A Petroleum Vapor Intrusion Model Involving Upward Advective Soil

Aug 31, 2015 - Laboratory of Environmental Engineering, Department of Civil Engineering and Computer Science Engineering, University of Rome “Tor Ve...
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A Petroleum Vapor Intrusion Model Involving Upward Advective Soil Gas Flow Due to Methane Generation Yijun Yao,†,‡,§ Yun Wu,†,‡,§ Yue Wang,†,‡,§ Iason Verginelli,∥ Tian Zeng,†,‡,§ Eric M. Suuberg,⊥ Lin Jiang,# Yuezhong Wen,*,†,‡,§ and Jie Ma*,¶ †

MOE Key Lab of Environmental Remediation and Ecosystem Health, College of Environmental and Resource Sciences, ‡ Research Center for Air Pollution and Health, and §Institute of Environmental Science, Zhejiang University, Hangzhou 310058, China ∥ Laboratory of Environmental Engineering, Department of Civil Engineering and Computer Science Engineering, University of Rome “Tor Vergata”, Via del Politecnico, 1 00133 Rome, Italy ⊥ School of Engineering, Brown University, Providence, Rhode Island 02912, United States # Beijing Municipal Research Institute of Environmental Protection, Beijing 100037, China ¶ State Key Laboratory of Heavy Oil Processing, Beijing Key Lab of Oil & Gas Pollution Control, China University of Petroleum-Beijing, Beijing 102249, China S Supporting Information *

ABSTRACT: At petroleum vapor intrusion (PVI) sites at which there is significant methane generation, upward advective soil gas transport may be observed. To evaluate the health and explosion risks that may exist under such scenarios, a one-dimensional analytical model describing these processes is introduced in this study. This new model accounts for both advective and diffusive transport in soil gas and couples this with a piecewise first-order aerobic biodegradation model, limited by oxygen availability. The predicted results from the new model are shown to be in good agreement with the simulation results obtained from a three-dimensional numerical model. These results suggest that this analytical model is suitable for describing cases involving open ground surface beyond the foundation edge, serving as the primary oxygen source. This new analytical model indicates that the major contribution of upward advection to indoor air concentration could be limited to the increase of soil gas entry rate, since the oxygen in soil might already be depleted owing to the associated high methane source vapor concentration.

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INTRODUCTION Subsurface vapor intrusion (VI) is a process by which volatile compounds (VOCs), released from contaminated soil and groundwater, migrate into the enclosed space of a building located above the contamination, potentially resulting in negative health effects for residents.1,2 In particular, the subsurface to indoor air VI pathway involving organic compounds such as petroleum hydrocarbons, which may be released into the subsurface from leakage of underground storage tanks, has gained increased attention in recent years as a potential mechanism for long-term exposure to VOCs.3 To identify the buildings that can be threatened by such hydrocarbon vapors, the U.S. Environmental Protection Agency (EPA) recently proposed screening criteria for vertical source-receptor separation distance considering the aerobic biodegradation potential of petroleum hydrocarbons.4,5 However, EPA also warned that such criteria might not be conservative enough for sites with the presence of significant methane generation.4 Indeed in such scenarios, petroleum vapor intrusion (PVI) potential can be increased due to © XXXX American Chemical Society

oxygen consumption by competitive methane bio-oxidation as well as the upward advective soil gas flow caused by the accumulation of fermentative gas (methane and carbon dioxide) in the source zone.6−9 Moreover, methane intrusion (MI) may itself in certain cases pose an explosion hazard in the enclosed space of a building located above a contaminant plume.9−16 Though there have been some studies of health risks caused by PVI and the potentially associated MI and explosion risk,9,11,13,15,16 only a few of these considered the role of upward soil gas advection. For instance, Salanitro et al. in 1989 conducted a soil column experiment by imposing a constant soil gas advection in order to study the biodegradation of aromatic hydrocarbons in unsaturated soil.17 Moyer et al. performed a biodegradation experiment by subjecting intact soil cores, which Received: March 14, 2015 Revised: August 25, 2015 Accepted: August 31, 2015

