Unsteady-State Mathematical Modeling of a Fungal Biofilter Treating

Article pubs.acs.org/IECR

Unsteady-State Mathematical Modeling of a Fungal Biofilter Treating Hexane Vapor at Different Operating Temperatures Reza Salehahmadi, Rouein Halladj,* and Seyed Morteza Zamir Chemical Engineering Department, Amirkabir University of Technology, Hafez Avenue, Tehran, Iran, PO Box 15875-4413 ABSTRACT: Fungal biofiltration is an efficient way to treat hydrophobic compounds. Although temperature is a key factor in the biofiltration, the process modeling based on temperature effect in the kinetic parameters has been rarely considered due to its complexity. Therefore, in this contribution, a dynamics mathematical model which takes into account dispersion in gas phase, diffusion in biofilm, and temperature effect in the kinetic constants and other physical properties has been presented. The model was calibrated and validated by using previously reported experimental research in which the effect of temperature and intermittent and continuous loading on the biodegradation of n-hexane vapor had been investigated. The model prediction results revealed that a zero-order kinetic reaction fitted intermittent loading in the temperature range of 30−35 °C and continuous loading in the temperature range of 35−45 °C. Sensitivity analysis showed that at high inlet loads, approaching optimum bed temperature could change the rate limited biodegradation to a diffusion limited condition, and a part of the biofilm became inactive.

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the optimum temperature range for the biofiltration.17,18 XQiang et al.19 studied the effect of temperature on biofiltration of benzene and toluene and concluded that the removal efficiency was optimum in the range of 30−40 °C. Effect of temperature on the biotrickling filter performance for the elimination of aromatic compounds was studied in a research which showed that increasing the temperature up to 30 °C enhanced biofiltration and at higher temperatures the biodegradation diminished.20 Jin et al.21 observed that removal efficiency (RE) increased as the temperature rose from 20 to 30 °C and an opposite trend was obtained at temperatures between 30 and 40 °C. In practice, the transient-state process is more common than the steady state due to the fluctuations of flow and concentration.7 As the inlet stream to the biofilter is a side product coming from other processes, it may be interrupted and fluctuated because of different reasons such as batch-wise process, operating malfunction, daily shift working, holidays, and scheduled and unscheduled shutdowns. Shock loads may cause instability of biological processes, perturbation in steady state, or even worse, make steady-state operation impossible. 21 Literature review revealed that most of the previous models have been developed under the assumption of constant bed temperature. Shareefdeen et al.16 presented a theoretical nonisothermal steady-state model to evaluate the temperature effect on the biofiltration. They developed mass and energy balance equations for their model; however, its validity had not been checked through experimental data. As temperature and variation of inlet load (IL) have important effects on the biofiltration, a model which incorporates the effect of these parameters is necessary for

INTRODUCTION Increasing concerns regarding the environmental pollution have led to legislate stringent regulation for controlling the emission of different pollutants into the atmosphere. Volatile organic compounds (VOCs) are produced from a variety of industries such as petrochemical, paint, paper, varnishing, and food plants. In recent years, due to some advantages like cost effectiveness, lower energy consumption, and process stability, biofiltration has become more applicable than other traditional technologies such as oxidation, adsorption, and scrubbing for treatment of waste gas streams.1 Commonly, biofilter is a reactor packed with organic or inorganic materials such as perlite, pit, or compost where the microbial population is immobilized on the outer surface of the packing material. Polluted air passes through the filter bed and the pollutant transfers from gas phase to the stationary biophase. In other words, biofiltration employs the metabolic activities of microorganism to degrade the pollutants which act as carbon or energy source for the microbial growth.2,3 On the other hand, bacterial systems are less efficient for treating hydrophobic compounds that are sparingly soluble in the biofilm which usually have a high water content.4,5 Use of fungi is an alternative way to overcome this limitation.6−11 It has some advantages over bacteria such as higher specific surface area,9,12−14 tolerating extreme environment conditions (low pH and water content), 4,15 and presenting a lower partition coefficient for the pollutants. 4 Hexane is one of the common hydrophobic compounds which emits from food and chemical industries into the air. Employing fungal biofiltration for the hexane elimination has been reported by many investigators.1,4 Various phenomena such as absorption, diffusion, adsorption and finally biodegradation are involved in a biofilter. One of the key factors in this process is the operating temperature which directly influences on the growth rate and kinetics of biological reaction. There is always an optimum range of temperature for microbial activity.16 Some researchers reported 25−35 °C as © 2012 American Chemical Society

