Numerical simulation for volatile organic compound ...

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Numerical simulation for volatile organic compound removal in rotating drum biofilter CHEN Hong, YANG ChunPing†, ZENG GuangMing, YU KongLiang, QU Wei, YU GuanLong & MENG Lei College of Environmental Science and Engineering, Hunan University, Changsha 410082, China

Rotating drum biofilters (RDBs) could effectively remove volatile organic compounds (VOCs) from waste gas streams. A mathematical model was developed on the basis of mass transport and mass balance equations in an RDB, the two-film theory, and the Monod kinetics. This model took account of mass transfer and biodegradation of VOC in the gas-water-biofilm three-phase system in the biofilter, and could simulate variations of VOC removal efficiency with a changing specific surface area and porosity of the media due to the increasing of biofilm thickness in the biofilter. Toluene was used as a model VOC. This model was further simplified by introducing a coefficient of the gas velocity and neglecting the water phase due to the complexity of operating conditions. The equations for the biofilm phase, gas phase, and biofilm accumulation in this model were solved using collocation method, analytic method, and the Runge-Kutta method separately. A computer program was written down as MATLAB to solve this model. Results of numerical solutions showed that toluene removal efficiency in the RDB increased and reached the maximum values of 97% on day 4 after the startup, and then decreased and remained at 90% after 5 more days of operation. Toluene concentration was high at the outermost layer where more than 70% toluene was removed, and was low at the innermost layer where less than 10% toluene was removed. The dynamic removal efficiencies from this model correlated reasonably well with experimental results for toluene removal in a multi-layered RDB. biodegradation, biofilms, model, numerical solutions, rotating drum biofilter, VOC

Biofiltration could cost-effectively remove volatile or― ganic compounds and odours from waste gas streams[1 3]. Effective simulation of the complex process is helpful to better understanding the mechanisms occurring in the biofilters, and consequently to better designing and operating biofilters. Many mathematical models were proposed for biofiltration processes including the basis of the adsorption-biodegradation model[4] and the absorption-biodegradation theory[5]. Biodegradation models for biotrickling filters were developed on the basis of the two-film theory and the Mechaelis-Menten equation[6]. A capillary tube model was presented which took account of the transport resistance in the gas-water interphase and the water phase[7]. The mass balance equations for biodegradation of ethyl mercaptan in a fungal biofilter were introduced on the basis of the adsorption-biodegradation theory [8]. Analytical solutions and numerical methods were www.scichina.com

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used to solve the complex models[7,9]. Unfortunately, credible models for reactor design and operation are still not available due to the complexity of the biofiltration process[10]. Therefore, more investigations are needed to better simulate biofiltration processes. Rotating drum biofilters (RDBs) displayed better performances than traditional biofilters or biotrickling filters, which overcame some important shortcomings including uneven distributions of nutrients, organic ― loadings, and biomass[11 14]. In this paper, a transportReceived October 12, 2006; accepted March 13, 2007 doi: 10.1007/s11434-007-0332-8 † Corresponding author (email: [email protected]) Supported by the Program for New Century Excellent Talents in University from the Ministry of Education of China (Grant No. NCET–05–0701), the China Postdoctoral Science Foundation (Grant No. 2005037206), the Scientific Research Foundation for the Returned Overseas Chinese Scholars from the Ministry of Education of China, and the Science Foundation and Postdoctoral Science Foundation of Hunan University

Chinese Science Bulletin | August 2007 | vol. 52 | no. 16 | 2184-2189

1 Materials and methods 1.1 Experimental apparatus and operation conditions The RDB with multi-layer foam media consisted of a closed stainless steel chamber in which four layers of spongy medium were mounted on a stainless steel drum frame with impermeable end plates at both ends. The media were rotated at 1.0 r/min with continuous submerging and emerging cycles. The lower portion of the biofilter chamber was filled with a nutrient solution where the media were submerged when rotating at its lowest position. The porosity of the medium with a pore size of about 4 pores/cm was 96%. The configuration of multi-layer biofilter is illustrated in Figure 1.