A

DOI: 10.1021/acs.est.5b01314 Environ. Sci. Technol. XXXX, XXX, XXX−XXX

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Environmental Science & Technology Table 1. Equations of the Screening Model

cases involving upward advection due to significant methane generation. Independent of building operational conditions, this new model can be easily employed to predict subslab vapor concentration for both methane and other hydrocarbons, in the presence or absence of upward advective soil gas flow. Simulation results from this new model are compared with those of a 3-D numerical model,9,23,24 and used to investigate the role of upward advection in PVI and MI.

were collected from an aviation gasoline release site, to an upward flow of nitrogen, oxygen, water vapor, and hydrocarbon vapors.18,19 In a recent study conducted by Ma et al.,9 a threedimensional (3-D) numerical model was employed to simulate the influence of source concentration of methane and soil gas pressure build-up in a situation involving ethanol-blended fuel release fermentation; the VI potential of both methane and benzene was examined. The authors reported that if the methanogenic activity is sufficiently strong to increase gas pressure and cause advective gas transport near the source zone, methane could build up to potentially flammable levels (>5% v/v) in overlying buildings. Furthermore, based on the different simulations carried out by the same authors it was shown that the presence of high concentrations of methane may deplete oxygen and inhibit benzene aerobic degradation, thus resulting in a higher benzene VI potential. Though these studies provided some basic understandings regarding the influence of upward advection in PVI and MI, up to now there have been few simple, effective models or screening tools that have included upward advection effects. Indeed, most of the current analytical mathematical models, used as PVI screening tools, such as BioVapor, AAMB, and the Verginelli & Baciocchi Model,20−22 are based on the assumption that diffusion dominates source-to-building soil gas transport. For example, in a previous study, BioVapor was used to simulate soil gas concentrations of methane and benzene in the absence of upward advective soil gas flow.13 In the presence of upward advective soil gas flow, subslab vapor concentrations and soil gas entry rate into a building can be significantly increased, raising the potential of PVI and MI.9 Under such scenarios, the explosion hazards of MI and health risks of PVI would be underestimated by using models that neglect the upward advective soil gas flow. In this study, we introduce a one-dimensional (1-D) analytical model as a screening tool for the risk assessment of PVI and MI in

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MODEL DEVELOPMENT In a 1-D PVI (and MI) scenario, the general governing equations for soil vapor transport in steady-state are shown as eq T1 and T2 in Table 1, for cases without and with upward advective soil gas flow, respectively. As employed in previous models,9,20−22,24 a piecewise aerobic biodegradation is assumed here, shown as eq T3 in Table 1. This means that a first-order biodegradation can occur only if the oxygen concentration is greater than 1% v/v; otherwise, there is no reaction. The boundary conditions for contaminants and oxygen are shown in eq T4 in Table 1. The effective diffusivities of contaminants and oxygen in soil are calculated according to the Millington and Quirk equation25 and the soil permeability can be obtained based on moisture content and soil type according to the van Genuchten equation,26 as also employed in the EPA spreadsheet version of the Johnson−Ettinger model.27 In this model, the contaminant concentration at open ground surface and oxygen flux at the bottom of the domain (usually the water table) are assumed to be zero. The transport length L for oxygen movement from open ground surface to subslab source zone can be estimated according to a recent study by Verginelli and Baciocchi,21 as shown in eq T5 and Figure 1. In summary, this analytical model is designed for application in a scenario involving a building with an impermeable foundation surrounded by open ground surface, where the atmosphere is regarded as the primary oxygen source. B

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Analytical Model in the Presence of Upward Advective Soil Gas Flow. At sites with significant methane generation, a pressure gradient may be observed between source and ground surface, inducing upward advective soil gas transport in the vadose zone.9,14 In eq T2, the constant soil gas velocity can be estimated using the following equation:

k p ps

u=

d ci dz 2

=

λiθw ci Hi

with boundary conditions ⎧ dci = 0, z = ds − df ⎪ ⎪ dz ⎨ cis ⎪ ci = , z = Lb ⎪ 1 + L b λiθw HiDi ⎩

(5)

It is generally assumed that diffusion dominates soil gas transport if Pe < 1.32 In the presence of upward advection due to significant methane generation, the thickness of the anaerobic zone can be obtained by assuming methane as the major oxygen consumer. Using a stoichiometric mass balance and assuming an instantaneous reaction at the aerobic/anoxic interface, we have an equation similar to eq 1:27,28

