance from the gas
distributor can be defined as:
In which
PhRi = Pt [1 + α(1 − hR,i )]
(6)
(2)
hi −1
PhRi yhRi
H
where α represents the ratio between the hydrostatic
pressure (at the gas distributor) and the total internal
column pressure Pt . The total internal column pressure
Pt at any distance hi below the surface is
α=
This gives
∗
=
Cl,h
i
Figure 1. Schematic
flow diagram of a
bubble column.
ηhhii −1 =
Cl,hi − Cl,hi −1
∗
Cl,h
− Cl,hi −1
i
(9)
Asia-Pac. J. Chem. Eng. 2008; 3: 440–451
DOI: 10.1002/apj
441
442
S. K. MAJUMDER
Asia-Pacific Journal of Chemical Engineering
The local efficiency is then represented with the
Eqn (3) as:
Cl,hi − Cl,hi −1
kl a(hi − hi −1 )
= 1 − exp[−
]
∗
Cl,hi − Cl,hi −1
usl
(10)
The Eqn (10) gives the efficiency of the bubble
column for mass transfer up to the height of gas–liquid
mixture hi . The equation also gives the imminent mass
transfer efficiency with respect to the column height.
If the bulk average concentration of the liquid at inlet
and outlet are Cl,in and Cl,out respectively, the mass
transfer efficiency of the entire column is defined as
ηhhii −1 =
ηBC =
Cl,hi =hm − Cl,in
kl ahm
= 1 − exp[−
]
∗
Cl,hi =hm − Cl,in
usl
(11)
∗
where Cl,h
is in equilibrium with Cg,hi . The relationship
i
between ηhhii −1 and ηBC can then be derived by integrating
the local ηhhii −1 for the entire column of gas–liquid
mixing height hm . The mass transfer efficiency of the
entire column depends on the degree of mixing of gas
and liquid: (1) if the liquid in the column is completely
backmixed everywhere with uniform concentration,
Cl,hi and the gas entering the segment hi is perfectly
mixed, ηhhii −1 = ηBC (2) if the movement of the liquid is
in plug flow with no mixing, while the gas entering the
segment hi is perfectly mixed, according to Kister’s
concept[20] the mass transfer efficiency of the entire
column can be represented as
ηBC =
Cl,hi =hm − Cl,in
PhRi
=
∗
Cl,h
−
C
HQ
l,in
R
i =hm
hi
HQR ηhi −1
exp
−1
PhRi
specific gas–liquid interfacial area is related to the gas
holdup, εg and the Sauter-mean bubble diameter, ds by
a=
6εg
ds
(13)
Thus, a precise knowledge of the gas holdup and
bubble size distribution is needed to determine the specific gas–liquid interfacial area. In gas–liquid reactors,
mass transfer from the gas to the liquid phase is the
most important goal of the process. The volumetric
mass transfer coefficient is a key parameter in the characterization and design of both industrial, stirred and
nonstirred gas–liquid reactors.[23 – 27] Ozturk et al .[26]
studied the mass transfer coefficient in alcohols, glycol
solution and various organic liquids. They compared
their results with the correlations developed by Akita
and Yoshida[23] and Hikita et al .[28] at superficial gas
velocity more than 0.01 m/s. They reported that using
the original form of the correlations gave a better fit if
a modification factor was allowed for the correlations
with a slightly smaller error. Even if modified by an
optimized factor, the literature correlations describe the
data with mean errors exceeding 20%. Ozturk et al .[26]
modified the Akita and Yoshida[23] correlation by considering the density ratio of the phases as:
Sh = 0.62Sc 0.50 Bo 0.33 Ga 0.29 Fr 0.68 (ρg /ρl )0.04
(14)
The dimensionless numbers were varied in the following ranges:
1.6 × 101 ≤ Sh ≤ 9.7 × 102 ; 3.2 × 101 ≤ Sc
≤ 1.5 × 105 ; 1.6 × 100 ≤ Bo ≤ 5.4 × 100 ;
(12)
(3) if the entering gas is well mixed but the liquid is
only partially mixed as per concept of Gerster et al .,[21]
the ratio of ηBC to ηhhii −1 is a function of dispersion
number of liquid, gas to liquid flow ratio and the axial
equilibrium distribution; (4) if both gas and liquid are
only partially mixed, as per Bennet’s[22] concept of
gas dispersion in liquid, the mass transfer efficiency
of the entire column may be a function of mixing
characteristic which depends on geometric, dynamic
and physical variables of the system. A correlation has
been developed by dimensional analysis to analyze the
efficiency of mass transfer for the entire column in terms
of physical, dynamic and geometric variables of the
system. The overall mass transfer rate per unit volume
of the dispersion in a bubble column is governed by the
liquid side mass transfer coefficient, kl a assuming that
the gas side resistance is negligible. In a bubble column
reactor the variation in kl a is primarily due to variations
in the interfacial area. Assuming spherical bubbles, the
 2008 Curtin University of Technology and John Wiley & Sons, Ltd.
8.3 × 102 ≤ Ga ≤ 1.5 × 106 ; 4.3 × 10−2 ≤ Fr
≤ 6.0 × 10−1 ; 9.3 × 10−5 ≤ ρg /ρl ≤ 2.0 × 10−3
The surface-to-volume mean bubble diameters ds
rather than the column diameter are used as the characteristic length, because even in highly viscous media
where coalescence to large bubbles and gas slug occurs,
the column diameter has little influence on kl a.[29] In
this study the Sauter-mean bubble diameter ds was calculated from the correlation developed by Wilkinson
et al .[30] as:
u µ −0.04
gρl ds2
sg l
= 8.8
σ
σ
σ 3 ρl
gµ4l
−0.12 ρl
ρg
0.22
(15)
The Sauter-mean bubble diameter may vary under
the axial pressure and the room temperature. Therefore
corrections for pressure and temperature of the Sautermean bubble diameter have to be made. The Sautermean bubble size is corrected at standard conditions
