Investigation of Small-Scale Preferential Flowwith a Forced-Gradient Tracer Testby Marco Bianchi1, Chunmiao Zheng2, Geoffrey R. Tick2, and Steven M. Gorelick3

AbstractA new tracer experiment (referred to as MADE-5) was conducted at the well-known Macrodispersion

Experiment (MADE) site to investigate the influence of small-scale mass-transfer and dispersion processes onwell-to-well transport. The test was performed under dipole forced-gradient flow conditions and concentrationswere monitored in an extraction well and in two multilevel sampler (MLS) wells located at 6, 1.5, and 3.75 m fromthe source, respectively. The shape of the breakthrough curve (BTC) measured at the extraction well is stronglyasymmetric showing a rapidly arriving peak and an extensive late-time tail. The BTCs measured at seven differentdepths in the two MLSs are radically different from one another in terms of shape, arrival times, and magnitudeof the concentration peaks. All of these characteristics indicate the presence of a complex network of preferentialflow pathways controlling solute transport at the test site. Field-experimental data were also used to evaluatetwo transport models: a stochastic advection-dispersion model (ADM) based on conditional multivariate Gaussianrealizations of the hydraulic conductivity field and a dual-domain single-rate (DDSR) mass-transfer model basedon a deterministic reconstruction of the aquifer heterogeneity. Unlike the stochastic ADM realizations, the DDSRaccurately predicted the magnitude of the concentration peak and its arrival time (within a 1.5% error). Forthe multilevel BTCs between the injection and extraction wells, neither model reproduced the observed values,indicating that a high-resolution characterization of the aquifer heterogeneity at the subdecimeter scale would beneeded to fully capture 3D transport details.

IntroductionTracer experiments are essential tools to characterize

aquifer properties and to understand the mechanismsresponsible for solute transport in porous and fracturedmedia. Experimental data collected during these testshave been essential for the development and testingof transport theories and mathematical models. In

1Corresponding author: Department of Geological Sciences,University of Alabama, Tuscaloosa, AL 35487; (205) 348-3015;fax: (205) 348-0818; mbianchi@bama.ua.edu

2Department of Geological Sciences, University of Alabama,Tuscaloosa, AL 35487.

3Department of Environmental Earth System Science, StanfordUniversity, Stanford, CA 94305.

Received November 2009, accepted July 2010.Copyright © 2010 The Author(s)Journal compilation © 2010 National Ground Water Association.doi: 10.1111/j.1745-6584.2010.00746.x

this context, the tracer experiments conducted at theMacrodispersion Experiment (MADE) site located inColumbus, Mississippi, have played a very important role.Three large-scale natural gradient tracer experiments wereconducted at the MADE site from the mid-1980s to theend of the 1990s. In the first two experiments, usuallyreferred to as MADE-1 and MADE-2, conservative tracersincluding bromide and tritium were injected in the uncon-fined aquifer underlying the site and concentrations werethen monitored through a dense network of multilevelsamplers (MLSs) extending over 280 m along the meanplume trajectory (Boggs 1991; Boggs et al. 1992, 1993).Due to the large number of MLSs (258 and 328), thesampling scheme provided only “snapshots” of the plumeevolution; concentrations were sampled eight times (overa period of 20 months) during the MADE-1 experimentand five times (over a period of 15 months) during theMADE-2 experiment. In the third tracer test, also referred

NGWA.org Vol. 49, No. 4–GROUND WATER–July-August 2011 (pages 503–514) 503

to as the Natural Attenuation Study (NATS or MADE-3),a source trench was used to inject six hydrocarbon com-pounds and bromide to mimic an instantaneous release.A total of six snapshots of the plume were sampled overa period of 20 months (Boggs et al. 1995; Libelo et al.1997; Julian et al. 2001). More recently, a small-scalesingle-well push-pull test (MADE-4) was conducted ina well located approximately 100 m NNW of the sourceinjection wells used for the MADE-1 and MADE-2 tracerexperiments (Liu et al. 2010). Bromide was injected for4.1 h and groundwater containing bromide was pumpedfrom the well for approximately 17 days after a restingperiod of about 19 h.

The analysis of the three large-scale experimentsrevealed the strongly non-Fickian, highly asymmetriccharacter of the generated tracer plumes, with the highestconcentrations localized close to the sources and extensivedown-gradient spreading of dilute solute. Several studiesemploying different transport modeling approaches haveattempted to simulate the collected experimental data(Adams and Gelhar 1992; Berkowitz and Scher 1998;Eggleston and Rojstaczer 1998; Feehley et al. 2000;Harvey and Gorelick 2000; Baeumer et al. 2001; Braunerand Widdowson 2001; Julian et al. 2001; Schumer et al.2003; Barlebo et al. 2004; Salamon et al. 2007; Zhang andBenson 2008; Llopis-Albert and Capilla 2009). Most ofthese works showed that transport behavior at the MADEsite cannot be reproduced with the classical advection-dispersion model (ADM). Harvey and Gorelick (2000)and Feehley et al. (2000) suggested that the aquifer at theMADE site is characterized by significant connectivity,resulting from the presence of a network of highlyconductive channels or preferential flow paths (PFPs)embedded in a low permeable matrix. The inability ofthe ADM to reproduce the observed plume spreadingwas then related to the scale of these PFPs which arelikely smaller than the grid spacing of the implementednumerical models.

