a model to predict long-term performance of vapor-phase bioreactors: a cellular automaton approach

A Model To Predict Long-TermPerformance of Vapor-PhaseBioreactors: A Cellular AutomatonApproachJ I H Y E O N S O N G A N D K E R R Y A . K I N N E Y *

Environmental and Water Resources Engineering, Departmentof Civil Engineering, ECJ 8.6, University of Texas at Austin,Austin, Texas 78712

A novel numerical model was constructed to predictperformance of vapor-phase bioreactors (VPBs) operatedover extended periods. This model incorporates twounique features to simulate changes in pollutant removalefficiency and biomass accumulation: (1) total biomass isdivided into two microbial components, active andinactive biomass, and (2) biomass growth and biofilmthickness changes are simulated by means of a cellularautomaton (CA) approach. The CA approach, a differential-discrete algorithm, numerically allows the excess quantityof biomass in each numerical element to move towardthe biofilm surface as biomass accumulates. One set ofexperimental bioreactor data was used to estimate unknownmodel parameters. A 90-day simulation using the estimatedparameters agreed with pollutant removal and biomassaccumulation profiles determined experimentally. Fouradditional model simulations using the same estimatedmodel parameters were generally consistent withexperimental data collected from a series of toluene-degrading VPBs operated over a range of conditions. Modelpredictions imply that the decline in bioreactor performanceobserved over extended operation was caused by adecline in the active biomass fraction and a decrease inthe biofilm specific surface area. This CA model providesinsight into biomass accumulation during complexbioreactor operation and improves our capability topredict long-term VPB performance.

IntroductionSince vapor-phase bioreactors (VPBs) have emerged as aviable treatment technology for volatile organic compoundsfrom various sources, many numerical models have beendeveloped to predict VPB performance (1-9). First- and zero-order kinetic expressions have been widely used for thebiodegradation process (1-3), while Monod type models withinhibition effects and dual substrates have been explored byseveral investigators (4-6). Models that take into accountpotential limiting factors have also been proposed, includingnitrogen limitations (7) as well as pH changes resulting fromCO2 accumulation and acid formation during the biodeg-radation processes (8, 9).

Efforts to model VPB processes have focused mainly onpseudo-steady-state conditions or short-term transient re-sponses. A common pseudo-steady-state assumption is that

the density and composition of the biofilm are homogeneousalong the bioreactor column and constant with time (1-8).For these pseudo-steady-state assumptions to be true, mostconventional models have been restricted to simulating shortperiods of operation (e.g., less than a few days) whenbioreactor performance is steady. These models have dif-ficulties predicting long-term bioreactor performance ac-curately, since non-steady-state conditions are encounteredfrequently in VPB operation.

Excess biomass accumulation and declines in pollutant-degrading activity are commonly observed in VPBs operatedfor long periods at high organic loading rates (10-13). Inaddition, biofilm systems in mixed-culture VPBs are het-erogeneous, containing active microbial components thatactively degrade pollutants and inactive microbial compo-nents that consist of secondary microbial populations, deadcells and exopolymeric substances. Changes in the relativequantities of these microbial components can lead to adecline in overall bioreactor performance (12, 13). Modelsthat incorporate this complexity are required to improvepredictions of VPB performance over long-term operation.

Several numerical models have recently been proposedto estimate temporal and spatial changes in biofilm thicknessand population dynamics using differential equations todescribe the relevant physical and biochemical processes (9,14-16). These models have adapted a biomass convectiveflux concept, in which biofilm thickness varies with time ata given biofilm expansion rate. Although these models includechanges in biofilm thickness and specific surface area as afunction of biomass growth, biomass density and activityare assumed to be constant. An alternative approachproposed by Okkerse et al. (9) incorporates an active biomassfraction (fact) and an inert biomass fraction (finert) into theVPB model to distinguish microbial components in thebiofilm phase.

A new mathematical approach based on a differential-discrete cellular automaton (CA) algorithm has recently beendeveloped to predict biomass growth and spatial heteroge-neities in a biofilm (17-20). The CA algorithm numericallyconstructs a network of discrete grids in the biofilm domain,and biofilm growth is simulated by relocating excess microbialcomponent to the next available grid. As the quantity of eachmicrobial component changes, biomass density is also alteredin each discrete grid. The CA approach is computationallyand conceptually advantageous since it is relatively easy toformulate numerical solutions, and it better describes thespatial heterogeneity of biofilms. Pizarro et al. (18) con-structed a fully quantitative CA model that described bothsubstrate and biomass as discrete particles in a numericaldomain. In another approach, Picioreanu et al. (19, 20)developed a hybrid CA model that used differential equationsfor substrate diffusion but employed the CA algorithm forbiomass growth.

In this study, a novel mathematical model that incor-porates biofilm growth and two microbial (active and inactive)components in the biofilm was constructed. The mainobjectives of this study were to demonstrate the utility of ahybrid type CA model for complex VPB systems and to providequantitative predictions of bioreactor performance andbiomass accumulation over long-term periods. Data collectedfrom five bioreactors, operated in either unidirectional (UD)or directionally switching (DS) mode and subjected to a rangeof inlet toluene concentrations (Table 1), were used tocalibrate and validate the model. These operating conditionswere selected for modeling purposes since the substantialchanges in biomass and pollutant degradation observed in

* Corresponding author phone: (512)232-2579; fax: (512)471-1720;e-mail: [email protected].

