Environ. Sci. Technol. 2000, 34, 2318-2323
Parameter Estimation in Biofilter Systems CRISTINA ALONSO, XUEQING ZHU, AND MAKRAM T. SUIDAN* Department of Civil and Environmental Engineering, University of Cincinnati, Cincinnati, Ohio 45221-0071 BYUNG R. KIM Chemistry Department, Ford Research Laboratory, Dearborn, Michigan 48121 BYUNG J. KIM U.S. Army Construction Engineering Research Laboratory, Champaign, Illinois 61820
The purpose of this research is to estimate the unknown parameters of a mathematical model of the biodegradation of volatile organic compounds (VOCs) in a gas phase tricklebed biofilter, using experimental results from a tworeactor pilot-scale system treating the VOC diethyl ether. The model considers a dynamic three-phase system, (biofilm, water, and gas), nonuniform bacterial population, and one limiting substrate. The nonlinear parameter estimation was done in two stages: estimates of the steady-state model parameters were obtained first, and then, these values were used in the estimation of the remaining parameters. Experimentally obtained biofilter performance curves and batch tests were used for the estimation of the steadystate parameters: maximum rate of substrate utilization (µmXf/Y), Monod constant (Ks), and biofilm/water diffusivity ratio for ether, rd. Dynamic biofilter performance data were used to obtain the estimates of the six remaining parameters: yield coefficient (Y). maximum growth rate (µm), rate of decay (kd), rate of biomass maintenance (b), initial fraction of active biomass (fa0 ) Xf/Fs), and coefficient of detachment (Cdet). Using the biofilter performance curves, the value of µmXf/Y was uniquely determined, but the estimates of the parameters Ks and rd were highly correlated. High values of Ks and rd gave similar results as low values of both parameters. Batch tests using the bacterial population from the reactor and ether as the only substrate were used to determine the value of Ks without diffusional interferences.
Introduction Although biofiltration has emerged as a reliable and costeffective technology for the control of VOC emissions, biofilters are living systems subject to dynamic changes, so they are still more difficult to control and design than traditional technologies. More fundamental knowledge of the processes that control reactor performance is needed to consolidate biofiltration as the choice for VOC control. This work analyzes the biofiltration process using experimental data and a mathematical model. * Corresponding author telephone: (513)556-3695; fax: (513)5562599, e-mail:
[email protected]. 2318
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Since the model of Jennings et al. (1) was first adapted to a gas-phase biofilter, a number of investigators have focused on this area. The transient model proposed by Shareefdeen and Baltzis (2) and Zarook et al. (3) considered oxygen limitations and variable biofilm thickness along the reactor with steady biofilm thickness and biomass density. Deshusses et al. (4) proposed dynamic multiple substrate degradation, assuming no net growth of biomass in the biofilter. Alonso et al. (5, 6) developed a dynamic model that studied the effect of biomass accumulation in the reactor. This model is enhanced here with the addition of new features. Two biofilm components are considered: active and inactive biomass. Both biomass fractions vary with time and along the reactor depth. One of the main concerns in mathematical modeling of biological systems is the determination of the unknown model parameters, such as bacterial kinetic parameters and physical variables. While in certain cases these values can be assumed or taken from published results, in the general case, they have to be estimated using experimental data and nonlinear techniques. For attached biomass systems, both biofilter and batch experiments can be used in the estimation of microbial kinetic parameters. In a batch test, the bacterial population from the reactor is dispersed in an aqueous solution in a closed completely mixed reactor with the contaminant as the only limiting substrate. Diks and Ottengraf (7) and Shareefdeen et al. (8) obtained some of the kinetic parameters of the biofilter bacterial population from the batch test, and the remaining unknown parameters were obtained from related literature. Deshusses et al. (4) and Alonso et al. (6) used degradation experiments in biofilters to estimate the unknown biofilter parameters. Both biofilter and batch experiments were used in this research. Earlier work by Alonso et al. (6) included the estimation of the unknown parameters of the biodegradation of toluene in a trickle-bed biofilter system with four reactors packed to a depth of 112 cm. The mathematical model calibrated with the estimated parameters was then used to simulate the effect of biomass accumulation and the variation of specific surface area on biofilter performance under different operational conditions. A different parameter estimation approach is presented here. Unlike the work described before (6), where the parameter estimation was not the main objective of the research, the purpose of this work is the precise and reliable estimation of the unknown parameters of the system in order to validate the improved mathematical model. Thus, a higher number of data points are used to increase the reliability of the parameter estimates. Experiments specifically designed for this purpose were conducted under very controlled conditions. The biofilters packed length was 11 cm. The smaller length of the biofilter allows for a low contaminant removal efficiency that will keep the VOC concentrations at the inlet and at the outlet of the biofilter similar in magnitude, thus ensuring a somewhat uniform biomass growth along the bed. To maximize the level of confidence, the steadystate parameters were determined before estimation of the dynamic parameters.
