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An overview on biofiltration modeling

Mohamad Ali Fulazzaky1;Amirreza Talaiekhozani1&2; Mohanadoss Ponraj1; M. Z. Abd Majid3

1- Institute of Environmental and Water Resources Management, Water Research Alliance,

Universiti Teknologi Malaysia, UTM Skudai, 81310 Johor Bahru, Malaysia

2- Department of Civil and Environmental Engineering, Jami Institute of Technology, Isfahan, Iran.

2- Construction Research Alliance, Faculty of Civil engineering, Universiti Teknologi Malaysia, UTM Skudai, 81310 Johor Bahru, Malaysia

4- Department of Mechanical Engineering, Jami Institute of Technology, Isfahan, Iran.

Abstract In this paper different approaches to model biofiltration processes to treat polluted air were reviewed. Removal of pollutants from air has been a challenge for engineers. Although, many approaches based on phase transfer, diffusion of pollutants within the biofilm, oxygen, pH, temperature, water, nutrients and substrate limitation and etc. have been developed by researchers, finding them is not easy. The main aim of this study is collecting differents approaches to biofilteration processes model to have a complete source for researchers and engineers. Results of this paper can be used to inspire new approaches for biofiltration processes modeling.

Keywords: Biofilter Modeling, Mathematical modeling, Biological air treatment modeling

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1. Introduction

These days, biofiltration process has been increasingly applied for the treatment of air contaminated with organic and in organic pollutants. Biofiltration processes can be used to treat insoluble and recalcitrant compounds, if it is properly designed [1, 2]. Duo to inhomogeneity of the packing material and complexity of the physical, chemical, and microbiological phenomena involving at biological processes, the use of a unique equation to design is not possible. Consequently, failure of poorly designed biofilters have been occurred when a wrong equation was used. It can cause some operators to prefer other treatment options. The scope of this part of literature review is identification of a certain models, which allows the transfer of bench- and pilot-scale experimental results into reliable design parameters for full-scale applications.

Many investigators have created mathematical models of biofilters and biotrickling filters in their efforts to know and improve reactor performance. While there has been significant success among investigators in describing and understanding laboratory results, no single model has become a generally accepted customary. Each research group has developed its own approach, typically specific to the experiments being performed. The design of complete applications continues to be for the most part done by rule of thumb, and application of biofilters to effluents under previously untested conditions of concentration, concentration fluctuation, and contamination combine typically requires pilot-scale testing. Biological air treatment might use either biofilters or biotrickling filters. By definition, biofilters are kept wet, but there is no moving water section, while water is consistently applied to biotrickling filters, producing a film of water that flows over the packing and also the biofilm. In practice, however, biofilters are typically washed with water at intervals to ensure adequate biofilm water content. Some are washed for as much as 20 min in each hour. On the other hand, water flow is inevitably interrupted from time to time in biotrickling filters, and it's recognized that as a result of unsaturated attraction flow in porous media is thus irregular, biotrickling filters are seemingly to include significant volumes that are not being washed. Thus, biological systems vary from true biofilters at one extreme to true biotrickling filters at the other, and most systems lie somewhere between [3]. Several of the phenomena shapely apply equally to biofilters and biotrickling filters. Others, however, could also be specific to at least one sort.

Several approaches about biological process designing to treat polluted air have been reported worldwide. Biological treatment of polluted air is a complex process, which includes many physical, chemical and biological phenomena [4]. It is commonly assumed that biofilms do not have any limitation about moistures, oxygen, and nutrients.

Suggested models in previous studies are divided into two categories, microkinetic and macrokinetic models. The following sections present an overview of some important macrokinetic and microkinetic models.

2. Biofiltration processes modeling

2.1. Microkinetic models

Many approaches have been used to develop a microkinetic model. Following Figure shows these approaches. More details about each approach are presented in next parts.

