Ind. Eng. Chem. Res. 1999, 38, 2765-2774
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Modeling and Simulation of a Biofilter Md. Amanullah, S. Farooq, and Shekar Viswanathan* Department of Chemical and Environmental Engineering, 10, Kent Ridge Crescent, National University of Singapore, Singapore 119260, Singapore
Treatment of air streams contaminated with volatile organic compounds in a biofilter under transient and steady-state conditions of operation is described with a mathematical model. The model incorporates convection and dispersion in the gas phase, partial coverage of the solid support, interphase mass transfer between the gas and the aqueous biofilm with an equilibrium partition at the interface followed by diffusion, direct adsorption to the exposed uncovered solid adsorbent media, transfer between the biofilm and the solid support, and biological reactions in both the biofilm and the adsorbent. The model equations were solved numerically by the method of orthogonal collocation using a MATLAB computer code. The effects of pollutant dispersion in the gas phase, specific surface area available for mass transfer, thickness of the biofilm, and adsorptive capacity of the solid support on the biofilter performance were investigated in detail. The steady-state removal efficiency appears to be nearly independent of gas-phase dispersion of the pollutant in the normal industrial range of operations. Results also indicate that the biofilter performance is a strong function of specific surface area for mass transfer and biofilm thickness. Simulation results further suggest that higher adsorptive support media are capable of handling load fluctuations irrespective of the rate of reaction in the adsorbed phase. Introduction Volatile organic compounds (VOCs), emitted from a variety of industrial sources, are raising concerns about the consequential damage inflicted on ecological systems. There are a number of processes that involve chemical or physical principles for the treatment of air streams with low VOC concentrations. Despite the ability of these processes to remove VOCs from contaminated air streams, some of these processes are technologically less attractive for economic and safety reasons.1,2 Chemical methods such as incineration, ozonation, and combustion are expensive, because they require elaborate equipment and substantial amounts of additional fuel. Physical methods such as adsorption on activated carbon are not only costly but also may result in the saturated carbon being treated as a hazardous waste and requiring either regeneration or disposal. Biofiltration, on the other hand, is a viable and potentially cost-effective alternative for the treatment of airstreams with low concentrations of pollutants. It utilizes a microbial population immobilized in the biofilm grown on a solid support to degrade organic pollutants in waste gas streams. The pollutants diffuse from the gas phase into the biofilm where they are metabolically consumed by the microorganisms and degraded to carbon dioxide and water. Under proper conditions biofilters can offer a high removal efficiency through a process that is environmentally friendly. Various types of porous materials have been employed as biofilter media, with compost and soil being the most common types.3 Other materials including wood bark,4 sand and loam,5 a mixture of compost and diatomaceous earth (DE),6 and granular activated carbon6,7 (GAC) have also been used. Biofiltration is a complex process that involves physical, chemical, and biological interactions. Ottengraf and * To whom correspondence should be addressed. Tel.: (65) 874-4309. Fax: (65) 65-872-3154. E-mail:
[email protected].
Van Den Oever,8 in their pioneering work, provided experimental results and theoretical analyses of this biological process for the elimination of VOCs in a compost biofilter. In that study, the authors proposed a steady-state model and used the concept of a bed of solid filter particles coated with a biologically active liquid layer called biofilm. A plug-flow model was assumed for the flow of contaminated gas through the filter bed. Pollutant removal from the gas phase was by absorption followed by simultaneous diffusion and a zero-order reaction in the biofilm. The model equations were analytically solved and verified with independent experimental results for the removal of toluene, ethyl acetate, butyl acetate, and butanol from the air stream. Shareefdeen et al.9 proposed a similar steady-state model in which the biodegradation was assumed to be first order with respect to both oxygen and the organic pollutant. Obviously the diffusion of oxygen in the biofilm was also taken into account. This model, originally applied to methanol vapor removal, was also used to describe the biofiltration of other substances such as benzene or toluene.10 Later, the same model was extended to describe the transient behavior for the removal of toluene vapor.11 It is in this study that the ideas of partial coverage of the support media with biofilm as well as adsorption of the pollutants on the solid media through the uncovered portion were introduced for the first time. The results demonstrated that oxygen diffusion might become rate limiting in cases where polar compounds are involved. In their transient simulation study, Hodge and Devinny6 used an axially dispersed plug-flow model for the gas phase and a linear driving force (LDF) model to approximate the interphase mass-transfer kinetics. In this simplified approach, the biofilm and the support media were viewed as a unified phase represented by a single, average concentration. Moreover, the pollutant degradation was assumed to be first order with respect to its average concentration in the unified phase.
