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Vapor Intrusion Screening Model for the Evaluation of Risk-Based Vertical Exclusion Distances at Petroleum Contaminated Sites Iason Verginelli and Renato Baciocchi* Laboratory of Environmental Engineering, Department of Civil Engineering and Computer Science Engineering, University of Rome “Tor Vergata”, Via del Politecnico, 1 00133 Rome, Italy S Supporting Information *

ABSTRACT: The key role of biodegradation in attenuating the migration of petroleum hydrocarbon vapors into the indoor environments has been deeply investigated in the last decades. Very recently, empirical screening levels for the separation distance from the source, above which the potential for vapor intrusion can be considered negligible, were defined. In this paper, an analytical solution that allows one to predict risk-based vertical screening distances for hydrocarbons compounds is presented. The proposed solution relies on a 1-D vapor intrusion model that incorporates a piecewise first-order aerobic biodegradation limited by oxygen availability and accounts also for the effect of the building footprint. The model predictions are shown to be consistent with the results obtained using a 3-D numerical model and with the empirical screening criteria defined by U.S.EPA and CRC care. However, the different simulations carried out show that in some specific cases (e.g., large building footprint, high methane concentration, and low attenuation in the capillary fringe), the respect of these empirical screening criteria could be insufficient to guarantee soil-gas concentrations below acceptable risk-based levels.

■

For instance, most risk assessment procedures15 do not include natural attenuation in the models used for developing cleanup levels.16 This choice can lead to unreasonably overconservative cleanup goals that can make the whole remediation economically unsustainable.17 Namely, for the vapor intrusion pathway, the Johnson and Ettinger18 model (J&E model) is still one of the most widely used algorithm for assessing the vapors intrusion to enclosed spaces.19,20 However, several field investigations have shown that the J&E model often overpredicts the indoor concentrations at sites impacted by petroleum hydrocarbon compounds.21 This is especially related to the fact that the J&E algorithm does not include biodegradation.22,23 To overcome this limitation, a wide range of numerical24−29 and analytical30−38 models accounting for aerobic biodegradation was developed. These models, as discussed in detail by Yao et al.,39 differ for the underlying assumptions and the conditions to which they can be applied. More recently, a big effort was also made to define safety exclusion distances for the vapor intrusion pathway.40 Namely, a statistical analysis of large empirical soil vapor data sets allowed to estimate separation screening distances from the source, beyond which the potential for vapor intrusion can be considered negligible.2 For instance, as reported in a recent CRC care report,41 Davis et al.42 have analyzed more than 200 benzene and

INTRODUCTION The assessment of risks for human health associated with groundwater or soil contaminated by volatile organic chemicals (VOCs) is a priority topic for the effective management of contaminated sites. In particular, the subsurface to indoor air vapor intrusion pathway of organic compounds such as chlorinated solvents or petroleum hydrocarbons has gained increased attention in recent years as a potential mechanism for long-term exposure to VOCs.1 As a result, at sites contaminated by VOCs, detailed field investigations aimed at assessing the impacts related to this migration pathway are generally carried out. However, according to several field studies reported in the literature, evidence of vapor intrusion is usually observed for chlorinated solvents, whereas the occurrence of petroleum hydrocarbons vapor intrusion is extremely rare and generally associated with high-concentration sources located in close proximity to the building foundations.2 The behavior observed for petroleum hydrocarbons is mainly ascribed to the degradation processes taking place in the vadose zone under oxygen-rich conditions by ubiquitous soil microbes, that typically reduce the potential of petroleum vapor intrusion relative to that of chlorinated compounds.3 Several field studies reported in the literature4−14 confirm that aerobic biodegradation in the vadose zone can significantly attenuate petroleum vapors by several orders of magnitude. Nevertheless, vapor intrusion is still considered a critical pathway in many sites contaminated by petroleum hydrocarbons. This is in large part due to the overly conservative regulatory screening criteria and guidelines that are generally adopted for the assessment of this migration pathway. © 2014 American Chemical Society

Received: Revised: Accepted: Published: 13263

March 18, 2014 October 17, 2014 October 20, 2014 October 20, 2014 dx.doi.org/10.1021/es503723g | Environ. Sci. Technol. 2014, 48, 13263−13272

