Modeling Enhanced In Situ Denitrification in Groundwater

experi-

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Modeling Enhanced In Situ Denitrification in GroundwaterMarc W. Killingstad1; Mark A. Widdowson2; and Richard L. Smith3

Abstract: A two-dimensional numerical solute transport model was developed for simulating an enhanced in situ denitrificationment performed in a nitrate-contaminated aquifer on Cape Cod, Massachusetts. In this experiment, formate~HCOO2! was injected for aperiod of 26 days into the carbon-limited aquifer to stimulate denitrification. Calibration of the vertical-profile site model was dstrated through error analysis and comparison with formate, nitrate, and nitrite concentration data monitored along a transecmultilevel groundwater sampling wells for 75 days after initial injection. Formate utilization rates were approximately 142 and 38mM/dayfor nitrate and nitrite reduction, respectively. Nitrate and nitrite utilization rates were approximately 29 and 8mM/day, respectively. Nitrateutilization rates under enhanced conditions were 1 order of magnitude greater than previously reported naturally occurring rnitrite production rate was approximately 29mM/day. Persistence of nitrite was attributed to a combination of factors, including eledonor~formate! limitation late in the experiment, preferential utilization of nitrate as an electron acceptor, and greater nitrite prorelative to nitrite utilization.

DOI: 10.1061/~ASCE!0733-9372~2002!128:6~491!

CE Database keywords: Denitrification; Groundwater; Nitrates; Massachusetts; Nitrites; Biological treatment.

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Introduction

Nitrate ~NO32! is the most common groundwater contamina

found in fresh water aquifers, particularly shallow unconfinaquifers in rural areas~Nolan et al. 1997!. The prevalence of ni-trate in the subsurface is attributed to both point and nonpsources, such as various agricultural practices~Hallberg 1989!and infiltration of municipal and rural wastewater effluent. Muler et al.~1995! found nitrate levels exceeded the EnvironmenProtection Agency~EPA! maximum contaminant level~MCL! in21% of shallow wells in agricultural areas. Discharge of nitracontaminated ground water to surface waters is also problemIn the Chesapeake Bay watershed, where there are extensivewith shallow groundwater underlying well-drained agricultursoils, Gallagher et al.~1996! reported that nitrate transport tcoastal waters via groundwater discharge may be significanboth local and regional flow systems. In some instances, nutrloading of coastal waters by way of groundwater discharge mexceed nutrient loading through surface runoff~Lee and Olsen1985; Giblin and Gaines 1990; Valiela et al. 1990!.

Nitrate is highly soluble and mobile, and thus poses significhealth hazards. Comly~1945! found that infants who had consumed nitrate-contaminated well water developed methemobinemia ~i.e., ‘‘blue baby syndrome’’!, a potentially fatal condi-

1ARCADIS Geraghty & Miller, Inc., 1131 Benfield Blvd. Suite AMillersville, MD 21108.

2Dept. of Civil and Environmental Engineering, Virginia PolytechnInstitute and State Univ., Blacksburg, VA 24061~corresponding author!.E-mail: [email protected]

3U.S. Geological Survey, 3215 Marine St., Boulder, CO 80303.Note. Associate Editor: Eric A. Seagren. Discussion open until N

vember 1, 2002. Separate discussions must be submitted for indivpapers. To extend the closing date by one month, a written requestbe filed with the ASCE Managing Editor. The manuscript for this pawas submitted for review and possible publication on July 31, 20approved on August 20, 2001. This paper is part of theJournal of En-vironmental Engineering, Vol. 128, No. 6, June 1, 2002. ©ASCE, ISS0733-9372/2002/6-491–504/$8.001$.50 per page.

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tion. When ingested, nitrate is converted to nitrite~NO22) by the

body and reacts with hemoglobin~which carries oxygen to allparts of the body! in the bloodstream to form methemoglob~which does not carry oxygen! resulting in suffocation of the vic-tim ~Comly 1945!. Intake of nitrate-contaminated drinking watehas also been linked to gastric cancer mortality rates~Forman1989! and non-Hodgkin’s lymphoma~Weisenburger 1991!. Inview of these health concerns, the EPA identified nitrate andtrite as primary water contaminants and, as required by the SDrinking Water Act of 1974, determined MCLs for nitrate annitrite at 10 and 1 mg N/L, respectively.

The ubiquitous nature of nitrate in the subsurface has hastethe development of novel remeditation and drinking water trement techniques. In situ treatment methods are especially dable because of the potential to provide safe and cost efficremediation of nitrate-contaminated groundwater with minimsite disturbance. Researchers~e.g., Vogel et al. 1981; Trudelet al. 1986; Starr and Gillham 1989; Smith et al. 1991a; Mogomery et al. 1997! have noted that in situ denitrification is thdominant biological process for naturally occurring microbiamediated process where nitrate is reduced to gaseous nitrog~N2!. During denitrification, nitrate serves as a terminal electracceptor in the metabolism of facultative anaerobic bacte~Tiedje 1988!. The presence of nitrate, nitrite, or nitrous oxid(N2O) as an electron acceptor, denitrifying bacteria, anaeroconditions, or restricted oxygen availability, and an adequate sply of electron donors are required for denitrification to occurany particular location in a groundwater system~Firestone 1982!.The presume pathway of denitrification, with the oxidation stof the nitrogen atom shown in parentheses, is presented as fol~Payne 1981!:

NO32

~15!

→NO22

~13!

→ NO~12!

→NO2

~11!

→NO2

~0!

In natural systems denitrification is often electron donor liited ~Smith and Duff 1988; Starra and Gillham 1989; DeSimoand Howes 1996! which, consequently, impedes the rate of detrification. Another complicating factor is the production and p

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tential persistence of nitrite, which is more toxic than nitratecause it reacts immediately with hemoglobin. While the problof nitrite accumulation has been investigated in activated slu~e.g., Wilderer et al. 1987! and bacterial cultures~e.g., Betlachand Tiedje 1981!, it has not received significant attention in thliterature as a groundwater contaminant.

