Modeling Enhanced In Situ Denitrification in Groundwater Marc 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 denitrification experiment performed in a nitrate-contaminated aquifer on Cape Cod, Massachusetts. In this experiment, formate 共HCOO⫺兲 was injected for a period of 26 days into the carbon-limited aquifer to stimulate denitrification. Calibration of the vertical-profile site model was demonstrated through error analysis and comparison with formate, nitrate, and nitrite concentration data monitored along a transect of three multilevel groundwater sampling wells for 75 days after initial injection. Formate utilization rates were approximately 142 and 38 M/day for nitrate and nitrite reduction, respectively. Nitrate and nitrite utilization rates were approximately 29 and 8 M/day, respectively. Nitrate utilization rates under enhanced conditions were 1 order of magnitude greater than previously reported naturally occurring rates. The nitrite production rate was approximately 29 M/day. Persistence of nitrite was attributed to a combination of factors, including electron donor 共formate兲 limitation late in the experiment, preferential utilization of nitrate as an electron acceptor, and greater nitrite production relative to nitrite utilization. DOI: 10.1061/共ASCE兲0733-9372共2002兲128:6共491兲 CE Database keywords: Denitrification; Groundwater; Nitrates; Massachusetts; Nitrites; Biological treatment.
Introduction Nitrate 共NO⫺ 3 兲 is the most common groundwater contaminant found in fresh water aquifers, particularly shallow unconfined aquifers in rural areas 共Nolan et al. 1997兲. The prevalence of nitrate in the subsurface is attributed to both point and nonpoint sources, such as various agricultural practices 共Hallberg 1989兲 and infiltration of municipal and rural wastewater effluent. Mueller et al. 共1995兲 found nitrate levels exceeded the Environmental Protection Agency 共EPA兲 maximum contaminant level 共MCL兲 in 21% of shallow wells in agricultural areas. Discharge of nitratecontaminated ground water to surface waters is also problematic. In the Chesapeake Bay watershed, where there are extensive areas with shallow groundwater underlying well-drained agricultural soils, Gallagher et al. 共1996兲 reported that nitrate transport to coastal waters via groundwater discharge may be significant for both local and regional flow systems. In some instances, nutrient loading of coastal waters by way of groundwater discharge may exceed nutrient loading through surface runoff 共Lee and Olsen 1985; Giblin and Gaines 1990; Valiela et al. 1990兲. Nitrate is highly soluble and mobile, and thus poses significant health hazards. Comly 共1945兲 found that infants who had consumed nitrate-contaminated well water developed methemoglobinemia 共i.e., ‘‘blue baby syndrome’’兲, a potentially fatal condi1
ARCADIS Geraghty & Miller, Inc., 1131 Benfield Blvd. Suite A, Millersville, MD 21108. 2 Dept. of Civil and Environmental Engineering, Virginia Polytechnic Institute and State Univ., Blacksburg, VA 24061 共corresponding author兲. E-mail:
[email protected] 3 U.S. Geological Survey, 3215 Marine St., Boulder, CO 80303. Note. Associate Editor: Eric A. Seagren. Discussion open until November 1, 2002. Separate discussions must be submitted for individual papers. To extend the closing date by one month, a written request must be filed with the ASCE Managing Editor. The manuscript for this paper was submitted for review and possible publication on July 31, 2000; approved on August 20, 2001. This paper is part of the Journal of Environmental Engineering, Vol. 128, No. 6, June 1, 2002. ©ASCE, ISSN 0733-9372/2002/6-491–504/$8.00⫹$.50 per page.
tion. When ingested, nitrate is converted to nitrite 共NO⫺ 2 ) by the body and reacts with hemoglobin 共which carries oxygen to all parts of the body兲 in the bloodstream to form methemoglobin 共which does not carry oxygen兲 resulting in suffocation of the victim 共Comly 1945兲. Intake of nitrate-contaminated drinking water has also been linked to gastric cancer mortality rates 共Forman 1989兲 and non-Hodgkin’s lymphoma 共Weisenburger 1991兲. In view of these health concerns, the EPA identified nitrate and nitrite as primary water contaminants and, as required by the Safe Drinking Water Act of 1974, determined MCLs for nitrate and nitrite at 10 and 1 mg N/L, respectively. The ubiquitous nature of nitrate in the subsurface has hastened the development of novel remeditation and drinking water treatment techniques. In situ treatment methods are especially desirable because of the potential to provide safe and cost efficient remediation of nitrate-contaminated groundwater with minimal site disturbance. Researchers 共e.g., Vogel et al. 1981; Trudell et al. 1986; Starr and Gillham 1989; Smith et al. 1991a; Montgomery et al. 1997兲 have noted that in situ denitrification is the dominant biological process for naturally occurring microbially mediated process where nitrate is reduced to gaseous nitrogen 共 N2兲. During denitrification, nitrate serves as a terminal electron acceptor in the metabolism of facultative anaerobic bacteria 共Tiedje 1988兲. The presence of nitrate, nitrite, or nitrous oxide (N2O) as an electron acceptor, denitrifying bacteria, anaerobic conditions, or restricted oxygen availability, and an adequate supply of electron donors are required for denitrification to occur at any particular location in a groundwater system 共Firestone 1982兲. The presume pathway of denitrification, with the oxidation state of the nitrogen atom shown in parentheses, is presented as follows 共Payne 1981兲: 共 ⫹5 兲
共 ⫹3 兲
共 ⫹2 兲
共 ⫹1 兲
共0兲
⫺ NO⫺ 3 →NO2 → NO →NO2→NO2
In natural systems denitrification is often electron donor limited 共Smith and Duff 1988; Starra and Gillham 1989; DeSimone and Howes 1996兲 which, consequently, impedes the rate of denitrification. Another complicating factor is the production and po-
tential persistence of nitrite, which is more toxic than nitrate because it reacts immediately with hemoglobin. While the problem of nitrite accumulation has been investigated in activated sludge 共e.g., Wilderer et al. 1987兲 and bacterial cultures 共e.g., Betlach and Tiedje 1981兲, it has not received significant attention in the literature as a groundwater contaminant. A number of researchers have found that denitrification activity in organic carbon-limited aquifers can successfully be enhanced with the addition of an electron donor 共Slater and Capone 1987; Smith and Duff 1988; Starr and Gillham 1989; Obenhuber and Lowrance 1991; Smith et al. 1994; Smith et al. 2001兲. Organic carbon additions such as methanol, ethanol, or glucose have been used in field experiments 共Slater and Capone 1987; Mercado et al. 1988兲. However, some denitrifiers are capable of autotrophic nitrate reduction coupled with hydrogen oxidation without excessive biomass buildup 共Smith et al. 1994兲. Under this scenario, the stoichiometric relationship for the reduction of nitrate to nitrogen gas is as follows:
The model incorporates the transport and utilization of nitrate and nitrite as electron acceptors. Nitrite production resulting from nitrate reduction was integrated, and growth and decay of a nitrate/ nitrite-reducing microbial population simulated. To test the conceptual and mathematical model for microbial processes, the model was first applied to a laboratory incubation experiment using aquifer sediments taken from the study area. A field-site model was developed for simulation of formate, nitrate, and nitrite transport and mirobial utilization in a 2D vertical domain oriented in the mean direction of transport. The transport and utilization model was then calibrated using formate, nitrate, and nitrite concentration versus time data measured at three multilevel sampling 共MLSs兲 wells located along the groundwater flow path. Model simulation results were subsequently used to interpret field data, to quantify utilization rates, to quantify the rate of nitrite production, and to investigate the persistence of nitrite.
