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Chemical Engineering and Processing 48 (2009) 1040–1046

Contents lists available at ScienceDirect

Chemical Engineering and Processing:Process Intensification

journa l homepage: www.e lsev ier .com/ locate /cep

teady-state biofilter performance under non-isothermal conditions

. Shareefdeena,∗, A.A. Shaikhb, Adeeb Ahmedb

Department of Chemical Engineering, American University of Sharjah (AUS), P.O. Box 26666, Sharjah, United Arab EmiratesDepartment of Chemical Engineering, King Fahd University of Petroleum and Minerals, Dhahran 31261, Saudi Arabia

r t i c l e i n f o

rticle history:eceived 19 June 2007eceived in revised form 17 January 2009ccepted 15 February 2009vailable online 3 March 2009

a b s t r a c t

In recent years, due to the economical and environmental benefits, biofiltration has been chosen by indus-tries as the preferred technology for volatile organic compound (VOC) removal even in regions such asthe Middle East where a warmer climate prevails throughout the year. In this work, a theoretical non-isothermal steady-state model is developed and the model has been used to evaluate temperature effectsof biofilter performance. The model predicts that toluene removal increases as the inlet and surroundingair temperatures increase. A 5 ◦C increase in the inlet air temperature results in a 20% increase in the

eywords:iofilteremperature effectsolueneodeling

teady-state

percent removal of toluene. A complete sensitivity analysis of the model is carried out. Heat of biologicalreaction (−�HR) has only a negligible effect on biofilter performance for the range of values (10–100 kJ/g)considered and overall heat transfer coefficient (Uov), for values <25 J s−1 m−2 K−1, have shown a profoundeffect on toluene removal. Although the results of this study are based on the assumption of complete sat-uration of incoming air, and negligible moisture loss from the media, the results and this non-isothermal

tima

on-isothermalolatile organic compound (VOC)

model will be useful in es

. Introduction

With growing awareness about the scale of environmental pol-ution and related hazards, the need for a cleaner and pollution freenvironment has become significant. Industries such as chemicalrocess industries, petrochemical industries, wastewater treatment

acilities, pulp and paper plants, etc. have been and still are a sourcef environmental pollution. The flue gases emitted from thesendustries contain nuisance odors and harmful volatile organicompounds (VOCs). As a result, these industries are in need of aimple and yet efficient air pollution control technology. Variousechnologies such as thermal oxidation, carbon adsorption, chem-cal scrubbing and biofiltration are used for removal of odors andOCs from contaminated air.

In comparison to the other technologies, biofiltration has manydvantages. For example, biofiltration does not generate any unde-irable by-products, and has low equipment and operating costs.n biofiltration, micro-organisms that are able to biodegrade VOCssubstrates) are immobilized on media which are usually porousolid support particles such as peat, compost, wood bark or man-

factured vendor supplied products. Bacteria grow on the porousolid particles and form thin biofilms where biodegradation of sub-trates takes place.

∗ Corresponding author. Tel.: +971 6 515 2988; fax: +971 6 515 2979.E-mail address: zshareefdeen@aus.edu (Z. Shareefdeen).

255-2701/$ – see front matter © 2009 Elsevier B.V. All rights reserved.oi:10.1016/j.cep.2009.02.002

ting key design parameters for full scale systems.© 2009 Elsevier B.V. All rights reserved.

In recent years, due to economical and environmental benefits,biofiltration has been chosen by industries as the preferred tech-nology even in regions such as the Middle East where a warmerclimate prevails throughout the year. In biofiltration in addition tonutrients, pH, oxygen content, moisture and carbon sources, tem-perature also plays a very important role. Temperature directlyaffects the growth rate of microbial population and in turn onthe biodegradation kinetics. Heat transfer between air, media andsurrounding takes place in the biofilter as a result of tempera-ture differences. There is an optimum temperature range in whichmost microbial cultures survive. The vast majority of microbes usedin process biotechnology have an optimum temperature range of20–40 ◦C for survival and growth [1]. Yang and Allen [2] studied theeffect of temperature on H2S removal in the temperature range of1.5–103 ◦C. The decrease in removal efficiency was significant fortemperatures lower than 25 ◦C and for temperatures greater than50 ◦C. Gibson et al. [3] observed that reduction of temperature to5 ◦C or less, reduced the VOC removal rate substantially. Corsi andSeed [4] suggested that the optimal temperature range for aerobiccompost biofilters is between 25 and 35 ◦C. Cox et al. [5] reporteda thermophilic biofiltration study of pollutants at temperatures upto 62 ◦C. Mysilviec et al. [6] presented a biofilter model which takesinto account heat and mass transport. The packing medium, in their