10.1021/ie9807708 CCC: $18.00 © 1999 American Chemical Society Published on Web 05/28/1999
2766 Ind. Eng. Chem. Res., Vol. 38, No. 7, 1999
Figure 1. Schematic concept of the biofiltration model.
Deshusses et al.12,13 proposed a transient model for biofiltration of methyl ethyl ketone/methyl isobutyl ketone (MEK/MIBK) mixtures in which kinetic interaction between the pollutants was taken into account in the degradation reaction model. Diffusion of pollutants in the biofilm was modeled as four mixed reactors in series while oxygen was assumed to be present in excess. Adsorption of pollutant in the support media was ignored. Baltzis et al.14 extended the model of Shareefdeen and Baltzis10,11 to include the potential existence of heterogeneity in the biofilm formed on the solid. They, however, neglected adsorption by the solid media and restricted their study to steady-state operation. Abumaizar et al.7 studied the removal of benzene, toluene, ethyl benzene, and xylene (BTEX) and investigated the effect of adding GAC to the compost biofilter. In their steady-state model, they used diffusion followed by Monod kinetics (first order at low concentration and zero order at high concentration) for biodegradation in a biofilm and were able to match the experimental results from columns containing varying amounts of GAC by further assuming that biodegradation also occurred in the adsorbed phase. Biodegradation in the adsorbed phase was assumed to be instantaneous which made diffusion of pollutant in the porous network of GAC followed by a zero-order adsorption rate the ratelimiting steps. The above biofilter models, which represent the major developments in this area, differ mainly in the following aspects: (1) model for fluid flow, (2) model for biodegradation reaction in the biofilm, (3) details of interphase transport, and (4) role of the support media. In the literature both plug-flow and axially dispersed plug-flow models have been applied for fluid flow. The choice of reaction model has differed based on the pollutants and the microorganisms used. Although firstorder irreversible kinetics is more common, there have
been other studies that have demonstrated the need for more involved reaction models. Because the reaction model is specific to the pollutants and microorganisms involved, other types of models are also likely to be explored in the future as the application of biofiltration becomes more widespread. It is important to note that a complex reaction model restricts the possibility of getting an analytical solution of the system of biofilters model equations. However, it does not create much problems for a numerical solution. The extent of details considered in modeling the interphase mass transfer is closely linked with the assumption regarding the role of support media. Early studies ignored any adsorption and reaction of pollutants in the compost material that was used to grow and maintain the colony of microorganisms. Pollutant biodegradation was assumed to be confined within the biofilm grown on the support media in the biofilter. The limitations of the early biofilter models were gradually released by first allowing only adsorption and then both adsorption and reaction in the solid support. A detailed diffusion model as well as a LDF approximation have been applied for transport of pollutant in the biofilm and support media. Use of a full diffusion model in biofilter modeling introduces parameters such as biofilm thickness and fraction of support media covered by biofilm. Although these concepts are physically more realistic compared to the lumped LDF approach, it is difficult to obtain practically meaningful independent estimates of these parameters which, in turn, reduce the physical significance to the remaining model parameters. Two pertinent questions arise from the above discussion (A) What is the impact of various model parameters on biofilter performance. (B) How much detail is required in the modeling of a biofilter that will capture the essential features of its
Ind. Eng. Chem. Res., Vol. 38, No. 7, 1999 2767
dynamics while ensuring unambiguous estimates of the model parameters? To answer these questions, a biofilter model is developed including all of the features, which were highlighted in our earlier discussion on the key publications in this area. Numerical solution of the model equations was verified by replicating some representative results from these key publications. A detailed parametric study was carried out to examine the effects of various operating variables and intrinsic properties on the transient response and conversion achieved at steady state. These results formed the basis on which the advantages and limitations of various biofilter models were analyzed. Model Development The model proposed in this study describes transport, physical, and biological processes that occur during biofiltration. As air passes through the filter, convection, dispersion, adsorption, absorption, diffusion, reaction, and characteristics of the biofilm affect the level of contaminant removal. The fundamental concepts of the proposed model are shown schematically in Figure 1. The model is based on the following assumptions. (1) Isothermal operation and the ideal gas law apply for the gas phase. (2) An axially dispersed plug flow is assumed for the gas flow through the packed bed. (3) The frictional pressure drop is assumed to be negligible. (4) Pollutant and oxygen at the biofilm/air interface are always in equilibrium as dictated by Henry’s law. (5) Biodegradation of the pollutant occurs aerobically in both the biofilm and the adsorbent. (6) Oxygen limitation does not occur in the adsorbed phase reaction. (7) The rate of biodegradation depends on the concentrations of the pollutant and oxygen. (8) Transport of pollutant and oxygen within the biofilm occurs through diffusion only. (9) The biofilm density and thickness are constant throughout the biofilter. (10) There is no net biomass accumulation in the biofilter bed. (11) The biofilm is modeled as a flat plate. This is a reasonable approximation because the thickness of the biolayer is much smaller compared to the diameter of the base particle. (12) Diffusivities of the components in the biofilm are those in water corrected by a factor given by the correlation of Fan et al.15 (13) The packing material is not entirely covered with the biofilm. The exposed patches of solid are in direct contact with the air stream. (14) Adsorption of the pollutant on the solid particles occurs primarily through a portion of the surface that is not covered with the biofilm. Provision is also made for adsorption at the biofilm/solid interface, provided the consumption rate would allow the pollutant concentration to extend through the entire biofilm thickness. (15) The adsorption isotherm is assumed to be linear. It is mathematically no more difficult to consider a nonlinear isotherm, but that may not be necessary because the pollutant concentration is normally very low.