Asia-Pac. J. Chem. Eng. 2008; 3: 440–451
DOI: 10.1002/apj
 2008 Curtin University of Technology and John Wiley & Sons, Ltd.
18
1203
2.02
38.1
1.63
17
863
0.63
28.4
3.63
16
866
0.58
28.5
3.83
15
1000
1.01
72.7
2.1
14
785
2.42
21.1
1.44
13
790
0.586
22.2
3.81
12
1033
1.303
32.2
1.97
11
1234
0.82
29.7
2.67
Keys for systems
ρl (kg/m3 )
µl (10−3 Pas)
σ (10−3 N/m)
Dl (O2 ) (10−3 m2 /s)
Nitrobenzene-air
Xylene-air
Toluene-air
Tap water-air
2-Propanol-air
Methanol-air
1,2-Dichloro ethane-air
2
1022
4.4
43.5
0.97
Systems
1,4-Dioxane-air
9
900
0.461
23.5
3.46
8
884
2.66
32.5
1.60
7
778
0.977
24.8
3.29
6
791
1.19
22.1
2.37
5
793
1.24
22.1
2.37
Ethanol
(99%)–air
Ethanol
(96%)–air
1-Butanol–
air
Benzeneair
1
790
0.327
23.1
5.85
Several authors[17,35 – 37] reported that the sparger design
significantly affects the hydrodynamics and gas holdup
Keys for systems
ρl (kg/m3 )
µl (10−3 Pas)
σ (10−3 N/m)
Dl (O2 ) (10−3 m2 /s)
Effect of distributor on mass transfer
efficiency of the bubble column
Aniline–
air
The influence of the operating variables on the mass
transfer efficiency in a gas–liquid system is a strong
incentive in bubble columns. In fact the reported studies
on mass transfer efficiency of bubble columns under
different conditions in different gas–liquid contactors
diverge. In this present study, the effects of different
operating variables on the mass transfer efficiency of a
bubble column in homogeneous flow conditions have
been discussed as follows:
Acetone–
air
RESULTS AND ANALYSIS
Table 1. Keys and physical properties of the system considered.
In this study, the mass transfer efficiency was analyzed
only in the homogeneous flow regime of bubble column.
The upper boundary of this flow regime was determined by the formulas of Reilly et al .[32] The mass
transfer efficiency of bubble column reactors is analyzed with different organic liquids and tap water at
293.2 K as shown in Table 1. The reported[33] physical
properties of the liquid are taken as measured by Ozturk
et al .[26] and Schumpe and Lühring.[34] The mass transfer coefficient for the analysis was considered within the
range of correlation equation presented in Eqn (14). The
experiments for mass transfer operation in the bubble
column were carried out by several authors with different operating variables. In this study, the operating
conditions are considered as minimum to maximum of
the existing data in the literature published as column
diameter: 0.01 ≤ dc ≤ 0.63 m, 0 ≤ hi ≤ 6.0 m, 0.1 ≤
dh ≤ 10 mm, 0 ≤ usg ≤ 0.89 m/s and 0 ≤ usl ≤ 0.044.
The physical properties vary within the range as shown
in Table 1.
Cyclohexane–
air
THE OPERATING VARIABLES CONSIDERED IN
THIS STUDY
4
809
2.94
24.6
1.29
Decalin–
air
Where, ds,st is the Sauter-mean bubble diameter corrected to standard conditions, ds,exp is the Sauter-mean
bubble diameter as calculated from the correlation, hi
is the axial distance from the gas distributor and Ti is
the liquid temperature in the column during the process operation. The gas holdup was calculated by the
correlation proposed by Hughmark.[31]
3
879
0.653
28.7
3.46
Ethyl acetate–
air
Ethyl
benzene–air
(298 K and 1 atmosphere) using the approximation
given by following equation[11] :
298
10.33 − hi
3
(16)
ds,st = ds,exp
10.33
Ti + 273
10
867
0.669
28.6
2.94
EFFICIENCY OF NON-REACTIVE ISOTHERMAL BUBBLE COLUMN
Systems
Asia-Pacific Journal of Chemical Engineering
Asia-Pac. J. Chem. Eng. 2008; 3: 440–451
DOI: 10.1002/apj
443
S. K. MAJUMDER
Asia-Pacific Journal of Chemical Engineering
Table 2. Gas holdup and overall mass transfer coefficient as a function of sparger design.
Type of sparger
Perforated plate with 163 holes
(0.50 mm), and has open area of
0.156%
Perforated plate with 163 larger holes
(1.32 mm), and has open area of 1.09%
Cross-sparger with four holes (2.54 mm),
each 25.4 mm off-center and facing
down, and has open area of 0.1%.
Values of α1 and β1 of
β
correlation: εg = α1 usg1
Values of α2 and β2 of
β
correlation: kl a = α2 usg2
α1 = 0.563, β1 = 0.391; R 2 = 0.936
α2 = 0.273, β2 = 0.482; R 2 = 0.953
α1 = 0.886, β1 = 0.719; R 2 = 0.972
α2 = 0.348, β2 = 0.676; R 2 = 0.966
α1 = 0.727, β1 = 0.748; R 2 = 0.973
α2 = 0.341, β2 = 0.742; R 2 = 0.998
in the bubbly flow regime, but only in the distributor
region in the churn-turbulent flow regime. The correlations which are shown in Table 2, attribute the variations of the overall gas holdup and the volumetric mass
transfer coefficient to the superficial gas velocities. The
correlations were made with the experimental data of
Han Al-Dahhan.[17] By comparison, the perforated distributor with small holes has the higher k1 a values and
the cross-sparger with large holes has the lower k1 a
values. This result shows the effect of the two different
sparger types (perforated plate and cross-sparger) and
the effect of hole size of the perforated plates on the
gas–liquid mass transfer coefficient and consequently
mass transfer efficiency of the bubble column. Han and
Al-Dahhan[17] reported that the sparger effect on k1 a
at low gas velocities (<0.15 m/s) is higher due to the
different bubble sizes formed at these spargers, which
affect the bubble sizes and interfacial area in the whole
reactor. The sparger effect becomes small in the high
gas velocity range (>0.20 m/s). It can be explained
by the nature of the coalescent system used in which
the bubbles further enlarge in size from the sparger.
