Simulating the dissolution of a complex dense nonaqueous phase

liquid source zone:

2. Experimental validation of an interfacial area–based mass

transfer model

G. P. Grant1,2 and J. I. Gerhard1,3

Received 14 March 2007; revised 10 July 2007; accepted 6 August 2007; published 20 December 2007.

[1] A multiphase flow–aqueous phase transport numerical model (DNAPL3D-MT) isdeveloped to simulate the dissolution of complex source zones containing both pooled andresidual dense nonaqueous phase liquids (DNAPLs). The multiphase flow model(DNAPL3D) is coupled to the aqueous species transport code (MT3D) via a flexible masstransfer function, which can employ the local equilibrium assumption or the single–boundary layer expression for rate-limited dissolution either incorporating a lumped(correlation function) coefficient or explicitly accounting for the interfacial area (IFA)between the fluids. For the latter, this work employs the thermodynamically based ExplicitIFA Submodel (Grant and Gerhard, 2007), which provides IFA as a function of saturationand saturation history. A bench-scale experiment is presented involving the complete,natural dissolution of a DNAPL source zone emplaced by a point source release intoheterogeneous porous media. DNAPL3D-MT simulations of the experiment, involving nocalibration to results, are compared with the observed evolution of both (1) measureddowngradient dissolved phase concentrations and (2) DNAPL source zone configuration.The model, employing a mass transfer expression equipped with the Explicit IFASubmodel, simulates the experiment more accurately than when equipped with either alocal equilibrium assumption or a published empirical correlation expression. Sensitivitysimulations indicate that this model validation is sensitive to a number of the keyassumptions in the Submodel derivation except one: the relationship between interfacialarea and residual DNAPL saturations. The employed assumption of a single masstransfer coefficient value is supported by an analysis of the evolution of Peclet numbersthroughout the DNAPL source zone, which reveals that the low hydraulic gradientemployed resulted in diffusion-dominated mass transfer conditions throughout theexperiment. This study suggests that simulations of global mass flux from complexDNAPL source zones are sensitive to the interrelationship of rate-limited mass transferand groundwater velocity (and thus aqueous phase relative permeability and DNAPLsaturation) at the local scale.

Citation: Grant, G. P., and J. I. Gerhard (2007), Simulating the dissolution of a complex dense nonaqueous phase liquid source zone:

2. Experimental validation of an interfacial area–based mass transfer model, Water Resour. Res., 43, W12409,

doi:10.1029/2007WR006039.

1. Introduction

[2] Understanding the relationship between source zoneconfiguration and downgradient solute concentrations is akey research objective since it is central to effectivelyassessing and managing sites contaminated with nonaque-ous phase liquids (NAPLs). For example, predicting thebenefits of partial mass removal from a source zone depends

on a reliable description of this relationship [Soga et al.,2004]. Numerous laboratory [e.g., Miller et al., 1990;Powers et al., 1992; Imhoff et al., 1993; Powers et al.,1994; Saenton and Illangasekare, 2003; Fure et al., 2006]and field experiments [Broholm et al., 2005; Guilbeault etal., 2005], theoretical studies [e.g., Sale and McWhorter,2001; Falta et al., 2005], and numerical modeling inves-tigations [e.g., Soga et al., 2004; Parker and Park, 2004;Park and Parker, 2005] have therefore explored the spatialand temporal aspects of NAPL dissolution and the impli-cations for emanating contaminated groundwater plumes.Underpinning the source zone–plume relationship is therate of mass transfer from the nonaqueous phase to theaqueous phase, and the factors that influence this rate.The ability to confidently predict mass transfer rates for

1Institute of Infrastructure and Environment, University of Edinburgh,Edinburgh, UK.

2Now at Geosyntec Consultants, Guelph, Ontario, Canada.3Now at Department of Civil and Environmental Engineering, University

of Western Ontario, London, Ontario, Canada.

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realistic NAPL release scenarios remains an important butelusive goal.[3] Mass transfer rate is known to be affected by a variety

of system, fluid, and geometric parameters and its depen-dence on these parameters varies significantly with the scaleat which the problem is examined [Sale and McWhorter,2001]. Figure 1 illustrates a typical release scenario for adense NAPL (DNAPL), such as a chlorinated solvent orcoal tar, in unconsolidated porous media. Figure 1 illustrateshow the field-scale mass transfer problem is understood tobe influenced by large-scale features such as DNAPL sourcezone configuration and flow bypassing [e.g., Sale andMcWhorter, 2001; Parker and Park, 2004; Park andParker, 2005]. In addition, it highlights the fact that field-scale behavior is ultimately dictated by the integration ofpore-scale phenomena. Mass transfer on the pore scale is

understood to be dictated by interfacial geometry and therelationship between mass diffusion and solute advectionrates [e.g., Pfannkuch, 1984; Sale and McWhorter, 2001].Moreover, Figure 1 schematically identifies the practicalscale of the representative elementary volume (REV), overwhich pore-scale phenomena can be effectively averaged[Bear, 1972], that acts as a useful intermediary and linkagebetween the field and pore scales.[4] The suitability of any expression or model for disso-

lution depends on the scale at which it is applied. The massflux from a DNAPL source zone calculated using a localequilibrium assumption (LEA) is independent of the mac-roscopic mass transfer rate and is, instead, dependent onadvection and dispersion within the aqueous phase. Asindicated in Figure 1, the LEA is applicable at the relevantlocal scale, or REV (REVLEA), over which bulk mass

Figure 1. Typical DNAPL release scenario and the various scales at which mass transfer expressionscan be applied. Embedded image illustrates a typical upscaled subvolume (profile i) that encompassesheterogeneous conditions such that the associated block-averaged concentration profile (profile ii),exhibits aqueous concentrations (C) less than solubility (Cs). Finer discretization sufficient to reproduceDNAPL migration (profile iii) is identified as the representative elementary volume of migration(REVmig). The corresponding concentration profile (profile iv) illustrates that at this scale mass transfermay be rate limited. In such a case, profile iv illustrates that several consecutive subvolumes exhibitingrate-limited mass transfer may comprise the scale at which the local equilibrium assumption (REVLEA)applies. Release scenario adapted from Longino and Kueper [1995].

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transfer can be considered to be independent of the masstransfer rate. The size of this REV is likely to vary, as theseepage velocity through a DNAPL source subzone and theinterfacial area between phases are both functions ofDNAPL saturation, which varies with time as dissolutionproceeds. Miller et al. [1990] and Imhoff et al. [1993]suggest that the REVLEA is generally on the order ofcentimeters for the one-dimensional, residual saturationsystems they examined.[5] At scales smaller than REVLEA, but at which the REV

concept remains applicable (i.e., at scales where continuum,local-scale parameters such as porosity and hydraulic con-ductivity are valid), a rate-limited description of masstransfer is necessary [Imhoff et al., 1993]; Figure 1 illustratesthe scale below REVLEA at which a rate-limited expressionapplies. Laboratory studies have examined the dissolution ofresidual DNAPL fixed in a source zone of simple geometrywithin an otherwise homogeneous, one-dimensional [e.g.,Miller et al., 1990; Powers et al., 1992; Imhoff et al., 1993;Powers et al., 1994] or heterogeneous, two-dimensional[Powers et al., 1998; Saba and Illangasekare, 2000;Brusseau et al., 2002; Nambi and Powers, 2003] system.The rate-limited mass transfer observed in these studies istypically expressed as a function of DNAPL saturationand aqueous phase velocity through correlations to theSherwood number, Sh; a function that is typically composedof dimensionless system parameters such as Reynoldsnumber, Re (approximating the ratio of inertial to viscousforces), and Schmidt number, Sc (approximating the ratio ofviscosity to mass diffusivity). The empirically derivedcorrelation expressions for mass transfer rate themselves,however, vary considerably.[6] Numerical modeling studies that compare published

correlation expressions have shown predicted dissolutionrates to be highly sensitive to the local-scale expressionutilized to simulate behavior in large-scale [Zhu and Sykes,2000] or heterogeneous [Mayer and Miller, 1996; Grantand Gerhard, 2004] systems. Imhoff et al. [1993] comparedthe correlation expressions of Miller et al. [1990], Parker etal. [1991], Powers et al. [1992], and Geller and Hunt[1993] and found that they produced Sh values that spanover 3 orders of magnitude for a fixed set of conditions.Imhoff et al. [1993] attributes this lack of agreement tolaboratory methods, including the different techniques usedfor establishing residual NAPL within the porous media.These studies suggest that empirical correlation expressionsmay have limited applicability, related to the conditionsunder which they were derived.[7] Describing dissolution at the laboratory and field

scale is further complicated by the fact that large-scale masstransfer rates are often found to be orders of magnitudelower than those predicted solely by local-scale masstransfer expressions [Mackay et al., 1985]. This is attributedto flow bypassing of DNAPL subzones, nonuniformDNAPL distribution, heterogeneity of permeability, ground-water flow velocity variation, and dilution associated withaqueous phase sampling [Brusseau et al., 2002; Parker andPark, 2004]: Figure 1 illustrates the dilution phenomenon atscales larger than REVLEA. Therefore, even if near-equilibriummass transfer occurs at the local scale, field-scale masstransfer is primarily controlled by advective-dispersivetransport [Sale and McWhorter, 2001; Soga et al., 2004].