Received: Revised: Accepted: Published: 2388

July 9, 2011 December 22, 2011 January 6, 2012 January 6, 2012 dx.doi.org/10.1021/ie2014718 | Ind. Eng.Chem. Res. 2012, 51, 2388−2396

Industrial & Engineering Chemistry Research

Article

Figure 1. Schematic of biofilter set up.

design purposes. Zamir et al.22 have assessed the behavior of a fungal biofilter for removing hexane vapor at different loads, temperatures, and under intermittent and continuous loading through an experimental work. In this contribution based on mass balance in gas and bio phases, a dynamic model is proposed to predict biofilter behavior for the biodegradation of volatile organic compounds in different temperatures. The model is validated using laboratory-scale experimental data which was reported by Zamir et al.22 Model simulations are then used to check the effect of design parameters on biofiltration performance.

biofilter was set to work under continuous aeration in the next 34 days to study the effect of temperature on the removal performance under continuous loading for low, medium, and high inlet loads.

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EXPERIMENTAL CONDITIONS The employed biofilter system, experiments, and analytical methods have been explained by Zamir et al.22 Figure 1 shows this biofilter setup schematically. The biofilter was subjected to operate under intermittent and continuous loading at specific temperatures and loads to check its performance during 261 days and in 8 different phases (Table 1). Under intermittent Table 1. Time Schedule and Operational Condition of the Experiments phase

time (day)

Tbed (°C)

IL (gm−3h−1)

loading mode

0 I II III IV V VI VII

0−20 21−122 123−157 158−203 204−227 228−238 239−248 249−261

ambient 30 35 40 45 35 40 45

10−60 9−300 9−597 8−212 13−565 120−500 89−320 109−420

intermittenta intermittent intermittent intermittent intermittent continuousb continuous continuous

MATHEMATICAL MODEL DEVELOPMENT

Assumptions. The following assumptions were made to derive the mathematical model equations: (i) Biofilm grows uniformly on the outer surface of the packing material and no reaction occurs in the pores. (ii) Biofilm thickness is small relative to the packing diameter and hence, planner geometry can be assumed. (iii) The biodegradation reaction rate constant follows an Arrhenius-type of temperature dependence. (iv) The regime of gas phase is considered to be plug flow with dispersion effect. Influences of different operating conditions (e.g., temperature and gas flow rate) on dispersion coefficient are considered by employing an empirical relation. (v) Diffusion coefficient for the pollutant in the biofilm is equal to that parameter in water corrected by a factor depending on biofilm density. (vi) Biofilm density is constant and there is no accumulation of biomass in the bed. (vii) Biofilm properties (thickness, specific surface area, density) are constant along the filter bed and at different operating conditions. Constant biofilm thickness assumption is cross checked by the experimental data and the mathematical model results. (viii) As compost and lava rock showed low adsorption in the experiments [unpublished data], adsorption phenomena is neglected in the mathematical model. Partial Differential Equations of Mass Transfer in Biofilm and Gas Phase. The proposed model, which is based on mass balance in the transient-state operation, includes the convection and dispersion in gas phase, diffusion and biodegradation in biofilm, considering temperature effect on

a

Loading was implemented 10 h per day. bLoading was implemented 24 h per day.

loading, 10 h aeration per day, the temperature was varied in the range of 30−45 °C during 227 days with different inlet loads. Following the intermittent loading experiments, the 2389

dx.doi.org/10.1021/ie2014718 | Ind. Eng.Chem. Res. 2012, 51, 2388−2396


Article

bed are characterized as dispersion coefficients. According to the method described by Levenspiel,23 the analysis of residence time distribution (RTD) is performed by introducing an ideal pulse of a tracer into the bed and measuring the outlet concentration. The tracer spreads in the bed and comes out at different times. In this paper, the dispersion coefficient was calculated based on the method proposed by Ruthven.24 He presented an empirical relation (eq 7) for a packed bed in which the dispersion coefficient was calculated as a function of bed porosity, gas velocity, packing diameter, and diffusion coefficient of substance.

the biological reaction rate, and other physical properties. The mathematical model is developed by inserting the time dimension into the presented equations by Shareefdeen et al.16 and incorporating the methodology of Jin et al.21 It was written as follows.

