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pubs.acs.org/est

Comparison of the Johnson-Ettinger Vapor Intrusion Screening

Model Predictions with Full Three-Dimensional Model Results

Yijun Yao, Rui Shen, Kelly G. Pennell,†and Eric M. Suuberg*

School of Engineering, Brown University, Providence, Rhode Island 02912, United States

b

S Supporting Information

ABSTRACT: The Johnson-Ettinger vapor intrusion model (J-E model) is the most widely used screening tool for evaluating

vaporintrusionpotentialbecauseofitssimplicityandconvenienceofuse.Sinceitsintroductionabouttwentyyearsago,theJ-Emodel

hasbecomeacornerstoneinguidancerelatedtothepotentialforsignificantvaporintrusion-relatedexposures.Afewpapershavebeen

publishedthatclaimitisaconservativepredictorof exposure,buttherehasnotbeenasystematiccomparisonintheopenliteratureof

the J-E model predictions with the results of more complete full three-dimensional descriptions of the phenomenon. In this paper,

predictionsfromathree-dimensionalmodelofvaporintrusion,baseduponfiniteelementcalculationsofhomogeneoussoilscenarios,

are directly compared with the results of the J-E model. These results suggest that there are conditions under which the J-E model

predictions might be quite reasonable but that there are also others in which the predictions are low as well as high. Some small

modificationstotheJ-Emodelarealsosuggestedthatcanbringitspredictionsintoexcellentagreementwiththoseofthemuchmore

elaborate 3-D models, in some specific cases of homogeneous soils. Finally, both models were compared with actual field data.

’INTRODUCTION

The vapor intrusion (VI) problem has been the focus of a

series of modeling studies, starting with a focus on radon1,2and,

more recently, concerned with contaminants of anthropogenic

origin.3-19Several numerical models have been developed and

proven to be useful tools in understanding the phenomenon,

since the first identification of the probable VI pathway into a

building in 1987.1

With improvement over time in understanding of VI pro-

cesses, different kinds of models have been developed to assess

thepotentialforindoorairqualityproblems.Thesemodelsrange

from simple screening, one-dimensional (1-D) models (e.g.,

Johnson and Ettinger model)3to full three-dimensional (3-D)

fluidflowmodels.7,9,15-17Amongtheformerclassofmodels,the

Johnson-Ettinger (J-E) model3is the most widely used in the

U.S. This model was proposed as a screening tool in the preli-

minary 2002 U.S. EPA Vapor Intrusion Guidance.5Prior and

subsequent to issuance of that guidance, the J-E model has

come under considerable scrutiny, and even some suggestion

fromwithinEPAthatthescreening toolshouldbereevaluated.11

Several useful articles have been written to clarify proper appli-

cation of the J-E model as a screening tool for identifying the

potential for VI problems, rather than as a quantitative predictive

model,4,7,9and it has been judged to be conservative in many

cases,6though not conservative enough in others.10There are

numerous other screening tools in use worldwide and these have

alsobeenrecentlyreviewed.18,19Again,theothersimplescreening

models tended to overpredict measured concentrations, but the

J-E model was one of two that was judged to provide closest

agreement with actual measurements.18

It is also important to recognize that what is commonly

referredtoastheJ-EmodelisactuallytheU.S.EPAspreadsheet

implementation of what was originally proposed byJohnson and

Ettinger, as noted by Johnson in 2005.4,8It is this EPA version of

the model that was examined in this paper, since this is the

version in widest use. Even then, there are multiple versions of

this model offered on the EPA Web site. The version used to

obtain the results presented here was the soil vapor screening

model (SG-ADV-Feb04).

TwobasicassumptionsoftheJ-Emodelarealsoexaminedin

this paper: that of diffusion dominated transport in the domain

and the other, mass conservation from a source to the enclosed

space built atop that source.