A number of researchers have found that denitrification acity in organic carbon-limited aquifers can successfully behanced with the addition of an electron donor~Slater and Capone1987; Smith and Duff 1988; Starr and Gillham 1989; Obenhuand Lowrance 1991; Smith et al. 1994; Smith et al. 2001!. Or-ganic carbon additions such as methanol, ethanol, or glucosebeen used in field experiments~Slater and Capone 1987; Mercadet al. 1988!. However, some denitrifiers are capable of atotrophic nitrate reduction coupled with hydrogen oxidation wiout excessive biomass buildup~Smith et al. 1994!. Under thisscenario, the stoichiometric relationship for the reduction oftrate to nitrogen gas is as follows:

2NO32~aq!15H2→N2~g!14H2O12OH2

Hydrogen-enhanced denitrification has been utilized with succin pilot-scale ex situ treatment applications in Europe~Gros et al.1988; Liessens et al. 1992!. Smith et al. ~1994! found thathydrogen-oxidizing dentifiers made up approximately 7% ofdentrifying population in a nitrate-contaminated aquifer aspeculated that this population could be specifically targeted wthe addition of hydrogen. While hydrogen is not readily solublewater, hydrogen-producing compounds~e.g., formate! have thepotential to serve as soluble hydrogen substitutes for enhancsitu denitrification. Smith et al.~2001! recently performed an insitu field experiment by adding formate to a nitrate plume. Thfound that the formate addition did stimulate in situ denitrifiction. However, is also appeared likely that the experimentriched a population of formate-utilizing denitrifiers rater than atotrophic hydrogen-oxidizing dentifiers, as was initially intende

An integral component of evaluating in situ field tests has bthe application of mathematical models to determine biologreaction rates and to interpret field data.~Harvey and Garabedian1991; Kinzelbach et al. 1991; Smith et al. 1991b; 1996!. Rela-tively few mathematical models have been developed thatscribe the fate and transport of nitrate in groundwater syst~e.g., Widdowson et al. 1988; Kinzelbach et al. 1991; Smith et1996! or that incorporate the process noted in field studies. Wdowson et al. ~1988! developed a one-dimensional transpomodel for the biodegradation of a carbon substrate subjecsequential aerobic and nitrate-based respiration. Smith e~1996! utilized a zero-order degradation term in a ondimensional model to describe nitrate reduction directly to nitrooxide ~in the presence of acetylene! to interpret naturally occur-ring denitrification in the Cape Code aquifer. Electron donor ccentration was not simulated and was assumed a constant flimiting denitrification. Kinzelbach et al.~1991! developed andapplied a two-dimensional~2D! model to simulate~1! naturallyoccurring denitrification in a carbon-limited aquifer and~2! en-hanced bioremediation of a hydrocarbon spill using nitrate injtion. None of the three modeling studies considered nitrite pduction or reduction of denitrification intermediates.

The purpose of this study was to develop and apply anumerical model to simulate an enhanced in situ denitrificatexperiment. The field experiment consisted of injecting grouwater amended with formate into a nitrate plume, and monitorthe microbial response of the nature denitrifying population initrate-contaminated aquifer on Cape Cod~Smith et al. 2001!.

492 / JOURNAL OF ENVIRONMENTAL ENGINEERING / JUNE 2002

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The model incorporates the transport and utilization of nitratenitrite as electron acceptors. Nitrite production resulting fromtrate reduction was integrated, and growth and decay of a nitrnitrite-reducing microbial population simulated. To test the coceptual and mathematical model for microbial processes,model was first applied to a laboratory incubation experimusing aquifer sediments taken from the study area. A field-model was developed for simulation of formate, nitrate, andtrite transport and mirobial utilization in a 2D vertical domaoriented in the mean direction of transport. The transportutilization model was then calibrated using formate, nitrate, anitrite concentration versus time data measured at three multilsampling~MLSs! wells located along the groundwater flow patModel simulation results were subsequently used to interpret fidata, to quantify utilization rates, to quantify the rate of nitrproduction, and to investigate the persistence of nitrite.

Enhanced Denitrification Experiment

Study Site

The study was conducted in a shallow, unconfined, sandgravel aquifer located on Cape Cod, Mass. Groundwater atlocation was contaminated from the long-term disposal~;60years! of dilute, treated sewage effluent, which has resulted icontaminant plume that is more than 4 km long~LeBlanc 1984!.Nitrate is a major constituent of the contaminant plume~LeBlanc1984; Smith et al. 1991a!. The plume is also characterized belevated concentrations of dissolved solids, boron, chloride,dium, phosphorous, ammonium, and detergents in additionvarious other constituents. In general, the plume consists of bvertical and horizontal gradients of dissolved oxygen~;0–8 mg/L!, pH ~5–7.1!, dissolved organic carbon~1–4 mg/L, much ofwhich is recalcitrant!, chloride ~0–28 mg/L!, sulfate~4–30 mg/L!, nitrate ~0–16 mg N/L!, and ammonium~0–10 mg N/L!~LeBlanc 1984; Thurman et al. 1986!. The in situ injection ex-periment was conducted at site F473~Fig. 1; also see map inSmith et al. 1996!, which is located 0.3 km downgradient fromthe source of contamination.

Incubation Experiment

Core material was collected from site F473 using a wire-line pton core barrel and stored at 4°C~Smith et al. 1996!. The corematerial was collected from the same depth but upgradient ofin situ injection experiment. Anoxic, sediment slurry incubatiowere prepared in 250-mL flasks using artificial groundwa~Smith et al. 2001!. Initial concentrations of nitrate and formatwere 687 and 3,270mM, respectively. The flasks were incubateat 15°C; water was periodically removed by syringe, filtered, aanalyzed for nitrate, nitrite, and formate concentrations~Smithet al. 2001!.

In Situ Injection Experiments

The field experiment was conducted in September 1994 atF473 in which sodium formate was added to nitrate-contaminagroundwater to test whether in situ denitrification could be stimlated by addition of an electron donor. Details are given in Smet al. ~2001!. Briefly, a sterile anoxic stock solution containinsodium formate and sodium bromide was metered into groundter that was being continuously pumped from one well andjected back into a second well at 6–8 L/h. The withdrawal a

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injection wells were screened from approximately 9.4–10.3above mean sea level~MSL!. Formate injection concentratio~Table 1! was variable over the 26-day injection period. The aerage background nitrate concentration was approximatelymM, and the average formate injectate concentration was appmately 5,400mM during the peak injection period. The traccloud that resulted from the injection process moved downgrent by natural groundwater flow and was intercepted and samby rows of MLSs~Fig. 1!. Groundwater samples were collectefrom the MLSs with a peristaltic pump and preserved for analy~Smith et al. 2001!.

Model Development

Conceptual Model

The model is an extension of a previously published odimensional model that describes transport and biodegradatiothree solutes~one electron donor and two aqueous-phase elecacceptors: oxygen and nitrate! coupled with the growth and decaof a facultative heterotrophic microbial population~Widdowsonet al. 1988!. For this study, the model was used to simulaformate-utilizing denitrification. The model was extended for 2transport and expanded to include the transport, production,reduction of nitrite. The result is a system of four differentequations describing the fate and transport of an electron d~formate!, electron acceptors~nitrate and nitrite!, and the growthand decay of a single homogeneous nitrate/nitrite-reducing mi

Fig. 1. Detail of site F473 on Cape Cod, Mass.; multilevel sampl~MLS! are designated by row and by number~e.g., MLS 12 in row 4is designated 4-12!

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bial population. The microbial population was modeled as anrangement of sediment-bound groups of bacteria, commonlyferred to as microcolonies, initially distributed uniformlthroughout the aquifer matrix. No geometry or dimensionsassociated with the microcolonies. Because the injectate andof the aquifer impacted by the injectate were anoxic~Smith et al.1991a!, dissolved oxygen was not included in the model. Othfactors that may potential inhibit or enhance denitrification~suchas, pH, temperature, and the presence of sulfur compounds! werealso assumed to be negligible.