model was assumed inert, thus removing the solid phase mass con-tinuity equation from the system. Ranasinghe and Gostomski [7]investigated the effect of water content changes on the biologi-cal degradation in low water content biofilter systems. Repeatedstudies have shown that media moisture content caused changes in

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he elimination capacities of toluene. Morales et al. [8], presentedmodel that considers the effect of incomplete water saturation

f gas stream on packing material drying and biodegradation rate.hey concluded that the surface of the support must be saturatedith water film for an optimal performance of the biofilter. Thus,

n full scale biofilter systems [9], media is always kept moist bypray irrigation and incoming air is always saturated with water.ingh and Ward [10] reported that most air treatment studies haveeen done under a mesophilic range of 15–40◦C regardless that theontaminated air from industrial plants are often higher than thisemperature range. Chandrakanthi et al. [11] reported an interest-ng study on thermal conductivity of leaf compost used in biofilters.hermal properties are required in heat and mass transfer modelshat are used in predicting temperature variations. Marie-Carolinet al. [12] also reported a study on the effect of temperature in theiofiltration of toluene. They reported that the biodegradation ratean be maintained by adding nutrients (nitrogen) in the irrigationolution and the water lost from the biofilter can be balanced byrrigation. Xia-Qiang et al. [13] reported a study on the temperatureffects of benzene and toluene. They reported that a biofilter per-orms well between temperature of 30–40 ◦C and moisture contentsf 40–50%. Liao et al. [14] presented an experimental and theoreti-al investigation of heat generation behavior in a biotrickling filterhich was used to treat toluene. They concluded that the tempera-

ure had a significant effect on the purification performance of therickling biofilter and the optimal temperature was between 30 and0 ◦C.

Although biofiltration literature emphasizes temperature as onef the significant parameters affecting biofilter performance, therere only few theoretical models that can be used to evaluateemperature effects. Therefore, in this contribution, we focus onhe development and evaluation of a non-isothermal steady-state

athematical model that can be used in evaluating temperatureffects of biofiltration.

. Theory and model development

The literature review on mathematical models [15–20] showshat most of the earlier models are based on the assumption that thentire biofiltration process is under isothermal conditions. In otherords, variations in the inlet air temperature, heat generation due

o exothermic bio-oxidation process and heat exchange betweenbiofilter and its surroundings were not considered. However, asentioned, Morales et al. [8], developed a model that considers

he effect of incomplete water saturation of gas stream on pack-ng material drying, and thus on biodegradation. Recently, Liao etl. [14] presented a non-isothermal model, but for a biotricklinglter.

In this contribution, a mathematical model which incorporatesa) heat generation due to bio-oxidation, (b) heat transfer betweenbiofilter and its surroundings (c) variation in the inlet air temper-tures and (d) variation in the ambient temperatures, is developed.he assumptions involved in the development of the mathematicalodel are given below.

.1. Assumptions

1. There is no variation in temperature along the radial direction ofthe biofilter media. The biofilter vessel is assumed to be cylin-drical and temperature variation is only along the media height.

The biofilter height is larger than the diameter of the vessel. Thus,this assumption is justified.

. Depending on the temperature difference between the sur-roundings and the biofilter media at a height (z), heat transferrates vary. Along the height of the biofilter concentration varies,

and Processing 48 (2009) 1040–1046 1041

thus temperature variation is more profound in the direc-tion of air flow than in the horizontal cross section of themedia.

