Numerical Model for Biological Fluidized-Bed Reactor Treatment of

A numerical BFBR model based upon basic physical, chemical, and biological processes including reaction stoichiometry, biofilm kinetics, and sequentia...
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Environ. Sci. Technol. 2005, 39, 850-858

Numerical Model for Biological Fluidized-Bed Reactor Treatment of Perchlorate-Contaminated Groundwater P E R R Y L . M C C A R T Y * ,† A N D TRAVIS E. MEYER‡ Department of Civil & Environmental Engineering, Stanford University, Stanford, California 94305-4020, and Richard P. Arber Associates, 1128 Grant Street, Denver, Colorado 80203

Biological fluidized-bed reactor (BFBR) treatment with 1.3 mm granular activated carbon as support medium is being used for removal of 2.6 mg/L perchlorate from contaminated groundwater in California. The California drinking-water action level of 4 µg/L for perchlorate requires 99.9% perchlorate removal. Sufficient ethanol, the electron donor, is added to remove oxygen and nitrate as well as perchlorate, as all three serve as electron acceptors, but with biological preference for oxygen and nitrate. A numerical BFBR model based upon basic physical, chemical, and biological processes including reaction stoichiometry, biofilm kinetics, and sequential electron acceptor usage was developed and evaluated with the full-scale treatment results. A key fitting parameter was bacterial detachment rate, which impacts reaction stoichiometry. For best model fit this was found to vary between 0.062 and 0.31 d-1, with an average of 0.22 d-1. The model indicates that GAC particle size, reactor diameter, and perchlorate concentration affect BFBR performance. While empty-bed detention time might be decreased somewhat below 10 min by an increase in either GAC particle size or reactor diameter, the current design provides a good factor of safety in operation. With a 10 min detention time, the effluent goal of 4 µg/L should be achievable even with influent perchlorate concentration as high as 10 mg/L.

Introduction Perchlorate (ClO4 -) is a groundwater contaminant of wide and growing concern (1-3). It inhibits thyroid function and has potential for carcinogenic, neurodevelopment, reproductive, and immunotoxic effects. Perchlorate is widely used in industry, especially as an oxidant in rocket fuels, flares, and fireworks, uses that are the primary causes of groundwater contamination. It is also used in automotive air bags, matches, batteries, and analytical chemistry. Although no national drinking water standard is yet available, the California Department of Health Services established an action level of 4 µg/L based upon a drinking water goal of 1 µg/L put forth by the U.S. Environmental Protection Agency. In a draft report for peer review, the California Environmental Protection Agency (4) proposed that a Public Health Goal for * Corresponding author phone: (650)723-4131; fax: (650)725-3164; e-mail: [email protected]. † Stanford University. ‡ Richard P. Arber Associates. 850

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perchlorate in drinking water be set in the 2-6 µg/L range. This range is near the current analytical reporting limit for perchlorate. Removal of perchlorate through biological reduction to chloride is one of the treatment methods used either in-situ or in above-ground reactors (5, 1-3, 6). Above-ground reactors used for perchlorate removal include fixed-bed (718), fluidized-bed (19, 20), and membrane reactors (21, 22). The fluidized-bed reactor was selected for model development here because full-scale operational data were available for its evaluation. However, the basic principles used may apply to other biological treatment systems as well. Biological fluidized-bed reactors (BFBR) have been widely used for treatment of contaminated water (23) and have been shown to have potential for removal of perchlorate (19, 20, 24). An industrial site in California serves as an example (19, 20). To address perchlorate contamination in the groundwater, a treatability study was conducted with four BFBRs operating at design flow rates of up to 5.5 m3/min (2.0 million gal/d) for the biological reduction of perchlorate to chloride. Reduction of about 2600 µg/L perchlorate to below the 2-4 µg/L analytical reporting limit (>99.9% reduction) was obtained using granular activated carbon (GAC) as support media and a minimum evaluated empty-bed detention time of 12 min. One of the objectives of this study was to develop an easy to use, but fundamentally based, numerical simulation model containing parameters of importance and to use the results of the treatability study to validate the model. The model was developed using a spreadsheet. Once developed and evaluated with the full-scale results, the model was used to ascertain the effects of water quality characteristics, GAC size, and reactor diameter on process performance. This evaluation may prove useful in applying this technology at other locations with different reactor configurations and water quality conditions. Also, the model may serve as an important design tool for evaluating, sizing, and configuring new perchlorate treatment systems. The numerical model takes into consideration the observation that microorganisms that use perchlorate as an electron acceptor can also use oxygen and nitrate as electron acceptors (9, 10, 25-30). While any of the three electron acceptors can be used in energy metabolism, the order of preference is oxygen, nitrate, and then perchlorate. In other words, to reduce perchlorate to chloride, sufficient electron donor must be present to reduce oxygen and nitrate as well. An important consideration in design then is that sufficient electron donor be present for reduction of all three electron acceptors. However, if more electron donor than required is added, then an excess of donor will be present in the reactor effluent, which can lead to other water quality problems. Also, since microorganisms can utilize sulfate as an electron acceptor, excess donor may lead to unwanted sulfate reduction to sulfide within the reactor. The operational problem then is to add sufficient donor, but no more than absolutely required. For this reason, reaction stoichiometry is an important component of the model and its evaluation.

