EPA/600/A-95/133
GAS TREATMENT IN TRICKLE-BED BIOFILTERS:
A MODELING APPROACH AND EXPERIMENTAL STUDY
Cristina Alonso, University of Cincinnati
Paul J. Smith, Trinity Consultants, Incorporated
Makram T. Suidan, University of Cincinnati •
George A. Sorial, University of Cincinnati
Pratim Biswas, University of Cincinnati
Francis L, Smith, University of Cincinnati
Richard C, Brenner, U.S. EPA
~Department of Civil and Environmental Engineering, University of Cincinnati. Cincinnati, OH 45221 -0071
ABSTRACT
The objective of this paper is to define and validate a mathematical model that describes the physical and biological processes
occurring in a trickle-bed air biofilter for waste gas treatment. The model assumes a two phase system, quasi-steady state and one
limiting substrate. Experimental data from the biodegradation of toluene in a pilot system with four packed bed reactors, are used to
test the validity of the model. The unknown biofilter variables are estimated using a non-linear parameter estimation technique. Using
these parameter values, simulations were carried out for different operational conditions, and the model predictions were compared
to experimental data.
Keywords: trickle-bed biofilter, mathematical model, VOC, waste gas treatment, biofiltration.
INTRODUCTION
Biofiltration as a control technology for VOC laden exhaust gases continues to receive attention in research and development
arenas. A biofilter consists of a packed bed of organic or synthetic materials on which microbial films are supported. Degradable
pollutant species in a waste gas pass through a biofilter, diffuse through these microbial films and are then consumed. Since pollutant
degradation occurs at normal temperatures and pressures, biofiltration represents a potential energy efficient technology in comparison
to traditional physical and chemical methods of control (e.g., thermal incineration, carbon adsorption). However, biofilters are
essentially living pollution control systems, subject to dynamic changes. This characteristic has hindered the widespread application
of biofiltration in the United States, where regulatory requirements typically stipulate continuous compliance with an emissions
limitation or destruction efficiency. To help develop biofiltration as a viable technology able to meet these regulatory constraints, much
research has focused on understanding their fundamental chemical and microbiological processes through the development of
theoretical models.
The development of biofilter models has occurred in two distinct stages. In the first stage, following the historical application
of biofiltration ideas to wastewater treatment, models of water-phase biofilm reactors were developed. In Biofilms, Characklis and
Marshall (1990) compiled the extensive body of research that has been published on biofilm models and provided detailed descriptions
of the processes involved. The first biofilter model, in which the processes of substrate degradation in a biofilm were coupled with
equations describing mass transport of pollutants through a packed bed filter, was developed by Jennings et al. (1976). However,
this model was developed for a submerged packed bed reactor. Ottengraf and Van der Qever (1983) were the first to adapt this liquid-
phase model by changing the transport phase to a gas, thus beginning the second stage of model development for gas-phase biofilters.
Since then, biofilter models of increasing sophistication have been derived for various system types and applications (Ottengraf, 1986,
Diks and Ottengraf, 1991a and 1991b; Hartmans and Tramper, 1991; Utgikar et al., 1991; Ockeloen et al., 1992; Smith, 1993;
Shareefdeen et al., 1993 ; Deshusses et al., 1995a and 1995b). Ottengraf (1986) analytically calculated the efficiency of the biofilm
for the limiting cases of first and zero order kinetics for diffusion and reaction limiting degradation. Diks and Ottengraf (1991 a and
1991b) considered a simplified model with a three phase system and zero-order kinetics that was numerically solved. Utgikar et al.
(1991) used a similar model with first order kinetics expressioa Hartmans and Tramper (1991) modeled a trickle-bed bioreactor
using a series of identical, ideally mixed tank reactors. Ockeioen et al. (1992) used the same approach as Diks and Ottengraf, but they
numerically solved the general model.
Recendy, biofilter models have been introduced that account for detailed representations of biofilm degradation mechanisms.
Shareefdeen et al. (1993) proposed a biofilter model for a single component waste stream that accounted for rate limitations of oxygen
in the biofilms. Smith et al, (1993) developed a two phase trickle-bed biofilter model that incorporated decay and shearing effects
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to determine the distribution of biomass in each section of the biofilter. Deshusses et al, {1995a and 1995b) developed a model that
accounted for transient processes during start-up and shut-down. Their dynamic model also handles multiple substrate degradation
through the incorporation of both noncompetitive and uncompetitive reaction rate expressions.
In this paper, a new theoretical modeling approach is presented for a synthetic media trickle-bed biofilter. The two-phase
model developed by Smith (1993) is used as a basis. His steady state model describes the degradation of one limiting substrate (VOC
pollutant) in a homogeneous biomass by one type of microorganism species. This approach is enhanced by the addition of a quasi-
steady state term that accounts for dynamics of the system. The model has been developed in conjunction with four pilot-scale trickle
bed biofilters that use ceramic pellets as the packing medium (Smith et al., 1994). The model presented is assessed against
experimental data collected in four trickle-bed biofilters for a variety of operational scenarios. A first set of experimental data were
used to estimate the unknown parameters of the biofilter using a non-linear parameter estimation technique. Using these parameter
values, simulations were carried out for different operational conditions, and the model predictions were compared with a second set
of experimental data The intent of the model is to facilitate the study of the effects and interdependence of key system variables, such
as initial substrate concentration, residence time, temperature, pollutant properties, and system geometry, on biofilter performance.
