Modeling of a pilot-scale trickle bed reactor for the catalytic oxidation of phenol
A mathematical model was developed to simulate the catalytic wet air oxidation (CWAO) of aqueous phenol in a trickle bed reactor (TBR). Both ‘axial dispersion’ and ‘plug flow’ models were proposed. ‘Steady-state’ mass transfers across different phases inside the reactor have all been considered in parallel with oxidation reactions catalyzed by heterogeneous copper catalyst supported on activated carbon. The changes in the concentrations of oxygen and phenol in various phases were thus depicted as a function of bed length. In order to validate the accuracy of the established TBR model, a series of experiments on phenol oxidation were performed on a pilot-scale TBR containing 5.6 l of catalysts. The model was found able to give satisfactory predictions for nearly half of all the runs. The discrepancies between the experimental and modeling results were investigated for the less promising runs. It was also noticed that similar simulation results could be attained from ‘axial dispersion’ model against ‘plug flow’ model. Following the discussion on the changes of phenol and oxygen concentrations in the various phases, it is finally concluded that the performance of the TBR of this study depends largely on gas-to-liquid mass transfer process. Further suggestions with regards to reactor optimization are also proposed on the basis of experimental outcome.
Separation and Puriﬁcation Technology 67 (2009) 158–165
Contents lists available at ScienceDirect
Separation and Puriﬁcation Technology
journal homepage: www.elsevier.com/locate/seppur
Modeling of a pilot-scale trickle bed reactor for the
catalytic oxidation of phenol
Qiang Wua, Xijun Hua,∗,PoLockYue
a, Jian Fengb, Xi Chenb, Huiping Zhang c, Shizhang Qiao d
aDepartment of Chemical Engineering, Hong Kong University of Science & Technology, Hong Kong, China
bDepartment of Control Science & Engineering, Zhejiang University, Hangzhou 310027, China
cSchool of Chemical and Energy Engineering, South China University of Technology, Guangzhou 510640, China
dARC Centre for Functional Nanomaterials, University of Queensland, Brisbane QLD 4072, Australia
Trickle bed reactor
Wet air oxidation
Copper/activated carbon catalyst
A mathematical model was developed to simulate the catalytic wet air oxidation (CWAO) of aqueous
phenol in a trickle bed reactor (TBR). Both ‘axial dispersion’ and ‘plug ﬂow’ models were proposed.
‘Steady-state’ mass transfersacross different phases inside the reactor have all been considered in parallel
with oxidation reactions catalyzed by heterogeneous copper catalyst supported on activated carbon. The
changes in the concentrations of oxygen and phenol in various phases were thus depicted as a function
of bed length. In order to validate the accuracy of the established TBR model, a series of experiments
on phenol oxidation were performed on a pilot-scale TBR containing 5.6l of catalysts. The model was
found able to give satisfactory predictions for nearly half of all the runs. The discrepancies between the
experimental and modeling results were investigated for the less promising runs. It was also noticed
that similar simulation results could be attained from ‘axial dispersion’ model against ‘plug ﬂow’ model.
Following the discussion on the changes of phenol and oxygen concentrations in the various phases, it
is ﬁnally concluded that the performance of the TBR of this study depends largely on gas-to-liquid mass
transfer process. Further suggestions with regards to reactor optimization are also proposed on the basis
of experimental outcome.
© 2009 Elsevier B.V. All rights reserved.
To detoxify highly polluted industrial wastewater of low
biodegradability, over the past decades, a number of studies have
been given to the application of wet air oxidation (WAO) tech-
nique for wastewater treatment, as reviewed by Mishra et al. .
WAO refers to the process in which liquid pollutants are oxi-
dized by oxygen at elevated temperature (125–320 ◦C) and pressure
(0.5–20 MPa). It is advantageous overconventional biological meth-
ods in the respect that high concentration non-biodegradable toxic
substances can be degraded with high efﬁciency. Nevertheless, the
operational cost of a typical WAO is tremendously high, owing to
the need to escalate system pressure and temperature. In view of
this, more recently, researchers have been focusing on the devel-
opment of a certain catalyst by which the same goal of oxidizing
organic pollutants can be achieved at mild pressure and temper-
ature. These attempts give rise to the catalytic wet air oxidation
(CWAO) process [2–18].