Methodology Experimental Apparatus. Biofilter System. Two pilot-scale trickle-bed biofilters packed with pelletized diatomaceous earth biological support media (Celite 6 mm R-635 BioCatalyst Carrier) to a length of 11 cm were used in this work (Figure 1A). The internal diameter was 76 mm. Diethyl ether (C2H5OC2H5) was selected as the model VOC. A 1 L/day 10.1021/es990329o CCC: $19.00
2000 American Chemical Society Published on Web 04/29/2000
FIGURE 1. Experimental setup. (A) Schematic of the trickle-bed system. (B) Schematic of the chemostat system used for the batch test. nutrient solution containing all necessary macronutrients, micronutrients, and buffers was added to the reactors. Nitrate was the sole nitrogen source. The temperature was maintained constant at 27 °C, and the outlet pressure was very close to atmospheric pressure. The biofilters were operated in a co-current gas/liquid downward flow mode. The biofilters were seeded with a diethyl ether-acclimated enriched aerobic microbial culture from a bench-scale activated sludge system receiving 2,4-diaminotoluene, ethanol, acetic acid, and diethyl ether (9). Excess biomass was removed using backwashing of the reactor with water and full media fluidization. An extensive description of this system can be found in Rihn et al. (10) and Zhu et al. (11). Loading rates varied from 4.5 to 53.4 kg of COD/m3 day, with 5-, 10-, and 20-s empty bed residence time (EBRT). Chemostat Reactor. A 12-L stainless steel chemostat with several sampling ports was used in this study (Figure 1B). The contents of the reactor were kept completely mixed with a magnetically coupled variable speed mixer. The temperature of the reactor was maintained constant at 27 °C. The chemostat was seeded with a mixed culture from an operating trickle-bed biofilter treating diethyl ether for 4 years. Backwash water was used for this purpose. The nutrient solution is the same as in the biofilter system. Reagent-grade diethyl ether was the sole source of organic carbon. Analytical Methods. Rihn et al. (10) provide an extensive description of the analytical methods. The concentrations of ether in the gas phase were measured with a gas chromatograph (HP 5890, series II, Hewlett-Packard) equipped with a flame ionization detector (FID) (Hewlett-Packard). The gas chromatograph used to measure the liquid-phase ether concentrations was equipped with a liquid sample concentrator (LSC 2000, Tekmar) and a photoionization detector (PID) (model 4430, OI Corp.). Volatile suspended solids (VSS) were analyzed according to ref 12.
To measure biofilm thickness and biofilm density, three samples, each with 30 packing solids covered with biofilm, were taken from the biofilter. Samples were baked at 103 and 500 °C; they were weighed each time to determine the biofilm VSS. The biomass density in the biofilm was calculated from the biofilm dry density (VSS per unit volume of biofilm), assuming that the biofilm water content is 90%. This value is the average of values measured in this system ranging from 85 to 95%. The volume of the pellets with and without biofilm (clean after baking at 500 °C) was determined by covering the sample with a known amount of water and measuring the total volume of the water plus the pellets. The difference is then the volume of the pellets. Assuming that both clean and biofilm-covered packing pellets are equivalent spheres, their radii are computed from the volume values. The biofilm thickness is the difference between both radii. Mathematical Model. The biodegradation of VOC in a trickle-bed biofilter packed with uniform synthetic solids is described with a mathematical model that defines the dynamic consumption of one limiting organic substrate (VOC pollutant) in nonhomogeneous biomass (active and inactive) by one type of microbial species with no limitations of oxygen and nutrients. This model constitutes an improvement of the mathematical model presented in Alonso et al. (5, 6). In the previous model, the biomass concentration in the biofilm (Xf) was assumed to be uniform along the reactor