Effect of Vapor Source−Building Separation and Building Construction

May 12, 2005 - Identification of Alternative Vapor Intrusion Pathways Using Controlled Pressure Testing, Soil Gas Monitoring, and Screening Model Calc...
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Environ. Sci. Technol. 2005, 39, 4550-4561

Effect of Vapor Source-Building Separation and Building Construction on Soil Vapor Intrusion as Studied with a Three-Dimensional Numerical Model LILIAN D. V. ABREU AND PAUL C. JOHNSON* Department of Civil and Environmental Engineering, Ira A. Fulton School of Engineering, Arizona State University, Tempe, Arizona 85287-5306

A three-dimensional numerical model of the soil vaporto-indoor air pathway is developed and used as a tool to anticipate not-yet-measured relationships between the vapor attenuation coefficient, R (indoor air concentration/ source vapor concentration), and vapor source-building lateral separation, vapor source depth, and building construction characteristics (depth of building foundation) for nondegrading chemicals. The numerical model allows for diffusive and advective transport, multicomponent systems and reactions, spatially distributed foundation cracks, and transient indoor and ambient pressure fluctuations. Simulations involving different lateral separations between the vapor source and building show decreasing R values with increasing lateral separation. For example, R is 2 orders of magnitude less when a 30 m × 30 m source located 8 m below ground surface is displaced from the edge of the building by 20 m. The decrease in R with increasing lateral separation is greater for shallower source depths. For example, R is ∼5 orders of magnitude less when a 30 m × 30 m source located 3 m below ground surface is displaced from the edge of the building by 20 m. To help visualize the effects of changing vapor source-building separations, normalized vapor concentration contour plots for both horizontal and vertical cross sections are presented for a sequence of lateral separations ranging from the case in which the 30 m × 30 m source and 10 m × 10 m building footprint centers are collocated to shifting of the source positioning by 50 m. Simulations involving basement and slab-on-grade constructions produce similar trends. In addition, when buildings are overpressurized to create outflow to soil gas on the order of 1-3 L/min, emissions to indoor air are reduced by over 5 orders of magnitude relative to intrusion rates at zero building underpressurization. The results are specific to simulations involving homogeneous soil properties, nondegrading chemicals, steady source concentrations and building underpressurizations, and the geometries studied in this work.

Introduction In 2002, the United States Environmental Protection Agency (EPA) issued draft guidance for assessing the subsurface vapor * Corresponding author phone: (480)965-9115; fax: (480)9650557; e-mail: [email protected]. 4550

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intrusion-to-indoor air pathway (1). That guidance acknowledged the potential for contaminant vapors originating from impacted soils and groundwater to migrate to buildings, and it provided a sequence of steps to follow when assessing the significance of the pathway under current conditions. Its development was stimulated in part by the recent measurement of unacceptable indoor air concentrations attributed to subsurface contamination at a few well-studied and wellpublicized sites (e.g., see refs 2, 3). The guidance was based in part on empirical analysis of a sparsely populated EPA database, use of the Johnson and Ettinger (4) screening-level model, and professional judgment. Professional judgment was used in defining conditions for which the pathway could be judged a priori not to be of concern. For example, vapor sources located more than 30 m laterally or vertically were deemed to not be of concern. In addition, professional judgment was used when deciding that building and foundation construction characteristics (e.g., basement, slabon-grade, and crawl-space construction) should not be a factor in assigning generic subslab and depth-specific attenuation factors (defined to be the ratio of the indoor air concentration to the soil gas concentration at some prescribed depth (4)). The use of professional judgment when developing regulatory guidance is not unusual, especially when there is an accepted technical knowledge base. In this case, however, the criteria are arguably arbitrary because there is neither an empirical nor a theoretical basis for the criteria that were selected. This study was conducted to help anticipate the as-yet-to-be-measured relationships between vapor sourcebuilding lateral separation, building construction, and indoor air impacts. The vapor intrusion-to-indoor air pathway has been studied since the 1980s, with the initial emphasis placed on assessing and mitigating impacts of naturally occurring radon intrusion (5-20). Since the early 1990s, there has also been recognition and study of the potential for anthropogenic chemicals to pose threats to indoor air quality (2-4, 21-39). These works collectively suggest that the resulting indoor air concentration is influenced by several factors, including the vapor source type (e.g., soil or groundwater); vapor source concentration; vapor source position relative to the building; chemical biodegradability; physical characteristics of the soil (e.g., air permeability, moisture, porosity); building construction and foundation characteristics (e.g., basement, slabon-grade, crawl-space, foundation bedding layer, foundation cracks and openings); building air exchange rate; indooroutdoor temperature difference; operation of heating, ventilation, and air-conditioning (HVAC) systems; wind blowing against the walls of the building; and atmospheric pressure fluctuations. Attempts to codify or predict the influence of these factors on indoor air concentrations have largely focused on the use of screening-level models (2-4, 21, 22, 25-27, 30, 31, 33, 34, 40-42) and more sophisticated numerical codes (6, 9, 10, 12-20, 24). Empirical analysis of field data is another option, but the number of well-studied sites is still small (2). As a result, verification of the practical utility and reliability of the models has also been limited. Because of its appearance in regulation and guidance, much attention has been focused on testing the Johnson and Ettinger (4) algorithm. For example, Hers et al. (2) recently summarized much of the published data, reduced it to vapor attenuation factors, and compared those with estimates produced using the Johnson and Ettinger algorithm. In addition, Johnson (21) reports on a sensitivity analysis and the identification of critical and 10.1021/es049781k CCC: $30.25