Although the sparger design greatly affects the initial
bubble formation,[38,39] the three distributors resulted in
similar interfacial area values with only small differences at 0.30 m/s. Consequently the effects of sparger
design provide insight into efficiency of the bubble column as shown in Fig. 2. On the other hand, an increase
in gas flow-rate (superficial gas velocity) produces a
clear increase in interfacial area due to the higher gas
volume fed to the contactor. Also the use of a gas
sparger with smaller pore diameter generates a higher
number of bubbles and then an increase in interfacial
area results in an increase in efficiency with smaller
pore diameter of the sparger.
Effect of operating pressure and gas velocity
on mass transfer efficiency of the bubble
column
The efficiency of a bubble column based on mass
transfer depends on the operating pressure because the
 2008 Curtin University of Technology and John Wiley & Sons, Ltd.
1.0
0.9
0.8
ηBC
444
usl = 0.044 m/s
hi = 1.814 m
dc = 0.162 m
0.7
0.6
Symbol Sparger type
Perforated plate (0.50 mm)
Perforated plate (1.32 mm)
Cross sparger (2.54 mm)
0.5
0.4
0.0
0.1
0.2
0.3
0.4
0.5
usg, [m/s]
Figure 2. Parity of mass transfer efficiency with sparger
design.
overall gas holdup and the volumetric gas–liquid mass
transfer coefficient, k1 a, have strong dependency on
operating pressures without varying sparger type as
shown in Table 3. The correlations in Table 3 are made
with the experimental result reported by Han and AlDahhan.[17] The values of both gas holdup and volumetric mass transfer coefficient increased with the
superficial gas velocity and the operating pressure, as
well explained by many studies.[17,40 – 42] The volumetric mass transfer coefficient increased greatly due to
the smaller bubble size generated at high pressures.[43]
The liquid side mass transfer coefficient, kl , unlike kl a,
decreased with the increase of pressure, especially from
ambient pressure to 0.4 MPa.[17] This verdict of the
pressure effect on the kl values was corroborated by
Lemoine.[44] The apparent decrease of kl is attributed to
the change in bubble dynamics and hydrodynamics at
0.4 MPa.[45] At high pressure, smaller bubble sizes have
lower slip velocity.[43] Therefore, smaller bubbles have
longer exposure time in the liquid interface renewal and
cause decrease in kl values at high pressure.[46] However, as pressure increases from 0.4 to 1.0 MPa, the kl
values do not seem to change much, which is due to
the unnoticeable differences in bubble sizes at 0.4 and
Asia-Pac. J. Chem. Eng. 2008; 3: 440–451
DOI: 10.1002/apj
Asia-Pacific Journal of Chemical Engineering
EFFICIENCY OF NON-REACTIVE ISOTHERMAL BUBBLE COLUMN
Table 3. Gas holdup and overall mass transfer coefficient as a function of operating pressure with a perforated
plate with 163 larger holes (1.32 mm).
Operating
pressures
Values of α3 and β3 of correlation:
εg = α3 Ln(usg ) + β3
Values of α4 and β4 of correlation:
kl a = α4 Ln(usg ) + β4
0.1 MPa
0.2 MPa
1.0 MPa
α3 = 0.089, β3 = 0.389; R 2 = 0.985
α3 = 0.145, β3 = 0.654; R 2 = 0.975
α3 = 0.215, β3 = 0.897; R 2 = 0.992
α4 = 0.044, β4 = 0.188; R 2 = 0.947
α4 = 0.062, β4 = 0.285; R 2 = 0.942
α4 = 0.084, β4 = 0.366; R 2 = 0.985
Effect of liquid velocity on mass transfer
efficiency
At low liquid phase flow-rate, an increase in superficial
gas velocity causes an increase in mass transfer coefficient due to a higher turbulence in the liquid phase
1.0
0.9
ηBC
0.8
usl = 0.044 m/s
hi = 1.814 m
dc = 0.162 m
0.7
0.6
Symbol Op. press.
0.1 MPa
0.4 MPa
1.0 MPa
0.5
0.4
0.0
0.1
0.2
usg, [m/s]
0.3
Figure 3. Parity of mass transfer efficiency with operating
pressure.
 2008 Curtin University of Technology and John Wiley & Sons, Ltd.
0.90
0.75
0.60
ηBC
1.0 MPa.[43] The result of mass transfer efficiency is
shown in Fig. 3. Therefore, the increase in mass transfer
efficiency with increase in pressure is due to the higher
volumetric mass transfer coefficient and gas holdup
resulted by formation of smaller bubbles at higher pressure. Figure 4 presents the variation of the volumetric
mass transfer coefficient, kl a, with the superficial gas
velocity for the different liquid phases. The Fig. 4 indicates that, whatever the liquid phases, the volumetric
mass transfer coefficient increases with the superficial
gas velocity, which in turn systematically induces an
increase in specific interfacial area. The values of ηBC
vary between 0.12 and 0.90 for superficial gas velocities varying between 0.008 and 0.10 m/s. An increase
in gas flow-rate (superficial gas velocity) produces a
clear increase in interfacial area due to the higher gas
volume fed to contactor. Also the use of a gas sparger
with smaller pore diameter generates a higher number
of bubbles and then an increase in interfacial area.
Symbol Keys
1
2
5
7
8
9
dc = 0.06 m
12
dh = 0.003 m
17
usl = 0.0352 m/s
18
0.45
0.30
0.15
0.00
0.00
0.02
0.04
0.06
0.08
usg [m/s]
0.10
0.12
0.14
Figure 4. Effect of gas velocity on mass transfer efficiency.
and a better surface renewal that increases the mass
transfer. At high values of liquid flow-rate the effect of
superficial gas velocity is negligible because the influence of liquid flow-rate is higher than that produced by
the gas flow-rate. An increase in liquid phase flow-rate
produces a clear increase in the value of mass transfer
coefficient due to the higher driving force existing in
the liquid phase, but the ratio of kl a/usl decreases with
increase in superficial liquid velocity which results is
decrease in mass transfer efficiency of the bubble column as shown in Fig. 5. The mass transfer efficiency is
the maximum (ideally 1.0 as per Eqn (11)) for a batch
liquid bubble column where superficial liquid velocity
is zero.
