WATER RESOURCESRESEARCH,VOL. 29,NO. 6, PAGES1675-1683,
JUNE 1993

Transportof Volatile OrganicCompounds
Acrossthe CapillaryFringe
KATHLEEN A. MCCARTHY• AND RICHARDL. JOHNSON
Departmentof Environmental
ScienceandEngineering,
OregonGraduateInstitute,Beaverton
Physicalexperiments
were conducted
to investigate
the transportof a dissolvedvolatileorganic
compound(trichloroethylene,
TCE) fromshallowgroundwater
to theunsaturated
zoneundera varietyof conditions
includingchangesin thesoilmoistureprofileandwatertableposition.Experimental
data
indicatedthat at moderategroundwatervelocities(0.1 m/d), vertical mechanicaldispersionwas
negligibleand moleculardiffusionwas the dominantverticaltransportmechanism.Under these
conditions,TCE concentrations
decreased
nearly3 ordersof magnitudeacrossthe capillaryfringeandsoil gas concentrations
remainedlow relative to thoseof underlyinggroundwater.Data collectedduring a water table drop showeda short-termincreasein concentrationsthroughout most of theunsaturatedzone, but theseconcentrations
quicklydeclinedand approachedinitial valuesafter thewatertable wasreturnedto its originallevel. In the deeppart of the unsaturatedzone, the watertable
drop resultedin a long-termdecreasein concentrations,
illustratingthe effectsof hysteresisin the soil
moisture profile. A two-dimensionalrandom walk advection-diffusionmodel was developed tosimulatethe experimentalconditions,and numericalsimulationsagreedwell with experimentaldata.
A simpler, one-dimensionalfinite-differencediffusion-dispersion
model was also developed. Onedimensional simulations based on molecular diffusion also agreed well with experimental data.
Simulationswhich incorporatedmechanicaldispersiontendedto overestimateflux acrossthe capillaryfringe. Good agreementbetween the one- and two-dimensionalmodels suggestedthat a simple,
one-dimensional
approximationof verticaltransportacrossthe capillaryfringe can be usefulwhen
conditionsare appropriate.

sectional area available for mass flux and the pathway

INTRODUCTION

tortuosityfor bothphasesvary. The variationin water-filled
Mass transport between the unsaturatedand saturated porosityalsoproducesa variationin relativepermeability
zonesplaysanimportantrole in controllingmanysubsurface for the aqueousphase and thereforeleadsto changesin
processes.
This is particularlythe casefor volatileorganic water velocity with depth.
contaminants(VOCs). Because many contaminantsources
The processes
involvedin massexchangebetweenthe
occur at the land surface or within the unsaturated zone,

saturated and unsaturated zones include aqueous and gas

masstransportfrom the unsaturated
zoneto the saturated phasemoleculardiffusion,mechanicaldispersion,aqueouszone is a commonmechanismof groundwatercontamina- and gasphaseadvection,and partitioningamongthe aquetion. Conversely, volatilization of contaminantsfrom ous,gas,andsolidphases.The extentto whicheachof thesegroundwaterand subsequenttransportto the atmosphere processes
contributes
to masstransferbetweenthesaturated
canprovidea naturalremediation
pathway.Microorganismsandunsaturatedzonesdependson both the propertiesof theactive in the saturatedzone may also rely on this transport compoundand the conditionswithin the subsurface.
Alpathwayeither to provide oxygenor other compounds thoughnumerous
investigators
havereportedfielddatathat
essential
for theirgrowth,or to rid theft'environmentof indicateexchangebetweenthe two zonescanbe significant
potentially
toxicmetabolicproducts.Finally,thesuccessof [Swallowand Gschwend,1983; Lappala and Thompson,
technologies
suchassoilgasmonitoring
to detectunderlying 1983;Hincheeand Reisinger,1985;Davis et al., 1986;Davisgroundwatercontamination
andenhanced
in situvolatiliza- and Matthews, !989; Pionke and Glotfelty, 1990],few havetionto remediateexistingpollutionproblems
requiresquan- specificallyexamined
the transportmechanisms
involved.
titativeknowledgeof the movementof contaminants
across Swallow and Gschwend [1983] formulated a onethe interface between the saturated and unsaturatedzones. dimensional
steadystatemathematicalmodelto describethe
In order to better understand mass transfer between the volatilizationof compoundsfrom unconfinedaquifers.The
saturated and unsaturated zones, it is necessary to more

three-box model was based on vertical dispersion in theclearlyunderstandthe natureof the interface
betweenthe saturatedzone, Henry's law phasepartitioningat the intertwo zones(Figure1). This interface,referredto subse- face,andgasphasediffusionin the unsaturatedzone.In an

quentlyasthe"capillaryfringe,"includes
boththetension- associatedlaboratoryexperimentthey measureddye dispersaturated
porousmedium
abovethewatertable(in which sion below the water table and calculateda vertical disperwaterpressure
islessthanatmospheric)andthedeeppartof sivityof 0.0033m. In anotherexperiment,they measured
theunsaturatedzone(in whichsoilmoisture
content
varies concentrationgradients resulting-from a saturated-zone
asafunction
ofdepth).Because
moisturecontent
andhence sourceof trichloroethylene(TCE), but were unableto detect
air-filled
porosityin thisregionvarywithdepth,thecross- TCE in the unsaturatedzone, possiblydue to the limited
scaleof their physicalmodel. They thereforeused mass
1Alsoat Water ResourcesDivision,U.S, GeologicalSurvey, balancecalculationsto estimate flux through the unsaturated
Portland,Oregon.
zone.By comparing
modelresultswith fluxestimatesfrom

