Journal of Environmental Treatment Techniques  
2019, Volume 7, Issue 1, Pages: 166-170  
J. Environ. Treat. Tech.  
ISSN: 2309-1185  
Journal web link: http://www.jett.dormaj.com  
Comparison of Regression Model and Modified  
Monod Kinetic Model to Predict the Removal of  
Ethanol in Trickling Biofilter  
1
1
1
2
3
Amin Goli , Susan Khosroyar , Behroz Vaziri , Fatemeh Sadat Dehghani , Reza Sanaye ,  
2
Mohammad Mohammadi *  
1
- Department of Engineering, Quchan Branch, Islamic Azad University, Quchan, Iran  
- Department of Medical Nanotechnology, Shiraz University of Medical Sciences, Shiraz, Iran  
- Department of Cancer proteomics, Shiraz University of Medical Sciences, Shiraz, Iran  
2
3
Received: 10/12/2018  
Accepted: 17/02/2019  
Published: 30/03/2019  
Abstract  
Ethanol is a toxic compound and a member of volatile organic compounds (VOCs). Ethanol is emitted to the atmosphere  
by several industries worldwide. Biotrickling filter technology is a well-known technology for removal of VOCs from air. The  
aim of this study is to compare two regression and modified monod models to predict the removal of ethanol using a  
biotrickling filter reactor (BTFR). The data of the previous study on ethanol vapor removal by bio-trickling filter were used for  
determination of rmax and K . Also by these data, a simple regression model was developed. Eventually, ethanol removal  
m
efficiency was predicted by both regression and kinetic models. All results were compared with actual data. Our results show  
that regression model could only predict the average of ethanol removal efficiency. However, kinetic model could additionally  
predict all changes in ethanol removal efficiency: it has had some good alignment with actual data.  
Keyword: Ethanol, Kinetic coefficient, Modeling, Biotrickling filter, Biodegradation  
1
applied by utilizing chemical scrubbers, are often  
1
Introduction  
expensivethese possess even less efficiency in ethanol  
reduction (19). In contrast, biochemical methods, despite  
their complications, could prove to be highly appropriate  
substitutes for the physical and chemical methods (20).  
The biological methods mostly involve bio-filters. It is to  
be noted that amongst all these, the trickling biofilters are  
deemed the most optimum for the elimination of ethanol.  
The models proposed by researchers to determine the best  
conditions of applying trickling biofilters, are actually  
divided into two groups of Micro kinetic and Macro  
kinetic (21, 22). In Micro kinetic models, it is attempted to  
take into consideration all parameters involved (23).  
These may well include the specific surface of the  
substrate, the thinness of the applied biofilm, the  
dispersion coefficient of input polluted air into the  
biofilter, and the constant coefficient of Henry in Mass  
Transference. These models are usually very complex;  
they require a vast array of parameters and coefficients  
which are normally unavailable to the engineers (24).  
Ottengraf and Van den Over offered one of the most  
referred-to microkinetic models. The macrokinetic  
models often avoid defining or investigating partial  
parameters and would only focus on the most prominent  
parameters including the concentration of the pollutant,  
input pollutant debit, and the degree of moisture and  
temperature. Studying the effects of these parameters on  
the system efficiency and providing the mathematical  
relations in the form of macro kinetic models require  
laboratory experiments; thence they are referred to as the  
The rapid evolution of industries during the last few  
centuries has left a significant impact on the environment  
1-3). The momentous scale of today’s environmental  
(
challenges has urged countless number of researchers  
continuously working in order to provide the best solution  
for various types of man-made harms dealt to the  
environment (4-7). Among these is the issue of air  
pollution caused by the exhaust gasses including ethanol  
emitted from various industries such as petrochemical and  
alcoholic drinks manufacturers, often beyond the  
acceptable capacities (8-10). Ethanol is one of such  
pollutants and it is categorized into the volatile organic  
compounds (VOCs), posing threats to the environment  
(11). Ethanol is widely used in the production of  
petrochemical compounds. Thus it is only natural to  
address this issue by considering the threats of this  
pollutant and its wide-scale usage and generation. In order  
to achieve reductions in air pollution to attain air quality  
standards, a set of specific techniques and measures  
should be identified and implemented. In this particular  
case, various systems of physical, chemical and  
biochemical nature have already been utilized so as to  
treat this pollutant (12-16). However, some of procedures  
including the physical methods applied by utilizing  
various adsorbents (17) and the chemical methods (18)  
Corresponding author: Mohammad Mohammadi,  
Department of Medical Nanotechnology, Shiraz  
University of Medical Sciences, Shiraz, Iran.  