Environ. Sci. Technol. 2002, 36, 2498-2507

2498 9 ENVIRONMENTAL SCIENCE & TECHNOLOGY / VOL. 36, NO. 11, 2002 10.1021/es0156183 CCC: $22.00 2002 American Chemical SocietyPublished on Web 05/01/2002

each experiment (12, 21) allowed comparison with modelsimulations. In the UD bioreactor, a skewed biomassdistribution developed quickly in the column along with arelatively rapid loss in pollutant degradation capacity nearthe bioreactor inlet. In the DS bioreactors, where the gasflow direction was periodically reversed between the top andbottom of the bioreactor column, a more uniform distributionof active biomass was observed. However, even in DSoperation, substantial changes in toluene removal andbiomass accumulation still occurred, particularly when theinlet pollutant loading was increased.

Model DevelopmentGeneral Assumptions. This model describes a VPB in whicha mixed-culture biofilm is growing on the surface of a solid,pelletized packing material. In the bioreactor describedherein, no free liquid is recirculated through the packingmaterials, but water and nutrients are continuously suppliedusing a nutrient-laden aerosol to minimize the effect ofnutrient limitation on biofilm growth. As shown in theconceptual diagram in Figure 1(a), overall VPB processestake place in two phases linked by one interface; the gasphase, the biofilm phase containing two different biomasscomponents, and a thin interfacial layer between the gas/biofilm phases. This model is also constructed to adapt toa change in gas flow direction; thus, it can be used to predictbioreactor operation in either a unidirectional (UD) feedmode or in a directionally switching (DS) feed mode. Thegeneral assumptions made in deriving this model are asfollows: (1) The biofilm is treated as a planar surface. (2)One substrate (toluene) is rate-limiting. (3) Toluene at thegas/biofilm interface is always in equilibrium as describedby Henry’s law. There is a concentration gradient (interfacialresistance) in the interfacial layer (Figure 1). (4) Diffusion/reaction inside the biofilm occurs in one direction only (1Dmodel). (5) Toluene transport in the biofilm is by diffusiononly, and the diffusivity of toluene is assumed to be constantthroughout the biofilm. (6) The biofilm consists of twodifferent biomass components: active biomass (Xact) andinactive biomass (Xinact) (i.e., Xtotal ) Xact + Xinact). Theconcentration of each biomass component varies inside thebiofilm along the column length and with time. (7) Only Xact

is capable of degrading toluene. Xact increases with microbialgrowth resulting from toluene biodegradation but decreaseswith microbial decay resulting from endogenous respirationand irreversible losses such as inactivation of Xact. (8)Microbial growth is described by Monod type kinetics, andkinetic coefficients are assumed to remain constant. (9)Microbial decay is assumed to be proportional to the activebiomass concentration. A fraction of active biomass decaysand is converted into inactive biomass (Xinact), e.g., dead cells

and extracellular polymeric substances. (10) The gas streampasses through this packed bed bioreactor in a plug flowmanner; therefore, the diffusive mass transfer of toluene inthe gas phase is negligible.

Mass Balance and Model Equations. Based on the aboveassumptions, model equations and boundary conditions areconstructed as follows:

1. Mass Balance in the Gas Phase. In the plug-flow reactor,the change in toluene concentration in the gas phase is afunction of the advective flux of toluene along the columnand the diffusive flux of toluene from the gas phase to thebiofilm phase due to the concentration difference across theinterfacial layer (see Figure 1(a))

where Cg is the toluene concentration in the gas phase (mg/Lgas), Cg,in is the inlet toluene concentration (mg/Lgas), v is thesuperficial gas velocity (m/h), εf is the porosity of the packedbed (m3 void space/m3 reactor volume), af is the specificbiofilm surface area (m2/m3), J is the diffusive flux of toluenefrom the gas phase to the biofilm (mg/m2-h), Cl,x)Lf is thetoluene concentration at the biofilm interface (mg/Lliquid), Lf

is the total biofilm thickness (m), kL is the mass transfercoefficient (m/h), and H is Henry’s law constant (mg/Lgas/mg/Lliquid).

2. Mass Balance in the Biofilm Phase. Toluene diffusionand biodegradation take place in the biofilm phase, asdescribed by the following mass balance equation usingMonod kinetics. As indicated in the general assumptions,only active biomass (Xact) is responsible for toluene biodeg-radation

TABLE 1. Bioreactor Operating Conditionsa

expt bioreactordays of

operation

directionally-switchingb

operationinlet tolueneconcn (ppmv)

inlettolueneloading(g/m3-h)

1 DS-3-day 78 3 day SFc 200 45.82 DS-7-day 68 7 day SF 200 45.83 UD 96 No 200 45.84 DS-400 45 3 day SF 200 (days 0-23), 45.8

400 (days 24-45) 91.15 DS-600 47 3 day SF 200 (days 0-23), 45.8

600 (days 24-47) 136.7

a A packed bed volume of 19.8 L, an air flowrate of 19.8 L/min, andan empty bed residence time of 1 min were used in all VPB experiments.b Directionally switching operation in which the direction of the air flowwas periodically reversed throughout the bioreactor column, i.e., every3 or 7 days. c Switching frequency.

FIGURE 1. (a) Conceptual diagram of the gas and biofilm phasesin the VPB model and (b) description of the numerical domain usedfor the cellular automaton approach. The dotted line in (a) representsthe pollutant concentration, and the dotted arrows in (b) representtoluene diffusion into the biofilm elements. For numerical purposes,the bioreactor column is conceptually divided into layers (12 inthese simulations) with identical dimensions, and each is connectedby gas-phase advection.