As a result, recent work has focused on the development ofupscaled mass transfer functions that account for flowbypassing in order for numerical models to simulate field-scale mass transfer [e.g., Park and Parker, 2005; Soga etal., 2004; Fure et al., 2006]. Assuming that behavior at thelocal scale (e.g., rate-limited dissolution and relative per-meability) is of secondary importance, these approachestend to employ LEA or correlation expressions and charac-terize the source zone with bulk or averaged terms (e.g.,DNAPL-occupied length and total DNAPL mass) and thenapply analytical and large-scale empirical correlationexpressions to predict aqueous contaminant flux [e.g., Parkand Parker, 2005; Soga et al., 2004; Fure et al., 2006].[8] An alternative approach is to explicitly describe the

distribution of DNAPL saturations at the local scalethroughout the source zone, and employ a rate-limited masstransfer expression appropriate for each location [e.g., Sabaand Illangasekare, 2000; Brusseau et al., 2002; Bradford etal., 2003]. This approach is ideal for numerical models thatcouple the solution of equations for multiphase flow andadvective-dispersive transport. The simplifying assumptionsof upscaled and averaging techniques are avoided in ex-change for additional computational expense [Fure et al.,2006]; however, recent advances in computing are makingfeasible such rigorous simulations at the field scale. Oncesuch models are validated, the benefit is achieved throughMonte Carlo suites of simulations that may reveal envelopesof expected behavior and key parameter sensitivity. Suchstudies can reveal patterns of expected contaminant fluxrelated to source zone architecture that account for both thelocal-scale processes (e.g., rate-limited dissolution andaqueous phase relative permeability) and field-scale pro-cesses (e.g., flow bypassing and groundwater velocityvariation) and the feedback interactions between the twosets of processes.[9] A multitude of DNAPLmigration/dissolution/aqueous

phase transport numerical models employ a continuum,Darcy-based formulation [e.g., Abriola, 1989; Kueper andFrind, 1991; Sleep and Sykes, 1993; Gerhard and Kueper,2003c]; thus a common REV (i.e., discretization) applicablefor the variety of simulated processes is of interest. Asmigration has been shown to be governed by porous mediaheterogeneity at the centimeter scale [Kueper et al., 1993;Brewster et al., 1995], the REV required to preciselydescribe DNAPL migration (REVmig) may be smaller thanthe scale above which dissolution can be adequately de-scribed using the LEA (i.e., REVmig < REVLEA); therelative concepts of REVmig and REVLEA are illustrated inFigure 1. Therefore a numerical model that simulates bothDNAPL migration and dissolution may be most reliablewhen the modeling domain is discretized at a scale equal toREVmig and a rate-limited expression for mass transfer isemployed. Such a model would calculate a range of aqueousspecies’ concentrations up to and including equilibriumconcentrations adjacent to the DNAPL when appropriate(e.g., when water velocities were low); thus it represents aconservative approach in its ability to simulate both LEAand rate-limited mass transfer.[10] This approach applied to simulating the dissolution

of a complex DNAPL source zone requires a rate-limitedmass transfer model valid for the entire range of DNAPLsaturations and saturation histories exhibited throughout a

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DNAPL release discretized at the REVmig scale. Onepossibility is the single boundary layer model [Powers etal., 1992]:

J ¼ klaawn Cs � Cð Þ ð1Þ

where J [ML�3T�1] is the solute mass flux from theDNAPL to the aqueous phase, kla [LT�1] is the averagemass transfer coefficient for the DNAPL-water interface,awn is the effective specific interfacial area (per unit volumeof porous media) [L2L�3] between DNAPL and groundwaterfor a representative elementary volume (REV), C [ML�3]is the aqueous phase solute concentration in the presence ofDNAPL and Cs [ML�3] is the aqueous phase concentrationthat corresponds to the condition of thermodynamicequilibrium with the nonaqueous phase (i.e., effectivesolubility). Applying equation (1) in this context requiresa methodology for independently approximating awn andkla. The interfacial area is known from detailed experimentsto be a function of saturation and saturation history[Culligan et al., 2004, 2006; Brusseau et al., 2006] andthe average mass transfer coefficient is known to be highlydependent on groundwater velocity [Seagren et al., 1999].As described above, a common approach employs a lumpedmass transfer term Kl = klaa

wn in equation (1) with Kl

determined from empirical correlation expressions to theSherwood number [e.g., Miller et al., 1990; Parker et al.,1991; Powers et al., 1992; Geller and Hunt, 1993; Imhoff etal., 1993; Powers et al., 1994; Saba and Illangasekare,2000; Nambi and Powers, 2003]. However, NAPL dissolu-tion in simple systems (e.g., one-dimensional flow andresidual NAPL) has been successfully modeled withequation (1) using established expressions of kla [e.g.,Ranz, 1952; Wilson and Geankopolis, 1966; Nelson andGalloway, 1975; Wakao and Funazkri, 1978; Pfannkuch,1984; Powers et al., 1994] in combination with an estimatedor measured value of interfacial area [e.g., Powers et al.,1994; Bradford and Abriola, 2001]. To the authors’knowledge, no mass transfer model has yet been validatedfor the dissolution of a NAPL source zone exhibitingheterogeneity of saturations or occurring within hetero-geneous porous media.[11] Grant and Gerhard [2007] presents a methodology

for predicting awn as a function of saturation and saturationhistory. That work demonstrates that the method, referred toas the Explicit Interfacial Area (IFA) Submodel, adequatelyreproduced published interfacial area saturation data sets[Culligan et al., 2004, 2006] using independently obtainedfluid and porous media properties. It is hypothesized thatutilizing the Explicit IFA Submodel in conjunction withequation (1) may be an effective approach for predicting thedissolution of complex DNAPL source zones.[12] The purpose of this study is to develop and validate a

numerical model for simulating the dissolution of a DNAPLsource zone emplaced by surface release in heterogeneousporous media. This manuscript presents data from a two-dimensional bench-scale experiment detailing the completedissolution of a DNAPL source zone that exhibits complex-ity with respect to spatial distribution, DNAPL saturation,and DNAPL saturation history. A new multiphase flow–mass transfer–aqueous phase transport model is developedto simulate DNAPL migration and dissolution scenarios.

Validation of the model is pursued by comparing experi-mental results with numerical model simulations of both theevolving physical configuration of the DNAPL source zoneand downgradient aqueous phase concentrations. Simula-tions explore the ability of the model to reproduce theobservations when incorporating the single boundary layermass transfer model incorporating the Explicit IFA Sub-model as well as several established mass transfer expres-sions. Further simulations examine the sensitivity ofDNAPL dissolution model results to assumptions andcharacteristics of the Explicit IFA Submodel.

2. Experimental Setup

[13] A two-dimensional bench-scale experiment was con-ducted to record the complete dissolution of a complexDNAPL source zone. Emplaced by a point release intoheterogeneous porous media, the DNAPL body exhibitedheterogeneity with respect to both saturation and saturationhistory. A constant hydraulic gradient, representative ofambient conditions, produced a dissolved phase plumeexhibiting spatially and temporally variable aqueous phaseconcentrations and thus mass transfer rates. Data setsquantifying the evolution of the DNAPL body and of thedowngradient dissolved concentrations provide a basis forcomparison with dissolution models.