Effect of bubble size on mass transfer
efficiency
The bubble size distribution has significant effects
on mass transfer efficiency, because it determines the
interfacial area per volume of the gas phase. The
bubble size distribution is determined by the bubble
coalescence and breakup. In a given system, the bubble
coalescence and breakup rates are mainly affected by
the local gas holdup and turbulent energy dissipation
rate. Owing to the nonuniform radial profiles of the
Asia-Pac. J. Chem. Eng. 2008; 3: 440–451
DOI: 10.1002/apj
445
S. K. MAJUMDER
Asia-Pacific Journal of Chemical Engineering
1.0
dc: 0.06 m
Symbol Keys
dh: 0.003 m
1
usg: 0.008 m/s
2
3
4
5
7
0.8
ηBC
0.6
0.4
0.2
0.0
0.00
0.01
0.02
0.03
usl, [m/s]
0.04
0.05
Figure 5. Variation of mass transfer efficiency with
superficial liquid velocity.
gas holdup (Fig. 6) and dissipation rate, especially in
the heterogeneous regime, the bubble size distribution
varies not only with the superficial gas velocity, but
also with the radial position.[47] An empirical correlation
based on the data in Fig. 5 has been developed as
follows:
εg = p(r/R)3 + q(r/R)2 + s(r/R) + t
(17)
where
0.28
, R 2 = 0.995
p = −1.32usg
(18)
0.19
, R 2 = 0.986
q = 1.41usg
(19)
0.24
s = −0.95usg
, R 2 = 0.990
(20)
0.33
, R 2 = 0.989
t = 0.85usg
(21)
Figure 7 shows the bubble size distribution at different radial positions. According to Wang and Wang,[47] at
low superficial gas velocities, the bubble size distributions are very similar at different radial positions. With
an increase in the superficial gas velocity, the difference in the bubble size distributions at different radial
positions becomes pronounced, especially after the flow
enters the heterogeneous regime. The bubble size distribution is quite homogeneous, for instance, around
0.0035 m at sparger level. This distribution spreads
with increasing gas velocity; the mean bubble diameter becomes so large that bubbles become unstable and
break up into a new population of tiny bubbles with
increase in interfacial area. Increase in interfacial area
increases the mass transfer efficiency. The efficiency of
mass transfer with bubble diameter is shown in Fig. 8.
At small gas velocity, the bubble size tends to increase
with height of the column and the smallest bubbles
form near the sparger due to higher dissipation rate of
energy. The smallest bubbles may coalesce and induce
an increase of the mean bubble size with column height.
At high gas velocity, in the sparger area very large bubbles are formed and the small bubble population fraction
increases with increase in height from the source of generation. These small bubbles probably result from the
breakup of the large unstable bubbles and rise slowly.
At low gas velocity the smaller bubbles formed at the
sparger coalesce with other bubbles, but the Sautermean diameter is smaller in less viscous liquid as shown
in Fig. 9. When the gas velocity increases, the bubble
400
System: Air-water
dc: 0.19 m
symbol usg [m/s]
0.5
0.3
350
PDF (volume) of db, 1/mm
0.02
0.08
0.12
0.16
0.4
εg
446
0.2
300
250
200
System: Air-water
usg: 0.02 m/s
dc: 0.19 m
r/R = 0
r/R = 0.44
r/R = 0.95
150
100
50
0.1
0
0.0
0.0
0.2
0.4
0.6
0.8
1.0
r/R, [-]
Figure 6. Radial profiles of the gas holdup in a bubble
column with air–water system. Lines and symbols: Data of
Wang and Wang[46] ; symbols: data of Sanyal et al.[48] .
 2008 Curtin University of Technology and John Wiley & Sons, Ltd.
0
50
20
30
40
50
db, mm
Figure 7. Bubble size distributions at different radial
positions at constant gas velocity. Data: Wang and
Wang.[46] .
Asia-Pac. J. Chem. Eng. 2008; 3: 440–451
DOI: 10.1002/apj
Asia-Pacific Journal of Chemical Engineering
EFFICIENCY OF NON-REACTIVE ISOTHERMAL BUBBLE COLUMN
diameter tends to increase. At high gas velocity a population of small bubbles appears, but this occurs at higher
gas velocity in a liquid of higher surface tension than
in that of lower surface tension and its bubble fraction
is always greater in liquid of lower surface tension.[47]
In the case of the liquid of lower surface tension, it
appears that those diameters differ; even at small gas
velocity there is a wider bubble distribution.
Effect of surface tension on mass transfer
efficiency of bubble column
Like the gas phase dispersion and the bubble size distribution, the liquid media have also a strong effect
0.9
0.8
0.7
ηBC
0.6
0.5
0.4
Symbol usl (m/s) usg (m/s)
0.0176 0.01
0.0352 0.04
0.0176 0.01
0.3
0.2
0.1
2.5
3.0
3.5
4.0
4.5
db, mm
5.0
5.5
Figure 8. Variation of mass transfer efficiency with bubble
diameter.
Model: 0.021x0.258
Chi2= 3.2316E-8
R2 = 0.94157
5.5
5.0
on mass transfer efficiency, but the liquid media effect
seems more complex and is still disputed. In fact, the
bubble size strongly depends on coalescence behavior
of the liquid, but the influence of the liquid properties on bubble coalescence and breakup remains difficult
to quantify, especially in industrial complex media.[49]
The most analyzed liquid properties are viscosity and
surface tension. A decrease in surface tension (due to
surfactant addition) diminishes the bubble coalescence
frequency: the bubbles are then smaller, slower[50] and
also more spherical.[51] In bubble columns, it is commonly accepted that, depending on the gas flow-rate and
on the liquid phase properties, two main regimes can be
distinguished. On the one hand, the homogeneous bubbly flow regime, encountered at low gas velocities (with
small holes sparger), is characterized by narrow bubble size distributions and a uniform spatial dispersion
of gas holdup.[7] In this regime, there is no interaction
between bubbles. Their motion is roughly vertical. On
the other hand the heterogeneous (churn-turbulent flow)
regime, at higher gas velocities (usg > 0.05 Sm/s), is
defined by a large bubble size distribution and a high
concentration of large bubbles on column axis, which
cause macro-circulation and curved shape gas holdup
profiles.[7] In the heterogeneous regime the bubble size
is governed by the coalescence–breakup equilibrium.