(1)

( ) = uc exp( ) − 1 uLb Dm

cms exp

The thickness of the anoxic zone Lb (see Figure 1) can be obtained by solving this equation, and the result is shown as eq 6 in Table 1. To reach a fully anoxic subslab condition, the position of aerobic/anoxic interface should be above the bottom of the building foundation, which means Lb ≥ (ds − df). In such scenarios, the methane and petroleum chemicals can be handled as nonbiodegradable contaminants just as are tetrachloroethylene (PCE) and trichloroethylene (TCE) and other chlorinated contaminants of concern in VI.29 Thus, the contaminant subslab vapor concentration can be estimated according to a previously developed method, as shown in eq T8. Conversely, if the calculated anoxic zone thickness is below the bottom of the foundation, Lb < (ds − df), the following equation can be used to estimate the subslab vapor concentration:

Di

uL Dm

Pe =

Analytical Model in the Absence of Significant Upward Advective Soil Gas Flow. If the source-to-subslab soil gas transport is dominated by diffusion, the position of aerobic/ anoxic interface can be determined by assuming instantaneous biodegradation reaction and a stoichiometric mass balance according to an equation suggested by Roggemans et al.:28

2

(4)

It should be noted that although the source pressure ps could be in principle estimated as a function of methane generation rate and soil permeability, in this study, similarly to a previous work,9 ps is required as an independent input of the model. An alternative way to estimate the upward soil gas velocity is to use the soil gas concentrations of nitrogen measured at different depths.32,33 Once a velocity is known, the Peclet number can be used to identify the dominant soil gas transport mechanism:

Figure 1. Conceptual scenario of the screening model (ds is the source depth below ground surface (m), Lb is the thickness of the anaerobic zone (m), df is the depth of the building foundation below ground surface, Lslab is the half side length of the building).

∑ δiDicis c atm − comin = Do o Lb L − Lb

μ L

uδm

uLb Dm

atm o

( ) )−1

− comin exp

(

exp

u(L − Lb) Do

u(L − Lb) Do

(6)

By assuming Dm ≈ Do, the position of the aerobic/anaerobic interface can be obtained by solving eq 6, as shown in eq T7 in Table 1. If the calculated Lb is greater than ds − df, the subslab vapor concentration is approximated to be equal to the source vapor concentration (i.e., no attenuation). Otherwise, the following equation needs to be solved to estimate the subslab vapor concentration: Di

d 2ci dz

2

=u

dci λθ + i w ci dz Hi

(7)

with boundary conditions ⎧ dci z = ds − df = 0, ⎪ ⎪ dz ⎪ uL ⎨ ucis exp Db − ci d2ci ⎪ i , z = Lb ⎪ uci − Di dz 2 = uLb exp D − 1 ⎪ ⎩ i

(2)

( ) ( )

(8)

The subslab vapor concentration is approximated as ci|z=ds − df, as shown in eq T9. It is worth noting that when the soil gas entry rate into the building can be increased by upward soil gas flow,9 the generic AF previously recommended by U.S. EPA34 may no longer be appropriate for estimating indoor air concentration. Also, while the traditional CST equation can still be used to calculate the indoor air concentration, the soil gas entry rate into the building should be estimated by using a modified Nazaroff equation, as shown in eq T11 in Table 1.

(3)

The subslab vapor concentration is represented as ci|z=ds − df, as shown in eq T8. On the basis of the calculated subslab vapor concentration, the indoor air concentration can be calculated by using either an empirical attenuation factor (AF) approach or the traditional equation of continuous stirred tank (CST),27,30 as shown in eq T12. The soil gas entry rate into the enclosed space may be estimated using the Nazaroff equation,31 as shown in eq T10. C

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Table 2. Input Parameters Used in Figures 2 and 3.9,24 Building/Foundation Parameters foundation footprint size: 10 m × 10 m depth of foundation(df): 2m crack width (Wck): 0.001 m thickness of crack (dck): 0.15 m crack location: perimeter disturbance pressure (ΔP): 5 Pa Soil Properties

Figure 2. Comparison of soil gas entry rate (Qb) into the building by using the 3-D numerical model9 and the analytical model proposed in this study.