Enhanced Denitrification Experiment
⫺ 2NO⫺ 3 共 aq 兲 ⫹5H2→N2共 g 兲 ⫹4H2O⫹2OH
Hydrogen-enhanced denitrification has been utilized with success in pilot-scale ex situ treatment applications in Europe 共Gros et al. 1988; Liessens et al. 1992兲. Smith et al. 共1994兲 found that hydrogen-oxidizing dentifiers made up approximately 7% of the dentrifying population in a nitrate-contaminated aquifer and speculated that this population could be specifically targeted with the addition of hydrogen. While hydrogen is not readily soluble in water, hydrogen-producing compounds 共e.g., formate兲 have the potential to serve as soluble hydrogen substitutes for enhanced in situ denitrification. Smith et al. 共2001兲 recently performed an in situ field experiment by adding formate to a nitrate plume. They found that the formate addition did stimulate in situ denitrification. However, is also appeared likely that the experiment enriched a population of formate-utilizing denitrifiers rater than autotrophic hydrogen-oxidizing dentifiers, as was initially intended. An integral component of evaluating in situ field tests has been the application of mathematical models to determine biological reaction rates and to interpret field data. 共Harvey and Garabedian 1991; Kinzelbach et al. 1991; Smith et al. 1991b; 1996兲. Relatively few mathematical models have been developed that describe the fate and transport of nitrate in groundwater systems 共e.g., Widdowson et al. 1988; Kinzelbach et al. 1991; Smith et al. 1996兲 or that incorporate the process noted in field studies. Widdowson et al. 共1988兲 developed a one-dimensional transport model for the biodegradation of a carbon substrate subject to sequential aerobic and nitrate-based respiration. Smith et al. 共1996兲 utilized a zero-order degradation term in a onedimensional model to describe nitrate reduction directly to nitrous oxide 共in the presence of acetylene兲 to interpret naturally occurring denitrification in the Cape Code aquifer. Electron donor concentration was not simulated and was assumed a constant factor limiting denitrification. Kinzelbach et al. 共1991兲 developed and applied a two-dimensional 共2D兲 model to simulate 共1兲 naturally occurring denitrification in a carbon-limited aquifer and 共2兲 enhanced bioremediation of a hydrocarbon spill using nitrate injection. None of the three modeling studies considered nitrite production or reduction of denitrification intermediates. The purpose of this study was to develop and apply a 2D numerical model to simulate an enhanced in situ denitrification experiment. The field experiment consisted of injecting groundwater amended with formate into a nitrate plume, and monitoring the microbial response of the nature denitrifying population in a nitrate-contaminated aquifer on Cape Cod 共Smith et al. 2001兲.
Study Site The study was conducted in a shallow, unconfined, sand and gravel aquifer located on Cape Cod, Mass. Groundwater at this location was contaminated from the long-term disposal 共⬃60 years兲 of dilute, treated sewage effluent, which has resulted in a contaminant plume that is more than 4 km long 共LeBlanc 1984兲. Nitrate is a major constituent of the contaminant plume 共LeBlanc 1984; Smith et al. 1991a兲. The plume is also characterized by elevated concentrations of dissolved solids, boron, chloride, sodium, phosphorous, ammonium, and detergents in addition to various other constituents. In general, the plume consists of both vertical and horizontal gradients of dissolved oxygen 共⬃0– 8 mg/ L兲, pH 共5–7.1兲, dissolved organic carbon 共1– 4 mg/L, much of which is recalcitrant兲, chloride 共0–28 mg/L兲, sulfate 共4 –30 mg/ L兲, nitrate 共0–16 mg N/L兲, and ammonium 共0–10 mg N/L兲 共LeBlanc 1984; Thurman et al. 1986兲. The in situ injection experiment was conducted at site F473 共Fig. 1; also see map in Smith et al. 1996兲, which is located 0.3 km downgradient from the source of contamination.
Incubation Experiment Core material was collected from site F473 using a wire-line piston core barrel and stored at 4°C 共Smith et al. 1996兲. The core material was collected from the same depth but upgradient of the in situ injection experiment. Anoxic, sediment slurry incubations were prepared in 250-mL flasks using artificial groundwater 共Smith et al. 2001兲. Initial concentrations of nitrate and formate were 687 and 3,270 M, respectively. The flasks were incubated at 15°C; water was periodically removed by syringe, filtered, and analyzed for nitrate, nitrite, and formate concentrations 共Smith et al. 2001兲.
In Situ Injection Experiments The field experiment was conducted in September 1994 at site F473 in which sodium formate was added to nitrate-contaminated groundwater to test whether in situ denitrification could be stimulated by addition of an electron donor. Details are given in Smith et al. 共2001兲. Briefly, a sterile anoxic stock solution containing sodium formate and sodium bromide was metered into groundwater that was being continuously pumped from one well and injected back into a second well at 6 – 8 L/h. The withdrawal and
Table 1. Formate Injection Concentration Data Formate injectate concentration 共M兲
Data of injection
Fig. 1. Detail of site F473 on Cape Cod, Mass.; multilevel samplers 共MLS兲 are designated by row and by number 共e.g., MLS 12 in row 4 is designated 4-12兲
injection wells were screened from approximately 9.4 –10.3 m above mean sea level 共MSL兲. Formate injection concentration 共Table 1兲 was variable over the 26-day injection period. The average background nitrate concentration was approximately 500 M, and the average formate injectate concentration was approximately 5,400 M during the peak injection period. The tracer cloud that resulted from the injection process moved downgradient by natural groundwater flow and was intercepted and sampled by rows of MLSs 共Fig. 1兲. Groundwater samples were collected from the MLSs with a peristaltic pump and preserved for analysis 共Smith et al. 2001兲.
