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Chinese Science Bulletin
2007 SCIENCE IN CHINA PRESS
Springer
www.scichina.com www.springerlink.com Chinese Science Bulletin| August 2007 | vol. 52 | no. 16 | 2184-2189
Numerical simulat ion for volat ile organic compound
removal in rotat ing drum biofil ter
CHEN Hong, YANG ChunPing, ZENG GuangMing, YU KongLiang, QU Wei, YU GuanLong & MENG Lei
College of Environmental Science and Engineering, Hunan University, Changsha 410082, China
Rotating drum biofilters (RDBs) could effectively remove volatile organic compounds (VOCs) from
waste gas streams. A mathematical model was developed on the basis of mass transport and mass
balance equations in an RDB, the two-film theory, and the Monod kinetics. This model took account of
mass transfer and biodegradation of VOC in the gas-water-biofilm three-phase system in the biofilter,
and could simulate variations of VOC removal efficiency with a changing specific surface area and
porosity of the media due to the increasing of biofilm thickness in the biofilter. Toluene was used as a
model VOC. This model was further simplified by introducing a coefficient of the gas velocity and ne-
glecting the water phase due to the complexity of operating conditions. The equations for the biofilm
phase, gas phase, and biofilm accumulation in this model were solved using collocation method, ana-
lytic method, and the Runge-Kutta method separately. A computer program was written down as
MATLAB to solve this model. Results of numerical solutions showed that toluene removal efficiency in
the RDB increased and reached the maximum values of 97% on day 4 after the startup, and then de-
creased and remained at 90% after 5 more days of operation. Toluene concentration was high at the
outermost layer where more than 70% toluene was removed, and was low at the innermost layer where
less than 10% toluene was removed. The dynamic removal efficiencies from this model correlated
reasonably well with experimental results for toluene removal in a multi-layered RDB.
biodegradation, biofilms, model, numerical solutions, rotating drum biofilter, VOC
Biofiltration could cost-effectively remove volatile or-
ganic compounds and odours from waste gas streams[13]
.
Effective simulation of the complex process is helpful to
better understanding the mechanisms occurring in the
biofilters, and consequently to better designing and oper-
ating biofilters. Many mathematical models were pro-
posed for biofiltration processes including the basis of theadsorption-biodegradation model[4]
and the absorp-
tion-biodegradation theory[5]
. Biodegradation models for
biotrickling filters were developed on the basis of the
two-film theory and the Mechaelis-Menten equation[6]
. A
capillary tube model was presented which took account of
the transport resistance in the gas-water interphase and the
water phase[7]
. The mass balance equations for biodegra-
dation of ethyl mercaptan in a fungal biofilter were intro-
duced on the basis of the adsorption-biodegradation the-
ory[8]
. Analytical solutions and numerical methods were
used to solve the complex models[7,9]
. Unfortunately,
credible models for reactor design and operation are still
not available due to the complexity of the biofiltration
process[10]
. Therefore, more investigations are needed to
better simulate biofiltration processes.
Rotating drum biofilters (RDBs) displayed better
performances than traditional biofilters or biotrickling
filters, which overcame some important shortcomings
including uneven distributions of nutrients, organic
loadings, and biomass[1114]
. In this paper, a transport-
Received October 12, 2006; accepted March 13, 2007
doi: 10.1007/s11434-007-0332-8Corresponding author (email: [email protected])Supported by the Program for New Century Excellent Talents in University from the
Ministry of Education of China (Grant No. NCET050701), the China Postdoctoral
Science Foundation (Grant No. 2005037206), the Scientific Research Foundation for
the Returned Overseas Chinese Scholars from the Ministry of Education of China,
and the Science Foundation and Postdoctoral Science Foundation of Hunan Univer-
sity
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CHEN Honget al. Chinese Science Bulletin| August 2007 | vol. 52 | no. 16 | 2184-2189 2185
ARTICLES
ENVIRONMENTALCHEMISTRY
biodegradation model for VOC removal in an RDB is
developed on the basis of the two-biofilm theory, mass
balance equations, and the Monod kinetics. This model
was further simplified by neglecting transport resistance
in the water phase and introducing an effective coeffi-
cient for gas velocity. The equations for the mass trans-port and bioreactions within the biofilm phase and gas
phase and the accumulation of biofilms in this model
were solved using collocation method, analytic method,
and the Runge-Kutta method separately. A computer
program was written down as MATLAB to solve this
model. It would help to better understanding the mecha-
nisms for toluene removal in RDBs and to better de-
signing and optimizing RDBs.