 2005 American Chemical Society Published on Web 05/12/2005

noncritical algorithm inputs. In brief, the Hers et al. (2) analysis suggests that efforts to estimate indoor air impacts and their dependence on soil type and depth have been reasonably successful (within about an order of magnitude) for relatively recalcitrant chemicals (e.g., chlorinated solvents) when the vapor sources were located directly beneath buildings. There is less confidence in our ability to quantitatively estimate the impacts of aerobically degrading chemicals: the data is too limited to empirically assess the influence of building construction, and the site studied by Hodgson et al. (23) appears to be the only published study for which the vapor source was known to be laterally displaced from the building. Recognizing the inherent limitations in screening-level models and the paucity of high-quality field data, this study utilized a three-dimensional numerical code to help better anticipate the relationships between vapor source-building lateral separation, building construction, and indoor air impacts. The use of numerical codes as tools for gaining a better understanding of this pathway is not new, but the specific application addressed here is. For example, Mowris and Fisk (9) used a two-dimensional numerical model to evaluate the effect of exhaust ventilation on radon entry rates through a perimeter shrinkage crack in a basement slab. The results gave an indication of the dependence of the entry rate on basement pressure and soil permeability. They also indicated that the relative significance of the resistance of the soil and the resistance of the basement slab crack to soil gas flow depended highly on soil permeability and concluded that the resistance of the gap is not significant unless the gap width is less than ∼0.002 m for soils with permeabilities on the order of 10-8 m2. Garbesi and Sextro (10) developed a two-dimensional, steady-state numerical soil gas flow model assuming airflow occurs through permeable substructure walls. Their model predictions agreed well with the pressure coupling observed in field measurements for the specific site being modeled. Loureiro et al. (6, 12) developed a steady-state, three-dimensional, finite-difference numerical code that coupled a soil gas flow equation with a radon transport equation, where the entry route for the soil gas into the basement was a foundation gap approximated by parallel plate geometry located at the perimeter wallfloor joints. The model was later reformulated by Revzan et al. (13, 14) to cylindrical coordinates in which the slabfooter-wall gap was changed to an L-shape, and only advective radon entry through the gap was considered. Both models allowed for a region around the basement filled with aggregate soil material having properties that can be different from those of the native soil. Both models also solved the system of equations with an iterative technique described by Patankar (43) and used an irregular grid that varied spatially in size. Robinson and Sextro (18) reported that the Loureiro et al. model correctly predicts the effect of a subslab gravel layer on soil gas entry rate into an experimental basement structure; however, the model underpredicts the absolute entry rate by a factor of 1.5 for the case studied. Building on the work cited above, this study involved the development of a numerical code to be used as a tool to help anticipate the relationships between vapor source-building lateral separation, building construction, and indoor air impacts. Because there is interest in studying the influences of aerobic biodegradation, foundation crack locations, and ambient pressure fluctuations on vapor intrusion, the numerical code described below allows for multicomponent transient transport by advection and diffusion, nonsymmetrical scenarios (necessary for this study of the effect of vapor source-building lateral separation), transient indoor and atmospheric pressure variations, a range of biodegradation kinetic expressions, heterogeneous soil lithology (varying

air permeability and moisture content), and the flexibility for distributing the cracks anywhere across the foundation. The development and validation of the numerical code are presented first below, and then its use as a tool to study the relationships between vapor source-building lateral separation, building construction, and indoor air impacts from nondegrading chemicals is discussed. More complete details of the model development and application can be found in Abreu (44), and study of the model applied to aerobically biodegradable chemicals is discussed in Abreu and Johnson (45).

Model Development The numerical code solves two equations: a continuity equation governing the vapor-phase pressure distribution and the resulting soil gas velocity field is coupled with a chemical transport equation that accounts for diffusion, advection, and biodegradation. The solution of these coupled equations generates three-dimensional pressure, soil gas velocity, and chemical concentration fields that are then processed to extract the soil gas flow rate into (or out of) the building, the emission rate of chemical into the enclosed space, the resulting indoor air concentration, and the vapor attenuation coefficient between the vapor source and the building. This model shares some features with the Loureiro et al. (6, 12) and Revzan et al. (13, 14) models (e.g., coupled continuity and transport equations, soil gas entry through cracks, variable grid spacing), but differs in other aspects (e.g., geometry, boundary condition details, multicomponent chemical reactions). The governing equations used in this work are summarized below. Soil Gas Flow. Massmann (46) showed that the soil gas continuity equation can be written

( )

∂P P h ∇ B ‚(Kg∇ B P) ) 0 ∂t φ g µg

(1)

where P is the absolute pressure [M/L/T2], P h [M/L/T2] is the mean pressure (approximated by the atmospheric pressure for the problems of interest here), φg is the gas-filled porosity [L3gas/L3soil], t is time [T], 3 B is the vector del operator [L-1], Kg is the soil permeability to soil gas flow [L2], and µg is the soil gas dynamic viscosity [M/L/T]. This equation neglects density-driven flow effects, which are expected to be insignificant for the problems of interest here. If the soil gas absolute pressure is expressed in terms of a disturbance pressure, p, [M/L/T2] relative to atmospheric conditions Po [M/L/T2]

P ) Po - p

(2)

then eq 1 becomes

( )

Po ∂p ∇ B ‚(Kg∇ B p) ) 0 ∂t φ g µg

(3)

and the soil gas specific discharge field can be obtained from the solution to eq 3 and Darcy’s law.

b qg )

Kg (∇ B p) µg

(4)

Chemical Transport and Biodegradation. Spatial and temporal changes in the concentration are described by the transport equation,

∂Ci +∇ B ‚Fi + Ri ) 0 ∂t

(5)

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concentration in the soil matrix [Mi/L3soil], B Fi is the mass flux vector [Mi/L2area/T], and Ri is the net loss rate of chemical i due to reaction [Mi/L3soil/T]. For simplicity, the model assumes that there is no immiscible phase present within the transport domain being modeled (it may be present at the source boundary) and each chemical partition between three phases: the gas phase (g), the dissolved phase (w) and the sorbed phase,

Ci ) φgCig + φwCiw + SiFb

(6)

where φw is the moisture-filled porosity [L3water/L3soil], Fb is the soil bulk density [Msoil/L3soil], Cig is the concentration of chemical i in the gas phase [Mi/L3gas], Ciw is the concentration dissolved in soil moisture [Mi/L3water], and Si is the mass of chemical i sorbed per unit mass of soil [Mi/Msoil]. The model accounts for chemical fluxes associated with advection of soil gas and soil moisture and with diffusion in the soil gas and soil moisture phases,

B F i ) Cigb q g + Ciwb q w - Dig∇ B Cig - Diw∇ B Ciw

(7)

where b qw is the specific-discharge vector for soil moisture infiltration [L3fluid/L2area/T]. Dig and Diw are the effective porous media diffusion coefficients for chemical i in soil gas and soil moisture [L2/T], as estimated by the Millington and Quirk (47) correlations,

Dig ) Dai

φg10/3

Diw ) Dw i

(8)

φT2 φw10/3

(9)

φT2

where Dai is the molecular diffusion coefficient of i in air [L2/T], Dw i is the molecular diffusion coefficient of i in water [L2/T], and φT is the total soil porosity () φg + φw) [L3pores/L3soil]. Local equilibrium is assumed and linear expressions are used to relate concentrations in the three phases,

Cig ) HiCiw

(10)