Environmental Science & Technology

Article

Figure 1. Conceptual Model. The contaminant vapor source is located at a depth L below the building. The symbol z represents the spatial variable and is positive with increasing depth. The origin of z is at the bottom of the basement of the building. Part a reports for each region the differential equations used and the corresponding boundary conditions adopted for the model derivation. Part b reports the assumed diffusion path length for oxygen replenishment below the building.

purpose. Nevertheless, this would require a cumbersome calibration step, consisting in iteratively changing the source depth, in order to identify the vertical distance required to meet the target indoor concentration of the different compounds of concern. In this paper, we propose a very simple and readily applicable approach that allows, using an explicit analytical solution, one to directly estimate risk-based vertical screening distances for hydrocarbons on a site-specific basis. The proposed solution relies on a 1-D vapor intrusion model that incorporates a steady-state subsurface vapor source, diffusion-dominated vapor transport in a homogeneous soil, piecewise first-order aerobic biodegradation limited by oxygen availability, diffusive and convective mass transfer across the building foundations, and mixing within the indoor environment. In addition, in order to predict the availability of oxygen in the subsurface, its transport in the subsurface and its consumption resulting from the different oxygen sinks (aerobic biodegradation of the compound(s) of concern and natural soil oxygen demand) have been included in the model. This is in line with the more recent models available in the literature.35−37 Furthermore, with respect to the above cited analytical models, the developed model accounts, in a simple but effective way, for the effect of the building footprint. This is a key aspect to be evaluated since the oxygen availability in the subsurface can significantly influence the overall attenuation of vapors migrating to enclosed spaces.44,45 Recently, Yao et al.46 proposed a method to account for the “blocking” effect of the building by introducing a semiempirical adjustment parameter, r, that is applied to the attenuation factors estimated assuming open ground conditions. Despite the introduction of the fitting adjustment factor “r” proposed by the authors can be very useful for the interpretation of 3-D numerical simulations and field data, its use in a screening phase is complicated since, as shown by the same authors, the choice of the value of “r” can significantly

total petroleum hydrocarbon vapor samples estimating that 1.5 m (5 ft) and 10 m (30 ft) thickness of clean soil is sufficient to attenuate to nondetectable levels, petroleum hydrocarbon vapors from dissolved-phase and LNAPL sources, respectively. McHugh et al.1 proposed a separation distance of 3 m (10 ft) for petroleum vapors resulting from dissolved phase groundwater sources and a separation distance of 10 m (30 ft) for LNAPL vapor sources. More recently, Lahvis et al.,2 who have developed new screening criteria from soil-gas measurements at hundreds of petroleum UST sites, have estimated a separation distance of 4 m (13 ft) for LNAPL sources (assuming a benzene soil-gas screening limit of 30 μg/m3), whereas for dissolved phase vapor sources the probability to detect benzene vapor above the screening level of 30 μg/m3 was found to be below 5%. Similar values are also reported by U.S. EPA43 where, depending on the method adopted for the data interpretation (i.e., vertical distance method or clean soil method), screening distances of 0 to 1.6 m (5.4 ft) for dissolved phase sources (benzene groundwater concentration below 1 mg/L and benzene soil-gas screening level of 100 μg/ m3) and 4.1 to 4.6 m (13.5 to 15 ft) for LNAPL sources at UST sites and 5.5 to 6.1 m (18 to 20 ft) for LNAPL sources at nonUST sites were defined. Very recently, CRC care41 has also determined vertical screening distances of 1.5 m for dissolved phase and 3 to 5.6 m for LNAPL sources (note that these values are the ones reported in the document not considering the 1.5 fold uncertainty factor). These empirical screening distances are associated with a certain probability (e.g., 95% of cases2) that for a given type and source concentration (e.g., dissolved-phase or LNAPL source) the contaminant of concern (typically benzene) will be attenuated below a given target soil-gas screening level. To support and further justify these empirical analyses, mathematical modeling can be certainly of help. For instance, some of the analytical models available in literature35−37 could be used to this 13264