f (X v)Dw

∂ 2S 2

− r (T ) =

∂S ∂t

(1) ∂x Mass Balance in Biofilm. Increasing temperature below the optimum temperature may lead to an increase in the biodegradation rate and decrease it above the optimum temperature. An Arrhenius-type equation is used to consider this effect in the reaction rate constant. The following formulation is applied for the determination of the biodegradation rate below the optimum temperature:21

⎧ ⎫ ⎪ ⎪ Ea ⎬ r(T ) = r(Topt) exp⎨ ( T − T ) opt ⎪ ⎪ RTT opt ⎭ ⎩

D = (0.45 + 0.55ε)DA + 0.5d pug /ε

Temperature effect on hexane diffusion coefficient in gas phase is correlated by the Fuller formula:25 1.75 DA (T2) ⎛ T2 ⎞ =⎜ ⎟ DA (T1) ⎝ T1 ⎠

(2)

The quantity Ea/(RTTopt) in eq 2 may be assumed to be almost constant (m1) in a narrow range of working temperature in the biological processes.21

r(T ) = r(Topt) em1(T − Topt) m1

Replacing e

(T − Topt)

(T ≤ Topt)

(3)

(4)

Applying the same procedure for operating temperatures above the optimum temperature results in the following relation:

r(T ) = r(Topt)θ2(Topt − T )(T > Topt)

(5)

Boundary conditions and initial condition for mass balance in the biofilm are as follows:

at

x = 0,

at

x = δ,

at

t = 0,

S=

C m

∂S =0 ∂x

Sj = Sj (0, x , z)

(1a)

K oc = 0.41K ow

(9)

Equation 9 is based on experiments in which a soil−water partition coefficient was measured for variety of soils of varying organic carbon content (y) and chemicals of different octanol− water partition coefficient.27 To calculate the soil (in this case biofilm)/water partition coefficient, he proposed the following relationship:

(1b) (1c)

Kbw = (ρ b/1000)yK oc

z = 0,

εD

∂C = ug (C 0+ − Ci) ∂z

at

z = H,

∂C =0 ∂z

at

t = 0,

C = C(0, z)

(10)

In which y and ρb are organic content and density of the biofilm, respectively. Kow may be obtained through multiplying the octanol/air partition coefficient (Koa) and the air/water partition coefficient (Kaw):

Mass Balance in Gas Phase. Danckwert’s boundary condition and initial condition for gas phase are as follows:

at

(8)

Hexane Partition Coefficient. The pollutant gas/biofilm partition coefficient is almost considered as the air/water pollutant partition coefficient which follows Henry’s law.2,16,26 This assumption may be reasonable for hydrophilic compounds as the biofilm consists of a high percentage of water and the solubility of such a compound is relatively high in water. However, for hydrophobic compounds such as hexane, Henry’s law is not valid. Vergara-Fernandez et al.4 observed that the solubility of hexane in a fungal species was 200 times more than that of hexane in water. They obtained the value of 0.2 for the hexane partition coefficient in the gas/biofilm interface. In this study, the air/biofilm partition coefficient for hexane was evaluated by the method proposed by Mackay.27 He indicated that the organic content of a cellular compartment is responsible for absorbing hydrophobic compounds, and this was closely related to the octanol/water partition coefficient (Kow) by following the empirical formula:

with another constant value (θ1) yields

r(T ) = r(Topt)θ1

(7)

(6a)

K ow = K oa × K aw

(11)

To estimate the hexane air/biofilm partition coefficient (m), the air/water partition coefficient should be divided by the biofilm/water partition coefficient:

(6b) (6c)

m = K aw /Kbw

Model Parameters. Axial Dispersion. Deviation from ideal plug flow may be caused by a variety of reasons such as a different size of packing, nonuniformity of feed distribution, or channeling and formation of dead zones in the bed. All these factors which have influence on the mixing of the fluid in the

(12) 28

Mohseni and Allen used the same approach for calculating the air/biofilm partition coefficient of α-pinene. They obtained the air/biofilm partition coefficient about three times lower than the air/water partition coefficient. 2390



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By taking 4% organic carbon content of biofilm,28 the air/ biofilm partition coefficient can easily be calculated. The temperature-dependent relationships for the air/water and octanol/air partition coefficients for hexane were taken from the literature29 and written as follows:

log K oa = − 5.63 + 3371.8/T

(13)

log K aw = 12.15 − 3143/T

(14)