Figure 10: Different approaches to model biofiltration processes

2.1.1. Models based on phase transfer

Pollutants transfer from gas part to liquid part is ready to be considered as restricted by diffusion resistance within a bedded layer of gas near the interface and by resistance within the liquid. In many studies, halikely that layer of water can't be a heavy barrier to transfer pollutants from gas part to biofilms and it's been neglected. However, in some studies the layers of moving water have included. In general, it is likely that water stream surrounding biofilms area unit well mixed due to its fast flow [3]. Mass transfer happens from the air, and once more at the interface between the water layer and the biofilm [5]. Different phenomena, however, may be significant: the water carries material downward (which counter-current to air flow) and if the water is recirculated, any material remaining in the water because it exits rock bottom of the biofilter may be came to the system at the highest. In an exceedingly system within which the air is flowing upwards, material may be transferred from the recirculating water to the outgoing air, causing some reduction in removal potency. The thickness of the flowing water layer has been approximated by Alonso et al. (2001) as [6]:

��� � ��������� �����

Where ��� is thickness of the flowing water layerarea of the packing, HT the height of the tower, ordinarily ascertained, however, that in biotrickling filters the flowing water doesn't manufacture an identical layer and wets a number of the packing surface whereas exploit alternative elements exposed to the gas part. Kimand and Deshusses (2003) sculptured this impact, employing a antecedently developed empirical relationship to predict the fraction of packing surface wetted [7].

“Water at intervals the biofilm is plausible to be stagnant, so molecular diffusion is that the somechanism. It's been typically accepted that part transfer is restricted by diffusion within the water phase: the pores are comparatively little, dispersion caused by temperature change tends to combine the gas part, and molecular diffusion constants in water in the order of 104 times are lesser than those in air (concentrations, and so concentration gradients, are typically higher within the biofilm, however sometimes solely by one order of magnitude)” [3]. Typically, modelers presume that t

Microkinetic

Models based on

phase transfer

Models based on

diffusion of

pollutants within

the biofilms

Models based on

adsorption on the

solid phase

Microorganisms

growing with

substrate

limitation

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Figure 10: Different approaches to model biofiltration processes

.1. Models based on phase transfer

Pollutants transfer from gas part to liquid part is ready to be considered as restricted by diffusion resistance within a bedded layer of gas near the interface and by resistance within the liquid. In many studies, halikely that layer of water can't be a heavy barrier to transfer pollutants from gas part to biofilms and it's been neglected. However, in some studies the layers of moving water have included. In general, it is likely that

lms area unit well mixed due to its fast flow [3]. Mass transfer happens from the air, and once more at the interface between the water layer and the biofilm [5]. Different phenomena, however, may be significant: the water carries material downward (which may be either co

current to air flow) and if the water is recirculated, any material remaining in the water because it exits rock bottom of the biofilter may be came to the system at the highest. In an exceedingly system within

air is flowing upwards, material may be transferred from the recirculating water to the outgoing air, causing some reduction in removal potency. The thickness of the flowing water layer has been approximated by Alonso et al. (2001) as [6]:

is thickness of the flowing water layer, Qw is the water flow rate, µw the viscosity, the height of the tower, ρw the density, and g is the acce

ordinarily ascertained, however, that in biotrickling filters the flowing water doesn't manufacture an identical layer and wets a number of the packing surface whereas exploit alternative elements exposed to the gas part.

nd Deshusses (2003) sculptured this impact, employing a antecedently developed empirical relationship to predict the fraction of packing surface wetted [7].

“Water at intervals the biofilm is plausible to be stagnant, so molecular diffusion is that the somechanism. It's been typically accepted that part transfer is restricted by diffusion within the water phase: the pores are comparatively little, dispersion caused by temperature change tends to combine the gas part, and

constants in water in the order of 104 times are lesser than those in air (concentrations, and so concentration gradients, are typically higher within the biofilm, however sometimes solely by one order of magnitude)” [3]. Typically, modelers presume that the concentration at the surface of the biofilm is