"Experimental models". Generally, in macro kinetic  
1
66  
Journal of Environmental Treatment Techniques  
2019, Volume 7, Issue 1, Pages: 166-170  
models having lower concentration of the input pollutant,  
the shifts in the fixation rate of the input pollutant within  
the system is linear. However, by increasing the  
concentration of the input pollutant, the fixation rate of the  
pollutant within the system shifts towards zero so that it  
can no longer remain linear. Strauss et al in 2000 provided  
the Eq. 1 for the determination of the biofilter's efficiency  
in eliminating VOCs, where a and b are the constant  
coefficients, t is the retention time within the biofilter, and  
ultimately u is the overall efficiency of the system. The  
constant coefficients in this equation are determined by  
calculating the log form from both sides of the equation  
and eventually by fitting the data based on the results  
obtained in the experiments within the various retention  
intervals.  
regression method, the daily efficiency of the system was  
obtained. After each cycle, the average efficiency within  
the upload was calculated. Therefore, in the end, 3  
different efficiency rates for every 3 upload were arrived  
at. By applying the linear regression amongst these data, a  
simple model is achieved. In order to practicalize this  
simple model in the design of the biofilter, or even for  
purposes of anticipating various states of the biofilters, it  
is combined with another model.  
2.2 The calculation of the kinetic parameters  
In the first step of analyzing the resulting data from  
the experiments, the development of a suitable model is  
necessary. The development of such a model is conducted  
in the following steps:  
The removal capacity (r) of the biofilter is  
determined by the following equation.  
-
bt  
)
μ = a (1-e  
Similar studies have also been conducted by Duplacis  
et al in 2003, leading to the successful modulation of an  
experimental model based on the completion of the  
previous equations. In all macro kinetic models, the  
efficiency of the biofilter depends on the concentration of  
input pollutant which is also, in its own turn, dependent on  
the input contamination rate into the system. It is worth  
mentioning that the rate of the input pollutant entering the  
biofilter is associated with the debit of the input  
contaminated air that gets into the totality of the system.  
The main purpose of this study is investigating into  
the kinetic parameters of a biotrickling filter and also  
providing a simple regression model. Furthermore, a  
comparison between the obtained anticipatory results of  
the biokinetic equations and the regression model is  
provided. In the first step, piloting the biotrickling filter  
was kept under examination for 61 days after which the  
biosynthetic parameters were calculated by the  
resulting data. The re-examined monod equation  
and the regression model are propounded, too. In the  
end, the resolution of these models in anticipating  
the efficiency of the system within various  
conditions has come to the fore.  
r = ((Cin-Cout)Q)/V  
Where Q is the debit of the input flow into the biofilter in  
3
-1  
-3  
m h , the concentration is in gm , and the volume of the  
reactor is in cubic meter. Furthermore, based on the  
monod equation, the removal capacity could also be  
expressed by the following equation:  
r = (rmax×Cg)/(Km+Cg)  
where C is the average concentration of the pollutant in  
g
-
3
gm , r  
is the maximum reaction speed of the  
max  
bio-decomposition associated with the bed volume in  
-
3 -1  
gm h and K is the saturation constant in the gas phase  
m
-
3
in gm . By combining the equation 1 and 2, and  
equalizing both, Eq.3 is attained for the calculation of the  
kinetic parameters.  