Model Development Conceptual Model The model is an extension of a previously published onedimensional model that describes transport and biodegradation of three solutes 共one electron donor and two aqueous-phase electron acceptors: oxygen and nitrate兲 coupled with the growth and decay of a facultative heterotrophic microbial population 共Widdowson et al. 1988兲. For this study, the model was used to simulate formate-utilizing denitrification. The model was extended for 2D transport and expanded to include the transport, production, and reduction of nitrite. The result is a system of four differential equations describing the fate and transport of an electron donor 共formate兲, electron acceptors 共nitrate and nitrite兲, and the growth and decay of a single homogeneous nitrate/nitrite-reducing micro-
02 Sept 02 SeptR 03 Sept 06 Sept 07 Sept 07 SeptR 08 Sept 09 Sept 10 Sept 11 Sept 11 SeptR 12 Sept 13 Sept 14 Sept 15 Sept 16 Sept 17 Sept 18 Sept 19 Sept 20 Sept 21 Sept 22 Sept 23 Sept 25 Sept 26 Sept 27 Sept Note:
R
1,601 1,592 1,486 1,025 874 867 98 0 19 11 12 0 0 217 4,841 4,383 3,919 4,458 10,582 8,510 3,444 3,258 7,067 4,570 138 44
denotes replicate sample.
bial population. The microbial population was modeled as an arrangement of sediment-bound groups of bacteria, commonly referred to as microcolonies, initially distributed uniformly throughout the aquifer matrix. No geometry or dimensions are associated with the microcolonies. Because the injectate and area of the aquifer impacted by the injectate were anoxic 共Smith et al. 1991a兲, dissolved oxygen was not included in the model. Other factors that may potential inhibit or enhance denitrification 共such as, pH, temperature, and the presence of sulfur compounds兲 were also assumed to be negligible.
Mathematical Model Transport Equations The general form of the 2D solute transport equation assuming vertically stratified flow including biological reactions is ⫺ x 共 z 兲
C C 2C 2C sink ⫺ z 共 z 兲 ⫹D x 共 z 兲 2 ⫹D z 共 z 兲 2 ⫺R bio,C x z x z
source ⫹R bio,C ⫽
C t
(1)
where C⫽aqueous phase concentration of a particular solute (M/L3); x and z⫽distances measured along the longitudinal and transverse vertical directions, respectively 共L兲; x and z ⫽average groundwater velocities in the longitudinal and transverse vertical directions, respectively 共L/T兲; D x and D z ⫽dispersion coefficients in the longitudinal and transverse versource tical directions, respectively 共L2/T); R bio,C accounts for the production of mass resulting from microbial processes 共M/L3 per T兲;
Table 2. Equations for Biological Utilization and Production Terms Biological utilization
Based on equations
Equation sink Rbio,F ⫽
Formate utilization
⫻ sink Rbio,N ⫽
Nitrate utilization
1
冋 冋
册冋 册冋
册 册冋 册 冋 册冋 册 冋 册冋 册 冋 册
max M F,N1 M F N1 ⫹ ed ea Y N1 K F,N ⫹F K F,N ⫹N1 max F,N
1
1
N2 KI F 2 ed ea Y N2 K F,N ⫹F K F,N ⫹N2 K I ⫹N1 2
2
sink Rbio,N ⫽ 2
1
F M N2 KI max ed ea N 2 F,N2 K F,N ⫹F K F,N ⫹N2 K I ⫹N1 2
2
sink and R bio,C represents mass loss due to biological utilization 共M/L3 per T兲. No other mass loss 共e.g., sorption兲 or production terms appear in Eq. 共1兲. Using Eq. 共1兲 as a general expression and substituting the appropriate terms for sources and sinks, mass balance equations for formate 共F兲, nitrate 共N1兲, and nitrite 共N2兲 concentrations, respectively, are written as
F F 2F 2F F sink ⫺ z 共 z 兲 ⫹D x 共 z 兲 2 ⫹D z 共 z 兲 2 ⫺R bio,F ⫽ x z x z t (2)
N1 N1 N1 N1 sink ⫺ x 共 z 兲 ⫺R bio,N ⫺ z 共 z 兲 ⫹D x 共 z 兲 2 ⫹D z 共 z 兲 1 x z x z 2 2
⫽
(3)
N2 N2 2 N2 2 N2 sink ⫺ z 共 z 兲 ⫹D x 共 z 兲 ⫹D z ⫺R bio,N 兲 共 z 2 x z x 2 z 2
source ⫹R bio,N ⫽ 2
N2 t
(4)
Reaction Terms sink The reaction term for formate utilization 共R bio,F ), expressed as the sum of utilization due to nitrate-based reduction 共r F,N1兲 and nitrite-based reduction 共r F,N2兲, is defined as sink R bio,F ⫽
共8兲
冉
M M F,N1 F,N2 ⫹ 共 r F,N1⫹r F,N2兲 ⫽ Y N1 Y N2
冊
(5)
where M⫽the amount of biomass per volume of porous medium 共M/L3兲; ⫽the aquifer porosity defined by the volume of voids per total volume; F,N1 and F,N2⫽the microbial specific growth rates for nitrate and nitrite reduction, respectively 共M/M per T兲; and Y N1 and Y N2⫽the yield coefficients 共M/M兲, which is the ratio of microbial biomass produced per mass of electron donor consumed, for nitrate- and nitrite-based reduction, respectively. sink Nitrate mass loss rate, R bio,N , resulting from utilization as an 1 electron acceptor, is expressed as sink R bio,N ⫽ 1
1
where N1⫽the nitrate utilization factor 共M of NO⫺ 3 /M of electron donor兲. Nitrite mass loss rate is similarly defined as sink R bio,N ⫽ 2
M N1 F,N1
(6)
M N2 F,N2
(7)
where N2⫽ nitrite utilization factor 共M of NO⫺ 2 /M of electron donor兲. Nitrite production resulting from denitrification is proportional to the amount of nitrate consumed. Biological nitrite production is defined by the following relationships: source sink R bio,N ⫽ N1R bio,N
2
N1 t
⫺ x 共 z 兲
共7兲, 共10兲
2
source⫽ R sink R bio,N N1 bio,N
Nitrite production
⫺ x 共 z 兲
共6兲, 共9兲
F N1 M max ed ea N1 F,N1 K F,N ⫹F K F,N ⫹N1 1
Nitrite utilization
共5兲, 共9兲, 共10兲
2
(8)
1
⫺ where N1⫽nitrite production constant 共M of NO⫺ 2 /M of NO3 兲. Table 2 lists the biological source and sink terms used in Eqs. 共2兲, 共3兲, and 共4兲 for formate, nitrate, and nitrite, respectively.