’MODELS

Full Three-Dimensional Finite Element Model of Vapor

Intrusion. The full 3-D model examined here is essentially that

presented earlier by this group.15-17The case of interest here is

the earlier discussed steady-state “base case”, that is, a single

structure built atop an otherwise flat, open field, underlain by a

homogeneous soil that stretches from the ground surface to a

water table serving as an infinite source of the contaminant of

interest. The important influence of soil layering, soil inhomo-

geneities and surface capping were earlier discussed,15-17but

thesearenotconsideredhere.Theassumeddomainsizeherewas

smaller than that in earlier base cases, but this is of no con-

sequence tothe results. Also, the earlier “Characteristic Entrance

Region (CER)” approximation to crack geometry was not

needed here15-17and had no significant impact on results.

Themodeledsituationconsistsofasinglesquare10m?10m

footprint structure built on otherwise open (uncapped) field of

24m?24m(seeFigure1).Thisdomainsizeissufficientlylarge

such that the boundaries do not substantially affect the solution

Received:

Accepted:

Revised:

August 10, 2010

January 20, 2011

December 27, 2010

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withinthedomain.Thestructurehaseitherabasementfoundation

or is built on a slab. For simplicity, the results are based on the

commonly assumed 0.005 m wide perimeter crack scenario. The

crack is assumed to run along the entire edge of the foundation or

Figure1. Crosssectionalviewof(a)fulldomainofinterest,(b)boundaryconditionsofmodeledquarterdomain,and(c)detailsofmodeledperimeter

crack.

Table 1. Summary of Model Equations for Steady State Simulation15

equation 1:

soil gas continuity

where

q = soil gas velocity (L/t)

k = intrinsic permeability (L2)

Fg= density of soil gas (M/L3)

μg= dynamic viscosity of soil gas (M/L/t)

g = gravitational acceleration (L/t2)

z = elevation (L)

p = pressure of soil gas (M/L/t2)

q ¼ -kFg

μg

rφ

φ ¼ gzþ

Zp

p0

rp

Fg

equation 2

chemical transport

where

JT= bulk mass flux of chemical (M/L2/T)

Deff= effective diffusivity coefficient of chemical in soil gas phase (L2/T)

Dg= molecular diffusion coefficient for chemical in gas (L2/T)

Dw= molecular diffusion coefficient for chemical in water (L2/T)

c = concentration of chemical in soil gas (M/L3)

H = air/water partition (Henry’s) coefficient (L3air/ L3water)

φg= porosity filled by gas (L3air/L3soil)

φw= porosity filled by water (L3water/L3soil)

φT= total porosity (L3pores/L3soil)

JT ¼ qc - Deffrc

Deff ¼ Dgφg10=3

φT2þDw

H

φw10=3

φT2

? Dgφg10=3

φT2

equation 3

chemical mass flux through the crack

qckdck

Dg

?

where

Jck= mass flux of chemical (M/L2/T)

qck= soil gas velocity at the crack (L/T), from solution of Darcy’s Law.

dck= thickness of the crack (L)

cck= concentration of chemical at the crack (M/L3)

Jck ¼ qck

exp

?

exp

?

cck-cindoor

?

qckdck

Dg

-1

?

qckexp

qckdck

Dg

qckdck

Dg

??

- 1

cck

exp

??

ðqck 6¼ 0Þ

equation 4

indoor air concentration

where

cindoor= concentration of chemical in the indoor air (M/L3)

Mck= mass flow rate of chemical through the crack (M/T)

Vb= volume of enclosed space (L3)

Ae= air exchange rate of building (T-1)

Qck= volumetric flow rate through the crack (L3/T)

Qbuilding= building ventilation rate (L3/T)

cindoor ¼

Mck

QckþVbAe

?Mck

VbAe

¼

Mck

Qbuilding

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slab, and the influences of different types of foundation openings

are the focus of ongoing research by the authors.

The key working equations are summarized in Table 1. Incom-

pressible soil gas flow is assumed, as is typical. All contaminant

vapor originates from the groundwater surface, and there are no

contaminant sources within the soil itself. The pressure driving

force for soil gas advection arises from the “chimney effect” within

the structure itself, transmitted to the soil through the foundation

perimeter crack, which itself is also the main pathway for con-

taminant vapor entry into the building.