Several mass-transfer-based modeling approaches,alternatives to the ADM, successfully reproduced theMADE site experimental data (Berkowitz and Scher1998; Benson et al. 2001; Baeumer et al. 2001; Lu et al.2002; Zhang et al. 2007; Zhang and Benson 2008). Thesimplest of these approaches, the dual-domain model,conceptualizes the aquifer as consisting of two distinctmobile and immobile domains and the effect of unresolvedheterogeneities is mimicked by mass-transfer processesbetween the two domains. This approach not only is ableto reproduce the two main characteristics of the plumesgenerated by the large-scale experiments (i.e., anomalousmass accumulation near the sources and extensive low-concentration spreading), as shown by several studies(Harvey and Gorelick 2000; Feehley et al. 2000; Julianet al. 2001; Guan et al. 2008; Llopis-Albert and Capilla2009), but also explains the apparent increase in solutemass observed during the early stages of the experimentsand the apparent mass loss at later times (Harvey andGorelick 2000). These models provide indirect evidenceof the importance of small-scale PFPs at the MADE site.

Salamon et al. (2007), however, suggested that solutespreading at the MADE site may be accounted for usingan ADM if aquifer heterogeneity is represented in detailwith values derived from the flowmeter measurementspresented in Rehfeldt et al. (1992). Using a fine-gridADM based on multiple realizations of the hydraulicconductivity (K) field, they found that the ADM canreproduce the average transport behavior during theMADE-2 experiment for a small subset of the K

realizations generated from a semivariogram structure thatemphasizes spatial continuity. This result was interpretedas an indication that the need for alternative transportmodels can be related to the suppressed spatial variationof the K field at the scale used by previous models.

From this review, it is evident that almost 25 yearsafter the first tracer experiment and many published papersand models, understanding the transport mechanisms atthe MADE site is still a work in progress. Here weprovide additional field-experimental data and modelingresults to help shed further light on some important issues,such as the importance of the presence and scale ofthe PFP network and which transport models providea feasible representation of the transport mechanisms.For this purpose, we designed and conducted a newtracer experiment (referred to hereafter as MADE-5)to investigate solute transport at the inter-well scale.The test was conducted under a local forced-gradientregime to generate well-defined experimental conditionsby minimizing the effects of natural gradient variationsand to reduce the duration of the experiment (Ptak et al.2004). Unlike previous tracer tests at the MADE site,the data set collected during the MADE-5 experimentinclude more highly resolved multilevel breakthroughcurves (BTCs) allowing a more detailed examination ofthe transport behavior in space and time. The test wasdesigned with the intent of providing a clear indicationof the existence and the scale of PFPs by comparing thecharacteristics of BTCs measured at different depths inthe aquifer. The new experimental data were then usedto evaluate two transport models: a stochastic ADM, withmultiple conditional K realizations, and a dual-domainsingle-rate (DDSR) mass-transfer model based on adeterministic reconstruction of aquifer heterogeneity. Thegoal was to test whether the support scale for the existingflowmeter K data is fine enough to effectively simulatethe MADE-5 experiment with the ADM or, alternatively,if the dual-domain model is needed since the availableK data do not provide an adequate representation of thecentimeter-scale heterogeneity.

Field Setting and ExperimentA comprehensive presentation of the geological

characteristics and hydrogeologic setting of the MADEsite has been offered by Boggs et al. (1990), Boggs et al.(1992), Rehfeldt et al. (1992), Bowling et al. (2005), andZheng (2006). Here we present only a brief descriptionof the stratigraphic setting but a detailed report of theinstrumentation used in this experiment.

504 M. Bianchi et al. GROUND WATER 49, no. 4: 503–514 NGWA.org

Site DescriptionThe MADE site is characterized by a shallow

unconfined aquifer composed of poorly to well-sortedsandy gravel and gravelly sand, with minor amounts ofsilt and clay. The three-dimensional K distribution wasinvestigated by means of flowmeter measurements in 66boreholes (Figure 1b) with a vertical support scale ofapproximately 15 cm. Statistical analysis of the collecteddata (more than 2500 measurements) revealed a lognormaldistribution and extremely high heterogeneity (Rehfeldtet al. 1992). The geometric mean of the flowmetermeasurements of K is about 4.3 × 10−3 cm/s, whilethe variance of the natural logarithms of the measuredK is 4.5. The MADE-5 tracer test was conductedin a sector of the MADE site located approximately65 m north of the source wells used in the previousMADE-1 and MADE-2 experiments. In particular, asshown in Figure 1c, this sector is located betweenboreholes K-21 and K-28 as labeled by Boggs (1991),Rehfeldt et al. (1992), and Boggs et al. (1993). Twocontinuous cores were collected at the test site usingdirect-push technology to minimize the disturbance ofthe samples and preserve the actual heterogeneity andstructure of the aquifer material. Lithologic analysisconfirmed the hydrostratigraphic setting found by previousstudies showing a predominance of sandy to gravelly claydeposits in the upper 2 m of the vertical profile, overlaying