∂Cg

∂t) - v

εf

∂Cg

∂z- Jaf, and

J ) kL (Cg

H- Cl,x ) Lf) @z ) 0, Cg ) Cg,in (1)

VOL. 36, NO. 11, 2002 / ENVIRONMENTAL SCIENCE & TECHNOLOGY 9 2499

where Cl is the toluene concentration in the liquid phase(mg/Lliquid), Df is the effective diffusion coefficient of toluene(m2/h), µm is the maximum growth rate of Xact (1/h), Ks is theMonod half saturation constant (mg/L), Xact is the microbialdensity of the active microbial component (mg COD/L), andYact is the yield coefficient of Xact (mg CODbiomass/mgtoluene).

3. Biomass Growth in the Biofilm Phase. The netaccumulation of Xact is the difference between microbialbiomass growth and biomass decay. Biomass decay is acomplicated microbial process that can include endogenousrespiration, cell death, and extracellular polymer secretionin the biofilm phase. In this model, biomass decay is assumedto be proportional to Xact, and a fraction of Xact is convertedinto inactive biomass (Xinact) such as cell debris and extra-cellular polymeric substances. Since biofilm detachment isnegligible in a bioreactor system without a recirculating liquidstream and inactive biomass is assumed to be high molecularweight polymers or dead cells, a loss term is not included inthe equation for Xinact.

where kd is the biomass decay rate (1/h), Xinact is the microbialdensity of the inactive microbial component (mg COD/L),and â is the formation coefficient for Xinact (-).

4. Changes in Biofilm Thickness (Cellular AutomatonApproach). Changes in biomass density calculated using thetwo partial differential equations above (eqs 3 and 4) areused to determine the increase in biofilm thickness by meansof a cellular automaton algorithm (i.e., the discrete-dif-ferential approach). In the algorithm, the numerical domainis divided into discrete grids that consist of biofilm, boundary,and bulk elements (17). A conceptual diagram of this schemeis provided in Figure 1(b). Only biofilm elements containmicrobial components (Xact and Xinact), and each biofilmelement is linked through diffusive mass transfer. Theboundary elements at the gas/biofilm interface mediate themass transfer between the two phases, but they do not containmicrobial components. The bulk elements are filled withtoluene at a constant gas-phase concentration. As the overallbiomass quantity increases, each interfacial grid in the biofilmphase moves to the next available grid according to thecellular automaton algorithm (19, 20).

The sum of each microbial component in each biofilmelement can vary from zero to a maximum hypotheticaldensity (Xset). This allows the biomass density and composi-tion within the biofilm to change with time. When the sumof the two microbial components (Xi

total ) Xiact + Xi

inact) in theith biofilm element exceeds the maximum density (Xset), theexcess microbial quantity (Xi

excess ) Xitotal - Xset) is moved to

the next, i+1th biofilm element. The excess biomass quantityof each microbial component is transferred from the ithelement at a ratio proportional to its fraction in the ithelement. For example, the concentration of the activemicrobial component in the ith biofilm element after theexcess quantity has been transferred out of the element is

where Xacti (t) is the concentration of the active microbial

component in the ith biofilm element at time t (mg/m3), andXact

i (t*) is the concentration of the active microbial compo-nent in the ith biofilm element after the excess biomassquantity has been transferred from the element (mg/m3).The concentration of each microbial component in the i+1thbiofilm element is recalculated by adding each microbialquantity transferred from the ith element to those previouslypresent in the element. If the total microbial density in abiofilm element does not exceed the maximum limit, noreallocation occurs. These redistributions of microbial com-ponents continue from the biofilm element adjacent to thepacking material (i.e., i ) 1) to the outermost biofilm element(i ) N). In this 1D model, biomass movement is always towardthe biofilm surface (i.e., expansion only), and biofilmdetachment or shrinkage is not considered. If the totalmicrobial concentration exceeds the maximum density inthe outermost biofilm element, a new biofilm element iscreated between the outermost biofilm and the boundaryelements. In this manner, biofilm expansion increases thenumber of biofilm elements, while the location of theboundary element is sequentially moved outward in thenumerical domain. The rearranged biomass distributionwithin the biofilm is used to predict mass transfer andbiodegradation of toluene for the next time step. The newbiofilm thickness (Lf) is calculated using the followingequation

where N is the number of the biofilm elements at each timestep (see Figure 1(b)), and W is the width of each biofilmelement (m). In this study, each biofilm element is assumedto be a cubicle with a width of 2.5 × 10-6 m, a value withinthe range used successfully by other researchers (18-20).The size of the biofilm element is considered to be a numericalconstruct, and no attempt is made to correlate this valuewith real biofilm clusters. Additional research would berequired to directly relate this value to heterogeneous biofilmsystems since biofilm clusters are highly variable anddependent on environmental conditions.

5. Changes in Specific Surface Area (af) and Porosity(Ef). An increase in biofilm thickness changes the specificsurface area of the biofilm (af) and the corresponding packingbed porosity (εf). Alonso et al. (14, 15) formulated equationsfor specific surface area and packing bed porosity, based ona packing spheres model where the biofilm expands into thevoid space left between the packing materials. The changesin af and εf can be expressed as a function of biofilm thickness(Lf)

where ε0 is the clean bed porosity, φ is the sphericity factorof pelletized packing materials, n is the coordinate numberof the characteristic packing spheres in contact with a givensphere, and R is the characteristic packing sphere radius(m). Since the packing material (porous silicate pellets, CeliteR-635, Celite Co., CA) used in this study was also used in thestudy by Alonso et al. (14, 15), the same model parametersdeveloped in their model studies were adapted for this study;i.e., coordinate number (n ) 10), clean bed porosity (εo )0.34), and sphericity factor of pelletized packing materials (φ) 0.857).

