Modeling Variably Saturated MultispeciesReactive Groundwater Solute Transport withMODFLOW-UZF and RT3Dby Ryan T. Bailey1, Eric D. Morway2, Richard G. Niswonger2, and Timothy K. Gates3
AbstractA numerical model was developed that is capable of simulating multispecies reactive solute transport in
variably saturated porous media. This model consists of a modified version of the reactive transport modelRT3D (Reactive Transport in 3 Dimensions) that is linked to the Unsaturated-Zone Flow (UZF1) package andMODFLOW. Referred to as UZF-RT3D, the model is tested against published analytical benchmarks as well asother published contaminant transport models, including HYDRUS-1D, VS2DT, and SUTRA, and the coupledflow and transport modeling system of CATHY and TRAN3D. Comparisons in one-dimensional, two-dimensional,and three-dimensional variably saturated systems are explored. While several test cases are included to verify thecorrect implementation of variably saturated transport in UZF-RT3D, other cases are included to demonstrate theusefulness of the code in terms of model run-time and handling the reaction kinetics of multiple interacting speciesin variably saturated subsurface systems. As UZF1 relies on a kinematic-wave approximation for unsaturated flowthat neglects the diffusive terms in Richards equation, UZF-RT3D can be used for large-scale aquifer systems forwhich the UZF1 formulation is reasonable, that is, capillary-pressure gradients can be neglected and soil parameterscan be treated as homogeneous. Decreased model run-time and the ability to include site-specific chemical speciesand chemical reactions make UZF-RT3D an attractive model for efficient simulation of multispecies reactivetransport in variably saturated large-scale subsurface systems.
IntroductionA thorough understanding of water movement and the
fate and transport of chemical species and nutrients in theshallow unsaturated zone is imperative owing to its control
1Corresponding author: Department of Civil and Environmen-tal Engineering, Colorado State University, 1372 Campus Delivery,Fort Collins, CO 80523-1372; 970-491-5387; fax: 970-491-7727;[email protected]
2United States Geological Survey, 2730 N. Deer Run Road,Carson City, NV 89701.
3Department of Civil and Environmental Engineering, ColoradoState University, 1372 Campus Delivery, Fort Collins, CO 80523-1372.
Received January 2012, accepted September 2012.Published 2012. This article is a U.S. Government work and is
in the public domain in the USA.doi: 10.1111/j.1745-6584.2012.01009.x
on the transformation, removal, and leaching of chemicalspecies, especially in agricultural settings. However, thecomplex physical and chemical processes that occur insuch systems (e.g., nonlinear flow patterns and nonlinearkinetic chemical reactions) as well as the accounting ofchemical sources and sinks for the system render such ananalysis prohibitive without the use of physically basedmultispecies (i.e., interactions between selected species)and multicomponent (i.e., mixed kinetic systems subjectto thermodynamic constraints) reactive transport models(Mayer et al. 2002). These models allow for the inclusionof chemical reactions and the interaction of multiplesolutes, in conjunction with the environmental factors thatgovern these relationships (e.g., soil water content andtemperature, microbial population density, and electron-[e−] acceptor and e−-donor concentration), and multiplesources and sinks of solute mass, such as from infiltrating
752 Vol. 51, No. 5–Groundwater–September-October 2013 (pages 752–761) NGWA.org
precipitation and irrigation water, seepage from irrigationcanals, organic and inorganic fertilizer, nutrient uptakeby crops, solute upflux from shallow water tables, andoxidative dissolution of consolidated and unconsolidatedmaterial.
The development of reactive transport codes has beenan ongoing research focus during the past three decades.Initially, numerical models capable of simulating reactivetransport of multiple species in groundwater were limitedto the zone of saturated porous media (e.g., Rubin 1983;RT3D [Reactive Transport in 3 Dimensions], Clement1997; PHT3D, Prommer et al. 2003; PHAST, Parkhurstet al. 2004, 2010) with the advective-dispersive processescoupled to chemical reactions described by equilibriumand/or kinetic relationships. RT3D is an especially use-ful model, being integrated with MODFLOW (Harbaugh2005) and allowing the use of predefined (e.g., sequentialdecay reactions, microbial growth and transport) or user-defined sets of kinetically controlled reactions with theoption of Monod and dual-Monod kinetics (e.g., Clementet al. 1997; Lee et al. 2006; Wriedt and Rode 2006). Itmost commonly has been used to simulate the interactionof species in the saturated zone, for example, the biodegra-dation of hydrocarbons via the sequential reduction ofe− acceptors such as dissolved oxygen, nitrate, Fe(II),and sulfate (Clement et al. 1998) or the sequential decayof chlorinated solvents such as tetrachloroethene (PCE),trichloroethene (TCE), dichloroethylene (DCE), and vinylchloride (VC) (Johnson et al. 2006). In such systems,the decay or production of species’ mass according tokinetic rate laws is dependent on the concentration of otherreactive solutes, and hence require an implicit ordinarydifferential equation (ODE) solver as utilized by RT3D.