Si ) Koc,ifocCiw

(11)

where Hi is the Henry’s law constant for chemical i [(Mi/L3gas)/(Mi/L3water)], Koc,i is the sorption coefficient of chemical i to organic carbon [(Mi/Moc)/(Mi/L3water)], and foc is the mass fraction of organic carbon in the soil [Moc/Msoil]. Substituting eqs 6-11 into eq 5 yields

( )

∂Cig Cig ai ) -∇ B ‚(Cigb q g) - ∇ B‚ b q +∇ B ‚(Di∇ B Cig) - Ri (12) ∂t Hi w where

(

)

(i) zero-order kinetics:

Ri ) φwλo,i

(15)

(ii) first-order kinetics:

Ri ) φwλiCiw

(16)

(iii) dual-Monod kinetics:

Ciw Cjw Ri ) φwRmax,i (hsat,i + Ciw) (hsat,j + Cjw)

(17)

where λo,i is a zero-order reaction rate [Mi/T/L3water], λi is a first-order reaction rate [1/T], Rmax,i is the maximum contaminant utilization rate [Mi/L3water/T], Cjw is the dissolved concentration of a second reactant [Mj/L3water], hsat,i is the half-saturation constant for chemical i [Mi/L3water], and hsat,j is the half-saturation constant for chemical j [Mj/L3water]. Although not explicitly shown here, reactions involving multiple chemicals must be balanced stoichiometrically. Kinetic expressions 16 and 17 have been written with an explicit dependence upon dissolved concentrations; however, they could have also been written to depend on the total soil concentration, the gas-phase concentration, or the sorbed-phase concentration. In any of those cases, kinetic expressions involving the sorbed, vapor, or total soil concentrations could be rewritten in terms of the dissolved concentration using the linear partitioning relations 10 and 11, and the resulting equations would be similar to kinetic expressions 16 and 17, with the modification that the firstorder rate in 16 and the maximum utilization rate in 17 would be proportional to quantities involving partitioning coefficients. Model Domain and Boundary Conditions. Figure 1a and b illustrates two common scenarios: (a) a symmetrical case with a very large source and (b) a nonsymmetrical case with a finite source offset laterally from the building footprint. The building foundation geometry shown is a basement scenario, but slab-on-grade foundations are also modeled in this work. Vertical parallel planes represent the foundation cracks, and the model allows for their distribution anywhere around the foundation. The results presented below correspond to foundations with perimeter cracks as depicted in Figure 2. No flow boundary conditions are assigned at all vertical planes of symmetry, at lateral boundaries, at solid foundation boundaries, and at the lower horizontal boundary:

∇ B p‚n b)0

(18)

where b n denotes the unit vector normal to the surface of interest. The disturbance pressure at the ground surface (soilatmosphere interface) and within the building, respectively patm and pindoor, are allowed to be time-varying functions, and each is represented by a series of periodic functions,

(13)

patm(t) ) A1 sin(φ1t + θ1) + A2 sin(φ2t + θ2) + A3 sin(φ3t + θ3) (19)

(14)

pindoor(t) ) A4 sin(φ4t + θ4) + A5 sin(φ5t + θ5) + A6 sin(φ6t + θ6) (20)

The user can select from three different kinetic expressions (zero-order, first-order, and dual-Monod kinetics):

where A, φ, and θ are user-defined amplitudes [M/L/T2], frequencies [radians/T], and phases [radians]. For simulation results presented below, patm(t) ) 0 and pindoor(t) ) constant,

ai ) φg +

[

φw Koc,ifocFb + Hi Hi

]

Diw Di ) Dig + Hi

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FIGURE 1. (a) Boundary conditions (BC) and grid distribution for a sample symmetrical scenario with very large source. (b) Boundary conditions (BC) and grid distribution for a sample scenario with finite-size source offset from building. where Qck is the soil gas flow rate per unit length of crack [(L3gas/T)/L], wck is the crack width [L], dck is the foundation thickness [L]. Loureiro (6) also used this algebraic expression for Qck, which neglects transient storage effects. No flux boundary conditions are assigned at all vertical planes of symmetry, at lateral boundaries, at solid foundation boundaries, and at the lower horizontal boundary,

b)0 ∇ B Cig‚n

(22)

where b n denotes the unit vector normal to the surface of interest. The one exception to this is the boundary condition for all chemicals originating at the vapor source zone boundary.

FIGURE 2. Plan view of the foundation with perimeter crack distribution used in the simulations presented in this work. and the effect of time-varying pressures will be examined in future studies. The disturbance pressure boundary condition at the soil-foundation crack interface results from a mass balance equating the soil gas flow rate within the crack to the soil gas flow rate in the soil adjacent to the foundation crack (both rates are expressed per unit length of crack). An analytical solution for laminar gas flow through a pair of parallel foundation crack walls and the mass balance are combined to produce

(

)

()

wck3 Kg ∂p Qck ) [p - pindoor] ) wck 12µgdck µg ∂z

(21)

Cig ) Csource (at the vapor source boundary) ig

(23)

The concentrations of chemicals at the ground surface (soil-atmosphere interface) are prescribed to be their atmospheric concentration; for contaminants originating in the subsurface, this concentration is generally approximated to be 0.

Cig ) Catm ig

(24)

The concentration boundary condition at the soilfoundation crack interface results from the need to maintain continuity of chemical emissions per unit length across the soil-foundation crack interface and use of the analytical solution for chemical transport in the crack, as presented by Johnson and Ettinger (4), VOL. 39, NO. 12, 2005 / ENVIRONMENTAL SCIENCE & TECHNOLOGY

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)] [ ( ) ] [ ( [ ( )( ) ( )] ( )( ) ( ) exp

Qck * 0 Qck

Qck ) 0 Di,ck

Qck d Cig - Cindoor ig wckDi,ck ck ) Qck exp d -1 wckDi,ck ck Kg ∂p ∂Cig wck Cig - Di µg ∂z ∂z

Cig - Cindoor Kg ∂p ∂Cig ig ) Cig - Di dck µg ∂z ∂z

(25)

(26)

where Di,ck is the effective diffusion coefficient for transport of chemical i in the crack [L2/T]. Equation 26 is redundant in that it is mathematically equivalent to eq 25 in the limit as Qck f 0; however, it is inserted in the code to ensure that the limit is computed correctly. Calculation of the Indoor Air Concentration. At any time, the indoor air concentration Cindoor is determined from a ig steady-state mass balance on the enclosed space, assuming rapid mixing of the indoor air, no indoor emission sources, and no indoor reactions,