Reactors The groundwater being treated contained oxygen and nitrate (Table 1), and these were removed in the BFBRs along with perchlorate. The groundwater was also contaminated with chlorinated aliphatic compounds, such as trichloroethene (TCE) and nitrosodimethylamine (NDMA), which also had to be removed from the groundwater. While some removal of the chlorinated aliphatic compounds did result in the BFBR during initial periods of operation due to adsorption onto 10.1021/es040303j CCC: $30.25

 2005 American Chemical Society Published on Web 12/24/2004

TABLE 1. Quality Characteristics of Groundwater Treated by the BFBRs constituent

mg/L

constituent

µg/L

chloride nitrate perchlorate sulfate total dissolved solids hardness (as CaCO3)

8.4 1.5 2.6 16 202 120

1400 16 8 90 3.8 0.14

alkalinity

120

trichloroethene cis-1,2-dichloroethene 1,1-dichloroethene chloroform 1,4-dioxane nitrosodimethylamine (NDMA) pH

7.2

the activated carbon media, this removal decreased significantly with time as the media became saturated with these compounds. For TCE an initial removal of 65% decreased linearly over a 6-month period to about 5%. Thus, to accomplish the overall treatment required for these compounds, a train of treatment processes was included in the site evaluation, including multimedia filtration, air stripping, packed-bed activated carbon adsorption, and UV oxidation was required. However, the BFBR was the first process in the treatment train and is the only one that addressed the perchlorate contamination, and so it is the only process discussed here. The BFBRs consisted of cylindrical stainless steel bioreactors, 4.27 m in diameter and 6.7 m tall containing 20 100 kg of 1.2-1.4 mm diameter granular activated carbon (GAC) as the support media (Table 2). Assuming bacteria colonize the outside surface of the spherical GAC particles only, the calculated surface area available to them in a single reactor was 63 000 m2. The influent groundwater was fed into the bottom of each reactor through a network of nozzles. Each activated carbon bed had a settled depth of 2.75 m but was fluidized during operation to a desired operating height of 4.6 m, which for the activated carbon particles used required a vertical liquid flow velocity of 0.48 m/min (empty bed) to counteract the particle settling velocity. This required a total flow rate to the BFBR (system influent plus recycle) of about 6.8 m3/min. This is thus the maximum system influent flow rate allowable, otherwise media particle washout would occur. This maximum flow rate translates to a minimum empty-bed detention time (reactor volume divided by system influent flow rate) for this reactor configuration of 9.6 min. To maintain the necessary constant flow rate to the reactor when the influent flow rate was less than 6.8 m3/min, a portion of the BFBR effluent was recycled and mixed with the influent groundwater flow. In this manner, the influent plus recycle flow rate was maintained constant throughout this study at 6.8 m3/min. Lower influent flow rates would result in higher treatment efficiencies because contaminant loading to the BFBR would be reduced. As biomass accumulated on the GAC, it increased the buoyancy of the particles, causing them to rise beyond the 4.6 m operating level. To prevent GAC from exiting the reactor with the effluent, an eductor system was used to shear accumulated biomass from the GAC and return both the clean GAC particles and the sheared biomass to the BFBR. The clean GAC was less buoyant and migrated to the bottom of the BFBR where growth began to accumulate on it again. The sheared biomass became suspended and exited the reactor with the effluent.

Methods Chemical Analyses. Analyses for all constituents were by approved commercial laboratories. Nitrate was analyzed by EPA Method 300.0, perchlorate was analyzed by EPA Method 300.0 MOD-inorg, and ethanol was analyzed by EPA Method 8015M. The analytical reporting limit for nitrate was given as 11 µg/L; for perchlorate, it was given as 2-4 µg/L (average 3 µg/L); and for ethanol, it was given as 0.2 mg/L.