3. Incoming air is saturated (i.e. relative humidity is kept >99%)and media is irrigated daily [9]. Thus, media moisture loss or thedrying effect is negligible due to changes in temperature. In addi-tion, enthalpy changes in the air stream due to bed temperaturechanges are ignored.

4. Temperature variation within the biofilm is negligible. Thus,temperature is uniform along the length of the biofilm.

5. The biodegradation reaction rate constant follows an Arrheniustype of temperature dependence [21]. It is also assumed that,at higher temperatures (>40 ◦C), biodegration ceases, thus thepresent model is valid for the mesophelic temperature rangeconsidered.

6. The type of pollutant or its concentration has negligible effect onthe density and the specific heat capacity of air.

7. Physical properties due to temperature changes are negligible.8. In addition to these, all the assumptions of our previous work

[20] are also valid. They are reinstated here as follows: (a) thebiofilm is formed on the exterior surface of the particles. Nobiomass grows in the pores of the particles, and thus no reac-tion occurs in the pores. Sizes of these pores are too small formicrobial growth. (b) The biofilm is not necessarily formed uni-formly around the solid particles. There are patches of biofilmon the solids leaving the bare surface of the solids in direct con-tact with the contaminated air stream. (c) The thickness of thebiofilm is small relative to the main curvature of the solid parti-cles, and thus planar geometry can be used. (d) The extent of thebiofilm patch is much larger than its depth. Hence, the VOC andoxygen transported into the biofilm through the side surfacesof the biofilm patch can be neglected, and diffusion/reaction inthe biofilm can be considered in a single direction only. (e) TheVOC and oxygen at the biofilm/air interface are always in equi-librium as dictated by Henry’s law. The distribution coefficientsare same as if the biofilm was made of water only. (f) The VOCand/or oxygen are depleted in a fraction of the actual biofilm.This fraction is called the effective biofilm ‘ı’. (g) Diffusivities ofthe VOC and oxygen in the biofilm are equal to the diffusivitiesof the same compounds in water, corrected by a factor depend-ing on the density of the biofilm and (h) The biofilm density,defined as the amount of dry mass per unit volume of biofilm, isconstant.

3. Dimensional differential equations

The dimensional form of mass and energy balance equations aresummarized as follows. The methodology used in the developmentof biofilter models are discussed in details in our previous work[17–20] as well as in the recent work of Liao et al. [14].

3.1. Mass balances in the biofilm

(a) Organic substrate (VOC)

f (Xv)Djwd2Sjdx2

− Xv

Yj�(Sj, So, T) = 0 (1)

(b) Oxygen

f (Xv)Dowd2So

dx2− Xv

Yoj�(Sj, So, T) = 0 (2)

where

� = �∗SjKj + Sj + (S2

j/KIj)

· So

Ko + Soexp

{−Ea

R

(1T

− 1Tref

)}

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ith the boundary conditions as,

t x = 0, Sj = Cjmj

; S0 = C0

m0(3a,3b)

t x = ı, dSjdx

= 0;dS0

dx= 0 (4a,4b)

.2. Mass balances in the gas phase

(a) Organic substrate (VOC)

�Dd2Cjdh2

− UgdCjdh

+ f (Xv)DjwdSjdx

∣∣∣∣x=0

As = 0 (5)

b) Oxygen

�Dd2Co

dh2− Ug

dCo

dh+ f (Xv)Dow

dSjdx

∣∣∣∣x=0

As = 0 (6)

ith Danckwert’s boundary conditions as,

th = 0, �DdCjdh

= Ug(Cj | − Cj∣∣) (7a)

th = 0, �DdC0

dh= Ug(Co | − Co

∣∣) (7b)

th = H, dCjdh

= 0,dCo

dh= 0 (8a,8b)

.3. Energy balances in the gas phase

Hd2T

dh2− (Ug�Cp)

dTdh

− Uov�Dc(T − Ta)Ac

+ı∫

0

(−�HR)XAs�(Sj, So, T)Yj

dx = 0 (9)

ith Danckwert’s boundary conditions as,

th = 0, DHdTdh

= Ug�Cp(T∣∣−T ∣∣) (10a)

th = H, dTdh

= 0 (10b)

It should be mentioned that gas phase energy balance (Eq. (9)) isased on the assumption 3. When air and biofilter media are fullyaturated or the moisture concentration difference between twohases is zero, energy loss term due to evaporative cooling in Eq. (9)an be neglected. However, for a process upset such as humidifierailure that can cause drying of the media, energy loss term shoulde included in Eq. (9).