The model can be used for simulation and analysis of the biodegradation process, prediction of biofilter performance and assistance
in biofilter design.
METHODOLOGY
Theoretical Model
The theoretical model is developed for a packed bed trickle biofilter
employing uniformly shaped solids. Due to the random packing, the flow
path for the waste gas is considerably tortuous, and the gas is assumed to be
well mixed radially across the biofilter cross section. Consequently, the
concentration of contaminant in the bulk gas is assumed to be uniform at any
given axial position. The packing solids are modeled as a bed of equivalent
spheres sized to have the same volume. All processes are assumed to be
uniform across the biofilter cross section, and reactor wall and end effects
are negligible. The model considers two phases, the gas phase and the
biofilm, A liquid layer, present due to a small and intermittent nutrient
solution feed rate, has minimal mass transfer resistance and is disregarded.
The temperature in the biofilter and the physical properties of the gas and
VOC are assumed to be constant. The variables of interest are the VOC
concentration profiles in the biofilm and gas phase, and the biofilm thickness
along the reactor. The model is solved for quasi-steady state conditions.
First, the biofilm thickness is considered constant to calculate the
concentration profiles, and then the biofilm thickness variation with time is
computed for a constant concentration profile.
Gas flow
Characleristic sphere
Biofilm covering
Figure 1. Biofilter system geometry.
In the formulation of the mass balance equations in the biofilter, the
following assumptions have been applied: the biofilm is a stagnant liquid; there is no convective transport; axial diffusion is negligible;
the microbial growth is described by Monod kinetics; VOC is the only growth limiting substance; and all kinetic parameters and the
bacterial density are constant along the biofilter. The biofilter geometry is represented in Figure 1. The mass balance equation for the
biofilm phase, expressed in spherical coordinates to account for the curvature of the spheres, is:
D,
d2Cf 2 dCt
dr~
r dr
r
k+c,
0)
where C^M/t5) is the VOC concentration in the biofilm, D/0J/t) is the contaminant difiusivity in the film, assumed to be a fraction,
of the contaminant difiusivity in water, Dw, {Df= rd* £)„), (t"1) is the maximum bacterial growth rate, Y (M biomass/ M VOC)
is the yield coefficient, K, (M/L5) is the Monod saturation constant, and Xf (M/L5) is the film bacterial density.
Radially across the bed, the gas flow and the VOC concentration are uniform, so plug flow can be assumed for the gas phase.
As there is no contaminant degradation in the gas phase, the mass balance equation in the biofilm interface can be expressed as:
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dC -Jaf
= —	(2)
where Cf (ppmv) is the VOC concentration in the gas phase, J (M/L: t) is the flux of VOC into the biofilm, o/ (L1) is the surface area
of the bed with biofilm, and «<,(L/t) is the gas approach velocity, i.e., the gas flow rate divided by the total bed cross sectional area.
The surface area per unit volume of the clean packing solids, a0 (L1), and with a biofilm growth, af (L*1) are given by:
_ 3(1-€o)	_ 3(1 -€/)
°Q <$>R ' °f $(R+Lj)
where $ is the packing solids sphericity, R (L) is the characteristic sphere radius, Lf (L) is the biofilm thickness, and ef is the actual
porosity of the reactor bed with a biofilm. The actual porosity is a function of the clean bed porosity e^, the clean bed surface area,
and the biofilm thickness:
€/=€o~ao^/	(4)
The boundary conditions necessary for equation (1) are derived by assuming that there is no flux of contaminant into the
surface of the packing solids, and that the concentration of VOC in the biofilm and in the gas phase are in equilibrium defined by
Henry's law:
dCf
Cer-R, .0	(5)
@r = R + Lr Cg = HCf	(g)
Assuming a uniform VOC gas concentration at the inlet of the biofilter, the initial condition for equation (2) is:
(7)
= 0, c. = c.
s
where Cg,, is the initial VOC concentration in the gas phase. For equation (2), the flux of VOC in the gas phase in equation (2) is equal
to the flux at the biofilm surface:
dC,
( PM\ .. uW
@r=R+lf	=Jf = rfi -
(8)
where P is the system pressure, M„ is the molecular weight of VOC, Rf is the universal gas constant and T is the system temperature.