Cindoor ) ig

Es + VbAexCi,amb VbAex + Qs

(27)

where Es is the emission of chemical i to enclosed space [M/T], Aex is the enclosed space air exchange rate [1/T], Vb is the enclosed space volume [L3], Ci,amb is the concentration of compound i in ambient air entering the enclosed space [M/L3] (set equal to 0 in all simulations presented below), and Qs is the soil gas flow rate to the enclosed space [L3/T]:

Qs )

Qck * 0

Es )

Qck ) 0

∫

Lck

∫

Lck

Es )

(28)

)] [ ( ) ] [ ( exp

Qck

Qck dLck

∫

Lck

Qck d Cig - Cindoor ig wckDi,ck ck dLck Qck exp d -1 wckDi,ck ck (29)

wckDi,ck

Cig - Cindoor ig dLck dck

(30)

where each integral is performed along the crack length Lck and Cig is evaluated at the soil-foundation crack interface. The combination of eqs 27, 29, and 30 is implicit in the indoor concentration Cindoor ; therefore, in the numerical method, ig they are solved using the indoor concentration from the previous time step. As with eq 26, it should be noted that eq 30 is redundant in that it is mathematically equivalent to eq 29 in the limit as Qck f 0.

Numerical Solution A finite-difference numerical method is used to solve the series of partial differential equations and boundary conditions presented above. The numerical algorithm allows the user to choose between implicit, explicit, or Crank-Nicolson schemes, and the system of equations obtained are solved by the Gauss-Seidel iterative method (48, 49). The program allows for variable grid sizes and time steps, with the time steps being adjusted automatically. Details on the numerical method used are given in Abreu (44). Variable grid spacing is critical to the solution of this problem because the critical physical dimensions range from the 10-3 m crack width to the 100 m full domain scale. In general, the grid spacing is 4554

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finest near the foundation cracks, domain boundaries, and chemical vapor source, as shown in Figure 1. Numerical Model Verification. The numerical accuracy of the code was assessed in a number of ways. First, the output was compared with available analytical and semianalytical solutions (31, 50) for simplistic one-dimensional steady-state and transient solutions of pressure and concentration profiles in homogeneous and layered settings. Second, the numerical model output was compared with published solutions from other numerical codes (12, 51). Finally, overall mass balance checks on all chemical species are conducted by the code (e.g., chemical influxes and losses across all boundaries are quantified and summed). Details on the model verification are given in Abreu (44), and the results are only briefly summarized below. With respect to predictions of pressure fields and gas discharges, agreement with the one-dimensional analytical test cases was >99.5%. The three-dimensional steady-state disturbance pressure distribution and soil gas entry rate to an underpressurized basement for a homogeneous soil scenario was compared with Loureiro et al. (6, 12). The pressure coupling results agree well qualitatively, but the numerical model developed here predicts a stronger pressure coupling than that for a scenario presented in Loureiro et al. (12). There are also differences in predicted soil gas entry rates to the building: the predicted soil gas entry rates are greater than those of Loureiro (6) by a range of ∼1.2 to 2.5 for the cases tested with crack widths of 0.001 and 0.0005 m and soil permeabilities ranging from 10-12 to 10-9 m2. In general, the discrepancy decreases with increasing permeability. The increased soil gas entry rates are quantitatively consistent with the stronger pressure-coupling observed; for example, a scenario having a soil gas entry rate that is roughly twice as high corresponds to pressure coupling that is strengthened by about a factor of 2 relative to Loureiro (6). Whereas the source of the discrepancy between the two models is unknown, the differences in pressure coupling and soil gas entry rate are likely attributable to differences in discretization of the soil-foundation gas flow boundary condition. A transient diffusion simulation was compared to the numerical model output reported by Mendoza and Frind (51) for a source of trichloroethylene (TCE) starting at a depth of 0.3 m below surface and penetrating 0.9 m in the soil (note that for this simulation, the source is placed at the vadose zone). The contour lines of contaminant distribution in the unsaturated soil matrix had close agreement, and predictions on the mass evaporated to the atmosphere per unit volume of contaminant source agreed to within 4% of the Mendoza and Frind (50) result. Results were also compared with analytical solutions for the cases of transient one-dimensional diffusion without reaction and steady-state cases with spatially uniform and layered first-order biodegradation rates (31, 50), and agreement was >99%. Mass balance checks are performed for airflow and for all chemicals, and the results are output by the code for each model run. These results are used as a tool for refining the numerical grid on a problem-specific basis. The mass balances are performed by integrating the fluxes across all boundaries and quantifying any losses by degradation. Air flow mass balances are typically in the range of 93-99%, and individual chemical mass balances are generally >98%. The results of interest here (indoor chemical concentrations) are relatively insensitive to changes in the air flow mass balance in this range.

Results and Discussion Steady-state no-biodegradation scenarios were simulated in this initial application of the model. Three-dimensional output was summarized by the following: (a) a disturbance

TABLE 1. Input Parameters Used in Generating Figures 3-9 and Table 2 (unless otherwise noted in the figures and table) building/foundation parameters length: 10 m width: 10 m depth in soil: (i) 2.0 m (basement type), (ii) 0.2 m (slab-on-grade type) foundation thickness (dck): 0.15 m enclosed space volume (Vb): 174 m3 air exchange rate (Aex): 0.5 h-1 crack width (wck): 0.001 m total crack length: 39 m crack location: perimeter disturbance pressure (pindoor): 5 Pa

algorithm parameters numerical scheme: implicit variable time step: (i) range: 0.001 s - 100 h percent change allowed/time step: (i) pressure: 10%, (ii) concentration: 5%

contaminant vapor source properties location: base of vadose zone source size: (i) entire domain footprint (symmetrical cases) (ii) 30 m × 30 m (nonsymmetrical cases) chemical-specific properties: source vapor concentration (C source ): 200 mg/Lvapor ig molecular diffusion coefficient in air (Dai ): (i) 3.17 × 10-2 m2/h -6 m2/h molecular diffusion coefficient in water (Dw i ): (i) 3.53 × 10 overall effective diffusion coefficient for transport of chemical i in porous media (Di): 3.73 × 10-3 m2/h overall effective diffusion coefficient for transport of chemical i in the crack (Di,ck): 3.17 × 10-2 m2/h Henry’s Law constant (Hi): 0.228 m3 of water/m3 of vapor sorption coefficient of chemical i to organic carbon (Koc,i): 61.7 kg/kg of oc

soil domain dimensions in (x, y, z) directions symmetricala cases 24 m × 24 m x (3-, 8-, or 18-m depths) discretizationb: (see sample grid in Figure 1a) no. of grid nodes: 33 × 33 × (18, 29 or 42) spacing in fine grid area 0.05-0.2 m spacing in coarse grid area 0.4-2.0 m nonsymmetrical cases 100 m × 70 m × (3- or 8-m depths) discretizationb: (see sample grid in Figure 1b) no. of grid nodes: 67 × 59 × (18 or 29) spacing in fine grid area 0.05-0.2 m spacing in coarse grid area 1-8 m soil properties soil bulk density (Fb): 1700 kg/m3 mass fraction of organic carbon in the soil (foc): (i) 0.001 kg of oc/kg of soil moisture-filled porosity (φw): 0.07 m3water/m3soil total soil porosity (φT): 0.35 m3solids/m3soil soil permeability to soil gas flow (Kg): 10-11 m2 others dynamic viscosity of air (µg): 0.0648 kg/m/h qw ) 0

a The symmetrical scenario domain includes only a quarter of the building footprint in the simulation. b Note that although the grid size and distribution vary over a wide range, the discretization around the building crack area is the same for all the simulated scenarios.