In bubble columns, the surface tension effect is similar
to the trend for single bubbles; a decrease in surface
tension decreases bubble size and bubble velocity[52]
and induces higher gas holdup[14,53,54] and higher mass
transfer coefficient.[55] Consequently the decrease in
surface tension increases the efficiency of mass transfer
as shown in Fig. 10. These tendencies are confirmed by
the classical correlations.[56] The surface tension effect
is particularly effective in homogeneous and transition
regime and less in the heterogeneous regime where the
reduction of coalescence is over-shadowed by the predominant effect of macro-scale turbulence.[53,57] Also
with increase in surface tension, the transition of bubbling regimes is delayed due to higher gas velocity,
whereas the heterogeneous regime appears almost at
the same gas velocity and the transition regime tends to
disappear.[52,58]
db, mm
4.5
dc: 0.06 m
dh: 3 mm
usl: 0.0176 m/s
Symbol usg (m/s)
0.01
0.02
0.03
0.04
4.0
3.5
3.0
Effect of viscosity of liquid on mass transfer
efficiency
2.5
0.0
1.0
2.0
3.0
4.0
5.0
µl × 103, kg/m.s
Figure 9. Variations of bubble diameter with viscosity of
liquid.
 2008 Curtin University of Technology and John Wiley & Sons, Ltd.
The efficiency of mass transfer of the bubble column
is quietly controlled by transport mechanism of species
in the liquid viscous boundary layer around the bubbles. The gas–liquid mass transfer between a single
bubble and the surrounding liquid is studied by Haut
and Cartage.[59] The contact time between liquid particles active for the transfer and the bubble, as well
as the interfacial area active for the transfer, result
in variation of mass transfer efficiency with viscosity
Asia-Pac. J. Chem. Eng. 2008; 3: 440–451
DOI: 10.1002/apj
447
S. K. MAJUMDER
Asia-Pacific Journal of Chemical Engineering
transfer of solute enters the liquid boundary layer near
the point of incidence and leaves it near the extreme
point of the bubble. The contact time between the
bubble and the liquid element active for the transfer of
solute is inversely proportional to gas–liquid relative
velocity of the bubble. The mass transfer rate between
the bubble and the surrounding liquid is increased with
the interfacial area and is decreased with increase in
contact time.[59] A more viscous liquid provides more
contact time between the bubble and the liquid element
active for the transfer of solute which may cause the
decrease in mass transfer efficiency with increase in
viscosity as shown in Fig. 10.
µl, [Pa-s]
ρl, [kg/m3]
σ, [N/m]
0.9
0.8
ηBC
448
0.7
0.6
0.5
0.4
0.0
1.0
2.0
ρl ×
Figure 10.
efficiency.
10-3;
3.0
σ×
10+2;
µl ×
4.0
5.0
10+3
Effects of liquid properties on mass transfer
of the liquid. According to Haut and Cartage[59] for
1 mm < db < 1 cm, the bubbles move with the superposition of two perfect spherical caps where only the
upper spherical cap is active for the transfer of A. The
contact time between a liquid element and the lower
spherical cap is significantly larger than the contact time
between a liquid element and the upper spherical cap.[60]
Therefore, the main part of the gas–liquid mass transfer
is ensured by liquid elements in contact with the upper
spherical cap. Using the correlation of Wellek,[59] the
expressions of volumetric mass transfer coefficient and
specific interfacial area can be written as:

 n
εg,j a(db,j )
Dl 

(22)
kl a = 2
π j =1
tc,j
a(db,j ) =
3(1 + Wj 2 )21/3
Wj
2/3
(3 + Wj 2 )2/3 db,j
(23)
The specific interfacial area depends on the wake
angle of the bubble. A wake angle of 1 radian gives a =
5.26/db,j .[59] For the bubble group, j the aspect ratio
(ratio of major and minor axis) is defined as Wj which
can be calculated by the correlation of Wellek[59,61] as:
Wj = [1 + 0.163Eo 0.757 ]−1
(24)
where Eo = gρl db,j 2 /σ is the Eotvos number of the
bubble of diameter db,j .
Also within the liquid viscous boundary layer, if
angular position of a bubble is less than the angle
of the wake, the transport of solute in a direction
normal to the interface is purely diffusional, while its
transport in a direction tangential to the interface is
purely convective.[59] A liquid element active for the
 2008 Curtin University of Technology and John Wiley & Sons, Ltd.
Effect of diffusivity on mass transfer efficiency
of the bubble column
Mass transfer theories are mainly developed for the process of absorption of a gas in a liquid, even though
their application might be extended to the cases where
mass transfer occurs between any two immiscible fluid
phases. The conventional and simplest picture of mass
transfer between two fluid phases is that there exists
a stagnant film at the interface.[62] The general dependence of liquid side film mass transfer coefficient is
kl ∝ Dln where n is dependent on fluid–fluid system
under given conditions.[63 – 65] The mass transfer efficiency can be expressed in this analysis by a correlation
which is represented as: ηBC ∝ Dl0.269 . Higbie[46] took a
major step forward to analyze the mass transfer mechanism by introducing the ‘penetration theory’ on the
dependency of diffusivity on mass transfer.
Mass transfer efficiency as a function of
energy dissipation
Numerous mass transfer measurements have been carried out on various types of modified bubble columns.