Fundamentally, the equations in Table 1 are present in the

J-E model as well, except that they represent one-dimensional,

as opposed to three-dimensional processes (see below). All

inputs to the three-dimensional model were the same as used

in the J-E model, except as noted below.

Since all scenarios modeled in this paper involve the illustrated

symmetricalsituation,simulationof onlyaquarter oftheFigure1a

domainfullydefines thesolution,asillustratedinFigure1b. (Con-

taminant mass entry rates given below are for the whole domain).

Planes of symmetry, the groundwater surface and the foundation

(except for the crack) are all no-flux boundaries, whereas the open

groundsurfaceistakentobeatatmosphericreferencepressureand

is a sink of zero contaminant concentration.

Table 2 gives the key input parameters explored in this study.

Though permeability and diffusivity are both related to the

porosity of the soil, small variations in diffusivity do not have a

significant impact on solution.17For purposes of presenting a

consistent comparison, a constant effective soil porosity and

diffusivity were assumed here, and again, small changes in these

valueshad littleeffecton theconclusions.Itshould alsobenoted

that while the simulations were carried out for trichloroethylene

(TCE)inthecaseoftheJ-Emodel,thechoiceofcontaminantis

largely unimportant because most volatile organic compounds

(VOCs) of concern have similar diffusivity values.

Johnson-Ettinger Model. The Johnson-Ettinger model

considered here is mainly based on two (steady state) working

equations.Thefirstexpressesthefactthatthecontaminantreleased

at the source must enter the crack (eq 5), and the second (eq 6)

shows that indoor air concentration is determined by building air

exchange

Deff? AB

LT

ðCsource-CckÞ ¼ Qck

exp

Qckdck

AckDck

?

?

exp

?

Cck- Cindoor

?

Qckdck

AckDck

-1

ð5Þ

Qck

exp

Qckdck

AckDck

?

?

exp

?

Cck- Cindoor

?

Qckdck

AckDck

- 1

¼ QbuildingCindoor

ð6Þ

where Csourceis the soil vapor concentration of the source, LTis

the distance from source to the bottom of the foundation, ABis

the surface area of enclosed space below grade, and Dckis the

effectivediffusivityofairinthecrack(othersymbolsdefinedasin

Table 1). The results of the J-E model are often presented in

terms of the indoor air concentration attenuation factor (R),

which may be solved for from the above two equations:

R ¼Cindoor

Csource

¼

Deff?AB

QbuildingLTexp

Qckdck

AckDck

Qckdck

AckDck

?

?

?

?

exp

Qckdck

AckDck

??

þDeff? AB

QckLT

ðexp

- 1Þ þDeff? AB

QbuildingLT

ð7Þ

’ESTIMATES OF SOIL GAS ENTRY RATE

Any pressure-driven soil gas flow into a foundation crack can

enhance contaminant entry rate over that which would exist be-

causeofpurediffusionthrough thecrack,throughadvectivecon-

veying of contaminant into the building. This aspect of the VI

phenomenon is already well understood and generally accepted

in currentmodels. In the J-E model of the U.S. EPA spreedsheet,

the estimate of this flow, Qck, is based upon the work of Nazaroff

and his colleagues,2and is embodied in a simple approximation

basedonflowintoaburiedporouspipe-likestructure.Johnsonhas

suggested that the Johnson and Ettinger3equation and the U.S.

EPAspreadsheetsbereformulatedsothattheratioofQck/Qbuilding

would be used to replace Qckfrom Nazaroff’s eq 8. This has not

been done here, in keeping with what is presently used.

The equation developed by Nazaroff for this soil gas volu-

metric advection into a buried pipe is

Qck_Na¼

2πkΔpLck

μglnð2df=rpÞ

ð8Þ

in which Lckis the length of a hypothetical buried pipe, dfis the

depth of the pipe below the soil surface, and rpis the radius of

pipe, and other symbols as already defined.