Table 2. Values of the Parameters Used in Solving the Model Equations

Hexane Diffusion Coefficient in Biofilm. The effective diffusion coefficient of the pollutant in the biofilm is affected by biomass density30,31 and it is reasonably smaller than its value in water. Zhang and Bishop31 have shown that the effective diffusivities of the organic compounds range from 38 to 45% in the bottom layer of biofilm to 68−81% in the top layer. On the basis of this method, Mohseni and Allen28 chose 40% for the ratio of effective diffusivity of α-pinene and methanol in the entire active region of biofilm. By using the hexane diffusion coefficient in water and the ratio chosen by Mohseni and Allen,28 the effective diffusivity of hexane in biofilm was calculated and applied in the model. The effect of temperature on hexane diffusivity in water was also implemented in the model by using the Wilke and Change estimation method which was given by Poling et al.32

μ T2 Dw (T2) = w1 Dw (T1) μw2T1

(15)

(16)

Biofilm Thickness. Biofilm thickness which is used in mathematical modeling of biofiltration is ranged from several micrometers to more than 100 μm.1,16,26,28,33 The value of biofilm thickness is usually estimated based on microscopic photography or model calibration. In this contribution, an average value of 100 μm was selected; then, its accuracy was checked and discussed. Mathematical solution. The model consists a set of partial differential equations varying with time. The gas phase concentration enters the boundary condition of the biofilm and the mass flux on the boundary condition enters the gas phase mass balance equation. The system of equations was solved by Comsol Multiphysics software (version 3.5a) in which finite element method is employed to solve engineering problems. Based on least-squares method, the following objective function (OF) is defined to obtain AS and zero reaction rate constants (r(T)) by employing experimental data at each operating temperature.

m−1 gm−3 m2s−1 m2s−1 m2s−1 m m °C °C ms−1

m

references present 22 present 25 1 22 32 22 present 22 22 22 present present present 22

study study

study

study study study

Figure 2. Experimental and model removal efficiency (30−35 °C, intermittent loading).

range of 30−35 °C under intermittent loading condition (phases I and II). As it can be observed, experimental results were well fitted by a zero order kinetics model with a maximum error of 10%. Favorable environmental conditions for the microbial growth and suitable temperature which affects hexane solubility caused the biofiltration to be implemented with high removal efficiency. As the operating temperature was favorable for the microbial activity, the kinetics of biodegradation was stable and the model well predicted experimental data despite the application of intermittent loading. The maximum error

N 2

∑ [Co ‐ m(As , r(T )) − Co ‐ expt] j=1

units

180 0.6−20.7 (1.07−2.38) × 10−5 (6.3−6.9) × 10−6 1.85 × 10−9 (2−3) × 10−3 0.4 0.75 0.2−0.4 30−45 35 (23−68) × 10−2 1.14 1.19 100 × 10−6 0.45

RESULTS AND DISCUSSION Parameters θ1 and θ2 which obtained from model calibration were 1.14 and 1.19, respectively. These values showed that temperature has a greater effect on the biodegradation at temperatures above optimum bed temperature than at below one. These parameters are comparable and in close agreement with those reported by other researchers. Parameters θ1 and θ2 which are estimated by Jin et al.21 for biofiltration of α-pinene are in the range of 1.024−1.15. These values are similar to the typical ranges for some commonly aerobic wastewater treatment processes, for example, 1.0−108 for activated sludge; 1.04−1.1 for aerated lagoons; 1.02−1.08 for biotrickling filters.34 Figure 2 shows the model prediction and experimental data with respect to the different inlet loads in the temperature

By taking the reported data for viscosity of water and hexane diffusivity in water (1.85 × 10−9 m2s−1 at 30 °C)1 and employing curve fitting, the following relationship results for the calculation of hexane diffusivity in water in the temperature range of 30−45 °C:

OF =

value

AS Ci D DA Dw dP f(Xv) H m Tbed Topt ug θ1 θ2 δ ε

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25

ln(Dw ) = 0.0323T − 29.88

parameters

(17) −1

A surface area of 180 m and reaction rate constants of 11500, 22400, 9500, and 4000 gm−3h−1 for 30, 35, 40, and 45 °C were obtained, respectively, through fitting one set of experimental data. Then, they were used for entire modeling work. All the necessary values for solving the mathematical model are shown in Table 2. 2391