.4. Normalization parameters

The model equations are written in dimensionless form usinghe following dimensionless variables and groups.

j = CjCji, Co = Co

Coi

= h

H, � = x

ı

j = SjKj, So = So

Ko

and Processing 48 (2009) 1040–1046

� = KjKIj, Q = T − Tf

Tf

= DjwKjYjDowKoYoj

, ω = KoDowCjiKjDjwCoi

ε1 = CjiKjmj

, ε2 = Coi

Komo

Pe = UgH

D�, 2 = Xv�∗ı2

f (Xv)DjwKjYj

Peq = (Ug�Cp)HDH

, � = f (Xv)DjwHKjAs

UgCjiı

�1 = Uov�DcH

(Ug�Cp)Ac, �2 = �HRKjAsf (Xv)DjwH

Tfı(Ug�Cp)

1 = − Ea

RTf, 2 = Tf

TR

With the normalization parameters defined as shown, the dimen-sionless form of Eqs. (1) to (10) are as follows:

3.5. Mass balances in biofilm

d2Sjd�2

− 2 Sj

1 + Sj + �S2j

So

1 + Soexp

{ 1

(1

Q + 1− 2

)}= 0 (11)

d2So

d�2− 2

Sj

1 + Sj + �S2j

So

1 + Soexp

{ 1

(1

Q + 1− 2

)}= 0 (12)

At � = 0, Sj = ε1Cj; So = ε2Co (13a,13b)

At � = 1,dSjd�

= 0;dSo

d�= 0 (14a,14b)

3.6. Mass balances in gas phase

1Pe

d2CjdZ2

− dCjdZ

+ � dSjd�

∣∣∣∣�=0

= 0 (15)

1Pe

d2Co

dZ2− dCo

dZ+ �ω dSo

d�

∣∣∣∣�=0

= 0 (16)

At z = 0,1Pe

dCjdZ

= Cj − 1;1Pe

dCjdZ

= Co − 1 (17a,17b)

At z = 1,dCjdZ

= 0;dCo

dZ= 0 (18a,18b)

3.7. Energy balances in gas phase

1Peq

d2Q

dZ2− dQ

dZ− �1(Q − Qa) + �2

dSjd�

∣∣∣∣�=0

= 0 (19)

At z = 0,1

Peq

dQdz

= Q (20a)

At z = 1,dQdz

= 0 (20b)

This non-isothermal model described by Eqs. (11)–(20) asymp-totically reaches to isothermal model presented in our earlier work[20] when temperature variations are neglected.

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The parameters needed to solve the model equations are esti-ated as follows. In our analysis, we selected toluene as the sampleOC pollutant. From the basic equation representing the biologicaleaction of toluene, the heat of the reaction (−�HR) is estimated asollows:

C7H8 + 5.97O2 + 0.53NH4Cl → 2.65CH1.8O0.5N0.2 + 1.91H2O

× (Biomass) + 4.35CO2 + 0.53HCl (21)

The values of the heat of formation of the individualpecies (@ Tref = 25 ◦C) are C7H8: 50 kJ/mol; O2: 0 kJ/mol; NH4Cl:297.6 kJ/mol; CH1.8O0.5N0.2: −91.4 kJ/mol; H2O: −285.6 kJ/mol;O2: −393.1 kJ/mol; HCl: −166.6 kJ/mol [22,23]. Substitutionf these values gives the heat of the reaction (−�HR) as2478.3 kJ/mol of toluene or −26.9 kJ/g of toluene. The overall heat

ransfer coefficient (Uov) for a cylinder is given by [24]:

OV = 1(1/hi) · (Ao/Ai) + (Ao ln(ro/ri)/2�kL) + (1/ho)

(22)

here hi, and ho are convective heat transfer coefficients inside andutside of the biofilter vessel respectively; ri and ro are the innernd the outer radius of the cylindrical biofilter vessel respectively;is the length of the cylinder and k is the thermal conductivity of

he material. Calculations yielded a range of values and we haveelected a value of Uov = 100 J s−1 m−2 K−1. This value may be moreuitable for the case of forced convection (i.e., windy conditions)eat transfer. A biofilter installed in an open plain area (as in theiddle East) is often subjected to winds from desert areas. The acti-

ation energy is taken as 60 kJ/mol from the reference [1]. Since heatispersion coefficient is not known, a value of 20 is chosen for Pecletumber Peq. All the other parameters, their values, and referencessed in solving the model equations are listed in Table 1.

The model Eqs. (11)–(20) constitute a non-linear boundary valueroblem. A computer code has been developed using the method ofrthogonal collocation which replaces the spatial derivatives by theollocation matrices and thus the set of differential equations (Eqs.11)–(20)) is reduced to a set of simultaneous algebraic equations.

total of 140 ODE’s on the biofilm side, 14 ODE’s for the gas phase,

nd 7 ODE’s for energy balance have been simultaneously solvedsing the DNSNEQ subroutine of the International Mathematicalubroutine Library (IMSL).

able 1alues of the parameters used in solving the model equations.

arameters Values Units References

oi 275 g m−3 [18]p 1.006 J g−1 K−1 [23]jw 1.03 × 10−9 m2 s−1 [18]ow 2.41 × 10−9 m2 s−1 [18]a 60,000 J/mol [1](Xv) 0.195 – [18]

0.64 m [18]Ij 78.94 g m−3 [18]j 11.03 g m−3 [18]o 0.26 g m−3 [18]j 0.27 – [18]o 34.4 – [18]

e 7.53 – [20]eq 20 – Present studyov 100 J s−1 m−2 K−1 Present studyv 105 g m−3 [18]j 0.708 – [18]oj 0.341 – [18]HR −26.93 × 103 J/g [23]

34–40 × 10−6 m [18]1.18 × 103 g m−3 [23]

* 4.167 × 10−4 s−1 [18]

Fig. 1. Model predicted air phase concentration profiles of oxygen and toluene alongthe biofilter (conditions: Tf = 303 K, Ta = 298 K and CTi = 1.5 g m−3).

4. Results and discussion

The model predicted gas phase concentration profiles of oxygenand VOC along the biofilter height and the temperature profile ofthe contaminated air stream are shown in Figs. 1 and 2, respectively.It is interesting to note that due to dispersion [refer to Dankwertboundary condition Eq. (7a) and (7b)], dimensionless toluene con-centration is less than 1 when z = 0. If we had assumed plug flow forthe gas phase, then dimensionless concentration would be equalto 1.0. It can also be seen from Fig. 1, the dimensionless oxygenconcentration remains constant along the biofilter height. For anair inlet temperature of 303 K (30 ◦C), the figure shows that the exittoluene concentration is 0.35, implying a 65% removal. Shareefdeenet al. [19] reported a removal of 52% when inlet air temperature

◦

was at 298 K (25 C). This increase in removal from 52% to 65% oftoluene is due to the fact that an increase in temperature enhancesthe biological reaction rate.

The temperature profile shown in Fig. 2 is a typical profile of anexothermic reaction in a packed-bed reactor. Biofilter is essentially

Fig. 2. Model predicted temperature profile of along the biofilter (conditions:Ta = 298 K and CTi = 1.5 g m−3).

1044 Z. Shareefdeen et al. / Chemical Engineering and Processing 48 (2009) 1040–1046

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ig. 3. Effect of inlet air (feed) temperature on the concentration of toluene (condi-ions: Ta = 298 K and CTi = 1.5 g m−3).

reactor packed with immobilized media particles. The tempera-ure increases at a rapid rate initially, attains a maximum and thenradually subsides along the length of the biofilter. The figure showshat heat release or biological uptake of VOCs is maximum at 10%f the biofilter media at the entrance region. This is due to highernlet concentration, hence higher rate of biological oxidation in thenlet section of the biofilter.