2.1. Materials

[14] Six natural sands with single mesh number grain sizedistributions were employed in the experiment, referred toas the N10, N16, N20, N30, N40 and N50 sandscorresponding to the standard mesh number retaining eachsand type. The N10 sand was separated from LeightonBuzzard DA 8/16 silica sand, the N16 and N20 sands wereseparated from Chelford BS 14/22 silica sand, the N30 andN40 sands from Chelford D30 silica sand (all supplied byWBB Minerals, Brookside Halls, Cheshire, UK), and theN50 sand from Lochaline L60A silica sand (Tarmac CentralLtd., Stoke-on-Trent, Staffordshire, UK). According tosupplier documentation, each of the source sands contain>97% silicon dioxide and the grain shape, with the excep-tion of the N10 sand, is classified as rounded. Each of thesands was acid washed in a 0.1M HCL solution, triplerinsed with deionized water and dried prior to use to removeany organic material or iron oxides coating the grains. As aconsequence, sorption was not considered to be significantin the experiment.[15] The DNAPL employed in the experiment was ana-

lytical reagent grade 1,2-dichloroethane (1,2,DCE) (FisherScientific Limited, Loughborough, Leicestershire, UK) thatwas dyed to solubility with Oil Blue A powder (Octel-Starreon, Littleton, Colorado). Deionizedwater was employedas the wetting phase. Table 1 lists the measured properties ofdyed 1,2-DCE and water. All physical properties weremeasured using blue-dyed DNAPL previously equilibratedwith the wetting phase. To ensure constant fluid properties,the laboratory was maintained at 22.0 ± 1.0�C throughoutthe experiment.

2.2. Methods

[16] The experiment was conducted in a flow cell with a210 cm � 1 cm internal horizontal cross section and aheight of 100 cm. The apparatus was constructed from

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aluminum, stainless steel, Viton#, and toughened plateglass, with only the latter three used in the interior of thecell since they are relatively unreactive with 1,2-DCE.[17] The bottom 91 cm of the flow cell were packed with

5 cm � 5 cm homogeneous blocks of the six single meshsands to generate a larger-scale heterogeneous sand pack,presented as the background greyscale in Figure 2. Thepermeability of each sand was determined independently ina purpose-designed 5 cm � 5 cm apparatus [Gerhard andKueper, 2003a]. A spatially correlated numerical intrinsicpermeability field was generated using FGEN 9.1 [Robin etal., 1991] assuming an exponential autocorrelation function.After the method of Silliman [2001], each node in thenumeric field was binned into one of six groups of equalsize corresponding to the intrinsic permeability of theutilized sand types. The binned permeability field was usedas a map during the emplacement of the homogeneousblocks of sand in the flow cell. The predetermined pattern

of the sand emplacement gave a heterogeneous medium thatcan be characterized with a mean lnk = �23.09 m2, avariance of lnk = 0.24 m2, a horizontal correlation length,lH = 15.2 cm, and a vertical correlation length, lV = 2.8 cmwhich closely matched the targeted statistical parametervalues. The end result was a heterogeneous porous mediastatistically similar to a fine to coarse sand aquifer withcorrelation lengths appropriately proportioned [Welty andElsner, 1997] to the size of the apparatus.[18] Despite the presence of steel bracing in the center of

the apparatus, the emplacement of sand and the subsequentsaturation of the porous medium resulted in some nonuni-form outward deflection of the glass plates and somecorresponding slumping of the sand pack (Figure 2). Thisresulted in a number of nonhorizontal sand layers ofnonuniform thickness. Note that the actual (final) three-dimensional spatial configuration of sands in the apparatuswas employed in the numerical modeling. Digital imagespermitted detailed mapping of the final permeability fieldwhile a nonreactive tracer test permitted independent quan-tification of the amount of glass deflection as a function oflocation in the flow cell [Grant et al., 2007]. The tracer test,employing a step input of bromide tracer along the upgra-dient boundary of the apparatus, was also employed toestimate the dispersion parameter values for numericalmodeling of the experiment. Further details regarding thetracer test and the quantification of the amount of glassdeflection are given by Grant et al. [2007] and Grant[2006].[19] During the experiment, a constant flux source of 1,

2-DCE was activated through the DNAPL injection point(see Figure 2). The source was active at a rate of 90 mL/h for130 min, such that 194.6 mL of 1,2-DCE was injected intothe flow cell. A light transmission/image analysis systemwas utilized to track the presence of DNAPL (following themethod of Gerhard and Kueper [2003a]). The systememployed a light bank positioned behind the apparatus

Table 1. Fluid Properties

Property Value Temperature, �C

1,2-DCEa density 1.259 ± 0.002 g/mL 221,2-DCEa viscosityb 0.887 ± 0.02 cP 22Waterc density 0.997 ± 0.002 g/mL 22Waterc viscosityb 0.959 ± 0.02 cP 22Waterc/1,2-DCEa

interfacial tensiond22.3 ± 0.5 mN/m 22

Solubility of1,2-DCE in watere

1260 ppm 15

1,2-DCE vapor pressuref 87 mm Hg 25

aDyed and equilibrate with water for 24 h.bGardner Bubble Viscometer (Pacific Scientific, Silver Spring, Maryland).cDeionized and equilibrated with dyed 1,2-DCE for 24 h.dKruss

TMring tensiometer (Hamburg, Germany).

eDean [1985].fClayton and Clayton [1981–1982].

Figure 2. Overlay of experimental results onto the numerical simulation domain to illustrate the bench-scale setup. The background greyscale illustrates the heterogeneously emplaced sandpack. Theforeground employs a black line to delineate the extent of the DNAPL source zone when migrationceased (at t = 2.6 h). The source zone is delineated to identify the experimentally determined spatialdistribution of saturation history. Also identified are dissolution zones utilized in the discussion of masstransfer rates.

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and computer-controlled video cameras capturing imagesfrom the front; this provided images of the spatial distribu-tion of the dyed DNAPL that integrates information acrossthe sandpack thickness. Images were collected duringDNAPL injection, during subsequent redistribution follow-ing termination of the source, and during source zonedissolution until no DNAPL remained.[20] Analysis of captured images was able to map the

presence/absence of DNAPL with a resolution of 0.3 pixelsper millimeter (11 mm2/pixel). While this methodology hasbeen previously employed to map DNAPL saturations[Gerhard and Kueper, 2003a, 2003b], several factors ex-cluded such analysis in this work: (1) the nonuniformsandpack thickness in the dimension parallel to light trans-mission resulted in spatially variable brightness whichcomplicates employing independently measured calibrationcurves, and (2) the employed hydrophobic dye does notdissolve, thereby becoming concentrated in the nonaqueousphase and increasing its color saturation with 1,2-DCE massloss. The latter factor also means that contaminant transportin the aqueous phase cannot be visualized. However, thisphenomenon is expected to have negligible impact on thedelineation of DNAPL presence/absence employed in thiswork. This is because the final image taken after theapparatus contained no 1,2-DCE whatsoever, in which verysmall amounts of precipitated blue dye powder are observedin the pores previously occupied by DNAPL, was digitallysubtracted from all other images before image analysis wasundertaken. Analysis of light intensity versus time furtherpermitted tracking the direction of saturation changes,providing information on the spatial distribution of satura-tion history [Grant et al., 2007].[21] An aqueous phase gradient of 0.01 was applied

across the flow cell (from left to right in Figure 2)throughout the experiment to enable the unaided (or natural)dissolution of the DNAPL source zone. Aqueous phasesamples were collected from nine microwells at the down-gradient end of the flow cell for analysis by gas chroma-tography. The microwells were emplaced in homogeneousN16 sand within the microwell chamber of the apparatussuch that each captured the outflow of a unique 10 cmvertical subsection of the sandpack (see Figure 2).[22] A multichannel Watson-Marlow 505s digital pump

(Falmouth, Cornwall, UK) combined with tubing of varyinglengths permitted equal volume samples to be extractedfrom all of the microwells quickly at a single time. In orderto prevent disruption of the flow field, the flow rate exitingthe outflow constant head boundary prior to each samplingevent was measured and the pump rate during sampling wasset to extract aqueous phase from the cell at the same rate.[23] Table 2 lists the number of aqueous phase samples

and sample frequency for the experiment. The aqueousphase samples were analyzed by headspace gas chromatog-

raphy (GC) with flame ionization detection (FID). Theanalysis employed an EquityTM-1 fused silica capillarycolumn (Supelco, Bellefont, Pennsylvania) in a Perkin-Elmer 8700 GC with a Perkin-Elmer HS-101 headspaceautosampler. The GC oven temperature was maintained at80�C for 5 min, the injector port was set to 150�C and thedetector port was set to 250�C. The employed carrier gaswas ultrahigh-purity helium (column pressure equal to10 psi). The autosampler needle temperature, sample tem-perature and transfer temperature were all set at 25�C andthe thermostat time was set for 5 min. Matrix spike (MS)recoveries between 90 and 110% of expected values andmatrix spike duplicate (MSD) differences less than 5.04%were observed for all 1,2-DCE analyses in the water/1,2-DCE system. The Method Detection Limit (MDL) andLimit of Quantification (LOQ), calculated according to amethod based on a student ‘t’ statistical analysis of data(WDNR PUBL-TS-056; 40CFR136), were 0.585 mg/L and1.46 mg/L, respectively.