1 Materials and methods
1.1 Experimental apparatus and operation condi-
tions
The RDB with multi-layer foam media consisted of a
closed stainless steel chamber in which four layers of
spongy medium were mounted on a stainless steel drum
frame with impermeable end plates at both ends. The
media were rotated at 1.0 r/min with continuous sub-
merging and emerging cycles. The lower portion of the
biofilter chamber was filled with a nutrient solution
where the media were submerged when rotating at its
lowest position. The porosity of the medium with a poresize of about 4 pores/cm was 96%. The configuration of
multi-layer biofilter is illustrated in Figure 1.
Figure 1 Cross-sectional view of the multi-layer biofilter.
Toluene was used as model VOC. The nutrient solu-
tion was fed at a rate of 4.2 L/d. Activated sludge taken
from a wastewater treatment plant was used for seeding
the RDB. GC was used to analyze the toluene concen-
trations of the influent and effluent gas streams. When
operation parameters were changed, toluene removal
efficiencies at various organic loading rates were ob-
tained. More detailed descriptions about the experiment
can be found in refs. [1113].
1.2 Model development
In the RDB, waste gas streams passed through the inter-
spaces of the solid and liquid phase within the chamber,
and exited the drum through the center of the drum[15]
.
According to the two-film theory, there were gas, water,
and biofilm phases in the RDB. There existed gas-water
and water-biofilm interfaces. The schematic of a charac-
teristic cell for transport and degradation in the medium
is illustrated in Figure 2.
A characteristic cell was selected whose volume was
WrR, in which Wwas the cell width perpendicular to
the R and r dimensions, r was perpendicular to the
biofilm support, andR was the radius of the drum. Massbalance equations in gas, water, and biofilm phases are
developed as follows.
1.2.1 Gas phase equations. VOC concentration in the
gas phase was considered uniform at a given diameterR
within the drum. Three assumptions were made. First,
only convection in the R dimension existed. Next, con-
vection in rdimension could be neglected. At last, VOC
transported through the gas-water interphase by diffu-
sion. VOC accumulation rate in characteristic cell
WrgR is given as
( )g g g 0 g g 0 g
g
( ) ( )
,
R R RC Wr R C u Wr C u Wr t
jW Rr
+
=
(1)
wfp
g
0
g
LLrrj
R
Cu
t
C
++=
=
, (2)
wherej is the flux of VOC into the water layer in a spe-
cific surface area, Cg the VOC concentration in gas
phase, u0 the empty-bed gas velocity, rp the radius of the
cell,Lf the width of biofilm, and Lw the width of liquid
film. The boundary conditions were obtained by assum-ing that the VOC concentrations in the water and gas
sides of the interface were in equilibrium, and the
Henrys law defined the relationship of the VOC con-
centrations. Therefore,
ww f w f
Cj J D
r
= =
, (3)
@ rrp+LfLw, CgHCw, (4)
@r>= rp+LfLw, 0g =
r
C, (5)
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Figure 2 Schematic of mass transport in the medium of the RDB.
whereDfis the diffusivity of VOC in water, Cw the VOC
concentration in water phase,Hthe Henrys constant of
the contaminant, and af the specific surface area. If the
VOC concentration in the gas phase was considered
nonuniform in the R dimension of the drum, VOC ac-
cumulation rate in WrR is
( ) ( ) ( )
( ) ( )
g g 0 g 0
g g ,
R R R
r r r
C W r R C u W r C u W r t
j W R j W R
+
+
=
+
(6)
2
g g g g g0 0 g 2
C C j C C u u D
t R r R r
= + = +
, (7)
whereDg is the diffusivity of VOC in air. The boundary
conditions are given as follows:
@r=rp+LfLw, Cg=HCw,
p f w p f w
wff w ,
r r L L r r L L
CCD D
r r= + + = + +
=
(8)
@r>= rp+LfLw, 0g
r
C. (9)
1.2.2 Water phase equations. Assuming that the domi-
nant mechanisms of mass transport were diffusion in rdimension and convection in R dimension in water
phase, and that VOC degradation in the liquid could be
neglected. Mass balance equations in the water phase for
the characteristic cell WrR were similar to those in
the gas phase when VOC concentration was nonuniform
in the R dimension. VOC accumulation rate in the cell
WrR is
( ) ( ) ( )w w w w wR R RC W r R C V W r C V W r t +
=
( ) ( )f fj j ,r r rW R W R + + (10)
2w w w wf
w w w 2
C C C C jV V D
t R r R r
= + = +
, (11)
where Vw is the average water velocity on the surface of
the medium and biofilm layer. The following boundary
conditions can be applied,
@r=rp+Lf, Cf=Cw,
p f p f
wff w .