In recent years, reactive transport models havebeen developed to extend the simulation capability tovariably saturated porous media. Typically, these modelshave been designed for one-dimensional (1D) systems(e.g., HYDRUS-1D, Simunek et al. 1998; RZWQM, Maet al. 2000; HP1, Jacques and Simunek 2005; RICH-PHREEQC, Wissmeier and Barry 2010) or for two-dimensional (2D) systems (e.g., VS2DT, Healy 1990;HYDRUS [2D/3D], Simunek et al. 2006), and are appliedin 1D soil profiles or 2D vertical profiles at the field scale.Models for three-dimensional (3D) variably saturatedsystems have also been designed in recent years, forexample, MIN3P (Mayer et al. 2002), SUTRA (Vossand Provost 2010), HYDRUS (2D/3D) (Simunek et al.2006), the flow-transport-coupled system of the catchmentflow models CATHY (Bixio et al. 2000; Camporese et al.2009) and TRAN3D (Gambolati et al. 1994), and theproprietary code MODFLOW-SURFACT (Panday andHuyakorn 2008). SUTRA and CATHY-TRAN3D arelimited to single-species reactive transport. MODFLOW-SURFACT was linked to MT3D (Zheng and Wang 1999)to simulate variably saturated flow and transport, andincluded the reaction package of RT3D to simulate thedecay of hydrocarbons.
Similar to the 1D and 2D models, however, these3D models solve the full Richards equation for variably
saturated flow, and hence are limited in applicationsbecause of a burdensome computational expense. Asan alternative to solving the full Richards equation,the Unsaturated-Zone Flow (UZF1) package (Niswongeret al. 2006) developed for MODFLOW-NWT, a New-ton formulation for MODFLOW-2005 (Harbaugh 2005;Niswonger et al. 2011), assumes vertical homogene-ity of the unsaturated zone and neglects the diffusiveterm in Richards equation, resulting in the kinematic-wave equation for vertical unsaturated flow, with theBrooks-Corey formulation used to define the relationshipsbetween water content and variably saturated hydraulicconductivity. MODFLOW-UZF1 requires less computa-tional effort than the aforementioned models that solve thefull Richards equation, and therefore provides an appeal-ing approach to simulating variably saturated groundwaterflow in large-scale aquifer systems, wherein the assump-tions inherent in the UZF1 formulation, that is, neglectof capillary pressure gradients and vertical homogeneityof the unsaturated zone can be assumed. Hence, trade-offs exist between the speed of UZF1 and the accuracyof Richards equation-based approaches, although accuracywith the latter requires detailed knowledge of the spatialdistribution of soil parameters.
Morway et al. (2012) present the linkage ofMODFLOW-UZF1 with MT3DMS (Zheng and Wang1999) to form UZF-MT3DMS for simulating advective-dispersive-reactive transport for multiple, noninteractivespecies. MODFLOW-UZF1, however, has yet to be linkedwith a multispecies reactive transport model that accountsfor interacting species and associated kinetics. The abilityto incorporate the dependence of chemical reaction rateson the presence of other reactive chemical species is avital component in numerous chemical transport systems.
In this paper, we present the modification of RT3D tosimulate multispecies reactive transport in variably satu-rated subsurface systems by linking it with MODFLOW-UZF1. RT3D was chosen as the base code because of(1) its widespread use when the simulation of interactingchemical species is required, (2) its ability to handle mul-tiple reactive solutes and interspecies chemical kinetics,(3) the option of implementing user-defined kinetic chem-ical reactions and developing new reaction modules, and(4) its linkage with MODFLOW and hence inclusion inthe readily accessible suite of MODFLOW-related codes.The resulting model, hereafter referred to as UZF-RT3D,incorporates the advantages of both models, that is, lowercomputational burden due to the kinematic-wave equationfor simulating unsaturated flow and simulation of multi-ple interacting species. UZF-RT3D hence offers a platformfor a number of applications not possible with the originalRT3D functionality, for example, the leaching of interact-ing nutrients and chemical species in soil profiles.
This paper also presents the results of testing UZF-RT3D against the numerical model HYDRUS-1D to verifythe coupling of interactive reactive species within UZF-RT3D, whereupon a more comprehensive 3D numericaltest case is simulated to demonstrate the transport ofmultiple interactive reactive species subject to inhibition
NGWA.org R.T. Bailey et al. Groundwater 51, no. 5: 752–761 753
and Monod kinetics in both the unsaturated and saturatedzones. Comparisons with an analytical solution by vanGenuchten (1981) and the numerical models VS2DT,SUTRA, and CATHY-TRAN3D, all of which can onlysimulate the reactive transport of a single species andhence can be solved by UZF-MT3DMS, are not includedhere but are presented in the Supporting Informationto verify the implementation of the variably saturatedtransport processes within RT3D, and it also providesa general assessment of computational effort requiredas compared with other models. Similar to the work ofMorway et al. (2012), UZF-RT3D is a step toward addingreactive solute transport to GSFLOW (Markstrom et al.2008) due to the use of UZF1 to simulate unsaturatedflow in GSFLOW.