Mathematical Model

Transport EquationsThe general form of the 2D solute transport equation assumvertically stratified flow including biological reactions is

2nx~z!]C

]x2nz~z!

]C

]z1Dx~z!

]2C

]x2 1Dz~z!]2C

]z2 2Rbio,Csink

1Rbio,Csource5

]C

]t(1)

where C5aqueous phase concentration of a particular so(M/L3); x and z5distances measured along the longitudinal atransverse vertical directions, respectively~L!; nx andnz5average groundwater velocities in the longitudinal and traverse vertical directions, respectively~L/T!; Dx andDz5dispersion coefficients in the longitudinal and transverse vtical directions, respectively~L2/T); Rbio,C

sourceaccounts for the pro-duction of mass resulting from microbial processes~M/L3 per T!;

Table 1. Formate Injection Concentration Data

Data of injection Formate injectate concentration~mM!

02 Sept 1,601

02 SeptR 1,592

03 Sept 1,48606 Sept 1,02507 Sept 874

07 SeptR 867

08 Sept 9809 Sept 010 Sept 1911 Sept 11

11 SeptR 12

12 Sept 013 Sept 014 Sept 21715 Sept 4,84116 Sept 4,38317 Sept 3,91918 Sept 4,45819 Sept 10,58220 Sept 8,51021 Sept 3,44422 Sept 3,25823 Sept 7,06725 Sept 4,57026 Sept 13827 Sept 44

Note: R denotes replicate sample.


Table 2. Equations for Biological Utilization and Production Terms

Based onBiological utilization Equation equations

Formate utilization

Rbio,Fsink 5

M

u

mF,N1

max

YN1F F

KF,N1

ed 1FGF N1

KF,N1

ea 1N1G1

M

u

3mF,N2

max

YN2F F

KF,N2

ed 1FGF N2

KF,N2

ea 1N2G F KI

KI1N1G

~5!, ~9!, ~10!

Nitrate utilization Rbio,N1

sink 5M

uhN1

mF,N1

maxF F

KF,N1

ed 1FGF N1

KF,N1

ea 1N1G ~6!, ~9!

Nitrite utilization Rbio,N2

sink 5M

uhN2

mF,N2

maxF F

KF,N2

ed 1FGF N2

KF,N2

ea 1N2G F KI

KI1N1G ~7!, ~10!

Nitrite production Rbio,N2

source5zN1Rbio,N1

sink ~8!

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andRbio,Csink represents mass loss due to biological utilization~M/L3

per T!. No other mass loss~e.g., sorption! or production termsappear in Eq.~1!.

Using Eq.~1! as a general expression and substituting thepropriate terms for sources and sinks, mass balance equationformate~F!, nitrate ~N1!, and nitrite~N2! concentrations, respectively, are written as

2nx~z!]F

]x2nz~z!

]F

]z1Dx~z!

]2F

]x2 1Dz~z!]2F

]z22Rbio,Fsink 5

]F

]t(2)

2nx~z!]N1

]x2nz~z!

]N1

]z1Dx~z!

]2N1

]x2 1Dz~z!]2N1

]z2 2Rbio,N1

sink

5]N1

]t(3)

2nx~z!]N2

]x2nz~z!

]N2

]z1Dx~z!

]2N2

]x2 1Dz~z!]2N2

]z2 2Rbio,N2

sink

1Rbio,N2

source5]N2

]t(4)

Reaction TermsThe reaction term for formate utilization~Rbio,F

sink ), expressed as thsum of utilization due to nitrate-based reduction~r F,N1

! andnitrite-based reduction~r F,N2

!, is defined as

Rbio,Fsink 5

M

u~r F,N1

1r F,N2!5

M

u S mF,N1

YN1

1mF,N2

YN2

D (5)

whereM5the amount of biomass per volume of porous medi~M/L3!; u5the aquifer porosity defined by the volume of voidper total volume;mF,N1

and mF,N25the microbial specific growth

rates for nitrate and nitrite reduction, respectively~M/M per T!;andYN1

andYN25the yield coefficients~M/M !, which is the ratio

of microbial biomass produced per mass of electron donor csumed, for nitrate- and nitrite-based reduction, respectively.

Nitrate mass loss rate,Rbio,N1

sink , resulting from utilization as an

electron acceptor, is expressed as

Rbio,N1

sink 5M

uhN1

mF,N1(6)


or

-

wherehN15the nitrate utilization factor~M of NO3

2/M of elec-tron donor!. Nitrite mass loss rate is similarly defined as

Rbio,N2

sink 5M

uhN2

mF,N2(7)

wherehN25 nitrite utilization factor~M of NO2

2/M of electrondonor!.

Nitrite production resulting from denitrification is proportionato the amount of nitrate consumed. Biological nitrite productiondefined by the following relationships:

Rbio,N2

source5zN1Rbio,N1

sink (8)

wherezN15nitrite production constant~M of NO2

2/M of NO32!.

Table 2 lists the biological source and sink terms used in Eqs.~2!,~3!, and~4! for formate, nitrate, and nitrite, respectively.

Microbial Population Growth DynamicsMicrobial specific growth rates were represented using dMonod kinetics, which assume that population growth rateslimited by both the electron donor and the electron accep~Table 2!. Harris and Hanford~1976! developed a modifiedMonod equation to represent the microbial growth rate using ogen as an electron acceptor. Molz et al.~1986! and Widdowsonet al. ~1988! adapted the modified Monod equation to poromedia transport. In this study, the specific growth rate equafor nitrate-based respiration is expressed as

mF,N15mF,N1

maxF F

KF,N1

ed 1FGF N1

KF,N1

ea 1N1G (9)

wheremF,N1

max5maximum specific growth rate for nitrate utilizatio

~M/M per T!; KF,N1

ed 5formate half-saturation constant for nitra

reduction ~M/L3!; and KF,N1

ea 5nitrate half-saturation constan

~M/L3!.In the present model, nitrate is preferentially utilized as

electron acceptor due to a higher energy yield relative to nit~Waddill and Widdowson 1998!. Based on the Widdowson et a~1988! model, the specific growth rate for nitrite-based respiratis expressed as

mF,N25mF,N2

maxF F

KF,N2

ed 1FGF N1

KF,N2

ea 1N1G F KI

KI1N1G (10)

of each
Fig. 2. Boundaries of two-dimensional vertical profile model and schematic of formate injection experiment. Identification numbermultilevel sampler is given in parentheses.
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~M/L3!, and KI5nitrate inhibition constant~M/L3!. Preferentialuse of nitrate is described using an inhibition function, repsented by the expression

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which is modified from previously published models~Widdowsonet al. 1988; Waddill and Widdowson 1998!.

