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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: yangc@hnu.cn)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

mailto:yangc@hnu.cnmailto:yangc@hnu.cn

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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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2186 CHEN Hong et al. Chinese Science Bulletin| August 2007 | vol. 52 | no. 16 | 2184-2189

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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2188 CHEN Hong et al. Chinese Science Bulletin| August 2007 | vol. 52 | no. 16 | 2184-2189

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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CHEN Honget al. Chinese Science Bulletin| August 2007 | vol. 52 | no. 16 | 2184-2189 2189

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