Copyright
1993bytheAmerican
GeophysicalUnion.
Paper number 93WR00098.
0043-1397/93/93WR-00098 $05.00

theexperiments,
theyconcluded
thattheirmodeladequately
describedthe vertical transportof TCE from groundwater.
Barber et al. [1990]investigatedthe transportof methane
1675

1676

MCCARTHYANDJOHNSON:TRANSPORTACROSSTHE CAPILLARYFRINGE
LAND

SURFACEthat region. To simulatethe movement of volatile organics
across the interface between the saturated and unsaturated

zones,theyuseda rangeof masstransfercoefficients.
They
alsomodeledinfiltrationof water into the subsurface,parti.
tioning of the volatile organics between the vapor andinfiltratingwaterphases,andincorporationof theinfiltratingwaterinto groundwater.
For the conditionssimulated,theyconcludedthat aqueousphasetransport into the groundwater was the primary transport pathway into the saturated
zone.

SATURATION

Mendoza and Frind [ !990] reported a model that simulates

diffusiveand advectivevapor transportin unsaturated
porous media.As with the modelof Sleep and Sykes[1989],+

their model allows increasing water content and decreased

PRESSURE

vapor diffusionrates near the water table. Transport fromthe unsaturatedzone to the groundwater was once again

0

MOISTURE

CONTENT(GAUGE)

simulated using mass transfer coefficients. Mendoza and(b)

McAlary [!990] investigatedthe potential for groundwater

Fig. 1. The shallow subsurfaceenvironment:(a) hydrologic
contaminationresulting from an unsaturated-zonevapor
components,(b) soil moisturecontentas a functionof depth, and(c) pressureheadas a function of depth [after Freezeand Cherry, source by using an unsaturated-zone transport model todefine the sourcefunction for a saturated-zonetransport

19791.

model. In their unsaturated-zone simulations, mass trans-

port at the upper and lower boundarieswas governedbyfrom groundwater to the unsaturated zone at a field site andconcludedthat the process was dominated by diffusionand

mass transfer coefficients and the soil moisture content wasthat diffusivity in the saturatedzone was the limiting mechanism. However, due to the scale of their field study, adetailed investigation of the interface between the saturated
and unsaturatedzones was not possible. Using a simple,
one-dimensionaldiffusion model, they obtained reasonably
good agreementwith their data, but changesin diffusivity
within the unsaturatedzone were neglected.
Numerical modelingof transportin and exchangebetween
the saturatedand unsaturatedzones posessignificantproblems resulting from (I) the abrupt change in spatial andtemporal scales of transport at the interface between thezones; (2) the large difference between horizontal (usually
advection dominated) and vertical (usually diffusion/
dispersiondominated) transport parametersin the saturated
zone; and (3) the paucity of data available on verticaldispersion, particularly above the water table, and mass
exchangerates between the two zones. As a result, the few
existingmodelsthat incorporatemassexchangebetweenthe
zones rely on assumptions that have not previously beenvalidated in the laboratory or in the field.
In a study of oxygen-limited hydrocarbonbiodegradation,
Borden and Bedlent [1986] modeled the exchange of hydrocarbons and oxygen between the saturated and unsaturated

rated-zonesimulationsindicate that the potential for groundwater contaminationis significant;however, this may be dueto the large value used for vertical dispersivity (0.1 m).
Vertical dispersionhas been examined in the field by anumber of researchers [e.g., Garabedian et al., 1991; LeBlanc et al., 1991; Rajaram and Gelhat, 1991; also S.
Feenstra, unpublisheddata, 1990]. At groundwatervelocities lessthan 0.5 m/d they observedvertical dispersionto beof the order of molecular diffusion, rather than more commonly usedvaluesbasedon dispersivitiesin the range0.01-1
m. For reference, at a groundwater velocity of 0. ! m/d, aassumed to be constant throughout the domain. Their satu-

f IANgPP•T%BUN.

zones. In their simulations, it was assumed that the moisture
content throughout the unsaturated zone was constant andthat the interface

betweenthe unsaturated

and saturated

1

zones occurred at the water table. Thus the zone of increas-

ing water content in the deep unsaturated zone and the zoneof tension-saturatedporous medium above the water tablewere not accountedfor. It was further assumedthat soil gas
concentrations immediately above the water table were in
equilibrium with groundwater immediately below the watertable.

Sleep and Sykes [1989] developed a numerical model tosimulate the transport of volatile organic compoundsin boththe saturated

and unsaturated

zones.

Their

model

allowed

0.75
M

"Iøq:

for variations in water content near the water table, so

diffusive vapor transport could be accurately representedin

Fig.2. Schematic
drawingoftheaquifer
model.

MCCARTHY AND JOHNSON:TRANSPORTACROSSTHE CAPILLARY FRINGE....