∗Corresponding author. Tel.: +852 23587134; fax: +852 23580054.
E-mail address: email@example.com (X. Hu).
CWAOprocess can be conducted either in a batch or in a contin-
uous reactor, the latter of which attracts more attention due to its
more operational convenience and treatment ﬂexibility. Trickle bed
reactor (TBR) is one of the ideal continuous reactor options and the
mathematical simulation of a CWAOprocess taking place in TBR has
been widely conducted. Some of the major ﬁndings in this regard
have been summarized in the following.
On the basis of their studies on the mass transfer coefﬁcients of
gas-to-liquid and liquid-to-solid processes in TBR, Goto and Smith
 established both ‘axial dispersion’ and ‘plug ﬂow’ models to
predict the conversion rate of oxidizing formic acid by oxygen at
temperatures of 212–240◦C and pressure of 40atm. The discrep-
ancies between the two models were found negligible and the
modeling results were in accordance with experimental data. This
work concluded that, in term of their effects on the conversion
rate, four mass transfer resistances are listed from the most to the
least signiﬁcance: gas-to-liquid mass transfer, intra-particle diffu-
sion, liquid-to-solid (particle) mass transfer and axial dispersion.
Bergault et al.  also observed that the hydrogenation of ace-
tophenone in a TBR is much more sensitive to the mass transfer
of gas-to-liquid than that of liquid-to-solid. The reviews conducted
by Al-Dahhan et al.  and Wu et al.  further suggested that
the incomplete wetting should also be taken into account as one
1383-5866/$ – see front matter © 2009 Elsevier B.V. All rights reserved.
Q. Wu et al. / Separation and Puriﬁcation Technology 67 (2009) 158–165 159
of the factors affecting the TBR performance. Another successful
example of the TBR modeling work completed byAvraam and Vasa-
los  also took energy balance into account when establishing
the governing equations for the prediction of hydro-processing of
oil in a pilot-scale TBR at steady-state. Singh et al.  attained
promising predictions of phenol conversion on alumina supported
However, as the CWAO in TBR is a fairly complex process
that comprises various steps of mass transfer and chemical reac-
tion, so far more literates have reported on the unsatisfactory
prediction of the developed models. In their attempts to predict
the hydro-processing of oil, Korsten and Hoffmann  had to
adjust the wetting efﬁciency before obtaining good agreement
between experimental and simulation results. Valerius et al. 
encountered the similar problem and later manually modiﬁed
the catalyst activity of the model so as to ﬁt the experimental
data. Pintar et al.  acknowledged that the intrinsic reac-
tion rate constant in their simulation model had to be increased
by three times to make the model outcome agree well with
experimental observations. They attributed such adjustment in
model parameters to the possible deactivation in catalytic activ-
ity. The adjusted parameter in Bergault et al.’s model  was
the gas-to-liquid mass transfer coefﬁcient, which was intention-
ally increased by two to three times to give better simulation
A non-steady-state TBR model was ﬁrst developed by Iliuta and
Larachi  to describe CWAO of phenol. In spite of this contribu-
tion, this model was merely theoretically established without any
supporting experimental evidence.
Guo and Al-Dahhan  carefully reviewed all the models
developed in the past and attributed the discouraging model-
ing results to the fact that liquid vaporization was predominately
ignored by many studies. This ﬁnding was agreed by Suwanpra-
sop et al.  who assessed the effect of liquid vaporization on the
phenol conversion by adjusting gas-to-liquid mass transfer coefﬁ-
It also has to be stressed that so far no TBR model consisting of
dimensionless numbers only has been proposed, leading to the dif-
ﬁculties in applying a very speciﬁc model to a more general CWAO
process with a wider operational range.