an interval of about 9 m of sandy gravel and gravellysand. The bottom part of the aquifer is characterizedby about 1.5 m of mixed sand and fine sediments. Inthe investigated portion of the MADE site, the clay-richmarine sediments of the Eutaw formation constitutingthe aquitard beneath the alluvial aquifer are found ata depth of about 12 m below the ground surface. Thegeneral direction of groundwater flow is northward andthe average water table depth is about 4 m below landsurface, with seasonal oscillations ranging from 2 to 3 m(Boggs et al. 1992).

MADE-5 Field Tracer ExperimentFour wells were installed for tracer injection,

extraction and monitoring. The boreholes for the wellsinstallation were created with a hollow stem auger andeach well was drilled to the bottom of the aquifer (12.2 mbelow the ground surface). The injection and extractionwells consist of a polyvinyl chloride (PVC) pipe with anoutside diameter of 10.16 cm and were screened over theentire saturated thickness (Figure 2a). These two wellswere located 6 m apart and the two MLS wells wereinstalled in between, at a distance of 1.5 and 3.75 m fromthe injection well (Figure 2c). The MLSs consist of cus-tom extruded, high-density polyethylene (HDPE) tubingwith an outside diameter of 4.1 cm and containing inter-nal partitions forming seven discrete channels (Figure 2b).

-50 0 50Easting (m)

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rth

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)

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)

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Extraction well

Injection well

MLS-2

MLS-1

Radar station

MLSs and wells used for the MADE-5 experiment

Flowmeter measurments(Rehfeldt et al. 1992)

Model domain for transport simulations

Mississippi

MADEsite

K-22

K-21

K-28

K-27

ba

c

N

Figure 1. Maps showing the location of the MADE site and the new MADE-5 tracer experiment: general location of theMADE site (a); model domain for transport simulation and location of the flowmeter wells and the wells used for the MADE-5 experiment (b); detailed location of the extraction and injection wells and the two MLSs (c). Note: the dashed line representsthe location of the cross section shown in Figure 4.

NGWA.org M. Bianchi et al. GROUND WATER 49, no. 4: 503–514 505

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Depth (m)

0.46 m (Filter sand)

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0.76 m (Bentonite)

MA

DE

site

het

erog

eneo

us a

quife

r

1

234

5 6 77-channelHDPE tubing

Stainless steelmesh

Holes drilledinto channel 3

Plug made of Polyhethylenesealant

1.22 m (distancebetween intake ports)

Injectionwell

ExtractionwellMLS-1 MLS-2

Screened interval

Screened interval

Intake port

6 m

1.5 m 2.25 m 2.25 m

Injection well

MLS-1 MLS-2 Extractionwell

a b

c

clay (Eutaw formation)

Figure 2. Design of the MADE-5 experiment: cross sections showing the screened intervals in the injection and extractionwells together with the investigated level in the two MLSs (a); details of the multilevel monitoring wells (b, modified fromEinarson and Cherry 2002); plane view showing the spacing between the wells (c).

In each MLS, seven intake ports were created by drilling1 cm diameter holes through the exterior wall of the tub-ing for groundwater sample collection at selected depths.The shallowest monitored depth (Level 1 in Figure 2a) isassociated with channel 1, and the other ports are drilledin the remaining channels of the tubing with a uniformspacing of 1.2 m. The central channel (Level 7) was leftopen to the bottom of the multilevel sampling well. Wellscreens were constructed by wrapping stainless-steel fab-ric mesh around the tubing over the sampling ports. Thechannels below the intake ports were plugged by injectinga polyethylene sealant and polyethylene plugs were alsoinjected into each of the outer six channels at the very bot-tom of the well to effectively seal the various channels.Layers of filter sand and bentonite pellets were used to fillthe annular space between the MLS tubing and the bore-hole walls. The thickness of the sand packs surroundingeach intake port was 0.46 m. More details on the charac-teristics of this type of multilevel groundwater monitoringsystem and the results of three field trials, including oneat the Canadian Forces Base Borden in Ontario (Canada),are presented by Einarson and Cherry (2002).