IMPERMEABLE

FULLY

ALUMINUMPERMEABLESHEETS

I•

[I T(

STIR1
•

1677

•

CONSTANT-HEA....x2'........m,qs'xos'•'d/•-'•'r/•'d•"'s!II [ L_!
[•-,]T

[I • .,-u•
ß,,

WATER

END RESERVOIRS(a)

SAMPLINGA

BUNDLESB

C"*"'l.....
I.....
I........

SAMPLING

PORTS

(b)

Fig.3. (a)Schematic
drawingoftheflowsystemusedforthemasstransfer
experiments.
(b)Cross-sectionalview
showing
thelocationsof selected
sampling
bundles
andports.

the entireregionbelowthe water table. To
verticaldispersivity
6f 0.0005m resultsin a verticaldisper- throughout
prevent
directcommunication
betweenthesoilgasof thesionequalin magnitude
to moleculardiffusion.
unsaturated
zone
and
the
headspaceofthereservoirs,aluThe assumptionof a constantsoil moisturecontent
platesextending
fromthetopofthemodel
to a depth
throughout
the unsaturated
zone,omissionof thetension- minum
0.55m wereinstalledat theinnersidesofsaturatedzone,andtheuseof unrealisticallyhighvaluesof ofapproximately
Theoutflowportfromthedownstream
reservoir
saturated-zone
verticaldispersivity
all serveto overestimatethescreens.
massflux betweenthe saturatedand unsaturatedzones.In

was connectedvia tubingto an adjustableconstant-head

addition,few dataareavailable
to quantify
theratecoeffi- reservoirthat controlledthe water level in the model.
A two-dimensional
samplingnetworkwasinstalledalong
cientscommonly
usedto represent
massexchange
at theinterface
betweenthe zones.The objectiveof the physical thelongitudinal
axisof the model.Ninebundlesof 1.6-mm
andnumericalmodelstudiesreportedwasto useTCE tooutsidediameter(o.d.),0.8-mminsidediameterTeflontub-

to 3.2-mmo.d. stainlesssteelsupport
rods
examineand quantifytransportof volatileorganiccom- ingattached
poundswithinthe capillaryfringeunderconditionsof low provided
0.1-mhorizontal
sampling
resolution.
Eachbundle
consistedof 20 lengthsof tubing,providing
0.03-mverticalgroundwatervelocityand no infiltration.
sampling
resolution
in themiddleportionof thetankand
EXPERIMENTALMETHODS

PhysicalModeling0.06-mverticalr•solutionin the upperandlowerparts.The

upper
endof eachtubewasfittedwithan18-gauge
syringeneedleandpluggedwith a Teflon stopper.

Themainpartof the aquifermodelwascarefully
filled
with
type
8
flint
shot
Ottawasandin
1-mmhorizontal
layers.
wide,1.0 m long,and 1.0 m deep(Figure2). It was

Theaquifer
model
usedintheseexperiments
was0.75m

constructedwithglassbottomandsidepanels
andacrylic The waterlevelwasadjustedto bejust belowthe working
throughout
thefillingprocedure.
Aseachthirdofthe
sheet
endpanels,
all supported
by a steelframe.Rigid surface
final
depth
was
achieved,aportable
concretevibratorwas
screens
wereinstalled
paralleltoandapproximately
0.025
m usedto ensurethat sandwas packeduniformly
into theinfromtheendsof themodeltoformendreservoirs(Figurebetweenthetubingandsupport
rodsofthesampling
3).In thisway,flowintoandoutof themodel
occurredspaces

1678

MCCARTHY AND JOHNSON:TRANSPORTACROSSTHE CAPILLARY FRINGE
0.0

'
A

groundwaterduringa water table drop. The water tablewas
lowered an additional 0.15 m at a rate of 0.05 m/d andx•7 TOPOFTENSION-

TCE concentrationsin the saturatedand unsaturatedzones

BUNDLE
x=0.3mallowedtoremainat thatlevelfor 3 days.Duringthisperiod,
0.2

SATURATED
ZONE[]

were monitored.

A third experiment was conducted to examine the move.
ment of TCE from groundwaterunder imbibition conditions(i.e., the "imbibition experiment"). After the water table.....

• •DRAINAGE
4.

ß

drop, the water level was raisedback to its originaldepthof•2 0.6-

0.61 m at a rate of 0.05 m/d. This resulted in an imbibiti0n
capillary fringe in which the tension-saturatedzone extended
approximately 0.09 m above the water table. Again, an
averagegroundwatervelocity of approximately 0.1 m/d wasmaintained through the model and steady state conditions

WATER TABLE

0.8 ~were reestablished in both the saturated and unsaturated

1.0

,,

.001

ß0'1

0Jl

RELATIVE

TCE

CONCENTRATION(a)

Fig. 4.

zones in about !0 days. This experiment was continuedfor
58 days.
At the conclusion of the experiments, soil cores weretaken from the aquifer model under both drainage and1.00,00,4

imbibition conditions. The cores were cut into 3-cm sections

MOISTURE

for determination of the soil bulk density, porosity, anddepth-dependentmoisture content.