Development of UZF-RT3DThe numerical model RT3D simulates the reactive
transport of one or more species in a multidimensionalsaturated aquifer environment by solving finite-difference(FD) approximations of a system of advection-dispersion-reaction (ADR) equations, with one ADR equation foreach chemical species (Clement 1997; Clement et al.1998). Assuming rigid porous media, linear equilibriumsorption, and saturated conditions, the system of ADRequations is
φ∂Ck
∂t= − ∂
∂xi
(φviCk) + ∂
∂xi
(φDij
∂Ck
∂xj
)
+ qsCsk − ρb
∂Ck
∂t+ φr k = 1, 2, . . . , m (1)
where m is the total number of aqueous-phase species;Ck is the concentration of the kth species (Mf/L3
f ), wheref denotes the fluid phase; Dij is the hydrodynamicdispersion coefficient (L2/T); v is the average seepagevelocity (Lb/T), where b denotes the bulk phase; φisthe soil porosity (L3
f /L3b); qs is the volumetric flux of
water representing sources and sinks of the species(L3
f /T/L3b); Csk is the concentration of the source or sink
(Mf/L3f ); r represents the rate of all reactions that occur in
the aqueous phase for the kth species (Mf/L3f /T); ρb is the
bulk density of the porous media (Mb/L3b); and Ckis the
concentration of the kth species sorbed on solids (Mf/Mb).To simplify Equation 1, the retardation factor Rk (−),equal to 1 + (ρbKdk
)/φ for linear sorption where Kdkis
the partitioning coefficient (Mb/L3f ) for the kth species and
is equal to Ck/Ck , is incorporated to yield
∂Ck
∂tRk = − ∂
∂xi
(viCk) + ∂
∂xi
(Dij
∂Ck
∂xj
)
+ qsCsk
φ+ r k = 1, 2, . . . , m (2)
Rate laws for r describing the decay or production ofspecies according to simple, Monod, or dual-Monod kinet-ics and in relation to the concentration of other species
can be simulated. Saturated thicknesses, groundwater flowvelocities, and volumetric flux of water into and out of themodel domain are supplied by the 3D groundwater flowmodel MODFLOW through a flow-transport link file. Thesystem of ADR equations are solved for the change in Ck
using the operator-split (OS) numerical scheme (Yeh andTripathy 1989; Clement 1997) either partially or in full. Inthe partial OS scheme, an iterative solver is used to solvethe change in Ck implicitly due to advection-dispersion-source-sink, whereupon the change in concentration dueto kinetic rate laws is calculated using an ODE solver. Inthe full OS scheme (i.e., fully explicit scheme), Equation2 is separated into four distinct equations, one each foradvection, dispersion, source-sink mixing, and chemicalreactions, with each equation solved for the change in Ck
(Clement et al. 1998). Fully explicit formulation requiresstability constraints on the length of the transport timestep, whereas the implicit scheme does not (Zheng andWang 1999).
In the remainder of this section, Equation 2 isreformulated to describe multispecies reactive transportin a variably saturated aquifer environment and thesolution procedures are described. Variably saturatedtransport processes are implemented in UZF-RT3D forboth the fully explicit and the implicit schemes. Morwayet al. (2012) describe the implementation of the implicitscheme, and only the implementation of the explicitscheme is presented here. By replacing the porosity termφ in Equation 1 with volumetric water content θ (L3
f /L3b),
the system of ADR equations for simulating multispeciesreactive transport under variable saturation is
∂(Ckθ)
∂t= − ∂
∂xi
(θviCk) + ∂
∂xi
(θDij
∂Ck
∂xj
)+ qsCsk
− ρb
∂Ck
∂t+ θr k = 1, 2, . . . , m (3)
where θ is a function of time and hence placedinside the time derivative. Bringing the aqueous-solidsurface sorption term to the left-hand side (Vander-borght et al. 2005) and multiplying it by ∂(Ckθ)/∂(Ckθ)
yields
∂(Ckθ)
∂t+ ρb
∂(Ckθ)
∂t
∂Ck
∂(Ckθ)
= − ∂
∂xi
(θviCk) + ∂
∂xi
(θDij
∂Ck
∂xj