TABLE 2. Symbols, Variables, and Design and Coefficient Values Used for the Full-Scale BFBR Study and the Simulation Model parameter

symbol

value

units

ref

Reactor diameter total reactor height fluidized-bed height fluidization flow rate influent flow rate reactor flow rate recycle flow rate effluent flow rate

W H Hf u Qo Q Qr Qe

settled depth bulk density settled porosity dry weight mean particle diameter particle total volume

Hg Fb s M dp Vg

density viscosity operating temperature

Fw µv T

4.27 6.7 4.6 69.2 variable 6.8 variable variable

m m m m/d m3/min m3/min m3/min m3/min

design design design measured measured fixed measured measured

m kg/m3 % kg cm m3

measured measured measured measured measured calculated

kg/m3 g/cm‚d °C

36 37 measured

GAC 2.75 1.35 35 20,136 0.13 25.5

Water 999 887 19

Molecular Diffusion De 1.28 cm2/d Do 2.5 cm2/d Dn 1.59 cm2/d Dp 1.55 cm2/d Biofilma density Xf 10 mg/cm3 endogenous decay b 0.15 1/d (20°C) cell degradable fraction fd 0.80 thickness wb variable cm volume Vb variable m3 Half-Velocity Coefficientb ethanol Ke 0.01 mg/cm3 oxygen Ko 0.001 mg/cm3 nitrate Kn 0.001 mg/cm3 perchlorate Kp 0.01 mg/cm3 substrate utilization rate q 1.00 1e- equiv/ ethanol oxygen nitrate perchlorate

36 36 37 37

32 32 calculated calculated

18 32

g of cells‚d a Biofilm density is typically between 10 and 40 mg/cm3. b Halfvelocity coefficients for the electron acceptors, oxygen, and nitrate are generally lower than 1 mg/L and for simple electron donors such as ethanol are generally in the range of a few mg/L (32). Values at the low end of these ranges for biofilm density and at the high end for halfvelocity coefficients were chosen to provide more conservative modeled estimates of removal in the BFBR. However, the model was rather insensitive to these coefficients for the system and data evaluated.

Stoichiometry. A key component of the simulation model for the BFBR is reaction stoichiometry. Ethanol was added to the BFBR influent to serve as a carbon source for biomass growth and oxygen, nitrate, and perchlorate reduction. To achieve perchlorate removal, sufficient ethanol must be added in order to remove all three electron acceptors. In addition to the ethanol required for the energy reactions, some ethanol must also be used for organism synthesis and growth. A stoichiometric oxidation-reduction equation that includes biological synthesis was developed for each electron donor-electron acceptor pair. The total electron donor concentration required to reduce each electron acceptor could then be determined when the respective concentration of each electron acceptor in the contaminated water is given. The stoichiometric equations were developed using the relationship for 1 electron equivalent (e- equiv) of electron donor (31, 32):

Ri ) feiRai + fsiRc - Rd and fei + fsi ) 1

(1)

where Ri ) stoichiometric equation for 1e- equiv of electron acceptor i, Rai ) half-reaction for 1e- equiv of electron VOL. 39, NO. 3, 2005 / ENVIRONMENTAL SCIENCE & TECHNOLOGY

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acceptor i, Rdi ) half-reaction for 1e- equiv of electron donor i, Rc ) half-reaction for 1e- equiv of cell synthesis, fei ) fraction of electron donor used for energy in reaction with electron acceptor i, fsi ) fraction of electron donor used for synthesis in reaction with electron acceptor i. i is the designator for electron acceptor: o ) oxygen, n ) nitrogen, and p ) perchlorate. The half-reactions of interest for eq 1 are as follows:

Rc: 5 1 29 1 CO + NO3- + H+ + e- ) C5H7O2N + 28 2 28 28 28 11 H O (2) 28 2 1 1 1 CO + H+ + e- ) CH3CH2OH + H2O 6 2 12 4

Rd:

(3)

Rao:

1 1 O + H + + e- ) H 2 O 4 2 2

(4)

Ran:

1 6 1 3 NO3- + H+ + e- ) N2 + H2O 5 5 10 5

(5)

Rap:

1 1 1 ClO4- + H+ + e- ) Cl- + H2O 8 8 2

(6)

The coefficient fsi is a function of reaction energetics and biological solids retention time as determined from the relationship (31, 32): o fsi ) fsi