CONTENT(b)(a) Steady state profilesof depth versusTCE concen-

trationunder
drainage(solidsquaresconnected
with
solid
curve)Sampling
andAnalysesßand imbibition (plusesconnectedwith dashedcurve) conditions.(b)Moisture content versus depth under drainage(solid squares)and
imbibition(pluses)conditions.(Concentrationsare reportedrelative
to the maximum concentration at bundle A (x = 0.3 m).)bundles.The end reservoirswere filled with pea gravel. The
surface of the sand was uncovered during all experiments.
Clean, helium-spargedwater was then flushedcontinuously
through the entire model for several weeks. The water level

was then lowered to a depth of 0.61 m below the top of themodel and clean, helium-spargedwater continued to flow
throughthe model for several weeks before the first experiment began.
The flow systemused for the masstransferexperimentsis

shown in Figure 3a. A peristalticpump deliveredhelium-

Pore air and water sampleswere collected by attachinga
gastight syringe (Hamilton, Inc., Reno, Nevada) to theneedle fitted into the samplingport tubing. Two samplingtube volumes were drawn to purge the sampling line before
the samplewas collected (purge volumes ranged from 0.2 to
1.1 mL).
Aqueous samples(2.0 mL) were collected from the saturated zone in 5-mL syringes. The sampleswere placedin
5-mL glass vials fitted with Teflon Mininert valves (Pierce,
Rockford, Illinois) and allowed to equilibrate, with periodic
vigorous shaking, for a minimum of 1 hour. (Preliminary
tests showed that this method resulted in equilibration
between the aqueousphaseand headspacewithin 30 min.)A
0.75-mL sampleof headspacewas then drawn from the vial
using a 1-mL gastight syringe and analyzed by gas chromatography(GC). Aqueousphase standardswere preparedin
45-mL vials equipped with Mininert valves. The vials were
initially cleaned with methanol and rinsed with deionizedwater. The vials were then weighed, and a known quantity(by weight) of deionized water was injected through thevalve. A known quantity (by weight) of a TCE-saturated

sparged deionized water to a 2-L glass bottle where it wascontinuouslystirredwith TCE. The resultingTCE-saturated
aqueous solution then flowed through the aquifer model.
Data from three of the nine samplingbundlesare reported
here. The horizontal and vertical positionsof the sampling
ports are shown in Figure 3b. Bundles A, B, and C, werelocated 0.3, 0.5, and 0.7 m, respectively, from the influent aqueousstocksolutionwas then injectedinto the bottomof
reservoir.

The first experiment was designed to investigate themovement of dissolved TCE from the groundwater to theunsaturatedzone under drainageconditions(i.e., the "drainage experiment"). Drainage conditionsproduceda capillaryfringe which includeda tension-saturatedzone that extended
approximately 0.14 m above the water table and a variably

the vial. The vials were storedin an inverted positionand
periodicallyshaken vigorously. Aqueous phase standards
were allowed to equilibrate for a minimum of 24 hours before

use and were preparedapproximatelyevery 3 days.
Soil gas samples(0.75-mL) were collected from the unsaturated zone in 1.0-mL gastightsyringesand were analyzed
directlyby GC. Gasphasestandardswerepreparedin 0.8-L
saturated zone which extended 0.25 m above the tensionstainlesssteelcanistersequippedwith stainlesssteelbellows
saturatedzone (Figure 4b). The averagegroundwaterveloc- valves (Whitey Company, Highland Heights, Ohio). The
ity throughthe model was maintainedat approximately0.1 canisterswereinitiallycleanedby alternatelyevacuatingand
m/d. After !6 days, measuredTCE concentrations
through- pressurizingto 10 atm with nitrogengas.A known quantity
out the model stabilized, indicating steady state conditions (by volume)of TCE was theninjectedinto eachcanisterwith
had been established.Steady state conditionswere main- a gastightsyringe.Eachcanisterwasthenpressurized
withtained for 42 days.
nitrogengasto obtain the desired TCE concentrations.Gas
Followingthe drainageexperiment,a secondexperiment phase standardswere prepared approximately.once per
was conducted to investigate the transport of TCE from month.

MCCARTHY
ANDJOHNSON:TRANSPORT
AcRoss
THECAPILLARYFRINGE

1679

Allanalyses
wereperformed
using
asix-port
gas-sampling
Z 0.02valveconnectedto a Hewlett-Packard
HP 5890 GC(Hewlett-Packard
Company,Avondale,Pennsylvania)
equippedwith a flameionization
detector.
Standards
wererun
atthebeginningandend
ofthesampling
sessions.
The
combinedcoefficientof variation of datafrom three succes-

sivesamplingsof bundleA overan 8-dayperiodduringthe
drainageexperimentwas4.8%.For a 13-dayperiodduring
the imbibition experiment, the combined coefficientof variation for data collected from bundle A was 7.6%.

A

DEPTH (m):-- - .16....
.28• 0.01
-

•

o

i

ii

I

,

I

(a)

.40

i

I

0.02 .....

i•,•'Q•'. t•"•RESULTS AND DISCUSSION

iiii

DEPTH
= .46m" BUNDLE
A\•.•//,/• •-,_'•x,.