and constant with time. The current model includes two biofilm components, active and inactive (or inert) biomass, and allows for the variation of biomass fractions with time, inside the biofilm and along the reactor depth. Three microbial processes are included: growth, decay, and a new one, endogenous respiration or biomass maintenance that, unlike decay, causes loss of active biomass without transforming it into inactive biomass. The equations already presented in Alonso et al. (5, 6) are summarized in the Supporting Information. The new equations are described next. Assuming that the density of the active and inactive biomass, Fs, is equal and constant, if fa and fi are the local volume fraction of the biofilm occupied by active and inactive biomass respectively (fa + fi ) 1), then the concentration of active biomass in the biofilm can be expressed as Xf ) Fs fa. The rates of production of active and inactive biomass per unit volume of biofilm (ra and ri) due to microbial growth (µm), endogenous respiration (b), and decay (kd) are given by
(
ra ) X f µ m
)
Cf - b - kd Lf + Ks
ri ) Xfkd
(1)
Following the formulation in Gujer and Wanner (14), the mass balance equations for Xf and Lf are
∂Xf 1 ∂ ) - 2 (r2Ja) + ra ∂t r ∂r
Ja ) νsXf
2 1 ∂(r νs) ra + ri ) Fs r 2 ∂r
at x ) Lf
(2)
dLf(t) ) νs|x)Lf + udet(z,t) dt
where Ja is the flux of active biomass in the biofilm per unit cross sectional area due to advection, and vs is the solidphase velocity resulting from volume change in the solid phase (active and inactive biomass). Neglecting biomass attachment, the variation of the biofilm thickness with time is due to vs and the detachment velocity (udet). Substituting the values of ra, ri, and vs, the equations become VOL. 34, NO. 11, 2000 / ENVIRONMENTAL SCIENCE & TECHNOLOGY
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(
)
∂Xf 1 ∂Xf Cf Xf2 µm -b )∂t Fs Cf + K s ∂r r 2 Cf Cf r Xf µm - b r 2 dr + Xf µm - b - kd Rp F C + K C s f s f + Ks
(
∫
)
∂Lf 1 ) ∂t (Rp + Lf)2
∫
Rp+Lf
Rp
(
(
)
)
Xf Cf µm - b r 2 dr + udet(z,t) (3) Fs Cf + K s
at t ) 0
Xf(r,z,0) ) Xf0
Lf(z,0) ) Lf0(z)
For r ) Rp, the term with the r derivative is null, so the equation itself provides the boundary condition. Table 1 shows the value of the known and estimated model parameters. Numerical Solution. The two-dimension system of coupled partial differential equations that defines the problem is solved using finite differences equation discretization implemented with a C computer program. A factor to consider here is the characteristic times of the processes. The bacterial growth is a much slower process than the diffusion and reaction of the dissolved compounds. This difference in times causes the stiffness of the equation system, but it also makes the assumption of quasi-steady-state acceptable. Dissolved compounds concentration profiles are calculated assuming fixed biomass distribution and biofilm thickness, and variations in the microbial distribution and biofilm thickness are calculated assuming steady-state dissolved compounds concentration profiles. Both problems were solved, and since the solutions were not significantly different, the quasisteady-state method was used without loss in accuracy to save computational time. Nonlinear Parameter Estimation Technique. Weighted least-squaresd errors was used. The parameter estimation problem is then
minimize SSE(p) ) n f i,measured - fi(p)
∑ i)1
(
wi
pj,min e pj e pj,max
)
2
p ) (p1, ..., pm) (4)
j ) 1, ..., m
where SSE is the weighted sum of squared errors function that has to be minimize, p ) (p1, ..., pm) is the set of parameters that need to be estimated, subject to the constraints pj,min e pj e pj,max; and fi,measured, fi(p), and wi are the measured value, the value calculated with the mathematical model for the set of parameters p, and the weighting factor, respectively. The parameter estimation is performed using an algorithm for solving constrained nonlinear optimization problems implemented in a C code called CFSQP (C code for Feasible Sequential Quadratic Programming) by Lawrence et al. (15).