RT / } " w dr
g
Since the biofilm thickness is not constant along the biofilter, another equation is needed to characterize its variation. The
variation of the biofilm thickness with time is due to the net bacterial growth with steady-state VOC concentration profiles. This
assumption of quasi-steady state is valid because the characteristic time of VOC transport and reaction is smaller than the one for
bacterial growth. If b (t"1) is the specific combined shear/decay coefficient, this equation is:
dLf
—Lxf
dt f
( dC\
¦ it
@ / = 0 Lp,t) = Lfl
,Y - w
f r	(9)
The combined shear/decay coefficient, represents the effects of biomass loss, combining biomass decay and physical
shearing, following the formulation of Rittmann (1982). The specific decay coefficient, b3 is assumed to be constant, and the specific
shear rate, b, is assumed to be a function of the biofilm thickness.
b=b, + bd	(10)
The different existing expressions to define the rate of biofilm detachment, suggest that this process is not very well
understood (Peyton and Characklis, 1993). In this case, the shear rate is assumed to be proportional to the shear stress, t, that is
proportional to the interpore gas velocity, w=«/e/
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(»)
/ 6/
The proportionality constant, p, is chosen to be the default shear rate coefficient, b,", corresponding to the default shear stress, t°, when
the bed is clean and there is no biofilm, then:
T°=Pfi) b' a PR)	(12)
«o	€o
Eliminating the constants, the expression for b is:
b =b& + bd	(13)
e/
The packed bed biofilter model is defined by equations (l)-(9), and (13). These equation can be written in dimensionless
form for mathematical simplicity and to reduce the number of model parameters. The new dimensionless variables are:
z* = - r* = - r = t(b! + b* C' = -S- C; =
L	R	1 ^ g	f Cf0
Li.i& a;^ *•- *	<14)
"/ ~R * ~R f
• = ^	r. =	\
The governing equations in dimensionless form are:
d2Cf 2 dCf _ , ( Cf
2 / .J C/' )
(15)
rfr-2
rfC*
—L=	(16)
az
dc; "
@r' = 1, —£. = 0	(17)
<*•*	V '
@r* = 1 + Lj, c; = c;	(18)
@** = o, c; = i	(19)
{/C *
@r* = 1 + L/, J" = —L	(20)
dr*
dLf j*
lk = ^Lfb'	<2l>
@/* = 0 1/ = L;	(22)
^*=4^)2+^	(23)
£, = ^-.4,(1-^;	(24)
(l-e)
7 (1 ~£/)(!-vg	(25)
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Equations (15) and (16) form a coupled set of
non-linear ordinary differential equations, which are
solved using the initial and boundary conditions given by
equations (17)-(20). Equations (21)-(22) define the
variation of the biofilm thickness, and equations (23)-(25)
are used to calculate the non-constant biofilter parameters.
There are eight dimensionless groups, A, to A,, that are
defined in Table 1.
A variable of interest is the concentration of
biomass in the reactor, Xr (M/L3), because it can be
measured and it is an indication of the biofilm thickness
Xr is mass of organic matter per volume of reactor, so it
varies along the reactor depth, as opposed to biomass
density in the biofilm, which is considered constant. The
biomass concentration in the reactor can be calculated as;
A'r = Xf af Lf = XfR a0 a] 1}	(26)
Numerical Solution
Equation (16) is solved using an Adams-
Moulton finite difference scheme. The solution is found by
marching axially through the biofilter. At each axial step,
the flux, biofilm concentration profile, biofilm thickness,
and packed bed characteristics are evaluated. Equation
(15) is solved with a second order two-point boundary
value problem direct method. Two levels of iteration are
required in each axial step, to handle the non linear term
of equation (15), and to calculate the biofilm thickness
given by the linearization of equation (21).
1. Dimensionless groups.
, _ '/>/- V
' V*2 PMJi
residence time
diffusion time
A =1
2 *
actual nackme solids surface area
characteristic sphere surface area
ii
r*>
biokinetic reaction rate order
„ _ Mr R2H
4 Y rJ>„C„
maximum erowth rate
diffusion rate
b°Xf r2H
5 y
shear/decav rate
diffusion rate
A6 = eo
clean bed porosity
+ K
shear rate
total shear/decay rate
„ _
decav rate
"8 "
A,° + K
total shear/decay rate
The thickness of the biofilm has a physical limit when the bed is clogged. Close to clogging, the assumption of spherical
packing solids with a shell ofbiofilm is not valid. Thus, a minimum bed porosity is defined, that gives a maximum biofilm thickness:
L>- - WJj	<27>
Experimental Design
The mathematical model and its numerical solution have been derived in a general manner, so they can be applied to any
VOC and any trickle-bed air biofilter. The biofilter system used to validate the theoretical work consists of four 15 cm diameter
stainless steel reactors, packed with pelletized biological support media (6 mm R-635 Celite) to a depth of 122 cm, with a free board
of 91.5 cm. The pelletized medium was selected after initial screening revealed it to be superior to two other candidate media (Sorial
et al., 1993). The packing solids are represented in the model as equivalent spheres, with a characteristic radius of 3 mm and
calculated sphericity of 0.857. The organic feed to the biofilter consists of a neat solution of toluene volatilized in a feed air stream.
The initial concentration of toluene is 250 ppmv. Prior to the addition of toluene, the feed air is purified and contains only oxygen and
nitrogen. The biofilters are fed 20 L of an aqueous solution of nutrients per day. There are two possible nitrogen sources, nitrate and
ammonia. The temperature of the reactors is maintained at 32 °C throughout the biofilter length and the outlet pressure is very close
to atmospheric. The empty bed residence time for both biofilters has been one and two minutes in two different sets of experiments.
The biofilters were operated in a co-current mode and backwashed once or twice a week. A more detailed description of the
experimental system and its performance can be found in Smith et al. (1994) and Sorial et al. (1995). Table 2 summarizes the values
of the system operational variables, biofilter size, packing media, operating conditions and VOC properties. There are two values for
the gas flow rate. The first value given in the table is for two minutes residence time and the second value for one minute. The units
of the parameters are the ones used in the equation and in the program.