Biofiltration

Modeling

Models based on

adsorption on the

solid phase

Models based on

microorganisms

growth

Microorganisms

growing with

oxygen limitation

Microorganisms

growing with

substrate and

nutrient limitation

Microorganisms

growing with

temperature,

water and pH

limitation

Makrokinetic

Models bsed on

inlet pollutants

concentration

Models based on

gas retantion time

Figure 10: Different approaches to model biofiltration processes

Pollutants transfer from gas part to liquid part is ready to be considered as restricted by diffusion resistance within a bedded layer of gas near the interface and by resistance within the liquid. In many studies, have likely that layer of water can't be a heavy barrier to transfer pollutants from gas part to biofilms and it's been neglected. However, in some studies the layers of moving water have included. In general, it is likely that

lms area unit well mixed due to its fast flow [3]. Mass transfer happens from the air, and once more at the interface between the water layer and the biofilm [5]. Different phenomena,

may be either co-current or current to air flow) and if the water is recirculated, any material remaining in the water because it

exits rock bottom of the biofilter may be came to the system at the highest. In an exceedingly system within air is flowing upwards, material may be transferred from the recirculating water to the outgoing

air, causing some reduction in removal potency. The thickness of the flowing water layer has been

the viscosity, a0 the surface is the acceleration of gravity. It's

ordinarily ascertained, however, that in biotrickling filters the flowing water doesn't manufacture an identical layer and wets a number of the packing surface whereas exploit alternative elements exposed to the gas part.

nd Deshusses (2003) sculptured this impact, employing a antecedently developed empirical

“Water at intervals the biofilm is plausible to be stagnant, so molecular diffusion is that the solely transport mechanism. It's been typically accepted that part transfer is restricted by diffusion within the water phase: the pores are comparatively little, dispersion caused by temperature change tends to combine the gas part, and

constants in water in the order of 104 times are lesser than those in air (concentrations, and so concentration gradients, are typically higher within the biofilm, however sometimes solely by one

he concentration at the surface of the biofilm is

Models based on

biofiltration

reactor height

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set by Henry’s Law equilibrium with the concentration of stuff within the bulk air part, which the flux of stuff into the biofilm is controlled by diffusion resistance within the biofilm at the surface:

��� � �� ������� ����

“Where Jbf is the flux of contaminant per unit of surface area, Cbf the concentration of contaminant in the

biofilm, and x is the coordinate perpendicular to the biofilm surface, which is zero at the air–biofilm interface. In a biotrickling filter, it's typical that transfer in the flowing water layer is slower than transport in the air and quicker than in the biofilm. An equivalent formulation is employed for transfer from water to the biofilm and a parallel type is employed for transfer from the air to the water. However, some investigators have ascertained mass transfer resistance at the interface. This is often most likely to occur wherever contaminant solubility is high and biodegradation is speedy. It's less probably in a biofilter treating volatile organic compounds, but Kim and Deshusses (2003) ascertained strong external mass transfer limitation in laboratory and complete biotrickling filters treating hydrogen sulfide [7]. In such cases, models presume that transfer is restricted by diffusion resistance in a bedded layer of gas at the surface, and transfer occurs at a rate determined by the degree to which the gas–liquid interface of the biofilm is below saturation” [3]: ��� � ������ �� !"� − $��� Where kair–bf is the gas transfer coefficient andH is the Henry’s Law constant for the contaminant. Li et al. (2003) additionally approximated the gas transfer coefficient for spherical packing particles and was further approximated by [8]:

������ � % !"&'( [2 + 1.1./�.012�.��] where Dair is the gas-phase diffusion constant, Rp the particle radius, Rethe Reynolds number, and Scis the Schmidt number. The flux terms should be multiplied by surface area of the biofilm to determine total flux, and further divided by the volume of the phase in order to determine the changes in concentration. 2.1.2. Models based diffusion of pollutants within the biofilm

Diffusion of the pollutants into the biofilm can be calculated by Fick’s Law. This Law is presented by following equation:

4�����5 67��� � ��� � 4�8�����8 6

Where Dw is the molecular diffusion constant of the contaminant present in water.Although, near all scientists agree with above equation, they cannot certainly confirm the appropriate values for the diffusion constant. Molecular diffusion constants are measured in pure water for most compounds;however diffusion within the biofilms may be different. The nature and abundance of cells and exuded polysaccharides present reduces the cross-section of water that are available for diffusion and restricts the contaminant to diffusion only along the tortuous pathways. Some investigators have used empirical equation as developed by Fan et al. (1990) which relates to the diffusion coefficient in the biofilm, then the diffusion coefficient being measured in water and finally the total biomass density in the film (in g/L) [9]:

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��� � �� 41 − �.9���.:8;;.;<=�.&��.::6

Miller and Allen (2004) noted that extra complications are possible. In biofiltration of pinene, they showed that biological materials in the biofilm would take up the contaminant, thus causing initial delay in the transport but not affecting the steady-state rates of transport [10]. They also found in biological films, but not in abiotic films, where the enzymatic reactions rapidly convert pinene to a secondary product which is far more soluble, thereby increasing the effective solubility and degradation rates over those expected for the parent compound.