pressure contour plot for a vertical cross section through the center of the building normalized to the disturbance pressure in the building; (b) two concentration contour plots normalized to the source zone vapor concentration at the lower boundary (a vertical cross section through the center of the building and a horizontal cross section at the foundation depth); (c) the soil gas flow rate into or out of the building, Qs, calculated by eq 34; and (d) the vapor attenuation coefficient (4).

R)

Cindoor ig Csource ig

(31)

Unless otherwise specified in the text and figures, the model inputs used are those summarized in Table 1. Reasonable inputs were chosen for the building dimensions, foundation thickness, crack widths, air exchange rate, and building underpressurizations on the basis of values reported in the literature (6, 7, 9, 10, 12-15, 18, 21, 28) and professional judgment. The chemical property inputs are specific to benzene, but the inputs most relevant to these steady-state and nondegradation simulations (diffusion coefficients in air and water) are representative of a wide range of chemicals of interest. The source vapor concentration was assumed to be steady (nondepleting) and chosen to be representative of total hydrocarbon concentrations measured at weathered gasoline sites (52); however, the normalized R-value and concentration contour plots for steady-state nondegradation cases are independent of the source vapor concentration. Simulations were conducted using soil properties (soil permeability, total porosity, and moisture content) representative of fine- to coarse-grained soil types. Steady-state solutions were obtained by running the model in transient

mode long enough to determine that concentrations had reached stable values. It should be noted that all simulations discussed here are for the case of uniform soil properties and good contact between the foundation and the adjacent soils. As pointed out by Garbesi et al. (19), near-surface soils adjacent to buildings may have systematically higher permeabilities at the house scale than at the small probe or laboratory measurement device scale. Higher near-foundation permeabilities or poor soil-foundation contact would allow more air flow along the foundation than is simulated here, and this would generally be expected to produce smaller indoor air concentrations and attenuation factors (R) than predicted here. The significance of this will be examined in future use of the model. General Model Behavior. Figure 3a and b presents representative normalized disturbance pressure contour plots for symmetrical basement and slab-on-grade scenarios with homogeneous soil properties (Kg ) 10-11 m2). Pressure coupling between the basement and the soil gas around the perimeter crack in the range of 25-45% is predicted. These values are in reasonable agreement with pressure coupling observed in field studies; for example, pressure coupling in the range of 20-40% in the vicinity of basement walls was observed by Nazaroff et al. (7) and Garbesi et al. (24). To gain insight into model dependencies on inputs and to assess the reasonableness of model output, symmetrical and homogeneous scenarios were studied first. These are summarized in Table 2 and are briefly discussed here. The dependence of soil gas entry flow rates (Qs) on crack width and soil permeability to vapor flow (Kg) was examined for basement scenarios with a lower boundary located 8 m below ground surface (bgs) (6 m below the basement foundation), VOL. 39, NO. 12, 2005 / ENVIRONMENTAL SCIENCE & TECHNOLOGY

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TABLE 2. Summary of Model Results for Symmetrical Scenarios inputs Oω

Qs (L/min)

r

Construction Type: Basement 20 1.0 × 10-11 0.35 10 1.0 × 10-11 0.35 5 1.0 × 10-11 0.35 2.5 1.0 × 10-11 0.35 0 1.0 × 10-11 0.35 -2.5 1.0 × 10-11 0.35 -5 1.0 × 10-11 0.35 20 1.0 × 10-12 0.35 5 1.0 × 10-12 0.35 0 1.0 × 10-12 0.35 -5 1.0 × 10-12 0.35 20 1.0 × 10-13 0.45 5 1.0 × 10-13 0.45 0 1.0 × 10-13 0.45 -5 1.0 × 10-13 0.45 20 1.0 × 10-11 0.35 10 1.0 × 10-11 0.35 5 1.0 × 10-11 0.35 2.5 1.0 × 10-11 0.35 0 1.0 × 10-11 0.35 -2.5 1.0 × 10-11 0.35 -5 1.0 × 10-11 0.35 20 1.0 × 10-11 0.35 5 1.0 × 10-11 0.35 0 1.0 × 10-11 0.35 -5 1.0 × 10-12 0.35 20 1.0 × 10-13 0.45 5 1.0 × 10-13 0.45 0 1.0 × 10-13 0.45 -5 1.0 × 10-13 0.45 5 1.0 × 10-14 0.45 5 1.0 × 10-13 0.45 5 1.0 × 10-12 0.35 5 1.0 × 10-11 0.35 5 1.0 × 10-10 0.3 5 1.0 × 10-9 0.3 5 1.0 × 10-11 0.35 -10 5 1.0 × 10 0.3

0.07 0.07 0.07 0.07 0.07 0.07 0.07 0.07 0.07 0.07 0.07 0.15 0.15 0.15 0.15 0.07 0.07 0.07 0.07 0.07 0.07 0.07 0.07 0.07 0.07 0.07 0.15 0.15 0.15 0.15 0.185 0.15 0.07 0.07 0.03 0.03 0.07 0.03

3.74 × 10-3 3.74 × 10-3 3.74 × 10-3 3.74 × 10-3 3.74 × 10-3 3.74 × 10-3 3.74 × 10-3 3.74 × 10-3 3.74 × 10-3 3.74 × 10-3 3.74 × 10-3 2.84 × 10-3 2.84 × 10-3 2.84 × 10-3 2.84 × 10-3 3.74 × 10-3 3.74 × 10-3 3.74 × 10-3 3.74 × 10-3 3.74 × 10-3 3.74 × 10-3 3.74 × 10-3 3.74 × 10-3 3.74 × 10-3 3.74 × 10-3 3.74 × 10-3 2.84 × 10-3 2.84 × 10-3 2.84 × 10-3 2.84 × 10-3 1.88 × 10-3 2.84 × 10-3 3.74 × 10-3 3.74 × 10-3 4.50 × 10-3 4.50 × 10-3 3.74 × 10-3 4.50 × 10-3