Table 2. Input Parameters Used in 3-D Simulation (Unless

Otherwise Noted in the Figures and Table)

building/foundation parameters

foundation foot print length

foundation foot printwidth

depth of foundation (df)

crack/foundation slab thickness (dck)

crack width (Wck)

crack area (Ack)

volume of intruded area (Vb)

air exchange rate in intruded volume (Ae)

depth to groundwater/source (dsource)

10 m

10 m

0.1 and 2 m

0.152 m

0.005 m

0.199 m2

3.66 ? 102m3

0.25 h-1

3, 5, 8, 11, 14, 18 m bgs

3-D finite element analysis parameters

size of the grid elements

number of elements

0.001-1 m

200k-600k

contaminant vapor source properties

contaminant

diffusivity of TCE in crack (Dck)

diffusivity of TCE in air (Dg)

effective diffusivity of TCE in soil (Deff)

TCE

7.4 ? 10-6m2/s

7.4 ? 10-6m2/s

1.04 ? 10-6m2/s

soil gas flow properties

viscosity of air/soil gas (μg)

density of air/soil gas (Fg)

soil permeability (k)

total soil porosity (φt)

soil porosity filled with gas (φg)

1.8648 ? 10-5kg/m/s

1.1614 kg/m3

10-10, 10-11, 10-12, 10-13, 10-14m2

0.35

0.296

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IntheJ-Emodel,aperimetercrackisapproximatedbyaform

equivalent to the buried pipe. The soil gas flow rate is approxi-

mated by a transformed equation

2πkΔpLck

μglnð2df=wckÞ

where rpis replaced by crack width.

Foraperimetercrack,acrackvelocitymaybecalculatedfromQck

vck ¼Qck

Qck_JE¼

ð9Þ

Ack

ð10Þ

Ack¼ Lckwck

ð11Þ

The average velocity vckcan be used to define a nondimensional

characteristic velocity U

?

inwhichkisthesoilpermeability,koisabasecasepermeabilityof

10-11m2, Δp is the pressure differential between the crack en-

trance and atmosphere, and Δp0is the base case pressure diffe-

rentialof-5Pa.dfoisthebasecasefoundationdepthof2m;this

leads to a standard reference velocity of vcko= 5.04 ? 10-4m/s,

calculated using the J-E model. The above nondimensionaliza-

tion recognizes the linearity of flow velocities with respect to soil

permeability and pressure driving force and chooses a reference

velocity characteristic of typical parameter choices.

Figure2apresentstheresultsofthefull3-Dsimulationsresults

for advective soil gas entry rates into the structure and are

nondimensionalized using eq 9. In this instance, the calculation

involvedk=ko=10-11m2andΔp=Δpo=-5Pa.Ifthe3-Dmodel

U ?

vck

vcko

?

ko

k

? ?

Δpo

Δp

!

ð12Þ

andtheJ-Emodelwereinagreement,Uwouldequal1forthedf=

dfo= 2 m deep basement scenario. The slab on grade condition is

represented by a foundation depth of 0.1 m, and other depths are

also shown, corresponding to possible crawl-space or basement

conditions. It is apparent that the J-E model actually provides a

verygoodapproximationtothemoredetailedsolutionprovidedby

solving the full fluid mechanics equation, but it typically over-

predicts the entry rate (the reference velocity in eq 12 is too high,

which is why the detailed simulation results are all seen to give

Ulessthanunity).Theapparentoverpredictionofentryvelocityis

seen to be near a factor of 2 in most cases, though a bit less in the

caseoftheslab.Thesourcedepthisseentobeofnoconsequence.

Similar results were obtained for different permeabilities.

This means that the estimate of the advective entry rate

assumed in the case of the J-E model can be slightly improved.

Onestep of improvement involvesassuming that onlyhalfof the

hypothetical buried pipe surface is available for receiving flow

from the soil, which recognizes the top half of the pipe cannot

receive flow because it is immediately adjacent to the building

floor.2The other small improvement is to relate the crack half-

widthtopiperadius,whichisinbetteragreementwithNazaroff’s

originalapproximation(eq8).Theresults ofthesemodifications

are shown in eqs 13 and 14

Qck_MNa¼

πkΔpLck

μglnð4df=wckÞ

!