The MADE-5 tracer experiment was conducted underdipole flow forced-gradient conditions. The experimentwas performed during the summer of 2007 and can bedivided into three successive phases. Initially clean waterwas injected for 48 h at a rate of 5.68 L/min. After arelative steady-state flow field was established, a knownvolume of 2078 L of bromide solution was introduced intothe aquifer as a step input for 366 min. The concentration

of the injected bromide solution was about 1000 mg/L.Clean water was injected again during the third and lastphase until the experiment was concluded after 32 daysfrom the injection of the bromide solution. During allphases, groundwater was continuously extracted from theextraction well and the extraction and injection rates(5.68 L/min) were kept constant and equal. The extractedgroundwater was reinjected into the aquifer using anotherwell located more than 100 m away in order to preventany interference with the established flow field. Pumpingrates, the total amount of injected and extracted water, andgroundwater levels in the injection and extraction wellswere also continuously monitored by flowmeters, total-izers, and submersible pressure transducers. Analysis ofthe transducers data showed that the average water tabledepth decreased 8.1 cm over time due to the absence ofprecipitation during the execution of the test. As this valuerepresents less than 1% of the saturated thickness of theaquifer, we assumed that the experiment was conductedunder steady-state conditions. Groundwater samples werecollected from the extraction well and from the two MLSsat different depths by using a peristaltic pump. Becauseof the very low extraction rate (20 mL/min) it is safe toassume that the flow field was practically not perturbedby the sampling procedures. For the first 3 days after theinjection, a 1 h sampling interval was used for the extrac-tion well and a 2 h interval was used for the MLSs. Sam-pling intervals were then progressively increased. Sampleswere analyzed using ion chromatography to measure thebromide concentrations. Groundwater samples were also

506 M. Bianchi et al. GROUND WATER 49, no. 4: 503–514 NGWA.org

collected before injecting the bromide solution. Chemicalanalyses showed that background groundwater concentra-tions of bromide were below the analytical detection limit.

Numerical ModelingA 3D finite-difference model was implemented to

simulate the field experiment. The model domain (thegray rectangle in Figure 1) is 123 m long by 98.25 mwide by 8.1 m thick, and it was discretized into a block-centered finite-difference grid consisting of 27 layers,164 rows, and 131 columns for a total of 580,068 cells.The grid spacing is constant and equal to 0.75 × 0.75 min the horizontal direction and to 0.3 m in the verticaldirection. Steady-state flow was simulated using theMODFLOW code (Harbaugh et al. 2000). Dirichlet-type(specified-head) boundary conditions along the northand south boundaries, and Neumann-type (zero-gradient)boundary conditions to the east, west, top, and bottomboundaries, were imposed on the model domain laterally.Because the ambient hydraulic gradient at the MADEsite is small (about 0.003 on average, Boggs et al.1992), as compared to the local gradient created bythe MADE-5 test (0.045 between the injection andthe extraction wells), the ambient gradient was ignoredby imposing equal constant heads at the north andsouth boundaries. The value used corresponds to theaverage of static groundwater levels measured at theinjection and extraction wells prior to the beginning ofthe experiment. In accordance with the design of thetracer test, two steady-state stress periods were simulatedto represent the injection of the bromide solution for366 min and the remaining time interval of 32 days forcompleting the experiment. During both stress periods,the injection and extraction wells were simulated usingthe Multi-Node Well Package (Halford and Hanson 2002)which simulates a multilayer well with a single wellhead.

Two different approaches were used to generate thespatial distribution of K in the model domain. Withthe first, the spatial distribution of K was considered

a stochastic process and equally probable conditionalrealizations were generated using Sequential GaussianSimulation. This stochastic approach was also taken bySalamon et al. (2007) who performed a thorough geo-statistical analysis of the flowmeter data concluding thata multivariate Gaussian random function is adequate tomodel the spatial distribution of LnK at the MADE site.In the second approach, the K field was treated as adeterministic process and it was estimated using ordi-nary kriging. The geostatistical analysis was performedby using the Stanford Geostatistical Modeling SoftwareS-GEMS (Remy et al. 2009). Spatial continuity of theLnK was evaluated by calculating the experimental semi-variogram using a subsample of the data of Rehfeldt et al.(1992). The subsample consists of 1636 K values mea-sured in the flowmeter wells located within the modeldomain plus three additional locations. As for other geo-statistical studies applied at the MADE site (Rehfeldt et al.1992; Salamon et al. 2007; Llopis-Albert and Capilla2009), we assumed that the depositional structures respon-sible for the variability of K are horizontal; hence thespatial correlation was investigated only in the completelyhorizontal and vertical directions. Directional horizontaland vertical variograms together with the fitted modelare shown in Figure 3. The variogram model consistsof a linear combination of a spherical and an exponen-tial model whose parameters are presented in Table 1.The spherical component effectively fits the experimentalvariograms at small lag distances, while the exponentialcomponent gives a better representation of the spatialcontinuity at larger lag distances. Directional variogramanalysis demonstrated that a good fit is obtained when themaximum correlation distance is rotated 150◦ clockwisewith respect to the y-axis in Figure 1. The determinedvariogram model was used both to estimate the kriged K

distribution (Figure 4a) and for generating 50 conditionalsequential Gaussian realizations (Figures 4b and 4c).

Two conceptual models of solute transport wereused to simulate the transport behavior observed inour small-scale tracer test. We first applied the ADMin the context of a Monte Carlo stochastic frameworkto simulate transport in the flow fields generated with

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60 degrees

0 degrees

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Vertical experimental variogram

Fitted anisotropic variogram model

γ

Figure 3. Directional horizontal (left) and vertical anisotropic (right) variograms and fitted model (shown for differentdirections) for the LnK flowmeter data. Variogram model parameters are presented in Table 1.