soil permeability (kp): 10−11 m2 viscosity of soil gas (μ): 1.8 × 10−6 kg/m/s soil bulk density (ρb): 1700 kg/m3 total porosity (θt): 0.35

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RESULTS AND DISCUSSIONS Comparison with 3-D Simulations. Figures 2 and 3 show the comparison between 3-D simulations9 and the new analytical model for the predicted soil gas entry rate into the building and indoor air concentrations, respectively. The parameters employed to generate Figures 2 and 3 are shown in Table 2,9,24 and the statistical results of the comparisons are shown in Table 3. In Figures 2 and 3, the 45° line shows where ideal agreement with the 3-D simulations would be found. It can be seen that most of the soil gas entry rates predicted by the analytical model fall in a range of 0.5−2 times of the simulated results obtained using the 3-D numerical model, showing a good agreement. Figure 2 also indicates that in the original 3-D modeling work,9 changes of source vapor pressure (in a range of 0−200 Pa) and vertical building-source separation distance resulted in a variation in the predicted soil gas entry rate (in a range of 1−13 m) of up to 2 orders of magnitude. It is also worth mentioning that although the van Genuchten equation is generally recommended for calculating soil permeability, for the comparisons in Figures 2 and 3, to be consistent with the 3-D simulations, a constant soil permeability of 10−11 m2 was used.

water-filled porosity (θw): 0.07 Vapor Source Properties depth to source (ds): 3, 5, 8, 15 m location: base of vadose zone size: entire domain footprints

Chemical Properties contaminant type: benzene and methane effective diffusivity of benzene in soil (Db): 1.03 × 10−6 m2/s air−water partition coefficient of benzene (Hb): 0.228 first order degradation rate constant of benzene in water (λb): 0.18 h−1 stoichiometric coefficient of benzene to oxygen (δb): 7.5 mol-oxygen/mol-benzene Effective diffusivity of methane in soil (Dm): 2.29 × 10−6 m2/s air−water partition coefficient of methane (Hm): 29.9 first order degradation rate constant of methane in water (λm): 82 h−1 stoichiometric coefficient of methane to oxygen (δm): 2 mol-oxygen/mol-methane effective diffusivity of oxygen in soil (Do): 2.34 × 10−6 m2/s air−water partition coefficient of oxygen (Ho): 31.6 minimum oxygen concentration required for biodegradation to occur (cmin o ): 1% v/v

Figure 3 shows a comparison of predicted methane (3a) and benzene (3b) indoor air concentrations from 3-D numerical simulations9 and the new analytical model developed in this study. It should be noted that for this comparison the traditional CST equation (see eq T12) was used for calculating indoor air concentrations. Points of different colors represent different simulated scenarios, as explained in the figures. It can be noted that the predictions of the soil gas entry rates and chemical indoor concentrations from the this new analytical model are both generally in good agreement with the 3-D numerical results, especially for cases involving positive source

Figure 3. Comparison of predicted indoor air concentration of (a) methane and (b) benzene using the 3-D model9 (x-axis) and the analytical methods proposed in this paper (y-axis). D

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Table 3. Statistical Results for the Comparison between the Analytical Predictions and Numerical Simulations (the Units of Qb, cin m, 3 and cin b are L/min, % v/v, and g/m , Respectively) variables log(Qb) log(cinm)

log(cinb )

scenarios

number of calculations

standard deviation

maximum deviation

pearson correlation coefficient (significance)

no biodegradation diffusion and biodegradation advection and diffusion and biodegradation diffusion and biodegradation advection and diffusion and biodegradation

40 48 48 36 48 36

0.36 0.15 0.62 0.29 1.43 0.26

0.36 0.21 1.79 0.62 1.82 0.61

0.95(0.00) 0.99(0.00) 0.99(0.00) 0.97(0.00) 0.99(0.00) 0.97(0.00)

Figure 4. Sensitivity analysis of model parameters on predicted contaminants source-indoor air concentration attenuation factors.