ð13Þ

UMNa¼

vck

vcko

??

ko

k

? ?

Δpo

Δp

¼

lnð2dfo=wckÞ

2 lnð4df=wckÞ

ð14Þ

The results of these modifications are shown in Figure 2b, in

whichthe result of the J-Emodel estimate is compared withthe

Figure 2. (a) Influence of foundation depth and depth of source on the soil gas entry flow through a perimeter crack based on 3-D simulation.

(b) Estimates of the soil gas flow through the crack using different calculational methods.

Table 3. Comparison of Measured and Model-Predicted Soil Gas Flow Rates into Building6

sitefoundation type measured (L/min)Qck_JE(L/min) Qck_MNR(L/min)

Chatterton Site (Hers et al. 2000)slab-on-grade

slab-on-grade

slab-on-grade

slab-on-grade

Basement

2.7

4.2

2.9

1.4

2913.2

4.4

3.8

1.1

51.0

9.6

8.2

2.4Alameda Site (Fischer et al. 1996)

Spokane Valley Houses (Revzan et al. 1991)102 110

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Figure 3. ComparisonoftheEPAimplementationoftheJ-Emodel(curves) withthefull3-Dsimulation(points) fora2mdepthfoundation(a) anda0.1m

depth foundation (b); the comparison of the revised J-E model (flow and diffusivity corrections) results with those of the full 3-D simulation, for a 2 m depth

foundation (c) and a 0.1 m depth foundation (d). The comparison of the revised J-E model (curves, which include flow, diffusivity and mass conservation

corrections)onindoorairconcentrationattenuationfactorwithdetailedsimulationresults(points)fora2mdeepfoundation(e)anda0.1mdepthfoundation(f).

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detailed 3-D simulation results and the modified Nazaroff ap-

proximation, using eqs 13 and 14. Similar agreement is achieved

withdifferentvaluesofk(10-10-10-14m2)andΔp(0-20Pa).

Therearefewspecifiedexperimentalresultsusingtracertools,

which offer insight into how well such models can predict gas

entry rates. A relevant selection is given in Table 3.6In some

cases,themodifiedapproachprovided theexpectedbetteragree-

ment,andinothersnot.Thebottomlineisthatoverallthemodi-

fied equation does seem to fit fairly well.

’COMPARISON OF THE FULL 3-D SIMULATION WITH

PREDICTIONS OF THE JOHNSON-ETTINGER MODEL

The results oftheattenuationfactorpredictionsfromtheJ-E

model can be compared with the results of the full 3-D simula-

tions. This is first done in Figure 3a for the J-E model, as imple-

mented by EPA. Figure 3a shows the comparison for different

soil permeabilities and source depths. It may be quickly seen in

the case of unusually high permeability soils (k = 10-10m2) that

the J-E model predictions are generally low, as compared with

the full 3-D simulation. In the more typical soil permeability

range (k = 10-11to 10-12m2), the J-E model predictions are

seen to be conservative as compared to the full 3-D simulation

predictions, which was also pointed out by others.6With low

permeability, clay-like soils (10-13-10-14m2), the J-E results

generally under-predict, as compared with a full 3-D simulation.

Figure 3b shows the same sorts of predictions as in Figure 3a,

but inthis case,for asimulated slab-on-grade scenario. The same

general trend is seen with the highest permeability soil as in the

2mdeepfoundationcase,butinthiscase,theJ-Emodelpredic-

tionsaregenerally conservativeevenforlowerpermeabilitysoils.

It is worth noting that in virtually all cases, the J-E model

predictionsarewithinanorderofmagnitudeofthemoredetailed

3-Dsimulationresults.Thisiscertainlyaffirmationofthevalueof

the simple J-E screening tool in geologically simple scenarios.