NGWA.org M. Bianchi et al. GROUND WATER 49, no. 4: 503–514 507

Table 1Geostatistical Parameters for the Variogram Model Used to Generate the K Fields

Ranges (m)

Model Maximum Medium Minimum Nugget Structure Sill Rotation Angle

Spherical 76 47.1 4.6 0.2 1.75 150◦

Exponential 21 21 5 3.0 150◦

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8

12Dep

th (

m)

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LnK (cm/s)0

-2

-4

-6

-8

-10

a

b

c

Figure 4. Hydraulic conductivity distribution along a cross section of the modeled domain generated with kriging (a) andwith conditional sequential Gaussian simulation (b and c). The location of the cross section is shown in Figure 1b.

conditional sequential Gaussian simulation. Salamon et al.(2007) showed that under limited circumstances it ispossible for the ADM to reproduce the average transportbehavior observed during the MADE-2 experiment whensmall-scale variability of K is modeled at the flowmetermeasurement vertical support scale (∼0.15 m). We testedif this holds also for the flowmeter horizontal support scaleand, in particular, if it is possible to use the flowmetermeasurements to generate downscaled flow fields thatcan be effectively used in combination with the ADM.The position of the wells used for our experiment isparticularly appropriate for this purpose since they arelocated in a sector of the MADE site close to severalflowmeter measurements (Figure 1c). The vertical gridspacing for the model was chosen to take into accountthe flowmeter vertical support scale and the fact thateach of the intake ports in the two MLSs is surroundedby 0.46-m-long sand packs. Therefore, 0.3 m verticalspacing was considered as a valid compromise betweenthe flowmeter support scale and the spatial scale of theconcentration measurements. The governing equation ofthe ADM for a conservative solute in a 3D groundwaterflow system can be written as follows (Zheng and Bennett2002):

∂(θC)

∂t= ∂

∂xi

(θDij

∂C

∂xj

)− ∂

∂xi(qiC) + qsCs (1)

where C is the solute concentration, θ is the effectiveporosity, t is time; xi are the respective Cartesiancoordinate axes directions, Dij is the hydrodynamicdispersion coefficient tensor (including both mechanicaldispersion and molecular diffusion); qi are the componentsof the specific discharge or Darcy flux in the coordinatedirections, Cs represents the solute concentrations inthe fluid sink/source, and qs represents fluid sink/sourcefluxes Tracer transport in each of the Monte Carlorealizations was simulated with MT3DMS (Zheng andWang 1999; Zheng 2010). The advective component inEquation 1 was solved with the highly accurate massconservative total-variation-diminishing (TVD) scheme tominimize numerical dispersion, artificial oscillation, andmass balance discrepancies.

A DDSR mass-transfer model was also imple-mented. Because the effect of unresolved heterogeneitiesis accounted for by mass transfer between the mobileand the immobile domains, the K field reconstructed withordinary kriging was considered to be an adequate approx-imation of the actual heterogeneity and we let the mass-transfer processes account for unresolved subgrid hetero-geneity due to the coarse and smoothed parameterization.For a conservative solute, the governing equations for theDDSR model are the following (Zheng and Bennett 2002):

θm∂Cm

∂t+ θim

∂Cim

∂t= ∂

∂xi

(θmDij

∂Cm

∂xj

)

508 M. Bianchi et al. GROUND WATER 49, no. 4: 503–514 NGWA.org

− ∂

∂xi(qiCm) + qsCs (2)

θim∂Cim

∂t= ξ(Cm − Cim) (3)

where Cm and θm are the concentration and porosity inthe mobile domain, Cim and θim are the concentration andporosity in the immobile domain, Dij is the dispersiontensor in the mobile domain, and ξ is the first-order mass-transfer rate coefficient which controls the mass-transferprocesses between the mobile and the immobile domain.The total porosity of the system is given by the sumof the mobile and immobile porosities. As for the ADMmodels, dual-domain simulations were conducted with theMT3DMS code employing the TVD solution scheme forthe solution of the advective term.

Results and Discussion

Observed Transport BehaviorFigure 5 shows the BTCs recorded at the extraction

wells as well as at different depths in the two MLSs.The shape of the BTC at the extraction well is stronglyasymmetric showing an early-time high peak followedby extensive tailing during the recovery stage. As theextraction well is screened over the entire saturatedzone, this BTC is representative of the depth-averagedtransport behavior as solute flux is vertically integratedover the entire well borehole. The peak concentration wasmeasured after 21.4 h from the beginning of the injectionand it is equal to 63 mg/L. After 4 days the concentrationdropped to about 1% of that of the injected bromidesolution (1000 mg/L) and then slowly decreased for theremaining duration of the experiment. The concentrationat the end of the experiment was equal to 0.23 mg/L.The zeroth-order moment of the BTC revealed that themass recovered was only 52% of the total injected mass.The early arrival time of the peak, the slow decrease ofthe concentrations following the peak as shown by theslope of the tail of the BTC, and the poor mass recovery,appear to be a reflection of solute transport controlledby connected preferential paths contained within low-permeability sediments. The fast peak could be causedby rapid advective transport of a fraction of solute massalong PFPs while the rest of the mass remained trappedin the low-K matrix where diffusion mechanisms werepredominant. Solute mass slowly released from the low-K matrix also explains the extensive tail and the slowmass recovery.