Time Scale. Physical, chemical, and biological processesin a VPB take place on different time scales. Diffusion and

Lf ) N × W (6)

af )3(1 - ε0)

2Rφ (1 +Lf

R)((2 - n)Lf

R+ 2) (7)

εf ) 1 - (1 - ε0)[(1 +Lf

R)3

- n4(Lf

R)2(3 + 2Lf

R)] (8)

∂Cl

∂t) Df

∂2Cl

∂x2-

µmCl

Ks + Cl

Xact

Yact@x ) 0,

dCl

dx) 0, and

@x ) Lf, Cl ) Cl,x)Lf (2)

∂Xact

∂t)

µmCl

Ks + ClXact - kdXact @t ) 0, Xact ) Xact,o (3)

∂Xinact

∂t) âkdXact @t ) 0, Xinact ) Xinact,o (4)

Xacti (t*) ) Xact

i (t) - Xexcessi Xact

i (t)

Xtotali (t)

, if Xtotali > Xset (5)

2500 9 ENVIRONMENTAL SCIENCE & TECHNOLOGY / VOL. 36, NO. 11, 2002

biodegradation processes have much shorter characteristictimes than changes in biomass quantity (growth, injury, anddecay). In general, substrate diffusion and reaction are atleast 10 times faster than biomass growth (20). The massbalance equations for the gas and biofilm phases can,therefore, be considered to be at a quasi steady-state for agiven biomass distribution. As a result, the partial differentialequations (eqs 1 and 2) can be simplified to coupled ordinaryequations as follows:

This assumption can provide stability and convergenceto the numerical solutions. Alonso et al. (15) showed that asolution using the quasi steady-state assumption did notsignificantly differ from the simulation results solved withoutthis assumption. In the numerical algorithm of the modeldeveloped in this study, a quasi-steady-state profile of tolueneconcentration was calculated first assuming a fixed biomassdistribution. Then, the new biomass quantity in the numericaldomain was calculated according to the toluene profile. Trialsimulations performed at time intervals of 6 and 12 minyielded almost identical results with less than a 5% differencein overall toluene removal predictions over a 50-day simula-tion. As a result, the 12-min (0.2 h) time interval was usedin this study to save computational time.

Numerical Approach. If each computational segment issmall enough, a packed bed reactor can be considered to bea series of well-mixed reactors. For modeling purposes, thebioreactor column is divided into a series of well-mixed layersfor the gas phase, and each gas phase reactor is combinedwith a biofilm reactor through a diffusive link, as shown inFigure 1(b). In each bioreactor layer, the bulk gas phaseconcentration was determined by averaging the tolueneconcentrations of the gas entering and exiting the layer. Inthe simulations reported herein, the bioreactor was dividedinto 12 equal volume layers of gas and biofilm phases. Modelsimulations with 24 equal layers were also conducted for a50-day period using the same model parameters. The twosimulations resulted in only a 1% discrepancy in predictedoverall toluene removal efficiency. Therefore, all simulationsin this study were performed using 12 layers along the VPBcolumn.

The mass balance for the biofilm phase (eq 10) and thegas-phase flux equation (eq 9) were converted to a paired setof equations using a finite difference scheme for a boundaryvalue problem, and the equations were solved by the Gauss-Seidel iteration method (22). Multiple iterations were requiredwhen dealing with this nonlinear, moving boundary problem.

Parameter Estimation. A weighted least-squares errormethod was employed to estimate each model parameter inthe coupled nonlinear equations (23). Since this model isconstructed to simulate VPB performance with respect totoluene removal efficiency along the bioreactor column andbiomass accumulation over time, normalized profiles oftoluene and biomass along the VPB column length were usedfor parameter estimation. The equation below representsthe objective function used in this study to minimize thesum of squared errors (SSE) between the actual experimentaldata and the simulated values for the set of estimatedparameters

where fmeasured is the experimentally measured value, f(p) isthe simulated value using a set of estimated parameters, andp ) (p1, p2, ..., pm) is the set of estimated parameters. Becausetoluene removal and biomass concentration were consideredto be key operating parameters, both were weighted equallyin the objective function.

Materials and MethodsBioreactor Configuration and Operation. Results obtainedfrom five lab-scale VPB experiments were used in this study.The bioreactors were configured identically and consistedof stainless steel columns with an inner diameter of 16.2 cm(see Figure SI-1, Supporting Information). Each column waspacked with pelletized biological support media (Celite R-635,Celite Co., CA) to an overall bed height of 1.0 m. Toluene wasused as a model volatile organic compound for all thebioreactor column studies. The air stream to the bioreactorwas contaminated with toluene and saturated with a nutrient-laden aerosol to continuously supply nutrients and moistureto the column. Table 1 summarizes the operating conditionsfor each of the five experiments. Four bioreactors (DS-3-day,DS-7-day, DS-400, and DS-600 in Table 1) were operated ina directionally switching (DS) mode, such that the directionof the air stream through the bioreactor column wasperiodically reversed. In previous studies, DS operation hasbeen shown to allow extended bioreactor operation bypromoting a more even biomass distribution along thecolumn (12, 21). For comparison purposes, one bioreactor(UD in Table 1) was operated in a unidirectional mannerwith the contaminated air flow continuously supplied to thebottom of the column. Details regarding bioreactor config-uration, operation, and inoculation as well as the chemicalcomposition of the nutrient-laden aerosol used in this studyhave been described previously (12, 21).