1.2 Model development In the RDB, waste gas streams passed through the interspaces of the solid and liquid phase within the chamber, and exited the drum through the center of the drum[15]. According to the two-film theory, there were gas, water, and biofilm phases in the RDB. There existed gas-water and water-biofilm interfaces. The schematic of a characteristic cell for transport and degradation in the medium is illustrated in Figure 2. A characteristic cell was selected whose volume was WΔrΔR, in which W was the cell width perpendicular to the R and r dimensions, r was perpendicular to the biofilm support, and R was the radius of the drum. Mass balance equations in gas, water, and biofilm phases are developed as follows. 1.2.1 Gas phase equations. VOC concentration in the gas phase was considered uniform at a given diameter R within the drum. Three assumptions were made. First, only convection in the R dimension existed. Next, convection in r dimension could be neglected. At last, VOC transported through the gas-water interphase by diffusion. VOC accumulation rate in characteristic cell WrgΔR is given as ∂ CgWrg ΔR = ⎡⎣(Cg u0Wrg ) R − (Cg u0Wrg ) R +ΔR ⎤⎦ ∂t (1) − jW ΔRrg ,

(

)

∂C g ∂t

Figure 1

Cross-sectional view of the multi-layer biofilter.

Toluene was used as model VOC. The nutrient solution was fed at a rate of 4.2 L/d. Activated sludge taken from a wastewater treatment plant was used for seeding the RDB. GC was used to analyze the toluene concentrations of the influent and effluent gas streams. When operation parameters were changed, toluene removal

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efficiencies at various organic loading rates were obtained. More detailed descriptions about the experiment can be found in refs. [11―13].

= −u 0

∂C g ∂R

− j r =r + L + L , p

f

(2)

w

where j is the flux of VOC into the water layer in a specific surface area, Cg the VOC concentration in gas phase, u0 the empty-bed gas velocity, rp the radius of the cell, Lf the width of biofilm, and Lw the width of liquid film. The boundary conditions were obtained by assuming that the VOC concentrations in the water and gas sides of the interface were in equilibrium, and the Henry’s law defined the relationship of the VOC concentrations. Therefore, ∂Cw j = J wα f = Dw αf , (3) ∂r (4) @ r＝rp+Lf＋Lw, Cg＝HCw, @r>= rp+Lf＋Lw,

∂Cg ∂r

CHEN Hong et al. Chinese Science Bulletin | August 2007 | vol. 52 | no. 16 | 2184-2189

= 0,

(5) 2185

ENVIRONMENTAL CHEMISTRY

biodegradation model for VOC removal in an RDB is developed on the basis of the two-biofilm theory, mass balance equations, and the Monod kinetics. This model was further simplified by neglecting transport resistance in the water phase and introducing an effective coefficient for gas velocity. The equations for the mass transport and bioreactions within the biofilm phase and gas phase and the accumulation of biofilms in this model were solved using collocation method, analytic method, and the Runge-Kutta method separately. A computer program was written down as MATLAB to solve this model. It would help to better understanding the mechanisms for toluene removal in RDBs and to better designing and optimizing RDBs.

Figure 2

Schematic of mass transport in the medium of the RDB.

where Df is the diffusivity of VOC in water, Cw the VOC concentration in water phase, H the Henry’s constant of the contaminant, and af the specific surface area. If the VOC concentration in the gas phase was considered nonuniform in the R dimension of the drum, VOC accumulation rate in WΔrΔR is ∂ ⎤ CgW Δr ΔR = ⎡ Cg u0W Δr − Cg u0W Δr ⎣ R R +ΔR ⎦ ∂t ⎤ , (6) + ⎡ j gW ΔR − j gW ΔR ⎣ r r +Δr ⎦

(

) (

) (

(

∂C g ∂t

= −u0

∂Cg ΔR

)

) (

+

jg Δr

= −u0

∂Cg ∂R

)

+ Dg

∂ 2Cg ∂r 2

,

(7)

where Dg is the diffusivity of VOC in air. The boundary conditions are given as follows: @r=rp+Lf＋Lw, Cg=HCw, − Df

∂Cf ∂r

r = rp + Lf + Lw

= − Dw

∂Cw ∂r

∂Cg

,

(8)

r = rp + Lf + Lw

(9) ≠ 0. ∂r 1.2.2 Water phase equations. Assuming that the dominant mechanisms of mass transport were diffusion in r dimension and convection in R dimension in water phase, and that VOC degradation in the liquid could be neglected. Mass balance equations in the water phase for the characteristic cell WΔrΔR were similar to those in the gas phase when VOC concentration was nonuniform in the R dimension. VOC accumulation rate in the cell WΔrΔR is ∂ ( CwW Δr ΔR ) = ⎡⎣( CwVwW Δr )R − ( CwVwW Δr )R +ΔR ⎤⎦ ∂t @r>= rp+Lf＋Lw,