(
ꢀ ꢃꢀ )ꢇ ꢊ  
ꢎꢀꢏ  
ꢋꢌꢍ  
ꢒꢒꢒꢒꢒꢒꢒꢒꢒꢒꢒꢒꢒꢒꢒꢒꢒꢒꢒꢒꢒꢒꢒꢒꢒꢒꢒꢒꢒꢒꢒꢒꢒꢒꢒꢒꢒꢒꢒꢒꢒꢒꢒꢒꢒꢒ(ꢓ)  
ꢄꢅꢆ  
ꢐ ꢑꢀꢏ  
By simplifying the Eq.3, Eq.4 is achieved:  
2
Materials and Methods  
ꢜ  
We began with designing a pilot for the biofilter,  
ꢎ ꢑ  
ꢒꢒꢒꢒꢒꢒꢒꢒꢒꢒꢒꢒꢒꢒꢒꢒꢒꢒꢒꢒꢒꢒꢒꢒꢒꢒꢒꢒꢒꢒꢒꢒꢒ(ꢢ)  
(
ꢔ ꢃꢔ )ꢚ ꢝ  
ꢜꢞꢟ  
ꢕꢖ  
ꢗꢘꢙ  
ꢜꢞꢟ  
based on the descriptions provided by Goli et al. This was  
examined in 3 debits of input air into the ethanol vapor in  
where C is the average logarithmic concentration in the  
g
9
0, 291 and 1512 liters per hour. Previous studies have  
biofilter. The following equation could be applied in order  
to obtain the average logarithmic concentration. In the  
first step, Eq.1 is solved, which would then lead to Eq.5:  
shown that the efficiency of the biofilter is highly  
associated with the hydraulic retention time and the pH of  
the environment. Therefore, based on the resulting  
conclusions, within 61 days the biofilter was subjected to  
(
ꢀ ꢃꢀ )ꢇ  
ꢁꢂ ꢄꢅꢆ  
ꢒꢒꢒꢒꢒꢒꢒꢒꢒꢒꢒꢒꢒꢒꢒꢒꢒꢒꢒꢒꢒꢒꢒꢒꢒꢒꢒꢒꢒꢒꢒꢒꢒꢒꢒꢒꢒꢒꢒꢒꢒꢒꢒꢒꢒꢒꢒꢒꢒꢒꢒꢒꢒꢒꢒꢒꢒꢒꢒꢒꢒꢒ(ꢣ)  
3
different uploads. Since the previous studies by Goli et  
al established the optimum pH for the highest efficiency at  
, the pH of system in this study is constantly maintained  
ꢈ ꢉ  
7
on 7 in all uploads. The uploads were maintained until the  
system came to be stabilized. The stable conditions for  
this study are defined in terms of stable or insignificant  
changes in system efficiency for at least 6 days. In each  
upload, the parameters of retention time, the input  
pollutant and the output pollutant were investigated. A  
simple model based on the linear regression and the  
reexamined monod equation was also studied based on the  
obtained data.  
The researchers also show that both r and the volume of  
the reactor could be expressed through the equations 6 and  
7.  
ꢎꢀꢏ  
ꢊ ꢉ  
ꢒꢒꢒꢒꢒꢒꢒꢒꢒꢒꢒꢒꢒꢒꢒꢒꢒꢒꢒꢒꢒꢒꢒꢒꢒꢒꢒꢒꢒꢒꢒꢒꢒꢒꢒꢒꢒꢒꢒꢒꢒꢒꢒꢒꢒꢒꢒꢒꢒꢒꢒꢒꢒꢒꢒꢒꢒꢒ(ꢦ)  
ꢠꢑꢐ ꢎ  
ꢂ  
ꢄꢅꢆ  
ꢧꢨꢩ  
ꢪꢑꢐ(ꢀꢁꢂ ꢃꢀꢄꢅꢆ)ꢇ  
ꢤ  
ꢈ ꢉ  
ꢒꢒꢒꢒꢒꢒꢒꢒꢒꢒꢒꢒꢒꢒꢒꢒꢒꢒꢒꢒꢒꢒꢒꢒꢒꢒꢒꢒꢒꢒꢒꢒꢒꢒ(ꢫ)  
2
.1 The calculation of the regression model  
In order to provide a simple model based on the  
1
67  
Journal of Environmental Treatment Techniques  
2019, Volume 7, Issue 1, Pages: 166-170  
By equalizing the two equations, Eq.8 is obtained:  
retention time is obtained by Eq.13 in which V is the  
volume of the filter in l, Q is the debit of the input polluted  
air into the filter in l/h, and t is the hydraulic retention time  
in seconds. By replacing Eq.12 with F factor and by  
replacing Eq.13 with t factor in Eq.11 and the simplifying  
thereof, we can achieve Eq.14. Eq.14 allows us to  
determine the volume of the filter in industrial scale by  
providing it with the input and output concentration of  
ethanol and the debit of the input polluted air by ethanol.  