.... BUNDLE
B

0.01- ',-7

Drainage ExperimentDuring the steady state "drainage experiment," TCE
concentrations
variedverticallynearly3 ordersof magnitude
betweenthe water table and the top of the capillaryfringe.
The steady state depth versus concentrationprofile thatdevelopedat 0.3 m into the aquifer model (bundle A) is
shownas a solid line in Figure 4a. Figure 4b shows thecorresponding
soil moistureprofile. A significantchangein
the vertical concentration gradient occurred near the watertable, resulting in a pronounced gradient acrossthe tensionsaturatedzone. Moving upward throughthe capillaryfringe,
concentrationscontinuedto drop, but at a decreasingrate. A
nonlinearsteady state concentrationgradient suchas this is
to be expected in a region of changingwater content. Thiscan be seen from the one-dimensional

BUNDLE

form of Fick's firstlaw:

Fz-'-OwDew•
c3Z/+ O!7De•'[•) (1)

(b)

N•&
...........
0

,,

I

I

I

0.46

'

ß' SATURATEDTOPOFTENSIONZONE

ß

WATER

(c)

TABLE

0.78

i,

94

104

109

114

TIME (days)
Fig. 5. Water table drop experiment: (a) TCE concentration
versustime at samplingbundle A (x = 0.3 m), (b) TCE concentration versustime at a depth of 0.46 m, and (c) water level versustime.
(Concentrations
are reportedrelative to influentconcentration.)whereF z is the verticalmassflux; 0wand0garethewaterandgas-filledporosities;
Dew and D ea are the effective

redistributionof water and soil gaswhich occurredover the
speciesof interest;andOCw/OZ
andOCg/Oz
arethevertical courseof this experiment. In responseto the decliningwater
concentrationgradients in the water and gas phases.If table, the water content in what had originally been themolecular diffusion was the dominant vertical transport capillaryfringe decreasedand water which had previously
mechanism(as will be shown in the numericalmodeling been part of the saturatedzone (and hencecontainedhighsection)and the gas-andwater-filledporositieschangedwith concentrationsof TCE) was increasinglyexposedto the gas

diffusioncoefficients, in the water and gas phases,for thecondepth(as shown in Figure 4b), it is clear from (1) that a phase.The gas and water phasesquickly approachedconstantvertical flux would occur only if the concentration centrationequilibrium,resultingin elevated soil gasconcentrations. However, because transport in the gas phase isgradientschangedwith depth.
quicklydissipated.Within 1
The observation that the bulk of the concentrationgradi- rapid, the highconcentrations
ent (i.e., -90% concentrationdecrease)occurredin the day, elevatedconcentrationsbeganfalling toward previous
tension-saturated
zone indicatesthat (1) the flux of VOCs levels. After the water table was raised to its original
throughoutmostof the unsatfromthe groundwaterwill be controlledby aqueousphase position,TCE concentrations
urated zone returned to near-initialvalues.

processesand (2) mixingwithin the shallowgroundwater
In contrast to the shallow unsaturated zone, TCE concenzonemustbe relativelyweak (otherwisethe depthto which
trations
at a depth of 0.46 m showedan overall decrease
concentrations
would be depletedwouldbe greater.)The
duringthewater table drop and did not returnto initial
implicationof these two observations
is that the flux of(Figure5b}.Thisbehavior
canalsobeexplainedbyVOCsfrom the saturatedzone, as describedby (1), will be values
the soil moistureprofile. Before the water table drop, thesmall.
0.46-msampling
portswere lessthan0.01m abovethetopof
the tension-saturated
zone and thus in a regionof very highWaterTable Drop Experimentmoisturecontent. Because the soil moistureprofile is not
Changesin TCE concentrationthat occurredat four linear,therelativeincreasein gas-filledporosityand,hence,different
depthsduringthewatertabledropexperimentare gasphasetransportwas muchgreaterat thisdepththanat
shown
in Figure5. At depthsof0.16,0.28,and0.40m in the shallowerdepths.As illustratedin Figure5b, the lowered
unsaturatedzone(Figure5a), concentrations
rosemarkedly concentrationspersistedeven after the water table wasandhadapproximately
doubledbythetimethewatertable raisedto its originallevel. This canalsobe attributedto thereachedits lowest level. This can be explainedby the soil moistureprofile.The verticalextent of the imbibition

1680

MCCARTHY AND JOHNSON: TRANSPORT ACROSS THE CAPILLARY FRINGE

tension-saturated zone that developed after the water table
drop was approximately0.05 m lessthan that of the previous
drainage tension-saturated zone (Figure 5c). As a consequence, the moisture content at a depth of 0.46 m decreased
from approximately 0.29 (prior to the water table drop) to
approximately 0.23 (after the water table was raised to its
original position). As shown by K. A. McCarthy and R. J.
Johnson (Measurement of trichloroethylene diffusion in soil
with a continuously-varyingmoisture content, submitted to
Journal of Contaminant Hydrology, 1993) this corresponds
to more than an order of magnitudeincreasein the effective

In theseexpressions,
Cr is thetotalconcentration;t istime;
x and z are the horizontal (longitudinal) and vertical coordi.

nates;Df,• andDœaarethefreewaterandfreegasdiffusion
coefficients;
Owand 0a are the water-andgas-filled
porosi.
ties; rw and ra are the water and gas phasetortuosity
factors;Cw, Ca, andCs arethewater,gas,andsolidphase
concentrations;vw is the groundwatervelocity;and Pbisthesoil bulk density. If equilibrium phase partitioning is assumed,

Ca = HCw(3a)

Cs = KaCw(3b)diffusion coefficient.