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+ ⎡⎣( jf W ΔR )r − ( jf W ΔR )r +Δr ⎤⎦ ,

(10)

∂Cw ∂C ∂C ∂ 2 Cw j , (11) = −Vw w + f = −Vw w + Dw ∂t ∂R ∂r ∂R ∂r 2

where Vw is the average water velocity on the surface of the medium and biofilm layer. The following boundary conditions can be applied, @r=rp+Lf, Cf=Cw, ∂Cw ∂Cf − Df = − Dw . (12) ∂r r = rp + Lf ∂r r = rp + Lf 1.2.3 Biofilm phase equations. Assuming that only diffusion existed in r dimension in biofilm phase, and all processes were irreversible. Mass balance equation for the cell W△r△R in biofilm phase could be expressed as dC ∂ ( Cf W Δr ΔR ) − biofilm W Δr ΔR = ( jf W Δr )r − ( jf W Δr )r +Δr , ∂t dt

(13) dC ∂ j ∂ ( Cf W Δr ΔR ) + voc Y −1W Δr ΔR = − f W Δr ΔR, ∂t ∂r dt (14) where Cbiofilm is the biomass concentration in the biofilm, and Cvoc the VOC concentration in the biofilm phase. The relationship of VOC biodegradation rate and the microorganism growth rate was defined by the Monod kinetics. Therefore, eq. (14) could be rewritten as

∂Cf μm X f + Y ∂t

⎡ Cf ⎤ ∂ ⎛ Df ∂Cf ⎞ (15) , ⎢ ⎥ = − ⎜− ∂x ⎝ r ∂r ⎟⎠ ⎣ Ks + Cf ⎦ where μm is the maximum specific growth rate, Ks the Monod constant, Y the yield coefficient, and Xf the biomass density. Assuming that VOC did not penetrate into


dCf = 0. dr

(16)

1.2.4 Biofilm growth equation. VOC was assumed to be the only limiting substrate for microorganism growth. Biomass decayed and was taken out of the medium due to hydraulic shear of the liquid. The net growth rate of biofilms was related to the VOC flux at the waterbiomass interface, the shear rate by the water phase and the decay rate of microorganisms[15–17]. The equation for biofilm thickness change could be expressed as

⎛ dC ⎞ dLf f ⎟Y − L X b , X f = ⎜ Df f f ⎜ dt dr r = rp + Lf ⎟ ⎝ ⎠ where b is the specific shear/decay coefficient.

(17)

1.3 Model solutions

1.3.1 Model simplification. The model could be further simplified according to the characteristic of the rotating drum biofiltration process. All toluene concentrations at a given R value in the gas phase could be considered uniform. At a steady-state, toluene concentration in a characteristic cell was consistent, ∂C f / ∂t = 0 . The mass balance equation for gas phase and its boundary condition could be expressed as dCg Ja =− f , (18) dR u0 (19) @R=Rm, Cg=Cg0. The rotating of the drum resulted in complexity of the movement of the liquid. The simplified model did not take account of the toluene transport in water phase. However, water and its movement within the medium influence the drum porosity and real velocity of gas streams significantly. Therefore, an effective coefficient of gas velocity, Kw, was introduced to make up the assumption of ignoring the water phase in the model. It could reflect the increase of gas real velocity when there existed water phase at a certain extent. (20) u0′ = u0 / K W . Toluene concentration in the biofilm did not change at a steady-state, so ∂C f / ∂t = 0 . Therefore, the mass balance equation and its boundary conditions in the biofilm phase were given as Df ⎡ d ⎛ dCf ⎞ ⎤ μm X f ⎡ Cf ⎤ r = ⎢ ⎥, r ⎣⎢ dr ⎝⎜ dr ⎠⎟ ⎦⎥ Y ⎣ Ks + Cf ⎦

(21)

dCf =0, dr

@ r = rp + Lf ,

Cf =

(22) Cg H

.