The effect of variations in the inlet air (feed) and surroundingemperatures are shown in Figs. 3 and 4 respectively. The increasen the inlet air temperature increases the net heat input to theystem. Heat input increases the reaction rate, in the sense of therrhenius equation, and thus the exit concentration drops signif-

cantly. Apparently at an air inlet temperature of 308 K (i.e. 10 Kbove 298 K) the exit concentration is found to be 0.25 showing5% toluene removal. Thus, as the air inlet temperature increasesrom 25 to 35 ◦C, toluene removal percentage increases from 55 to5%.

ig. 4. Effect of ambient (surrounding) temperature on concentration of tolueneconditions: Tf = 298 K and CTi = 1.5 g m−3).

Fig. 5. Effect of heat of reaction on toluene concentration (conditions: Ta = 298 K,Tf = 303 K and CTi = 1.5 g m−3).

The effect of surrounding temperature on toluene removal ispresented in Fig. 4. As seen in Fig. 4, when the temperature outsideof the biofilter vessel is low, heat lost from the biofilter becomessignificant. Thus, biodegradation rate of toluene decreases and theexit concentration increases. However, when the surrounding tem-perature increases above 303 K, the heat flow direction is reversed.This results in heat flow into the biofilter system, serving as a sourceof heat in addition to the heat of biological reactions. Consequently,there is an increase in the removal of toluene or a reduction inthe exit concentration. However, if ambient temperature is alwayshigher than the media temperature, this trend will not be seen.

A complete sensitivity analysis of the model revealed importantbiofilter parameters that affect performance under non-isothermalconditions. Fig. 5 is a semilog plot showing the effect of the heat

of reaction (−�HR) on toluene removal. Over a wide range of val-ues of heat of reaction, the toluene exit concentration decreasesbut marginally. It can be seen that the heat of reaction (−�HR) hasminor effects on toluene removal rates for a range of values from 10

Fig. 6. Effect of overall heat transfer coefficient (Uov) on toluene concentration (con-ditions: Ta = 298 K, Tf = 303 K and CTi = 1.5 g m−3).

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o 100 kJ/g. It should be mentioned that the heat of reaction for ourystem is about 26.9 kJ/g which falls in the above mentioned range.owever, when the heat of reaction exceeds 100 kJ/g, dimension-

ess exit concentration drops. Fig. 5 indicates toluene removal is notery sensitive to heat of reaction (−�HR), this may be due to higherverall heat transfer coefficient (or higher heat loss term) used inur model simulation. Fig. 6 shows the effect of overall heat trans-er coefficient (Uov) on the toluene exit concentration. This figurehows that the exit toluene concentration rapidly decreases for Uov

25 J s−1 m−2 K−1. Since heat lost to the surrounding is a function ofhe overall heat transfer coefficient (Uov), decrease in overall heatransfer coefficient results in lower exit concentration or greateremoval of toluene. At higher values of Uov, the biofilter may bepproaching isothermal behavior, thus removal rate remains con-tant. In this region, removal rate is controlled by the temperaturenfluence of growth rate only.