Imbibition Experiment

Similar to the "drainage experiment," data from the"imbibition experiment" were also characterizedby a pronouncedconcentrationgradient within the tension-saturated

where H is Henry's constant and K a is the soil waterpartition coefficient,both in their dimension!essforms. Us.
ing the relationshipsgiven by (3), (2a) may be rewrittenaszone and a decrease in concentration of nearly 3 orders ofmagnitude between the water table and the top of thecapillary fringe (Figure 4a, dashed curve). However, incontrast to the drainage case, concentrations above thewater table dropped more abruptly. This is consistentwith
what would be expected based on the imbibition moisture
contentprofile (Figure 4b), which is characterizedby a lessextensive tension-saturatedzone within the capillary fringe.

0
+m

Oz

OCw
(D*)\
Oz
/]

(4a)

where

D* = DfwOwrw+ DfaOgrgH(4b)

As discussedby Johnson et al. (submitted manuscript,
1993), in order to satisfy the requirements of particletracking theory, the governingtransport equation (4a) must
Two-Dimensional Advection-Diffusion Modelbe expressedin the form of the Ito-Fokker-Planck equation.
The physical model experiments discussedpreviously Appropriaterearrangementleads towere simulatedusinga two-dimensional,advection-diffusion
numerical model. As mentioned earlier, the spatial andtemporalscalesof transport within the capillary fringe spanmore than 3 orders of magnitude. This necessitatesprohibNUMERICAL

MODELING"Or=8--•5(D*RCr)- •xx
RCrL'-•'x] - •xx(vwOwRCr)

itive discretizationin standard finite-difference

and finite-element numerical models in order to prevent numericaldispersion.To partially overcome discretizationrequirements, random walk particle tracking was chosen as thenumericaltechniquefor this model. The modeldevelopment
is presentedin detail by R. L. Johnsonet al. (Developmentof a two-dimensionalparticle-trackingmodel to simulate+0'-•(D*RCr)-• L(Sa)

R = (Ow+ OaH+ Kap•,)
-1

(5b)

where

transportacrossthe capillary fringe, submittedto Water The two-dimensional numerical model was based on (5a).
ResourcesResearch, 1993; hereinafter Johnsonet al., subFor the simulationspresentedhere, tortuosityfactorsfor
mittedmanuscript,1993)and is discussedonly briefly here. each phasewere calculatedusing the method of Millington
For a three-phasesystemin which aqueousandgasphase [!959]:
diffusionand horizontalgroundwateradvectionare the dominant transportmechanisms,the transportequationmay be,ri = 0i7/3/0
r2(6)
written

whereOr istotalporosity.The valuesusedfor porosity,bulk
density, and depth-dePendent
soil moisture content were

0 [v,vOwCw]+ (DfwO
w L57'/j(2a)+-whereCT -- CwOwnt'CaO•Int'Cspb(2b)

those measuredfrom the soil cores taken from the aquifer
model. The valuesused for free water and free gas diffusion
coefficients,Henry's constant, and the soil water partition
coefficientare given in Table 1. A rectangulardomain was
definedto approximatethe experimental conditions(Figure3). Data collected from sampling bundle A were used todefinea constant-fluxupstreamboundaryat x = 0.3 m. The
top boundary (z = 0.0 m) was open, and the bottom
boundary (z = 1.0 m) was reflective. The downstream

boundary(x = 1.0 m) was reflectiveabovez = 0.55 m andopenbelow this level. The lengthof time simulated'
was 4

MCCARTHY
ANDJOHNSON:TRANSPORTACROSS
THECAPILLARYFRINGEdays,whichcorresponded
to 0.4 m of horizontalgroundwa-

1681

0.0

ter movementin the physical model.
The results from four identical simulationsare shownsuperposed
in Figure6. Theseresultsareverticalprofilesof

0.2

concentrationfrom 0.4 m downstream of the constant-flux
boundary and represent the simulated concentrations at

sampling
bundleC. Theexperimental
datashownin Figure6
arefromsampling
bundleC andwerecollected4 daysafter

0.4

the data used as initial conditions(bundle A). The model

resultsagreewell with the experimental
dataconsidering
thatno fitting parameters were used in the simulations.The

0.6

valuesused for all variableswere either experimentally
determinedor obtainedfrom the literature.The important

WATER TABLE

observationto be made from these simulationsas well as the
0.8experimental
data is that a sharpconcentrationgradientis
maintained
acrossthe capillaryfringeduringthe 4 daysoftransportbetween bundlesA and C. As will be discussedin

thenextsection,this can occuronly if verticaldispersion
isof the order of aqueousphase moleculardiffusion.

.0001

.001

RELATIVE

One-DimensionalDiffusion-DispersionModel

.01

0.1

1.0

TCE CONCENTRATION

Fig. 6. Superposedresultsfrom the two-dimensionalnumerical

The particle-trackingmodel providesan accuratemeans model (curves) and experimental data (symbols) from sampling
bundleC (x = 0.7 m). (Concentrationsare reportedrelativeto thefor simulatingtransport across the capillary fringe while maximumconcentrationat bundle A (x = 0.3 m).)partiallyovercomingthe discretizationrequirementsof standardfinite-differenceand finite-elementmodels. However,the large changes in concentration that occur across thecapillaryfringe necessitatethe use of very large numbersof
particlesin order to obtain meaningful results. As a conse-

quence,the model is numericallyvery intensive.A simpler
meansof simulatingtransport acrossthe capillaryfringe is

OCr=
at

(Dœw
+ a vw)0

therefore desirable.