(23)

1.3.2 Parameter estimation. Assuming that the foam medium consisted of cells that reticulated jointly with each other and a cube could be considered as the basic configuration unit of the foam medium[15]. The specific surface area through which toluene molecules diffused from the gas into the biofilm equaled the quotient of the average surface area to the average volume contained in each cube. This was defined as the water-gas interfacial surface area per unit bed volume, and could be approximated by 2( Lm − 2rp − 2 Lf ) (24) af = , (rp + Lf )( Lm − rp − Lf ) where Lm is the length of the cube. The porosity of the spongy medium in the drum could be expressed as 3π (rp + Lf )( Lm − rp − Lf ) . (25) εf = 1 − Lm3 Biofilm decay/shear coefficient took account of biofilm losses from biofilm decay and detachment of biofilms due to hydraulic shearing of liquid, and could be calculated using eq. (26). 2

b = bs + bd =

bs0

⎛ ε0 ⎞ ⎜ ⎟ + bd , ⎝ εf ⎠

(26)

where bs0 is the initial specific shear rate, bd the decay rate coefficient, ε0 the initial porosity of the media where there are not any biofilms, and εf the porosity of the media to which biofilms has attached. Empty-bed gas velocity in the gas phase equations could be expressed as follows: Q × 103 , (27) ⎛ arccos ( 2.55 / R ) ⎞ 2π R × ⎜1 − ⎟ × Ld π ⎝ ⎠ where Q is the gas flow rate (L/s), S the cross section area of the medium cylinder within the drum, and Ld the length of the medium cylinder within the drum. Values for the parameters in this model were selected ― (Table 1) to solve the model equations[16 18]. u0 =

Q = S

1.3.3 Model solution. After the successful startup of the RDB, all the medium could be immerged in liquid, and nutrients and VOC were supplied to the biofilms. So


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@ r = rp ,

@ r = rp ,

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the medium, therefore,

Table 1

Parameter values used for solving the model equations

Parameter Maximum specific growth rate, μm, (d) Decay rate coefficient, bd, (d) Default shear rate coefficient, bs0, (d) Monod constant, Ks (mg VOC/L) Yield coefficient, Y, (mg VSS/mg VOC) VOC biofilm/water diffusivity ratio, rd Biomass density, Xf, (mg VSS/L) Initial biofilm thickness, Lf0, (cm) Toluene conversion factor, (kg COD/kg VOC) Toluene diffusivity in water, Dw, (cm2/s) Effective coefficient of gas velocity, Kw Henry’s constant of toluene, H, ((mg/L)gas/(mg/L)water)

Value 1.8 0.004 0.7 0.15 0.84 0.9 6000 0.0004 3.126 10.8×10−6 0.6 0.338

it was reasonable to assume that the biofilm thickness in the drum was no less than the initial biofilm thickness. The mass balance equations for the biofilm phase (eq. (21)) and gas phase (eq. (18)) and the equations of biomass accumulation (eq. (17)) in this model were solved using collocation method, analytic method, and the forth-fifth-order Runge-Kutta method, respectively. In order to get convergent and precise solutions, close attention should be paid to the characteristic time of the biofiltration process and the characteristic length of the drum. The inner functions of bvpinit, bvp4c, and deval in the MATLAB software were used respectively to calculate the initial results, the final numerical results, and the results at any position of R=xint. A computer program was written down as MATLAB to solve this model. First, the initial biofilm thickness and toluene concentration were used to solve mass balance equation in biofilm phase. Then, the calculation results from the earlier step were substituted for the corresponding variables in the mass balance equation for gas phase to get the toluene concentration in the next R value. These two steps were repeated to obtain toluene concentration profile along the R dimension, and the effluent toluene concentration also resulted. Then moving to the next time span, the biofilm growth rate in this time span was calculated using biofilm growth equation. Repeating the previous steps could lead to the effluent toluene concentration at each time span. The calculation stopped until all the time spans were completed.

2 Results and discussion Performances of the RDB over a long period were calculated at an organic loading rate of 2.0 kg COD/(m3·d) and a gas flow rate of 0.590 L/s. The simulation results 2188

and corresponding experimental results[11–13] are presented in Figure 3.

Figure 3 Toluene removal efficiencies in the multi-layer RDB over 20 d after startup.