The objective of this study is to develop a TBR model on the
basis of dimensionless numbers and parameters that helps to facil-
itate the scale-up of CWAO process. In doing so, a TBR model was
ﬁrst developed for the oxidation of aqueous phenol by using all
the parameters determined from lab-scale studies. The speciﬁc TBR
model was then normalized and the steady-state dimensionless
concentrations of phenol and oxygen were simulated along bed
length. Subsequently, a series of continuous CWAO experiments
were conducted in a pilot-scale TBR to verify the modeling out-
2.1. Model assumptions
In developing the TBR model, some general assumptions were
made as following:
(a) The entire TBR is under isothermal and isobaric conditions;
(b) Both the concentrations of phenol (A) and oxygen (B) are time-
independent or have reached ‘steady-state’;
(c) A is non-volatile compound and there is no existence of A
in the gas phase, meaning the possible effect of water vapor-
ization on phenol oxidation is not taken into account in this
Governing equations for ‘axial dispersion’ and ‘plug ﬂow’ model.
‘Axial dispersion’ model
dl +kGLaGL CB,G
dl −LSkLS aLS(CA,L−CA,L–S)=0 (1.2)
dl −kGLaGL CB,G
−CB,L+LSkLS aLS(CB,L−CB,L–S)=0 (1.3)
kLSaLS (CA,L−CA,L–S)=e,A(1 −ε)RA,V(1.4)
kLSaLS (CB,L−CB,L–S)=7e,A(1 −ε)RA,V(1.5)
CA,L=CA,Li at l=0 (1.6)
CB,G=CB,Gi at l=0 (1.8)
‘Plug ﬂow’ model
dl +kGLaGL CB,G
dl +LSkLS aLS(CA,L−CA,L–S)=0 (2.2)
dl −kGLaGL CB,G
−CB,L+LSkLS aLS(CB,L−CB,L–S)=0 (2.3)
kLSaLS (CA,L−CA,L–S)=e,A(1 −ε)RA,V(2.4)
kLSaLS (CB,L−CB,L−S)=7e,A(1 −ε)RA,V(2.5)
CA,L=CA,Li at l=0 (2.6)
CB,G=CB,Gi at l=0 (2.7)
(d) The oxidation takes place between the adsorbed A and B on
the catalyst surface only and there is neither reaction between
gaseous A and aqueous B nor mass transfer of A to the unwetted
area of catalyst; and,
(e) The changes of superﬁcial velocities in the gas and the liquid
phases throughout the whole TBR are negligible.
2.2. Model governing equations
This modeling work has investigated the effect of axial dis-
persion on the TBR’s performance by establishing both ‘axial
dispersion’ and ‘non-axial dispersion’ or ‘plug ﬂow’ models. The
governing equations for these two models are listed in Table 1.
The semi-empirical or empirical correlations quoted for calcu-
lating the model parameters as shown in the above table were
obtained from other lab-scale studies and summarized in Table 2.
For the purpose of normalizing the governing equations, the
model parameters were grouped into various dimensionless num-
bers as detailed in Table 3.
The incorporation of these dimensionless numbers or parame-
ters into the original equations has therefore produced dimension-
less governing equations as shown in Table 4.
160 Q. Wu et al. / Separation and Puriﬁcation Technology 67 (2009) 158–165
Correlations for calculating coefﬁcient/parameter.
Parameter Correlation References
LGosset et al. 
DL,Z=13 Re 0.4
LSingh et al. 
TWu, PhD Thesis, HKUST, 2001
T−2.3854Wu, PhD Thesis, HKUST, 2001
BL Gosset et al. 
DAL =3.77 Re0.8
AL Wu, PhD Thesis, HKUST, 2001
khet exp −4258.7
T+5.62Wu et al. 
(1+KACA,L−S)2.0Wu et al. 
L(uL<2.12×10−3m/s); or 1.0 (uL>2.12×10 −3m/s) Wu, PhD Thesis, HKUST, 2001
2.3. Estimate of effectiveness factor
To estimate the effectiveness factor accounting for the impact
of intra-particle diffusion on reaction rate: e,A, the intra-particle
diffusion equation that couples the ‘Langmuir–Hinshelwood’ type
of reaction kinetics has to be solved numerically. This step is quite
time consuming in terms of initial value settings and calculation
by iteration method. In view of this, alternatively, the approximate
estimation of e,A was made by conducting magnitude analysis as
Dimensionless numbers or parameters used in the TBR model.
