An overview of approaches for biofiltration process modeling

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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, ha
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
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 layer
area 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 so
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
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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.1. Models based on phase transfer
within a bedded layer of gas near the interface and by resistance within the liquid. In many studies, ha
lms area unit well mixed due to its fast flow [3]. Mass transfer happens from
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
air is flowing upwards, material may be transferred from the recirculating water to the outgoing
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
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 so
constants in water in the order of 104 times are lesser than those in air (concentrations,
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
within a bedded layer of gas near the interface and by resistance within the liquid. In many studies, have
lms area unit well mixed due to its fast flow [3]. Mass transfer happens from
may be either co-current or
current to air flow) and if the water is recirculated, any material remaining in the water because it
air is flowing upwards, material may be transferred from the recirculating water to the outgoing
the viscosity, a0 the surface
is the acceleration of gravity. It's
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
constants in water in the order of 104 times are lesser than those in air (concentrations,
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./
.0
12
.
]
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
6
7
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].
0
su
s
S SkXS
r
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
1
values can be calculated by plotting
0
X
S S
θ
−
versus
1
S
. Yand kd Values were calculatedby the
following equation:
1 su
d
c
r
Y 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)d
c
k
X
SS
Y −
−
=
θθ
01

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Yand kdvalues were calculated by plotting
cθ
1
versus
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 4
ST .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= =
h8
i!jk
l 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 p
e
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 )p
e c
`8
mab`8= `8 p
e
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
Kƒ
rƒ…†
1
C‡
+
1
rƒ…†
(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~•€
ˆZ 4 !j
‰Š‹
6
(2)
By solving equation 1 to find V, equation 3 can be calculated.
V
(C|} − C~•€)(Kƒ + C‡)Q
rƒ…† C‡
(3)

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As you can see, equation 1 is similar to • ŽB + • 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 • ŽB + • 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!j
h‰Š‹
e=•8 ( !j ‰Š‹)
•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].
(] Ž − ŽA 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
Ž
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; š)
(9)
œ 14.82 − (74.7 [) + (328.86 [&) − (201.24 [ ) (10)
w −28.14 ABC •−0.5 4
.9P
. ž
6
;.&<
Ÿ (11)

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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 4
ST .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]:
72
75
− (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]:
œ™
œ¡
−¢¡ (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 •5
p (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
¡
s
e
V
š
g
¢
8
š
¢
V
š
¡l +
1
(¢ )
V
š
(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
Ž
•
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.

١٣
1692
.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
YesNo
Select appropriate
equation
Calculate constant
coefficients based
instructions
Calculate the required
biofilter volume
Make biofilter

١۴
1692
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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