r r L r r L
CCD D
r r= + = +
=
(12)
1.2.3 Biofilm phase equations. Assuming that only
diffusion existed in rdimension in biofilm phase, and all
processes were irreversible. Mass balance equation for
the cell WrR in biofilm phase could be expressed as
( ) ( ) ( )biofilmf f fj j ,r r rdC
C W r R W r R W r W r t dt +
=
(13)
( ) 1v ffj
,r
ocdCC W r R Y W r R W r Rt dt
+ =
(14)
where Cbiofilm is the biomass concentration in the biofilm,and Cvoc the VOC concentration in the biofilm phase.
The relationship of VOC biodegradation rate and the
microorganism growth rate was defined by the Monod
kinetics. Therefore, eq. (14) could be rewritten as
f m f f f f
s f
,C X C D C
t Y K C x r r
+ = +
(15)
where m is the maximum specific growth rate, Ks the
Monod constant, Ythe yield coefficient, and Xf the bio-
mass density. Assuming that VOC did not penetrate into
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Table 1 Parameter values used for solving the model equations
Parameter Value
Maximum specific growth rate, m, (d) 1.8
Decay rate coefficient, bd, (d) 0.004
Default shear rate coefficient, bs0, (d) 0.7
Monod constant,Ks (mg VOC/L) 0.15
Yield coefficient, Y, (mg VSS/mg VOC) 0.84VOC biofilm/water diffusivity ratio, rd 0.9
Biomass density,Xf, (mg VSS/L) 6000
Initial biofilm thickness,Lf0, (cm) 0.0004
Toluene conversion factor, (kg COD/kgVOC) 3.126
Toluene diffusivity in water,Dw, (cm2/s) 10.8106
Effective coefficient of gas velocity,Kw 0.6
Henrys constant of toluene,H, ((mg/L)gas/(mg/L)water) 0.338
it was reasonable to assume that the biofilm thickness in
the drum was no less than the initial biofilm thickness.
The mass balance equations for the biofilm phase (eq.
(21)) and gas phase (eq. (18)) and the equations of bio-mass accumulation (eq. (17)) in this model were solved
using collocation method, analytic method, and the
forth-fifth-order Runge-Kutta method, respectively. In
order to get convergent and precise solutions, close at-
tention should be paid to the characteristic time of the
biofiltration process and the characteristic length of the
drum. The inner functions ofbvpinit, bvp4c, and deval
in the MATLAB software were used respectively to
calculate the initial results, the final numerical results,
and the results at any position ofR=xint.
A computer program was written down as MATLABto solve this model. First, the initial biofilm thickness
and toluene concentration were used to solve mass bal-
ance equation in biofilm phase. Then, the calculation
results from the earlier step were substituted for the cor-
responding variables in the mass balance equation for
gas phase to get the toluene concentration in the next R
value. These two steps were repeated to obtain toluene
concentration profile along the R dimension, and the
effluent toluene concentration also resulted.
Then moving to the next time span, the biofilm
growth rate in this time span was calculated usingbiofilm growth equation. Repeating the previous steps
could lead to the effluent toluene concentration at each
time span. The calculation stopped until all the time
spans were completed.
2 Results and discussion
Performances of the RDB over a long period were cal-
culated at an organic loading rate of 2.0 kg COD/(m3d)
and a gas flow rate of 0.590 L/s. The simulation results
and corresponding experimental results[1113]
are pre-
sented in Figure 3.
Figure 3 Toluene removal efficiencies in the multi-layer RDB over 20 d
after startup.