Results The parameters of the steady-state model were estimated first, and the calculated values were used in the estimation of the remaining parameters that appear in the dynamic model. Steady-State Parameter Estimation. Reactor performance curves were used to estimate three steady-state parameters: maximum rate of substrate utilization (µmXf/ Y), Monod constant (Ks), and biofilm/water diffusivity ratio (rd). The performance curve represents the biofilter performance for different loads measured in a short period of time so the conditions can be considered stable and the system at steady state. Since these data were insufficient to uniquely 2320
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FIGURE 2. Variation of the minimum SSE as a function of rd and Ks. The points of this graph were obtained fixing the parameters rd and Ks and allowing mmXf/Y to vary to minimize SSE. estimate all the parameters, batch experiments were conducted to estimate Ks without the interference of mass transfer limitations. Reactor performance curves were obtained for three different values of the detention time: 5, 10, and 20 s. Five biofilter loadings were used: 4.5, 8.9, 17.8, 35.6, and 53.4 kg of COD m-3 day-1. The whole experiment was carried out in 5 days using two identical bench scale biofilters. On day 1, the reactors were loaded with the same amount of biofilmcovered media and were backwashed, so the initial state of the two biofilters was assumed to be equal. The experiment was replicated running both biofilters in parallel. Days 2-4 were dedicated to 20-, 10-, and 5-s EBRT, respectively. On day 5, the biofilters were opened, and the biofilm thickness and biomass density were measured as explained before. Using the results from both biofilters, the averaged biomass density in the biofilm (39.5 kg of COD/m3) and averaged biofilm thickness (0.01314 cm) were calculated. These values were assumed to be representative of the whole period. The reactor performance was described with the contaminant removal efficiency. To obtain the performance curve, the middle load (17.8 kg of COD m-3 day-1) was used as a reference. The performance of the reactors was evaluated after running for at least 8 h with this load. The load was then changed, and the efficiency was measured after 2 h. Previous experiments showed that 2 h is enough time for the biofilter performance to stabilize. The load was changed back to the reference, and the efficiency was measured after another 2 h. This technique assured that the state of the biofilters did not change during the experiment. Equation 4 was used in the nonlinear parameter estimation, with the measured values as weighting factors. Figure 2 shows the minimum value of SSE obtained fixing rd and Ks and allowing µmXf/Y to vary. Each curve in the graph corresponds to a value of Ks. For each Ks, different values of rd are selected, and the SSE is minimized with respect to the only parameter not fixed, µmXf/Y. For each Ks, there is a value of rd that gives a minimum SSE. It can be observed that different values of Ks and rd give close minimum values of SSE and similar model fits (Ks ) 0.1 mg of COD/L, rd ) 0.14, SSE ) 0.0488; Ks ) 15 mg of COD/L, rd ) 2, SSE ) 0.03). The minimum SSE for each Ks is obtained with very close values of µmXf/Y, ranging from 83 to 97 kg of COD m-3 day-1. These results suggest that a reliable estimate can be obtained for µmXf/Y but not for Ks and rd. A batch spike test was conducted with the objective of determining the real value of the Monod kinetic constant. The chemostat was seeded with a fresh culture taken from
TABLE 1. Estimated Parameter Values and Known Model Valuesa estimated parameter values name and symbol
estimated value
Monod constant, Ks biofilm/water diffusivity ratio, rd ) Df/Dw yield coefficient, Y max growth rate, µm decay rate coefficient, kd biomass maintenance rate, b initial fraction of active biomass, fa ) f1(t ) 0) detachment coefficient, Cdet
0.1 mg of COD/L 0.04 mg of VOC/L 0.14
∆SSE 2.92 -1.97
0.19 g of COD/g of COD 0.35 g of biomass/g of VOC 0.38 day-1 0.035 day-1 0.1 day-1 0.97 0.06 day-1
known model values biofilter packing length ether diffusivity in water (25 °C), Dw ether Henry’s constant, H
17.75 28.72 0.99 8.68 13.26
water flow, Qw empty bed porosity, 0 characteristic sphere radius, Rp no. of contacting spheres, n characteristic sphere sphericity, φ
11 cm 0.85 10-5 cm2/s 0.034 (mg/L)gas/ (mg/L)water 1 L/day 0.34 0.3 cm 9 0.87
1.28
The average Y observed in dynamic experiment was 0.135 g of COD/g of COD. ∆SSE ) (SSEj - SSE0)/SSE0 × 100. SSE0 obtained with the estimated parameters, and SSEj obtained when parameter j is varied 1%. a
