Modeling Variably Saturated Multispecies Reactive Groundwater Solute Transport with MODFLOW-UZF and RT3D

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<ul><li><p>Modeling Variably Saturated MultispeciesReactive Groundwater Solute Transport withMODFLOW-UZF and RT3Dby Ryan T. Bailey1, Eric D. Morway2, Richard G. Niswonger2, and Timothy K. Gates3</p><p>AbstractA numerical model was developed that is capable of simulating multispecies reactive solute transport in</p><p>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.</p><p>IntroductionA thorough understanding of water movement and the</p><p>fate and transport of chemical species and nutrients in theshallow unsaturated zone is imperative owing to its control</p><p>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;</p><p>2United States Geological Survey, 2730 N. Deer Run Road,Carson City, NV 89701.</p><p>3Department of Civil and Environmental Engineering, ColoradoState University, 1372 Campus Delivery, Fort Collins, CO 80523-1372.</p><p>Received January 2012, accepted September 2012.Published 2012. This article is a U.S. Government work and is</p><p>in the public domain in the USA.doi: 10.1111/j.1745-6584.2012.01009.x</p><p>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</p><p>752 Vol. 51, No. 5GroundwaterSeptember-October 2013 (pages 752761)</p></li><li><p>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.</p><p>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.</p><p>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.</p><p>Similar to the 1D and 2D models, however, these3D models solve the full Richards equation for variably</p><p>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.</p><p>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.</p><p>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.</p><p>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</p><p> R.T. Bailey et al. Groundwater 51, no. 5: 752761 753</p></li><li><p>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.</p><p>Development of UZF-RT3DThe numerical model RT3D simulates the reactive</p><p>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</p><p>Ck</p><p>t= </p><p>xi(viCk)+ </p><p>xi</p><p>(Dij</p><p>Ck</p><p>xj</p><p>)</p><p>+ qsCsk bCk</p><p>t+ r k = 1, 2, . . . , m (1)</p><p>where m is the total number of aqueous-phase species;Ck is the concentration of the kth species (Mf/L3f ), 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; isthe soil porosity (L3f /L</p><p>3b); qs is the volumetric flux of</p><p>water representing sources and sinks of the species(L3f /T/L</p><p>3b); Csk is the concentration of the source or sink</p><p>(Mf/L3f ); r represents the rate of all reactions that occur inthe aqueous phase for the kth species (Mf/L3f /T); b is thebulk density of the porous media (Mb/L3b); and Ckis theconcentration of the kth species sorbed on solids (Mf/Mb).To simplify Equation 1, the retardation factor Rk (),equal to 1 + (bKdk )/ for linear sorption where Kdk isthe partitioning coefficient (Mb/L3f ) for the kth species andis equal to Ck/Ck , is incorporated to yield</p><p>Ck</p><p>tRk = </p><p>xi(viCk)+ </p><p>xi</p><p>(Dij</p><p>Ck</p><p>xj</p><p>)</p><p>+ qsCsk</p><p>+ r k = 1, 2, . . . , m (2)</p><p>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</p><p>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 Ckusing 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).</p><p>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 term in Equation 1 with volumetric water content (L3f /L</p><p>3b),</p><p>the system of ADR equations for simulating multispeciesreactive transport under variable saturation is</p><p>(Ck)</p><p>t= </p><p>xi(viCk)+ </p><p>xi</p><p>(Dij</p><p>Ck</p><p>xj</p><p>)+ qsCsk</p><p> b Ckt</p><p>+ r k = 1, 2, . . . , m (3)</p><p>where 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 (Ck)/(Ck)yields</p><p>(Ck)</p><p>t+ b (Ck)</p><p>t</p><p>Ck</p><p>(Ck)</p><p>= xi</p><p>(viCk)+ xi</p><p>(Dij</p><p>Ck</p><p>xj</p><p>)+ qsCsk + r</p><p>k = 1, 2, . . . , m (4)</p><p>which can be simplified to</p><p>(Ck)</p><p>t</p><p>(1 + b Ck</p><p>(Ck)</p><p>)</p><p>= xi</p><p>(viCk)+ xi</p><p>(Dij</p><p>Ck</p><p>xj</p><p>)+ qsCsk + r</p><p>k = 1, 2, . . . , m (5)</p><p>754 R.T. Bailey et al. Groundwater 51, no. 5: 752761</p></li><li><p>Substituting the following expression</p><p>Rk = 1 + b Ck(Ck)</p><p>(6)</p><p>into Equation 5 yields</p><p>(Ck)</p><p>tRk = </p><p>xi(viCk)+ </p><p>xi</p><p>(Dij</p><p>Ck</p><p>xj</p><p>)</p><p>+ qsCsk + r k = 1, 2, . . . , m. (7)</p><p>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 Ck , Equation 7 is divided into four distinctequations to solve for the change in Mf...</p></li></ul>


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