. Conclusions

In this work a theoretical non-isothermal steady-state models developed. The model equations have been discretized usingrthogonal collocation and solved. The model predicts that the VOCemoval can be affected significantly when inlet air and surround-ng temperatures vary. A 5 ◦C increase in the inlet air temperatureesulted in a 20% increase in the removal of VOC. A complete sen-itivity analysis of the model is carried out. Effect of parameters,eat of biological reaction (−�HR), and overall heat transfer coef-cient (Uov), have been presented with respect to the removalfficiency of toluene. The results show that for a range (10 kJ/go 100 kJ/g) values considered, sensitivity effect of heat of reac-ion (−�HR) is not significant. Furthermore, for values of overalleat transfer coefficient <25 J s−1 m−2 K−1, the removal efficiencyf toluene increases significantly. In conclusion, successful appli-ation of biofilter technology in warmer climates, as in the Middleast, requires efficient control of heat transfer parameters, and heatxchange between a biofilter and its surroundings. It should beoted that the model presented here is under the assumption ofomplete saturation of incoming air, and negligible moisture lossrom the biofilter media; both of which are carefully controlled inommercial biofilter systems through humidification and irrigationystems. Thus, the non-isothermal steady-state model presented inhis work will be useful in evaluating preliminary design parame-ers for full scale systems that are exposed to temperature effects.owever, the model may not be applicable to evaluate temperatureffects when incoming air is under saturated or there is significantrying of the media.

cknowledgement

The authors are grateful to American University of Sharjah, Shar-ah, UAE and King Fahd University of Petroleum and Minerals,hahran, KSA for the support of this work.

ppendix A. Nomenclature

s biofilm surface area per unit volume of the reactor (m−1).c cross sectional area of the biofilter column (m2).j concentration of the pollutant j in the air at a position ‘h’

along the biofilter column (g m−3).

o concentration of oxygen in the air at a position ‘h’ along

the biofilter column (g m−3).ji value of Cj at h = 0 (g m−3).Ti value of toluene concentration at h = 0 (g m−3).o dimensionless concentration of oxygen in the air.

and Processing 48 (2009) 1040–1046 1045

Cj dimensionless concentration of the pollutant j in the air.Cp specific heat capacity of humid air (J/g K).D dispersion coefficient (m2 s−1).Dc diameter of the column (m).Djw diffusion coefficient of pollutant in water (m2 s−1).Dow diffusion coefficient of oxygen in water (m2 s−1).DH heat dispersion coefficient (J K−1 m−1 s−1).Ea activation energy (J/mol)f(Xv) ratio of diffusivity of a compound in the biofilm to that in

water.h position in the column (m); h = 0 at the entrance, h = H at

the exit.H total height of the filter bed (m).�HR heat of biological reaction (J/g).Kj constant in the specific growth rate expression of a culture

growing on compound j (g m−3).KIj inhibition constant in the specific growth rate expression

of a culture growing on compound j (g m−3).Ko constant in the specific growth rate expression of a culture

expressing the effect of oxygen (g m−3).mj distribution coefficient for the substance j/water system.mo distribution coefficient for the oxygen-in-air/water sys-

tem.Peq Peclet number for heat.Pe Peclet number for pollutant.Q dimensionless temperature.R universal gas constant.Sj concentration of the pollutant j at a position ‘x’ in the

biofilm at a point ‘h’ along the column (g m−3).So oxygen concentration at a position ‘x’ in the biofilm at a

point ‘h’ along the column (g m−3).Sj dimensionless concentration of substance j at a point ‘�’

in the biofilm.So dimensionless oxygen concentration at a point ‘�’ in the

biofilm.T temperature in the bed (K).Tf temperature of the inlet air (K).Ta ambient temperature (K).Tref reference temperature (K).Ug superficial air velocity in the biofilter (m/s).Uov overall heat transfer coefficient (J s−1 m−2 K−1).Xv biofilm density (g dry cells m−3).x position in the biofilm (m).Yj yield coefficient of the culture based on VOC j (g-

biomass/g-compound).Yoj yield coefficient of the culture based on oxygen (g-

biomass/g-oxygen), when VOC j is the carbon source.Z dimensionless position along the biofilter column (h/H).

Greek symbols˛ fraction of the biofilm surface available for adsorption.ı effective biofilm thickness (m).ı* actual biofilm thickness (m).ε1 dimensionless parameter.ε2 dimensionless parameter. Thiele modulus.� inverse dimensionless inhibition constant defined as

Kj/KIj� dimensionless parameter. dimensionless parameter.

�∗j

constant in specific growth rate expression (s−1).� dimensionless position in the biofilm defined as x/ı� density of humid air (g m−3).� porosity of the filter bed.ω dimensionless parameter.

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