The extremely heterogeneous distribution of sedi-ments with very sharp contrasts in hydraulic conductivityfavoring PFPs is even more evident from the observa-tion of the BTCs measured at different depths in thetwo MLSs. The differences in terms of shape, arrivaltimes of the concentration peaks and their magnitudeare remarkable especially considering that the verticaldistances between each sampling level is only 1.2 m andthe distance between the injection well and the two MLSs

Level 1

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Figure 5. Breakthrough curves measured in the extractionwell (a), in MLS-1 (b), and MLS-2 (c) at different depths.

is only 1.5 and 2.25 m. The BTCs observed in MLS-1clearly showed that a fraction of the injected mass movedpreferentially at the depth of sampling level 3. This islocated at a depth of 7.1 m below ground surface. Infact, the BTC measured at this level has the highest peak(169.3 mg/L) with the fastest arrival time. The BTCs mea-sured at levels 4 and 5 in MLS-1 have a similar shapeas the one at level 3 with extensive tailing at later times.However, the concentration peaks are much lower in mag-nitude. The highest concentration at level 4 was measuredafter 1.71 days from the beginning of the injection whilethe peak time at level 5 was observed after about 3 days.These characteristics indicate that transport at these twolevels is still influenced by the PFPs responsible for thehigh peak observed at level 3. The most likely explana-tion is that the bromide tracer moving preferentially atthe depth of level 3 diffused into the lower-K sediments

NGWA.org M. Bianchi et al. GROUND WATER 49, no. 4: 503–514 509

that characterize levels 4 and 5. Also, the BTCs at level7 in the both MLS-1 and MLS-2 reveal the complexityof the transport pattern. At this level, which correspondsto the bottom of the aquifer, the measured concentrationin MLS-1 remained very low (less than 0.5 mg/L) untila sharp peak was observed after 7.86 days from injec-tion. Interestingly, this peak of 69.4 mg/L was not seenin MLS-2 where the concentration remained less than0.3 mg/L for the entire duration of the test.

Considering the BTCs measured in MLS-2, it isnoteworthy that the BTCs measured at levels 3 and 4are very similar indicating an homogenization of theconcentration contrasts observed in MLS-1, probably dueto the effect of mixing. In both levels 3 and 4 theconcentration peaks were observed after about 3 daysfrom the injection of the bromide solution. As expected,the concentrations measured in MLS-2 are lower thanthose observed at the corresponding levels in MLS-1. Theonly exceptions are the BTCs measured at level 2 whichshowed almost identical concentrations peaks to MLS-1(about 12 mg/L in both MLSs), even though the shapeof the two BTCs are very different. Most significantly,the arrival time of the peak at this level in MLS-2 ismore than two times sooner (6.2 vs. 14.4 d) than thatobserved in MLS-1, which is closest to the injectionwell. This can be interpreted as another indication ofthe presence of a network of PFPs controlling the tracertransport between the injection and extraction wells. It isalso remarkable that none of the concentration peaks ofthe BTCs measured in MLS-2 precedes the peak observedat the extraction well. In particular, the arrival times ofthe fastest peaks in MLS-2, observed at levels 3 and 4,are about 54 h slower than that of the peak observedat the extraction well. This observation suggests that themonitoring ports in MLS-2 do not intercept some of PFPsconnecting MLS-1 and the extraction well.

Modeling ResultsFigure 6 shows the concentration data recorded at the

extraction well, together with the ADM-calculated results

Time (days)4 8 12 20 24 28 32

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Figure 6. BTC observed in the extraction well and predic-tions using the stochastic ADM.

based on each of the 50 conditional K realizations. Forall simulation runs, a single effective porosity of 0.32was assigned. The same uniform porosity was also usedin other transport modeling studies at the MADE site(Feehley et al. 2000; Salamon et al. 2007; Llopis-Albertand Capilla 2009) and this value corresponds to theaverage porosity determined from soil cores collected byBoggs et al. (1992). In this study, a sensitivity analysiswas performed on one K field realization to evaluatethe effect of varying effective porosities on the peakarrival time of the bromide concentration at the extractionwell. Results showed that by increasing or decreasing theeffective porosity by 10% with respect to the assigned0.32 value, the arrival time becomes 9.5% (220 min)slower or faster, indicating a moderate sensitivity ofthe model with respect to this parameter. The matchbetween the calculated and observed BTCs did not changenoticeably. While some trial-and-error calibration runswere attempted to adjust the longitudinal dispersivitybased on the match between simulated and observedconcentrations in the extraction well in a subset of K

realizations, none could produce a reasonably good matchbetween the observed and simulated concentrations. Thus,for simplicity, the ADM simulation results shown inFigure 6 are all based on a single longitudinal dispersivityvalue (0.4 m), while the transverse horizontal and verticaldispersivity values were assumed to be one order and twoorders of magnitude less than the longitudinal dispersivity,respectively, based on earlier studies (Feehley et al. 2000;Julian et al. 2001). The longitudinal dispersivity assignedfor the ADM simulations is within the range of thevalues used by Salamon et al. (2007) and Llopis-Albertand Capilla (2009) for simulating solute transport atthe MADE site (0.1 and 1 m, respectively). It is alsocomparable to the value calculated by Harvey andGorelick (2000) from the BTC observed in a soil column1 m long of aquifer material collected at the MADE site(0.16 m). As in Harvey and Gorelick (2000), a valueof 8.0 × 10−5 m2/d was considered as the moleculardiffusion coefficient for bromide in porous media.