It has already been noted that the J-E model uses a soil gas

entryratethatisabithighcomparedwithfull3-Dsimulation.Itis

of interest to see the influence of employing the presumably

more accurate estimate of that velocity, such as provided by a

detailed3-D calculation of that velocity. In addition, the effective

diffusivityinthecrack usedintheJ-Emodelisoften takentobe

that in the soil, whereas the higher molecular diffusivity of

contaminant in air has been used to model the crack in our full

3-Dsimulations,(andthisassumptionwasalsousedinJohnson’s

later research7,9). To explore the influence of these differences,

comparisonsweremadebetweenthefull3-Dsimulationsandthe

J-Emodelmodifiedinonlythesetwoways.Resultscorrespond-

ing to those in Figure 3a and b are provided in Figure 3c and d;

the results for the 3-D simulations are the same as in Figure 3a

and b, since it was only the J-E model results that changed.

In Figure 3c, the predictions of indoor air contaminant con-

centration slightly decreased for the higher soil permeabilities, as

would be expected as a result of a lower soil gas entry flow rates.

On the other hand, the revised J-E model predictions for the

lower soil gas permeabilities greatly increased, by virtue of the

higher diffusivity assumed in the crack (since the advective con-

tribution to contaminant entry is minimal, under those con-

ditions). In Figure 3d, for the slab on grade, the revised J-E

modelresultstendtoclusterinanarrowband,andareoftenquite

conservative, relative tothefull3-Dsimulation results (again,ex-

ceptfortheunusuallyhighpermeabilitysoil,inwhichtherevised

J-E model again under-predicts relative to the full simulation).

Thus the importance of the crack diffusivity assumption is

illustrated.

According to the 3-D model, the subslab or crack concentra-

tionismainlydeterminedbythegeometryofthedomainandnot

by soil permeability or diffusivity. In high permeability cases,

where convection is determining the contaminant mass flow

through the crack, and the solution is thus not sensitive to the

diffusivity of the contaminant in the soil. This is not true for the

J-E model, because of its requirement of mass balance between

contaminant transport in the soil and its mass flow into the

house.ThusthesoildiffusivityalsomakesadifferenceintheJ-E

model prediction, just as did the crack diffusivity.

Figure 4 shows the J-E model predicted variation in R with

contaminant soil diffusivity. In general, R is linear in soil

diffusivity,withotherconditionsunchanged.For3-Dsimulation,

R is not sensitive to soil diffusivity for high permeability because

it is advection that then dominates contaminant entry rate. Even

for low permeability, R is much less sensitive to soil diffusivity

than that in the J-E model. This is an important difference

between the model predictions.

’MASS CONSERVATION CONSIDERATIONS

The original J-E model was based on two important assump-

tions.Thefirstisthatdiffusiondominatescontaminanttransport

through the soil (and this is what determines soil gas contami-

nantconcentrationprofiles).Thishas beenaffirmed bythe more

detailed simulations as well.15-17Thus, the role of advection in

establishing the contaminant soil gas profile is actually quite

minimal. Where advection plays a role is in pulling contaminant

into the structure from a diffusion-determined zone of high

concentration beneath the structure.

The second assumption in the J-E model development was

that of mass conservation in contaminant transport. In the J-E

model, the surface area of the enclosed space in contact with soil

was used as the effective source area, which arises from the need

to maintain a 1-D modeling approach, in which the contaminant

only moves upward from a source beneath the structure, and

Figure 4. Relationship between indoor air concentration attenuation

factor and effective diffusivity for a source at8 mbgs forthe J-E model.

(Here, the modified Qckand Dcrackcorresponding to gas-phase diffu-

sivityhavebeenused.LinesarefromtheJ-Emodel,andpointsarefrom

3-D simulation.)

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cannot be lost by diffusion in an orthogonal direction (nor aug-

mentedbyinwarddiffusionfromoutsideofthefootprint).Thisis

clearly a significant restriction, and it is worthwhile examining its

consequences.