)+ qsCsk + θr
k = 1, 2, . . . , m (4)
which can be simplified to
∂(Ckθ)
∂t
(1 + ρb
∂Ck
∂(Ckθ)
)
= − ∂
∂xi
(θviCk) + ∂
∂xi
(θDij
∂Ck
∂xj
)+ qsCsk + θr
k = 1, 2, . . . , m (5)
754 R.T. Bailey et al. Groundwater 51, no. 5: 752–761 NGWA.org
Substituting the following expression
Rk = 1 + ρb
∂Ck
∂(Ckθ)(6)
into Equation 5 yields
∂(Ckθ)
∂tRk = − ∂
∂xi
(θviCk) + ∂
∂xi
(θDij
∂Ck
∂xj
)
+ qsCsk + θr k = 1, 2, . . . , m. (7)
To solve Equation 7 in the fully explicit scheme,UZF-RT3D employs the full OS numerical scheme interms of species mass. Substituting the mass per bulkporous media volume Mfk
of the kth species in the fluidphase for Ckθ , Equation 7 is divided into four distinctequations to solve for the change in Mfk
: the advectionequation(
∂Mfk
∂t
)ADV
= − 1
Rk
∂
∂xi
(θviCk) k = 1, 2, . . . , m,
(8a)
the dispersion equation(∂Mfk
∂t
)DSP
= 1
Rk
∂
∂xi
(θDij
∂Ck
∂xj
)k = 1, 2, . . . , m,
(8b)
the source-sink mixing equation(∂Mfk
∂t
)SSM
= qsCsk
Rk
k = 1, 2, . . . , m, (8c)
and the reaction equation(∂Mfk
∂t
)RCT
= θr
Rk
k = 1, 2, . . . , m. (8d)
Equations 8a, 8b, and 8c are solved sequentially usingexplicit FD methods to calculate the changes inMfk
foreach of the m species due to advection, dispersion, andsource-sink mixing, whereupon Equation 8d is solvedsimultaneously for all m species using an ODE solver.Equation 8d assumes that chemical reactions occur only inthe aqueous phase. For immobile species, only the reactionequation in the form of (∂M/∂t) = rs is solved, with rs
representing the rate of all reactions that occur in the solidphase s. Rk is equal to 1 + (ρbKdk
)/θ because Equation 8is solved explicitly and uses θ only from the current timestep. The implicit scheme was implemented in a similarfashion to Morway et al. (2012), the difference beingthat the chemical reaction term for all species is solvedsimultaneously using the OS scheme once the change inCk due to advection, dispersion, and source-sink mixinghas been solved implicitly for each species.
Other modifications made to RT3D to implementvariably saturated transport with 1D downward flow inthe unsaturated zone include reading and storing UZF1-specific flow output data, modifications to subroutines
within the advection, source-sink mixing, and chemicalreaction packages to handle new data arrays as well asthe reaeration term described in the next section, andchanges to RT3D input files to incorporate data requiredfor variably saturated transport. Volumetric fluxes ofinfiltrating water are used in conjunction with specifiedsolute concentration values to calculate the mass ofeach species entering the model domain via infiltratingwater at the ground surface. As a function of θ , Rk isrecalculated at the beginning of each flow time step. Thesemodifications constitute the VST (Variably SaturatedTransport) package for UZF-RT3D, which can be turnedoff to revert to the original RT3D functionality.
Description of Testing and NumericalExperiments
Testing of UZF-RT3D was made through a number ofcomparisons to both an analytical benchmark model andsimulation results from published numerical models. Theanalytical model is a solution published by van Genuchten(1981) for single-species reactive transport, and thenumerical models are HYDRUS-1D, VS2DT, SUTRA,and CATHY-TRAN3D. Tests using the analytical modeland the numerical models VS2DT, SUTRA, and CATHY-TRAN3D are presented in the Supporting Information.Run-times are also reported in the Supporting Informationfor the 3D system to provide comparisons for large-scalesystems. Numerical experiments presented here deal withproblems that cannot be solved by UZF-MT3DMS, thatis, the reactive transport of multiple, interacting species.All 1D and 2D simulations use the fully explicit scheme.The 3D simulations use the implicit scheme.