FIGURE 3. Batch test results. Specific rate of diethyl ether consumption in the batch reactor as a function of the concentration of diethyl ether in the water phase, assuming constant amount of biomass in the reactor during the experiment. the backwash liquid of the biofilters and was spiked with known amounts of ether substrate. The liquid and gas volumes in the chemostat were 4.0 and 8.0 L. Given these conditions and since high mixing was provided, it was assumed that the concentration of oxygen was not a limiting factor in this study. Figure 3 shows the batch test results as the specific rate of ether consumption, that is, the rate divided by the value of VSS in the reactor versus the concentration of ether in the water phase. The rate of ether consumption is obtained from the mass balance equation in the completely mixed reactor assuming that there is no biomass decay; therefore, the active biomass concentration in the reactor (Xf) remains constant during the duration of the experiment. If Vw and Vg are the volume of water and gas in the reactor, respectively, and CwVw+ CgVg is the total mass of ether in the chemostat:
[
] ]
d(CwV2 + CgVg) Cw µmXf V w )dt Y K s + Cw w µmXf dCw Vg dCg Cw rate ) ) (5) + dt Vw dt Y Ks + Cw
[
[
]
Although the value of the active biomass in the reactor cannot be measured, it can be assumed constant during the experiment since the initial and final VSS in the reactor were found not to be significantly different. These VSS values are shown in Figure 3. Because it was not possible to collect
FIGURE 4. Model fitted values (lines) using the estimated parameters and experimental results used in the parameter estimation (symbols). (A) Biofilter performance curves for 5-, 10-, and 20-s detention time. (B) Dynamic biofilter performance for 5-, 10-, and 20-s detention time. Daily removal efficiency and biofilm thickness at the beginning and end of each run. enough data in the low range of ether concentrations in the water phase, only an upper limit for the Monod kinetic constant was obtained. From eq 5, when Ks ) Cw, the rate is half of the maximum rate. The averaged maximum specific rate and half of it are shown in Figure 3. The line Cw ) 1 mg/L approximately intersects the plot at half of the maximum rate. Then, it can be concluded that Ks e 1 mg/L ) 2.6 mg of COD/L, and the higher values of Ks and rd suggested by Figure 2 are not realistic. From Figure 2, for Ks < 2.6 mg of COD/L, the minimum SSE is obtained for Ks e 0.1 mg of COD/L. Ks ) 0.1 mg of COD/L and rd ) 0.14 were the values selected since the results for lower values of Ks were similar. Figure 4A shows the observed and model fitted values of biofilter performance curves obtained with the selected set VOL. 34, NO. 11, 2000 / ENVIRONMENTAL SCIENCE & TECHNOLOGY
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of parameters. Error bars in the data points represent the standard deviation. Dynamic Model Parameter Estimation. Once the parameters that appear in the steady-state model were known, the six remaining unknown parameters were estimated: yield coefficient (Y), maximum growth rate (µm), decay rate coefficient (kd), biomass maintenance rate coefficient (b), initial fraction of active biomass (fa(t ) 0) ) Xf0/Fs), and coefficient of detachment (Cdet). The dynamic performance of two biofilters loaded with 17.8 and 8.9 kg of COD m-3 day-1, respectively, was monitored for three different values of the detention time, 5, 10, and 20 s. In the following discussion, the operation of a biofilter corresponding to a specific value of the detention time is going to be referred to as a run. The duration of each run was as follows: 10 days for 10 s, 14 days for 5 s, and 16 days for 20 s. During each run, the biofilters were continuously operated without backwashing, so the mathematical model could be used to simulate a controlled system isolated from external influences. The first day of each run both reactors were loaded with the same amount of biofilm-covered media and were backwashed. The biofilm thickness and biofilm dry density were measured before backwashing on the first day of the experiment and at the end of each run. Since the media from both biofilters were mixed before they were loaded, the initial biofilm thickness for each run was assumed to be the average of the values measured in both biofilters. Uniform biofilm thickness along the reactor was assumed. On the basis of data from the measurement of VSS in the backwashing liquid, the average reduction in the biofilm thickness due to backwashing is 8%. Therefore, the biofilm thickness measured before backwashing was corrected using this value. The biofilter removal efficiency was monitored daily. The nonlinear parameter estimation technique described above (eq 4) was used. The daily reactor removal efficiency and the initial and final biofilm thickness for each run were the measured values. The weighting factors for biofilm thickness measurements were the corresponding standard deviations, which were between 4% and 11% of the measured biofilm thickness. For the removal efficiency, 10% of the measured value was used as weighting factor, since the standard deviation was unknown. In this way, the weighting factors for both type of data are in the same range and less weight is given to each individual efficiency value, since they are higher in number than the thickness values. This empirical method was used because the model fitted results were visually better in following the trend of the data. Since the biofilters needed some time to stabilize after the detention time was changed, the first 2 days of each run were not used in the estimation process. Figure 4B shows the experimental results and the fitted values of the reactor removal efficiency with time