1 + (1 - fd)bθx 1 + bθx

(7)

o where f si ) maximum fraction synthesized for electron acceptor i reaction, fd ) degradable portion of bacteria, and θx ) biological solids retention time (d). From reaction thermodynamics for ethanol oxidation with o oxygen (32, 33), f si was calculated to be 0.69. Reaction thermodynamics indicates this value with nitrate as electron acceptor would be a little lower and that with perchlorate a little higher, but for simplicity, the value for these electron acceptors was taken to be the same as for oxygen. For a biofilm reactor, θx is equal to the inverse of the detachment rate, bdet (d-1) (32). The detachment rate becomes a highly important variable that significantly affects reaction stoichiometry and, thus, the quantity of electron donor required for efficient perchlorate removal. This is demonstrated by the results of full-scale evaluation. An example of a half-reaction for perchlorate developed from eqs 1 and 2 with bdet of 0.23 d-1, yielding fsp of 0.48, is

0.0833CH3CH2OH + 0.0171NO3- + 0.0650ClO4- + 0.0171H+ f 0.0809CO2 + 0.0171C5H7O2N +

0.1986H2O + 0.0650Cl- (8)

Equation 8 indicates that to remove 0.0650 mol (6470 mg) of perchlorate requires 0.0883 mol (3830 mg) of ethanol, consuming 0.0171 mol (239 mg) of nitrate-nitrogen and producing 0.0171 mol (1930 mg) of cells. The equations for oxygen and nitrate reduction are developed similarly. To be noted is that perchlorate, nitrate, and oxygen removals result in consumption of some nitrate for cell synthesis, and this nitrate need not be removed through denitrification. Such nitrate removal by cell synthesis was included in the model. Model Development. A fluidized-bed bioreactor can be considered as a biofilm process having a biofilm surface area that is a function of the surface area of the GAC particles. Such a one-dimensional steady-state biofilm simulation 852

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FIGURE 1. Conceptual model of electron donor and acceptor penetration into biofilm; (a) ethanol in excess showing effect on Swe, (b) small deficiency of ethanol showing effect on Swp, (c) large deficiency in ethanol showing full penetration of perchlorate and measurable Swn. model was developed for the sequential removal of oxygen, nitrate, and perchlorate. The model is based upon fundamental aspects of mass transfer from the fluid to the biofilm, mass transfer of electron acceptors and donor within the biofilm, reaction stoichiometry, and biofilm reaction kinetics for microorganism growth and substrate utilization. Rather than using an advective-dispersion model, dispersion was simulated by dividing the reactor into n equal-volume segments, with each volume segment being treated as a completely mixed biofilm reactor. One key aspect of the simulation model is the sequential reduction of the three electron acceptors with depth in the biofilm, starting at the surface and progressing through the biofilm to the GAC particle in the order oxygen, nitrate, and perchlorate as indicated in Figure 1. The total quantity of electron donor required is the sum total of that required for the reduction of each of the three electron acceptors as determined from reaction stoichiometry. If the donor concentration in a given volume segment is more than the required amount, then the excess will penetrate through the biofilm and will be represented by the GAC support surface or wall concentration, Swd (Figure 1a). If it is less than required, then the deficiency will be reflected in proportionally less perchlorate removal and an equivalent perchlorate wall concentration Swp (Figure 1b). If donor concentration is reduced further, then there could be no perchlorate removal and only partial nitrate removal (Figure 1c), and if donor is

reduced further, there could be no perchlorate removal or nitrate removal and only partial oxygen removal (result not shown). The relationship between substrate diffusion and rate of removal of the electron donor and each of the electron acceptors within the biofilm is provided by the following differential equation (32, 34):

qiSfiXf ∂2Sfi D ) 2 fi S ∂z fi + Ki

(9) Sii )

where Sfi ) concentration of substrate i within biofilm at locations undergoing biotransformation, Dfi ) coefficient of molecular diffusion in biofilm for substrate i (cm2/d), and Xf ) concentration of active biomass in biofilm (mg/cm3). This equation can be integrated to give the flux of substrate i into the biofilm where substrate i removal is taking place (32):

[

{

)]}

(

Jij ) 2qiXfDfi Ssij - Swij + Ki ln

Ki + Swij Ki + Ssij

1/2

(10)

where j ) designator for reactor volume segment, where j ) 1 to n; Jij ) flux of substrate i into biofilm in volume segment j (mg/cm2‚d); qi ) maximum specific rate of substrate i utilization (mg/mg‚d); Ssij ) substrate i concentration in volume segment j at biofilm depth where substrate i biotransformation begins (mg/cm3); Swij ) substrate i concentration at biofilm support (wall) surface (mg/cm3); and Ki ) substrate i concentration giving one-half the maximum rate (mg/cm3). Substrate is transferred from the bulk solution to the surface of the biofilm at a rate proportional to the difference between the substrate concentration in the bulk fluid and the biofilm surface (34):