Microbial Population Growth Dynamics Microbial specific growth rates were represented using dual Monod kinetics, which assume that population growth rates are limited by both the electron donor and the electron acceptor 共Table 2兲. Harris and Hanford 共1976兲 developed a modified Monod equation to represent the microbial growth rate using oxygen as an electron acceptor. Molz et al. 共1986兲 and Widdowson et al. 共1988兲 adapted the modified Monod equation to porous media transport. In this study, the specific growth rate equation for nitrate-based respiration is expressed as max F,N1⫽ F,N
冋
1
F
册冋
N1
ed ea K F,N ⫹F K F,N ⫹N1 1
1
册
(9)
max ⫽maximum specific growth rate for nitrate utilization where F,N 1 ed 共M/M per T兲; K F,N ⫽formate half-saturation constant for nitrate 1 ea 3 reduction 共M/L 兲; and K F,N ⫽nitrate half-saturation constant 1 3 共M/L 兲. In the present model, nitrate is preferentially utilized as an electron acceptor due to a higher energy yield relative to nitrite 共Waddill and Widdowson 1998兲. Based on the Widdowson et al. 共1988兲 model, the specific growth rate for nitrite-based respiration is expressed as
max F,N2⫽ F,N
冋
2
册冋
册冋 册
F N1 KI ed ea K F,N ⫹F K F,N ⫹N1 K I ⫹N1 2
2
(10)
Fig. 2. Boundaries of two-dimensional vertical profile model and schematic of formate injection experiment. Identification number of each multilevel sampler is given in parentheses. max where F,N ⫽maximum specific growth rate for nitrite utilization 2 ed 共M/M per T兲; K F,N ⫽formate half-saturation constant for nitrite 2 ea 3 reduction 共M/L 兲; and K F,N ⫽nitrite half-saturation constant 2 3 共M/L 兲, and K I ⫽nitrate inhibition constant 共M/L3兲. Preferential use of nitrate is described using an inhibition function, represented by the expression
冋
K1 K 1 ⫹N1
册
which is modified from previously published models 共Widdowson et al. 1988; Waddill and Widdowson 1998兲. Changes in the microbial population during periods of growth and decay are simulated by a mass balance equation that accounts for biomass growth and decay terms 1 M ⫽ F,N1⫹ F,N2⫺k d M t
(11)
where k d ⫽biomass decay coefficient 共M/M per T兲. Because nitrate and nitrite are electron acceptors that support the microbial biomass, Eq. 共11兲 includes growth terms for both electronaccepting processes. Eq. 共11兲 is solved directly so that the microbial biomass is expressed as the minimum of Eqs. 共12a兲 and 共12b兲 M ⫽M initial exp关共 F,N1⫹ F,N2⫺k d 兲兴
(12a)
M ⫽M max
(12b)
where M initial⫽initial amount of biomass per volume of porous medium 共M/L3兲 and M max⫽maximum or upper limit to the biomass per volume of porous medium 共M/L3兲.
Site Model The formate injection experiment was simulated using 2D, vertical profile model. The site model was oriented along the principal direction of groundwater flow and incorporated three MLSs at travel distances of 7.02, 10.10, and 15.58 m downgradient of the injection well 共located in Rows 4, 6, and 8, respectively兲, henceforth referred to as the 7-, 10-, and 15-m MLS, respectively. The vertical profile model incorporated a 2D, stratified flow field. The groundwater flow field was not specifically solved using a numerical model but, instead, the velocity profile was entered based on site data and depth-dependent tracer breakthrough curves measured at individual sampling ports 共described below兲. Flow disturbance at the formate injection well was assumed to be negligible based on the ratio of the injection rate to the mean rate of groundwater flow 共approximately 0.05兲. Fig. 2 is a representation of the vertical profile model domain, showing the location of the
three MLSs and the injection well. In the field, sampling ports were positioned at identical elevations for each MLS. Sampling port spacing was uniform 共0.254 m兲. A 2D mesh-centered, finite-difference grid system was employed consisting of a 498 node 共longitudinal兲⫻34 node 共vertical兲 matrix, which covers a 63.08 m⫻4.32 m area. Grid spacing was determined primarily by the injection experiment layout. The upper and lower grid boundaries to the site model were set at 12.127 and 7.809 m 共MSL兲, respectively, and were no-flow, zeroflux boundaries for all three solutes. The elevations of these boundaries were selected to provide adequate distance above and below the injection and sampling zones to minimize undue influence on the simulation of the formate plume. Vertical node spacing was uniform 共⌬z⫽0.127 m兲, and horizontal grid lines were positioned to match up with the MLS sampling ports. Longitudinal node spacing was also uniform 共⌬x⫽0.127 m兲, and vertical grid lines were positioned to match up with the three MLSs. Initial conditions for the solute transport model were based on sampling data collected immediately prior to the formate injection experiment and several site characterization reports. Background concentrations for formate were negligible. The starting nitrate concentration distribution was estimated using vertical concentration profiles from the initial sampling data and ranges from 7.17 to 15.80 mg N/L. The initial nitrite concentration was uniform 共0.246 mg N/L兲 and was based on the average measured concentration of the initial sample set. Boundary conditions along the inflow boundary 共x⫽0兲 for the three solutes were specified as a function of space, and for formate, as a function of time. At boundary nodes associated with the injection well screen, delineated from 9.460 to 10.222 m 共MSL兲, formate concentrations were uniform with space. Because the formate mass flow rate delivered to the aquifer was transient, formate concentrations were specified as a function of time to match measured injection data. Influent boundary concentrations for nitrate and nitrite were steady, nonuniform line sources and were estimated from field data. The downgradient boundary was a free-gradient condition 共Widdowson et al. 1988兲.
Modeling Approach The model was first applied to a laboratory incubation study performed by Smith et al. 共2001兲 using site sediment to primarily test the mathematical formulation of the reaction terms. The secondary purpose of this initial step was to provide starting parameter estimates for field-scale model simulations. Advective transport and dispersion transport parameters 共i.e., D x , D z , x , and z 兲 for simulation of the field experiment were determined by calibrating
Eq. 共1兲 to bromide data collected from a previous injection exsource periment 共where R sink bio ⫽R bio ⫽0兲 as well as transport parameters reported by LeBlanc 共1984兲 and Garabedian et al. 共1991兲. For the field-scale model simulations, the overall approach was to calibrate the model to data collected at the 7-m MLS and then evaluate the model calibration over the entire model domain using data collected from the 10- and 15-m MLSs. Model accuracy was evaluated qualitatively by comparing simulated and observed concentration versus time breakthrough curves for formate, nitrate, and nitrite at each of the three MLSs. A quantitative measure of the relative error between simulated and field results for each constituent was obtained by calculating the ratio of the root mean 共RMS兲 of square residual errors to the total measured concentration change 共RMSerror). Calibration was achieved by minimizing RMSerror for each constituent simultaneously. Model sensitivity was also investigated.