Dimensionless numbers/parameters Deﬁnition
Commonly used numbers
rAi,G catkhet CAL,iL
rAi,L catkhet CAL,iL
The volumetric consumption rate of A at catalyst surface is
If we take quasi-1st order reaction approximation with respect
to CA, the volumetric reaction rate constant can be written as
The magnitudes of cat,khet ,C
Band (1 + KACA)2were estimated
to be: 103kg/m3,10
−2m6/(mol kg s), 10−4mol/m3and 100to 101,
respectively. The Thiele Module L, as expressed in Eq. (7), is there-
fore calculated to be less than 10−1and e,A can be considered
In other words, the effect of intra-particle diffusion on reaction
rate can be disregarded and Eqs. (3.4),(4.4),(3.5) and (4.5) can be
respectively rewritten into Eq. (3.4), (4.4), (3.5) and (4.5)
(1 +AizA)=0(3.4) and (4.4)
(1 +AizA)=0(3.5) and (4.5)
The ﬁnalized model equations at various input parameters were
numerically solved using gPROMS®software.
Copper supported by activated carbon waschosen as the hetero-
geneous catalyst for the CWAO of phenol in this work. Cylindrical
activated carbon was provided by Norit Co., U.S. and has a mean
diameter of 0.8 mm. The copper in elementary form was success-
fully incorporated into the activated carbon by hydrogen reduction
following wet impregnation, resulting in a copper loading of
82.0 mg/g and BET surface area of 919.55 m2/g.
Aqueous phenol (90%) was purchased from Riedel-de Haën AG,
Germany. The nitrogen and oxygen cylinders at industrial grade
served as the gas sources, taking into account the large reactor
volume in this study.
Q. Wu et al. / Separation and Puriﬁcation Technology 67 (2009) 158–165 161
Normalized governing equations of the TBR model.
‘Axial dispersion’ model
d +8.52 Re0.45
ˇ(1 −ε)(xB−yB)=0 (3.1)
d −4.41 ˛ˇ(1 −ε)PeAZRe0.13
AL (yA−zA)=0(ReL<0.75),or; d2yA
−3.77 ˛ˇ(1 −ε)PeAZRe−0.2
AL (yA−zA)=0 (ReL>0.75) (3.2)
d −4.41 ˛ˇ(1 −ε)PeBZRe0.13
BL (yB−zB)(ReL<0.75),or +8.53˛2PeZRe−0.55
d −3.77 ˛ˇ(1 −ε)PeBZRe−0.2
BL (yB−zB) (ReL>0.75) +8.53˛2PeZRe−0.55
(1 +AizA)2=0 (3.4)
(1 +AizA)2=0 (3.5)
d =0at=1 (3.6)
d =0at=1 (3.10)
‘Plug ﬂow’ model
d +8.53 Re0.45
ˇ(1 −ε)(xB−yB)=0 (4.1)
d +4.41ˇ(1 −ε)Re0.13
AL (yA−zA)=0 (ReAL <0.75),or dyA
d +3.77ˇ(1 −ε)Re−0.2
AL (yA−zA)=0 (ReAL >0.75) (4.2)
d +4.41ˇ(1 −ε)Re0.13
d +3.77ˇ(1 −ε)Re−0.2
(1 +AizA)=0 (4.4)
(1 +AizA)=0 (4.5)
3.2. Apparatus and procedure
The pilot-scale TBR system employed by this study was manu-
factured by Toyo Koatsu Co., Japan that totals a bed volume of 10 l.
The schematic diagram and operational procedure of this system
are given in Fig. 1 and the following paragraphs, respectively.
Prior to each run, phenol solution was prepared at certain ini-
tial concentration and stored with the presence of stirring in the
liquid feeding vessel. All the line-heater, pre-heater and TBR heater
were then switched on after setting the temperature slightly higher
than the desired value, taking into account the subsequent cooling
effects of liquid and gas inputs. After the system had reached the set
temperature, nitrogen was introduced to pressurize the system to
the required pressure. The gas ﬂow comprising oxygen and nitro-
gen was then introduced into the TBR concurrently with aqueous
phenol being fed through a high-pressure pump. The ﬂow rates of
the gas and the liquid were controlled by gas mass ﬂow controllers
and high-pressure liquid pump, respectively.