12.36 6.18 3.09 1.54 0.00 -1.54 -3.09 1.25 0.31 0.00 -0.31 0.12 0.03 0.00 -0.03 15.89 7.95 3.97 1.99 0.00 -1.99 -3.97 1.60 0.40 0.00 -0.40 0.16 0.04 0.00 -0.04 0.004 0.04 0.38 2.35 4.95 5.56 3.69 21.26

5.50 × 10-3 3.21 × 10-3 1.75 × 10-3 9.08 × 10-4 7.80 × 10-5 6.25 × 10-9 9.30 × 10-14 7.35 × 10-4 2.07 × 10-4 7.80 × 10-5 1.84 × 10-5 1.20 × 10-4 8.60 × 10-5 7.60 × 10-5 6.70 × 10-5 3.93 × 10-3 2.19 × 10-3 1.17 × 10-3 6.08 × 10-4 3.99 × 10-5 8.99 × 10-11 2.36 × 10-17 4.99 × 10-4 1.33 × 10-4 3.99 × 10-5 5.54 × 10-6 6.99 × 10-5 4.57 × 10-5 3.90 × 10-5 3.30 × 10-5 1.12 × 10-5 1.82 × 10-5 1.20 × 10-4 7.14 × 10-4 1.45 × 10-3 1.65 × 10-3 1.09 × 10-3 5.04 × 10-3

1 1 1 1 1 1 5 5 5 5 5 10 10 15 15 15 15 15 15 1 1 1 1 1 1 1

Construction Type: Basement 5 1.0 × 10-14 0.45 5 1.0 × 10-13 0.45 5 1.0 × 10-12 0.35 5 1.0 × 10-11 0.35 5 1.0 × 10-10 0.3 5 1.0 × 10-9 0.3 5 1.0 × 10-14 0.45 5 1.0 × 10-13 0.45 5 1.0 × 10-12 0.35 5 1.0 × 10-11 0.35 5 1.0 × 10-9 0.3 5 1.0 × 10-12 0.35 5 1.0 × 10-9 0.3 5 1.0 × 10-14 0.45 5 1.0 × 10-13 0.45 5 1.0 × 10-12 0.35 5 1.0 × 10-11 0.35 5 1.0 × 10-10 0.3 5 1.0 × 10-9 0.3 20 1.0 × 10-11 0.35 10 1.0 × 10-11 0.35 7.5 1.0 × 10-11 0.35 5 1.0 × 10-11 0.35 2.5 1.0 × 10-11 0.35 -0.5 1.0 × 10-11 0.35 -2.5 1.0 × 10-11 0.35

0.185 0.15 0.07 0.07 0.03 0.03 0.185 0.15 0.07 0.07 0.03 0.07 0.03 0.185 0.15 0.07 0.07 0.03 0.03 0.07 0.07 0.07 0.07 0.07 0.07 0.07

1.88 × 10-3 2.84 × 10-3 3.74 × 10-3 3.74 × 10-3 4.50 × 10-3 4.50 × 10-3 1.88 × 10-3 2.84 × 10-3 3.74 × 10-3 3.74 × 10-3 4.50 × 10-3 3.74 × 10-3 4.50 × 10-3 1.88 × 10-3 2.84 × 10-3 3.74 × 10-3 3.74 × 10-3 4.50 × 10-3 4.50 × 10-3 3.74 × 10-3 3.74 × 10-3 3.74 × 10-3 3.74 × 10-3 3.74 × 10-3 3.74 × 10-3 3.74 × 10-3

0.004 0.04 0.40 3.97 36.16 190.16 0.004 0.04 0.40 4.00 398.16 0.40 401.28 0.004 0.04 0.40 4.00 40.16 401.59 16.31 8.15 6.12 4.08 2.04 -0.41 -2.04

3.77 × 10-5 4.57 × 10-5 1.33 × 10-4 1.17 × 10-3 7.65 × 10-3 1.45E-02 1.14 × 10-4 1.42 × 10-4 2.22 × 10-4 1.19 × 10-3 2.59E-02 2.95 × 10-4 2.61E-02 1.73 × 10-4 2.36 × 10-4 3.40 × 10-4 1.21 × 10-3 8.40 × 10-3 2.61 × 10-2 2.17 × 10-3 1.12 × 10-3 8.50 × 10-4 5.75 × 10-4 2.89 × 10-4 2.34 × 10-6 2.53 × 10-11

1 1 1

Construction Type: Slab-on-Grade 20 1.0 × 10-11 0.35 10 1.0 × 10-11 0.35 5 1.0 × 10-11 0.35

0.07 0.07 0.07

3.74 × 10-3 3.74 × 10-3 3.74 × 10-3

19.78 9.89 4.94

3.62 × 10-3 2.12 × 10-3 1.17 × 10-3

depth bgs (m)

Lsa (m)

Ab (m2)

Lck (m)

wck (mm)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38

3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8

1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6

100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100

39 39 39 39 39 39 39 39 39 39 39 39 39 39 39 39 39 39 39 39 39 39 39 39 39 39 39 39 39 39 39 39 39 39 39 39 39 39

1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0.25 0.25 0.25 0.25 0.25 0.25 0.5 0.5

39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64

8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 18 18 18 18 18 18 18

6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 16 16 16 16 16 16 16

100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100

39 39 39 39 39 39 39 39 39 39 39 39 39 39 39 39 39 39 39 39 39 39 39 39 39 39

65 66 67

3 3 3

100 100 100

39 39 39

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2.8 2.8 2.8

outputs

Dig + Diw/Hi (m2/h)

simulation no.

pindoor (Pa)

ENVIRONMENTAL SCIENCE & TECHNOLOGY / VOL. 39, NO. 12, 2005

Kg (m2)

OT

TABLE 2. (Continued) inputs simulation no.

depth bgs (m)

Lsa (m)

Ab (m2)

Lck (m)

wck (mm)

68 69 70 71 72 73 74 75 76

3 3 3 18 18 18 18 18 18

2.8 2.8 2.8 17.8 17.8 17.8 17.8 17.8 17.8

100 100 100 100 100 100 100 100 100

39 39 39 39 39 39 39 39 39

1 1 1 1 1 1 1 1 1

a

pindoor (Pa)

outputs

Kg (m2)