2.1.3. Modeling based on Adsorption on the solid phase

Pollutantscan penetrate to the bottom of the biofilm, especially during the early stages of treatment when the biofilmsarevery thin, can be adsorbed on the surface of the supporting materials. Adsorption capacities can be widely changedbyusing of different supporting materials. The use of absorption models is very necessary to descript contaminated gases treatment when activated carbon is used as supporting materials. In some cases, have assumed supporting materials are porous and includeconsiderable amounts of water that is able to absorb pollutants[11, 12, 13, 14]. Pollutants adsorption can be ignored if some supporting materials such as lava rock were applied. For the most of the supporting materials, reducing adsorption of the pollutants is observed by pollutants compete for adsorption sites. Therefore, is steady state condition adsorption is not very effective and has not a significant effect on pollutant removal. Adsorption and desorption are enclosed in nonsteady-state models, where it is probably presumed that the mass of material adsorbed per unit surface area at equilibrium is linearly proportional the concentration of the contaminant present in the biomass at the bottom of the biofilm, Cbfbot.

$7>/? � �7> � $���@5 Where Kads is an empirically determined constant. Ranasinghe et al. 2002in their approach further modeled the adsorption constant having Arrhenius-type dependence on temperature [14]:

�7> � �� � ABC 4�∆�'E 6

Where ∆H is the heat of adsorption, R isthe gas constant, T the temperature and K0 is a constant.

Zarook et al. (1997) and Ranasinghe et al. (2002) considered non-equilibrium adsorption, by assuming that the flux from the biofilm to surface occurred at a rate proportional to the degree to which itwas belowequilibrium [11, 14] andtheir formulations were equivalent to:

�7> � �7>($7>/? − $7>) Where Jads is the flux per unit surface area, kads the rate constant, and Cads is the concentration adsorbed.

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2.1.4. Modeling based on microorganisms growth

2.1.4.1. Microorganisms growing with substrate limitation (Monod model) Monod equation can be used to model BTFRs, BFs or SGRs. “The kinetic coefficient values accustomed to predict the rate of substrate utilization and biomass growth can vary as a function of the wastewater source supply, microbial population and with temperature. These coefficient values can be used to design a full scale wastewater treatment plant” [17]. Kinetic coefficient values can be determined from the results of bench-scale testing or full-scale plant tests. Based on Talaie et al., (2011) following procedure was followed to find suitable equations. For a reactor under steady state condition, the mass balances to describe substrate degradation rate can be defined as equation 17 [18].

0su

s

S SkXSr

K S θ−= − = −

+ (17)

In the equation, 1 rsu is substrate degradation rate (in g/m3.d), S0 is initial concentration of substrate (in g/m3), S is concentration of substrate after biodegradation process (in g/m3), θ is hydraulic retention time (in day), k is maximum specific substrate utilization rate (in g substrate/g microorganisms.d), X is microorganisms concentration (in g/m3), and Ks is the Monod half-saturation constant.By dividing the equation 17 by X, the following equation could be obtained:

0

S

S SkS

K S Xθ−=

+ (18)

K and Ks can be calculated by rearranging and simplifying equation 18 to take the form of the Lineweaver–Burk equation below (equation 19):

0

1 1SKX

S S k S k

θ = +− (19)

Ksand k

1values can be calculated by plotting

0

X

S S

θ−

versus1

S. Yand kd Values were calculatedby the

following equation: 1 su

dc

rY k

Xθ= − −

(20)

In the equation 20, θc is microbial retention time (in day), Y is microorganisms yield (in g/g), kd bacteria decay rate (in g VSS/g VSS.d), rsu is substrate degradation rate (in g/m3.d), and X is the microorganism

concentration (in g/m3). With replacing of sur instead of θ

SS −− 0 , the equation 20 will be used as

following:

(21)dc

kX

SSY −

−=

θθ01

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Yand kdvalues were calculated by plotting cθ

1versus

θX

SS −0 . The equation 22 was used to describe the

maximum specific bacterial rate (µmax) for a single substrate

Ykd ×=maxµ (22)

In equation 22, µmax is maximum specific bacterial growth rate (in g new cell/g cell.d), kd bacteria decay rate (in g VSS/g VSS.d), and Y is microorganisms yield (in g/g). Based on Equation 17, bigger Ks mean less rate of substrate concentration change due to microbial activities (rsu). Typical value of Ks and k for municipal wastewater is 40 mg/l and 5 d-1, respectively. In other hand bigger maximum specific substrate utilization rate (k)mean bigger rsu [17]. Biodegradation rates are fundamentally controlling the factorsthat are responsible for the effectiveness of biofilters. Most commonly, Monod kinetics are assumed for growth as a function of existing concentrations of biomass and the concentrations of contaminant. For determining high values of C, the growth rate is constant, and some modelers have presumed that growth mostly follows zero-order kinetics. For low values of C, growth is linear with contaminant concentration, and some modelers have presumed it to be with first-order kinetics. However, when the model includes sufficient details to show biodegradation rates as a function of depth within the biofilm, the concentrations will mostly range from the Henry’s equilibrium value at the surface of the biofilm to zero at the maximum depth of penetration. Often the appropriate values for KS and µmax are uncertain. Both these values are strongly dependent on the conditions in which they are determined and most of the data in the literature are from experiments performed on microorganisms in stirred, well-aerated suspensions, rather than in biofilms (and are highly variable even so). Thus, these parameters are often fitted to the biofilter data developed in the experiment being modeled. 2.1.4.2. Microorganisms growing withoxygen limitation

Because the solubility of oxygen in water is low and most often much lower than the solubility of the contaminant, it is sometimes predicted that oxygen concentrations, rather than contaminant concentrations, will limit the rate of biodegradation.The relationship between pollutants removal efficiency and oxygen concentration at various BTFR or BF bed depths has been described byEq. 14 to Eq. 16 [19].

.A � H[I8]J=[I8] (14)

Where, Re is pollutants removal efficiency (in percentage) and m and n are constant coefficients. m

and n can be calculated using Eq. 15 and 16. L � −180.31 + &P�.Q9

�;=/�R�4ST�.UU�.V: 6�W:.�8 (15)

Z � 3.54 − (3.08 � [) (16) Where, H is BTFR or BF height (in m). Another model on oxygen limitation has been reported by Ozis et al., (2004) and Shareefdeen et al., (1993) [20, 21]. This model has been design based on Monod equation. ] � ^ _��`8��ab`8=�`8��

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Where CO2bf is the concentration of oxygen present in biofilm and KSO2 is the Monod half-saturation constant for oxygen. Where O2 limitation is assumed, it's necessary to grasp the O2 concentration profile inside the biofilm. In these cases, O2 concentrations are determined only as pollutant concentrations are: equilibrium with the gas phase is presumed at the surface, pollutants and O2 concentration into biofilm can be controlled by influence through the biofilm and by consumption in biological activities. 2.1.4.3. Microorganisms growing insubstrate and nutrient limitation

Nutrients, particularly for systems applying supporting materials, is limiting if the amounts provided by operators don't seem to be adequate.In some regimes, two species could also beat the same time limiting. Alonso and Suidan (1998) have applied a double-limit equation called Jacques Monod, wherever N is that the nitrate concentration [22]:

] � c^ _��d��ab=�d�� e � c^ _��f��abf=�f�� e

Where CNbf is the concentration of nutrient in the biofilm. In most reactors, nutrient concentrations of reactors are controlled. Then why do researchers try to model nutrient concentration? The purpose of modeling the effects of nutrients is simply to determine what supply rates are appropriate. Then results of nutrient concentrations can be used to operate reactors at optimum amount of nutrients. Sometimes substrate is toxic and in the high concentration it can have a inhibition effect on biological systems. Then to describe inhibition effect of high concentration of toxic substrates Zarook et al. (1997) used Haldane kinetics [11]:

] � g ^ _����ab=���= h��8

i!jkl � c �`8��a`8=�`8��e

Where Kinh is the Haldane constant for inhibition of degradation of species i in the presence of species j. In practic, polluted air is contaning many pollutants. These pollutants may reacte with each other. A modified Michaelis–Menton equation equivalent to the Monod form was developt by Deshusses et al. (1995) to describe biodegradation of air contaminated with methyl isobutyl ketone and methyl ethyl ketone [13].