Parameter Estimation Microbial Population Data Harvey et al. 共1984兲 found that free-living bacterial populations in the Cape Cod aquifer varied from a maximum of 2⫻1016 cells/mL near the sewage effluent infiltration beds to 2.5⫻105 cells/mL at a distance of 1 km downgradient from the beds. However, more than 90% of the bacteria in the aquifier were attached to particulate surfaces. Population densities of particle-bound bacteria range from about 2⫻107 to 4⫻107 cells/cm3 of aquifer material 共Harvey et al. 1984兲. Several studies have shown that an active denitrifying zone exists within the contaminant plume 共e.g., Smith and Duff 1988; Smith et al. 1991a; Smith et al. 1994; Smith et al. 1996兲. Smith et al. 共1994兲 reported most probable number 共MPN兲 estimates of heterotrophic denitrifying bacteria to be 91 per gram of moist sediment for samples taken from the active zone of denitrification in the Cape Cod aquifer. For initial laboratory-scale and field-scale model simulations a starting estimate of 20 g/m3 for M initial was used. This value was based on measured aquifer properties, the MPN estimate, and an assumed cell mass of 9⫻10⫺14 mg/cell. Growth Rates and Utilization Factors Growth rates and utilization factors were estimated by simulating the incubation experiment. The incubation experiment 共concentration versus time兲 was simulated by solving Eqs. 共2兲–共4兲 with the transport parameters 共 x , z , D x , and D z 兲 set to zero and then solving the resulting set of ordinary differential equations. Starting formate and nitrate concentrations were specified to match the initial concentrations in the laboratory study. A porosity of 80% was used for simulating the incubation experiment to reflect conditions of the sediment slurry. Model simulations were conducted to match observed formate, nitrate, and nitrite concentration data by systematically varying appropriate microbial parameter values. For example, decreasing M initial increased the simulated lag period 共i.e., initial period of reduced formate and nitrate utilization兲 observed at the beginning of the incubation. Varying utilization facmax max tors 共 N1 and N 2 兲 and maximum growth rates 共 F,N and F,N 兲 1 2 directly altered reaction rates and the resulting concentration histories. Advection–Dispersion Parameters Horizontal groundwater velocities were based on arrival times measured from breakthrough curves constructed from a bromide injection experiment performed in the study area 12 months prior to the formate experiment. Vertically stratified horizontal veloci-
ties, x (z), were determined using bromide breakthrough curves for MLSs located approximately 7.3 and 10.5 m downgradient at sampling ports with elevations of 9.079, 9.333, 9.587, 9.841, 10.095, and 10.349 m 共MSL兲, respectively. Where data were available, the calibration x (z) for the formate injection simulation was approximately 10% less than the bromide-calibrated model to better match the formate breakthroughs curves at the appropriate elevation. This adjustment was attributed to an assumed decrease in the ambient hydraulic gradient between experiments. Calibrated model velocities x (z) were 0.356, 0.379, 0.400, 0.453, 0.510, and 0.550 m/day at elevations of 9.079, 9.333, 9.587, 9.841, 10.095, and 10.349 m 共MSL兲, respectively. Above and below the specified elevations an average uniform groundwater velocity of 0.425 m/day was used. All velocities were within the range reported by LeBlanc 共1984兲. Bromide breakthrough curves also indicated that groundwater flow was unidirectional 共i.e., z ⬇0兲. Dispersion coefficients are a function of groundwater velocity and were determined using the following equations: D x 共 z 兲 ⫽␣ x x 共 z 兲
(13)
D z 共 z 兲 ⫽␣ z x 共 z 兲
(14)
where ␣ x ⫽longitudinal dispersivity and ␣ z ⫽transverse vertical dispersivity. Molecular diffusion was assumed negligible. Solution of the model using a uniform longitudinal dispersivity value of 0.01 m and a transverse vertical dispersivity value of 0.001 m provided the best match to the bromide breakthrough curves. Both values closely approximated dispersivities reported by Garabedian et al. 共1991兲. To limit the effects of numerical dispersion, the time step size for model simulations was contingent upon the Courant number approaching unity 共Anderson and Woessner 1992兲, where Courant⫽
x ⌬t ⬇1.0 ⌬x
(15)
where ⌬x⫽longitudinal grid spacing and x ⫽groundwater velocity. A time step size of 0.333 days was used for all field-scale model simulations. Aquifier porosity 共兲 in the Cape Cod aquifier varies from 0.20 to 0.40 共LeBlanc 1984兲 and was set to 0.30 for al field simulations.
Calibration Procedure and Error Analysis The objective of the calibration was to minimize the average RMerror for each constituent. Calibration was performed by first qualitatively evaluating goodness of fit between concentration versus time plots of model simulation results and field data for formate, nitrate, and nitrite at each port at the 7-m MLS. A manual trial-and-error adjustment of parameter values was used to achieve the objective combined with a quantitative evaluation of the relative error. According to Thomann 共1982兲, the RMS is a statistically well-behaved measure of error and is defined as RMS⫽
冋
1 N
N
兺
i⫽1
共 simi ⫺obsi 兲 2
册
1/2
(16)
where simi ⫽simulated concentrations for a particular solute; obsi ⫽observed concentrations for a particular solute; and N⫽number of observations. Zheng and Bennett 共1995兲 suggest using relative error to evaluate goodness-of-fit, particularly if the variation in observed data is large, such as in the case of breakthrough curves. Relative error 共RMSerror) was obtained by calcu-
lating the ratio of RMS to the total observed concentration change over the model domain independently for formate, nitrate, and nitrite RMSerror⫽
RMS ⫻100% 共obsmax⫺obsmin兲
(17)
where obsmax and obsmin⫽maximum and minimum observed concentrations. During calibration, a RMSerror was calculated for each constituent and each port at the 7-m MLS. An average error (RMSerror兲 was calculated for each constituent from the RMSerror for all ports. For model-wide evaluation of the calibrated model, a total RMSerror for formate, nitrate, and nitrite was calculated at all three MLSs. Measured concentrations had an associated error of ⫾5%.
Sensitivity Analysis A sensitivity analysis was performed to evaluate model uncertainty. Microbial model parameters were systematically changed, one parameter value at a time, within a predetermined range of values. The magnitude of change in simulated concentrations relative to the calibrated model results measured the sensitivity of the solution to that particular parameter. For this study, a single coefficient for each constituent was used as a measure of sensitivity. Zheng and Bennett 共1995兲 suggest a normalized sensitivity coefficient using the following calibration criterion: X i,k ⫽
冏
冏冏
RMSerrori RMSerror共 a k ⫹⌬a k 兲 ⫺RMSerror共 a k 兲 ⬇ a k /a k ⌬a k /a k
冏
(18)
where X i,k ⫽sensitivity coefficient of the model dependent variable RMSerror with respect to the kth parameter, a k 共base case兲, at the ith observation point; ⌬a k ⫽small change in the parameter; and RMSerror(a k ) and RMSerror(a k ⫹⌬a k )⫽ values of the dependent variable for the base case and the case where a k has been changed by ⌬a k , respectively. Sensitivity coefficients were determined for several microbial model parameters using the total RMSerror described above for simulated formate, nitrate, and nitrite concentration variables.
Results and Discussion Model Results—Incubation Experiment Figs. 3共A–C兲, respectively, show measured and simulated formate, nitrate, and nitrite concentration data for the laboratory incubation experiment. An initial period of minor formate utilization, attributed to acclimation by the microbial population, was observed during the first 8 days of Fig. 3共A兲. A lag in significant electron acceptor utilization was also observed in Figs. 3共B and C兲 during the same time, indicating only a relatively minor rate of nitrate reduction or nitrite production. Because the sediments were collected from the zone of active denitrification, some endogenous heterotrophic activity could be expected 共e.g., Smith et al. 1994兲; however, the model did not account for denitrifying bacteria utilizing other sources of organic carbon 共which may be influencing the laboratory data兲. An initial microbial concentration 共M initial) of 8 g/m3 best simulated the lag period. During this time, the rates of both formate and nitrate mass loss were gradually increasing due to an increasing microbial population. Following the lag period, the microbial population was functioning at peak activity and formate and nitrate utilization followed a uni-
Fig. 3. Simulated and measured time course 共with regression analysis兲 of formate 共A兲, nitrate 共B兲, and nitrite 共C兲 aqueous concentrations for slurry incubation experiment. Inset graphs show linear relationship between measured and simulated values. Sediments had not been previously exposed to added formate. Error bars on measured values represent ⫾5% error.
form zero-order rate. Consequently, at this point 共⬃8 –13 days兲, the maximum rates of formate and nitrate utilization were reached 关Figs. 3共A and B兲, respectively兴 and continued until the nitrate had been sufficiently depleted 共⬃13 days兲. During the same time, there was a corresponding net production of nitrite 关Fig. 3共C兲兴. Throughout the ensuing period 共t⬎13 days兲, formate utilization resulted from nitrite-based respiration. Both formate and nitrite utilization appears to follow a zero-order rate during this time. Similar results 共with slightly different lag periods兲 were obtained by Smith et al. 共2001兲 for incubations conducted with core material collected 3 years later from the same location.