Analytical Methods. Previous column studies have dem-onstrated that overall removal efficiencies and concentrationprofiles along the bioreactor column can be used to monitorbioreactor performance (12, 21). To measure toluene con-centrations, gas samples were collected from gas samplingports and analyzed immediately using a gas chromatograph(series 6890, Hewlett-Packard, CA) equipped with a flameionization detector. The gas sampling ports were located at0, 0.25, 0.5, 0.75, and 1 m along the bioreactor column (FigureSI-1, Supporting Information). Chemical oxygen demand(COD) was employed to determine biomass accumulation.Biofilm samples (biomass-covered pellets) were collectedfrom packing media sampling ports located at 0.08, 0.33,0.67, and 0.92 m along the column and analyzed using aCOD vial (Hach, CO). A detailed description of the analyticalprocedures is reported elsewhere (12).

Results and DiscussionThe model presented herein was developed to predict thechanges in bioreactor performance as well as biomassaccumulation and distribution that occur in VPBs withincreasing operation time. Model parameters were estimatedby fitting the model to experimental data collected from atoluene-degrading VPB (DS-3-day, Table 1). Using the sameestimated model parameters, model predictions were vali-dated and compared with actual experimental data collectedfrom a series of toluene-degrading VPBs operated under arange of conditions (DS-7-day, UD, DS-400 and DS-600).

0 ) - vεf

∂Cg

∂z- kLaf(Cg

H- Cl,x)Lf) (9)

0 ) Df

∂2Cl

∂x2-

µmCl

Ks + Cl

Xact

Yact(10)

minimize SSE(p) ) ∑i

1

2(ftoluene,measured - ftoluene(p))2 +

∑j

1

2(fbiomass,measured - fbiomass(p))2, and

p ) (p1, p2, ‚ ‚ ‚, pm) (11)


Model Parameter Estimation and Sensitivity. Parameterestimation was performed by optimizing the objectivefunction (eq 11) using the toluene removal and biomassprofiles determined in the DS-3-day column on day 75. Sixparameters were obtained from the literature (14, 24, 25),while three initial conditions and seven unknown parameterswere fit to the experimental data using the objective function.Parameter values reported in the literature for similar VPBmodels were used as starting points in the estimation processfor four of the seven unknown parameters (Table 2). Forexample, Alonso et al. (14) employed a decay rate coefficientof 0.018 h-1, and this value was used as the initial estimatefor the biomass decay rate (kd). The starting points for theother three unknown parameters, the microbial kineticcoefficients, were based on experimental results obtained ina series of batch kinetic tests (data not shown). The kinetictests were performed using a pure strain of Rhodococcusrhodochrous which was the predominant microbial speciesfound in the VPB biofilm (21). To obtain a set of modelparameters that optimized the objective function, modelsimulations were iteratively conducted with combinationsof modified parameters within a (100% range from thesestarting points. Table 2 presents the model parameters whichyielded the best fit (i.e., the minimum SSE) to the actualexperimental data. As an example of this iterative fittingprocess, Figure SI-2 in the Supporting Information illustratesthe minimum value of SSE obtained by modifying Xset andYact, while the other parameters were held constant.

A sensitivity analysis was performed on the seven esti-mated parameters and three initial conditions to determinethe ones most critical to model predictions. The impact ofeach estimated parameter was measured as the change inSSE using eq 11 when each parameter was varied from itsnominal value by (60%, while the other model parametersremained unchanged (Figure SI-3 in the Supporting Infor-mation). In addition, sensitivity indexes (i.e., one-pointperturbation results) were determined as differences of SSEsbetween model simulations based on nominal parametervalues and the results obtained by increasing each value by10% (Table 2).

The sensitivity analyses indicate that the mass transfercoefficient (kL) has the greatest impact on model predictions.

This analysis suggests that an accurate estimate of the masstransfer coefficient is needed to increase the accuracy ofmodel predictions and applications. The biomass yieldcoefficient (Yact), biomass decay coefficient (kd), and maxi-mum biomass density (Xset) are also sensitive parametersaffecting model predictions. Alonso et al. (14) found thatsimilar parameters in their model, the yield coefficient, decayrate coefficient, and biomass density constant had the greatestimpact on model predictions. Since their model and themodel developed in this study were both constructed toincorporate biomass growth and decay, sensitivity of thepredictions to these parameters was anticipated in both.Experimental methodologies are still under development todetermine not only the in situ biochemical characteristics ofthe biofilm in complex VPB systems but also to directly relateVPB model parameters to these biofilm characteristics. Suchmethodologies have not been fully established for use inexisting CA models even for simple biofilm systems (18). Forinstance, the maximum biomass density (Xset) is a conceptualvalue in this CA model, and extensive research would berequired to obtain a more reliable value for model applica-tions.

Model Simulation and Validation. Figure 2 illustratesoverall toluene removal efficiencies, toluene concentrationprofiles, and biomass accumulation along the column for a90-day simulation of the DS-3-day bioreactor. The simulationresults for removal efficiencies and normalized concentrationprofiles along the column are consistent with experimentalfindings. In the early phase of bioreactor operation, expo-nential removal of toluene was observed in the DS-3-daybioreactor. This exponential removal phase was followed bya slow decline in biodegradation activity, resulting in a shiftto a near-linear toluene removal profile and eventuallytoluene breakthrough (less than 95% overall removal ef-ficiency) on day 78 (Figure 2(a)). The model simulation alsoclearly demonstrates the gradual decline in removal efficiencyand the shift in toluene removal from an exponential to anear-linear profile over the 90-day period. The model wasused to simulate an additional 22 days after actual bioreactoroperation was terminated. On day 90 in the simulation, aremoval efficiency of approximately 80% is predicted (Figure2(a)).