]� � c !^ _��!��mab!=�!��=n!o=�o��pe

Where the subscripts i and j refers to two contaminants being treated simultaneously, and pij is the inhibition constant. Deshusses et al. (1995) model is not really applicable if more than two pollutants be into polluted air [13]. To solve this problem following model has been described by Nguyen et al. (1997) [22]. This modeldescribed the inhibition among various pollutants in general using inhibition constants, pij, for each pair of pollutants, and including oxygen limitation:

]� � c !^ _��!��maq!=∑(n!o��o��)pe � c �`8��mab`8=�`8��pe

Where piiis equal to one.

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2.1.4.4. Microorganisms growing with Temperature, water and pH limitation In some cases, other factors such as temperature and water content may limit biofilm activity. Sometimes temperature of polluted air and water content of biofilms may be too low or too high. Following empirical model has been developed by Morales et al. (2003) based on several experimental data of biofilter performance over a range of temperature and water content conditions [23]. s$ � s$H� � t; � (u) � t& � v�� � t� � $�� Where T is the temperature (◦C), EC is maximum elimination capacity (in mg/l), W the water content (in g/g), Cair the gas-phase pollutant concentration (in g/m3), and β1, β2, and β3 are functions fitted to the data. Based on this empirical model biofilm activity is raised with temperature to an optimum range from 25 to 33 ◦C. The biofilm activity is linearly raised with water content above a critical value until it reaches an optimum. While the formula applies to overall biofilter performance rather than a point within the biofilm, the effects of contaminant concentration have a form much like Monod kinetics [3]. Effect of pH on biodegradation rate of pollutants has been reported by a wide numbers of researchers (Fulazzaky et al., 2013). Therefore, many researchers try to use effect of pH at their models. Model of Okkerse et al. (1998) included a biodegradation rate multiplier that indicates the effects of pH [27]: wR� � ABC(−x(C[ − y)&) Where B is the pH of maximum activity and A is a constant that is inversely proportional to the range of pH over which the organisms can be active.

2.2. Macrokinetic models Many different approaches were applied to develop models for describing biofiltration behavior. The most important approaches are models based on inlet pollutants concentration, gas retention time and biofiltration reactor height. More details are presented at next parts.

2.2.1. Models based on inlet pollutants concentration The following equation has been suggested by Zamir et al. (2010) for biofilter or biotrickling filter designing [28]: z(C|} − C~��)Q � K�r��� � 1C� + 1r��� (1)

Where rmax, maximum elimination capacity (mg/L.min); Cg, logarithmic average of the inlet and outlet concentrations of pollutants in the gas phase (mg/L); Km, saturate constant (mg/L); Cin, inlet concentration (mg/L); Cout, outlet concentration (mg/L);V, gas flow rate (L/min); and Q, bio-filter volume (L). To calculate logarithmic average (Cg) equation 2 is usable. $� � C|} − C~���Z 4 �!j����6 (2)

By solving equation 1 to find V, equation 3 can be calculated.