None of the 50 realizations of the hydraulic conduc-tivity field evaluated in this study was able to reproducethe observed BTC. In particular, the ADM models producea large underestimation of the high-concentration peak andan equally significant overestimation of the late-time con-centration tail. Furthermore, a large mismatch is evidentbetween the observed and calculated arrival times of theconcentration peak. As the ADM is not able to repro-duce the depth-averaged transport behavior observed atthe extraction well, it is obvious that its inaccuracy is evengreater when we consider the BTCs measured at differentdepths in the two MLSs. For the sake of brevity, the com-parison of observed and ADM-calculated concentrationsin the two MSLs is not shown here.

Our analysis shows that the flowmeter supportscale, in both the vertical and horizontal directions,is not fine enough to provide the level of detailneeded to effectively apply the ADM for simulating thecomplex transport behavior observed during the MADE-5

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experiment. Several previous studies have emphasized theextreme heterogeneity of the MADE site aquifer. Forexample, Harvey and Gorelick (2000) demonstrated thatsignificant layering is present at a scale even smallerthan the vertical flowmeter support scale as shown bycolumn permeameter studies of vertical core samples.However, much of the attention was focused on theaquifer variability in the vertical direction. With this studywe showed that high variability, at a scale smaller thanthat indicated by flowmeter measurements, also exists inthe horizontal direction.

Figure 7 shows the comparison between the observedconcentrations and those calculated by the dual-domainmodel at the extraction well. The total porosity of theDDSR model was initially set equal to the single porosityused in the ADM (0.32). The longitudinal dispersivity,the ratio of mobile to total porosities, and the mass-transfer rate coefficient were calibrated manually tooptimize the match between the simulated and observedconcentrations in the extraction well. Sensitivity analysisshowed that simulation results are more sensitive tochanges in the porosity ratio and the mass-transfer ratecoefficient than to variations in the dispersivity value.The calibrated longitudinal dispersivity for the DDSR was0.4 m, which was also used in the ADM as describedpreviously. After calibration, the optimal mobile andimmobile porosities are equal to the 22% and 78% of thetotal porosity (0.32) corresponding to a ratio of mobile tototal porosities of 1/4.5. The calibrated value for the mass-transfer rate coefficient was equal to 1.37 × 10−2 d−1.Previous modeling studies at the MADE site (Harvey andGorelick 2000; Feehley et al. 2000; Julian et al. 2001;Llopis-Albert and Capilla 2009) calculated a ratio ofmobile to total porosities in the range between 1/8 and 1/7and a mass-transfer rate coefficient in the range between5.0 × 10−4 d−1 and 2.5 × 10−3 d−1.

The higher ratio of mobile to total porosities deter-mined in this study is likely related to the location ofour experiment which was conducted in a sector of theMADE site characterized by high conductivity as shown

by the distribution of depth-averaged flowmeter measure-ments presented by several authors (Boggs et al. 1990;Rehfeldt et al. 1992; Bowling et al. 2005). Furthermore,the average of the log-transformed K values observedin three boreholes in close proximity to the investigatedsector (K-21, K-27, and K-28 in Figure 1c) are equal to−5.0, −2.7, and −4.0 while the mean for the entire site islower and equal to −5.2 (Rehfeldt et al. 1992). The mass-transfer rate coefficient determined for our dual-domainmodel is more than an order of magnitude higher thanthose used in previous studies. This discrepancy seems toindicate that this parameter is dependent of the transportscale at the MADE site. It can also be explained by therelatively short duration of our test compared to the pre-vious large-scale natural gradient experiments. The recentwork by Guan et al. (2008) in fact demonstrated that thefirst-order mass-transfer rate coefficient at the MADE sitedecreases with the increasing travel distance and conse-quentially the experimental duration.

Compared to the stochastic ADM model, the deter-ministic DDSR model yields a considerably better matchbetween the observed and calculated concentrations at theextraction well (Figure 7). This result is not surprisingbecause, as shown by Liu et al. (2007), the dual-domainmass-transfer model is effective when solute transport iscontrolled by small-scale PFPs The implemented modelis very accurate especially in simulating the concentra-tions measured during the first 6 days of the experiment.The magnitude of the simulated peak is 63.8 mg/L andthe predicted arrival time is equal to 21.1 h; compared tothe measured values, the predicted values correspond to amismatch of less than 1% for the magnitude of the peakand of only l.4% (less than 15 min) for the peak arrivaltime. However, the DDSR model tends to overestimatethe extensive late-time concentration tail even if it signif-icantly improves the prediction made with the stochasticADM.