TABLE 2. Model Parameter Values Used in This Study and Sensitivity Indexes

parameters value units

values used asstarting points

for fitting ∆SSEa

estimated µm (maximum growth rate) 0.05 1/h 0.028b 0.019Ks (half-saturation constant) 0.10 mg/L 0.29b 0.002Yact (yield coefficient) 0.76 mgCOD/L 0.80b 0.027kd (biomass decay rate) 0.016 1/h 0.018 (14) 0.058â (inactive biomass formation) 0.17 mg/mg 0.13 (9) 0.001Xset (maximum biomass density) 25.0 g/L 17.0 (14) 0.032kL (mass transfer coefficient) 2.8 m/h 1.8 (9) 0.083

known Z (total biofilter height) 1.0 mV (total packed volume) 19.8 LQ (gas-phase flowrate) 1188 L/hH (Henry’s law constant) 0.265 (24, 25) mg/L/mg/LDf (toluene diffusion coefficient) 3.5 × 10-6 (24, 25) m2/hR (packing sphere radius) 0.003 (14)φ (sphericity of packing) 0.857 (14)ε0 (clean bed porocity) 0.340 (14)n (number of characteristic spheres) 10 (14)

initial conditions (estimated) Lf0 (initial biofilm thickness) 15.0 µm 15.0 0.003Lf0 for UD simulation only 37.5 µm 0.023c

Xact0 (initial Xact) 4.0 g/L 1.6 0.002Xinact0 (initial Xinact) 0.0 g/L 0.0 0.001d

a Differences between SSEo (the SSE calculated using eq 11 with nominal parameter values) and SSEj (the SSE when each parameter is increasedby 10% while the others remain unchanged). b Experimentally determined in batch kinetic tests. c ∆SSE resulting from modifying the initial biofilmthickness estimate from 15.0 to 37.5 µm for UD simulation only. d Used Xinact0 of 0.1 g/L to calculate SSEj.


Figure 2(c) demonstrates that predicted results for thebiomass accumulation are consistent with experimental dataas a function of operation time. As shown in the figure,biomass accumulated continuously and relatively evenlyalong the DS-3-day column. Over the 90-day model simula-tion, biofilm thickness increases by a factor of 24 in the middleof the column and by a factor of 33 near the inlet of thecolumn. As the biofilm thickens, the specific surface areaavailable for mass transfer diminishes correspondingly, andby day 90, the model predicts that the specific surface areain the inlet zone is reduced by 59%. Even though the masstransfer coefficient remains constant, the reduced surfacearea actually decreases the toluene mass flux into the biofilm.This model prediction suggests that the decrease in specificsurface area for mass transfer is one of the key reasons fordeterioration in bioreactor performance over extendedperiods of operation.

Model simulation results for the DS-7-day bioreactor werecompared with the experimental data (Figure 3) to validatethis model and to test the estimated model parametersdetermined in the model fitting above. In this experiment,the decline in bioreactor performance in the DS-7-daybioreactor progressed faster than that observed at the DS-3-day, and toluene breakthrough occurred on day 68, i.e., 10days earlier than that in the DS-3-day bioreactor. The morerapid deterioration in the DS-7-day bioreactor was primarilydue to the longer reacclimation period required after each

airflow reversal as well as a decline in the toluene-degradingactivity in the inlet zone of the column (21). The modelaccurately predicts the decline in performance and toluenebreakthrough for the DS-7-day bioreactor over a 90-daysimulation. Figure 3(b) demonstrates that the toluene profilesshift more quickly from an exponential to a linear shapewith increasing operation time. In addition, as shown inFigure 3(c), a continuous increase in biomass quantity wasobserved along the DS-7-day column, which is consistentwith predicted results.

Model prediction results indicate that the active biomassfraction (fact ) Xact/Xtotal) in the outlet zone of the DS-7-daybioreactor substantially decreases over one cycle of DSoperation. For example, the active biomass fraction in theoutlet, carbon (toluene) deprived zone of the DS-7-daybioreactor decreases from 81% to 16% over the simulationperiod between days 7-14. Following each flow directionreversal in DS operation, the new inlet zone of the DS-7-daycolumn requires 72 h to recover biodegradation activity,because it was previously the outlet, carbon deprived zone.This predicted result is consistent with the recovery periodsexperimentally observed in the DS-7-day bioreactor (21). Inthe DS-3-day bioreactor, model predictions and experimentalobservations support a less substantial decline in activebiomass fraction in the outlet zone.

Overall, this model yields a relatively accurate predictionof VPB performance at different switching frequencies using

FIGURE 2. Simulation results (lines) and experimental data (symbols)obtained in the DS-3-day bioreactor: (a) overall toluene removalefficiencies, (b) normalized toluene profile along the column, and(c) biomass accumulation.

FIGURE 3. Predicted results (lines) and experimental data (symbols)obtained in the DS-7-day bioreactor: (a) overall toluene removalefficiencies, (b) normalized toluene profile along the column, and(c) biomass accumulation.


the same estimated parameters. In addition, the modelsimulation provides insight into how biomass accumulationaffects the specific surface area and mass transfer of tolueneinto the biofilm as well as how changes in active biomasshave a significant effect on overall biofilter performance.These results suggest that the CA model presented herein isa useful tool for predicting bioreactor performance forextended periods.

Model Application. Model predictions were also com-pared to experimental results of the unidirectional (UD)bioreactor operation (Figure 4(a) and (b)). During the initial18-day period, the chemical composition of the nutrientsolution supplied to the experimental bioreactor was alteredthree times to investigate nitrogen requirements and biore-actor start-up performance (12). Following this initial period,overall toluene removal efficiencies of greater than 99% wereobserved. However, bioreactor performance gradually de-clined over time with increasing biomass accumulation inthe inlet zone and pressure drop across the column. Thedecline eventually resulted in system failure with a rapiddrop in overall toluene removal efficiency.