Enough attention has to be paid to the fact that this  
equation will only be applicable if the utilized bed is  
identical to the bed used in this study. This is because  
different beds are characterized by different porosity rates  
and especial surfaces. As a result, the cultured biomass on  
these beds could be different. The input air into the system  
only contains ethanol. The bio-decomposition rate of the  
biofilter is of course different in the presence of other  
compounds. Finally, the concentration of ethanol must be  
within the scope of this study. In order to prove the  
interpolation capacity of this model and also the  
extrapolation resolution, further experiments are required.  
ꢂ  
ꢄꢅꢆ  
ꢧꢨꢩ  
ꢪꢑꢐ (ꢀ ꢃꢀ )ꢇ  
(
ꢀ ꢃꢀ )ꢇ  
ꢁꢂ  
ꢄꢅꢆ  
ꢄꢅꢆ  
ꢒꢒꢒꢒꢒꢒꢒꢒꢒꢒ(ꢬ)  
ꢤ  
By replacing the Eq.6 with the r factor in Eq.8, Eq.9 is  
arrived at:  
ꢂ  
ꢆ  
ꢧꢨꢩ  
ꢪꢑꢐ (ꢀ ꢃꢀ )ꢇ  
(
ꢀ ꢃꢀ )ꢇ  
ꢐ ꢎꢏ  
ꢁꢂ  
ꢄꢅꢆ  
ꢄꢅꢆ  
ꢒꢒꢒꢒꢒꢒꢒꢒꢒ(ꢭ)  
ꢤ  
ꢠꢑꢐ ꢎꢀꢏ  
The expansion of the Eq.9, simplifying it and  
ultimately solving it for C leads to the identification of  
g
the following equation as the average logarithmic  
concentration in bioreactor which is expressed as Eq.10:  
ꢂ  
ꢄꢅꢆ  
ꢒꢒꢒꢒꢒꢒꢒꢒꢒꢒꢒꢒꢒꢒꢒꢒꢒꢒꢒꢒꢒꢒꢒꢒꢒꢒꢒꢒꢒꢒꢒꢒꢒꢒꢒꢒꢒꢒꢒꢒꢒꢒꢒꢒꢒꢒꢒꢒꢒꢒꢒꢒꢒꢒꢒꢒꢒꢒꢒꢒꢒꢒꢒꢒꢒ(ꢠꢮ)  
ꢏ  
ꢂ  
ꢧꢨꢩ  
ꢄꢅꢆ  
1
00  
By applying Eq.10 we can attempt to calculate the  
y = 0.0524x + 94  
R² = 0.9098  
average logarithmic concentration, and by replacing it in  
Eq.4 we can obtain the synthetic parameters. In order to  
determine the kinetic coefficients in this study, the  
parameters of V/[(C -C )Q] is plotted against 1/C in  
9
9
9
9
9
8
7
6
in out  
g
Eq.4 which leads to  and .  
2
.3 Experimental methods  
In this study, an ethanol measurement device was  
utilized (Inters can company, model: 4160) which  
provided fast and direct examination of the ethanol  
present in the air.  
95  
94  
3
3
Results and Discussions  
.1 Regression model  
0
50  
100  
150  
The previous studies by Goli et al suggested that the  
Retention Time  
efficiency of the biological filter studied here is  
statistically associated with retention time and the pH of  
the environment. Since the optimum pH for the studied  
biofilter was established at 7, it is only natural that any  
future navigation is also the most efficient in neutral pH;  
therefore, the calculation of Eq.11 by the regression  
method is conducted based on this pH. It is noticeable that  
Eq.11 is achieved by considering the average efficiency of  
the system in each upload obtained during the 61  
experiments conducted on each upload on a daily basis.  
The results of this regression are shown in Fig.1. As  
demonstrated there, the correlation coefficient in this  
equation is equal to 0.909.  