The removal efficiency in the RDB increased and reached the highest removal efficiency of 97% in the first 4 days after startup, and then gradually declined to and stabilized at about 90% in 5 more days. It can be seen from Figure 3 that this model could simulate the dynamic performances of the RDB pretty well in the early period of the operation. However, the model removal efficiencies of toluene were a little lower than the experimental results. Neglecting water phase when the model equations were solved or the estimation of the parameters or the both was considered to contribute to the difference. Alonso et al.[17] developed a dynamic model for simulating toluene removal in biotrickling filters. The removal efficiency calculated using Alonso’ model showed the same change trend as the model developed here for toluene removal in the RDB, and reached the maximum value earlier and then dropped much quick. The relative error of the calculation values to the experimental results was only 5.73%, which has a standard deviation about 2.54%. The calculation results correlated with the experimental results very well, which confirms that the model could simulate the long-term performance of the multi-layer RDB. Contaminant profile along medium depth in a biofilter is important for biofilter design and operation. Figure 4 illustrates the calculation results of toluene concentration and corresponding removal efficiency at different locations within the drum on the 4th day after startup. Toluene concentration decreased along the drum depth from the outermost to the innermost, and the increasing rates at the outer layers were bigger than those at the inner layers. On the outermost surface of the drum (R =


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sequently lower removal efficiency. This model could take account of the temporal variation of biofilm thickness; therefore, dynamic performance of the RDB could be simulated and predicted. On the basis of earlier research[15], this model took account of the effect of water phase on mass transfer by introducing the effective efficient of gas velocity, which resulted in a better correlation of the calculation result with the experimental data.

3 Conclusions

21.6 cm), the initial toluene concentration was 220 mg/m3. The effluent toluene concentration at the innermost surface of the medium (R = 2.55 cm) was 8 mg/m3. Toluene degradation rate was the highest at the outermost layer where more than 70% toluene was removed, and was the lowest at the innermost layer where less than 10% toluene was removed. The results from the capillary tube model showed a similar result on the variation of the contaminant biodegradation rate along medium depth[7]. Biofilm accumulation within media in an RDB decreased the interfacial area and the porosity of the media which resulted in a lower rate of mass transfer and con1

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Wang Q, Tian S, Xie W, et al. Treatment of mix gas containing butyl acetate, n-butyl alcohol and phenylacetic acid from pharmaceutical factory by bio-trickling filter. Chin J Environ Sci (in Chinese), 2005, 26(2): 55–59 Liu Y, Quan X, Sun Y, et al. Simultaneous removal of ethyl acetate and toluene in air streams using compost-based biofilters. J Hazard Mater, 2002, 95(1–2): 199–213 Zhu X, Suidan M T, Pruden A, et al. Effect of substrate Henry’s constant on biofilter performance. J Air Waste Manag Assoc, 2004, 54(4): 409–418 Sun P, Huang B, Huang R, et al. Kinetic model and simulation of the adsorption-biofilm theory for the process of biopurifying VOC waste gases. Chin J Environ Sci (in Chinese), 2002, 23(3): 14–17 Ottengraf S P P, van den Oever A H C. Kinetics of organic compound removal from waste gases with a biological filter. Biotechnol Bioeng, 1983, 25(12): 3089–3102 Li G, Hu H, Hao J, et al. Bio-degradation model of VOCs in bio-trickling reactor and its application. China Environ Sci (in Chinese), 2001, 21(1): 81–84 Liao Q, Chen R, Zhu X. Theoretical model for removal of volatile organic compound (VOC) air pollutant in trickling biofilter. Sci China Ser E-Tech Sci, 2003, 46(3): 245–258 Zhu G, Liu J. Study on dynamic model of fungi to VOCs treatment. Acta Sci Circumstant (in Chinese), 2005, 25(10): 1320–1324

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Figure 4 Simulating toluene concentration profile along the media depth of the RDB on the 4th day after startup.

A transport-biodegradation model for VOC removal in an RDB was developed on the basis of the two-biofilm theory, mass balance equations, and the Monod kinetics. The dynamic performances of the RDB for toluene removal were calculated using a program written down as MATLAB. The simulation results showed that toluene removal efficiency in the RDB increased and reached the maximum values of 97% on day 4 after the startup, and then decreased and remained at 90% after 5 more days of operation. Toluene concentration was high at the outermost layer where more than 70% toluene was removed, and was low at the innermost layer where less than 10% toluene was removed. The dynamic removal efficiencies from this model correlated reasonably well with experimental results for toluene removal in a multi-layered RDB.