3. Numerical Modeling

3.1. Model Formulation

[24] The numerical model developed for this study is thethree-dimensional, finite difference two phase flow modelDNAPL3D-MT. This model was developed for the simula-tion of DNAPL infiltration and redistribution, mass transferbetween the nonaqueous and aqueous phases, and advec-tive-dispersive aqueous phase transport of contaminants inheterogeneous porous media. This was achieved by cou-pling the migration model DNAPL3D [Gerhard et al.,1998] and the dissolved phase transport model MT3D[Zheng, 1990] through a mass transfer module. Each ofDNAPL3D [Gerhard and Kueper, 2003a, 2003b; Grant etal., 2007] and MT3D [Zheng, 1990] have undergoneconsiderable verification and validation for their respectiveprocesses. The linking of the models follows a standard splitoperator (SO) approach [e.g., Barry et al., 2002], whereby atime step of DNAPL migration is followed by dissolvedphase transport conducted over the same time period. Thistime lagging of the transport and migration models intro-duces a source of error proportional to the numerical timestep size [Barry et al., 2002].[25] The mass transfer module can take several forms.

The first form is a local equilibrium assumption (LEA):

C ¼ Cs ð2Þ

[26] The second form is a rate-limited, single boundarylayer expression that employs a lumped mass transfer term,Kl [T

�1] [Powers et al., 1992]:

J ¼ Kl Cs � Cð Þ ð3Þ

where Kl is specified by an empirical correlation expression[e.g., Miller et al., 1990; Parker et al., 1991; Powers et al.,1992; Geller and Hunt, 1993; Imhoff et al., 1993; Powers etal., 1994; Saba and Illangasekare, 2000; Nambi andPowers, 2003].[27] The third form of mass transfer is a rate-limited,

single boundary layer expression that explicitly accounts forthe interfacial area between the fluid phases as presented in

Table 2. Aqueous Phase Sampling Frequency

IntervalSample

FrequencyNumber of

Sampling EventsTotal Numberof Samples

0–24 h 2 h 12 10824 h to 1 w 12 h 12 1081–6 w 24 h 41 369

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equation (1). In this work, equation (1) is combined with theExplicit IFA Submodel of Grant and Gerhard [2007] toobtain effective specific interfacial area, awn, and with anaverage mass transfer coefficient, kla, estimated fromPfannkuch [1984] (further details in section 3.3). TheExplicit IFA Submodel estimates awn as a function of wettingphase saturation (SW) on the basis of the thermodynamicapproach, which assumes that changes in interfacial areareflect mechanical work done on the system [Leverett, 1941;Dalla et al., 2002]. The method only requires independentinformation on PC(SW) constitutive relationships and poros-ity to predict awn(SW) relationships. In computing IFA, themethod accounts for (1) saturation history, (2) the dissolutionof residual NAPL, (3) the difference between total andeffective interfacial area (the latter excluding water filmsthat do not contribute to mass transfer) [Kim et al., 1999;Dalla et al., 2002], and (4) the incomplete conversion ofwork to IFA [Dalla et al., 2002] via an energy dissipationfactor, Ed [Grant and Gerhard, 2007].

3.2. Domain and Boundary Conditions

[28] DNAPL3D-MT was utilized to simulate the experi-ment, including both the simultaneous migration and disso-lution occurring during source zone formation and thecomplete dissolution of the final source zone configuration.The permeability field employed in the model was a 1 cmby 1 cm replica of the sand pack emplaced in the flow cell,mapped using the light transmission system. To correctlyaccount for the nonuniform thickness of the sand pack, theexperiment was simulated in three dimensions. The solutiondomain employed was 202 cm wide by 91 cm high by 3 cmthick. The amount of glass deflection as a function oflocation in the flow cell was independently determined withthe aid of the light transmission system and a dyed tracertest. The cell thickness function was validated throughanalysis of the microwell tracer recovery concentrationprofiles, such that the nonreactive tracer test could not bematched without employing the cell thickness functions[Grant, 2006; Grant et al., 2007]. The obtained functionwas employed in constructing the numerical domain suchthat it determined, for each location in vertical cross section,the proportion of the 3 cm domain thickness occupied byporous media versus that occupied by the glass plates. Intotal, the domain was discretized into 220,584 nodes with anodal spacing of 1 cm horizontally, 1 cm vertically, and0.25 cm in the third dimension.[29] The DNAPL relative permeability and capillary

pressure–saturation constitutive parameter values utilizedin the simulations were determined in independent, detailedlocal-scale experiments for each of the six sand types.Details regarding the apparatus, methods, and results ofthese local-scale experiments are presented by Grant et al.

[2007]. The transport parameters, presented in Table 3 andutilized in the simulations, were determined from thenonreactive tracer test (results and calculations not shown)[Grant, 2006; Grant et al., 2007].[30] The initial and boundary conditions employed in the

simulations match those of the experiment (see section 3.2).Hydrostatic constant head boundaries were applied to boththe left and right sides of the model domain with the waterelevation of the left boundary set at 0.93 m and that of theright boundary at 0.91 m (i.e., coincident with the top of thesand pack). Both the top and bottom of the domain were setas no-flow boundaries, and a constant flux DNAPL source(active at a rate of 90 mL/h for 130 min) was located 0.5 mfrom the left boundary of the sand pack, at a depth of 0.03 mbelow the top of the sand. The domain was initially fullywater saturated.

3.3. Determination of kla

[31] The average mass transfer coefficient for the inter-face between DNAPL and groundwater, kla, is a function offluid and system properties, with a strong dependence onaqueous phase velocity, vx [Seagren et al., 1999]. Typically,laboratory experiments of NAPL dissolution vary hydraulicgradient to develop a correlation between kla and vx or thePeclet number, Pe = vx � dm/D, (dimensionless ratio ofadvection to diffusion), where dm is mean grain diameter [L]and D is free liquid diffusivity [m2/s] [e.g., Ranz, 1952;Wilson and Geankopolis, 1966; Nelson and Galloway,1975; Wakao and Funazkri, 1978; Pfannkuch, 1984;Powers et al., 1994]. The study of Pfannkuch [1984] isconsidered in detail as it is one of the few that employs datathat encompass the low Pe values observed in the experi-ment conducted in this work.[32] Figure 3 (adapted from Pfannkuch [1984] with

permission of the National Water Well Association) plotsSherwood number (Sh = kla � dm/D, dimensionless masstransfer coefficient) as a function of Pe for a number ofpublished experimental data sets: Hoffmann [1969], Zillioxet al. [1973], and Seagren et al. [1999]. These studies allexperimentally investigated the mass exchange between oiland groundwater in natural porous media. The two earlystudies, from which Pfannkuch [1984] derived an empiricalSh(Pe) correlation, are particularly relevant in that theyutilized groundwater velocities similar to those employedin this study (as evidenced by the range of Pe values plottedin Figure 3). Figure 3 reveals that for Pe <� 10–20, Sh (andthus kla) is insensitive to aqueous phase velocity since masstransfer is diffusion controlled. In contrast, for Pe >� 20,Pfannkuch [1984] correlates kla to aqueous phase velocitysince mass transfer is solubility controlled under theseconditions. On the basis of the tracer test conducted in thewater-saturated heterogeneous sandpack, it is estimated thatthe mean Pe = 42 for this experimental setup in the absenceof DNAPL. However, because of relative permeabilityeffects, aqueous phase Pe values through the DNAPLsource zone are generally expected to be less than thismean value. Therefore it is hypothesized that it is reasonableto model this experiment by employing a single (i.e., con-stant) kla value. For lowPe, where kla is independent of vx, thePfannkuch [1984] correlation expression gives kla = 6.8 �10�7 m/s.[33] It should be noted that the numerical model

DNAPL3D-MT simulates the aqueous phase velocity field

Table 3. Numerical Model Input Parameters

Parameter Value

Dispersivity 0.015 mTransverse/longitudinal dispersivity ratio 0.0011,2-DCE free liquid diffusion coefficienta 9.908 � 10�10 m2/s

aAfter the method of Wilke and Chang [1955] cited by Reid andSherwood [1966].