dx.doi.org/10.1021/es503723g | Environ. Sci. Technol. 2014, 48, 13263−13272


Article

⎧ ⎛ A ⎞ ⎪R R mix − b ⎟⎟·(exp(− ξ) − 1) (Δp ≠ 0) ⎜ crack = ⎜ ⎪ Qs⎠ ⎝ ⎨ ⎪ Lcrack (Δp = 0) ⎪ R crack = Dcrack ·η ⎩

influence the predicted subslab concentration. On the contrary, the approach proposed in this work allows one to calculate the aerobic layer depth below the building by introducing an equivalent diffusive length for oxygen that is calculated as a function of building width and foundations depth. In this paper, after a description of the proposed approach, the results of several simulations are reported and discussed. In particular, the capability of the developed model is first tested by comparing its results with those obtained with a more detailed numerical model. Then, the vertical exclusion distances predicted by the developed model are compared with the empirical screening criteria reported in the literature.

with: ξ=

MODELING Governing Equations and Model Derivation. The firstorder steady-state reactive transport of petroleum hydrocarbons vapors and oxygen can be described by two coupled diffusionconvection differential equations with reaction terms:37

C0 =

C indoor

(1)

1 Lmix ·ER

Lcrack Dcrack ·η

(5)

Ca cosh(kLa) +

sinh(kLa) k·Dv ·(R crack + R mix )

⎛ λ ·θ ⎞1/2 k=⎜ w⎟ ⎝ H ·Dv ⎠

(6)

(7)

where λ is the intrinsic biodegradation rate constant, θw the water-filled porosity of the soil, and H the dimensionless Henry’s law constant. Note that for layered soils, the effective diffusion coefficients, Dv, can be calculated using the harmonic averaging method reported by Johnson et al.30 For biodegradation rate constants, λ, typical of hydrocarbon compounds34 (λ > 0.05 h−1), eq 6 can be approximated as follows: C0 =

Ca

(1 +

1 k·Dv ·(R crack + R mix )

)·

e kLa 2

(8)

Finally, the concentration at the interface between the aerobic to anaerobic zones, Ca, can be calculated as follows: Ca =

Csource 1 + k(L − La)

(9)

where L is the source vertical distance from the bottom of the basement and Csource the vapor concentration of the compound at the source:37

(2)

⎧Csource = Csource, gw·H ·αcap groundwater ⎪ ⎨ ρ s·H soil ⎪Csource = Csource,soil· θ θ + · H w a + ρ s· Koc · foc ⎩

where Rmix and Rcrack are the dilution factor due to air building exchange and the contribution to attenuation of the cracks, respectively:37 R mix =

Ab

·

where Ca is the concentration of the compound at the interface between the aerobic and anaerobic zones, La the thickness of the aerobic zone, Dv the effective porous medium diffusion coefficient in the vadose zone, and k a parameter that gives an indication of the relevance of biodegradation with respect to diffusion, in terms of the inverse of the diffusive reaction length:36,37

where the subscripts v and O2 refer to the vapor phase contaminant and to oxygen, respectively. C is the concentration of hydrocarbons in the soil-gas phase, D the effective porous medium diffusion coefficient, λ the first order biodegradation rate constant in the water phase, θw the water-filled porosity of the soil, H the dimensionless Henry’s law constant, and γ the stoichiometric mass ratio between oxygen and the compound(s) of concern. Equation 1 is valid up to a minimum oxygen concentration (e.g., 1% v/v), below which aerobic biodegradation of hydrocarbons stops, or slows down to very low rates.29 To solve the two coupled differential equations (eq 1), we adopted the procedure outlined by Verginelli and Baciocchi,37 although with different boundary conditions. In particular, the whole domain was divided into regions characterized by different behaviors (see Figure 1a). For each region, the differential equations were separately integrated by imposing the boundary conditions at the interfaces (see Figure 1a), allowing to obtain the expressions for the vapor phase concentration and flux profile along each zone. Next, the expressions for the concentrations at the different interfaces were derived by equating the fluxes at the interface between the contiguous layers. The derivation of the model is described below. Attenuation Factor. The indoor concentration, Cindoor, can be calculated as a function of the concentration at the bottom of the building, C0, using the following expression:36,37 ⎛ ⎞ R mix = C 0· ⎜ ⎟ ⎝ R crack + R mix ⎠