Table 3. Microbial Model Parameter Values Units
Parameter values 共laboratory equivalent simulation兲
Parameter values 共calibrated simulation兲
% change
ed K F,N 1
M
22.22
22.22
0
ed K F,N 2
M
22.22
22.22
0
ea K F,N 1
M N
14.29
14.29
0
ea K F,N 2 KI
M N M M
14.29 142.86
14.29 142.86
0 0
max F,N 1
day⫺1
1.40
0.65
⫺54
max F,N 2
day⫺1
0.34
0.20
⫺41
Y N1
mg/mg
0.19
0.19
0
Y N2
mg/mg
0.22
0.22
0
M initial
g/m
8
20
⫹150
M max Kd
g/m3 day⫺1
1.0 0.010
0.56 0.010
⫺44 0
N1 N2
mg/mg mg/mg
1.22 0.65
0.33 0.29
⫺73 ⫺55
N1
mg/mg
1.02
1.02
0
Parameter
3
Zero-order utilization rates 共R sink bio ) were calculated using the equations listed in Table 2 and the model parameters listed in Table 3. Rate calculations were based on the maximum biomass concentration and peak solute concentrations. The resulting zeroorder rates for formate loss under nitrate and nitrite reduction were 205 and 43 M/day, respectively. Nitrate and nitrite utilization rates were 152 and 20 M N/day, respectively, and the nitrite source production rate 共R bio,N 兲 was 156 M N/day. 2 These results demonstrate that the model was able to simulate the major data trends of the incubation experiment. Fig. 3 also includes a regression analysis of measured against simulated concentrations for each constituent with each R 2 coefficient approximating a value of unity 共0.99 or greater兲. The RMSerror for each of the three constituents was 4% or less, with a combined average of 3.4%. Sensitivity analysis indicated that laboratory simulation results were sensitive to changes in primarily seven input parameters: formate maximum specific growth rate for nitrate and nitrite remax max duction 共 F,N and F,N , respectively兲, nitrate and nitrite utiliza1 2 tion factors 共 N1 and N2 , respectively兲, nitrate inhibition constant K I , and biomass concentration (M initial and M max兲. To ed simulate the zero-order response, half-saturation constants 共K F,N , 1 ea ed ea K F,N1 , K F,N2 , and K F,N2兲 were set to values considerably smaller than the peak concentrations. The analysis showed that model results were relatively insensitive to decreases in the halfsaturation constants but when these parameters were substantially increased above the calibrated values, the zero-order response was poorly simulated.
Model Results—Field Experiment Calibration Breakthrough curves using model simulation results and measured data for formate, nitrate, and nitrite from the 9.587-m port
at the three MLSs along the flowpath are shown in Figs. 4, 5, and 6, respectively. As shown in Fig. 2, the 9.587-m port was aligned with the approximate center elevation of the injection well screen. Formate was not detected in the field at the 10.349- and 10.603-m ports. The early-time formate breakthrough at the 7-m MLS 关Fig. 4共A兲兴 was due to the unsteady mass flux at the injection zone boundary where a first pulse of formate arrived ahead of the main formate injection. The model was calibrated for the second larger peak of formate, and not for the first peak. As a result, simulation results for formate at the 10- and 15-m MLS show the first pulse of formate surviving. Overall, Figs. 4 – 6 show a decreasing peak formate concentration with increasing travel distance, and a corresponding decrease in the nitrate concentration. Nitrite concentration data and simulation results show a corresponding increase, but the peak concentration of nitrite at the 15-m MLS 关Fig. 6共C兲兴 did not increase above the peak concentration observed at the 10-M MLS. Two model simulations are presented in Fig. 4 for each solute at the 7-m MLS: 共1兲 an initial run with no calibration, employing parameter values derived from the laboratory incubations 共Laboratory Equivalent兲 and 共2兲 a calibrated simulation 共Calibrated兲. Laboratory Equivalent model simulations overpredicted the degree of microbial utilization for both formate and nitrate and failed to adequately match the field data. Based on the simulation results of the laboratory experiments, selected parameters were initially targeted for adjustment during the trial-and-error calibration approach. The model was calibrated to the formate, nitrate, and nitrite concentration data at the 7-m MLS, reflecting decreased utilization rates relative to the laboratory-derived rates. Table 3 lists microbial parameters and corresponding values for both the laboratorycalibrated and field-calibrated simulations with the percent change.
Fig. 4. Simulated 共laboratory equivalent and calibrated兲 and measured time course of formate 共A兲, nitrate 共B兲, and nitrite 共C兲 concentrations in groundwater collected from 9.587-m port at 7-m multilevel samplers for formate injection experiment. Error bars on measured values represent ⫾5% error. Inset graph shows formate injection concentration history from Table 1.
Model-Wide Calibration Evaluation Simulation results at the 10- and 15-m MLSs 共Figs. 5 and 6兲 demonstrate that the calibrated site model was capable of matching the observed data trends. Similar modeling results were obtained for the 9.841-m port at both the 10- and 15-m MLS 共data not shown兲. The 9.587- and 9.841-m ports, which were located within the vertical injection zone, intercepted the formate cloud along the entire flow path and, therefore, provided the most reliable data. These findings serve as further evidence that the model matched the transport and utilization of all three solutes along the flow path in both time and space.
Fig. 5. Simulated 共calibrated兲 and measured time course of formate 共A兲, nitrate 共B兲, and nitrite 共C兲 concentrations in groundwater collected from 9.587-m port at 10-m multilevel samplers. Error bars on measured values represent ⫾5% error.