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between model and experiment was less than 10% even in the inlet load of 597 gm−3h−1. Phase (III) of the experiments was started from day 158, and the bed temperature was adjusted to 40 °C. The experimental data and model prediction for this set of experiments is shown in Figure 3. With an increase in the inlet load in the first days,

Figure 4. Experimental and model removal efficiency (35−45 °C, continuous loading).

temperature range of 40−45 °C in continuous loading, while it could not predict data in the intermittent loading in the same temperature range. This contributes to the stability of the environment condition in continuous loading which is not valid in intermittent loading. The effect of intermittent loading on biofilter performance has been also examined by other researchers. Metris et al.35 modeled the response of the biofilter for different periods of starvation and changes in inlet concentration of toluene and xylene mixture. They concluded that their model produced a good outlet concentration prediction for small changes in the inlet concentration; however, for a more stressful situation like starvation and resumption of the feed, the mathematical model predicted experimental data with positive error. In another study, a cyclically operated biofilter was simulated with an unsteady-state model by Dirk-Faitakis and Allen.36 Their dynamic model, using constant kinetic parameters, predicted the biofilter operation at short cycles of minutes and hours; however, the model overestimated the experimental data at a longer time scale and the deviation became worse. They related this deviation to a change in kinetic parameter which was not accounted for in the model. Figure 5 shows the predicted maximum elimination capacities by model for intermittent loading and those obtained

Figure 3. Experimental and model removal efficiency (40−45 °C, intermittent loading).

the discrepancy between model and experiments was increased, although the model predicted the general shape of an actual reduction of RE. Adaptation of microorganisms to 35 °C in the previous phase and perturbation of the environment are the main reasons for this deviation. As it was assumed that kinetic parameters were constant at each operating temperature in the model, the predicted RE was somewhat higher than the experimental data especially in the first days. Despite an increase in the inlet load to 200 gm−3h−1 at the last days, the error between the model prediction and experimental data decreased, which showed that the microbial population was adapted to the new condition. The biofilter performance was examined at 45 °C from day 204. As it can be seen from Figure 3, higher inlet loads resulted in higher deviation between model outcome and experimental data for RE. Increasing the inlet load makes a positive error between the model and experiments. It seems that 45 °C was high for a biological reaction. The microbial population decreased dramatically in this phase.22 The system used the shutdown periods, where temperature reached ambient, to recover its performance. Therefore, the proposed model in some points overestimates and in other points underestimates the experimental results. Increasing the inlet load to 565 gm−3h−1 has led to an increase in the error. Continuous loading at 35 °C was started from day 228. According to Figure 4, experimental data were well predicted by the mathematical model in this condition with a maximum error of 7%. Continuous loading 24 h per day led to stable microbial activity. As the environmental condition was stable for microorganisms and adaptation was completed at 35 °C, the assumption of constant kinetic parameters was appropriate; hence, the model predicted the experimental data with a good agreement. In phase (VI) and (VII) of experiment, the effect of continuous loading at 40 and 45 °C was tested. As it can be easily observed from Figure 4, experimental data were well fitted with the proposed mathematical model. A comparison of results reveals that the model fitted the experimental data in the

Figure 5. Experimental and model prediction for ECmax at different temperatures for intermittent loading.

through experimental data. There was a good agreement between model results and experimental data. This shows that the proposed mathematical model can be used for the 2392



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this case, the biofilm thickness may be derived from the following relationship given by Ottengraf and Van den Oever:37

prediction of maximum elimination capacity in the temperature range of 30−45 °C. On the basis of Mackay’s method,27 a value of 0.19 was obtained for the hexane air/biofilm partition coefficient at 30 °C. This value was in close agreement with the reported partition coefficient of 0.2 by Vergara-Fernandez et al.3 Employing eq 14 yields a value of 59 for Henry’s coefficient, which is 300 times higher than the calculated air/biofilm partition coefficient. This comparison shows the significant impact of organic constituents on the solubility of hydrophobic compounds in the biofilm. Therefore, neglecting this effect may lead to a significant error in mathematical modeling results of the biofiltration process. Simulation and Sensitivity Analysis. One of the main objectives in the mathematical modeling of biofiltration is to examine the effect of various parameters on biofilter performance. This may help to have a more clear understanding of complex phenomena which occur in biofiltration. Also, some parameters cannot be easily measured directly such as biofilm thickness, concentration profile in biofilm, and specific surface area. These parameters can be estimated through simulation and sensitivity analysis in a short time. Therefore, a thorough investigation about model sensitivity of parameters was performed. Effect of temperature on hexane concentration in biofilm at a high inlet load (443 gm−3h−1) was checked. According to Figure