The simulation details and parameters for the numer-ical tests are summarized in Table 1. For Scenario 1,the coupling between solutes involved in sequential first-order decay reactions is tested for UZF-RT3D againstHYDRUS-ID in a 200-cm 1D soil profile system. Thefollowing four-species nitrification-denitrification chain issimulated, in which ammonium NH4 is nitrified to nitriteNO2 and then to nitrate NO3, which undergoes denitrifi-cation to dissolved nitrogen N2:
NH4μNH4−−−→ NO2
μNO2−−−→ NO3μNO3−−−→ N2 (9)
where μNH4 , μNO2 , and μNO3 are the first-order rateconstants (per day) for nitrification of NH4 and NO2 andthe denitrification of NO3, respectively. Denitrificationtypically does not occur in the unsaturated zone becauseof the presence of dissolved oxygen O2. However, itis included in this test case for comparison purposeswith HYDRUS-1D. The inhibition of denitrification in thepresence of O2 is included in the 3D test case. A steadyinflow rate of 0.072 m/d at the top of the soil columnis used, with the concentration of NH4, NO2, and NO3
set to 50, 0, and 10 g/m3f , respectively, during the 5-d
simulation. Initial concentration, Ci, for each of the threesolutes is set to 0 g/m3
f throughout the profile. For the
NGWA.org R.T. Bailey et al. Groundwater 51, no. 5: 752–761 755
Table 1Summary of Simulation Setup and Parameter
Values for the HYDRUS-1D ComparisonSimulation and the 3D Test Case
Scenario 1 2
Benchmark model HYDRUS-1D —Flow condition Steady UnsteadyDimension 1 3Simulation time 5 d 5 yearsCell length �X — 25 mCell height �Y — 25 mCell length �Z 1 cm 0.5 mDomain length — 1000 mDomain width — 300 mDomain height 200 cm 45 mPorosity φ 0.4 0.35Initial θ 0.2 0.1Horizontal condition Kh — 5 m/dVertical condition Kv 0.5 m/d 5 m/dvan Genuchten α 14.5/m 1.65/mvan Genuchten n 3.1 2Brooks-Corey ε 5.2 4Inflow rate q 0.072 m/d MonthlyLongitunal dispersivity αL 0.04 m 2 mTransverse dispersivity αT — 0.2 mDecay rate k Multiple Multiple
first simulation, the first-order rate constants simulate a“slow” reaction chain, with μNH4 , μNO2 , and μNO3 setto 0.12, 0.048, and 0.012 per day, respectively. For thesecond simulation, the rate constants simulate a “fast”reaction chain, and are set to 0.48, 0.12, and 0.048 perday. Assessment of the agreement between UZF-RT3Dand HYDRUS-1D is made through a comparison ofconcentration profiles on the basis of the coefficient ofdetermination R2 (Vanderborght et al. 2005):
R2 = 1 −∑
i (ui − bi)2
∑i (bi)2 − (
∑i bi)N
2 (10)
where N is the number of grid cells in the soil profile forScenario 1, and ui and bi are the simulated concentrationvalues of the ith grid cell for UZF-RT3D and HYDRUS-1D, respectively. R2 values are also reported in theSupporting Information.
For Scenario 2, a system of multiple, interactingspecies is employed similar to that of Kim et al. (2004)in their study of the reactive transport of organic andnitrogen species in a variably saturated subsurface system.The model domain is shown in Figure 1, with a speciesspill site located in the western portion of the system.Groundwater flow direction is west to east, with constanthydraulic head specified as 41, 44, 5, and 1 m, in thesouthwest, northwest, northeast, and southeast corners ofthe aquifer, respectively, with the specified hydraulic headvarying linearly along the western and eastern edges ofthe aquifer. The resulting flow field provides 1D leaching
of species mass through a shallow unsaturated zone(∼5 m), followed by lateral species plume migration inthe saturated zone due to the imposed hydraulic gradient.No-flow boundaries were specified for the northern andsouthern edges of the aquifer, as well as at the aquiferbase. The simulation is run for 5 years, with infiltrationvarying on a monthly basis (see Figure 1). Ci throughoutthe model domain was set to 0 g/m3
f and concentrationof the species in the infiltrating water was set to1.0 g/m3
f .The defined reaction package is not only similar to
the sequential first-order decay reaction in Equation 9, butalso includes the chemical reduction of O2, the oxidationof dissolved organic carbon DOC (represented by ageneric organic compound CH2O) through the reductionof both O2 and NO3, and the inclusion of inhibition andMonod terms. Both O2 and NO3 are e− acceptors withpreferential chemical reduction in the order of O2 andNO3, hence establishing inhibitive sequential reductionkinetics in which denitrification does not proceed at anappreciable rate until the concentration of O2 is belowa specified threshold value, termed the O2 inhibitionconstant IO2 (M/L3
f ).The rate laws for the reactions of nitrification, O2
reduction, and denitrification are specified using dual-Monod expressions wherein the rate of reaction isdependent on the presence of the chemical reactants aswell as the presence of inhibitive e− acceptors:
rNH4 = −μNH4CNH4
(CNH4
KNH4 + CNH4
) (CO2
KO2 + CO2
)(11a)
rO2 = −μO2CO2
(CO2
KO2 + CO2
) (CDOC
KDOC + CDOC
)(11b)
rNO3 = −μNO3CNO3
(CNO3
KNO3 + CNO3
)
×(
CDOC
KDOC + CDOC
)(IO2
IO2 + CO2
)(11c)
where KNH4 , KO2 , and KNO3 are the Monod half-saturation constants (Mf/L3
f ). In this species system, NH4
is consumed via nitrification, NO2 is produced via nitri-fication, O2 is consumed via nitrification and throughchemical reduction, NO3 is produced through nitrifica-tion of NH4 and consumed through denitrification, andDOC is consumed during the chemical reduction ofboth O2 and NO3. The rate of DOC consumption isbased on the stoichiometric relationship between DOCand O2 and between DOC and NO3 for the chemi-cal reactions of O2 reduction and denitrification, respec-tively. Corresponding stoichiometric constants are 0.9375(30 g/mol/32 g/mol) and 0.605 (150 g/mol/248 g/mol),respectively.