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The value of the kinetic and shear
parameters (Monod constant, yield coefficient,
maximum specific growth rate, decay coefficient,
default shear coefficient and biomass density in
the biofilm), the biofilm/water diflusivity ratio,
and the initial biofilm thickness are not known a
priori and cannot be measured in this system, so
they are estimated simultaneously with the
validation of the model. Assuming that the
unknown parameters depend on the nitrogen
source, two groups of estimates are calculated,
group A and B for the biofilters using nitrate and
ammonia respectively.
The experimental data used in the
validation of the model are:
-	The performance of the biofilter with
depth, which is obtained from
measurements of the substrate
concentration in the bulk gas phase for
different depths. Data were collected from experiments where the residence time was maintained at one and two minutes.
The VOC concentration was measured immediately and two days after the backwashmg of the biofilter.
-	The biomass concentration profile along the biofilter. This concentration profile was determined at the end of the
experimental run Samples of the media were collected at different depth and analyzed for VSS content. The concentration
determined is mass of organic matter per unit volume of biofilter. Two sets of values for each biofilter were available: the
biomass concentration immediately after backwashing, and the biomass concentration nine or seven days after backwashing,
depending on the biofilter. The residence time was one minute in this experiment.
RESULTS AND DISCUSSION
The study of the mathematical model was earned out in two stages, estimation of the parameters and validation of the model.
The validation process involves the test of the accuracy of the model predictions when the estimated values were used. Therefore,
two different sets of data were required. Four biofilters were available for this study and two series of experiments were conducted.
Initially, three biofilters were running, two using ammonia and one using nitrate as the nitrogen source, and afterwards, the four
biofilters were restarted with nitrate. For the first part of the analysis, the estimation of the parameters, the experimental data collected
from two biofilters of the first series of experiments were used, each with a different nitrogen source, nitrate in biofilter A, and
ammonia in biofilter B. The model was then tested for the two groups of calculated parameters, group A for biofilters using nitrate,
and group B, for biofilters using ammonia as a nitrogen source. Data from the four biofilters of the second series of experiments were
compared with the model predictions with the parameters of group A (nitrate). The four biofilters were operating at diffrent detention
time and initial VOC concentration.The data used to validate the parameters of group B were collected from the other biofilter using
ammonia in the first series of experiments. These two different sets of data will be referred to as estimation data set and validation data
set in the discussion that follows.
The data of the estimation data set were non-homogeneous: For each biofilter there were two types of observations, removal
efficiency and biomass density. Measurements were taken at different sampling points along the reactor depth, and the value of the
variable in each point is considered an observation that can be predicted by the mathematical model. Observations are assumed to
be independent random variables. Efficiency was measured at four points in biofilter A, and five points in biofilter B. Biomass density
was measured at five points in both reactors. The data were taken when both biofilters were considered to be at steady state. For each
experiment the initial time, (time=0), is defined as the time immediately after the backwashing of the biofilter. The backwashing
technique was practically the same during the realization of all the experiments in the first series, so the state of the system depends
only on the time elapsed since backwashing, and therefore, experiments can be replicated.
Two experiments for efficiency measurements were conducted, at one and two minutes detention time. Each experiment was
replicated a different number of times, eight replications for one minute detention time and eleven for two minutes. As the reactor
Table 2. System Parameters.
Packing media
parameters
Operatine parameters
Biofilter size
R
0.3 cm
r
305.35 K
L
121.92 cm
~
0.857
P
1 atm
Ar
167.23 cm2
60
0.34

250 ppmv
VOC nrooerties

0.025
Qt
169.93 cmVsec
339.86 cmVsec

D.
10.8 10"* cmVsec
H
104.03 ppmv/(mg/L)
K
92.13 g/mol
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efficiency at each sampling port is assumed to be a random variable, its mean and variance can be calculated as those of the sample
generated with the set of replications. In each experiment, the efficiency was measured immediately and two days after backw ashing
The value of the initial efficiency has not been used in the validation of the model, because the quasi-steady state derivation of the
model is not enough to explain the variation of contaminant concentration profiles with time. As a consequence, the number of model
variables corresponding to efficiency observations is eight for biofilter A and ten for biofilter B, (twice the number of sampling ports
in the reactor, for one and two minutes detention time).
Two sets of biomass concentration values were available: the initial concentration, and the concentration after nine or seven
days, depending on the reactor. There was only one set of measurements for those variables, but as the initial concentration is assumed
to be constant along the reactor, we can presume that the five measurements along the bed are realizations of the same random
variable, the initial concentration, and therefore, we can calculate the mean and the variance of the variable. For the concentration
measurements after nine or seven days there was only one replication, so this value was taken as the mean, and the variance was
calculated from the other one adjusted to account for the difference in the number of observations.