Ci − Co ‐ expt Ci

=

A s δHr(T ) Ciug

(18)

Rearranging the equation and introducing elimination capacity instead of gas concentration yields the following simple and useful relationship:

EC = r(T )A s δ

(19)

Using experimental data for ECmax in eq 19 gave a biofilm thickness in the range of 100−120 μm. Thus, the value of 100 μm which was used for the biofilm thickness in the mathematical model was in the range and acceptable. Sensitivity analysis was also carried out to check the effect of various parameters on the biofiltration removal efficiency at high inlet loads previously described at 35 °C. Effects of specific surface area (AS), hexane partition coefficient (m), and bed temperature (Tbed) on RE have been shown in Figure 7.

Figure 7. Effect of AS, m ,and Tbed on removal efficiency (Ci = 12 gm−3, Q = 0.18 m3h−1).

Horizontal axis indicates the percentage of changing the parameter in compare to its original value (180 m−1, 0.27, and 35 °C for AS, m and Tbed, respectively). Results showed that the reduction of specific surface area and increasing hexane partition coefficient had a counter-effect on the removal efficiency. Similar results for the effects of hexane air/biofilm partition coefficient and transport area on the biofilter performance have been observed and reported by other researchers3 for hexane elimination in a fungal biofilter. To compensate the inverse effects of these parameters, the use of a higher bed length is needed for enhancing the biofilter performance, which may cause the higher pressure droop and more energy consumption. As a fungal biofilter presents higher specific surface area and lower partition coefficient for hydrophobic compounds in comparison to those in a bacterial system, treatment of hydrophobic compounds in such a system has great advantages. In Figure 7, the key rule of temperature on biofiltration performance has been shown. As it can be observed, biofiltration efficiency has a maximum at around optimum bed temperature (35 °C). Deviation from the optimum bed temperature has an inverse effect on the removal efficiency. Therefore, control of the optimum temperature for higher performance in the biofilter is very important.

Figure 6. Temperature effect on hexane concentration in biofilm at high inlet load (443 gm−3h−1).

6, approaching the optimum bed temperature led to a change in the rate limited biodegradation to diffusion rate limited at which a part of biofilm became inactive. At 35 °C, this change happened at around an 80 μm depth of biofilm and as temperature increased or decreased, the inactive biofilm layer became thinner. The temperature effect on the reaction rate and also hexane partition coefficient are the main explanation for this phenomenon. Results from this simulation show that although at around optimum temperature and high inlet load some part of biolayer is not fully active, the predominant regime of operation in biofilm is rate limited rather than diffusion. Biofilm thickness can be cross checked by experimental ECmax and reaction rate constants. When the reaction rate is considered as zero-order kinetics, two different regimes may occur in biofilm; diffusion rate limited and reaction rate limited regimes. In case of reaction rate limited or fully penetrated regime, the biological reaction rate is slower than diffusion. In 2393



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The effect of gas mixing on the biofiltration performance was also studied through sensitivity analysis. Gas mixing can be characterized by a Peclet number. A lower Peclet number means higher dispersion coefficient or higher gas mixing in the reactor and causes the reactor to approach a stirred tank. On the other hand, a higher Peclet number means lower dispersion which results in a plug flow reactor. Figure 8a shows the effect

Figure 9. Effects of r(T), f(Xv), and δ on removal efficiency (Ci = 12 gm−3, Q = 0.18 m3h−1).

percentage of changing parameters in comparison to their original values (22500 gm−3h−1, 0.4 and 100 μm for r(T), f(Xv) and δ, respectively). f(Xv) which represents hexane diffusivity in biofilm, has a moderate effect on the removal efficiency. Higher diffusivity results in higher removal efficiency. RE almost increases linearly with increasing f(Xv). However, this behavior is somewhat different for r(T) and δ. RE increases with a sharp slope up to a parameters ratio of 80%. Then, then the rate of increasing RE has a significant drop. The change of operating regime in the biofilm from rate limited to diffusion limited is the main explanation for this behavior. In this case, less hexane may reach to the deeper layer of biofilm and the biological degradation rate is limited. A sensitivity analysis of gas residence time from 23 to 65 s was carried out and the results have been presented in Figure