A north-south line source of O2, NO3, NH4, NO2, andDOC (6.0, 2.0, 10.0, 2.0, and 8.0 g/m3
f , respectively) in theinfiltrating water is specified at a distance of 162.5 m from
756 R.T. Bailey et al. Groundwater 51, no. 5: 752–761 NGWA.org
Figure 1. Conceptualization of the 3D aquifer system for Scenario 2. Monthly infiltration is specified during a 5-yearsimulation.
the western edge of the aquifer. IO2 is set to 1.0 g/m3f , and
KNH4 , KO2 , and KNO3 are set to 2.0, 2.0, and 1.0 g/m3f ,
respectively. To further demonstrate the flexibility ofthe RT3D code, spatially variable first-order kineticrate constants are specified, with the parameter fieldgenerated using the geostatistical model SKSIM (Bau andMayer 2008), a sequential Kriging Gaussian simulationalgorithm, wherein the mean and standard deviation ofa logarithmic distribution and spatial correlation scalesare specified. Lognormality of first-order reactions hasbeen reported in the literature (e.g., Parkin and Robinson1989). For this example, the mean, standard deviation, andcorrelation scale are set to 0.001 per day, 0.30 per day,and 100 m, respectively. The resulting field of spatiallyvariable rate constants is multiplied by 4 to establish thefield of μNH4 values and by 2 to establish the field of μO2
and μNO3 values.A key feature of the reaction system, the one which
is necessary when simulating processes that are O2-dependent such as the sequential degradation of e− accep-tors or the bioattenuation of petroleum hydrocarbons, isthe inclusion of a reaeration term in UZF-RT3D that sup-plies O2 to the saturated zone via gaseous diffusion fromthe ambient atmosphere through the unsaturated zone. Theinclusion of such a term prevents the simulation of rapidO2 degradation and subsequent onset of anaerobic pro-cesses when in reality the presence of O2in the saturatedzone may persist due to replenishment of O2via the unsat-urated zone. Including this term is an advantage of theUZF-RT3D model. On the basis of the results from Nealeet al. (2000, 2002), the groundwater reaeration equationused in the reaction package accounts for soil type (inthe form of porosityφ), water content θ , the thickness ofthe unsaturated zone z, and the difference between thesaturation concentration of O2 in groundwater,CO2(aq),sat,and the present O2 concentration, CO2(aq), and is givenby (Neale et al. 2002):
dCO2
dt= Ds
z2(CO2(aq),sat − CO2(aq)) (12)
where the diffusion coefficient of O2 in porous media Ds
is a function of φ and θ (Millington and Quirk 1961):
Ds = Doθ
10/3a
φ2(13)
where Do is the diffusion coefficient of O2 in air (L2/T),with values ranging from 1.52 to 1.99 m2/d, and θa =φ − θ is the volumetric air content of the porous mediain the unsaturated zone. Thickness z and θa are updatedat each time step, with θ a calculated using the averageθ for the cells in the unsaturated zone. The 5-year sim-ulation is run both with and without the inclusion of thereaeration term. It should be noted that the flow-transportsystem neglects the supply of O2 to the pore water in theunsaturated zone via gaseous transport. Depletion of O2 inthe unsaturated zone thus may be overestimated, althoughlikely not to a great extent when applying the model toareas where infiltrating water introduces a large mass fluxof O2 into the unsaturated zone (e.g., irrigated areas).
Results and Discussion
1D Test Simulation ResultsResults for the two simulations for Scenario 1
are shown in Figure 2, with accompanying R2 valuesfor each concentration profile. The concentration profilecomparisons for NH4, NO2, and NO3 for the “slow”reaction simulation are shown in Figure 2A to 2C, and thecomparisons for the “fast” reaction simulation are shownin Figure 2D to 2F. As with simulation results presentedin the following section for the 3D system, mass balanceerror for the UZF-RT3D simulation is less than 0.005%.Excellent matches between UZF-RT3D and HYDRUS-1Doccur, with R2 values ≥0.991 for all profiles. The resultsin Figure 2 reflect the sequential reactions in Equation 9,with the concentration of NO2 and NO3 increasing duringthe 5-d simulation and the concentration of NH4 belowthe infiltrating concentration of 50 g/m3
f throughout thedepth of the profile. This is especially apparent for
NGWA.org R.T. Bailey et al. Groundwater 51, no. 5: 752–761 757
A
D E F
B
C
Figure 2. Simulation results of UZF-RT3D and HYDRUS-1D (Simunek et al. 1998) for a 200-cm soil profile, showing theconcentration profiles of NH4, NO2, and NO3 after 1, 2, and 5 d. Concentration profiles resulting from “slow” kinetic reactionsare shown in (A), (B), and (C) for NH4, NO2, and NO3, respectively, and the profiles resulting from “fast” kinetic reactionsare shown in (D), (E), and (F).