and the initial and final biofilm thickness for each run for both biofilters. Since the biofilm density for each biofilter and run was different, the value measured at the end of the run was used in the model: for biofilter 1, Fs was 31.4, 31.7, and 28.8 kg of COD/m3 for 10, 5, and 20 s, respectively; for biofilter 2, Fs was 33.4, 31.3, and 30.3 kg of COD/m3 for 10, 5, and 20 s, respectively. For each run after the first one, the initial biofilm thickness and fraction of active biomass were calculated in the model as the average of the values in both reactors at the end of the previous run. The biofilm thickness was reduced 8% to account for the effect of backwashing. The value of the maximum rate of substrate utilization (µmXf/Y) obtained before could not be used directly because Xf is not the same in both experiments (steady and dynamic) and cannot be measured. Since µmXf/Y ) 83.5 kg of COD m-3 day-1 and Fs ) 39.5 kg of COD/m3 are known in the steadystate experiment, a relationship can be obtained and used in the estimation process: 2322
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Xf ) faFs w Xf ) 39.5fa kg of COD/m3 µmXf µm fa kg of COD ) ) 39.5 Y Y m3 83.5
kg of COD µm fa w 2.11 day-1 (6) Y m3 day
0 e fa e 1 w 2.11 day-1 e
µm Y
Table 1 summarizes the value of the estimated parameters and the known variables used in the model.
Discussion The dynamic mathematical model of the biodegradation of VOCs in a gas phase trickle-bed biofilter has been validated with the estimation of the unknown parameters of the system. The parameters that play a role when the steady-state model is used were estimated first. Then the dynamic biofilter performance was used to estimate the remaining parameters that are relevant only when the dynamic form of model is used. The reliability of the estimates is increased when the estimation is performed in two steps, as opposed to determining all the parameters at the same time, because a lower number of parameters are estimated simultaneously; therefore, the interactions between parameters that are correlated decrease. The disadvantage of this technique is that the parameters that are initially estimated have a high influence in the ones estimated afterward, the inaccuracies in the first step are transmitted to the second, and there is no possibility of modifying the initial parameters with the second set of data. In this case, using the biofilter performance curves the estimates of the parameters Ks and rd were highly correlated, so batch tests using the bacterial population from the reactor were used to determine the value of Ks without diffusional interferences. Therefore, the estimation of Ks with batch tests is critical in the parameter estimation process since it determines the value of rd and the value of the dynamic model parameters. To determine the most critical dynamic parameters in the estimation process, a sensitivity analysis of the model was performed. The impact of each parameter was measured as the percentile variation of SSE when each parameter is modified 1% while keeping the others constant. The results of this study are presented in the third columns of Table 1 as ∆SSE. The most influential parameters are the ones with the highest impact values, in this case µm and Y. The impact of Ks and rd is also included. It can be observed that the value of ∆SSE for rd is negative, meaning that increasing this parameter results in a decrease of the SSE, confirming one of the disadvantages of the parameter estimation in two steps. This analysis indicates which parameters should be more accurately evaluated. The mathematical model and estimated parameters were used to predict the performance of a full-length biofilter. Figure 5 summarizes these results and the reactor operating conditions. The biofilter performance was measured after opening the biofilter, mixing the media, and reloading it again, so the biofilm thickness and biomass density were considered uniform along the biofilter. These values were measured before the biofilter was loaded, and their averages were used in the program. The fit of the model for the dynamic biofilter performance are better than those for the biofilm thickness (Figure 4B). This suggests that more attention could be paid to the expression used for detachment; it is possible that a different expression could work better. Future work includes the incorporation of backwashing of the biofilter into the model so that the dynamic performance of operating biofilters using
Rp
characteristic packing sphere radius
u0
gas approach velocity to the biofilter
udet
velocity of detachment
vw, vw, vg water velocity, average water velocity, and average gas velocity Xf
active biomass density in the biofilm (also used as active biomass density in the batch reactor)
Y
yield coefficient
Greek Letters
FIGURE 5. Measured and predicted performance of a full-length biofilter. The biofilter system is described in ref 11. The estimated model parameters were used to predict the contaminant removal efficiency along the bed. backwashing can be predicted. An analysis of the predicting capabilities of the calibrated model would be very valuable if the model is going to be used for prediction and design.