The removal efficiency in the RDB increased andreached the highest removal efficiency of 97% in the
first 4 days after startup, and then gradually declined to
and stabilized at about 90% in 5 more days. It can be
seen from Figure 3 that this model could simulate the
dynamic performances of the RDB pretty well in the
early period of the operation. However, the model re-
moval efficiencies of toluene were a little lower than the
experimental results. Neglecting water phase when the
model equations were solved or the estimation of the
parameters or the both was considered to contribute to
the difference. Alonso et al.[17] developed a dynamic
model for simulating toluene removal in biotrickling
filters. The removal efficiency calculated using Alonso
model showed the same change trend as the model de-
veloped here for toluene removal in the RDB, and
reached the maximum value earlier and then dropped
much quick. The relative error of the calculation values
to the experimental results was only 5.73%, which has a
standard deviation about 2.54%. The calculation results
correlated with the experimental results very well, which
confirms that the model could simulate the long-term
performance of the multi-layer RDB.
Contaminant profile along medium depth in a biofil-
ter is important for biofilter design and operation. Figure
4 illustrates the calculation results of toluene concentra-
tion and corresponding removal efficiency at different
locations within the drum on the 4th day after startup.
Toluene concentration decreased along the drum depth
from the outermost to the innermost, and the increasing
rates at the outer layers were bigger than those at the
inner layers. On the outermost surface of the drum (R =
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ARTICLES
ENVIRONMENTALCHEMISTRY
Figure 4 Simulating toluene concentration profile along the media depth
of the RDB on the 4th day after startup.
21.6 cm), the initial toluene concentration was 220
mg/m3. The effluent toluene concentration at the inner-
most surface of the medium (R = 2.55 cm) was 8 mg/m3.
Toluene degradation rate was the highest at the outer-
most layer where more than 70% toluene was removed,
and was the lowest at the innermost layer where less
than 10% toluene was removed. The results from the
capillary tube model showed a similar result on the
variation of the contaminant biodegradation rate along
medium depth[7]
.
Biofilm accumulation within media in an RDB de-
creased the interfacial area and the porosity of the media
which resulted in a lower rate of mass transfer and con-
sequently lower removal efficiency. This model could
take account of the temporal variation of biofilm thick-
ness; therefore, dynamic performance of the RDB could
be simulated and predicted. On the basis of earlier re-
search[15]
, this model took account of the effect of water
phase on mass transfer by introducing the effective effi-cient of gas velocity, which resulted in a better correla-
tion of the calculation result with the experimental data.
3 Conclusions
A transport-biodegradation model for VOC removal in
an RDB was developed on the basis of the two-biofilm
theory, mass balance equations, and the Monod kinetics.
The dynamic performances of the RDB for toluene re-
moval were calculated using a program written down as
MATLAB.
The simulation results showed that toluene removal
efficiency in the RDB increased and reached the maxi-
mum values of 97% on day 4 after the startup, and then
decreased and remained at 90% after 5 more days of
operation. Toluene concentration was high at the outer-
most layer where more than 70% toluene was removed,
and was low at the innermost layer where less than 10%
toluene was removed.
The dynamic removal efficiencies from this model
correlated reasonably well with experimental results for
toluene removal in a multi-layered RDB.
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http://dx.doi.org/10.1016/S0304-3894(02)00139-5http://dx.doi.org/10.1002/bit.260251222http://dx.doi.org/10.1016/j.cej.2005.03.005http://dx.doi.org/10.1002/ep.670220210http://dx.doi.org/10.1002/(SICI)1097-0290(19970620)54:6%3C583::AID-BIT9%3E3.0.CO;2-Fhttp://dx.doi.org/10.1021/es9711021http://dx.doi.org/10.1021/es990329ohttp://dx.doi.org/10.1021/es990329ohttp://dx.doi.org/10.1021/es9711021http://dx.doi.org/10.1002/(SICI)1097-0290(19970620)54:6%3C583::AID-BIT9%3E3.0.CO;2-Fhttp://dx.doi.org/10.1002/ep.670220210http://dx.doi.org/10.1016/j.cej.2005.03.005http://dx.doi.org/10.1002/bit.260251222http://dx.doi.org/10.1016/S0304-3894(02)00139-5