Results averaged over all ports and all wells for formate computed a total RMSerror for the Laboratory Equivalent of 23%, compared to 16% for the Calibrated Simulation. Total RMSerror for nitrate and nitrite were 33 and 39% for the Laboratory Equivalent and 22 and 21% for the Calibrated Simulation, respectively. The greater error assisted with both nitrate and nitrite, relative to the formate error, was attributed to variability of the background nitrate concentration distribution and the uncertainty in specifying initial conditions. It is common for trail and error solutions to produce nonunique solutions. However, using a large number of calibration targets distributed over the entire model domain 共with a small associated error兲 should increase the probability of obtaining a unique solution. In this study, the calibration of the site transport
results at the 7-m MLS showed greater sensitivity to variations in these parameter values relative to model output at the 10- and 15-m MLSs. Additionally, adjustments to the initial biomass concentration M initial exhibited a marked influence on model output for all three constituents. Biological Reaction Rates Zero-order reaction rates for the calibrated site model were calculated as described previously using the equations listed in Table 2 and the calibrated model parameters provided in Table 3. These rates represent maximum rates, which occur when electron donor and acceptor concentrations were at peak levels. Given the calibrated parameter set and concentration range, the Monod model predicts a zero-order reaction rate. This allows a comparison with published field-measured zero-order denitrification rates. Formate loss under nitrate and nitrite reduction was 142.2 M/day 共6.4 mg L⫺1 day⫺1兲 and 37.8 M/day 共1.7 mg L⫺1 day⫺1兲, respectively. Nitrate and nitrite utilization rates were 28.6 M N/day 共0.40 mg-N L⫺1 day⫺1兲 and 7.9 M N/day 共0.11 ⫺1 mg-N L day⫺1兲, respectively. Nitrite production was 29.3 M N/day 共0.41 mg-N L⫺1 day⫺1兲. Disparity between the fieldderived rates and laboratory-derived rates were expected because in situ microbial activity is generally slower than the activity observed in slurry incubations, which incorporating mixing effects 共DeSimone and Howes 1996兲. The nitrate utilization rate resulting from the formate injection experiment 共28.6 M N/day兲 was 1 order of magnitude higher than the naturally occurring denitrification rates reported by Brooks et al. 共1994兲 and Smith et al. 共1996兲 at the same site. Smith et al. 共1996兲 calculated in situ rates of 1.5 and 3.9 M N/ day 共0.021 and 0.054 mg-N L⫺1 day⫺1, respectively兲 in two successive tracer sets. DeSimone and Howes 共1996兲 measured a nitrate reduction rate of 0.51 M N/day 共0.0071 mg-N L⫺1 day⫺1兲 in another Cape Cod aquifer with similar geochemistry and hydrogeology. The addition of formate clearly accelerated denitrification in this aquifer.
Fig. 6. Simulated 共calibrated兲 and measured time course of formate 共A兲, nitrate 共B兲, and nitrite 共C兲 concentrations in groundwater collected from 9.587-m port at 15-m multilevel samplers. Error bars on measured values represent ⫾5% error.
model relied on discrete measurements taken over both time and space 共i.e., concentrations at multilevel samplers兲 to produce a solution that is free of interpretive bias. Sensitivity Sensitivity coefficients calculated for formate, nitrate, and nitrite using Eq. 共18兲 are presented in ranked order in Table 4. Formate showed the greatest sensitivity to three parameters that directly max impact the rate of utilization under nitrate reduction: F,N , 1 M max , and Y N1 . Both the simulated nitrate and nitrite concentrations showed greatest sensitivity to the same three parameters: max F,N , M max , and N1 . The product of these three variables di1 rectly determined the rate of nitrate utilization. Significant nitrite production resulted when these parameters were increased. Model
Nitrite Accumulation Nitrite production resulting from nitrate reduction occurred at a rate almost four times greater than nitrite utilization, which likely accounts for the gradual nitrite accumulation. Disproportionate nitrite production and reduction was also observed in the laboratory incubation. However, the rate of nitrite utilization in the laboratory experiment was 2.5 times greater than the field rate. Nitrite accumulation is characteristic of denitrification and has been observed in previous studies. Wilderer et al. 共1987兲 indicated that changes in pH and temperature inhibited nitrite utilization, while Korner and Zumft 共1989兲 found that nitrite utilization could be inhibited by the presence of low levels of oxygen or high levels of nitrate. Betlach and Tiedje 共1981兲, however, suggested that transient nitrite accumulation in pure cultures could be attributed to differential nitrate and nitrite utilizations rates rather than any specific inhibition process. The length of time and travel distance required to consume the nitrite produced during the field test was investigated with the model. Figs. 7, 8, and 9 show simulated formate, nitrate, and nitrite concentration distributions, respectively, at 50, 76, and 100 days after the formate injection was initiated. Figs. 7共A兲, 8共A兲, and 9共A兲 are calibrated model results for formate, nitrate, and nitrite, respectively, at the approximate time when the center of the formate plume passed through the 15-m MLS. Fig. 7共B兲 predicts that the second pulse of formate was consumed by 76 days. The remaining formate at 76 days is theresidual from the first
Table 4. Summary of Model Sensitivity Formate sensitivity Parameter
Nitrate sensitivity
Nitrite sensitivity
Sensitivity Coefficient
Parameter
Sensitivity Coefficient
Parameter
Sensitivity Coefficient
max F,N 1
37.10
max F,N 1
1.73
max F,N 1
1.74
M max
13.29
M max
0.70
M max
0.64
Y N1
9.63
N1
0.54
N1
0.63
M initial
7.76
M initial
0.41
M initial
0.19
ed K F,N 1
2.34
Y N1
0.16
Y N1
0.13
Kd
0.78
ed K F,N 1
0.05
ed K F,N 1
0.08
N1
0.63
Kd
0.037
N2
0.04
max F,N 2
0.54
Y N2
0.009
Kd
0.027
Y N2
0.47
max F,N 2
0.006
max F,N 2
0.025
KI
0.35
KI
0.004
KI
0.02
0.01
ed K F,N 2
0.0007
Y N2
0.008
0.004
ea K F,N 1
0.0002
ed K F,N 2
0.003
ea K F,N 1
0.0
ea K F,N 2
0.0002
ea K F,N 1
8.0E-6
ea K F,N 2
0.0
N2
0.0002
ea K F,N 2
8.0E-6
ed K F,N 2
N2
Fig. 7. Simulated concentration distribution for formate at 50 共A兲, 76 共B兲, and 100 days 共C兲 after start of formate injection experiment
Fig. 8. Simulated concentration distribution for nitrate at 50 共A兲, 76 共B兲, and 100 days 共C兲 after start of formate injection experiment
reducing conditions, which produced nitrite at a relatively high rate. Nitrite utilization is substantial only in zones where the concentration of nitrate falls to below approximately 72 M and formate is available. Thus, several conditions must be met in order for nitrite to be consumed: sufficient depletion of nitrate 共combined with nitrite production兲 accompanied by an adequate supply of formate. Contact time between formate and nitrite then becomes a complicating factor because the nitrite utilization rate is approximately 3.6 times less than the rate of nitrate utilization 共and thus, the rate of nitrite production兲. As shown in Fig. 6, sediment-bound nitrite-reducing bacteria have a limited time frame 共approximately 4 – 6 days at the 15-m MLS兲 to utilize formate and nitrite in the absence of nitrate. All of these conditions, along with a decreasing supply of formate, contribute to the accumulation of nitrite. Another contributing factor is the reintroduction of nitrate into the thin zone of overlap between the formate and nitrite clouds over time, depicted by the decreasing size in the zone of nitrate depletion 关compare Fig. 8共B兲 to 8共C兲兴. The gradual dispersive mass flux of nitrate into the overlap zone between the formate and nitrite clouds could inhibit downgradient nitrite consumption. That being the case, it is thought then that the primary mechanism for nitrite attenuation after 100 days would be dilution and dispersion of the nitrite plume as it travels down gradient with minor reductions occurring due to the residual denitrification. Fig. 9. Simulated concentration distribution for nitrite at 50 共A兲, 76 共B兲, and 100 days 共C兲 after start of formate injection experiment