vapor pressures (see “Advection & diffusion and piecewise aerobic biodegradation” in Table 1). In those cases, the predicted indoor air concentrations are within a range of 1−2 times of the results obtained from the 3-D numerical model. Conversely, from Figure 3b it can be seen that in a few diffusion-dominated cases involving very low indoor air concentrations the analytical model tends to overestimate the attenuation expected in the subsurface. This result can be mainly ascribed to the fact that for such scenarios, the blocking effect of the building foundation considered in the analytical model, which prevents atmospheric oxygen from entering the soil matrix directly beneath the building, is not relevant in the presence of a deep and low-concentration vapor source.35 The difference in predicted indoor concentration between two models becomes significant only when the oxygen can penetrate into deep soil in the subslab zone, which is unlikely to occur when there is strong fermentation/methanogensis activity in the source zone. Overall, the comparison between the 1-D analytical predictions and 3-D numerical simulations shown in Figures 2 and 3 suggests that the new analytical model can provide a simple and effective way to predict methane and hydrocarbon indoor air concentrations. Thus, the analytical model can be a useful tool for explosion and health risk screenings at sites where there is significant upward advection. Sensitivity Analysis. A sensitivity test was applied to the newly developed model by calculating the responses of sourceto-indoor air concentration attenuation factors (AFs) to ±10% parameter change of given values shown on the Y axis36−38 in

Figure 4. The obtained results indicate that the factor which has the greatest influence on the calculated AF is source vapor depth, followed by source vapor pressure, methane source vapor concentration, and building size. On the other hand, the results reported in Figure 4 show that the new analytical model, in line with other previous studies,38−41 is relatively insensitive to benzene source vapor concentration, reaction kinetics (see eq T9) and building foundation properties (except for the footprint size). An increase of soil moisture content can decrease the effective diffusivities of soil gas and the upward advection (for a constant source pressure), but increase the biodegradation rate (see eq T3). A higher moisture content would thus lead to lower source-to-indoor air concentration AFs with current conditions, similar to models based on diffusion dominated transport.20−22,42 Finally, it should be noted the influence of indoor air exchange rate is not explored here; the importance of this factor was examined in Johnston et al.40,41 Influences of Upward Advection on PVI. Figure 5 presents the sensitivity of the source-to-indoor air concentration AF for benzene to methane source vapor concentration and to Peclet number in cases involving only benzene and methane. It can be noted in Figure 5 that the AF for benzene increases with methane source vapor concentration, due to a decrease of aerobic zone thickness, until complete oxygen depletion, which explains the horizontal lines in the presence of higher methane source vapor concentration (e.g., >20% v/v). This is true also in the case of Pe = 0 which suggests that in the presence of methane, even in the absence of upward advection, the PVI potential is E

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Figure 5. Sensitivity of benzene source-to-indoor air concentration attenuation factor to methane source vapor concentration for cases with different Peclet numbers (ds = 3 m, df = 0.2 m, and csb = 10 g/m3).

Figure 6. Sensitivity of methane subslab vapor concentration to methane source vapor concentration for cases with different Peclet numbers (ds = 3 m and df = 0.2 m; the red line refers to the 5% v/v flammable limit of methane in air).

significantly increased due to the high oxygen consumption in the soil.9,13 The same figure also highlights that increasing the Peclet number leads to a higher AF at lower methane source vapor concentration. The latter result is mainly due to the increased soil gas entry rate resulting from upward advection. Employing a CST assumption to calculate the indoor air concentration makes it easy to show that changing the Peclet number from 0 to 20 increases the benzene indoor air concentration by roughly 1 order of magnitude. A similar conclusion was also reached in a previous study.32 Influences of Upward Advection on Safety Hazard Assessment of MI. Compared to assessing the health risk associated with long-term exposure to low-concentration toxic chemicals (e.g., benzene), the explosion risk assessment associated with methane should involve the worst-case short-term conditions.43 Therefore, when the traditional CST equation is used to predict short-term maximum indoor air concentrations, more conservative input parameters should be employed than those usually adopted to predict the long-term health risks of petroleum products. According to the statistical analysis of U.S. EPA’s VI database by EPA and other researchers, after the influences of background sources are minimized the observed subslab-to-indoor air concentration AFs typically vary from 1 to 10−4.34,44 It should be noted that most data sets recorded in U.S. EPA’s VI database were obtained at sites contaminated by chlorinated chemicals, and in those cases there was no upward advective soil gas flow to increase the soil gas entry rate into the building (and thus increase subslab-to-indoor air concentration AF). Considering the worst cases recorded in the EPA database, which is no attenuation from subslab to indoor air, an appropriately conservative approach might involve employing the lower explosion limit concentration of methane, 5% v/v, as the screening value for subslab methane vapor concentration in explosion risk assessments of MI.43,32 It should be noted that the identification of a lower explosive limit (LEL) concentration of methane in the subslab zone does not automatically imply explosion risk in the indoor space, but it is a conservative assumption. The results in Figure 6 suggest that at high methane source vapor concentrations (e.g., >20% v/v), the predicted subslab