Jij ) kmi(Soij - Ssij) )

Di Loij

(Soij - Ssij)

(11)

where kmi ) bulk water to biofilm mass transfer coefficient for substrate i (cm/d), Loij ) biofilm boundary layer length for substrate i (cm), and Di ) coefficient of molecular diffusion in water for substrate i (cm2/d). Oxygen is used first as it enters the biofilm, then nitrate utilization begins at the depth where oxygen is nearly depleted, and then perchlorate utilization begins at the depth where nitrate is nearly depleted. Nitrate and perchlorate follow simple molecular diffusion through the biofilm until reaching the depths where their consumption begins. The diffusion distances (Loij) for oxygen, nitrate, and perchlorate where thus modified from eq 11 to the following: o Loj ) Lo

o Lnj ) Ln +

o Lpj ) Lp +

[

(12)

( )

Joj Dn Ssjo Dfn qo X f Ko + Ssjo

(

)

Joj Jnj + Ssjo Ssjn qo X f qnXf Ko + Ssjo Kn + Ssjn

(

)

(

(13)

]

)

( ) Dp Dfp

(14)

The values for Li were obtained using the correlation by Jennings (1975):

Li )

where Rem ) modified Reynolds number ) 2Fwdpv/(1 - )µv, µv ) viscosity (g/cm‚d), Fw ) water density (g/cm3), v ) superficial flow velocity (cm/d) ) Q/Ac, dp ) diameter of particle with biofilm attached (cm),  ) porosity of fluidized bed, Ac ) cross-sectional area of fluidized bed (cm2), and Q ) volumetric flow rate through fluidized bed (cm3/d). The influent concentration to the reactor of each substrate was determined from mass balance:

Di(Rem)0.75(Sc)0.67 5.7v

(15)

QoSoi + QrSei Q o + Qr

and Q ) Qo + Qr

(16)

where Sii ) reactor influent concentration of substrate i (mg/ cm3), Sei ) reactor effluent concentration of substrate i (mg/ cm3), Qo ) influent flow rate to reactor (cm3/d), and Qr ) reactor recycle flow rate (cm3/d). Key coefficients used in model simulations are listed in Table 2. In the first iteration for solving the above set of equations for the reactor, Sei was assumed to equal Swi. Sii is then recalculated using effluent concentrations, and if it differs from the originally assumed value by more than 1%, a subsequent iteration is made using the calculated effluent concentrations from the previous iteration. However, in the evaluation of several steady-state cases from full-scale treatment reported here, no second iteration was found necessary.

Results Model Evaluation. Data for nine different steady-state operational test periods were available for the BFBRs (Table 3). The first series of three tests represent different flow rates through a single BFBR. The last two series were the result of operating two BFBRs in series, the first BFBR was operated primarily for removal of oxygen only, and the second was operated for removal of nitrate and perchlorate. These two series provided information on the effect of both detention time and donor deficiency. The concentrations of ethanol added to the influent water (without recycle flow) for each test are also listed in Table 3. As a biological nutrient, the BFBRs were dosed with an influent phosphorus concentration of 0.1-0.5 mg/L during all except test 3. During test 3, which lasted 91 d and had the highest influent flow rate, no phosphorus was added, but this did not appear to adversely impact test results. The groundwater being treated was found to have a phosphorus concentration of 0.1 mg/L, which perhaps was sufficient to satisfy the need. An examination was made of the number of completemix segments (n) that would provide a best fit between modeled and measured results for nitrate and perchlorate in the lower 2 m of the reactor where dispersion effects are of most significance. Use of 15 segments was found to yield a much better fit than either 8 or 30 segments. Thus, the number of complete-mix segments (n) assumed for the simulation of the full-scale BFBRs was 15. A 15-segment simulation corresponds to a relatively low dispersion coefficient of 6 cm2/s and, therefore, closely resembles strict plugflow. The only adjustable parameter then used in the model was the biological solids detachment rate (bdet), which can vary depending upon the status of the biofilm. While initially growing, the detachment rate is likely to be low but should increase and stabilize as operation reaches steady-state and mechanical detachment becomes necessary to maintain the bed height. The value of bdet was adjusted to a value resulting in the minimum sum of the squared differences between modeled and measured effluent perchlorate, nitrate, and oxygen concentrations. The percentage ethanol overdose listed in Table 3 is a result of modeled stoichiometry resulting from use of the best-fit detachment rate. Negative values VOL. 39, NO. 3, 2005 / ENVIRONMENTAL SCIENCE & TECHNOLOGY