The mass transfer efficiency can be considerably
increased by incorporating rigid or mobile components
or by additional energy input. From the literature[49] it
is found that the mass transfer enhancing variables are
incorporated with the volume-based energy input to the
bubble column. The mass transfer coefficient is exponentially dependent on the volume-based energy input
to the bubble column, (kl a ∝ ∈n ).[49] in which n = 1.2
for a bubble column with perforated plates of 1 and
3 mm holes and 1.2 ≤ n ≤ 1.85 for a hole diameter
of 0.5 mm. This implies that energy input has a usually
strong influence on the mass transfer efficiency. According to Kamp et al .,[66] the rate of energy dissipation of
turbulent kinetic energy per unit volume in the bubbly
flow zone can be estimated by the following Equation,
∈=
2ρl u∗3
κdc
(25)
Asia-Pac. J. Chem. Eng. 2008; 3: 440–451
DOI: 10.1002/apj
EFFICIENCY OF NON-REACTIVE ISOTHERMAL BUBBLE COLUMN
where, κ is the von Karman constant, equal to 0.41, and
u∗ is the friction velocity. The friction velocity can be
estimated from Blasius equation[67] for the bubbly pipe
flow as follows,
0.079Rem−1/4
(26)
u∗ = (usl + usg )
2
where, Rem is the gas–liquid mixture Reynolds number
which is defined as
Rem =
ρl (usl + usg )dc
µl
DEVELOPMENT OF A CORRELATION TO
INTERPRET THE MASS TRANSFER EFFICIENCY
The mass transfer process is the most important industrial reactor-specific phenomenon. The mass transfer
efficiency cannot be analyzed completely by a specific
theoretical model due to simultaneous effect of various
variables on mass transfer efficiency. From the above
analysis and the literature it is found that the mass
transfer efficiency depends on different dynamic, geometric and physical variables of the system. The effect
of all these variables independently on the mass transfer efficiency is very complicated and thus, a correlation
has been developed by dimensional analysis to incorporate the mass transfer efficiency in terms of dynamic,
Table 4. The constants of Eqn (27) against the different
systems at dc = 0.01 m, dh = 0.003 m, usl = 0.044 m/s
and usg = 0.008 to 0.1 m/s.
1.96,
0.42,
1.16,
0.67,
1.00,
1.02,
1.09,
0.67,
1.43,
0.37;
0.45;
0.32;
0.46;
0.38;
0.37;
0.35;
0.45;
0.34;
0.92
0.97
0.91
0.95
0.92
0.92
0.91
0.95
0.91
α5 , β5 of
Systems
ηBC = α5 (∈)β5 ; R 2
keys
10
11
12
13
14
15
16
17
18
0.6
0.4
0.2
The results for coefficients (α5 , β5 ) are shown in
Table 4. From the exponential results, it is found that
the mass transfer efficiency increases with the increase
in energy dissipation per unit volume of the mixture.
1
2
3
4
5
6
7
8
9
0.8
(27)
A correlation has been developed for mass transfer
efficiency in terms of energy input per unit of dispersion
volume as:
(28)
ηBC = α5 (∈)β5
α5 , β5 of
Systems
ηBC = α5 (∈)β5 ; R 2
keys
1.0
ηBC-developed correlation
Asia-Pacific Journal of Chemical Engineering
1.14,
1.09,
0.89,
1.32,
0.78,
0.76,
1.21,
1.17,
0.73,
0.34;
0.33;
0.39;
0.33;
0.43;
0.45;
0.32;
0.32;
0.43,
0.91
0.90
0.93
0.90
0.94
0.95
0.90
0.90
0.94
 2008 Curtin University of Technology and John Wiley & Sons, Ltd.
0.0
0.0
0.2
0.4
0.6
ηBC-calculated
0.8
1.0
Figure 11. Comparison of the values of mass transfer
efficiency calculated by the proposed correlation Eqn (29)
with those calculated from Eqn (11).
geometric and physical variables of the system. Combining the relevant dimensionless groups obtained by
the dimensional analysis and regression analysis, the
following functional relationship was obtained:
ηBC = 0.5364Ln(X ) + 0.9106;
R 2 = 0.9906
(29)
where,
X = 9.71 × 10−2 Re−1.204 Sc −0.269
Fr 0.686 Ga 0.672 Mo 0.077 Pe 0.609
(30)
The regression analysis of Eqn (30) was done on
31 998 data with different operating conditions. The correlation coefficient (R 2 ) and standard error of Eqn (30)
were calculated and found to be 0.9734 and 0.057
respectively. The calculated values of mass transfer
efficiency (ηBC ) from Eqn (28) were plotted against
the values obtained by Eqn (11) and are shown in
Fig. 11. The correlation has been found to be satisfactory within the range of the different variables as 20 <
Re < 6.70 × 104 ; 70 < Sc < 4.44 × 103 ; 0.03 < Fr <
0.60; 5.29 × 105 < Ga < 1.44 × 1013 ; 1.14 × 10−11 <
Mo < 6.08 × 10−8 ; 0.044 < Pe < 373.88. The correlation Eqn (29) is valid for 0.19 < X ≤ 1.0 and 0.25 ≤
ηBC < 1.0.
CONCLUSION
Mass transfer coefficients governing the transport processes in bubble contactors is a growing concern in
chemical and biotechnological mass transfer processes
which are influenced by different physical, dynamic and
Asia-Pac. J. Chem. Eng. 2008; 3: 440–451
DOI: 10.1002/apj
449
450
S. K. MAJUMDER
geometric variables. In the present work, efficiency of
mass transfer was analyzed in a two-phase homogeneous bubble column reactor with different types of
liquids. The efficiency was analyzed with the theoretical model. This gives an insight into the performance of
the bubble column reactor based on different operating
variables. The efficiency is strongly dependent on the
various geometric, dynamic and physical variables. The
developed correlations will give the further understanding and scale-up of the bubble column reactor for its
industrial installation.
NOMENCLATURE
a
Ac
Cl
Cl,hi
∗
Cl,h
i
Cg,hi
Dl
Eo
db
dbj
dc
dh
ds
Fr
Ga
hi
hm
H
i
kl
kl a
Mo
p
PhRi
PR
Pb,R
Pt
Patm
Pe
q
Ql
r
R
R2
Re
Specific interfacial area (m−1 )
Column cross-sectional area (m2 )
Molar concentration of solute in liquid (mol/
m3 )
Concentration of liquid at section of height, hi
(mol/m3 )
Equilibrium concentration at section of height,
hi (mol/m3 )
Concentration of gas at section of height, hi
(mol/m3 )
Molecular diffusion coefficient (m2 /s)
Eotvos number of the bubble of diameter,
db,j (gρl db,j 2 /σ )
Bubble diameter (m)
Bubble diameter of bubble group j (m)
Column diameter (m)
distributor hole diameter (m)
Sauter-mean bubble diameter
(m)
√
Froude number (usg / gdb )
Gallilei number [(gdc3 ρl2 )/µ2l ]
Gas–liquid mixing height at section i (m)
Gas–liquid mixing height of entire column (m)
Henry’s law of constant
Column sections 1, 2, 3,. . .