Changes in the microbial population during periods of growand decay are simulated by a mass balance equation that accfor biomass growth and decay terms

1

M

]M

]t5mF,N1

1mF,N22kd (11)

wherekd5biomass decay coefficient~M/M per T!. Because ni-trate and nitrite are electron acceptors that support the microbiomass, Eq.~11! includes growth terms for both electronaccepting processes. Eq.~11! is solved directly so that the microbial biomass is expressed as the minimum of Eqs.~12a! and~12b!

M5M initial exp@~mF,N11mF,N2

2kd!# (12a)

M5Mmax (12b)

where M initial5initial amount of biomass per volume of poroumedium~M/L3! and Mmax5maximum or upper limit to the bio-mass per volume of porous medium~M/L3!.

Site Model

The formate injection experiment was simulated using 2D, vecal profile model. The site model was oriented along the princdirection of groundwater flow and incorporated three MLSstravel distances of 7.02, 10.10, and 15.58 m downgradient ofinjection well ~located in Rows 4, 6, and 8, respectively!, hence-forth referred to as the 7-, 10-, and 15-m MLS, respectively. Tvertical profile model incorporated a 2D, stratified flow field. Tgroundwater flow field was not specifically solved using a nmerical model but, instead, the velocity profile was entered baon site data and depth-dependent tracer breakthrough curvessured at individual sampling ports~described below!. Flow dis-turbance at the formate injection well was assumed to be negible based on the ratio of the injection rate to the mean ratgroundwater flow~approximately 0.05!. Fig. 2 is a representationof the vertical profile model domain, showing the location of t

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three MLSs and the injection well. In the field, sampling powere positioned at identical elevations for each MLS. Samplport spacing was uniform~0.254 m!.

A 2D mesh-centered, finite-difference grid system was eployed consisting of a 498 node~longitudinal!334 node~vertical!matrix, which covers a 63.08 m34.32 m area. Grid spacing wadetermined primarily by the injection experiment layout. Tupper and lower grid boundaries to the site model were se12.127 and 7.809 m~MSL!, respectively, and were no-flow, zeroflux boundaries for all three solutes. The elevations of thboundaries were selected to provide adequate distance abovbelow the injection and sampling zones to minimize undue inence on the simulation of the formate plume. Vertical node sping was uniform~Dz50.127 m!, and horizontal grid lines werepositioned to match up with the MLS sampling ports. Longitunal node spacing was also uniform~Dx50.127 m!, and verticalgrid lines were positioned to match up with the three MLSs.

Initial conditions for the solute transport model were basedsampling data collected immediately prior to the formate injectexperiment and several site characterization reports. Backgroconcentrations for formate were negligible. The starting nitrconcentration distribution was estimated using vertical concention profiles from the initial sampling data and ranges from 7to 15.80 mg N/L. The initial nitrite concentration was unifor~0.246 mg N/L! and was based on the average measured contration of the initial sample set.

Boundary conditions along the inflow boundary~x50! for thethree solutes were specified as a function of space, and formate, as a function of time. At boundary nodes associated wthe injection well screen, delineated from 9.460 to 10.222~MSL!, formate concentrations were uniform with space. Becathe formate mass flow rate delivered to the aquifer was transformate concentrations were specified as a function of timematch measured injection data. Influent boundary concentratfor nitrate and nitrite were steady, nonuniform line sources awere estimated from field data. The downgradient boundary wfree-gradient condition~Widdowson et al. 1988!.

Modeling Approach

The model was first applied to a laboratory incubation study pformed by Smith et al.~2001! using site sediment to primarily testhe mathematical formulation of the reaction terms. The secoary purpose of this initial step was to provide starting parameestimates for field-scale model simulations. Advective transpand dispersion transport parameters~i.e.,Dx , Dz , nx , andnz! forsimulation of the field experiment were determined by calibrat


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Eq. ~1! to bromide data collected from a previous injection eperiment~whereRbio

sink5Rbiosource50! as well as transport paramete

reported by LeBlanc~1984! and Garabedian et al.~1991!. For thefield-scale model simulations, the overall approach was to cbrate the model to data collected at the 7-m MLS and then evate the model calibration over the entire model domain using dcollected from the 10- and 15-m MLSs. Model accuracy wevaluated qualitatively by comparing simulated and obserconcentration versus time breakthrough curves for formate,trate, and nitrite at each of the three MLSs. A quantitative msure of the relative error between simulated and field resultseach constituent was obtained by calculating the ratio of themean~RMS! of square residual errors to the total measured ccentration change~RMSerror). Calibration was achieved by minimizing RMSerror for each constituent simultaneously. Model sesitivity was also investigated.

Parameter Estimation

Microbial Population DataHarvey et al.~1984! found that free-living bacterial populationin the Cape Cod aquifer varied from a maximum of 231016

cells/mL near the sewage effluent infiltration beds to 2.53105

cells/mL at a distance of 1 km downgradient from the beds. Hoever, more than 90% of the bacteria in the aquifier were attacto particulate surfaces. Population densities of particle-boundteria range from about 23107 to 43107 cells/cm3 of aquifermaterial~Harvey et al. 1984!. Several studies have shown thatactive denitrifying zone exists within the contaminant plume~e.g.,Smith and Duff 1988; Smith et al. 1991a; Smith et al. 199Smith et al. 1996!. Smith et al.~1994! reported most probablenumber~MPN! estimates of heterotrophic denitrifying bacteriabe 91 per gram of moist sediment for samples taken fromactive zone of denitrification in the Cape Cod aquifer. For initlaboratory-scale and field-scale model simulations a startingmate of 20mg/m3 for M initial was used. This value was basedmeasured aquifer properties, the MPN estimate, and an assucell mass of 9310214 mg/cell.

Growth Rates and Utilization FactorsGrowth rates and utilization factors were estimated by simulathe incubation experiment. The incubation experiment~concentra-tion versus time! was simulated by solving Eqs.~2!–~4! with thetransport parameters~nx , nz, Dx , andDz! set to zero and thensolving the resulting set of ordinary differential equations. Staing formate and nitrate concentrations were specified to matchinitial concentrations in the laboratory study. A porosity of 80was used for simulating the incubation experiment to reflect cditions of the sediment slurry. Model simulations were conducto match observed formate, nitrate, and nitrite concentrationby systematically varying appropriate microbial parameter valuFor example, decreasingM initial increased the simulated lag perio~i.e., initial period of reduced formate and nitrate utilization! ob-served at the beginning of the incubation. Varying utilization fators ~hN1

andhN2! and maximum growth rates~mF,N1

max andmF,N2

max!

directly altered reaction rates and the resulting concentrationtories.

Advection–Dispersion ParametersHorizontal groundwater velocities were based on arrival timmeasured from breakthrough curves constructed from a brominjection experiment performed in the study area 12 months pto the formate experiment. Vertically stratified horizontal velo


-

t

-

-

d

e

.