The model simulation of the UD bioreactor was startedon day 18 (after the nitrogen limitations had been resolved)with a modified initial biofilm thickness (Lf0), while the otherparameters remained constant as listed in Table 2. A modifiedinitial biomass thickness of 37.5 µm was selected based onthe average biofilm thickness predicted for the DS-3-daycolumn on day 18. As indicated by the ∆SSE value in Table2, this modification has less impact on model simulations

than do the more sensitive parameters such as the masstransfer coefficient and the biomass decay rate. Figure 4(a)illustrates predicted toluene removal efficiencies on days 18-90. Overall, the model predictions agree reasonably with theexperimental data, and this model predicts the rapid systemfailure observed. In addition, predicted toluene removalprofiles along the column on days 30 and 60 are consistentwith the experimental data (Figure 4(b)). However, in theUD experiment, the removal efficiencies remained greaterthan 99% until day 70 and then dropped rapidly withincreasing pressure drop across the column. In contrast, themodel predicts a relatively smooth decline in removalefficiency. The rapid system failure observed in the UDoperation was primarily associated with near-completeclogging of the inlet zone and channeling of the airflow.However, the model assumes that biomass accumulatesevenly across a given cross-sectional area, and the effect ofpressure drop is not incorporated. A potential solution forthis extreme clogging condition is to include a pore networkalgorithm into the model (26). In the pore network algorithm,as biomass grows, the open diameter of the pore narrowsdown, resulting in an increase in pressure drop along thecolumn.

In addition to comparing model predictions to theexperimental data from the UD bioreactor, model simulationswere conducted for two additional sets of operating condi-tions at higher toluene inlet concentrations. The two bio-reactors (referred to as DS-400 and DS-600 in Table 1) wereoperated for a period of 45 and 47 days, respectively, to

FIGURE 4. Overall toluene removal efficiencies (a, c, and e) and normalized toluene removal profiles along bioreactor columns (b, d, andf) for the UD (unidirectional), the DS-400 and the DS-600 experiments, respectively. Predicted results are indicated as lines and symbolsrepresent measured data. The dotted vertical lines in (c) and (e) indicate the days when loading rates were increased in the DS-400 andDS-600 bioreactors.


investigate the effects of high inlet toluene concentrationson bioreactor performance. Both bioreactors were initiallyoperated for 24 days at an inlet toluene concentration of 200ppmv identical to that of the DS-3-day bioreactor. On day 24,the inlet concentrations were increased to 400 ppmv in theDS-400 and 600 ppmv in the DS-600 bioreactor. After a shortpseudo-steady state following the loading increase, a rapiddecline in overall removal efficiency was observed in eachbioreactor.

Model simulations for these increased concentrationconditions were conducted using the same estimated pa-rameters presented in Table 2. Figure 4(c),(e) illustratestoluene removal efficiencies over 50 days of simulation inboth bioreactors, and Figure 4(d),(f) shows toluene removalprofiles along each column over the operational period.During the initial start-up period, model predictions areconsistent with the experimental data. Following the increasein toluene concentration, rapid declines in removal efficiencyare predicted in the model simulations for both bioreactors.The model predicts that the biofilm thickness increases muchfaster at the higher inlet toluene concentrations than at thelower toluene concentrations provided to the DS-3-daybioreactor (e.g., approximately 4.6 times faster overall forthe DS-600 than in the DS-3-day). This biomass accumulationresults in a rapid decrease in specific surface area andeventually overall removal efficiency. Another interestingfinding in the model simulations is that the toluene removalprofiles along the column length rapidly shift from expo-nential curves to linear profiles as VPB performance dete-riorates and toluene breakthrough occurs. The tolueneremoval profile determined experimentally on day 45 of theDS-600 (Figure 4 (f)) is a straight line (R2 ) 99.7%) whichagrees well with model predictions.

Despite its reasonable prediction of rapid system failureat high toluene concentrations, this model overestimatesbioreactor activity, resulting in a slower decline in predictedremoval efficiency than that observed in the DS-400 (Figure4(c)). The model also predicts higher removal efficienciesimmediately after the concentration increase in the DS-600,although the decline is accurately predicted at the end of thesimulation (Figure 4(c)). These inaccuracies at higher tolueneconcentrations may be due to the fact that the model doesnot consider intrinsic changes that may occur in the kineticcoefficients in the biofilm phase. In a multispecies modeldeveloped by Mirpuri et al. (5) to predict VPB performanceat two different inlet toluene concentrations (150 and 770ppmv), the microbial loss coefficients had to be varied to fitthe experimental data. In the model simulations presentedherein, the biomass decay rate may need to be modifiedwhen used to predict the performance of bioreactorssubjected to higher toluene concentrations. Nitrogen avail-ability in the biofilm phase may also affect the microbialkinetics (µm, Ks, Yact) of the toluene-degrading population.Although the nitrogen supply to both experimental bio-reactors was increased following the toluene loading increasesto maintain a constant carbon-to-nitrogen ratio, the alterednitrogen supply presumably resulted in a change in microbialkinetics, an effect that is not included in the currentformulation of the model. Further investigation of themicrobial kinetic parameters would be required to providebetter insight into the influence of higher substrate con-centrations and nitrogen availability on each individualparameter.