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TABLE 3. Operational Conditions for BFBRs and Best-Fit Detachment Rate for Model series

test

steady-state period (d)

1

1 2 3 4 5 6 7 8 9

46 70 91 61 30 31 61 30 31

2 3

a

flow rate (m3/min) influenta recycle 2.6 2.8 5.5 2.5 3.2 3.8 2.5 3.2 3.8

Untreated flow excluding recycle.

b

4.2 4.0 1.3 4.3 3.6 3.0 4.3 3.6 3.0

empty-bed detention time (min) 26 23 12 27 20 17 27 20 17

influent ethanol (mg/L)b % overdosec 9.64 10.5 10.4 4.7 4.4 4.6 4.8 4.4 4.6

model bdet (d-1)

-1.6 0.0 0.3 -51 -52 -54 -0.4 -3.4 -20

0.23 0.31 0.29 0.20 0.16 0.25 0.22 0.062 0.22

Concentration based upon influent flow only. c Based upon model-calculated stoichiometry.

TABLE 4. Measured Influent and Effluent Concentrations (mg/L) for Oxygen, Nitrate, and Perchlorate and Percentage Removals for Each oxygen

nitrate

perchlorate

percent removal

series

test

influent

effluent

influent

effluent

influent

effluent

oxygen

nitrate

1

1 2 3 4 5 6 7 8 9

5.57 5.62 5.64 5.58 5.57 5.68 0.10 0.80 1.00

0.13 99.9 >99.9 4.2 -3.7 1.2 98.8 87.8 35.1

FIGURE 2. Comparison between model (lines) and measured (symbols) results for the test cases 1 (a), 2 (b), and 3 (c) for series one. 4a). However, the ethanol dose was insufficient for complete oxygen removal in tests 5 and 6 (Figure 4b,c). Figure 5 illustrates results for operational series 3 from operation of the second BFBR in a series of two BFBRs. For

FIGURE 3. Log concentration comparison for perchlorate and nitrate for test cases 1-3. Modeled results are shown as lines, and measured results are shown as symbols. Measured results below the reporting limit are shown at the reporting limit.

FIGURE 5. Comparison between model (lines) and measured (symbols) results for the test cases 7 (a), 8 (b), and 9 (c) for series three. 8 and 9, resulting in 340-1790 µg/L perchlorate in the effluent. In these three cases, dissolved oxygen and nitrate were removed to below reporting limit. These results confirm the selective removal of nitrate over perchlorate by the BFBR. Bacterial Detachment. The major variable used in the model to permit matching of modeled and experimental results was the rate of bacterial detachment from the GAC particles. This affects reaction stoichiometry or the relative proportion of electron donor used both for reduction of electron acceptor and for cell synthesis. A high detachment rate (low biological solids retention time) leads to more ethanol consumption for cell synthesis. Detachment rate for the BFBR was controlled mechanically by the eductor system used to shear excess biomass from the GAC particles. As noted in Table 3, the best-fit detachment rates found varied over a relatively small range with an average (as well as median) of 0.22 d-1 and standard deviation of 0.07 d-1. Biofilm thickness is a function of electron-donor organic loading, reaction stoichiometry, GAC surface area, and detachment rate and can be calculated as follows:

dpart wb ) FIGURE 4. Comparison between model (lines) and measured (symbols) results for the test cases 4 (a), 5 (b), and 6 (c) for series two. these tests, influent oxygen concentrations were low. In all three tests, the ethanol dosage was below the stoichiometric requirement for complete removal of all three electron acceptors. In test 7, only a slight deficiency was present (0.4%), but this was sufficient to cause 30 µg/L of perchlorate to remain in the effluent. The deficiency was greater for tests

(

)

Vg + Vb Vg 2

1/3

- dpart (17)

where

Vg ) Vb )

HgW2π(1 - s) 4

(18)

fsQo(Sod - Sed) 113/28 bdetXf 46/12

(

)

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(19)

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Sod and Sed represent the ethanol influent and effluent concentrations, respectively. The coefficients at the end of eq 19 represent the ratio between the equivalent concentration of bacterial cells and electron donor, based upon eqs 2 and 3. The thickness computed for steady-state operation for the nine test cases varied from 32 µm for tests 4 and 7 with low organic loading up to 109 µm for test 3 with the highest organic loading, with a median thickness found for the nine tests of 56 µm. The best-fit detachment rates listed in Table 3 might be compared with that determined from an empirical formula (35) for detachment rate resulting from reactor shear forces only:

bdet ) 0.0842σ0.58

(20)

where σ is the shear stress, which for a fluidized-bed reactor with biofilm thickness less than 30 µm (the case here) is given by:

σ)

(Fp - Fw)(1 - )g a

(21)

A key parameter here is Fp. The particle density of interest is that with biofilm attached, which was estimated from the expanded bed vertical liquid velocity and Stoke’s law to equal 1.006 g/cm3. Also using Fw of 0.999 g/cm3,  of 0.72, g of 980 cm/s2, and a of 10/cm, bdet from fluid shear alone from eq 20 would equal 0.03 d-1. This low value as compared with the average of 0.22 d-1 found for the BFBRs indicates that mechanical shearing by the eductor system, rather than fluidflow shearing of the GAC, was the major factor controlling the bacterial detachment rate. This demonstrates the importance of including some form of mechanical shearing device to control the fluidized-bed height and prevent loss of media in this type of reactor. Operational Variables. An advantage to the use of a model based upon basic principles is that the model can have broad application. BFBR operational conditions are likely to be different at different sites. The effects of a few such variables on operation were evaluated. The data obtained indicate that, even at the shortest empty-bed time evaluated (12 min), > 99.9% removal of perchlorate to less than the 3 µg/L reporting limit was obtained. The question arises as to whether even lower detention times might be used. With the GAC particle size evaluated here, the lowest detention time obtainable without particle washout is 9.6 min (no recycle). To reduce the detention time further, a support media with greater specific gravity or larger GAC particles with a higher settling velocity might be used. Also, the reactor could be redesigned to have a greater diameter to height ratio, allowing a higher flow rate while keeping the vertical velocity constant. The effects of changing particle size and reactor diameter on performance were evaluated. The computed effect of higher flow rate obtained by increasing GAC particle diameter is illustrated in Figure 6. Here, influent conditions were maintained the same as in the first series of three case studies, using a constant detachment rate of 0.22 d-1. The maximum flow rate for each particle size was estimated using Stokes’ law (36) and a particle specific gravity of 1.006. Effluent concentrations increase rapidly as flow rate is increased in this manner. Increasing particle size from 1.3 to 1.7 mm results in a calculated increase in effluent perchlorate to 4 µg/L, while reducing the empty-bed detention time to 7 min. Allowing for some safety factor in design, the 1.3 mm used at the site appears to be the largest size that should be used for a site with a treatment goal of 4 µg/L. Figure 7 illustrates the effect of increasing reactor diameter and reducing height while maintaining total reactor volume 856

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FIGURE 6. Model predictions of the effect of GAC particle diameter on maximum allowable flow rate (m3/s) and effluent dissolved oxygen, nitrate, and perchlorate concentrations (mg/L) when operating at that flow rate.

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FIGURE 7. Modeled effect of empty-bed detention time and influent perchlorate concentration on effluent perchlorate concentration. Detention time changed by increasing reactor diameter while maintaining particle fluidized rate constant without recycle. the same as in the current design. All other conditions remained the same as in the first series of three case studies except that influent perchlorate concentration was also varied. By increasing the reactor diameter, significant reductions in detention time can be achieved. With the 2.7 mg/L perchlorate concentration for the test cases, the 4 µg/L perchlorate treatment objective could be achieved with a calculated detention time of 3.5 min, corresponding to a reactor diameter of 7 m and total height of 3.8 m, which includes 2.1 m of freeboard. This contrasts with the current design of 4.27 m diameter and 6.7 m height. The larger diameter reactor would require more land space and a greater number of flow distributors, which would tend to offset some of the advantage gained in lower total reactor volume. Again, allowing for some safety factor, the current design diameter is perhaps near optimal. Figure 7 also indicates the influence of influent perchlorate concentration. With the current design, the goal of 4 µg/L should be achievable even with an influent perchlorate concentration of 10 mg/L, but for stoichiometry more ethanol would be required. The minimum detention time that could be used to meet the goal is higher with higher concentrations, as expected.

Discussion The modeled results for the nine test cases are compared with experimental results in Figures 2-5. In general the agreements are quite good. The model contains several biological variables, and a question arises as to the importance of each in the fit obtained between model results and field data. To answer this, a sensitivity analysis was conducted. For this, a sum was obtained of the squares of the differences between modeled and measured (mean) values for all reactor and effluent concentrations that are above the reporting limit.