V � (C|} − C~��)(K� + C�)Qr��� � C� (3)

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16 ������� ��92

As you can see, equation 1 is similar to � � �B + � where a and b are slope and interception of curve y versus x. In this equation y is 1/Cg and x is t/(Cin-Cout). Also a and b are Km/rmax and 1/rmax, respectively. By plotting 1/Cg versus t/(Cin-Cout) constant coefficients rmax and Km in equation 5 are calculable. Another equation reported by Streese et al. (2005) to model BFs or BTFRs is [19]: ;�(2) � ;�V � ;2 + �8�V (4)

Where r(c), is degradation rate at concentration c (mg m-3 h-1); k1, is kinetic constant (h-1); k2, is kinetic constant (m3 mg-1

); Equation 4 is also similar to � � �B + � where a and b are slope and interception of curve y versus x. In this equation y is 1/r(c) and x is 1/c. Also a and b are 1/k1 and k2/k1, respectively. By plotting 1/r(c) versus 1/c constant coefficients k1 and k2 in equation 4 are calculable. After calculation of k1 and k2 using equation 5 volume of BF or BTFR is calculable.

z � c�J h!jh���e=�8�(�!j�����)�V � � (5)

Where, Cin is inlet concentration (mg m-3); Cout is discharge concentration (mg m-3); Q is gas flow rate (m3 h-

1); and V is bio-filter volume (m-3). Kinetic constants in above equations (k1 and k2 or rmax and Km) can be determined by conduction of BF at different inlet concentration, including given range from the expected inlet concentration to the targeted discharge concentration. The detected degradation rates are plotted over a suitable logarithmic average of the inlet and outlet concentrations of pollutants in the gas phase (Cg) for the respective experiment. Logarithmic average is calculable using equation 2. 2.2.2. Models based on biofiltration reactor height Strauss et al. (2000) also described the relationship between removal efficiency, loading rate, bed height and retention time according to Eq. 6 [19]. (] � � − �A��5) (6) Where μ is pollutant removal efficiency (in percentage), t is gas retention time (in s) and a and b are constant coefficients. These constant coefficients can be individually fitted to describe their relationship with loading rate at different bed heights H. This relationship can be described using Eq. 7 and Eq. 8 for constant coefficients a and b, respectively � � 2;=/�R�(�T�� ) (7)

� � � + ℎ� (8) Where L is organic loading rate (in g/m3.h), c, d, f, h and g are constant coefficients. Theses constant coefficient can be calculated using equation 9 to 13, respectively. � � &;P.��(�0&��)=(;<0.PQ��8);�(;.�P��)=(�.0;���) (9)

� � 14.82 − (74.7 � [) + (328.86 � [&) − (201.24 � [�) (10) w � −28.14 � ABC �−0.5 4���.9P�.�� 6;.&<� (11)

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16 ������� ��92

ℎ � 0.08 − (0.16 � [)(12) � � −1.26 + (8.27 � [) (13) Where, H is reactor height (in m). Substitution of Eq.9 to Eq. 13 into Eq. 7 and Eq. 8, and Eq. 7 and Eq. 8 into Eq. 6, provided an empirical model that described the removal efficiency of pollutants as a function of gas retention time, loading rate, and bed height. The relationship between pollutants removal efficiency and oxygen concentration at various BTFR or BF bed depths has been described by Eq. 14 to Eq. 16 [19]. .A � H[I8]J=[I8] (14)

Where, Re is pollutants removal efficiency (in percentage) and m and n are constant coefficients. m

and n can be calculated using Eq. 15 and 16. L � −180.31 + &P�.Q9

�;=/�R�4ST�.UU�.V: 6�W:.�8 (15) Z � 3.54 − (3.08 � [) (16) Where, H is BTFR or BF height (in m). Stress et al. (2000) used Eq. 6 to 16 to model a BTFR for removal of toluen from polluted air successfully [19].

2.2.3. Models based on gas retention time The mass balance equation is written for the removal of pollutants using the BTFR to level of the system (macroscopic balance) in different conditions of its functioning using the following formula [24]: 7275 � −  (17)

Where c is pollutant concentration (in mg/L), t is gas retention time (in s), and r is formaldehyde removal rate (in mg/L.s). It is assumed that if r is first order, then rearrangement of Eq. 17 gives a continuous equation expressed in the form of [25]: ���¡ � −¢¡ (18)

Where k is biochemical reaction rate coefficient (in mg/L.s). When we separate the variables, Eq. 18 can be integrated in form of: $ � $� � A��5 (19) Where Co is inlet formaldehyde concentration (in mg/L). As schematized in Fig. 2, theoretically if we recognize that E is amount of pollutants which has been already removed in the BTFR (in mg/l) and L is maximum removal of pollutants in BTFR (in mg/L). This gives L - E = C (20)