-

e

ties, nx(z), were determined using bromide breakthrough curfor MLSs located approximately 7.3 and 10.5 m downgradiensampling ports with elevations of 9.079, 9.333, 9.587, 9.810.095, and 10.349 m~MSL!, respectively. Where data weravailable, the calibrationnx(z) for the formate injection simula-tion was approximately 10% less than the bromide-calibramodel to better match the formate breakthroughs curves atappropriate elevation. This adjustment was attributed to ansumed decrease in the ambient hydraulic gradient between exments. Calibrated model velocitiesnx(z) were 0.356, 0.379,0.400, 0.453, 0.510, and 0.550 m/day at elevations of 9.09.333, 9.587, 9.841, 10.095, and 10.349 m~MSL!, respectively.Above and below the specified elevations an average unifgroundwater velocity of 0.425 m/day was used. All velocitiwere within the range reported by LeBlanc~1984!. Bromidebreakthrough curves also indicated that groundwater flow wunidirectional~i.e., nz'0!.

Dispersion coefficients are a function of groundwater velocand were determined using the following equations:

Dx~z!5axnx~z! (13)

Dz~z!5aznx~z! (14)

where ax5longitudinal dispersivity andaz5transverse verticaldispersivity. Molecular diffusion was assumed negligible. Sotion of the model using a uniform longitudinal dispersivity valuof 0.01 m and a transverse vertical dispersivity value of 0.001provided the best match to the bromide breakthrough curBoth values closely approximated dispersivities reported byrabedian et al.~1991!.

To limit the effects of numerical dispersion, the time step sfor model simulations was contingent upon the Courant numapproaching unity~Anderson and Woessner 1992!, where

Courant5nxDt

Dx'1.0 (15)

whereDx5longitudinal grid spacing andnx5groundwater veloc-ity. A time step size of 0.333 days was used for all field-scmodel simulations. Aquifier porosity~u! in the Cape Cod aquifiervaries from 0.20 to 0.40~LeBlanc 1984! and was set to 0.30 for afield simulations.

Calibration Procedure and Error Analysis

The objective of the calibration was to minimize the averaRMerror for each constituent. Calibration was performed by fiqualitatively evaluating goodness of fit between concentratversus time plots of model simulation results and field dataformate, nitrate, and nitrite at each port at the 7-m MLS.manual trial-and-error adjustment of parameter values was uto achieve the objective combined with a quantitative evaluatof the relative error. According to Thomann~1982!, the RMS is astatistically well-behaved measure of error and is defined as

RMS5F 1

N (i 51

N

~simi2obsi !2G1/2

(16)

where simi5simulated concentrations for a particular soluobsi5observed concentrations for a particular solute; aN5number of observations. Zheng and Bennett~1995! suggestusing relative error to evaluate goodness-of-fit, particularly ifvariation in observed data is large, such as in the case of brthrough curves. Relative error~RMSerror) was obtained by calcu-

ngend

-

rror

l, aallor o

er-ede oionsy ogleensy

ri-

r;-

r-otalni-

or-in-

a-as

ofnts

en-

g

isaduw-at

ni-

hed

ritee.

-

son-t beenlues

lating the ratio of RMS to the total observed concentration chaover the model domain independently for formate, nitrate, anitrite

RMSerror5RMS

~obsmax2obsmin!3100% (17)

where obsmax and obsmin5maximum and minimum observed concentrations. During calibration, a RMSerror was calculated for eachconstituent and each port at the 7-m MLS. An average e(RMSerror! was calculated for each constituent from the RMSerror

for all ports. For model-wide evaluation of the calibrated modetotal RMSerror for formate, nitrate, and nitrite was calculated atthree MLSs. Measured concentrations had an associated err65%.

Sensitivity Analysis

A sensitivity analysis was performed to evaluate model unctainty. Microbial model parameters were systematically changone parameter value at a time, within a predetermined rangvalues. The magnitude of change in simulated concentratrelative to the calibrated model results measured the sensitivitthe solution to that particular parameter. For this study, a sincoefficient for each constituent was used as a measure of stivity. Zheng and Bennett~1995! suggest a normalized sensitivitcoefficient using the following calibration criterion:

Xi ,k5U]RMSerrori

]ak /akU'URMSerror~ak1Dak!2RMSerror~ak!

Dak /akU(18)

whereXi ,k5sensitivity coefficient of the model dependent vaableRMSerror with respect to thekth parameter,ak ~base case!, atthe ith observation point;Dak5small change in the parameteandRMSerror(ak) andRMSerror(ak1Dak)5 values of the dependent variable for the base case and the case whereak has beenchanged byDak , respectively. Sensitivity coefficients were detemined for several microbial model parameters using the tRMSerror described above for simulated formate, nitrate, andtrite concentration variables.

Results and Discussion

Model Results—Incubation Experiment

Figs. 3~A–C!, respectively, show measured and simulated fmate, nitrate, and nitrite concentration data for the laboratorycubation experiment. An initial period of minor formate utiliztion, attributed to acclimation by the microbial population, wobserved during the first 8 days of Fig. 3~A!. A lag in significantelectron acceptor utilization was also observed in Figs. 3~B andC! during the same time, indicating only a relatively minor ratenitrate reduction or nitrite production. Because the sedimewere collected from the zone of active denitrification, somedogenous heterotrophic activity could be expected~e.g., Smithet al. 1994!; however, the model did not account for denitrifyinbacteria utilizing other sources of organic carbon~which may beinfluencing the laboratory data!. An initial microbial concentra-tion ~M initial) of 8 mg/m3 best simulated the lag period. During thtime, the rates of both formate and nitrate mass loss were grally increasing due to an increasing microbial population. Folloing the lag period, the microbial population was functioningpeak activity and formate and nitrate utilization followed a u

f

,f

f

i-

-

form zero-order rate. Consequently, at this point~;8–13 days!,the maximum rates of formate and nitrate utilization were reac@Figs. 3~A and B!, respectively# and continued until the nitratehad been sufficiently depleted~;13 days!. During the same time,there was a corresponding net production of nitrite@Fig. 3~C!#.Throughout the ensuing period~t.13 days!, formate utilizationresulted from nitrite-based respiration. Both formate and nitutilization appears to follow a zero-order rate during this timSimilar results~with slightly different lag periods! were obtainedby Smith et al.~2001! for incubations conducted with core material collected 3 years later from the same location.

Fig. 3. Simulated and measured time course~with regression analy-sis! of formate~A!, nitrate~B!, and nitrite~C! aqueous concentrationfor slurry incubation experiment. Inset graphs show linear relatiship between measured and simulated values. Sediments had nopreviously exposed to added formate. Error bars on measured varepresent65% error.