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(as well as that for the nonaqueous phase) at every timestep. First, this means that the model could employ the fullPfannkuch [1984] function (or any other kla approximationmethod) if desired. However, an objective of this work wasto investigate the sensitivity of simulations of the experi-ment to kla, which is more straightforward if a constantvalue is assumed. Second, this means that, with a simulationthat accurately predicts the observed DNAPL configurationand transient dissolution, it is possible to evaluate Penumbers throughout the DNAPL source zone (as a functionof time) to confirm that the assumption of constant kla isvalid; this exercise is provided in section 4.2.

3.4. Base Case Simulation and Comparison of MassTransfer Models

[34] Numerical simulations of the experiment were con-ducted with DNAPL3D-MT employing each of the threemass transfer forms: (1) the single boundary layer expres-sion (equation (1)) employing the Explicit IFA Submodel,(2) the local equilibrium assumption (LEA), and (3) thelumped mass transfer expression (equation (3)) employingthe empirical Correlation Model of Saba and Illangasekare[2000]. None of the simulations were calibrated to theexperimental results whatsoever. All simulations employedthe independently measured fluid properties provided inTable 1. The Explicit IFA Submodel simulation employedhysteretic PC(SW) parameters and porosity values indepen-dently measured for each of the employed sands [Grant et

al., 2007], and kla = 6.8 � 10�7 m/s determined fromPfannkuch [1984] (see section 3.3).[35] The correlation model of Saba and Illangasekare

[2000] was selected for comparison since (1) it is one of thefew that has been derived from experiments of more thanone dimension and (2) it is designed for scaling to systemsof proportions different from those used in the derivation ofthe expression. Nevertheless, it is acknowledged that thisexpression was derived for the case of residual DNAPLdissolution, and at a length scale greater than that utilizedfor numerical modeling in this study. The mass transfercorrelation model is [Saba and Illangasekare, 2000]:

Kldm

D¼ Sh ¼ 11:34Re0:2767Sc0:33

dmqNtL

� �1:037

ð4Þ

where Sh is the Sherwood number, Re = dmvxg�1, where g

is the kinematic viscosity of water, Sc = gD�1, qN is thevolumetric NAPL content, t is the wetting phase tortuosity,and L is the length of the contaminated numerical soil blockin the flow direction. All of the relevant parameters inequation (4) are independently known for this study on anode-by-node basis apart from t; therefore t = 2.0 isassumed throughout the domain, as this was utilized in theexpression’s derivation [Saba and Illangasekare, 2000]. Intotal, there are three simulations in this suite.

Figure 3. Pfannkuch [1984] correlation for Sherwood number (Sh) as a function of Peclet number (Pe)including the experimental data sets of Zilliox et al. [1973], Hoffmann [1969], and Seagren et al. [1999]for comparison. Also included are box plots (first percentile, lower quartile, median, upper quartile, and99th percentile) providing a summary of the Pe values throughout the DNAPL source zone obtained fromthe base case validation numerical simulation at four key times (see text) during dissolution. Note that thebox plots refer only to the Pe axis and not to the Sh axis.

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3.5. Sensitivity Simulations

[36] Further simulations of the experiment were conductedto examine sensitivity to assumptions made in the derivationof the Explicit IFA Submodel [Grant and Gerhard,2007]. That work demonstrated that the hypotheses pre-sented in designing the IFA prediction procedure werevaluable for reproducing experimentally measured IFA(SW)relationships in the literature (i.e., at the REV scale). Theobjective of these simulations is to evaluate their influenceon processes at the bench scale, and thus their relativeimportance in validating the developed model for DNAPLdissolution.[37] Examined first is the sensitivity of results to the

energy dissipation parameter, Ed. The base case simulationemployed Ed = 0.21, which was obtained by calibration to thepeak interfacial area experimentally measured by Brusseauet al. [2006]. The comparison simulation employs Ed = 0.60,which represents the average energy dissipation factor(associated with Haines jump energy losses) as determinedin the pore network modeling study of Dalla et al. [2002].[38] Examined second is the distinction between total and

effective (also known as capillary [Brusseau et al., 2002,2006]) interfacial area. Effective IFA disregards the inter-facial area associated with wetting phase films that coat soilgrains in porous media that is water wetting with respect toNAPL. The base case simulation employs the Explicit IFASubmodel assumption that the effective IFA is the arearelevant to mass transfer calculations. While thermodynamictheory directly provides total IFA, effective IFA is thencomputed as a fraction of total IFA that varies withsaturation [Grant and Gerhard, 2007] as informed by theresults of Dalla et al. [2002]. The comparison simulationinstead utilizes the total specific interfacial area directlypredicted by the Explicit IFA Submodel for mass transfercalculations via equation (1).[39] Examined third is the relationship assumed between

interfacial area and saturation for residual NAPL. Thermo-dynamic theory is not able to provide information on IFAassociated with residual NAPL since the associated satu-rations exist outside the bounds of PC(SW) relationships.The base case simulation (Explicit IFA Submodel) assumesthat interfacial area decreases linearly with increasing SW asNAPL dissolves [Grant and Gerhard, 2007]. A comparisonsimulation is conducted that assumes interfacial area doesnot decrease as residual DNAPL dissolves, instead remain-ing constant at the IFA value corresponding to nonwettingphase flow extinction (i.e., when DNAPL becomes discon-tinuous at the REV scale [Gerhard and Kueper, 2003b]). Itis not anticipated that either of these descriptions accuratelyportrays the changing IFA of dissolving residual DNAPL;however, the descriptions vary substantially from one an-other and will thus allow an evaluation of the relativeimportance of this relationship in the examined system.[40] Examined fourth is the influence of accounting for

saturation history. The base case simulation incorporates theconcept of saturation history continuity at water drainage/water imbibition saturation reversals in both PC(SW) func-tions and their integrals (from which work on the system iscomputed) [Grant and Gerhard, 2007]. For comparison, asimulation is conducted in which IFA is calculated accord-ing to the method of Leverett [1941] and Bradford and Leij[1997], such that saturation history is not considered (i.e.,

interfacial area under water imbibition conditions is calcu-lated independently of interfacial area changes under waterdrainage conditions).