NO2 (Figure 2B and 2E), which is not contained in theinfiltrating solution and hence is present due solely to thenitrification of NH4. It is also indicated by the increase inNO3 concentration above the infiltrating concentration of10 g/m3
f after 5 d (Figure 2C and 2F), as NO2 nitrifiesto NO3. Note that the highest concentrations of NO2
and NO3 result in the “fast” reaction simulation dueto the higher rate of nitrification of NH4. In the “fast”reaction simulation, the maximum concentration after 5 dfor NO2 and NO3 is 27.5 and 14.5 g/m3
f , respectively,compared with 12.9 and 10.3 g/m3
f for the “slow” reactionsimulation.
3D Test Simulation ResultsFigures 3 and 4 show results from the multispecies
simulation in areal extent and profile view, respectively,and demonstrate the interactive behavior of the fivesimulated species as specified in Equations 11a to 11cand the influence of the reaeration term as defined byEquations 12 and 13. The extent of the water table isshown in the Supporting Information (Figure S5), andchemical reactions occur as the species are leachedthrough the approximately 5-m thick unsaturated zone andthen transported in the saturated zone. Figure 3 shows thegenerated base first-order rate constant field (top pane),and the resulting extent of the NH4 (second pane), NO3
(third pane), and O2 (fourth pane) plumes after 5 yearsfor the simulation that does not include the reaerationterm, at an elevation of 30 m above the aquifer base. Notethat, for NH4, the spatial distribution of concentrationis directly related to the spatial distribution of the rateconstant of nitrification, with areas of higher and lower
Figure 3. Contour plot of the spatially varying base rateconstant (top pane) (per day), followed by plan views atelevation 30 m of plume migration after 5 years at Z = 30 mfor NH4, NO3 (simulation without reaeration), O2 withoutreaeration, and O2 with reaeration. Solute concentrations areshown in g/m3
f .
concentration occurring in the vicinity of lower and higherrate constants, respectively. As a product of nitrification,the concentration of NO3 is hence higher in the southernportion of the plume where the rate of nitrification is thehighest, and lower in the northern portion of the plumewhere the rate of nitrification is the lowest.
The interaction between the species is further demon-strated in Figure 4, which shows the vertical extent of thespecies plumes at a cross section located 87.5 m from thesouthern edge of the aquifer. NH4 (top pane), with aninput concentration of 10.0 g/m3
f in the infiltrating water,
758 R.T. Bailey et al. Groundwater 51, no. 5: 752–761 NGWA.org
Figure 4. Cross-sectional view of plume migration after5 years at Y = 87.5 m for O2 (simulations without andwith reaeration) and NO3 (simulations without and withreaeration). Solute concentrations are shown in g/m3
f .
is consumed whereas both NO2 (second pane) and NO3
(third pane) are produced to result in concentrations muchhigher than their respective input concentrations (2.0 g/m3
ffor both). Due to the inhibitive presence of O2, NO3 doesnot undergo extensive denitirification and is transportedfreely through the saturated zone.
The O2 plume for the simulation with the reaerationterm is shown in the bottom panes of both Figures 3 and 4,and when compared with the fourth panes from each figuredemonstrates the significance of including reaeration tothe saturated zone via gaseous diffusion. In Figure 3, theareal extent of the O2 plume is much more pronounced,and in Figure 4, the supply of O2 to regions of thesaturated zone outside the spill site area is evident, withhigher concentrations of O2 occurring in locations wherethe unsaturated zone is shallow (i.e., the western portionof the aquifer). For the simulation setup, NO3 enters thesystem at the specified north-south line source, and henceis not affected by the increased O2 concentration in othersections of the saturated zone, although NO3 also can becreated from the nitrification of NH4 in the presence of O2.However, for systems where nonpoint sources of nitrogenare an important source of NO3 to the subsurface, such asin agricultural settings, the inclusion of the reaeration termwill have an important influence on NO3 as O2 inhibitsdenitrification throughout the aquifer system.
ConclusionsThe numerical model UZF-RT3D is presented for
simulating the reactive transport of multiple interactingspecies in variably saturated subsurface systems. Anumber of simulations in variably saturated subsurfacesystems were used to introduce and test simulationcapabilities of UZF-RT3D. Tests were made against ananalytical solution as well as a suite of published variablysaturated flow and transport models (HYDRUS-1D,VS2DT, SUTRA, CATHY-TRAN3D), with most resultspresented in the Supporting Information. Qualitative and
quantitative assessments of agreement between UZF-RT3D and the benchmark models were made, withsatisfactory agreement attained for all scenarios.