(16) The rate of mass transfer into the solid is approximated by a LDF model. Under the stated assumptions, the transient biofiltration operation is described by the following equations: Mass Balance for Air. These balances express the amount of VOCs and oxygen depleted from the gas phase by equating it to those transported to the biofilm by diffusional flux and to the support media by adsorption.
∂ci 1 - ∂ci ∂2ci ) DL 2 - v × ∂z ∂z ∂z ∂si -RAsDi + (1 - R)ki,g-ads(q*i,g-ads - qi) (1) ∂x x)0
(
)
|
|
∂co 1 - ∂2co ∂so ∂co ) DL 2 - v + RAsDo ∂t ∂z ∂x ∂z
x)0
(2)
Initial conditions ci(z,0) ) 0
(3)
co(z,0) ) 0
(4)
Boundary conditions DL
DL
|
∂ci ∂z
z)0
|
∂co ∂z
) -v(ci|0- - ci|0+)
∂ci ∂z z)0
|
z)L
)0
) -v(co|0- - co|0+)
∂co ∂z
|
z)L
)0
(5) (6) (7) (8)
Pollutant and Oxygen Balance in the Biofilm. These balances indicate that the amount of VOCs transported via diffusion within the biofilm are equal to those lost in biodegradation.
∂2si ∂si ) Di 2 - Ri,bf ∂t ∂x
(9)
∂so ∂2so ) Do 2 - Ro,bf ∂t ∂x
(10)
Initial conditions si(z,x,0) ) 0
(11)
so(z,x,0) ) 0
(12)
Boundary conditions si|x) 0 ) ci/m1,i - RAsDi
|
∂si ∂x
x)δ
) ki,l-ads(q*i,g-ads - qi)
so|x)0 ) co/mo ∂so ∂x
|
x)δ
)0
(13) (14) (15) (16)
2768 Ind. Eng. Chem. Res., Vol. 38, No. 7, 1999 Table 1. Summary of the Various Parameter Values Used in the Present Study to Replicate Some Key Published Models unit
Shareefdeen et al.10,11
Deshusses et al.12,13
Hodge and Devinny6
Abumaizar et al.7
Ottengraf and Van Den Oever8
cm2/cm3 g cm-3 g cm-3 cm2 s-1 cm2 s-1 cm2 s-1 s-1 g cm-3 s-1 g cm-3 g cm-3 cgs units cm dimensionless dimensionless dimensionless dimensionless g cm-3 s-1 g cm-3 s-1 cm s-1 dimensionless cm dimensionless
1.90 2.81 × 10-6 2.75 × 10-4 2.00 × 10-6 3.40 × 10-2 c 4.70 × 10-6 3.20 × 10-4 78.94 × 10-6 0.00 11.3 × 10-6 0.26 × 10-6 not significantf 6.86 × 101 2.70 × 10-1 2.00 × 10-2 3.44 × 101 not significantf Xvµm/Yj Xvµm/Yok 4.95 × 10-1 3.00 × 10-1 3.76 × 10-3 3.00 × 10-1
3.00 2.97 × 10-6 not significantb 2.85 × 10-6 1.99 × 10-1 c not significantb not significantd 1 × 1030 g 4.74 × 10-4 1.37 × 10-6 0 not significantf 9.00 × 101 2.35 × 10-3 5.05 × 10-3 h not significantb not significantf Vm ) 22.5 × 10-7 not significantb 2.21 1.00 1.00 × 10-2 5.00 × 10-1
not significanta 1.13 × 10-5 not significantb not significanta 5.28 × 10-1 not significantb 1.67 × 10-5 not significanta not significanta not significanta not significanta 9.72 × 10-7 9.00 × 101 not significanta 1.12 × 10-4 not significantb 1.00 not significanta not significantb 2.63 0.00 not significantb 2.50 × 10-1
2.17 × 101 1.77 × 10-7 not significantb 8.60 × 10-6 1.10 × 10-1 c not significantb 3.58 × 10-6 e 1 × 1030 g 0.00 0 0 6.08 × 10-7 7.50 × 101 2.71 × 10-1 1.44 × 10-5 Not significantb 0.00 (k1 ) 0.138)km not significantb 1.47 7.65 × 10-1 1.20 × 10-1 7.00 × 10-1