The temperature of the TBR system was designed to be control-
lable by the temperature controllers mounted in the adjacency of
the wall heaters. However, owing to the signiﬁcant heat resistance
of activated carbon and high catalyst loading, as the reaction pro-
ceeded, the temperature inside the TBR was unable to be controlled
precisely at the set values. The actual temperature, as displayed
by means of the temperature controller, ﬂuctuated around the set
value within a deviation range of 10 ◦C.
Having reacted in the TBR, the gas–liquid mixture was cooled
down by a heat exchanger and a cooler. This was followed by the
separation of liquid and gas in a gas–liquid separator located behind
the cooler. The outlet liquid was stored in a liquid receiver and sam-
pled at a time interval of 30 min for analysis. The gas phase was
vented through the outlet gas line located above the separator.
162 Q. Wu et al. / Separation and Puriﬁcation Technology 67 (2009) 158–165
Fig. 1. Schematic diagram of the TBR system of this study. (1) Wastewater feeding
vessel; (2) valves; (3) pump; (4) pre-heater; (5) heat exchanger; (6) static mixer;(7)
trickle bed; (8) catalyst; (9) wall heater; (10) cooler; (11) gas–liquid separator; (12)
wet gas meter; (13) oxygen cylinder; (14) nitrogen cylinder; (15) water receiver.
The range of operational parameters.
Temperature, K 313.0–333.0 (±10.0)
Pressure, MPa 1.0–3.0
Superﬁcial liquid velocity, m/s 0.46–1.38×10 −3
Liquid Reynolds number 2.0–5.9
Superﬁcial gas velocity, m/s 0.24–2.13 ×10−3
Gas Reynolds number 0.18–0.53
Phenol initial concentration, mol/m320.0
Oxygen initial concentration, % (in volume) 10.0
Tables 5 and 6 give the range of the operational parameters in
the experimental work and the actual conditions of the series of
experiments for model validation purpose, respectively.
Given the settings of initial phenol and oxygen concentrations,
the reduction in the superﬁcial liquid and gas velocities due to
reaction consumption can be ignored, satisfying assumption (e).
All the collected liquid samples were immediately sealed and
stored at 20 ◦C to prevent any reaction inside the samples proceed-
In determining the aqueous phenol concentration, the sampled
solution ﬁrst reacted with 4-amionantipyrine solution in a prepared
buffer solution. The product was then colored with the addition
of K3Fe(CN)6. A Shimadzu UV–vis spectrophotometer was used
The conditions of experimental runs for model validation.
Test N o. T,K P,MPa uL, mm/s uG, mm/L
1 323 1.0 0.46 0.71
2 323 1.0 0.46 1.42
3 323 1.0 0.46 2.13
4 323 1.0 1.38 0.71
5 323 1.0 0.92 0.71
6 313 1.0 0.46 0.70
7 333 1.0 0.46 0.73
8 323 2.0 0.46 0.36
9 323 3.0 0.46 0.24
to estimate the phenol concentration by measuring the intensity
of the light that passed through the colored solution at a wave-
length of 510 nm. Prior to each measurement, a series of standard
phenol solutions with concentrations ranging from 0 to 5mg/L
were prepared for calibration purpose. Good linear relationship
was achieved, indicating that the chosen wavelength was able to
well serve the sample measurement. More details of this analytical
method can be found elsewhere [31,32].
4. Results and discussion
4.1. Model validation
To verify the precisionand accuracy of the TBR model, the effects
of the following factors on phenol degradation rate were investi-
gated: gas velocity, liquid velocity, bed temperature and pressure.
The simulated phenol outlet concentrations were compared with
those in the ﬁnal samples of each run and depicted in Fig. 2.
Fig. 2 indicates that all the simulation results yield higher out-
let phenol concentration or lower conversion rate when compared
with the actual situation. Furthermore, out of nine experimental
runs there are only four runs having a discrepancy below 20%,
accounting for less than 50% of the total number of runs. The highest
discrepancy is about 570% whereas the lowest is 3.6%.
Two reasons are believed to account for the poor prediction in
some of the runs.