OT

Construction Type: Slab-on-Grade 2.5 1.0 × 10-11 0.35 0.5 1.0 × 10-11 0.35 -2.5 1.0 × 10-11 0.35 20 1.0 × 10-11 0.35 10 1.0 × 10-11 0.35 5 1.0 × 10-11 0.35 2.5 1.0 × 10-11 0.35 0.5 1.0 × 10-11 0.35 -2.5 1.0 × 10-11 0.35

Oω

Dig + Diw/Hi (m2/h)

Qs (L/min)

r

0.07 0.07 0.07 0.07 0.07 0.07 0.07 0.07 0.07

3.74 × 10-3 3.74 × 10-3 3.74 × 10-3 3.74 × 10-3 3.74 × 10-3 3.74 × 10-3 3.74 × 10-3 3.74 × 10-3 3.74 × 10-3

2.47 0.49 -2.47 20.42 10.21 5.10 2.55 0.51 -2.55

6.08 × 10-4 1.29 × 10-4 2.55 × 10-12 1.10 × 10-3 5.62 × 10-4 2.84 × 10-4 1.40 × 10-4 2.83 × 10-5 2.59 × 10-13

Ls: source-foundation vertical separation.

and a building underpressurization of 5 Pa, and the results are reported in Table 2. The behavior of Qs vs Kg and crack width is similar to that presented by Mowris and Fisk (9) and Loureiro (7); changes in Qs are generally proportional to changes in Kg and are relatively insensitive to crack width >0.1 mm, except where the soil permeability is >10-11 m2 (corresponding to relatively coarse materials). Even then, the dependence on crack width is only evident for crack widths 1 m, and it is expected that Figure 4 would show a linearly increasing relationship between R and Qs, at high Qs, for vapor sources located adjacent to foundations. Although not evident in Figure 4 because of the vertical scale, building pressurization can have a significant effect in reducing contaminant vapor intrusion; there are significant reductions in R for negative values of Qs (corresponding to building overpressurization; see Table 2). Figure 4 also illustrates that the model anticipates decreasing R values (increasing attenuation) with increasing vapor source depth. For reference, field-measured R values summarized by Hers et al. (2) for nondegrading chemicals often fall in the range of 10-5-10-2, which is consistent with the model output presented in Figure 4. Results for a slab-on-grade construction overlying a 3-m- and an 18-m-deep vapor source are similar to those for basement constructions; the R-values are slightly smaller and generally exhibit the same dependence on Qs. Effect of Vapor Source-Building Lateral Separation on Vapor Attenuation Coefficients. As discussed previously, there is interest in using the numerical code to begin developing a better understanding of the relationships between vapor source-building lateral separation, building construction, and indoor air impacts. For this purpose, all model inputs were held fixed (as summarized in Table 1)

FIGURE 3. (a) Normalized soil gas disturbance pressure distribution for a symmetrical basement scenario with homogeneous soil permeability (Kg ) 10-11 m2). The contours are normalized to the building disturbance pressure. (b) Normalized soil gas disturbance pressure distribution for a symmetrical slab-on-grade foundation scenario with homogeneous soil permeability (Kg ) 10-11 m2). The contours are normalized to the building disturbance pressure. except the lateral distance between the source and building and the vapor source depth. As suggested by the results in Table 2 and Figure 4, the qualitative and quantitative behavior presented below is likely not to be affected significantly by reasonable changes in crack width and soil gas permeability over a range of conditions typical of many settings (crack widths >1 mm and permeabilities 1 m below a foundation, the dependence of R on building underpressurization can be either subtle (at higher soil gas entry rates) or drastic (at low to negative soil gas entry rates). Thus, the establishment of regulatory criteria for vapor source-building distances beyond which the pathway is a priori not of concern would need to be, at a minimum, dependent on the depth to the vapor source, the vapor source strength, and the chemical-specific target breathing concentration. The results also hint at the need to examine other scenarios, in particular, those involving degrading chemicals. It is anticipated that the R vs separation distance relationship

FIGURE 11. Sample output for a slab-on-grade scenario similar to the basement scenario in Figure 5, but with aerobic biodegradation (λi ) 0.18 h-1) and stoichiometrically related hydrocarbon and oxygen rates (3 mg of O2/mg of hydrocarbon). Vertical profiles through the building and source footprint centerlines: (a) hydrocarbon contours normalized to the vapor source concentration and (b) oxygen contours normalized to the atmospheric concentration. could be much more sensitive to separation distance than shown in Figure 9 for nondegrading chemicals. Simulations involving permeable layers adjacent to foundations for both degrading and nondegrading chemicals and simulations involving foundation soil gas entry points different from those studied here would also be of interest. Scenarios involving aerobically biodegrading chemicals are being studied and reported in Abreu (44) and Abreu and Johnson (45). Figure 10 presents preliminary output from VOL. 39, NO. 12, 2005 / ENVIRONMENTAL SCIENCE & TECHNOLOGY

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this work for a case similar to Figure 5, with λi ) 0.18 h-1, oxygen consumption linked stoichiometrically to hydrocarbon biodegradation at the rate of 3 mg of O2/mg of hydrocarbon, and a minimum oxygen threshold concentration for biodegradation equal to 5% of the atmospheric oxygen concentration (normalized concentration of 0.05 in Figures 10 and 11). For the simulations presented in Figures 10 and 11, the following oxygen properties were used: Dai ) 7.2 × -6 10-2 m2/h, Dw m2/h, Di ) 8.48 × 10-3 m2/h, Di,ck i ) 8.7 × 10 ) 7.2 × 10-2 m2/h, Koc,i ) 0, Hi ) 31.6 m3 water/m3 vapor. Figure 10 presents vertical cross sections showing oxygen and hydrocarbon concentration contours, normalized to the maximum concentrations of each. The effect of biodegradation is evident in a visual comparison of Figures 5 and 10 and in their R values, which differ by ∼2 orders of magnitude. Figure 11 presents the comparable slab-on-grade simulation. In this case, the R value for the biodegradation scenario (R ) 10-8) is ∼5 orders of magnitude less than the R value for the equivalent no-biodegradation scenario plotted in Figure 9. Whereas the concentration contours for the no-biodegradation case are not presented, the decrease in R appears to reflect an increased attenuation of vapor concentrations beneath the periphery of the foundation. The ongoing studies are examining the effects of changes in kinetic parameters, source vapor concentration, source placement (depth and lateral location) and foundation crack location.

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Acknowledgments The authors acknowledge the generous support of CNPqBrazil under grant No. 201046/97-0 and the Mobil Foundation for this research. The authors also thank the reviewers of this article for their encouragement and constructive suggestions.