(7)

In the physical experimentspresentedhere, the groundwatervelocity was low and flow was horizontal. In addition,
horizontalconcentrationgradientswere small. This is illus- where a is mechanicaldispersivity and all other variablesare
trated in Figure 5b, which shows that concentrationsde- as defined in the previous section. Recalling (2b) and (3),Ow,H, Or, Pb, andK a do not changeovercreasedonly slightlybetween samplingbundlesA and C. It andassuming
was hypothesized that, under these conditions, vertical time, (7) may be writtentransportthrough the capillary fringe was not significantly
affectedby horizontalprocessesin the unsaturated
zoneand
couldtherefore be adequatelyapproximatedin one dimen....
(8)
sion where the frame of reference moves along with theOt(Ow+ OaH+ PbKd)

OCw
O-•
[(Dfw
+av•,)Owr•,+OfaOa,aH]•-•-z/

flowing groundwater. To test this hypothesis, a oneThe one-dimensional numerical model was based on a finitedimensional
finite-differencemodelwas developed.
For a three-phasesystemin which moleculardiffusionand differenceapproximationof (8) and incorporatedDirichletaqueousphase mechanical dispersion are the dominant boundary conditions.
For the simulations presented, tortuosity factors wereverticaltransportmechanisms,the one-dimensional
form ofagaincalculatedusing(6), and the valuesusedfor all otherthetransportequationis
variables

TABLE 1. NumericalModel Input Parametersfor TCE at 20øCParameter

Value

Freewaterdiffusion
coefficient,m2/sFreegasdiffusion
coefficient,m2/s

9.1 x 10-10a
8.3 x 10-6b

Henry'sconstant,dimensionless
Soilwaterpartitioncoefficient,dimensionless

0.38 c0.126 caEstimatedby the Hayduk and Laudiemethod[Lymanet al.,1982].

werethesame as those used in the two-

dimensionalsimulations.Data collectedfrom samplingbundle A were used as initial conditions, and the length of time
simulatedwas once again 4 days.
The results from three simulations of the drainage experiment are shown in Figure 7 along with the experimental
data. The experimentaldata points shown are the sameas

thoseshownin Figure6, collectedfrom samplingbundleC 4

daysafterthedatausedasinitialconditions.
The solidlinein
Figure7 is the result of a simulationbasedon molecular
diffusionalone(dispersivity
equalto 0). The dottedlineisthe
result of a simulationwhich incorporateda saturated-zone

dispersivityof 0.001m, andthedashedlineis theresultof abEstimatedbytheFuller,Schettler,
andGiddings
Method[Lay- simulationwhichincorporateda saturated-zone
dispersivity

man et al. 1982].

CFromMabeyet al. [1982].

of 0.01m. (Thesedataare similarto resultsobtainedwiththe

1682

MCCARTHY AND JOHNSON:TRANSPORTACROSSTHE CAPILLARY FRINGE
0.0

CONCLUSIONSIn the masstransferexperiments
described
above,strong
verticalconcentration
gradientsdevelopedin the capillary0.2-

fringe and very low concentrations were observed in. theunsaturated zone. Because gas phase diffusion coefficientsare approximately4 ordersof magnitudegreaterthan aqueousphasediffusioncoefficients,unsaturated-zonetransportof TCE was relatively rapid. This maintained soil gas concentrationsat low levels and resulted in large concentration
gradientsin the tension-saturatedzone. TCE concentrations
decreased nearly 3 orders of magnitude between the water

0.6

table and the top of the capillaryfringe. This sharpdropin
0.8

RELATIVE

TCE CONCENTRATION

Fig. 7. Results from the one-dimensional numerical model(curves)and experimentaldata (symbols)from samplingbundleC (x= 0.7 m). (Concentrations are reported relative to the maximum
concentration at bundle A (x = 0.3 m).)two-dimensionalmodel in which the aqueousdiffusion coefficient was increasedto simulate mechanicaldispersion.)
The similarity between the experimental data and thenumerical model results based on molecular diffusion, andthe differences

betweenthe data and the cases in which

dispersionwas included, indicate that molecular diffusionis
the dominant transport process responsible for mass exchange between the saturated and unsaturated zones under
the conditions tested. Using a saturated-zone mechanicaldispersivity of 0.01 m greatly overestimated vertical masstransport. This is consistentwith recent field observationsof
vertical dispersionat similar groundwatervelocities [GarabedJan et al., 1991; Rajaram and Gelhat, 1991; also S.
Feenstra, unpublished data, 1990]. For the experimental
conditions, even a mechanical dispersivity of 0.001 m overestimated flux to the unsaturatedzone.