Seven unknown parameters were estimated: the yield coefficient Y, that can have values from 0 to 1; the biofilm/water
diffusivity ratio, rd, with values from 0 to 1; the maximum growth rate, ji„ the Monod constant, Ks; the biofilm biomass density, Xf \
the initial biofilm thickness, Lp and the default shear rate and the decay rate coefficients, which were assumed to be equal, and were
represented as b0. To solve the nonlinear parameter estimation problem the method of maximum likelihood was used. The
mathematical model can be expressed as:
y = Ax) + e
y = tVi- vVj, /= \fv ~fm], x =	e =	(28)
where y is the vector of the m observed variables, e is the residual vector,/ is the vector of the model predicted values, and x is the
vector of the rt parameters. Assuming independent and normally distributed errors, the maximum likelihood parameter estimate, x",
is the one that minimizes the objective function given by:
l, > _ T^14 ei _ VN4 (V, "./|(X))
= 2-.-1 — = L-i	1—	(29)
o,	o,
where o,, is the standard deviation of the ith residual, e„ the same as the one of the ith observation, . This is equivalent to the
weighted least squares method, with the inverse of the variances as weights. Some prior information, for example, preferred values
for the parameters similar to the published ones, was not included in the objective function.
The estimation process was done after a parameter sensitivity analysis. The problem was ill-posed, so conventional methods
were not very efficient. The diflusivity ratio, r# couldn't be accurately estimated, because the other unknown parameters could be
adjusted to get the same reactor response when the value of rd was modified. Therefore, a typical value was chosen, r/O.85. For each
value oLY^. there was an optimum value of the initial biofilm thickness, Lp which was calculated from the initial biomass concentration
in the reactor that only depends on these two variables, (Xp Lp). When these three magnitudes were fixed (r# Xf, L/o)> the number of
parameters was reduced to four. Then the reduced problem was solved for different values of Xf and until the optimum combination
was found. It should be noted that when K, was also fixed, the objective function had a very well-determined minimum, and the
optimum estimates for the three remaining parameters (jim Y, b„) were well-defined. The problem was solved with an iterative
technique based on this information, using the estimation data set described before.
The resulting estimated parameters are presented in Table 3 for both biofilters, and the observed and predicted values of the
model variables are in Figure 2 for biofilter A and in Figure 3 for biofilter B. The error bars shown in the removal efficiency graphs
correspond to the 95% confidence value for the mean. The values are plotted against the relative reactor depth, that is, the depth
divided by the total length of the reactor, L. The value of z is the axial coordinate, so z=0, corresponds to the inlet of the reactor.
Although the optimum parameter values for biofilter B are those of set number 1, in Figure 3 the results corresponding to a different
set of parameters, set number 2, are shown. The values are given also in Table 3. The reason to consider this new set is that the fit
for the efficiency observations is much better. The fit for the biomass is worse, though. We have more confidence in the efficiency
observations because there are various replications of the experiment, and, on the other hand, the measurements of biomass can be
inaccurate, due to the presence of inactive biomass that is not included in the model. It is possible then, to prefer parameter set 2 as
the optimum, although the objective function does not reach a minimum in this point. This arises the problem of defining an objective
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Table 3. Biofilter parameter estimates.

Xf
L*
K,
Y
ri

b,

(mg/L)
(cm)
(mg VOC/L)
(mgVSS/
mg VOC)

sec"'
day'1
sec"'
day'1
Biofilter A
10,000
0.0345
0.5
0.15
0.85
0.095* 10"4
0.82
0.12*10"'
0.001
Biofilter B









Set 1
10,000
0.041
0.1
0,2
0.85
0.04* 10"4
0.35
1.2*10-7
0.01
Set 2
10,000
0.041
5.0
0.15
0.85
0.36* 10"4
3.11
0.12*10-'
0.001
A) Biofilter A, biomass with depth.
I observed after 9 days
¦ observed @ t=0
	predicted @t=0
—	predicted after 9 days (b=O 001 d-1)
—	predicted after 9 days (b=0 01 d-1)
B) Biofilter A. 2 min detention time.
observed efflcency
predicted efficiency
100 -
\\
C) Biofilter A, 1 min. detention time.

# observed efficiency
predicted efficiency
—i	1	r-
0 2 0.4 0 8
z/L
"1
1.0
z/L
Figure 2. Performance of biofilter A using nitrate as the nitrogen source. A) Biomass concentration
in the reactor with depth, the detention time is 1 minute. B) and C) Removal efficiency with depth,
the detention time is 2 minutes in B) and 1 minute in C).
s
1
2
A) Biofilter B, biomass with depth.
	predicted @t=0
— predicted after 7 days (set 1)
predicted after seven days (sat 2)
•	observed ®t=0
•	observed after 7 days
B) Biofilter B. 2 min. detention time.
—•
—	predicted efficiency, (set 1)
—	predicted efficiency, (set 2)
• observed effieency
Biofilter B, 1 min, detention time.
""MOO
	!	!	[	1	1
0 0 0.2 0.« 0 8 0.1 10
z/L
predicted efficiency, (set 1)
predicted efficiency, (set 2)
observed efficiency
Figure 3. Performance of biofilter B using ammonia as the nitrogen source. A) Biomass
concentration in the reactor with depth, the detention time is 1 minute. B) and C) Removal efficiency
with depth, the detention time is 2 minutes in B) and 1 minute in C).
function that would include all the
prior information. Here the solution
is considered non-unique, and more
objective information is needed to
select a set. When the model is used
for prediction, set 1 gives slightly
better results. This problem was not
found in biofilter A, but although the
optimum value is bg=0,12 * 10'? sec'1,
another value of b0 is considered for
comparison.