Qs

Lmix is the enclosed space volume/infiltration area ratio, ER the air building exchange, Lcrack the foundation thickness, Ab the foundation area in contact with soil, Dcrack the effective diffusion coefficient through the foundation cracks, Δp the pressure difference between the soil and the building, η the foundation cracks fraction, and Qs the convective flow rate from the soil into the building. The concentration at the bottom of the building, C0, is given by the following:

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⎧ d 2C λ ·θw dC ⎪ Dv 2v − vD· v − · Cv = 0 ⎪ dz dz H ⎨ ⎪ d 2CO2 dCO2 λ·θ − vD· − γ · w · Cv = 0 D ⎪ O2 2 ⎩ dz H dz

(4)

(10)

where Koc is the chemical-specific organic carbon partition coefficient, foc the organic carbon fraction of the soil, θa the airfilled porosity, and ρs the bulk soil density. αcap is the attenuation

(3) 13265



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factor of vapors in the capillary fringe that can be estimated as follows: ⎛ hcap ⎞ Dw αcap ≈ ⎜1 − ⎟· L ⎠ Dv ⎝

(11)

with: Dw =

hcap

+

L − hcap Dv

(12)

where Dcap is the effective diffusion coefficient in the capillary fringe, and hcap the thickness of the capillary fringe. Hence, substituting eq 8 and eq 9 in eq 2, the attenuation factor, αindoor, is given by the following: αindoor =

C indoor R mix = e kLa Csource (R crack + R mix + R bio) ·(1 + kL b) · 2

(14)

For negligible biodegradation (i.e., k = 0) Rbio can be substituted with Rbio = L/Dv to obtain the solution given by Johnson and Ettinger.18 For large kLa and high oxygen replenishment (i.e., La ≫ Lb), eq 13 can be approximated as follows: αindoor =

C indoor R mix = e kLa Csource (R crack + R mix + R bio) · 2

(15)

For the outdoor volatilization, the attenuation factor can be calculated as follows: αoutdoor =

Coutdoor R amb = e kLa Csource (R amb + R bio) · 2

R O2(La) = ρs ·La ·Λbase +

∑ γi·Dv ,i · i=1

W Uair·δair

⎞ ⎟ ⎟⎟ ⎠

(18)

⎞ ⎟ ⎟ ⎟ ⎠

⎞ ⎟ ⎟ ⎟ ⎠

(22)

Csource, i·ki·coth(kiLa) 1 + ki(L − La)coth(kiLa)

(23)

n

R O2(La) = ρs ·La ·Λbase +

∑i = 1 γi·Dv , i ·Csource, i L − La +

1 n

n

1

∑i = 1 k

i

(24)

For open ground conditions, the oxygen flux migrating in the subsurface, ΦO2, was assumed be equal to the following:

Next, replacing Cindoor with the risk-based indoor concentration corresponding to an acceptable target risk, C*indoor, the minimum aerobic depth, La*, required to exclude the vapor intrusion pathway is given by the following: ⎛ ⎜ R mix 1 La* = ln⎜2 * C indoor k ⎜ (R crack + R mix + R bio) · C ⎝ source

(21)

where Λbase is the zero-order baseline soil oxygen respiration term,34 ρs the soil density, and γ the stoichiometric mass ratio between oxygen and the i-th compound. If methane is detected near the source zone, then it should also be included in eq 23, in order to properly assess the overall oxygen demand rate resulting also from methane oxidation in the subsurface.14,29,37 For large λ and high oxygen replenishment (i.e., La ≫ Lb), eq 23 can be approximated as follows:

(17)

where W is the width of source-zone area along the wind direction, Uair the ambient air velocity in the mixing zone, and δair the mixing zone height. Safety Aerobic Thickness Zone. Equation 15 can be rearranged in order to calculate the aerobic layer thickness required to obtain a specific attenuation factor (Cindoor/Csource): ⎛ R mix 1 ⎜ La = ln⎜2 k ⎜ (R crack + R mix + R bio) · Cindoor ⎝ Csource

non‐carcin. compds.