Table 3. Microbial Model Parameter Values

Parameter values Parameter values %Parameter Units ~laboratory equivalent simulation! ~calibrated simulation! change

KF,N1

ed mM 22.22 22.22 0

KF,N2

ed mM 22.22 22.22 0

KF,N1

ea mM N 14.29 14.29 0

KF,N2

ea mM N 14.29 14.29 0

KI mM M 142.86 142.86 0

mF,N1

max day21 1.40 0.65 254

mF,N2

max day21 0.34 0.20 241

YN1mg/mg 0.19 0.19 0

YN2mg/mg 0.22 0.22 0

M initial mg/m3 8 20 1150

Mmax g/m3 1.0 0.56 244

Kd day21 0.010 0.010 0

hN1mg/mg 1.22 0.33 273

hN2mg/mg 0.65 0.29 255

zN1mg/mg 1.02 1.02 0

d inasero

tion-

ulatlsoco

e o

ltsersre-

er

odealf-tiaons

eaort

andeden.3-m

oneaingerionlse

atedingatabut

the

ch

ory

stheldoryforheen-tesialory-ent

Zero-order utilization rates~Rbiosink) were calculated using the

equations listed in Table 2 and the model parameters listeTable 3. Rate calculations were based on the maximum biomconcentration and peak solute concentrations. The resulting zorder rates for formate loss under nitrate and nitrite reducwere 205 and 43mM/day, respectively. Nitrate and nitrite utilization rates were 152 and 20mM N/day, respectively, and the nitriteproduction rate~Rbio,N2

source! was 156mM N/day.

These results demonstrate that the model was able to simthe major data trends of the incubation experiment. Fig. 3 aincludes a regression analysis of measured against simulatedcentrations for each constituent with eachR2 coefficient approxi-mating a value of unity~0.99 or greater!. The RMSerror for each ofthe three constituents was 4% or less, with a combined averag3.4%.

Sensitivity analysis indicated that laboratory simulation resuwere sensitive to changes in primarily seven input parametformate maximum specific growth rate for nitrate and nitriteduction ~mF,N1

max andmF,N2

max , respectively!, nitrate and nitrite utiliza-

tion factors~hN1and hN2

, respectively!, nitrate inhibition con-stant KI , and biomass concentration (M initial and Mmax!. Tosimulate the zero-order response, half-saturation constants~KF,N1

ed ,

KF,N1

ea , KF,N2

ed , andKF,N2

ea ! were set to values considerably small

than the peak concentrations. The analysis showed that mresults were relatively insensitive to decreases in the hsaturation constants but when these parameters were substanincreased above the calibrated values, the zero-order respwas poorly simulated.

Model Results—Field Experiment

CalibrationBreakthrough curves using model simulation results and msured data for formate, nitrate, and nitrite from the 9.587-m p


s-

e

n-

f

:

l

llye

-

at the three MLSs along the flowpath are shown in Figs. 4, 5,6, respectively. As shown in Fig. 2, the 9.587-m port was alignwith the approximate center elevation of the injection well screFormate was not detected in the field at the 10.349- and 10.60ports. The early-time formate breakthrough at the 7-m [email protected]~A!# was due to the unsteady mass flux at the injection zboundary where a first pulse of formate arrived ahead of the mformate injection. The model was calibrated for the second larpeak of formate, and not for the first peak. As a result, simulatresults for formate at the 10- and 15-m MLS show the first puof formate surviving.

Overall, Figs. 4–6 show a decreasing peak formconcentration with increasing travel distance, and a correspondecrease in the nitrate concentration. Nitrite concentration dand simulation results show a corresponding increase,the peak concentration of nitrite at the 15-m MLS@Fig. 6~C!# didnot increase above the peak concentration observed at10-M MLS.

Two model simulations are presented in Fig. 4 for easolute at the 7-m MLS:~1! an initial run with no calibration,employing parameter values derived from the laboratincubations ~Laboratory Equivalent! and ~2! a calibratedsimulation~Calibrated!. Laboratory Equivalent model simulationoverpredicted the degree of microbial utilization for boformate and nitrate and failed to adequately match the fidata. Based on the simulation results of the laboratexperiments, selected parameters were initially targetedadjustment during the trial-and-error calibration approach. Tmodel was calibrated to the formate, nitrate, and nitrite conctration data at the 7-m MLS, reflecting decreased utilization rarelative to the laboratory-derived rates. Table 3 lists microbparameters and corresponding values for both the laboratcalibrated and field-calibrated simulations with the percchange.

tchob

edudeli-odthe

m--

enthetheni-ing

n-ion

aort

velredn-

tel-on

Model-Wide Calibration EvaluationSimulation results at the 10- and 15-m MLSs~Figs. 5 and 6!demonstrate that the calibrated site model was capable of maing the observed data trends. Similar modeling results weretained for the 9.841-m port at both the 10- and 15-m MLS~datanot shown!. The 9.587- and 9.841-m ports, which were locatwithin the vertical injection zone, intercepted the formate cloalong the entire flow path and, therefore, provided the most rable data. These findings serve as further evidence that the mmatched the transport and utilization of all three solutes alongflow path in both time and space.

Fig. 4. Simulated~laboratory equivalent and calibrated! and mea-sured time course of formate~A!, nitrate~B!, and nitrite~C! concen-trations in groundwater collected from 9.587-m port at 7-m multilesamplers for formate injection experiment. Error bars on measuvalues represent65% error. Inset graph shows formate injection cocentration history from Table 1.

--

el

Results averaged over all ports and all wells for formate coputed a totalRMSerror for the Laboratory Equivalent of 23%, compared to 16% for the Calibrated Simulation. TotalRMSerror fornitrate and nitrite were 33 and 39% for the Laboratory Equivaland 22 and 21% for the Calibrated Simulation, respectively. Tgreater error assisted with both nitrate and nitrite, relative toformate error, was attributed to variability of the backgroundtrate concentration distribution and the uncertainty in specifyinitial conditions.

It is common for trail and error solutions to produce nounique solutions. However, using a large number of calibrattargets distributed over the entire model domain~with a smallassociated error! should increase the probability of obtainingunique solution. In this study, the calibration of the site transp

Fig. 5. Simulated~calibrated! and measured time course of forma~A!, nitrate ~B!, and nitrite ~C! concentrations in groundwater colected from 9.587-m port at 10-m multilevel samplers. Error barsmeasured values represent65% error.


an

iteatectl

a-teri-

iteod

inandn-ut

cal-ableese

onorcali-odel

withate

3

ausetyf-

nrby

.

hy-rifi-

t alyatera-

o-triteob-

ile

of-to

ny

thetheand00

ndr of

ays.rst

tel-on

model relied on discrete measurements taken over both timespace~i.e., concentrations at multilevel samplers! to produce asolution that is free of interpretive bias.