Liquid side mass transfer coefficient (m/s)
Volumetric mass transfer coefficient (1/s)
Morton number [(gµ4l )/(ρl σ 3 )]
Constant defined in Eqn (18)
Pressure at sectional height, hi (N/m2 )
Pressure ratio defined as Patm /(ρl ghm )
Pressure ratio defined as 4σ/(ρl ghm db )
Total pressure (N/m2 )
Atmospheric pressure (N/m2 )
Peclet number ((usl hi )/Ez )
Constant defined in Eqn (19)
Liquid flow-rate (m3 /s)
Radial distance of the column from center
Radius of the column (m)
Correlation coefficient
Reynolds number [(dc usl ρl )/µl ]
 2008 Curtin University of Technology and John Wiley & Sons, Ltd.
Asia-Pacific Journal of Chemical Engineering
Gas–liquid mixture Reynolds number ({ρl
(usl + usg )dc }/µl )
s
Constant defined in Eqn (20)
Sc
Schmidt number [µl /(Dl ρl )]
t
Constant defined in Eqn (21)
gas–liquid contact time for bubble group j (s)
tc
Superficial liquid velocity (m/s)
usl
Superficial gas velocity (m/s)
usg
Friction velocity (m/s)
u∗
Aspect ratio
Wj
X
Parameter defined in Eqn (30)
y
Mole fraction of gas
α
Parameter defined in Eqn (7)
α1 − α5 Constants
β1 − β5 Constants
Local mass transfer efficiency of volume of
ηhhii −1
height between hi and hi −1
ηBC
Mass transfer efficiency of entire bubble column
Viscosity of liquid (kg/ms)
µl
Density of liquid (kg/m3 )
ρl
Density of gas (kg/m3 )
ρg
σ
Surface tension (N/m)
Fractional gas holdup
εg
Fractional gas holdup contributed by bubble
εg,j
group j
κ
von Karman constant
∈
Average energy dissipation per unit volume
(kg/ms3 )
Rem
REFERENCES
[1] M. Bouaifi, G. Hebrard, D. Bastoul, M. Roustan. Chem. Eng.
Process., 2001; 40, 97–111.
[2] M.Z.A. Anabtawi, S.I. Abu-Eishah, N. Hilal, N.B.W. Nabhan.
Chem. Eng. Process., 2002; 1, 1–6.
[3] A. Forret, J.-M. Schweitzer, T. Gauthier, R. Krishna, D.
Scweich. Chem. Eng. Sci., 2003; 58, 719–724.
[4] C. Tang, T.J. Heindel. Chem. Eng. Sci., 2004; 59, 623–632.
[5] S.K. Majumder, G. Kundu, D. Mukherjee. Chem. Eng. Sci.,
2006a; 61(20), 6753–6764.
[6] S.K. Majumder, G. Kundu, D. Mukherjee. Can. J. Chem.
Eng., 2007; 85(3), 380–389.
[7] H. Chaumat, A.M. Billet, H. Delmas. Chem. Eng. Sci., 2007;
62(24), 7378–7390.
[8] H. Essadki, I. Nikov, H. Delmas. Exp. Therm. Fluid Sci.,
1997; 14, 243–250.
[9] H. Li, A. Prakash. Chem. Eng. Sci., 1999; 54, 5265–5271.
[10] R. Schäfer, C. Marten, G. Eigenberger. Exp. Therm. Fluid Sci.,
2002; 26, 595–604.
[11] S.K. Majumder, G. Kundu, D. Mukherjee. Chem. Eng. J.,
2006b; 122(1–2), 1–10.
[12] S. Degaleesan, M. Dudukovic, Y. Pan. AIChE J., 2001; 47,
1913–1931.
[13] V.V. Buwa, V.V. Ranade. Chem. Eng. Sci., 2002; 57,
4715–4736.
[14] M.T. Dhotre, K. Ekambara, J.B. Joshi. Exp. Therm. Fluid Sci.,
2004; 28, 407–421.
[15] C.O. Vandu, R. Krishna. Chem. Eng. Process., 2004; 43,
987–995.
[16] R. Sardeing, P. Painmanakul, G. Hébrard. Chem. Eng. Sci.,
2006; 61(19), 6249–6260.
[17] L. Han, M.H. Al-Dahhan. Chem. Eng. Sci., 2007; 62(1–2),
131–139.
Asia-Pac. J. Chem. Eng. 2008; 3: 440–451
DOI: 10.1002/apj
Asia-Pacific Journal of Chemical Engineering
EFFICIENCY OF NON-REACTIVE ISOTHERMAL BUBBLE COLUMN
[18] T.J. Lin, S.P. Wang. Chem. Eng. Sci., 2001; 56, 1143–1149.
[19] Y.J. Cho, K.J. Woo, Y. Kang, S.D. Kim. Chem. Eng. Process.,
2002; 41, 699–706.
[20] H.Z. Kister. Distillation Design, McGraw-Hill: New York,
1992.
[21] J.A. Gerster, A.B. Hill, N.H. Hochgraf, D.G. Robinson. Tray
Efficiencies in Distillation Columns, Final Report from the
University of Delaware, AIChE: New York, 1958.
[22] D.L. Bennett, D.N. Watson, M.A. Wiescinski. AIChE J., 1997;
43(6), 1611–1626.
[23] K. Akita, F. Yoshida. Ind. Eng. Chem. Process Des. Dev.,
1974; 12, 76–80.
[24] M. Nakanoh, F. Yoshida. Ind. Eng. Chem. Process Des. Dev.,
1980; 19(1), 190–195.
[25] W.D. Deckwer, K. Nguyen-Tien, A. Schumpe. Biotechnol.