n

(16)

with: R amb =

THQ· AT· RfC EF·ED

(20)

Note that eq 19 should not be used in cases of Csource lower than C0* (calculated with eq 2 using C*indoor) as this scenario implies that the attenuation occurring in the foundations and building is already high enough to get indoor concentrations below riskbased levels. Safety Source-Building Depth. The last step consists of calculating the source depth that ensures the establishment of the aerobic zone thickness obtained using eq 19 (or eq 22). This can be made by linking the oxygen replenishment to the oxygen demand related to the aerobic biodegradation reaction of the n degradable compounds and to the baseline soil respiration. Namely, in the developed model the aerobic zone depth, La, was estimated by equating, at the aerobic to anaerobic interface (z = La), the oxygen flux migrating into the subsurface with the total oxygen demand rate. The total oxygen demand rate, RO2, can be calculated accounting for the contribution of aerobic biodegradation of the n degradable compounds and the baseline oxygen respiration:

with:

1 k·Dv

* C indoor =

carcin. compds.

⎛ R amb ⎜ 1 La* = ln⎜2 * Coutdoor k ⎜ (R amb + R bio) · C ⎝ source

(13)

R bio =

TR·AT URF·EF·ED

where TR is the target cancer risk, THQ the target hazard quotient, AT the averaging time, EF the exposure frequency, ED the exposure duration, URF the inhalation unit risk factor and RfC the inhalation reference concentration of the compound of concern. For outdoor air volatilization, eq 19 becomes the following:

L Dcap

* C indoor =

ΦO2(La) =

) DO2 ·(COmax − COmin 2 2 La

(25)

where DO2 is the effective oxygen diffusion coefficient in the soil, CO2max the maximum oxygen concentration entering to the soil (e.g., ambient air concentration) and CO2min the minimum oxygen concentration required to sustain aerobic biodegradation (e.g., 1% v/v).

(19)

with: 13266



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Figure 2. Comparison between predicted benzene indoor concentrations from 3-D numerical simulations (Abreu et al.45) and (a) BioVapor,36 (b) Verginelli and Baciocchi model,37 (c) developed model, and (d) developed model using a k* = 0.85k with respect to the k calculated with eq 7.

calculate the safety vertical distance. Hence, in this work we propose a simplified solution, obtained assuming that oxygen diffuses vertically to the subsurface from the open ground around the perimeter of the building and then laterally under the foundations. Thus, the presence of the building leads to a greater diffusive length for oxygen with respect to vapors migrating from the source located below the foundations (see Figure 1b). Under these assumptions, eq 25 was modified as follows:

Hence, by equating eq 25 with eq 24 and neglecting the soil oxygen respiration term, the aerobic layer extension, La, is given by the following: L+ La =

1 n

n

1

∑i = 1 k

1+

i

A B

(26)

with: n

A=

∑ γi·Dv ,i ·Csource,i i=1

B=

DO2(COmax 2

−

COmin ) 2

(27)

ΦO2(La) =

) DO2 ·(COmax − COmin 2 2 La + Lfootprint

(29)

(28)

with:

It can be readily checked that for very large k (i.e., assuming an instantaneous reaction) eq 26 approaches to the expression reported by Davis et al.35 For subslab conditions, this equation is not more valid. Knight and Davis38 have recently proposed a model that allows one to estimate the oxygen availability in the subsurface using a 2-D model, which accounts for the building footprint, assuming an instantaneous reaction. Unfortunately, this solution cannot be directly incorporated in the developed model presented here, since it would not allow one to explicitly

Lfootprint =

⎛π ⎞ π ·L building + ⎜ − 1⎟ ·Lsub ⎝2 ⎠ 2

(30)

where Lsub is the subslab half width of the building and Lbuilding the depth of the bottom of the basement. Hence, by equating eq 29 with eq 24, the aerobic layer thickness below the building, is given by the following: 13267