SensitivitySensitivity coefficients calculated for formate, nitrate, and nitrusing Eq.~18! are presented in ranked order in Table 4. Formshowed the greatest sensitivity to three parameters that direimpact the rate of utilization under nitrate reduction:mF,N1

max ,

Mmax, andYN1. Both the simulated nitrate and nitrite concentr

tions showed greatest sensitivity to the same three paramemF,N1

max , Mmax, andhN1. The product of these three variables d

rectly determined the rate of nitrate utilization. Significant nitrproduction resulted when these parameters were increased. M

Fig. 6. Simulated~calibrated! and measured time course of forma~A!, nitrate ~B!, and nitrite ~C! concentrations in groundwater colected from 9.587-m port at 15-m multilevel samplers. Error barsmeasured values represent65% error.


d

y

s:

el

results at the 7-m MLS showed greater sensitivity to variationsthese parameter values relative to model output at the 10-15-m MLSs. Additionally, adjustments to the initial biomass cocentrationM initial exhibited a marked influence on model outpfor all three constituents.

Biological Reaction RatesZero-order reaction rates for the calibrated site model wereculated as described previously using the equations listed in T2 and the calibrated model parameters provided in Table 3. Thrates represent maximum rates, which occur when electron dand acceptor concentrations were at peak levels. Given thebrated parameter set and concentration range, the Monod mpredicts a zero-order reaction rate. This allows a comparisonpublished field-measured zero-order denitrification rates. Formloss under nitrate and nitrite reduction was 142.2mM/day ~6.4mg L21 day21! and 37.8 mM/day ~1.7 mg L21 day21!, respec-tively. Nitrate and nitrite utilization rates were 28.6mM N/day~0.40 mg-N L21 day21! and 7.9 mM N/day ~0.11mg-N L21 day21!, respectively. Nitrite production was 29.mM N/day ~0.41 mg-N L21 day21!. Disparity between the field-derived rates and laboratory-derived rates were expected becin situ microbial activity is generally slower than the activiobserved in slurry incubations, which incorporating mixing efects ~DeSimone and Howes 1996!.

The nitrate utilization rate resulting from the formate injectioexperiment~28.6 mM N/day! was 1 order of magnitude highethan the naturally occurring denitrification rates reportedBrooks et al.~1994! and Smith et al.~1996! at the same siteSmith et al.~1996! calculated in situ rates of 1.5 and 3.9mM N/day ~0.021 and 0.054 mg-N L21 day21, respectively! in two suc-cessive tracer sets. DeSimone and Howes~1996! measured a ni-trate reduction rate of 0.51mM N/day ~0.0071 mg-N L21 day21!in another Cape Cod aquifer with similar geochemistry anddrogeology. The addition of formate clearly accelerated denitcation in this aquifer.

Nitrite AccumulationNitrite production resulting from nitrate reduction occurred arate almost four times greater than nitrite utilization, which likeaccounts for the gradual nitrite accumulation. Disproportionnitrite production and reduction was also observed in the labotory incubation. However, the rate of nitrite utilization in the labratory experiment was 2.5 times greater than the field rate. Niaccumulation is characteristic of denitrification and has beenserved in previous studies. Wilderer et al.~1987! indicated thatchanges in pH and temperature inhibited nitrite utilization, whKorner and Zumft~1989! found that nitrite utilization could beinhibited by the presence of low levels of oxygen or high levelsnitrate. Betlach and Tiedje~1981!, however, suggested that transient nitrite accumulation in pure cultures could be attributeddifferential nitrate and nitrite utilizations rates rather than aspecific inhibition process.

The length of time and travel distance required to consumenitrite produced during the field test was investigated withmodel. Figs. 7, 8, and 9 show simulated formate, nitrate,nitrite concentration distributions, respectively, at 50, 76, and 1days after the formate injection was initiated. Figs. 7~A!, 8~A!,and 9~A! are calibrated model results for formate, nitrate, anitrite, respectively, at the approximate time when the centethe formate plume passed through the 15-m MLS. Fig. 7~B! pre-dicts that the second pulse of formate was consumed by 76 dThe remaining formate at 76 days is theresidual from the fi

ficient

Table 4. Summary of Model Sensitivity

Formate sensitivity Nitrate sensitivity Nitrite sensitivity

Parameter Sensitivity Coefficient Parameter Sensitivity Coefficient Parameter Sensitivity Coef

mF,N1

max 37.10 mF,N1

max 1.73 mF,N1

max 1.74

Mmax 13.29 Mmax 0.70 Mmax 0.64

YN19.63 hN1

0.54 hN10.63

M initial 7.76 M initial 0.41 M initial 0.19

KF,N1

ed 2.34 YN10.16 YN1

0.13

Kd 0.78 KF,N1

ed 0.05 KF,N1

ed 0.08

hN10.63 Kd 0.037 hN2

0.04

mF,N2

max 0.54 YN20.009 Kd 0.027

YN20.47 mF,N2

max 0.006 mF,N2

max 0.025

KI 0.35 KI 0.004 KI 0.02

KF,N2

ed 0.01 KF,N2

ed 0.0007 YN20.008

hN20.004 KF,N1

ea 0.0002 KF,N2

ed 0.003

KF,N1

ea 0.0 KF,N2

ea 0.0002 KF,N1

ea 8.0E-6

KF,N2

ea 0.0 hN20.0002 KF,N2

ea 8.0E-6

Fig. 7. Simulated concentration distribution for formate at 50~A!, 76~B!, and 100 days~C! after start of formate injection experiment

Fig. 8. Simulated concentration distribution for nitrate at 50~A!, 76~B!, and 100 days~C! after start of formate injection experiment


late

the

butted

e toetrite

annd

asias

atef thay

meisigs

thelagnsse,ffi-of

rite

ite:sni

thete-

ghn-

t inte

teen

rateion

me

ns,ac-o-or-size

be-ntthe

uldwnni-

en-te-there-

e of

henni-

hefor

thesedtes

and

the

undap-ltsdicttionatealnten-beay

injection pulse, but because the model did not accurately simuthe leading edge of the formate@see Fig. 6~A!#, it is likely thatboth formate pulses were depleted by 76 days and no furdenitrification would be expected. Figs. 8~A and B! predict anexpansion in the zone of nitrate depletion from 50 to 76 days,between 76 and 100 days no further nitrate utilization is indica@Fig. 8~C!#. Instead, an increase in nitrate concentrations dudispersion was noted. Figs. 9~A–C! suggest that the nitrite plumwould have increased in size over the entire period but that niconcentrations would decrease from 76 to 100 days.

These observations are supported by calculations of zerothfirst moments for the formate and nitrite plumes at 50, 76, a100 days. Between 50 and 76 days, formate mass was decreand nitrite mass was increasing, but changes in the formate mand nitrite mass were negligible from 76 to 100 days. The formcenter of mass at 50 days was located 1.0 m downgradient onitrite center of mass. This distance increased to 7.0 m by 76 dand 7.5 m by 100 days, as the remaining formate was consufrom day 50 to day 76, resulting in limited denitrification. Thseparation of the plumes is demonstrated by comparison of F7~C! and 9~C!. The lingering formate plume in Fig. 7~C! repre-sents the formate delivered during the first several days ofinjection period, which persisted in the simulations due to thein formate utilization as the cloud of formate moved into regioof the aquifer with a low level of ambient biomass. In this cathe concentration of formate and rate of utilization are not sucient to stimulate enough biomass growth in the time framesolute transport to result in significant nitrate removal and nitproduction/removal.