Acknowledgments This research is sponsored by a contract from the U.S. Army Construction Engineering Research Laboratory and by the Ford Motor Company. We want to acknowledge C. T. Lawrence, J. L. Zhou, and A. Tits, the authors of CFSQP routine, for allowing its free use in research and development.
Nomenclature A
biofilter cross-sectional area
a0, af
specific surface area per unit volume of reactor, for clean bed and for bed with biofilm
b
biomass maintenance rate coefficient
Cdet
detachment coefficient
Cf, Cw, Cg biofilm, water, and gas-phase VOC concentrations Df, Dw
VOC diffusivity in biofilm and water. respectively
fa, fi
local volume fractions of active and inactive biomass in the biofilm
H
Henry’s law constant
Jw
flux of VOC into the water layer
Ks
Monod saturation constant
kd
decay rate coefficient
Lf, Lw
biofilm and water layer thickness
n
number of characteristic packing spheres in contact with a given one
Qg, Qw
gas and water flow rate
rd
ratio between VOC diffusivities in biofilm and water
0, f
clean bed porosity and bed porosity with biofilm
φ
sphericity of packing solids
µm
maximum growth rate
Fs
biomass density (active and inactive) in the biofilm
Supporting Information Available An appendix summarizing the features of the Alonso et al. model (5, 6) that are used in the current mathematical model (3 pages). This material is available free of charge via the Internet at http://pubs.acs.org.
Literature Cited (1) Jennings, P. A.; Snoeyink, V. L.; Chian, E. S. K. Biotechnol. Bioeng. 1976, 18, 1249-1273. (2) Shareefdeen, Z.; Baltzis, B. C. Chem. Eng. Sci. 1994, 49 (24A), 4347-4360. (3) Zarook, S. M.; Shaikh, A. A.; Ansar, Z. Chem. Eng. Sci. 1997, 52 (5), 759-773. (4) Deshusses, M. A.; Hamer, G.; Dunn, I. J. Environ. Sci. Technol. 1995, 29, 1048-1058. (5) Alonso, C.; Suidan, M. T.; Kim, B. R.; Kim, B. J. Environ. Sci.Technol. 1998, 32, 3118-3123. (6) Alonso, C.; Suidan, M. T.; Sorial, G. A.; Smith, F. L.; Biswas, P.; Smith, P. J.; Brenner, R. C. Biotechnol.. Bioeng. 1997, 54, 583549. (7) Diks, R. M. M.; Ottengraf, S. P. P. Bioprocess Eng. 1991, 6, 9399, 131-140. (8) Shareefdeen, Z.; Baltzis, B. C.; Oh, Y. S.; Bartha, R. Biotechnol. Bioeng. 1993, 41, 512-524. (9) VanderLoop, S. L.; Suidan, M. T.; Moteleb, M. A.; Maloney, S. W. Water Res. 1999, 33, 1287-1295. (10) Rihn, M. J.; Zhu, X.; Suidan, M. T.; Kim, B. J.; Kim, B. R. Water Res. 1997, 31, 2997-3008. (11) Zhu, X.; Rihn, M. J.; Suidan, M. T.; Kim, B. J.; Kim, B. R. Water Sci. Technol. 1996, 34 (3-4), 573-581. (12) Standard Methods for the Examination of Water and Wastewater, 18th ed.; American Public Health Association: Washington, DC, 1992. (13) Alonso, C. Ph.D. Thesis, University of Cincinnati, 1999. (14) Characklis, W. G.; Marshall, K. C. Biofilms; John Wiley & Sons: New York, 1990; p 423. (15) Lawrence, C. T.; Zhou, J. L.; Tits, A. User’s Guide for CFSQP Version 2.5: A C Code for Solving (Large Scale) Constrained Nonlinear (Minimax) Optimization Problems, Generating Iterates Satisfying All Inequality Constraints; Technical Report TR-94-16r1; Institute for Systems Research, University of Maryland, College Park, MD, 1997.
Received for review March 23, 1999. Revised manuscript received March 7, 2000. Accepted March 20, 2000. ES990329O
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