Overall, the model is close
to the observed values. The fit is
much better for the removal efficiency
than for the biomass reactor
concentration, although the efficiency
in the points closer to the reactor inlet
is consistently underpredicted. The
overall predicted efficiency is very
close to the observed value, in fact,
this is the point with less variability in
the measurements. The initial biomass
is also very close, but not the rest of
biomass values.
Most of the parameters
found are in the typical range.
Areangeli and Arvin (1992) reported
a set of kinetic parameters for toluene
degradation in a bioreactor: ^=0.9;
£,=0.6 mg COD/L=0.19 mgVOC /L,
and Xf= 12000 mg/L, The rest of the
kinetics values in the mentioned paper
are referred to the two bacterial
species considered in their model, so
they are not compared with the ones
here. Ottengraf (1986a) calculated the
maximum growth rate for toluene
degradation as; ^=0^"'. All these
values are in good agreement with the
ones computed here, The value of b0
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is too low, because typically it is reported to be around 0. Id"1, In Figure 2, the biomass concentration profile is shown for two %-alues
of b0 the optimal value and 4=0.01 d"1, with the rest of the parameters unchanged. The concentration profile is the same for both
values. It can be seen that the profile has the same shape but the magnitudes are lower, and the fit is worse. This is another reason to
prefer parameter set 1 in biofilter B, because the value of the decay coefficient is higher. One possible explanation for this low shear
and decay rate can be that we are considering all biomass as active, when it is not, so the model should be modified to account for non-
homogeneous biomass. In fact, the model assume that the inactive biomass produced by decay is lost, and this may not be true. The
observed net yield coefficient calculated from experimental data, the VSS lost and removed with backwashing and the amount of
toluene consumed, is 0.23 mg VSS/ mg TOL for biofilter A, and 0.27 mg VSS/ mg TOL for biofilter B. This values are close to the
estimated yield coefficients.
100 —
1.33 min
C go =506 ppmv
m
'0
i
1 mm
Cgo=242 ppmv
«o -
6=0.67 nun.
Cgo=24Q ppmv
0=2 min.
Cgo =505 ppmv
The model was tested in the prediction of the removal efficiency of biofilters fed with nitrate and ammonia, operating at
different conditions. As mentioned before, the validation data set was used. The new set of observations contains six subsets of data.
Four of them will be compared with
the model predictions with parameter
group A (nitrate), and the last two
ones with the model predictions with
parameter group B (ammonia). The
results and the conditions of operation
for biofilters using nitrate are in
Figure 4, and for biofilters using
ammonia in Figure 5 The detention
time of the reactor, 0, and the initial
VOC concentration in the gas phase,
Cgo, were the parameters varied.
Measurements were conducted for
different backwashing techniques in
the four biofilters using nitrate. This
process is not included in the
mathematical model but it is
presumed that it will have an effect in
the biofilter performance because the
removal efficiency differs with the
backwashing technique. A description
of this system can be found in Sorial
et al (1995), Two sets of
measurements are presented for each
biofilter in Figure 4, and it can be
seen that the best fit does not
corresponds to the same backwashing
technique in all of them. This suggests
the need of including the backwashing
process in the model. The prediction
for the biofilter using ammonia has
been done with parameter set 1, and
the fit is reasonably good. The
backwashing technique was not
varied in the experiments with
ammonia.
observed efficiency, backwash twice a week
observed efficiency, backwash every other day
0.2 0.4 0.9
z/L
predicted efficiency
Figure 4. Predicted and observed removal efficiency values for biofilters using nitrate as the
nitrogen source.
e
?
s
e
w
0=1 rain.
Cgo=125 ppmv
6=2 min.
Cgo=125 ppmv
0.8
1.0
observed efficiency
predicted efficiency
Figure 5. Predicted and observed removal effcicncy values for a biofilter using ammonia as the
nitrogen source.
CONCLUSIONS
A mathematical model to describe the biodegradahon of a waste gas in a trickle-bed reactor has been proposed and validated.
The model considers a two phase system, one limiting substrate and quasi-steady state. In the model analysis the unknown reactor
parameters have been estimated and the model has been validated. Two sets of observations have been employed. For the estimation
of the parameters, the biofilter removal efficiency profiles and the biomass concentration in the reactor have been calculated and
compared with experimental data from two different reactors, one using nitrate as a nitrogen source and the other one using ammonia.
9

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These parameters are the kinetic constants; biomass density in the film, Monod constant, maximum growth rate, yield coefficient and
decay and shear rate coefficients; and the initial biofilm thickness and the ratio between the VOC diffusivity in the biofilm and water.
Once the values of the parameters are known for both systems, the model has been tested in the prediction of the biofilter efficiency
for the same type of reactors operating in different conditions. The detention time and the initial VOC concentration were the varied
parameters.