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Literature Cited (1) ) USEPA Draft guidance for evaluating the vapor intrusion to indoor air pathway from groundwater and soils (subsurface vapor intrusion guidance). OSWER, 2002. http://www.epa.gov/ correctiveaction/eis/vapor/guidance.pdf (accessed Oct 2004). (2) Hers, I.; Zapf-Gilje, R.; Johnson, P. C.; Li, L. Evaluation of the Johnson and Ettinger model for prediction of indoor air quality. Ground Water Monit. Rem. 2003, 23 (1), 62-76. (3) Johnson, P. C.; Ettinger, R. A.; Kurtz, J.; Bryan, R.; Kester, J. E. Migration of soil gas vapors to indoor air: Determining vapor attenuation factors using a screening-level model and field data from the CDOT-MTL Denver, Colorado. API Soil and Groundwater Task Force Bulletin No. 16; American Petroleum Institute: Washington, DC, 2002. (4) Johnson, P. C.; Ettinger, R. A. Heuristic model for predicting the intrusion rate of contaminant vapors into buildings. Environ. Sci. Technol. 1991, 25, 1445-1452. (5) Nazaroff, W. W.; Feustel, H.; Nero, A. V.; Revzan, K. L.; Grimsrud, D. T. Radon transport into a detached one-story house with a basement. Atmos. Environ. 1985, 19(1), 31-46. (6) Loureiro, C. O. Simulation of the steady-state transport of radon from soil into houses with basements under constant negative pressure. LBL-24378; Ph.D. Dissertation, Lawrence Berkeley Laboratory, Berkeley, CA, 1987. (7) Nazaroff, W. W.; Lewis, S. R.; Doyle, S. M.; Moed, B. S.; Nero, A. V. Experiments on pollutant transport from soil into residential basements by pressure-driven airflow. Environ. Sci. Technol. 1987, 21, 459-466. (8) Radon and Its Decay Products in Indoor Air; Nazaroff, W. W., Nero, A. V., Eds.; John Wiley & Sons: New York, 1988. (9) Mowris, R. J.; Fisk, W. J. Modeling the effects of exhaust ventilation on 222Rn entry rates and indoor 222Rn concentrations. Health Phys. 1988, 54(5), 491-501. (10) Garbesi, K.; Sextro, R. G. Modeling and field evidence of pressuredriven entry of soil gas into a house through permeable belowgrade walls. Environ. Sci. Technol. 1989, 23, 1481-1487. (11) Narasimhan, T. N.; Tsang, Y. W.; Holman, H. Y. On the importance of transient air flow in advective entry into buildings. Geophys. Res. Lett. 1990, 17(6), 821-824. (12) Loureiro, C. O.; Abriola, L. M.; Martin, J. E.; Sextro, R. G. Threedimensional simulation of radon transport into houses with 4560

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(36) Chowdhury, S.; Brock, S. L. Indoor air inhalation risk assessment for volatiles emanating from light nonaqueous phase liquids. Soil Sediment Contam. 2001, 10(4), 387-403. (37) DeVaull, G. E.; Ettinger, R. A.; Gustafson, J. B. Chemical vapor intrusion from soil or groundwater to indoor air: significance of unsaturated zone biodegradation of aromatic hydrocarbons. Soil Sediment Contam. 2002, 11(4), 625-641. (38) MADEP (Massachusetts Department of Environmental Protection); Indoor air sampling and evaluation guide. Office of Research and Standards, Boston, MA, 2002; http://www.mass.gov/dep/ors/files/indair.pdf (accessed Oct 2004). (39) MADEP (Massachusetts Department of Environmental Protection); Guidelines for the design, installation, and operation of sub-slab depressurization systems. Northeast regional office, 1995; http://www.state.ma.us/dep/nero/bwsc/files/ssd1e.pdf (accessed Oct 2004). (40) Parker, J. C. Modeling volatile chemical transport, biodecay, and emission to indoor air. Ground Water Monit. Rem. 2003, 23(1), 107-120. (41) Sanders, P. F.; Talimcioglu, N. M. Soil-to-indoor air exposure models for volatile organic compounds: the effect of soil moisture. Environ. Toxicol. Chem. 1997, 16(12), 2597-2604. (42) Turczyowicz, L.; Robinson, N. A model to derive soil criteria for benzene migrating from soil to dwelling interior in homes with crawl spaces. Hum. Ecol. Risk Assess. 2001, 7(2), 387-415. (43) Patankar, S. V. Numerical Heat Transfer and Fluid Flow, 1st ed.; McGraw-Hill Book Co.: New York, 1980. (44) Abreu, L. D. V. A transient three-dimensional numerical model to simulate vapor intrusion into buildings. Ph.D. Dissertation, Arizona State University, Tempe, AZ, 2005.

(45) Abreu, L. D. V.; Johnson, P. C. Modeling the effect of aerobic biodegradation on soil vapor intrusion into buildingssinfluence of degradation rate, source concentration, and depth. Environ. Sci. Technol., submitted for publication. (46) Massmann, J. W. Applying groundwater flow models in vapor extraction system design. J. Environ. Eng. 1989, 115(1), 129149. (47) Millington, R. J.; Quirk, J. P. Permeability of porous solids. Trans. Faraday Soc. 1961, 57, 1200-1207. (48) Carnahan, B.; Luther, H. A.; Wilkes, J. O. Applied Numerical Methods; John Wiley & Sons: New York, 1969. (49) Rao, S. S. Applied Numerical Methods for Engineers and Scientists; Prentice Hall: Upper Saddle River, NJ, 2002. (50) Johnson, P. C.; Herts, M. B.; Byers, D. L. Estimates for hydrocarbon vapor emissions resulting from service station remediation and buried gasoline-contaminated soil. In Petroleum Contaminated Soils; Kostecki, P. T., Calabrese, E. J., Eds.; Lewis Publishers: Chelsea, MI, 1989; Vol. 3, Chapter 22. (51) Mendoza, C. A.; Frind, E. O. Advective-dispersive transport of dense organic vapors in the unsaturated zone 2. Sensitivity analysis. Water Resour. Res. 1990, 26(3), 388-398. (52) Roggemans, S.; Bruce, C. L.; Johnson, P. C. Vadose zone natural attenuation of hydrocarbon vapors: an empirical assessment of soil gas vertical profile data. API Technical Bulletin No. 15; American Petroleum Institute: Washington, DC, 2002.

Received for review February 12, 2004. Revised manuscript received November 10, 2004. Accepted February 24, 2005. ES049781K

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