Several factors combine to explain the persistence of nitrelectron donor~formate! availability, preferential use of nitrate aan electron acceptor over nitrite, and the difference betweentrite utilization and nitrite production rates. The data show andmodel predicts formate utilization first occurring under nitra

Fig. 9. Simulated concentration distribution for nitrite at 50~A!, 76~B!, and 100 days~C! after start of formate injection experiment


r

d

ngs

esd

.

-

reducing conditions, which produced nitrite at a relatively hirate. Nitrite utilization is substantial only in zones where the cocentration of nitrate falls to below approximately 72mM andformate is available. Thus, several conditions must be meorder for nitrite to be consumed: sufficient depletion of nitra~combined with nitrite production! accompanied by an adequasupply of formate. Contact time between formate and nitrite thbecomes a complicating factor because the nitrite utilizationis approximately 3.6 times less than the rate of nitrate utilizat~and thus, the rate of nitrite production!. As shown in Fig. 6,sediment-bound nitrite-reducing bacteria have a limited tiframe ~approximately 4–6 days at the 15-m MLS! to utilize for-mate and nitrite in the absence of nitrate. All of these conditioalong with a decreasing supply of formate, contribute to thecumulation of nitrite. Another contributing factor is the reintrduction of nitrate into the thin zone of overlap between the fmate and nitrite clouds over time, depicted by the decreasingin the zone of nitrate depletion@compare Fig. 8~B! to 8~C!#. Thegradual dispersive mass flux of nitrate into the overlap zonetween the formate and nitrite clouds could inhibit downgradienitrite consumption. That being the case, it is thought then thatprimary mechanism for nitrite attenuation after 100 days wobe dilution and dispersion of the nitrite plume as it travels dogradient with minor reductions occurring due to the residual detrification.

Conclusions

A 2D numerical solute transport model was applied to anhanced in situ denitrification experiment performed in a nitracontaminated aquifer on Cape Cod, Mass. By incorporatingproduction and reduction of nitrite, this model expands upon pvious models that describe nitrate transport~e.g., Widdowsonet al. 1988; Kinzelbach et al. 1991; Smith et al. 1996! and pro-vides a novel approach and useful tool to investigate the ratenhanced denitrification to interpret laboratory and field data.

A site model was developed, calibrated to field data, and tevaluated using breakthrough curves of formate, nitrate, andtrite at three multilevel ground water sampling devices. Tmodel simulation results match trends in both time and spaceformate, nitrate, and nitrite. However, uncertainty regardinginitial concentration distribution for nitrate appears to have biamodel results for both nitrate and nitrite. Formate utilization rafor the simulation of the field experiment were 142.2mM/day ~6.4mg L21 day21! and 37.8mM/day ~1.7 mg L21 day21! under nitrateand nitrite reduction, respectively. Reduction rates for nitratenitrite were 28.6mM N/day ~0.40 mg -N L21 day21! and 7.9mMN/day ~0.11 mg -N L21 day21!, respectively. Nitrite productionwas 29.3mM N/day ~0.41 mg -N L21 day21!.

Intrinsic denitrification rates reported in previous studies atCape Cod study site~Brooks et al. 1994; Smith et al. 1996! are atleast 1 order of magnitude lower than the enhanced rates fohere, which demonstrates the potential efficacy of using thisproach for in situ remediation of nitrate. However, model resualso suggest nitrite accumulation along the flow path, and prea persistence of nitrite after formate depletion. The accumulaand apparent persistence of nitrite, primarily due to a lower rof nitrite utilization relative to nitrate utilization and the eventudepletion of formate in the nitrite plume, limits the denitrificatioprocess in this experiment. The persistence of nitrite is a potially serious problem, because of nitrite toxicity, which shouldinvestigated further with in situ pilot testing. This problem m

atecalas-r t

o-ndnceber.S.

eo-

al

ates-

ll

y,

-

nds

apective

at-

’’ts in

ted

ake

sub-

r,o.

s

W. C.g

ts.’’

ns-

be remedied by more concentrated, additional, or larger forminjections or possibly through augmenting the natural biologicommunity. The feasibility of the remedial design may besessed via model simulations and should be investigated prioimplementation of any enhanced remediation scheme.

Acknowledgments

The writers thank D. R. LeBlanc, coordinator of the U.S. Gelogical Survey Cape Cod Site, and M. H. Brooks for field atechnical assistance. They also thank D. N. Miller for assistawith the laboratory incubations and K. M. Hess and M. Schreifor manuscript reviews. This study was funded in part by the UDept. of Agriculture Grant No. 95-37101-1713 and the U.S. Glogical Survey Toxic Substances Hydrology Program.

Notation

The following symbols are used in this paper:

VariablesF 5 formate concentration~M/L3!;M 5 biomass concentration~M/L3!;N1 5 nitrate concentration~M/L3!; andN2 5 nitrite concentration~M/L3!.

ParametersDx 5 horizontal dispersion coefficient~L2/T);Dz 5 vertical dispersion coefficient~L2/T);

KF,N1

ed5 formate half-saturation constant for nitrate reduc-

tion ~M/L3!;KF,N2

ed5 formate half-saturation constant for nitrate reduc-

tion ~M/L3!;KF,N1

ea5 nitrate half-saturation constant~M/L3!;

KF,N2

ea5 nitrite half-saturation constant~M/L3!;

KI 5 nitriate inhibition constant~M/L3!;kd 5 biomass decay coefficient~M/M per T!;

Rbio,Fsink 5 formate biological consumption rate~M/L3/T);

Rbio,N1

sink5 nitrate biological consumption rate~M/L3 per T!;

Rbio,N2

sink5 nitrite biological consumption rate~M/L3 per T!;

Rbio,N2

source5 nitrite biological production rate~M/L3 per T!;

t 5 time ~t!;x 5 horizontal coordinate~L!;

YN1 5 yield coefficient for nitrate reduction~M/M !;YN2 5 yield coefficient for nitrite reduction~M/M !;

z 5 vertical coordinate~L!;ax 5 horizontal dispersivity~L!;az 5 vertical dispersivity~L!;

zN1 5 nitrite production constant~M/M !;hN1 5 nitrate utilization factor~M/M !;hN2 5 nitrite utilization factor~M/M !;

mF,N1 5 growth rate for nitrate reduction~M/M per T!;mF,N2 5 growth rate for nitrite reduction~M/M per T!;mF,N1

max5 maximum growth rate for nitrate reduction~M/M

per T!;mF,N2

max5 maximum growth rate for nitrite reduction~M/M

per T!;nx 5 horizontal velocity~L/T!; andnz 5 vertical velocity~L/T!.

o

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Modeling Enhanced In Situ Denitrification in Groundwater

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