The fit of the model is reasonably good for the efficiency values and somew hat worse for the biomass concentration
measurements. There is a systematic underprediction of the efficiency observations close to the reactor inlet. The values of the
estimated parameters are close to the typical values reported by previous investigators, except for the decay coefficient that is unusually
low. The model was tested with different sets of observations of biofilter efficiency profiles, for different scenarios. The results
conclude that the model is valid and can be used for prediction with acceptable accuracy, especially in the overall biofilter efficiency
value.
Some problems in the mathematical model have been identified. First, it cannot predict the variation of the contaminant
concentration profiles with time, a dynamic model is necessary, it has to account for time variations in the concentration and in the
biomass distribution. Second, the prediction of the biomass concentration is not very good, nonhomogeneous biomass, active and
inactive microorganisms, should be considered. The calculated decay rate coefficient is very low, this value should be verified with
a more accurate model or with more observations. Some operational parameters should be included in the model, as oxygen and
nutrient limitations, and backwashing technique effects. This will be done in future work-
There are also problems in the parameter estimation technique. The objective function does not include all the pnor
information and thus, the selection of the optimum parameter set is subjective in some cases, Also the problem is ill-posed and
conventional algorithms do not give good results. A careful study of the problem is needed to determine what parameters can be
accurately estimate, what is the most suitable method to approach this problem and what kind of experiments should be carried to
obtain the more valuable information.
APPENDIX
Notation
a0 (cm"1), surface area per unit volume
af{cmv), surface area per unit volume accounting for biofilm in bed
A,-A4i dimensionless groups
b (sec"1), shear/decay rate coefficient
b° (sec"1), default shear/decay rate coefficient
bd (sec'1), decay rate coefficient
b0 (sec'1), decay and shear rate coefficient for the parameter estimation
b, (sec'1), shear rate coefficient
b°s (sec1), default shear rate coefficient
(^(mg/L), biofilm VOC concentration
Cf (ppmv), gas phase VOC concentration
Cgo (ppmv), inlet gas phase VOC concentration
(cm2/sec), VOC diflusivity in the biofilm
Dw (cm2/sec), VOC diflusivity in water
H (ppm/(mg/L)), Henry's law constant
J{ ppm cm/sec ), VOC flux in gas phase
J;(mg cm/L sec), VOC flux in biofilm
K, (mg/L), Monod saturation constant
L (cm), biofilter packing media length
Lf (cm), biofilm thickness
L/mb (cm), maximum biofilm thickness
M, (g/mol), VOC molecular weight
r (cm), radial coordinate
rd, ratio between VOC diffusivities in biofilm and water
R (cm), characteristic packing sphere radius
Rg (cm3 atm/mol K), universal gas constant
t (sec), time
10

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T (K), system temperature
u0 (cm/sec), approach velocity to the biofilter
A}(mg/L), biomass density
Y (mg biomass/ mg VOC), yield coefficient
2 (cm), axial coordinate
Greek letters
P, stress proportionality constant
Eg, clean bed porosity
€f> porosity in bed with biofilm
£,„ minimum porosity allowed in packed bed
$, sphericity of packing solids
[ia (sec"'), maximum growth rate
t (dyne/cm2), shear stress
8 (min), and detention time.
REFERENCES
Arcangeli, JP. and Arvin, E., (1992). Modeling of Toluene Biodegradation and Biofilm Growth in a Fixed Biofilm Reactor, Wat. Sci.
Tech., V26, no3-4 617-626
Characklis, W.G. and Marshall, K.C., (1990). Biofitms, John Wiley & Sons, Inc., New York.
Deshusses, M.A., Hamer, G. and Dunn, I.J., (1995a). Behavior of Biofilters for Waste Air Biotreatment. 1. Dynamic Model
Development, Environ. Sci. Techno!., 29:1048-1058.
Deshusses, M.A, Hamer, G. and Dunn, I,J., (1995b). Behavior of Biofilters for Waste Air Biotreatment. 2. Experimental Evaluation
of a Dynamic Model, Environ. Sci. TechnoL, 29:1059-1068.
Diks, R.MM and Ottengraf, S.P.P., (1991a). Verification Studies of a Simplified Model for the Removal of Dichloromethane from
Waste Gases using a Biological Trickling Filter (part I), Bioprocess Eng., 6: 93-99.
Diks, R.M.M. and Ottengraf, S.P.P., (1991 b). Verification Studies of a Simplified Model for the Removal of Dichloromethane from
Waste Gases using a Biological Trickling Filter (part II), Bioprocess Eng., 6: 131-140.
Hartmans, S. and Tramper, J„ (1991). Dichloromethane Removal from Waste Gases with a Trickle-Bed Bioreactor, Bioprocess Eng.,
6: 83-92.
Jennings, P.A, Snoeyink, V.L. and Chian, E.S.K., (1976). Theoretical Model for a Submerged Biological Filter, Biotechnol. Bioeng.,
18: 1249-1273.
Ockeloen, H.F., Overeamp, T.J. and Grady Jr., C.P.L., (1992). A Biological Fixed-Film Simulation Model for the Removal of Volatile
Organic Air Pollutants, presented at the 85th Annual Meeting & Exhibition of the Air and Waste Management Association, June 21 -
26,1992, Kansas City, MO,
Ottengraf, S.P.P, and Van der Oever, AH.C., (1983). Kinetics of Organic Compound Removal from Waste Gases with a Biological
Filter, Biotechnol. Bioeng., 25: 3089-3102.