Similar to the results for the UZF-MT3DMS model,UZF-RT3D yielded improved run-times, as shown inthe Supporting Information. This was further shownthrough an assessment of grid discretization in the verticaldirection (Supporting Information) and demonstrated thesustained accuracy in the flow and reactive transportsolution for large cell sizes (e.g., 1.0 to 3.0 m layerthicknesses) and hence significant saving in model CPUtime. It should be noted, however, that providing anexact comparison of CPU times between the models wasnot the aim of this study, and a comprehensive set ofcomparison tests was not carried out. However, the run-time comparison demonstrates the potential advantage ofUZF-RT3D in large-scale systems when the conceptualmodel of the system suits the assumptions of UZF1, thatis, homogeneous soil parameters. The fate and transport ofchemical species in variably saturated subsurface systemsthat do not conform to these assumptions likely should beinvestigated using Richards equation-based models.
Also, UZF-RT3D offers a platform for a number ofapplications not possible with the original RT3D function-ality, for example, leaching of nutrients and other chemi-cal species in soil profiles, particularly when the reactionkinetics of a given species are dependent on the presenceof other species, as in the case of sequential reductionof e− acceptors. An example is the selenium–nitrogen-coupled reactions recently investigated and described byBailey et al. (2012). The 3D multispecies reactive trans-port scenario demonstrated these features in simulatingthe interactive behavior of chemical species during leach-ing in the unsaturated zone and lateral plume migrationin the saturated zone. A reaeration term, in which O2 issupplied to the saturated zone via gaseous diffusion in theunsaturated zone, has been added to the implementationof RT3D for systems simulating the fate and transport ofO2 and O2-dependent species and reactions, although O2
is not supplied directly to the pore water in the unsatu-rated zone. A final, important point is that UZF-RT3D fitswithin an entire suite of models available to the worldwidecommunity that are based on MODFLOW.
Combined with the computational advantages ofUZF1, UZF-RT3D is an attractive option for multispeciesreactive transport in large-scale variably saturated flowsystems wherein the unsaturated zone plays an importantrole in the movement and transformation of chemicalspecies over large landscapes, such as in agriculturalwatersheds. Furthermore, as UZF1 is the basis forsimulating unsaturated flow in the coupled groundwaterand surface-water flow model GSFLOW (Markstromet al. 2008), these developments are a step towardimplementing solute transport in GSFLOW.
AcknowledgmentsThe authors gratefully acknowledge the financial
support of the Colorado Nonpoint Source Program
NGWA.org R.T. Bailey et al. Groundwater 51, no. 5: 752–761 759
of the Colorado Department of Public Health andEnvironment and the Colorado Agricultural ExperimentStation. The authors thank Mario Putti and DomenicoBau for providing access to the CATHY and TRAN3Dmodels. We also thank three anonymous reviewers andthe associate editor for helpful comments and suggestionsin improving the content of this paper.
Supporting InformationAdditional Supporting Information may be found in
the online version of this article:
Appendix S1. Description of testing and numericalexperiments for single-species reactive transport.
Table S1. Summary of simulation setup and param-eter values for testing UZF-RT3D against analytical andnumerical simulation benchmarks.
Table S2. Details for the 2D aquifer system testsimulations, belonging to Scenario S4 shown in Table S1.The measure of agreement with VS2DT, as indicated byR2 values, is shown in the far-right column.
Figure S1. Conceptualization of the 2D verticalprofile aquifer system for the 2D test problem. Eight testsimulations are performed with varying flow and transportmodel parameters with results compared against VS2DT.
Figure S2. Simulation results of UZF1-RT3D andthe van Genuchten (1981) analytical model for a 200-cm soil profile, showing (A) species concentration profileafter 10 d for five dispersivity values (αL = 0.1, 1, 2.5,5.0, and 10.0 cm) and (B) species concentration profileafter 10 d for various retardation coefficients (R) andfirst-order rate constants (μ). R2 values are presentedto provide a quantitative measure of agreement betweenUZF1-RT3D and the analytical solution.
Figure S3. Simulation results of UZF-RT3D andVS2DT for the 500-cm soil profile 1D unsteady flowscenario, showing simulated solute concentrations at fourdepths (25, 50, 100, and 150 cm) for the (A) silt profilewith μ = 0.005/d and (B) sand profile with μ = 0.05 perday.
Figure S4. Species concentration contour plots forthe eight 2D test simulations described in Table S2.VS2DT results are shown in a solid black line, UZF-RT3Dresults are shown in a dashed red line, and water tableelevation is displayed in a blue line. R2 values comparingUZF-RT3D to VS2DT are presented in Table S2.
Figure S5. Comparison of plume migration at1825 d of SUTRA, CATHY-TRAN3D, and UZF1-RT3Dsimulations for (A) the cross section located at Y =162.5 m and (B) the areal section at Z = 30.25 m. Thewater content θ from the UZF1 simulation is shown inblue contours, whereas the water table elevation at eachcolumn of nodes for the SUTRA and CATHY simulationsare shown in blue and red squares, respectively.
Figure S6. Comparison of plume migration forthe three UZF-RT3D simulations with varying verti-cal grid cell discretization (0.5, 1.0, and 3.0 m cellthicknesses).
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