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Table 1. Input Parametersa parameter

symbol

indoor air mixing height air exchange rate areal cracks fraction of the foundation area foundation width foundation thickness foundation area building pressure convective flow rate foundation depth soil bulk density fraction of organic carbon in the soil moisture-filled porosity soil porosity soil gas permeability attenuation factor in the capillary fringe source vapor concentration TPH mixture vapor phase mass fraction methane source concentration biodegradation rate constant ratio of oxygen to benzene consumed vapor diffusion coefficient in the vadose zone vapor diffusion coefficient through the cracks oxygen atmospheric concentration oxygen threshold concentration oxygen diffusion coefficient in the vadose zone soil oxygen respiration rate

Lb ER η 2 × Lsub Lcrack Ab Δp Qs Lbuilding ρs foc θw θe kv αcap Csource

unit m h−1 m m m2 Pa L/min m kg/m3 g/g

m2 g/m3

% v/v h−1 gO2/gHC m2/h m2/h g/m3 g/m3 m2/h mgO2 /gsoil-h

λ γ Dv Dcrack CO2max CO2min DO2 Λbase

value (Figure 2, SI Figure S.1)

value (Figure 3)

value (Figure 4)

2.44 0.5 0.00039 10 0.15 100 5 calculated 0.2/2 NR NR 0.054 0.375 10−11 NRb see SI Table S.1 no NR 0 see SI Table S.1 3 5.1 × 10−3 3.2 × 10−2 279 13.7 1.2 × 10−2 0

2.44 0.5 0.00039 10 0.15 100 NR 10 2 1700 0.01 0.04 0.375 NR 0.2 see Figure 3 yes see Table 2 1 see Table 2 3 calculated calculated 279 13.7 calculated 7.04 × 10−4d

2.44 0.5 10−5 −10−3 10−50 0.15 100−2500 NR 1−10 0.2−3 1700 0.001- 0.01 0.03−0.1 0.375 NR 0.05−0.2 see Figure 4 yes see Table 2 0.001−1 see Table 2 3 calculated calculated 279 13.7 calculated calculatedd

Unless otherwise noted in figures. The data used for Figure 2 and SI Figure S.1 are the ones adopted by Abreu et al.45 NR = Not required. bThe attenuation in the capillary fringe was not considered by Abreu et al.45 in their simulations. cCalculated using eq 11 with hcap = 10 cm and Dcap= 5.8 × 10−5 m2/h. dCalculated with the equation reported by DeVaull.34 a

A

La =

L − B Lfootprint + 1+

1 n

n

1

∑i = 1 k

approaches the safety aerobic zone thickness calculated with eq 19 or eq 22.

i

A B

■

(31)

RESULTS AND DISCUSSION Comparison with Other Screening Tools. Figure 2 reports a comparison of benzene indoor concentrations from 3-D numerical simulations45 and the values obtained by applying the BioVapor tool36 (Figure 2a), the Verginelli and Baciocchi (V&B, 2011) model37 (Figure 2b) and the developed model (Figure 2c,d). In all models, the input parameters used by Abreu et al.45 for their simulations (see Table 1 and SI Table S.1) were used. The BioVapor simulations were run by directly specifying, as a boundary condition for oxygen, the oxygen surface concentration (that was set equal to the oxygen atmospheric concentration). The V&B (2011) model was applied neglecting the contribution of anaerobic biodegradation. Making reference to these figures, it can be noticed that the indoor concentrations calculated using either BioVapor (Figure 2a) or the V&B model (Figure 2b) are in many cases underestimated with respect to the results obtained with the 3-D numerical model. This is due to the fact that these models do not account for the building footprint which can significantly reduce the oxygen replenishment below the subslab, leading to an overestimation of the aerobic layer depth under the building and consequently, of the attenuation due to aerobic biodegradation. Note that the higher underestimations are observed for the basement scenarios that, with respect to slab-on-grade conditions, affect more the oxygen replenishment below the building. On the contrary, a better correlation with the 3-D numerical simulations is observed for

Finally, eq 26 and eq 31 can be rearranged in order to estimate the source depth, L*, required to ensure the minimum aerobic thickness, La*, needed to attenuate vapors at acceptable levels for open-ground (eq 32) and subslab (eq 33) conditions: ⎛ A⎞ 1 L* = ⎜1 + ⎟La* − ⎝ ⎠ B n

n

∑ i=1

1 ki

A 1 L* = La* + (La* + Lfootprint) − B n

(32) n

∑ i=1

1 ki

(33)