Ottengraf, S.P.P., (1986a). Exhaust Gas Purification, in Biotechnology, Vol 8, Rehn, H.J. and Reed, G., eds., VCH Verlagsgesellsch.,
Weinham.
Ottengraf, S.P.P., (1986b). Biological Elimination of Volatile Xenobiotic Compounds in Biofilters, Bioprocess Eng., 1: 61-69.
Peyton, B.M., and Characklis, W.G., (1993). A Statistical Analysis of the Effects of Substrate Utilization and Shear Stress on the
Kinetics of Biofilm Detachment, Biotechnol. Bioeng., 41 728-735.
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Rittmann, B E., (1982). The Effect of Shear Stress on Biofilm Loss Rate, Biotechnol. Bioeng., 42:501-506.
Shareefdeen, Z., Baltzis, B.C., Oh, Y.S. andBartha, R., (1993). Biofiltration of Methanol Vapor, Biotechnol. Bioeng41:512-524.
Smith, F.L., Suidan, M.T., Sorial, G A., Biswas, P. and Brenner, R.C., (1994). Trickle Bed Biofilter Performance: Biomass Control
and N-nutrient Effects. Presented at the 67th Annual Conference and Exposition of the Water Environmental Federation, Chicago,
IL, October 15-19, 1994.
Smith, P J., (1993). A Fundamental Approach to Modeling the Treatment of VOC Laden Exhaust Gases in Biofilters. M.S. Thesis,
University of Cincinnati.
Sonal, GA, Smith, F.L , Pandit, A, Suidan, M.T., Biswas, P. and Brenner, R.C., (1995). Performance of Trickle Bed Biofilters under
High Toluene Loading. Paper no. 95-TA9B.04 presented at the 88th Annual Meeting and Exhibition of the Air and Waste
Management Association, San Antonio, TX, June 18-23.
Sorial, G.A., Smith, F.L., Smith, P.J., Suidan, M.T., Biswas, P. and Brenner, R.C., (1993). Evaluation of Biofilter Media for
Treatment of Air Streams Containing VOCs. Proceedings of the Water Environment Federation 66th Annual Conference and
Exposition, Facility Operations Symposia, Volume X, p429-439.
Utgikar, V., Govind, R., Shan, Y,, Safferman, S. and Brenner, R.C., (1991). Biodegradation of Volatile Organic Chemicals in a
Bioilter, in Emerging Technologies in Hazardous Waste Management II, D. W. Tedder and F.G. Pohland, eds , ACS Symposium
Series, American Chemical Society, Washington, DC, p.233-260.
12

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TECHNICAL REPORT DATA
(Mease read Instructions on the reverse before completi•*
1. REPORT NO. a.
EPA/600/A-95/133
3.
4. TITLE ANO Subtitle Gas Treatment in Trickle-Bed Biofilters;
A Modeling Approach and Experimental Study
5. wr-< » 1 c
e. PERFORMING ORGANIZATION COOE
7. author(s) cristina Alonso, Paul Smith, Makram Suidan,
George Sorial, Pratim Biswas, Francis Smith*, and
Richard C. Brenner 2
8. PERFORMING ORGANIZATION REPORT NO.
9 PERFORMING ORGANIZATION NAME AND ADDRESS
1University of Cincinnati, Cincinnati, OH 45221-0071
2U.S. EPA, NRMRL, Cincinnati, OH 45268
10. PROGRAM ELEMENT NO.
11. CONTRACT/GRANT NO.
CR-821029
12. SPONSORING AGENCY NAME ANO ADORESS
National Risk Management Research Laboratory—Cinti, OH
Office of Research and Development
U.S. Environmental Protection Agency
Cincinnati, OH 45268
13. TYPE OF REPORT AND PERIOD COVERED
Published Paper
14. SPONSORING AGENCY CODE
EPA/600/14
15. supplementary NOTES project officer = Richard C. Brenner (513) 569-7657
68th Annual Conference and Exposition, Water Environment Federation, Miami Beach, FL,
10/21-25/95
16. abstract objective of this paper is to define and validate a mathematical model
that describes the physical and biological processes occurring in a trickle-bed air
biofilter for waste gas treatment. The model assumes a two phase system, quasi-steady
state and one limiting substrate. Experimental data from the biodegradation of toluene
in a pilot system with four packed bed reactors, are used to test the validity of the
model. The unknown biofilter variables are estimated using a non-linear paramter
estimation technique. Using these parameter values, simulations were carried out for
different operational conditions, and the model predictions were compared to
experimental data.
17. KEY WORDS AND DOCUMENT ANALYSIS
a. DESCRIPTORS
b. IDENTIFIERS/OPEN ENOEO TERMS
c. COS ATI Field/Group
VOC
biofiltration
trickle-bed biofilter,
mathematical model,
waste gas treatment

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RELEASE TO PUBLIC
19. SECURITY CLASS (This Report!
UNCLASSIFIED
21. NO, OF PAGES
20. SECURITY CLASS (This page)
UNCLASSIFIED
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