Figure5a shows, from thedetailed3-D simulations,theflux of

contaminant from a source beneath the building, J, as a function

of soil permeability. This quantity J is simply the mass flux over

the whole domain, normalized by the theoretical diffusion flux

between a source at Csourceand a sink at zero, using the depth of

source as the diffusion path length

Mreleaseddsource

AsourceDeffCsource

whereMreleasedisthecontaminantmassflowratefromthesource

andAsourceistheareaofthesource,bothofwhichwerefrom3-D

simulation.

Not surprisingly, consistent with a diffusion-dominated release

of contaminant from the source, the value of J is very near unity

for all cases. The presence of the structure on the domain does

not change this fact. This conclusion is independent of soil

permeability, except when the permeability gets very high, and

even then, the influence on contaminant release rate is quite

modest. (The value of J goes up to only about 1.4, that is, a 40%

increase)

Figure 5b shows a “mass conservation” ratio, defined as

J ¼

ð15Þ

Rf ¼

Mck

Mf-released

ð16Þ

whereMckisthecalculatedcontaminantentry rate intothecrack

and where Mf-releasedis the release rate of the contaminant from

the source directly beneath the building footprint. The release

ratefromdirectlybeneaththefoundationmaybecalculatedfrom

Mf-released¼ MreleasedAfoundation

Asource

ð17Þ

For a 10 m ? 10 m footprint foundation, Afoundation= 100 m2,

where necessary account is taken for the quarter domain

calculation. It is important to note that Figure 5 is for the model

parametersspecifiedinthispaper;thatis,pressuredifferenceand

effective diffusivity.

It is apparent that only a small fraction of the mass released

beneath the structure might actually enter the structure. This in

effectshowsthe“violation”ofthesituation thatisinvolvedinthe

J-Emodelingapproximation.Inthecaseofasoilpermeabilityof

10-11m2,theapproximationisactuallyquitegood(especiallyfor

the2mdepthfoundationcase),butforhigherpermeability,con-

taminant entry can actually be enhanced by soil gas drawn in

from outside of the building footprint. In the case of low perme-

abilitysoils,muchofthecontaminantreleasedbeneaththebuild-

ing is lost to diffusion away from the building. This is seen to be

relativelyinsensitivetothesourcedepth,explainingwhytheJ-E

model is relatively conservative as compared with the detailed

3-D simulation.

Since Figure 5b shows that the mass conservation ratio is inde-

pendentofsourcedepth,theseresultscanbeaveragedirrespective

of depth to provide one further “correction” to the one-dimen-

sionalJ-Emodel.Inthisapproach, the left-handside of eq5 may

bemodifiedusingthevalueofRffromthisfiguretocorrectforthe

fractionofcontaminantreleasedbeneaththebuildingthatactually

enters the building. This value is independent of source concen-

tration or depth, but does depend upon the value of Deffand, of

course, k. The resulting corrected equation for R is

R ¼cindoor

csource

¼

Deff?Af

QbuildingLTexp

QckLcrack

AcrackDcrack

QckLcrack

AcrackDcrack

?

ðexp

?

1

Rf

exp

QckLcrack

AcrackDcrack

??

þDeff? Af

QckLT

??

- 1Þ þDeff? Af

QbuildingLT

ð18Þ

Figure5. (a)Influenceofsoilpermeabilityoncontaminantreleaseratefromthesourcebasedon3-Dsimulationfor2m(solidpoints)and0.1m(open

points)depthfoundation.(b)Theinfluenceofsoilpermeabilityonmassconservationratiofrom3-Dsimulationfor2m(solidpoints)and0.1m(open

points) depth foundation. The values in the legends refer to source depth (m).

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ARTICLE

Application of this correction along with the previously des-

cribed modifications to the J-E model, result in the predictions

shown in Figure 3e and f. In some respects,it may be argued that

this correction is circular in nature; that is, the J-E model is

being forced to fit the 3-D simulation results by applying those

same results as a correction. On the other hand, note that the

mass conservation correction is really, to an excellent approx-

imation,onlyafunctionofsoilpermeabilityinthespecifiedcases.