Fig.1: The dependence of filter efficiency on retention  
time  
ꢔ ꢃꢔ  
ꢕꢖ  
ꢗꢘꢙ  
ꢒꢒꢒꢒꢒꢒꢒꢒꢒꢒꢒꢒꢒꢒꢒꢒꢒꢒꢒꢒꢒꢒꢒꢒꢒꢒꢒꢒꢒꢒꢒꢒꢒꢒꢒꢒꢒꢒꢒꢒꢒꢒꢒꢒꢒꢒꢒꢒꢒꢒꢒꢒꢒꢒꢒꢒꢒꢒꢒꢒꢒꢒꢒꢒꢒꢒꢒ(ꢠꢱ)  
ꢳ ꢉ  
ꢕꢖ  
ꢉ ꢒꢒꢒꢒꢒꢒꢒꢒꢒꢒꢒꢒꢒꢒꢒꢒꢒꢒꢒꢒꢒꢒꢒꢒꢒꢒꢒꢒꢒꢒꢒꢒꢒꢒꢒꢒꢒꢒꢒꢒꢒꢒꢒꢒꢒꢒꢒꢒꢒꢒꢒꢒꢒꢒꢒꢒꢒꢒꢒꢒꢒꢒꢒꢒꢒꢒꢒꢒꢒꢒꢒꢒꢒꢒꢒꢒꢒꢒꢒꢒꢒꢒꢒꢒ(ꢠꢓ)  
ꢚ[ꢠꢮꢮꢎ(ꢔ ꢃꢔ )ꢃꢭꢦꢰꢱ]  
ꢒꢒꢒꢒꢒꢒꢒꢒꢒꢒꢒꢒꢒꢒꢒꢒꢒꢒꢒꢒꢒꢒꢒꢒꢒꢒꢒꢒꢒꢒ(ꢠꢢ)  
ꢕꢖ  
ꢗꢘꢙ  
ꢮꢰꢮꢦꢣꢖ  
ꢯꢉꢮꢰꢮꢣꢱꢲꢒꢑꢒꢭꢢꢒꢒꢒꢒꢒꢒꢒꢒꢒꢒꢒꢒꢒꢒꢒꢒꢒꢒꢒꢠꢠꢒꢒꢒꢒꢒꢒ  
3
.2 Calculation of the kinetic parameters  
In this study, Eq.12 is applied in order to obtain the  
efficiency of the system. Where Cout is the output ethanol  
In this study, Eq.4 was used in order to determine the  
kinetic parameters. In Eq.4 the rates of  and  is  
obtained by plotting the V/[(C -C )Q] against 1/C . ꢒ  
from the system in mg/l and C is the concentration of the  
in  
in  
out  
g
input ethanol into the system in mg/l. Moreover, the  
1
68  
Journal of Environmental Treatment Techniques  
2019, Volume 7, Issue 1, Pages: 166-170  
Table1: The calculation results of kinetic parameters  
Debit of  
the  
input  
flow  
0.09  
0.291  
1.512  
Average  
logarithmic  
concentration (V/Q)/(C -Cout)  
Outlet  
Ethanol  
concentration  
Inlet Ethanol  
concentration  
Volume  
1/Cg  
in  
(Cg)  
-
-
-
5
5
6
-3  
-3  
-3  
0
0
0
.1130ꢀ  
.00319  
.00319  
485  
485  
485  
53.26  
18.32  
26.54  
195.449  
142.447  
157.790  
8.209*10  
2.348*10  
4.601*10  
5.116*10  
7.020*10  
6.337*10  
The above values are then applied in order to provide  
The data retrieved from various experiments were  
then inserted into these equations and the results were  
then compared with the real experimental results. It is  
worth mentioning that these data were applied to the  
system in three different loadings. The load shift was  
applied by changing the hydraulic retention time by  
increasing the debit. The range of retention time changes  
includes: 90, 291 and 1512 lit/h. The results of these  
experiments are presented in Fig.3. As it is illustrated in  
this figure, the real percentage of formaldehyde  
elimination by the biofilter shows severe shifts. On the  
other hand, the regression model has only determined the  
average of the formaldehyde removal without the capacity  
to anticipate the possible shifts. However, the accuracy of  
these models is still remarkable. Based on Fig.3, the  
provided results by Eq.4 are about 10% lower than the real  
experimental results; nonetheless, they were successful in  
anticipating the various shifts that occurred within the  
biofilter. This is considered as a big advantage in applying  
this equation.  
the linear regression between the V/[(C -Cout)Q] and 1/Cg  
in  
columns and calculating the associated equation. Equation  
5 is the result of the respective regression model in which  
1
the intercept was 1/rmax, and the constant coefficient of X  
was K /r (thus allowing easy calculation of the kinetic  
m
max  
parameters needed).  