6.13 8.40 × 10-7 not significantb 8.50 × 10-6 8.20 × 10-1 c not significantb not significantf 1 × 1030 g 0.00 0 0 not significantf 3.00 × 102 2.70 × 10-1 not significanti not significantb not significantf k0 ) 1.39 × 10-8 not significantb 9.45 1.00 1.20 × 10-1 2.90 × 10-1
parameter As ci,0 co,0 Di DL Do ki,g-ads KI,i ki,l-ads km,i ko,i krxn,i′ L m1,i m2,i mo n′ Rmax,i Rmax o,i v R δ
a Does not depend on this value (Hodge and Devinny considered solid/biofilm a single phase). b Does not depend on this value (these investigators did not consider oxygen limitation). c Chosen to nullify the effect of dispersion (Peclet number ∼ 1000). d Deshusses et al.12,13 did not consider direct adsorption from the gas phase. e Fitted value. f Does not depend on this value (these investigators did not consider reaction in the support media). g Very high value ∼ ∝. h Chosen to match the transient part of the Deshusses et al.12,13 model prediction. i Does not depend on this value (Ottengraf and Van Den Oever8 did not consider adsorption). j X ) 100 × 10-3; µ ) 4.17 × 10-4; Y ) v m 0.708 (to simulate the effect of biofilm thickness µm ) 2.085 × 10-4 was used to facilitate the demonstration of both reaction and diffusion control. k Yo ) 0.0.341.
Pollutant Balance in the Support Media (Adsorbent).
∂qi ) Rki,l-ads(q*i,g-ads - qi) + ∂t (1 - R)ki,g-ads(q*i,g-ads - qi) - Rads (17) Initial condition qi(z,0) ) 0
(18)
Reaction Kinetics. An appropriate kinetic expression with oxygen limitation has been used for the biodegradation of VOCs in the biofilm. It is assumed that microorganisms consume substrates from both the biofilm and the adsorbent. A general nth-order reaction is assumed to describe the biodegradation in the solid media. Biodegradation in the biofilm can be expressed by the following expression:
Ri,bf(si,so) )
(
rmax,isi 2
km,i 1 +
)
si + si KI,ikm,i
so ko,i + so
Ro,bf(si,so) )
(
km,i 1 +
)
si2 + si KI,ikm,i
q*i,g-ads ) ci/m2,i
(22)
The above system of equations is valid for one pollutant. Extension to multiple pollutants is mathematically straightforward. Competitive reaction kinetics may, however, add some difficulty. Numerical Solution. The set of partial differential equations was written in the dimensionless form and then discretized in space, using the method of orthogonal collocation. The nondimensionalized model equations are given in Appendix I. Ten points were used along the bed length, and 10 points were used along the biofilm thickness. The resulting set of ordinary differential equations was then integrated in the time domain using Gear’s multistep method provided in MATLAB. Concentration profiles of both pollutant and oxygen in the bed and the biofilm and the average concentration of the pollutant in support media were obtained as a function of time. Computation was continued until steady state was reached. Results and Discussion
16
Baider interactive model rmaxo,isi
Adsorption Isotherm.
(19)
so ko,i + so
Baider interactive model16 (20)
Biodegradation in the adsorbent is expressed by an nth-order reaction term.