4. Results

[41] Figure 2 presents the experimentally determinedDNAPL saturation distribution following the cessation ofmigration, which occurred 2.6 h after the experiment beganand 26 min after the source was terminated. The lighttransmission/image analysis system permitted the delinea-tion of zones of (1) increasing DNAPL saturation (ondrainage), (2) reducing DNAPL saturation (on imbibition),and (3) residual DNAPL saturation. The relative saturationhistory experienced at each point during migration wasobtained by tracking the relative color intensity versus timeat each pixel (further details are give by Grant et al. [2007]).Examination of Figure 2 reveals that DNAPL migratedprimarily through the higher-permeability sands but didaccumulate upon and eventually penetrate several lowerpermeability capillary barriers. As a result, the final sourcezone configuration exhibits a nonuniform distribution andcomplex saturation history. The map of saturation historyshown in Figure 2 reveals a repeating pattern in the sourcezone that agrees with expectations: low-permeability lensessupport an upward sequence of (1) high DNAPL saturationson water drainage pathways at the base of hydrostaticDNAPL pools, (2) intermediate DNAPL saturations onwater imbibition pathways at the top of hydrostatic DNAPLpools, and (3) residual DNAPL zones. At this time, residualDNAPL accounts for approximately 53% of the source zonecross-sectional area (i.e., the perspective in Figure 2) butonly 22% of the released mass. The simulated DNAPLdistribution reproduces that observed in the experiment(figure not shown); details of the validation of the multi-phase flow component of DNAPL3D-MT are presented byGrant et al. [2007].[42] Figure 2 also illustrates the locations of the water

sampling microwells and subdivides the apparatus into threedissolution zones, which are considered in the discussion tofollow. Zone 1 encompasses the region dominated by asmall DNAPL pool located near the bottom of the flow cell.Zone 2 corresponds to the area of highest DNAPL mass andincludes the large DNAPL pool located between 0.5 and0.7 m from the bottom boundary of the flow cell; Zone 2also includes the large area exhibiting residual DNAPLbeneath this pool. Zone 3 is located at the top of the flowcell, and includes a region of exclusively residual DNAPLsaturations.

4.1. Experimental Concentration Profile

[43] Figure 4 plots the aqueous phase 1,2-DCE concen-tration observed exiting the downgradient (right hand)boundary of the flow cell, obtained by averaging samplescollected simultaneously from each of the microwells. Thebreakthrough curve reveals flux-averaged dissolved phase1,2-DCE first exiting the flow cell approximately 6 h afterthe start of the experiment. Concentrations rise sharply andpeak at approximately 30% of solubility (2580 mg/L) at t1 =20 h, followed by a steep decrease in concentration to t2 =84 h; note that such key times associated with significantchanges in the slope of the breakthrough curve are num-bered in the text and Figure 4 to aid in the subsequent

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discussion. Dissolved phase 1,2-DCE concentrations pla-teau between t2 and t3 = 192 h, after which concentrationsdecrease once more until time t4 = 264 h. Approximatelyconstant average effluent concentrations continue beyond t4until decreasing to nondetect levels at approximately 672 ±12 h (4 w) following the start of the experiment; note thatlight transmission confirmed complete DNAPL disappear-ance at t = 654 h. The cumulative aqueous phase massexiting the cell, as estimated by integrating under the curvein Figure 4, was approximately 16% less than the mass ofDNAPL 1,2-DCE released. This cumulative mass balanceerror is likely because of volatilization during sampling,uncertainty in the measurement of aqueous phase flow rates,and the occasional appearance of small air bubbles in themicrowell sampling device. This mass balance error hasbeen incorporated into the plotted error bars for the exper-imental data.

4.2. Aqueous Phase Velocities in the DNAPL SourceZone

[44] Figure 5 plots DNAPL saturation (SN) as a functionof the Peclet number at the four key times identified insection 4.1 (t1, t2, t3, and t4) for all DNAPL source zonenodes in the base case simulation (employing the ExplicitIFA Submodel). As can be seen in Figure 5, the number ofdata points decreases from t1 through t4 as the DNAPLdissolves and the number of DNAPL containing nodesdecreases with time. However, the general pattern of Peas a function of SN remains constant for each of these times:Pe is a nonlinear function of SN in the examined system.This reflects the combined effect of the absolute permeabil-ity (a function of the porous media) and the relativepermeability (a function of SN, saturation history and theporous media) that governs groundwater velocity (andtherefore Pe) for a given set of boundary conditions. Thus,

for a given sand type it is possible to have different Pevalues depending on the local value of SN; conversely, for agiven SN, the value of Pe will vary between sand types. Ingeneral, as mass transfer proceeds and the DNAPL satura-tion at a location decreases, the value of Pe will shift alongthe main Pe(SN) curve in Figure 5 toward higher Pe values,reaching a maximum Pe at SN = 0. The small percentage ofvalues that do not conform to the main Pe(SN) curve at t1 inFigure 5 represent a subset of the nodes exhibiting DNAPLresidual when migration terminated; particularly those inhigh-permeability porous media. The SN of these nodes isobserved to decrease substantially by t2 and are virtuallyeliminated by t3; this suggests that the main Pe(SN) pathwayrepresents the dominant dissolution of pools and less easilyaccessed residual.[45] Figure 5 also reveals that, throughout the simulation,

Pe numbers are in the range where kla is independent ofaqueous phase velocity [Pfannkuch, 1984]. Approximately91%, 75%, 60% and 86% of the DNAPL-containing nodesat t1, t2, t3, and t4, respectively, exhibit Pe < 10. Moreover,greater than 99% of all DNAPL-containing nodes exhibitPe < 20 at each of these key times. This provides confi-dence that, for simulating the experiment conducted in thisstudy, the kla = 6.8 � 10�7 m/s calculated from Pfannkuch[1984] can reasonably be employed as a single, constantvalue for the entire domain (see Figure 3). The data ofFigure 5 are summarized in the four box plots on Figure 3,emphasizing that groundwater velocities are low and masstransfer is diffusion controlled throughout the DNAPLsource zone in this experiment.

4.3. Base Case Simulation and Comparison of MassTransfer Models

[46] For comparison against the experimental results,Figure 4 plots the DNAPL3D-MT simulated concentration

Figure 4. Observed and simulated average 1,2-DCE concentration at the downgradient boundary of theflow cell. Experimental observations are plotted as unconnected points (squares) and include theassociated uncertainty. Plotted lines correspond to the three validation simulations described insection 4.2. Key times identified correspond to significant changes in the slope of the observedbreakthrough curve.

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profile utilizing the Explicit IFA Submodel mass transferroutine, incorporating the independently determined kla withequation (1). Figure 4 also presents the concentrationprofiles simulated when the LEA and correlation modelmass transfer expressions are employed in the model.Figure 4 demonstrates that the Explicit IFA Submodelsimulation is in agreement with the experimental results.The simulation reproduces the peak concentration (at t1)both in time and magnitude. In addition, DNAPL3D-MTaccurately simulates the breakthrough curve’s most signif-icant slope changes at t1 and t2 as well as the more subtleslope changes at t3 and at t4. However, the simulationcontinues to predict 1,2-DCE concentrations exiting theflow cell beyond that observed (672 h). This occurs becauseat this time the simulation predicts that approximately 12%of the released DNAPL volume has yet to dissolve. It ispossible that experimental mass balance error (16%) ispartly responsible for this discrepancy.[47] Figure 4 demonstrates that DNAPL3D-MT is less

successful at reproducing the experimental results whenequipped with the other mass transfer routines. The LEAsimulation predicts much higher peak concentrations(3480 mg/L) than actually measured (2580 mg/L), an

overestimation of approximately 35%, and generally overpredicts the average downgradient concentration exitingthe flow cell throughout the simulation. As a result, theLEA simulation predicts total 1,2-DCE mass removal atapproximately 552 h, which is 5 d (120 h) earlier thanmeasured experimentally.[48] In addition, Figure 4 demonstrates that the model

significantly under predicts the mass transfer rate when thecorrelation model is utilized. As a result, the correlationmodel simulation fails to predict a peak concentration at t1,does not reproduce the observed slope changes, and overpredicts (by 66%) the proportion of released mass remain-ing in the flow cell at t = 672 h. Both the LEA andcorrelation model simulations predict concentration datathat lie outside the uncertainty limits on the measured data(Figure 4), particularly prior to t3.[49] Figure 6 shows the measured and simulated aqueous

phase 1,2-DCE concentrations for Zone 2 for each of thekey times t1 (20 h), t2 (84 h), t3 (192 h), and t4 (264 h).Zone 2 results are examined here in more detail as thissubsection of the experiment contains the most complexDNAPL distribution pattern observed in the source zone(see Figure 2). Zone 2 exhibits a number of both high

Figure 5. Peclet Number (Pe) (Pe = vx � dg/D, dimensionless ratio of advection to diffusion) as afunction of DNAPL saturation at every DNAPL-containing node in the model domain at key times in theexperiment. Pe obtained from base case numerical simulation (validation simulation using Explicit IFASubmodel [Grant and Gerhard, 2007] with independently obtained input parameters).