Bioeng., 1982; 14, 461–481.
[26] S.S. Ozturk, A. Schumpe, W.D. Deckwer. AIChE J., 1987; 33,
1473–1480.
[27] Y. Kang, Y.J. Cho, K.J. Woo, S.D. Kim. Chem. Eng. Sci.,
1999; 54, 4887–4893.
[28] H. Hikita, S. Asai, K. Tanigawa, K. Segawa, M. Kitao. Chem.
Eng. J., 1981; 22(1), 61–69.
[29] A. Schumpe, W.D. Deckwer. Bioprocess Eng., 1987; 2,
79–94.
[30] P. Wilkinson, H. Haringa. Chem. Eng. Sci., 1994; 49(9),
1417–1427.
[31] G.A. Hughmark. Ind. Eng. Chem. Process Des. Dev., 1967; 6,
218–222.
[32] I.G. Reilly, D.S. Scott, T.J.WD. Bruijn, D. MacIntyre. Can. J.
Chem. Eng., 1994; 72, 3–12.
[33] S. Nedeltchev, U. Jordan, A. Schumpe. Chem. Eng. Sci.,
2007; 62(22), 6263–6273.
[34] A. Schumpe, P. Lühring. J. Chem. Eng. Data, 1990; 35,
24–25.
[35] D.L. George, K.A. Shollenberger, J.R. Torczynski. Fed Am.
Soc. Mech. Eng., 2000; 251, 1487–1494.
[36] C. Vial, R. Laine, S. Poncin, N. Midoux, G. Wild. Chem. Eng.
Sci., 2001; 56(3), 1085–1093.
[37] J.H.J. Kluytmans, B.G.M. Van Wachem, B.F.M. Kuster, J.C.
Schouten. Chem. Eng. Sci., 2003; 58(20), 4719–4728.
[38] K. Terasaka, Y. Hieda, H. Tsuge. J. Chem. Eng. Jpn., 1999;
32(4), 472–479.
[39] S. Hsu, W. Lee, Y. Yang, C. Chang, J. Maa. Ind. Eng. Chem.
Res., 2000; 39(5), 1473–1479.
[40] H.M. Letzel, J.C. Schouten, R. Krishna, C.M.V. Bleek. Chem.
Eng. Sci., 1999; 54(13–14), 2237–2246.
[41] U. Jordan, K. Terasaka, G. Kundu, A. Schumpe. Chem. Eng.
Technol., 2002; 25(3), 262–265.
[42] R. Lau, W. Peng, L.G. Velazquez-Vargas, G.Q. Yang,
L.-S. Fan. Ind. Eng. Chem. Res., 2004; 43(5), 1302–1311.
 2008 Curtin University of Technology and John Wiley & Sons, Ltd.
[43] J. Xue, M. Al-Dahhan, M.P. Dudukovic, R.F. Mudde. Can. J.
Chem. Eng., 2003; 81(3–4), 375–381.
[44] R. Lemoine, A. Behkish, B.I. Morsi. Ind. Eng. Chem. Res.,
2004; 43(19), 6195–6212.
[45] P. Gupta, B. Ong, M.H. Al-Dahhan, M.P. Dudukovic, B.A.
Toseland. Catal. Today, 2001; 64(3–4), 253–269.
[46] R. Higbie. Trans. AIChE, 1935; 31, 365–389.
[47] T. Wang, J. Wang. Chem. Eng. Sci., 2007; 62(24),
7107–7118.
[48] J. Sanyal, S. Vasquez, S. Roy. Chem. Eng. Sci., 1999; 54,
5071–5083.
[49] W.D. Deckwer. Bubble Column Reactors, Wiley: New York,
1992.
[50] K. Malysa, M. Krasowska, M. Krzan. Adv. Colloid Interface
Sci., 2005; 114–115, 205–225.
[51] N.A. Kazakis, A.A. Mouza, S.V. Paras. Chem. Eng. J., 2008;
137(2), 265–281.
[52] P. Dargar, A. Macchi. Chem. Eng. Process., 2006; 45(9),
764–772.
[53] E. Camarasa, C. Vial, S. Poncin, G. Wild, N. Midoux,
J. Bouillard. Chem. Eng. Process., 1999; 38, 329–344.
[54] R. Krishna, J.M. Van Baten. Catal. Today, 2003; 79–80,
67–75.
[55] N. Kantarci, F. Borak, K. Ulgen. Process Biochem., 2005; 40,
2263–2283.
[56] Y.T. Shah, S.P. Godbole, W.D. Deckwer. AIChE J., 1982; 28,
353–379.
[57] J. Zahradnı́k,
M. Fialová,
M. R – žiŠka,
J. Drahoš,
F. Kaštánek, N.H. Thomas. Chem. Eng. Sci., 1997; 52(21–22),
3811–3826.
[58] B.N. Thorat, J.B. Joshi. Exp. Therm. Fluid Sci., 2004; 28,
423–430.
[59] B. Haut, T. Cartage. Chem. Eng. Sci., 2005; 60(22),
5937–5944.
[60] B. Haut, V. Halloin, T. Cartage, A. Cockx. Chem. Eng. Sci.,
2004; 59, 5687–5694.
[61] R. Clift, J.R. Grace, M.E. Weber. Bubbles, Drops and
Particles, Academic Press: New York, 1978.
[62] W.K. Lewis, W.G. Whitman. Ind. Eng. Chem., 1924; 16,
1215–1220.
[63] H.L. Toor, J.M. Marchello. AIChE J., 1958; 4(1), 97–101.
[64] A.A. Kozinski, C.J. King. AIChE J., 1966; 12(1), 109–116.
[65] J.C. Lamont, D.S. Scott. AIChE J., 1970; 16(4), 513–519.
[66] A.M. Kamp, A.K. Chesters, C. Colin, J. Fabre. Int. J.
Multiphase Flow, 2001; 27(8), 1363–1396.
[67] C. Colin, J. Fabre, A. Dukler. Int. J. Multiphase Flow, 1999;
17, 533–544.
Asia-Pac. J. Chem. Eng. 2008; 3: 440–451
DOI: 10.1002/apj
451
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