Ri,ads ) krxn,i′qin′ (nth-order reaction)
(21)
The model proposed in this study was validated by replicating the results from some key published models discussed earlier. The parameters used in these simulations are summarized in Table 1. The proposed model reduces to the Ottengraf and Van Den Oever8 model by setting R ) 1 (particle completely covered by the biofilm, no adsorption, and no biodegradation in the support media), kl-ads ) 0 (no mass transfer between the biofilm and support media), and a high Peclet number in order to approximate plug flow. Although the model takes oxygen diffusion into account, it does not make any difference to the solution because the reaction is zero
Ind. Eng. Chem. Res., Vol. 38, No. 7, 1999 2769
Figure 4. Results showing that the present work can adequately approximate the model by Hodge and Devinny.6 Figure 2. Results of Ottengraf and Van Den Oever8 compared with the present model. In the present simulation, starting from profile 1, the diffusion coefficient was increased until the profile became constant at 2 (reaction limited). Similarly, starting from profile 1, the reaction rate constant value was increased until the profile became constant at 3 (diffusion limited).
Figure 5. Present work compared with the work of Deshusses et al.12,13
Figure 3. Present work compared with the results from the work of Shareefdeen et al.11
order. Results obtained from the proposed model under the above limiting conditions are compared with the Ottengraf and Van Den Oever8 model along with their experimental results in Figure 2. The results are in complete agreement under all three conditions investigated, namely, the regime in which both diffusion and the reaction rate are important, the system is reaction controlled, and the system is diffusion controlled. The model proposed by Shareefdeen et al.11 was simulated by using a high Peclet number, and the reaction in the adsorbed phase was prevented by assigning a zero value to the corresponding reaction rate constant. The results from the model proposed in this study are in reasonable agreement with that of Shareefdeen et al.’s11 steady-state part of the simulation results as shown in Figure 3. However, the present work is unable to predict the hump seen in the work of Shareefdeen et al.11 prior to reaching steady state. It is important to note that the model by Shareefdeen et al.11 does not consider reaction in the support media. This is important when partial coverage of support media by the biofilm occurs and reaction takes place on the surface of support media. The results of Hodge and Devinny6 were also replicated using the proposed model. To approximate the biofilm and the support media as one single phase, as considered by Hodge and Devinny,6 the value of R was set to zero in the proposed model. The comparison shown in Figure 4 indicates a close agreement between
the two model results. However, it is apparent that the model of Hodge and Devinny did not predict the experimental values closely. To obtain a better fit with experimental data, the present model was used with an increased reaction rate as shown in Figure 4. The proposed model was also able to reproduce the results of Deshusses et al.12 by assigning high values for KI (which reduced Baider16 kinetics to MichaelisMenten kinetics as used by Deshusses et al.,12 for a single pollutant) and Peclet number. In addition, R and krxn′ were set to 1 and zero, respectively. A LDF approximation was used to account for sorption of pollutants by the support media from the biofilm. The close agreement shown in Figure 5 clearly demonstrates the versatility of the present approach. A steady-state concentration profile along the height of the bed obtained by Abumaizar et al.7 is compared with present simulation results in Figure 6. The proposed model was reduced to the model of Abumaizar et al.7 by using a high Peclet number, equating the value of R to the fraction of GAC in the bed, and appropriately modifying the reaction term. It is important to note that a key assumption of Abumaizar et al.7 relating to the accumulation of microorganisms in the internal pore spaces of the GAC particles and resulting in rapid consumption of substrate may be valid only for macropores. Micropores that contribute to the bulk of the surface area of an adsorbent may not be available for biodegradation. This observation draws support from the typical size of microorganisms (of the order of micrometers) with respect to that of micropore (of the order of nanometers). It has been established in the preceding paragraphs that the proposed model can be appropriately modified to capture the features of a large number of published
2770 Ind. Eng. Chem. Res., Vol. 38, No. 7, 1999
Figure 6. Results showing close agreement between the present work and that by Abumaizar et al.7
Figure 9. Effect of the specific surface area on the exit concentration.
Figure 7. Steady-state concentration profiles of substrate along the biofilm and the bed.
Figure 10. Effect of the biofilm thickness on the exit concentration.
Figure 8. Effect of the Peclet number on the exit concentration.
biofilter models through appropriate approximation of those parameters that are not relevant to simpler models. Hence, the right tool to investigate how the system dynamics and steady-state performance are affected by the various model parameters has been developed. Results obtained from a detailed parametric study using the proposed model are discussed in the following section. The parameters used for the base case were taken from Shareefdeen et al.11 and are given in Table 1. Figure 7 shows a typical steady-state concentration profile along the thickness of the biofilm and the bed of the biofilter. It is clear that the concentration of the substrate varies nonlinearly along the biofilm and bed. Effect of Peclet Number. The effect of the Peclet number on the exit concentration is shown in Figure 8. The results indicate that the sharpness of the breakthrough and the level of the steady-state exit concentration increase with decreasing Peclet number. These changes are very pronounced in the low Peclet number regime (