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Fig 2: Schematic of theoretical model for biodegradation of formaldehyde using BTFR

Source: by authors By combining Eq.19 and Eq.20 we can calculate Eq.21 � − s � $� � A��5 (21) But Co is equal L, rearrangement of Eq. 21 gives s � � − � � A��5£ s � �m1 − A��5p (22) "A variety of methods may be used to determine k from an experimental set of E data. The simplest and least accurate method is to plot E versus t. This results in a hyperbolic first-order curve of the form as shown in Fig. 2. The rate equation is used to solve k. It is often difficult to fit an accurate hyperbola to data that is frequently scattered. Methods that linearize the data are preferred. One simple method using in this study is called Thomas’ graphical method" [29]. Rearranging Eq. 22 in form of the linear equation yields:

c ¡seV� � g ¢8�¢ � �V� � ¡l + 1

(¢ � �)V � (23)

Equation 13 is similar to the equation y = a (x) + b, where a is defined as slope and b is interception of curve (t/E)1/3 versus t, y is (t/E)1/3, and x is t. Biochemical reaction rate coefficient (k) is constant and is thus expressed in the following relation that: ¢ � 6 4��6 (24)

Equation 24 permits us to calculate the biochemical reaction rate coefficient (k) if the values of the parameters (a; b) are verified analyzing the linear regression generated from the experimental data by plotting the curve (t/E)1/3 versus t. Relation between outlet pollutants concentration (C) and pollutants removal efficiency (RE) is defined by Eq. 25. $ � 100$� − (.s � $�)100 (25)

By combining Eq. 19 and 25 Eq. 26 was created. Amount of pollutants removal efficiency in different gas retention time can be determined using Eq. 26.

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.s � 1 − A��5 (26) To find constant coefficients (a and b) the BTFR was conducted in different gas retention times. Outlet pollutants concentration of BTFR was monitored during each gas retention time.

2.2.4. Suggestion of protocol to biofiltration design Based on previous studies following standard protocol for designing of BFs to treat polluted air can be established: First step: choice one of the above approaches for designing. Second step: conduct BF or BTFR at different concentrations. The single experiments should not focus on degradation but rather to cover a limited concentration range for each setting. The total of the experiments must cover at least the whole concentration range (Cin–Cout) expected for the considered application. Third step: the degradation rate (r) should be plotted versus logarithmic average (Cg). The degradation rate and logarithmic average can be calculated by equation 27 and 2, respectively.   � ($�J − $@¤5) � �z (27)

Fourth step: the status of the plot must be assessed. If the degradation rate approaches a constant value at higher concentrations, a shift from first to zero-order kinetics must be considered and this results is satisfactory for doing next step. If the plot is fitted by linear regression with high correlation coefficient, first order kinetics can be assumed. In this situation, more experiments should be carried out with higher concentration. Fifth step: based on the approach that was selected in step one constant coefficients can be calculated. For example: when equation 1 has been chosen, constant coefficients rmax and Km should be calculated by plotting 1/Cg versus t/(Cin-Cout). When equation 4 has also been chosen, constant coefficients k1 and k2 should be calculated by plotting 1/r(c) versus 1/c. Sixth step: Calculate the required biofilter volume. These steps has been summarized at Figure 5.

Figure 5: A standard protocol to biological processes designing to treat polluted air

Start to design a BF Conduct BF or BTFR pilot at different

concentrations

Does the biodegradation rate approaches a constant value at higher concentrations?

More experiments should be carried out with higher concentration

Yes No

Select appropriate

equation

Calculate constant coefficients based

instructions

Calculate the required biofilter volume

Make biofilter

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3- Conclusion

In this paper different approaches to model biofiltration processes to treat polluted air were reviewed. Removal of pollutants from air has been a challenge for engineers. Many approaches based on phase transfer, diffusion of pollutants within the biofilm, oxygen, pH, temperature, water, nutrients and substrate limitation have been reviewed in this article. Also, standard protocol to biological processes designing to treat polluted air was suggested by this article which can reduce number of biological process failures. Results of this paper can be used to inspire new approaches for biofiltration processes modeling.

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