ꢯꢒꢉꢒꢱꢢꢰꢣꢬꢲꢒꢃꢒꢮꢰꢮꢠꢠꢒꢒꢒꢒꢒꢒꢒꢒꢒꢒꢒꢒꢒꢒꢒꢒꢒꢒꢒꢒꢒꢒꢒꢒꢒꢒꢒꢒꢒꢒꢒꢒꢒꢒꢒꢒꢒꢒꢒꢒꢒꢒꢒꢒꢒꢒꢒꢒꢒꢒꢒꢒꢒꢒ(ꢠꢣ)  
The results of this table illustrate that the  
-
3 -1  
biofilter rmax is equal to - 0.011 gm h and Km is  
-
3
equal to 24.58 gm . The r  
is less than zero  
max  
because of the relative increase of the efficiency  
against the increase of the formaldehyde  
concentration.  
0
0
0
0
0
0
.06  
.05  
.04  
.03  
.02  
.01  
0
Financial supports  
y = 24.588x - 0.0111  
R² = 0.9862  
Jami Institute of Technology and Shiraz University of  
Medical Sciences financially supported this study (Vot.  
No. 000105).  
Competing interests  
The authors declare that there is no conflict of interest  
that would prejudice the impartiality of this scientific  
work.  
Author’s contributions  
It is certified that all of the authors have made the  
same contribution in the experiments and manuscript  
writing.  
0
0.001  
0.002  
0.003  
-
3
1
/Cg (gm )  
Fig.2: The results of the linear regression in 3  
different loadings.  
Acknowledgements  
This study is the result of the Bachelor’s degree thesis  
by Amin Goli, air conditioning engineering student in the  
Jami Institute of Technology (JIT), Isfahan, Iran. The  
authors of this study appreciate the financial and spiritual  
support provided by JIT which specified the requirements  
of this study.  
3
.2 Comparing the results of the regression model and  
the kinetic model in anticipating the biofilter’s efficiency  
At this stage, equation 4 (the kinetic model) and 14  
the regression model) were solved in order to determine  
the efficiency of the biofilter. These equations were then  
applied in the forms of Eq.16 and Eq.17.  
(
Ethical considerations  
Authors are aware of, and have complied with, best  
practices in ethics, specifically with regard to authorship  
ꢆ  
ꢑꢔ ꢒꢒꢒꢒꢒꢒꢒꢒꢒꢒꢒꢒꢒꢒꢒꢒꢒꢒꢒꢒꢒꢒꢒꢒꢒꢒꢒꢒꢒꢒꢒꢒꢒꢒꢒꢒ(ꢠꢦ)  
ꢕꢖ  
ꢜ  
(avoidance of guest authorship), dual submission,  
ꢟ  
ꢟ  
ꢚꢶ  
manipulation of figures, competing interests and  
compliance with policies on research ethics. Authors  
adhere to publication requirements that the submitted  
work is original and has not been published elsewhere in  
any language.  
ꢡ  
ꢕꢖ  
()ꢕꢖ  
ꢙ  
ꢒꢒꢒꢒꢒꢒꢒꢒꢒꢒꢒꢒ(ꢠꢫ)  
ꢠꢮꢮ  
1
69  
Journal of Environmental Treatment Techniques  
2019, Volume 7, Issue 1, Pages: 166-170  
logarithmic equation applied to a bio-trickling filter  
reactor for formaldehyde removal from synthetic  
contaminated air. RSC Adv. 2013;3(15):5100-7.  
4. Talaiekhozani A, Talaei MR, Fulazzaky MA, Bakhsh  
HN. Evaluation of contaminated air velocity on the  
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