The agreement between the experimental data and theresultsof theone-dimensionalmodel

indicates

that

the

concentrationindicates that the vertical mixing processin
the aqueousphaseis weak, a conclusionwhich is supportedby the mathematical modeling.
Data from the water table drop experiment illustrate two
mechanismsthat affected transport from the saturated zone
to the unsaturated zone during a water table fluctuation.
First, as the water table dropped, the soil moisture profile
partially drained. As water-filled porosity decreased andgas-filled porosity increased in the new capillary fringe,
water which had previously been part of the saturated zone
(and hence contained high .concentrations of TCE) was
increasingly exposed to the gas phase. The gas and waterphases quickly approached concentration equilibrium, andsoil gas concentrations increased. However, because transport in the gas phase is rapid, the high concentrations
quickly dissipated. This was the dominant effect observed
throughout most of the unsaturated zone. A second effectwas observed

when

the watertable

was returned

to itsoriginal position. Due to the effects of hysteresisin the soil
moisture profile, the vertical extent of the tension-saturated
zone was reduced by approximately 0.05 m after the watertable rise. As a result, the reduced concentrations deep inthe unsaturated zone persisted even after the water table wasreturned to its original level. This has implicationsfor fieldwork where the position of the water table is routinely
monitored, but the extent of the tension-saturated zone andthe effectsof hysteresisare generally unknown.
The agreementbetween experimental data and the numerical model

simulations

based on molecular

diffusionwasvery good. This indicatesthat at low groundwatervelocities(e.g., 0.1 m/d) and in the absence of infiltration, aqueous
phase molecular diffusion, rather than mechanical dispersion, is the dominant mechanism for mass transfer between

groundwaterand the unsaturated zone. The agreementbe-

physical experiment was adequately approximated in one
dimension. This suggeststhat a simple, one-dimensional
approximation of vertical transport across the capillaryfringe can be useful, at least in a qualitative sense, whenconditionsare appropriate. For many casesin which groundwater velocities are low, flow is predominantly horizontal,
and horizontal concentration gradients are small, a onedimensionalapproximation may be adequate. Because thetween the one-dimensional

one-dimensional model does not allow for lateral transport,
the condition of small horizontal concentrationsgradients is
critical. This condition will often be satisfied, however,transport from the saturated zone to the unsaturated zone
has a numberof important implications,including(1) mass

when depths are small relative to the lateral extent of thespeciesof interest. For example, transportof oxygenfrom
the atmosphereto groundwater,or volati!izationfrom withina shallow, laterally extensive groundwater plume will not
typically producestronghorizontal concentrationgradients.

diffusion model and the twodimensionaladvection-diffusion
model suggeststhat verticaltransport may be adequately simulated with a onedimensionaldiffusionmodelwhen the conditionsare appropriate. Suchconditionsincludelow groundwatervelocities,
predominantlyhorizontalflow, and weak horizontal concentration gradients.

The conclusionthat aqueousphasediffusioncontrolsmass

flux from the groundwaterzonewill be relatively smalland,even after very long transporttimes, will be confinedto theuppermostpart of the saturatedzone; (2) numerical simulationsthat incorporateverticalmechanicaldispersionin thesaturated zone, particularly above the water table, may

significantlyoverestimatethe importanceof masstransfer

MCCARTHYANDJOHNSON:TRANSPORTACROSS
THECAPILLARYFRINGE

1683

paperpresented
at NWWA/API Conferenceon Characterization
acrossthe capillaryfringe;(3) soilgasconcentrationsin theandMonitoringof the VadoseZone,Natl. Well WaterAssoc./
unsaturated
zone are stronglydependentupon moisture Am.
Pet. Inst., Las Vegas, Nev., Dec. 1983.
conditionsin the porousmediumandthephysicalproperties LeBlanc,D. R., S. P. Garabedian,K. M. Hess,L. W. Gelhar,R. D.
ofthematerialbeingtransported;and(4) astheresultof the
Quadri,K. G. Stollenwerk,
andW. W. Wood,Large-scale
naturalgradient
tracertestin sandandgravel,CapeCod,Massachusetts,
thirdimplication,
therelationshipbetweengroundwater
condesignand observedtracermovement,Water
centrations
and soil gas concentrations
is not straightfor- 1, Experimental
ward.

Resour. Res., 27, 895-910, 1991.

Lyman,W. J., W. F. Reehl,andD. H. Rosenblatt,HandbookofChemical
Property
Estimation
Methods:Environmental
Behaviorof OrganicCompounds,
McGraw-Hill,New York, 1982.
Acknowledgments.Thisworkwassupported
in partby theU.S. Mabey,W. R., J. H. Smith,R. T. Podoll,H. L. Johnson,
T. Mill,
Geological
SurveyunderAward14-08-0001-G1917
andby theUniT. W. Chou, J. Gates, I. W. Partridge,H. Jaber,and D.
versityConsortium
Solvents-In-Groundwater
Research
Program, Vandenberg,
Aquaticfate process
datafor organicprioritypolsponsoredby Giba-Geigy
Corporation,
GeneralElectric
Corpora- lutants,Rep.440/4-81-014,
Environ.Prot.Agency,Washington,tion,DowChemical
Corporation,
Eastman
KodakCorporation,
andD.C., 1982.
Boeing
Corporation.
Theuseof productnamesin thispaperis for Mendoza,
C. A., andE. O. Frind,Advective-dispersive
transportofidentification
purposes
onlyanddoesnotconstituteendorsement
bydense
organic
vaporsin theunsaturated
zone,!, ModeldeveloptheOregon
Graduate
Instituteor theU.S. Geological
Survey.
ment, WaterResour.Res., 26, 379-387,1990.
Mendoza,C. A., andT. A. McAlary, Modelingof ground-watercontamination
causedby organicsolventvapors,GroundWater,
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