Figure 8. (a) Effect of Peclet number on removal efficiency at different temperatures (Ci = 12 gm−3, Q = 0.18 m3h−1). (b) Effect of Peclet number on the concentration profile in the biofilter (Ci = 12 gm−3, Q = 0.18 m3h−1, Tbed = 35 °C).

of Peclet number on the biofilter performance. As it can be seen, Peclet number has a moderate effect on removal efficiency at 35 °C but as the predominant regime in biofilter is reaction rate limited rather than diffusion rate limited, it has no effect on the other operating temperatures. Figure 8b shows the effect of gas mixing on hexane profile along the reactor height at bed temperature of 35 °C. Each line in this figure represents a Peclet number which denotes gas mixing. As it can be easily observed, lower Peclet number or higher gas mixing tends to flatten the hexane profile along the entire bed and more hexane is degraded at inlet zone of the reactor. In extreme case of high gas mixing, the profile converted to a straight line as typical behavior of well mixed reactors. The same trend was observed for other temperatures but results are not shown here. Results of this section indicated that for design purpose, mixing pattern in the reactor should be experimentally analyzed through RTD experiments and used in mathematical modeling for accurate model prediction. Effects of the biofilter parameters r(T), f(Xv), and δ, on the removal efficiency for high inlet load of 443 gm−3h−1 at 35 °C have been shown in Figure 9. The horizontal axis denotes the

Figure 10. Effect of residence time on removal efficiency at different temperatures (Ci = 12 gm−3, Q = 0.18 m3h−1).

10. As it can be seen, the removal efficiency is very sensitive to the change in residence time. A longer residence time resulted in higher RE due to increase in contact time available for microorganisms to degrade hexane.

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CONCLUSION A mathematical model with zero order reaction was proposed to describe hexane degradation in a vapor phase fungal biofilter at different inlet loads and operating temperatures. The model was developed with the consideration of temperature effect on the reaction rate and other physical properties. Results of the 2394



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mathematical model showed that zero order reaction best fitted experimental data in the working temperatures of 30 and 35 °C in intermittent loading and at entire range of operating temperature under continuous loading. The stability of conditions for microbial growth and activity was the main reason for this agreement. Simulation results revealed that biodegradation was limited mainly by biological reaction especially when bed temperature deviated from 35 °C. Sensitivity analysis showed that by approaching the optimum temperature, a part of the biofilm became inactive and the diffusion limited region changed to the rate limited region. Moreover, simulation showed that bed temperature had a significant effect on the biofilter performance.

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θ1, θ2 = coefficients of temperature effect on reaction kinetic μw1, μw2 = water viscosity in temperature T1, T2 (cp)

REFERENCES

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NOMENCLATURE AS = specific surface area (m−1) C = hexane concentration in gas phase (gm−3) C (0,z) = hexane concentration in gas phase at time zero (gm−3) Co‑exp = hexane concentration at bed outlet (gm−3) Co‑m = hodel prediction for hexane concentration at bed outlet (gm−3) D = dispersion coefficient (m2s−1) DA = hexane diffusion coefficient in air (m2s−1) Dw = hexane diffusion coefficient in water (m2s−1) Ea = activation energy of biological reaction(Jmol−1) EC = elimination capacity (gm−3h−1) ECmax = maximum elimination capacity (gm−3h−1) f(Xv) = ratio of hexane diffusion coefficient in biofilm to that value in water H = bed height (m) IL = inlet load (gm−3h−1) j = counter Kaw = air/water partition coefficient Kbw = biofilm/water partition coefficient Koa = octanol/air partition coefficient Kow = octanol/water partition coefficient m = VOC partition coefficient in air/biofilm m1 = constant N = number of experimental data Peclet = (Hug/(εD)) Q = volumetric gas flow (m3 h−1) R = universal gas constant (Jmol−1·°K) RE = removal efficiency (%) rmax = maximum rate of biological reaction (gm−3h−1) S = VOC concentration in biofilm (gm−3) S (0,x,z) = VOC concentration in biofilm at time zero (gm−3) T, T1, T2 = bed temperature (K) t = time (s) Tbed = bed temperature (°C) Topt = optimum temperature of biological activity (K) ug = superficial gas velocity (ms−1) x = spatial dimension along biofilm Xv = biofilm density (kgm−3) z = spatial dimension along the bed height δ = biofilm thickness (m) ε = bed porosity 2395



Article

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Unsteady-State Mathematical Modeling of a Fungal Biofilter Treating

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