Conclusions injection pulse, but because the model did not accurately simulate the leading edge of the formate 关see Fig. 6共A兲兴, it is likely that both formate pulses were depleted by 76 days and no further denitrification would be expected. Figs. 8共A and B兲 predict an expansion in the zone of nitrate depletion from 50 to 76 days, but between 76 and 100 days no further nitrate utilization is indicated 关Fig. 8共C兲兴. Instead, an increase in nitrate concentrations due to dispersion was noted. Figs. 9共A–C兲 suggest that the nitrite plume would have increased in size over the entire period but that nitrite concentrations would decrease from 76 to 100 days. These observations are supported by calculations of zeroth and first moments for the formate and nitrite plumes at 50, 76, and 100 days. Between 50 and 76 days, formate mass was decreasing and nitrite mass was increasing, but changes in the formate mass and nitrite mass were negligible from 76 to 100 days. The formate center of mass at 50 days was located 1.0 m downgradient of the nitrite center of mass. This distance increased to 7.0 m by 76 days and 7.5 m by 100 days, as the remaining formate was consumed from day 50 to day 76, resulting in limited denitrification. This separation of the plumes is demonstrated by comparison of Figs. 7共C兲 and 9共C兲. The lingering formate plume in Fig. 7共C兲 represents the formate delivered during the first several days of the injection period, which persisted in the simulations due to the lag in formate utilization as the cloud of formate moved into regions of the aquifer with a low level of ambient biomass. In this case, the concentration of formate and rate of utilization are not sufficient to stimulate enough biomass growth in the time frame of solute transport to result in significant nitrate removal and nitrite production/removal. Several factors combine to explain the persistence of nitrite: electron donor 共formate兲 availability, preferential use of nitrate as an electron acceptor over nitrite, and the difference between nitrite utilization and nitrite production rates. The data show and the model predicts formate utilization first occurring under nitrate-
A 2D numerical solute transport model was applied to an enhanced in situ denitrification experiment performed in a nitratecontaminated aquifer on Cape Cod, Mass. By incorporating the production and reduction of nitrite, this model expands upon previous models that describe nitrate transport 共e.g., Widdowson et al. 1988; Kinzelbach et al. 1991; Smith et al. 1996兲 and provides a novel approach and useful tool to investigate the rate of enhanced denitrification to interpret laboratory and field data. A site model was developed, calibrated to field data, and then evaluated using breakthrough curves of formate, nitrate, and nitrite at three multilevel ground water sampling devices. The model simulation results match trends in both time and space for formate, nitrate, and nitrite. However, uncertainty regarding the initial concentration distribution for nitrate appears to have biased model results for both nitrate and nitrite. Formate utilization rates for the simulation of the field experiment were 142.2 M/day 共6.4 mg L⫺1 day⫺1兲 and 37.8 M/day 共1.7 mg L⫺1 day⫺1兲 under nitrate and nitrite reduction, respectively. Reduction rates for nitrate and nitrite were 28.6 M N/day 共0.40 mg -N L⫺1 day⫺1兲 and 7.9 M N/day 共0.11 mg -N L⫺1 day⫺1兲, respectively. Nitrite production was 29.3 M N/day 共0.41 mg -N L⫺1 day⫺1兲. Intrinsic denitrification rates reported in previous studies at the Cape Cod study site 共Brooks et al. 1994; Smith et al. 1996兲 are at least 1 order of magnitude lower than the enhanced rates found here, which demonstrates the potential efficacy of using this approach for in situ remediation of nitrate. However, model results also suggest nitrite accumulation along the flow path, and predict a persistence of nitrite after formate depletion. The accumulation and apparent persistence of nitrite, primarily due to a lower rate of nitrite utilization relative to nitrate utilization and the eventual depletion of formate in the nitrite plume, limits the denitrification process in this experiment. The persistence of nitrite is a potentially serious problem, because of nitrite toxicity, which should be investigated further with in situ pilot testing. This problem may
be remedied by more concentrated, additional, or larger formate injections or possibly through augmenting the natural biological community. The feasibility of the remedial design may be assessed via model simulations and should be investigated prior to implementation of any enhanced remediation scheme.
Acknowledgments The writers thank D. R. LeBlanc, coordinator of the U.S. Geological Survey Cape Cod Site, and M. H. Brooks for field and technical assistance. They also thank D. N. Miller for assistance with the laboratory incubations and K. M. Hess and M. Schreiber for manuscript reviews. This study was funded in part by the U.S. Dept. of Agriculture Grant No. 95-37101-1713 and the U.S. Geological Survey Toxic Substances Hydrology Program.
Notation The following symbols are used in this paper: Variables F ⫽ M ⫽ N1 ⫽ N2 ⫽
formate concentration 共M/L3兲; biomass concentration 共M/L3兲; nitrate concentration 共M/L3兲; and nitrite concentration 共M/L3兲.
Parameters D x ⫽ horizontal dispersion coefficient 共L2/T); D z ⫽ vertical dispersion coefficient 共L2/T); ed K F,N1 ⫽ formate half-saturation constant for nitrate reduction 共M/L3兲; ed K F,N2 ⫽ formate half-saturation constant for nitrate reduction 共M/L3兲; ea K F,N1 ⫽ nitrate half-saturation constant 共M/L3兲; ea 3 K F,N 2 ⫽ nitrite half-saturation constant 共M/L 兲; 3 K I ⫽ nitriate inhibition constant 共M/L 兲; k d ⫽ biomass decay coefficient 共M/M per T兲; sink R bio,F ⫽ formate biological consumption rate 共M/L3/T); sink R bio,N1 ⫽ nitrate biological consumption rate 共M/L3 per T兲; sink 3 R bio,N 2 ⫽ nitrite biological consumption rate 共M/L per T兲; source R bio,N2 ⫽ nitrite biological production rate 共M/L3 per T兲; t ⫽ time 共t兲; x ⫽ horizontal coordinate 共L兲; Y N1 ⫽ yield coefficient for nitrate reduction 共M/M兲; Y N2 ⫽ yield coefficient for nitrite reduction 共M/M兲; z ⫽ vertical coordinate 共L兲; ␣ x ⫽ horizontal dispersivity 共L兲; ␣ z ⫽ vertical dispersivity 共L兲; N1 ⫽ nitrite production constant 共M/M兲; N1 ⫽ nitrate utilization factor 共M/M兲; N2 ⫽ nitrite utilization factor 共M/M兲; F,N1 ⫽ growth rate for nitrate reduction 共M/M per T兲; F,N2 ⫽ growth rate for nitrite reduction 共M/M per T兲; max F,N 1 ⫽ maximum growth rate for nitrate reduction 共M/M per T兲; max F,N ⫽ maximum growth rate for nitrite reduction 共M/M 2 per T兲; x ⫽ horizontal velocity 共L/T兲; and z ⫽ vertical velocity 共L/T兲.
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