methane vapor concentration would exceed 5% in all cases, resulting in a potential explosion risk. As noted above, methane could still be attenuated through the building foundations, leading to indoor concentrations significantly lower than those in the subslab. The overlap of the curves in Figure 6 indicates the methane subslab vapor concentration is essentially independent of upward advection, which, however, may still contribute to a higher indoor air concentration by increasing the soil gas entry rate, as discussed above. The Estimate of Methane Source Vapor Concentration Required to Deplete Subslab Oxygen. Since the biodegradation rate of methane in soil is usually much higher than that for petroleum hydrocarbons,9,45,46 in scenarios where source vapor concentration of methane is much higher than that of hydrocarbons, methane can be assumed as the only contaminant consuming oxygen. For such scenarios eq T6 can be used to calculate the critical methane source vapor concentration required to reach a complete anoxic condition in the subslab zone (i.e., the thickness of anoxic zone equals the vertical sourcebuilding separation, Lb = ds − df): cms,cri =

Do(coatm − comin)

(

Dmδm

L ds − d f

)

−1

(9)

cs,cri m

Figure 7 shows the calculated as a function of vertical source-building separation (ds − df) in the absence of upward advection. The calculated results suggest that a complete anoxic condition in subslab zone can be reached, regardless of the building foundation type, for cases with ds − df = 6 m and cs,cri m > 20%. Similar findings were also reported by Ma et al.9 It should be noted that this conclusion is limited by the assumptions employed in the analytical model, such as infinite emission source of methane and limited oxygen migration pathway (i.e., only diffusion from the open ground surface beyond the foundation edge). A field experiment indicated that some preferential lateral advection below the foundation or vertical advection through the foundation might help maintain high oxygen level (19%) immediately below the foundation even F

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results as a definitive prediction of the vapor concentrations expected in the field, in the presence of advective flows. Indeed because of the lack of experimental data, neither the numerical nor analytical model can yet be considered as validated; rather they can only provide a first screening estimate, to be verified by further field investigations.

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ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.est.5b01314. Methane results used in Figures 2 and 3 (PDF) Spreadsheet of the new analytical model (XLS)

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AUTHOR INFORMATION

Corresponding Authors

*Phone: +86-571-88982470; fax: +86-571-88982470; e-mail: [email protected] (Wen, Y). *Phone: +86-10-89744284; fax: +86-10-89734285; e-mail: [email protected] (Ma, J).

Figure 7. Dependence of critical methane source vapor concentration required for a subslab oxygen depletion zone on vertical source-building separation distance for different building foundations (full basement, df = 2 m; partial basement, df = 1 m; slab-on-grade, df = 0.2 m; the red line refers to the 6 m vertical screening distance suggested by the U.S. EPA4).

Notes

The authors declare no competing financial interest.

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in the presence of 13% v/v methane at 2−3 m below the foundation.47 Limitations of this Model. In this study an explicit algebraic approach has been introduced as a screening tool for cases involving upward advective soil gas flow due to methane generation. The different comparisons carried out in this work established that the newly developed model can replicate quite well the results obtained by 3-D numerical simulations. According to the predictions of this model, oxygen in the subslab zone would be depleted by the associated high methane source vapor concentration with upward advection due to significant methane generation, and the major contribution to indoor air petroleum compound concentrations might only be the increase of the soil gas entry rate (increase of about 1 order of magnitude when the Peclet number changes from 0 to 20. However, due to the conservative assumptions of vapor source distribution and oxygen migration pathway, the results obtained using this new screening model can be in some cases overestimate indoor air concentrations. For example, this new analytical model was developed on the basis of the existence of a very large source plume at the bottom of the domain of interest (9, 39). The assumption of large source plume for cases where only a part of building footprint is actually overlying the source plume can result in overprediction of the hydrocarbon entry rate mainly due to an underestimation of the presence of oxygen in the soil. Furthermore, in the analytical model it is assumed that oxygen migrates into the soil only by diffusion from the open ground surface beyond the foundation edge,23,24,39 while in practice there is a possibility of alternative pathways, including lateral advection inward from the edge of the foundation due to wind effect, and vertical diffusion and advection through foundation cracks followed by some lateral spreading mechanism in subslab zone.47 Moreover, with respect to more sophisticated 3-D numerical models, the analytical model is also incapable of simulating complex contamination scenarios involving transient transport, soil heterogeneities, and preferential pathways. Finally, it is worth pointing out that although the results of the analytical model presented in this work were found to be consistent with those returned by more sophisticated 3-D simulations, practitioners should be cautious in using these