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DNAPL saturation pooled areas and low DNAPL saturationresidual areas at t1, the majority of residual removed by t2,and is dominated by single large pool throughout t3 and t4.Zone 2 exiting concentrations are averaged from the micro-wells (3, 4, 5, 6, and 7) that span the zone (see Figure 2).[50] Figure 6 illustrates the ability of the Explicit IFA

Submodel to most accurately simulate the observed aqueousphase concentrations at each of the key times presented. Ingeneral, the LEA simulation over predicts, and the correla-tion model simulation under predicts, the aqueous phaseconcentration at each of the key times. As previously noted,the correlation model simulation is most inaccurate at earlytime and becomes less inaccurate at late time when obser-vations reflect a long period of low concentrations associ-ated with the remaining pool. Conclusions drawn regardingthe ability of the various mass transfer routines to simulateexperimental results were no different when examiningZone 1 (primarily residual DNAPL) and Zone 3 (primarilypooled DNAPL) (figures not shown).[51] Figure 7 compares the experimentally determined

presence of DNAPL to that predicted by the simulations att2 (84 h). Figure 7 reveals that the Explicit IFA Submodelsimulation best predicts the observed source zone configu-ration. The simulation properly predicts the existence ofthree pooled DNAPL regions: a large area within Zone 2; asmaller area immediately beneath this first area; and a smallarea within Zone 1 at the bottom of the domain. The LEAsimulation predicts that the pool in Zone 3 at the bottom ofthe domain has already completely dissolved by t2, and thecorrelation model simulation predicts virtually no change inthe DNAPL configuration from that predicted at t = 2.6 hwhen migration ceased (note that the observed DNAPLconfiguration at t = 2.6 h is presented in Figure 2).[52] Although the observed and simulated aqueous phase

concentrations converge for all three mass models at time t3and beyond (Figure 4), this does not represent equal abilities

to reproduce the experiment at late time. Figure 8, illustrat-ing DNAPL presence at t3, indicates that while a substantialportion of the released mass has dissolved between t2 and t3(approximately 20%) the same three areas of DNAPLdescribed for Figure 7 are still present within the experi-mental apparatus. The Explicit IFA Submodel continues toagree with observations by simulating DNAPL at theselocations (Figure 8b). The LEA assumption predicts theexistence of only the largest pool in Zone 2 (Figure 8c), andthe correlation model predicts very little change in thepattern of DNAPL since the cessation of migration atapproximately 2.6 h (Figure 8d). Therefore, while thecorrelation model and the LEA model aqueous phaseconcentrations reproduce the measured concentrations at t3(Figure 4), they do not reproduce the observed DNAPLdistribution. The difference in simulated DNAPL configu-rations for the LEA and correlation model from observa-tions in Figure 8 suggests that the convergence of totaldowngradient concentration is largely coincidental, partic-ularly for the latter.[53] At the other key times (t1 and t4) the simulated

DNAPL saturations for DNAPL3D-MT employing thedifferent mass transfer models continued to follow thistheme (figures not shown): (1) the Explicit IFA Submodelaccurately predicted the location and longevity of DNAPLpooled regions, (2) the LEA predicted the premature disap-pearance of pooled regions (as a result of overpredictedmass transfer rates), and (3) the correlation model simula-tion continued to predict very little change in the distribu-tion of DNAPL from that following the cessation ofmigration (as a result of underpredicted mass transfer rates).

4.4. Sensitivity Simulations

[54] Figure 9 plots the simulated average aqueous phase1,2-DCE concentration exiting the downgradient boundaryof the flow cell as a function of time for the Explicit IFA

Figure 6. Simulated and observed aqueous phase concentrations for Zone 2 at key times in theexperiment.

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Figure 7. Laboratory measured and numerical model simulations of DNAPL presence at t2 (84 h) in theexperiment. DNAPL presence is outlined by solid black lines on all four figures. (a) Observationsdelineate DNAPL presence only while (b)–(d) the simulations additionally present the predicteddistribution of DNAPL saturations.

Figure 8. Laboratory-measured and numerical model–simulated DNAPL presence at t3 (192 h) in theexperiment. DNAPL presence is outlined by solid black lines. (a) Observations delineate DNAPLpresence only while (b)–(d) the simulations additionally present the predicted distribution of DNAPLsaturations.

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Submodel (kla = 6.8 � 10�7 m/s) simulations employingeither an energy dissipation value of Ed = 0.21 or Ed = 0.60.Figure 9 demonstrates that the simulated concentrationprofile is sensitive to this value embedded in the predictionof IFA. Note that Ed is a scalar in the Explicit IFASubmodel’s calculation of awn [Grant and Gerhard, 2007]and thus acts proportionally on mass transfer rate as does kla(equation (1)) when kla is assumed to be a constant.Therefore Figure 9 in fact also demonstrates sensitivity tokla for a given energy dissipation factor; that is, assumingthe base case Ed = 0.21, Figure 9 presents a comparisonbetween kla = 6.8 � 10�7 m/s and kla = 2.0 � 10�6 m/s).[55] At early time, Figure 9 reveals that the magnitude of

the initial aqueous phase peak is a positive function of Ed

and/or kla, which is expected from the associated increasesin local-scale mass transfer rates. However, the long-terminfluence of Ed and/or kla is not trivial; the simulateddissolution behavior (encompassing numerous benchmarkvalues such as the peak concentration, the rate of concen-tration decrease following the peak, the life span of thesource zone, etc.) is not linearly related to changes in Ed

and/or kla. Clearly the appropriate value of Ed and/or kla isnot only expressed directly at the local scale of masstransfer, but is also expressed by the ensemble dissolutionbehavior of the entire DNAPL source zone. This behavior isa function of both the local-scale mass transfer rates, and theeffect these rates have on the evolution of the source zoneand the (interrelated) aqueous phase flow field.[56] This phenomenon is illustrated in Figure 10, which

plots the simulated vertical position of the DNAPL body’scenter of mass during the first 24 h of the experiment.Figure 10 presents simulations for the LEA simulation, thetwo Explicit IFA Submodel simulations (Ed = 0.60 and Ed =

0.21), and a simulation ignoring dissolution (listed in de-creasing order of REV-scale mass transfer rate). Figure 10illustrates that local-scale mass transfer directly affects thedistribution of mass within the DNAPL source zone. Whilethe regions occupied by DNAPL within the experimentalapparatus remains generally unchanged, local-scale masstransfer affects the evolution of DNAPL saturations withinthose regions. This occurs both during and subsequent toDNAPL migration. During migration, the DNAPL pene-trates the capillary barrier in Zone 2 at approximately 2.16 h;subsequently, increased local mass transfer rates are ob-served to decrease the time at which the DNAPL migrationpathway through the barrier is cut off by residual formation(resulting from a combination of migration-related waterimbibition and dissolution). As a result, increased DNAPLmass is predicted to be retained within the upper portion ofthe cell for increased mass transfer rates (Figure 10). Afterthe cessation of migration, the simulated center of massof the DNAPL body is shown to increase in elevationmore quickly for faster descriptions of mass transfer, withthe range bounded by the minimum mass transfer rate (zero,no dissolution) simulation and the maximum mass transferrate (LEA) simulation.[57] This shift in the distribution of saturations within the

source zone has a significant effect on the aqueous flowfield, as DNAPL saturations directly affect the wettingphase relative permeability, and consequently aqueousphase velocities and mass flux rates. Therefore generalconclusions regarding the influence of Ed and/or kla onbench-scale mass transfer rates are difficult to make. Theinterplay between local-scale mass transfer, distribution ofDNAPL saturations, and bench-scale aqueous phase flow isdynamic and complex with compounding (feedback) inter-

Figure 9. Sensitivity of simulated average 1,2-DCE concentration at the downgradient boundary of theflow cell to the energy dissipation factor (Ed) or mass transfer coefficient (kla) assumption of the ExplicitIFA Submodel.