Firstly, given the limited volume of wastewater, the TBR oper-
ation in some of the runs might not reach steady-state. All the
aqueous phenol was prepared prior to each run, the volume of
which was constrained to the designed volume of feeding tank
totaling 40 l. The retention time of each run therefore ranged from
100 to 200 min. However, the TBR is built on a pilot-scale and
such retention time was presumably unable to provide stabilized
treatment efﬁciency, as also reﬂected in the ﬂuctuation in the con-
centration of the outlet phenol solution against retention time. The
relatively high phenol removal rate in the actual cases might well be
more attributed to the adsorption effect, which plays more impor-
tant role during the start-up period of the bed operation.
Secondly, there existed differences between the model and
experimental parameters. The model kinetic parameters were esti-
mated on the basis of fresh catalyst. In reality, however, owing to
the ‘bed washing’ effect as a result of a large number of experimen-
Fig. 2. Comparison of the outcomes between experimental and modeling work at
the operational conditions listed in Table 6.
Q. Wu et al. / Separation and Puriﬁcation Technology 67 (2009) 158–165 163
Fig. 3. Veriﬁcation of catalyst deactivation(P= 1.0 MPa, t=150◦C, uG=1.4×10−4m/s,
uL= 4.6 ×10−4m/s).
tal runs, the deactivation of the copper catalyst occurred during the
TBR operation. This conclusion was made by means of a compar-
ative run where all the experimental parameters were set exactly
the same as the run using fresh catalysts. It was observed that there
existed signiﬁcant differences in term of outlet phenol concentra-
tion as displayed in Fig. 3.
Obviously, despite that the fresh catalysts were able to degrade
100% of the aqueous phenol as soon as the liquid passed throughthe
bed, the spent catalyst achieved 90% of the phenol oxidation after
about 2 h of running. This has indicated that part of the catalyst for
modeling veriﬁcation has deteriorated.
4.2. Effect of axial dispersion
A comparison has been made between the ‘axial dispersion’
model and ‘plug ﬂow’ model, with the purpose to investigate the
effect of axial dispersion. The changes of phenol and oxygen con-
centrations as functions of bed length are given in Fig. 4.
It is noticed that in both models xBand yAexhibit quite close
descending trends, expect for the bed outlet zone (= 0.9–1.0)
Fig. 4. Comparison of phenol degradation and oxygen consumption rates between
‘axial dispersion’ and ‘plug ﬂow’ models.
Fig. 5. Simulated concentration proﬁles of phenol and oxygen in various phases in
run No. 1 as detailed in Table 6.
where yAin the ‘axial dispersion’ model is less than 10% higher
than that in the ‘plug ﬂow’ model. This gives rise to the implication
that axial dispersion does not play an important role in the phenol
degradation process in TBR.
4.3. Characters of TBR
Fig. 5 gives a typical proﬁle of all the simulated phenol and
oxygen concentrations along bed length direction.
It can be clearly concluded from Fig. 5 that TBR is a typical
‘gas-to-liquid’ mass transfer limited type of reactor. In spite of
the signiﬁcant concentration gradient between the gas and liquid
phase, the consumption of gaseous oxygen is still less than 20%
after passing through the whole bed. Moreover, the nearly over-
lapped trends of yAand zAand the closeness between yBand zB
indicate that the mass transfer from bulk liquid to solid surface is
very fast. Or in other words, the resistance of liquid-to-solid mass
transfer can be ignored. The reactor is undoubtedly more sensi-
tive to the variations in the gas ﬂow than in the liquid ﬂow. The
considerable gas-to-liquid mass transfer resistance also hinders the
catalytic reaction taking place on the catalyst surface, resulting in
low conversion of phenol.
By means of the investigation on axial dispersion discussed in
the previous section, we may list the descending order of various
resistances in term of their signiﬁcances as following: gas-to-liquid
mass transfer, liquid-to-solid mass transfer and axial dispersion.
Methods aiming to improve the gas-to-liquid mass transfer in TBR
therefore should be taken as top priority in improvingthe treatment
efﬁciency and oxygen utility of TBR.
Fig. 5 also indicates that throughout the whole TBR the changes
in the concentrations of aqueous phenol and gaseous oxygen are
fairly little, echoing our assumption made previously in approxi-
mating the estimation of effectiveness factor e,A.