ACKNOWLEDGMENTS This work was funded in the part by the National Natural Science Foundation of China (Grant No. 21307108, Grant No. 21407180 and Grant No. 21320102007), National Institute of Environmental Health Sciences (Grant No. P42ES013660), National Public Fund for Environmental Protection (Grant No. 201409047), Scientific Research Fund of Zhejiang Provincial Education Department (Grant No. Y201326597), Science Foundation of China University of Petroleum-Beijing (Grant No. 2462014YJRC016), and the Fundamental Research Funds for the Central Universities (Grant No. 2014QNA6010).

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NOMENCLATURE

Symbol Unit, Parameter

−, mass unit of benzene −, mass unit of chemical i −, mass unit of methane −, mass unit of oxygen −, subslab-to-indoor air concentration attenuation factor Mo M−1 b , stoichiometric conversion factor of benzene Mo M−1 i , stoichiometric conversion factor of chemical i Mo M−1, m stoichiometric conversion factor of methane T−1, first order biodegradation rate to benzene in water phase λi T−1, first order biodegradation rate to chemical i in water phase λm T−1, first order biodegradation rate to methane in water phase θt −, total porosity of the soil θw −, moisture filled porosity of the soil μ M L−1 T−1, viscosity of soil gas ρb M L−3, soil bulk density of soil Δp M L−1 T−2, pressure difference between indoor air and atmosphere Ae T−1, air exchange rate of intruded zone cinb Mb L−3, indoor air concentration of benzene csb Mb L−3, vapor source concentration of benzene ci Mi L−3, concentration of chemical i in the soil gas phase Mb Mi Mm Mo αinsub δb δi δm λb

G

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Environmental Science & Technology cini csi csub i cinm csm cs,cri m co catm o cmin o dck df ds Db Di Dm Do Hb Hi Hm Ho kp L Lb Lck Ls Lslab ps Pe Qb Ri Ro u Vb wck z

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Mi L−3, indoor air concentration of chemical i Mi L−3, source vapor concentration of chemical i Mi L−3, subslab vapor concentration of chemical i Mm L−3, indoor air concentration of methane Mm L−3, source vapor concentration of methane Mm L−3, critical methane source vapor concentration required to deplete oxygen in soil Mo L−3, soil gas concentration of oxygen Mo L−3, oxygen concentration in the atmosphere Mo L−3, minimum oxygen concentration required for biodegradation L, thickness of crack L, depth of the building foundation below ground surface L, depth of contaminant source below ground surface L2 T−1, effective porous medium diffusivity of benzene L2 T−1, effective porous medium diffusivity of chemical i L2 T−1, effective porous medium diffusivity of methane L2 T−1, effective porous medium diffusivity of oxygen −, air−water partition coefficient of benzene −, air−water partition coefficient of chemical i −, air−water partition coefficient of methane −, air−water partition coefficient of oxygen L2, soil permeability L, total transport length of oxygen L, thickness of anoxic zone L, total crack length L, half length of contaminant source plume side L, half length of the building footprint side M L−1 T−2, source vapor pressure −, Peclet number L3 T−1, soil gas entry rate into the enclosed space Mi L−3 T−1, reaction rate of chemical i Mo L−3 T−1, reaction rate of oxygen L T−1, velocity of upward soil gas flow in steady state L3, volume of intruded zone L, width of the crack L, coordinate in the vertical direction

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DOI: 10.1021/acs.est.5b01314 Environ. Sci. Technol. XXXX, XXX, XXX−XXX