Active Layers and Conventional Models. Changes inconcentration profiles of both toluene and active biomassinside the biofilm are predicted using the model. Figure5(a),(b) illustrate predicted profiles of the active biomassfraction (fact ) Xact/Xtotal) and toluene inside the biofilm nearthe inlet zone (0.042 m) of the column. On day 15, the activebiomass is evenly distributed throughout the biofilm, but

the substrate (i.e., toluene) diffuses through only half of thebiofilm thickness. As the biofilm thickens, the active biomassshifts toward the biofilm surface, and by day 90, only 40%of the biofilm depth from the surface contains active microbialcomponents. The remaining portion of the biofilm iscomprised of inactive biomass only. In this model prediction,the active biomass fraction decreases rapidly from the surfaceto the substratum of the biofilm (i.e., from 85% to 0%), sincetoluene degradation takes place in the outermost biofilm.These results suggest that biomass near the bottom of thebiofilm suffers from a lack of diffused toluene, resulting ina gradual drop in the quantity of active biomass by endog-enous decay. Several studies of simplified biofilm systemshave determined the distribution of active biomass andsubstrate inside biofilms using microelectrodes and mi-croslicing techniques (27, 28). These studies have found thatsubstrate and active biomass profiles in thick mixed-culturebiofilm are similar to those predicted in this study.

The existence of an active layer (or penetration depth) ina thick biofilm is also assumed in most pseudo-steady-statemodels developed using simplified assumptions such as zero-order kinetics or first-order kinetics (1, 2). These conventional,pseudo-steady-state models generally yield fixed biodegra-dation rates expressed as exponential functions or squareroot relationships as a function of column height. Thesemodels fail to explain changes in VPB performance and linearremoval profiles that develop with time along the column.Only in the case where diffused toluene reaches the bottomof the biofilm (i.e., the reaction-limited condition) doconventional models with zero-order kinetics predict linearremoval profiles along the column. However, the reaction-limited condition is not realistic for VPB systems with thickor active biofilms, and many conventional models have reliedinstead on a diffusion-limited condition based on an activelayer concept.

Simplified pseudo-steady-state models are only applicableto limited time periods and operating conditions where modelparameters are assumed to remain constant. However, touse these models to predict long-term VPB performance,model parameters must be modified with time, since

FIGURE 5. Predicted profiles of (a) active biomass fraction (fact) and(b) toluene concentration along the normalized biofilm thicknessin the DS-3-day bioreactor, 0.042 m from the contaminated gas inlet.The x-axis presents the dimensionless biofilm thickness; thus, adimensionless thickness of one represents the surface of the biofilm.


significant changes in biomass quantity and activity com-monly occur in these systems. The model developed in thisstudy is an important step toward simulating performanceunder a broader range of bioreactor operating conditionswithout arbitrary modification of model parameters andshould improve our capability to predict long-term perfor-mance of VPBs and system failure. This knowledge, in turn,may allow one to develop better biomass control strategiesand to determine when a supplementary control methodsuch as backwashing must be applied to maintain stablebioreactor performance.

Nomenclatureao and af specific biofilm surface area for clean bed

and bed with biofilm (m2/m3)

Cg and Cl toluene concentrations in the gas andbiofilm phases (mg/Lgas)

Cl,x)Lf toluene concentration at the biofilm inter-face (mg/Lliquid)

Df effective diffusion coefficient of toluene inthe biofilm phase (m2/h)

fmeasured experimentally measured value used forparameter estimation

f(p) simulated values using a set of estimatedparameters

H Henry’s law constant for toluene (mg/Lgas/mg/Lliquid)

J diffusive flux of toluene from the gas phaseto the biofilm (mg/m2-h)

Ks Monod half saturation constant (mg/L)

kd biomass decay rate (1/h)

kL mass transfer coefficient (m/h)

Lf and Li biofilm thickness and interface thickness(m)

N number of biofilm elements in a layer

n coordinate number of the characteristicpacking spheres in contact with a givensphere (-)

p set of estimated parameters

R characteristic packing sphere radius (m)

v superficial gas velocity (m/h)

W dimension (width) of each biofilm element(m)

wi weighting factor for the parameter estima-tion

Xact andXinact

biomass densities of the active and inactivemicrobial components (mg COD/L)

Xacti (t) andXinact

i (t)biomass densities of the active and inactive

microbial components in the ith biofilmelement at time t (mg/L)

Xtotali sum of the active and inactive microbial

components in the ith biofilm element(mg/L)

Xset maximum biomass density allowable in abiofilm grid element (mg/L)

Xexcess excess biomass quantity grater than Xset ina biofilm grid element (mg/L)

Xacti (t*) andXinact

i (t*)

biomass densities of the active and inactivemicrobial components in the ith biofilmafter the excess biomass quantity hasbeen transferred from the element (mg/L)

Yact yield coefficient of Xact (mg CODbiomass/mgtoluene)

Greek Letters

â formation coefficient of Xinert (-)

εo and εf clean bed porosity and bed porosity of thepacked column (m3 void space/m3 reac-tor volume)

φ sphericity factor of pelletized packing ma-terials (-)

µm maximum growth rate of Xact (1/h)

AcknowledgmentsThis research was funded by the U.S. Environmental Protec-tion Agency (Grant No. R826168-01-0) and the StrategicEnvironmental Research and Development Program (GrantNo. F08637-98-C-6005). The results and conclusions ex-pressed in this publication are solely those of the authorsand do not necessarily reflect the view of the sponsors. Theauthors would also like to thank the anonymous reviewersfor their helpful comments.

Supporting Information AvailableFigures showing (1) schematic of the experimental bioreactorsystem, (2) an example of the model parameter estimationprocess, and (3) results of the sensitivity analysis for theestimated model parameters. These materials are availablefree of charge via the Internet at http://pubs.acs.org.

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Received for review July 20, 2001. Revised manuscript re-ceived March 27, 2002. Accepted April 5, 2002.

ES0156183


a model to predict long-term performance of vapor-phase bioreactors: a cellular automaton approach

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