In this study a dimensionless TBR model was established that
integrates all the mass transfer and the chemical reactions involved
in the CWAO of phenol by oxygen when the process has arrived at
‘steady-state’. The major ﬁndings of this study are:
(a) A dimensionless TBR model is able to scale-up lab observations
to pilot-scale applications. Nevertheless, as result of catalyst
164 Q. Wu et al. / Separation and Puriﬁcation Technology 67 (2009) 158–165
deactivation and insufﬁcient retention time, the developed
dimensionless model achieved satisfactory prediction results
for nearly half of the pilot-scale runs.
(b) The effects of axial dispersion and liquid-to-solid mass transfer
in a typical TBR are considerably unimportant when compared
with gas-to-liquid mass transfer. In light of the ‘gas-to-liquid
mass transfer dominated’ character a typical TBR possesses, it
is further recommended that reactor conﬁguration efforts of
enhancing gas-to-liquid mass transfer be made to improve the
It is further suggested that in the future the below improve-
ments be taken into account in respect of pilot-scale TBR design for
•Enlargement of feeding tank volume so as to ensure the continuity
of the feeding solution;
•Better design of reactor heaters to maintain the stability of the
temperature inside the reactor, e.g. provision of additional wall
heaters, increase of bed length/radius ration, etc.
aGL speciﬁc gas–liquid contact area per unit volume of bed
aLS speciﬁc liquid–solid contact area per unit volume of bed
apspeciﬁc surface area per unit volume of particle (m−1)
CA,Li inlet aqueous phenol concentration (mol/m3)
CA,L aqueous phenol concentration in bulk liquid (mol/m3)
CA,L–S aqueous phenol concentration at liquid–solid interface
CB,Gi inlet oxygen molar concentration in bulk gas (mol/m3)
CB,G oxygen concentration in bulk gas (mol/m3)
CB,L dissolved oxygen concentration in bulk liquid (mol/m3)
CB,L–S dissolved oxygen molar concentration at liquid–solid
DAL diffusivity of phenol in liquid phase (m2/s)
DL,Z axial dispersion coefﬁcient of liquid (m2/s)
DBG diffusivity of oxygen in gas phase (m2/s)
dpbed particle diameter (m)
Fr Froude number
GaLGalaleo number of liquid
HBHenry’s law constant for dissolved oxygen in water
KAadsorption equilibrium constant of phenol (m3/mol)
kGL gas-to-liquid mass transfer coefﬁcient (m/s)
kLS liquid-to-solid mass transfer coefﬁcient (m/s)
khet,app apparent reaction rate constant (m6/(kg mol s))
kVvolumetric rate constant as deﬁned in Eq. (6) (s−1)
lvariable bed length (m)
Lwhole bed length (m)
Poperational pressure (MPa)
PeZPeclet number of liquid
RA,V phenol disappearance rate per unit volume of catalyst
(mol Phenol/(m3catalyst s))
ReLReynolds number of liquid phase
ReGReynolds number of gas phase
rpbed particle radius (m)
ScAL Schmidt number of aqueous phenol
ScBL Schmidt number of dissolved oxygen
ScBG Schmidt number of oxygen in gas phase
Treaction temperature (K)
uGsuperﬁcial gas velocity (m/s)
uLsuperﬁcial liquid velocity (m/s)
WeLWeber number of liquid phase
xBdimensionless molar fraction of oxygen in bulk
gas = CB,G/CBG,i
yAdimensionless molar fraction of phenol in bulk liq-
uid = CA,L/CA,Li
yBdimensionless molar fraction of dissolved oxygen in bulk
liquid = CB,L/CB,Gi
zAdimensionless molar fraction of phenol at liquid–solid
interface = CA,L–S/CA,Li
zBdimensionless molar fraction of dissolved oxygen at
liquid–solid interface = CB,L–S /CB,Gi
˛dimensionless bed parameter
ˇdimensionless bed parameter
e,A effectiveness factor of A
LS wetting efﬁciency
Ggas viscosity (Pa s)
Lliquid viscosity (Pa s)
A,i model parameter
normalized bed length= l/L
cat catalyst bulk density (kg/m3)
Ggas density (kg/m3)
Lliquid density (kg/m3)
LThiele Module as deﬁned in Eq. (7)
This work was supported by the Research Grants Council (RGC)
of Hong Kong Government under the grant No. 613705.
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