It simply reflects the interplay between diffusion and advection,

which needs to be accounted for in many soils, which is not

reflected in the pure 1-D formulation.

’MODEL RESULTS AND FIELD DATA

The work by Hers et al.5has already established that the

predictions oftheJ-Emodelareinreasonable agreement witha

great deal of field data, if perhaps a bit on the conservative side.

This reasonable agreement, when considered in the context of

thegenerallyfairtogoodagreementbetweentheJ-Emodeland

the 3-D model considered here, already helps establish that the

latter is providing reasonable results. Recognizing, too, that the

3-Dmodelisbuiltuponastructuresuggestedbytheearlierradon

modeling work (and its validation), the latter comes as little

surprise.

Themainpurposeofthisstudywasnottoprovideavalidation

of any particular VI modeling approach, but to provide a com-

parisonoftheresultsfromtheJ-Eapproachtoafull3-Dmodel,

for the same set of input parameters. Again, the sensitivity of the

respective models to the input parameters has been recognized

andnotedinpreviouslypublishedarticles,5,14,15butthechoiceto

use the same parameter sets here makes the comparison as con-

sistentaspossible.Thecomparisonrangesfromgoodtofair,and

this is the key conclusion of this paper.

This might still leave open a question as to whether it can be

shown that the 3-D simulation by itself offers reasonable predic-

tions,andthisledtoofferingtheverybasiccomparisoninTable4

of the full 3-D model predictions to some results obtained from

an actual PCE contaminated site located in New England. The

details of this site (and consultant-provided field data) are

provided in the Supporting Information.

Again, it is recognized that this does not yet by any means

represent afullvalidationof the3-Dmodel, but itis afirststepin

thisdirectionandotherresultsarebeingobtainedbyusfromthis

same site. What are shown are the indoor and subslab concen-

trationsofPCE(here,thesubslabvalueistakentobethevalueat

the inlet to an assumed perimeter crack).

In general, the 3-D simulations and EPA version of the J-E

model both provide reasonable estimates of indoor air and

subslab concentrations. There were no indoor depressurization

nor air exchange datato guide themodeling work, so atypicalair

exchangerateof0.45/hwasassumed,andtwodifferentextentsof

indoor depressurization were assumed (-5 and -20 Pa), as

shown. The ranges shown are for the upper and lower limits of

concentrations,showninTable5oftheSupportingInformation,

but briefly, the measured basement concentration of PCE was

163 μg/m3, while the subslab concentrations varied from

16400-21600 μg/m3and the groundwater concentration of

PCE ranged from 198-261 μg/L. Applying the corrections

discussed above to the J-E model, the agreement between that

model and measurements is even better.

Onthebasisoftheresearchinthework,itisseenthattheJ-E

model(asimplementedbyEPA)providesagoodapproximation

to the results of a 3-D simulation, generally to within an order of

magnitude in indoor air attenuation factor. However, it is possi-

ble to improve the theoretical basis of the J-E model approx-

imation even further by making small changes to the estimate of

soilgasentryrateandrecognizing therestrictionthatanassump-

tion of contaminant mass conservation places upon a 1-D model

such as J-E. Also the difference in the role that advection and

diffusion play in establishing contaminant entry rates has been

highlighted.

’ASSOCIATED CONTENT

b

S

Supporting Information.

and Table 4. This material is available free of charge via the

Internet at http://pubs.acs.org.

Tabulated results for Figure 3

’AUTHOR INFORMATION

Corresponding Author

*Phone: (401) 863-1420; e-mail: Eric_Suuberg@Brown.EDU.

Present Addresses

†Department of Civil & Environmental Engineering University

of Massachusetts-Dartmouth, Dartmouth MA02747; e-mail:

kpennell@umassd.edu

’ACKNOWLEDGMENT

This project was supported by Grant P42ES013660 from the

National Institute of Environmental Health Sciences. The con-

tent is solely the responsibility of the authors and does not

necessarilyrepresenttheofficialviewsoftheNationalInstituteof

Environmental Health Sciences or the National Institutes of

Health.

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