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actions. As a result, it appears that the overall averagedowngradient concentration is a relatively unique signal thatis sensitive to a number of aspects of a local-scale masstransfer model.[58] Figure 11 compares the experimental breakthrough

curve to simulations obtained with the model employingeach of the three simplified assumptions within the ExplicitIFA Submodel (described in section 4.3). The ConstantResidual Interfacial Area simulation closely matches thecomplete Explicit IFA Submodel simulation, exhibiting

minor differences near t1 and just after t2. This indicatesthat the simulated dissolution behavior of this DNAPLrelease is insensitive to the local-scale description of inter-facial area at residual DNAPL saturations. This insensitivityis not surprising since only approximately 22% of thesource zone mass exists as residual DNAPL followingmigration. Although all locations in the source zone expe-rience residual at some point during complete dissolution,and thus the IFA(SW) relationship in this range is appliedthroughout the simulation, the results indicate that predicted

Figure 10. Simulated center of mass for the DNAPL body versus time as a function of the energydissipation factor (Ed) or mass transfer coefficient (kla). The DNAPL was released at an elevation of0.88 m.

Figure 11. Sensitivity of simulated average 1,2-DCE concentration at the downgradient boundary of theflow cell to assumptions of the Explicit IFA Submodel. Note that the Constant Residual Interfacial Areacurve is obscured because it predominantly coincides with the Explicit IFA Submodel curve.

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ensemble mass transfer rate is highest and most sensitive atearly time when source zone mass is high and architecture iscomplex. This suggests that for DNAPL source zonesdominated by pools, knowledge of the relationship betweenIFA and residual saturation (which in turn requires knowl-edge of the distribution of DNAPL blob sizes and shapes)may not be necessary; this conclusion contrasts that ofstudies [e.g., Dobson et al., 2006] that consider only thedissolution of residual. However, it should be noted that thisconclusion is drawn from the results of a single two-dimensional experiment. Further study involving numericalsimulation, as well as further experiments, would enable amore thorough evaluation of this conclusion.[59] Figure 11 further reveals that the Total Interfacial

Area simulation differs distinctly from the observed resultsand from the Explicit IFA Submodel simulation. The TotalInterfacial Area simulation predicts higher concentrations(i.e., higher mass transfer rate) than the Explicit IFA Sub-model, particularly at early time. This is unsurprising, sinceat early time DNAPL saturations are highest (e.g., at the endof migration, approximately 57% of the released DNAPL ispredicted to exhibit SW < 0.5) and it is in this saturationrange that the total specific interfacial area is much greaterthan the effective specific interfacial area [Grant andGerhard, 2007]. The poor fit to the observed data suggeststhat total specific interfacial area is inappropriate for masstransfer calculations, particularly in regions dominated byDNAPL pools. Comparisons of images depicting simulatedand actual DNAPL disappearance with time (not shown)confirm this conclusion.[60] Figure 11 further reveals that the No Saturation

History simulation is also distinct from the Explicit IFASubmodel simulation. At early time (e.g., at t < 156 h),when a large proportion of the DNAPL resides in hydro-static pools on water drainage PC(SW) pathways, the NoSaturation History simulation predicts an aqueous phaseconcentration profile similar in shape and character to thatof the complete Explicit IFA Submodel. However, at latetime (e.g., at t > 156 h), when DNAPL saturations decreaseas a result of dissolution and the DNAPL body becomesdominated by regions experiencing water imbibition, the NoSaturationHistory simulation over predicts the aqueous phaseconcentrations exiting the downgradient boundary. The devi-ations from the base case result from the interplay betweenincreased local-scale mass transfer, the distribution ofDNAPL saturations, and the bench-scale aqueous phase flowfield (as discussed above for the case of sensitivity to ED).

5. Conclusions

[61] A two-dimensional bench-scale experiment involv-ing the release and complete dissolution of a transientDNAPL source zone in heterogeneous porous media wasconducted. The coupled multiphase flow–aqueous phasetransport model DNAPL3D-MT, elsewhere validated for theDNAPL migration component of the experiment [Grant etal., 2007], was employed to simulate the dissolution of thecomplex source zone. The ability of the numerical model tosimulate the experiment is found to depend on the masstransfer expression assumed in the model. The thermody-namically based Explicit Interfacial Area (IFA) Submodel[Grant and Gerhard, 2007] was employed with a singleboundary layer expression for mass transfer and populated

with independently obtained input parameters (measureddirectly or derived from relevant published data). Compari-son of experimentally observed downgradient dissolvedphase concentrations and source zone DNAPL configurationin time and space with those predicted from DNAPL3D-MTreveal that employing the proposed Explicit IFA Submodelprovides results that agree with both sets of observationswithin experimental uncertainty.[62] In addition, it is concluded that when the model

employs a local equilibrium assumption or a relevant local-scale empirical (lumped) correlation expression, it is lesssuccessful at reproducing the experiment. No calibration ofthe model to the experiment was undertaken for any of thesimulations; however, it is acknowledged that the correla-tion model may perform better if such a calibration isconducted. Sensitivity simulations reveal that altering theinput parameters (energy dissipation factor and/or masstransfer coefficient) for the Explicit IFA Submodel or twoof its key assumptions (saturation history continuity, totalIFA not effective IFA) result in the model failing to predictthe experiment adequately. However, altering the IFA(SW)relationship for residual NAPL failed to have a substantialinfluence on model results, suggesting that the specificshape of this function is not needed for modeling theconducted experiment; this conclusion may apply for otherscenarios involving source zones dominated by DNAPLpools.[63] Sensitivity analysis revealed an important character-

istic of mass transfer at the bench scale: that the local-scalemass transfer expression causes bench-scale mass transferdifferences by feedback interactions with DNAPL satura-tions and aqueous phase velocities (via relative permeabilityeffects). As a result, the average downgradient concentra-tion at the bench scale is demonstrated to be a sensitivesignal against which to evaluate coupled multiphase flow/mass transfer models.[64] It was already known that accurate multiphase flow

modeling of DNAPL source zones required detailed ac-counting of intrinsic permeability and constitutive relation-ships at the local scale. This work implies that whencoupling such models with dissolution to examine massfate, it is valuable, and, in cases such as the one consideredhere, necessary, to use a rate-limited approach at the localscale that links interfacial area to nonwetting phase satu-rations, saturation history, and aqueous phase relative per-meability. With this comprehensive approach, simulationsare able to account for the influence of local mass flux onglobal mass flux through modification of the groundwaterflow field. The Explicit IFA Submodel employs parametersthat are already defined for multiphase flow models, sim-plifying its integration into such codes. It is anticipated thatemploying this method for predicting IFA throughout anevolving NAPL source zone combined with the Pfannkuch[1984] function (including the dependence on groundwatervelocity) may provide reasonable simulations of enhanceddissolution (e.g., via increased hydraulic gradients or otheraggressive remediation approaches), although this has yet tobe shown.[65] The conclusions of this work are relevant for two-

dimensional experiments and simulations examining thenatural dissolution of complex DNAPL source zones inheterogeneous porous media. The presented numerical

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model and mass transfer approach is expected to be equallyapplicable in three dimensions; however, it remains to beseen whether a LEA or other simpler approaches may besufficient (because of the expected increased significance offlow around rather than through NAPL source subzones).

Notation

awn effective specific interfacial area between thenonwetting phase and the wetting phase.

C dissolved phase concentration.Cs effective solubility.dm mean grain diameter.Ed energy dissipation factor.J solute mass flux.

kla average mass transfer coefficient for the nonwettingphase/wetting phase interface.

Kl lumped mass transfer term.L length of the contaminated numerical soil block in

the flow direction.PC capillary pressure.Pe dimensionless ratio of advection to diffusion.Re Reynolds number.Sc Schmidt number.Sh Sherwood number.SW wetting phase saturation.SN nonwetting phase (DNAPL) saturation.vx aqueous phase velocity.t wetting phase tortuosity.qN volumetric NAPL content.

[66] Acknowledgments. Financial support for this research was pro-vided, in part, by the School of Engineering and Electronics at theUniversity of Edinburgh through a scholarship to the first author. Addi-tional funding was provided by The Royal Society, Nuffield Foundation,and the Natural Environment Research Council in the form of operatinggrants to the second author. The authors would like to acknowledge thevaluable comments of the three anonymous reviewers, which led toimprovements in the presented work. The authors also wish to acknowledgethe input of Jason Mohan.

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����������������������������J. I. Gerhard, Department of Civil and Environmental Engineering,

University of Western Ontario, London, ON, Canada N6A 5B9.(jgerhard@eng.uwo.ca)

G. P. Grant, Geosyntec Consultants, 130 Research Lane, Suite 2, Guelph,ON, Canada N1G 5G3.

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