From the comparison between the simulated andmeasured concentrations at the extraction well, it can beconcluded that the dual-domain mass-transfer model isable to capture the overall transport behavior observedduring the MADE-5 experiment. However, like thestochastic ADM, the performance of the dual-domainmass-transfer model in predicting the BTCs observed inthe two MLSs at different depths is generally poor. Onlyfor a selected few of the investigated levels (MLS-1 andMLS-2) the prediction is sufficiently accurate (Figure 8a),whereas for most of the BTCs the dual-domain modeltends to either underestimate the concentration data(Figure 8b) or significantly overestimate the concentra-tion peak and its arrival time (Figure 8c). These resultsshow that an accurate prediction of the point concentra-tion distribution at the local centimeter scale is beyondthe capability of either model without even more detailedinformation about microscale variations in groundwatervelocities due to aquifer heterogeneity. With current tech-nological and characterization constraints, reaching thislevel of detail seems to be impractical. However, a new

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Figure 8. Comparison between observed and predicted con-centrations in the MLSs: level 4 in MLS-1 (a); level 3 inMLS-2 (b); level 2 in MLS-2 (c).

generation of cost-effective techniques (Butler and Diet-rich 2004; Hyndman and Tronicke 2005; Dietrich et al.2008; Butler et al. 2009) is currently under developmentto map detailed K variability and connectivity at spatialresolutions far greater than anything possible until veryrecently. Preliminary testing of some of these new tech-niques at the MADE site have showed promising results(Liu et al. 2009).

ConclusionsA new forced-gradient tracer test (MADE-5) was

conducted at the MADE site in an effort to obtain furtherfield data for more fundamental understanding of transportprocesses in highly heterogeneous media. The highlyasymmetric shape of the BTC measured in the extractionwell and the varying and erratic BTCs at different depthsin the two MLSs between the extraction and injectionwells indicate the presence of a complex network of small-scale preferential flow pathways that exerts a controllingeffect on solute transport processes. The BTC measuredat the extraction well shows a fast peak arrival andextensive late-time tailing, which suggests that a portionof the bromide tracer was able to travel rapidly alongPFPs while most of the mass moved slowly through andinto or out of the relatively low-K matrix. This transportmechanism also explains the limited amount of tracer thatwas recovered.

The BTCs measured at different depths in the twoMLSs are dramatically different in shape, arrival timesand magnitude of the concentration peaks. The BTCmeasured at a sampling port located approximately in themiddle portion of the saturated zone (level 3) shows asignificantly higher peak concentration and faster arrivaltime than any other investigated depth, indicating that aportion of the injected mass moved preferentially at thislevel. A rapid concentration peak is recorded at the bottomof the aquifer in the MLS closer to the injection well. Thispeak does not correspond to that in the other MLS whichis located only 2.25 m away. The arrival time of the peakat the depth corresponding to level 2 is more than twotimes faster in MLS-2, further away from the source, thanin MLS-1 that is closer to the injection well.

The dataset collected during the new tracer exper-iment proved to be valuable for testing two numericalapproaches by comparing predicted and observed trans-port behaviors. An ADM based on 50 realizations ofhighly resolved multi-Gaussian conditional K fields wasnot effective in reproducing either the BTCs measuredin the two MLSs or the transport behavior observed atthe extraction well. This result suggests that the existingflowmeter data, in both vertical and horizontal directions,do not provide enough resolution to effectively applythe ADM at the scale of the MADE-5 experiment. Con-versely, a dual-domain single-rate mass-transfer modelbased on a less-detailed representation of the aquifer het-erogeneity matched the early-time concentrations mea-sured at the extraction well closely. In particular, theconcentration peak and its arrival time are predicted withinan error of less than 1.5%. However, the DDSR model stillyields significant mismatches when applied to simulatethe BTCs observed at different depths in the two MLSs.Thus, while the DDSR model, as an alternative to the clas-sic ADM, successfully reproduced the overall transportbehavior for the MADE-5 experiment, a highly resolvedcharacterization of the aquifer heterogeneity at the sub-decimeter scale would still be needed to fully capture the3D transport details. For this reason, development andtesting of new high-resolution and cost-effective aquifer

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characterization tools is an important direction for futureresearch.

AcknowledgmentsThis material is based upon work supported by

the National Science Foundation under Grant Nos.EAR 0538011, EAR 0537668, and EAR 0738960. Anyopinions, findings, and conclusions or recommendationsexpressed in this material are those of the author(s) and donot necessarily reflect the views of the National ScienceFoundation. We are grateful to Jaydeep Ghosh, CristinaLira, and Elizabeth Graham for helping in field test setup,sampling and laboratory analysis. Special thanks are givento Shane Reed of Columbus Air Force Base for site accessand critical field support. Review and comments from twoanonymous reviewers are also gratefully acknowledged.

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