A sensitivity analysis was performed to determine the impact of a 10% change in each of the biological coefficients (Xf, Ki, qi, b, and bdet) on the sum of squares. This change, with only two exceptions, caused only a 0-3% change in the sum of squares. The exceptions were b and bdet,which changed the sum of squares by 57-143%. Thus, the model results are highly sensitive to these two coefficients, mainly because of their significant impact on reaction stoichiometry. Cell decay rate (b) should be relatively constant since it is an intrinsic property of the microorganisms, while the detachment rate is a function of many factors and is controlled by system operation. Because bdet is a major control variable and b is not, bdet was used as the main variable in model fitting. While a biofilm is developing, the detachment rate is low. When the biofilm becomes sufficiently well developed on a given particle, its overall settling velocity becomes reduced and the particle rises until it reaches the desired operational height in the reactor. The particle is then removed from the reactor and the biofilm is mechanically removed from the particle. Following this, the particle is reinjected into the lower portion of the reactor, where biofilm growth again commences. While some natural biofilm detachment occurs within the reactor itself as a result of shear stresses (eq 20), most detachment occurs as a result of this mechanical cleaning, which is under the control of the operator. The average detachment rate found here of 0.22/d is thus system- and operation-dependent and may not apply directly to other situations where conditions are quire different than they were in this field evaluation. Using the model to determine the effect of GAC particle size, reactor diameter, and influent perchlorate concentration on performance suggests that the current design is a good one for the study location, allowing achievement of the 4 µg/L goal within a good design safety factor. The model can also be useful in other situations for hypothesis testing in order to determine the potential effect of different design configurations on likely performance. Such an analysis should be done as an aid in designs for pilot testing so that the most important variables for evaluation can better be determined. One optional design configuration that could be considered is the use of a fixed-bed reactor instead of a fluidizedbed reactor. The BFBR has many similarities to a fixed-bed reactor. However, there are several differences that need to be considered in a comparison between the two. The model used here may be adapted for use in fixed-bed reactor evaluation, but in order to do so, the differences need to be understood. A limitation of the BFBR is that it requires a constant and fixed upflow velocity, sufficiently large to keep the media suspended, but not so large that it results in media washout. For a given media size, this sets an upper limit on the permissible flow rate. It also means that the recycle rate becomes a direct function of the influent flow rate. This limitation is not present in a fixed-bed reactor. The advantages of the BFBR that offset this disadvantage are that with fluidization, clogging, which plagues fixed-bed reactors, is not a major operational concern. With the expanded bed, suspended particles, unless they have a higher settling velocity than the BFBR media itself, will not be filtered out to cause clogging but will pass up and out of the reactor. With fluidization, flow channeling is much less of a problem than in a fixed-bed unit, all the media surface area in the reactor can participate in substrate removal, and mass transfer from bulk fluid to the biofilm on the particle surface can be quite high. A further advantage of the BFBR is that a good biofilm is established throughout the reactor so that highly efficient removal of contaminants occurs even at the top of the reactor were substrate concentrations are very low. This means highly efficient removal (>99.9%) can be achieved with empty-bed detention times as low as 12 min as demonstrated here. The biofilm distribution in a BFBR is the result of GAC particles

becoming less dense as their biofilm thickens, causing the particles with more biofilm to slowly rise to the top or effluent end of the reactor. In fixed-bed reactors, on the other hand, the thickest biofilm results near the reactor entrance, and the biofilm can thin out considerably as substrate concentration decreases near the reactor effluent. Good performance of the BFBR for perchlorate removal depends on the addition of sufficient electron donor to satisfy bacterial needs for complete reduction of oxygen, nitrate, and perchlorate. The performance with respect to perchlorate is very sensitive to ethanol dosage, a slight decrease in ethanol below the stoichiometric requirement results in a significant increase in effluent perchlorate. If too much electron donor is added, then electron donor or its degradation products can be expected to be present in the effluent. This is undesirable as it decreases effluent quality, and so application of electron donor as near as possible to the stoichiometric requirement should be a goal of operation. At the full-scale site here studied, the concentration of constituents in the feed to the BFBRs remained quite constant with time, and so adjusting the ethanol electron donor to just meet the need was not a major problem. However, if the influent concentrations vary significantly with time, then this would be much more difficult and may require time-variant addition of donor and continuous monitoring of influent water characteristics, or use of an over dosage with subsequent treatment for removal of the excess donor added. In any event, the BFBR has proven to be a reliable method for highly efficient removal of perchlorate from groundwater at relatively short detention times. The numerical model developed here and tested with full-scale operational data may prove useful for application elsewhere for the evaluation of a BFBR for possible treatment of nitrate as well as perchlorate-contaminated waters.

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Received for review January 2, 2004. Revised manuscript received November 3, 2004. Accepted November 4, 2004. ES040303J