Furthermore, in cases of significant baseline soil oxygen respiration rates (i.e., Λbase > 0), eq 32 and eq 33 can be further modified as follows: ⎞ ⎛ A 1 ⎟La* − L* = ⎜1 + 2 * n B − ρ ΛbaseLa ⎠ ⎝

L* = La* +

n

∑ i=1

1 ki

A ·(La* + Lfootprint) 1 − 2 * n B − ρ Λbase·(La + Lfootprint)

(34) n

∑ i=1

1 ki (35)

Note that when oxygen is sufficient to sustain the aerobic reaction throughout the vadose zone down to the source, the vertical exclusion distance calculated with eq 34 or eq 35 13268



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Figure 3. Vertical exclusion distance (L*) calculated with the developed model as a function of benzene groundwater concentration for three biodegradation rates (λ = 0.1 h−1, λ = 0.25 h−1, and λ = 1 h−1 for BTEX and other aromatic hydrocarbons and λ = 10 h−1, λ = 25 h−1, and λ = 100 h−1 for CH4 and aliphatic hydrocarbons). The simulations were carried out assuming that benzene is present in a TPH mixture (see Table 2). Part a also reports the vertical screening distances provided in the U.S. EPA database47 for UST and non-UST sites (method 2: Thickness Clean Soil Benzene). Part b reports the screening criteria defined by U.S.EPA43 (VD = separation distance method, CS = Clean soil method), CRC care,41 and Lahvis et al.2

Table 2. Chemico-Physical Properties and Vapor Phase Composition of the Compounds of Concern (Unless Otherwise Noted in Figures) parameter vapor phase mass fractiona H (−) Dair (cm2/s) Dw (cm2/s) λ-low (h−1) λ-moderate (h−1) λ-high (h−1) γ (gO2/gHC) a

benzene

ethylbenzene

toluene

xylenes

0.0023

0.0048

0.0024

0.0002

0.228 0.088 9.8 × 10−6 0.1 0.25 1 3.07

0.323 0.075 7.8 × 10−6 0.1 0.25 1 3.16

0.272 0.087 8.6 × 10−6 0.1 0.25 1 3.13

0.314 0.087 7.8 × 10−6 0.1 0.25 1 3.16

other hydrocarbons (aliphatic) 0.99 75 0.07 7 × 10−6 10 25 100 0.48

other hydrocarbons (aromatic)

CH4

0.0015 0.3 0.07 7 × 10−6 0.1 0.25 1 0.42

29.9 0.19 1.7 × 10−5 10 25 100 4

API (2010)36

the indoor concentrations calculated with the developed model (Figure 2c) suggesting that the simplified approach allows to account in a simple but effective way for the building footprint. However, for the lower predicted indoor concentrations, typical of oxygen-rich conditions down to the source depth (i.e., fully aerobic vadose zone, see Supporting Information, SI), the developed model tends to overestimate the vapor attenuation, following a trend similar to the one obtained with BioVapor and the V&B model. Considering that for fully aerobic conditions the input parameters in the numerical and analytical models are actually the same, the observed trends could be ascribed to a difference between the value of the diffusive reaction length (i.e., 1/k) used in the numerical model and the one adopted in the analytical one (see eq 7). To verify this hypothesis, further simulations were carried out, where a correction factor of 0.85 to the k values obtained from eq 7 was introduced. The obtained results, reported in Figure 2d, clearly show that in this case, the analytical model provides results well in agreement with the ones obtained from 3-D numerical simulations. However, regardless of the correction factor introduced, the difference observed between the numerical model and the analytical model is significant only for conditions leading to very high attenuation (i.e., very low values of the attenuation factor, α), typically

corresponding to predicted indoor concentrations well below the risk-based acceptable levels. This suggests that in practice the use of this correction factor to k is not required and for this reason it was not applied in the rest of the paper. Risk-Based Vertical Exclusion Distances. Figure 3 reports the risk-based vertical exclusion distances estimated with the developed model (eq 35) as a function of the source concentration and of different biodegradation rates representative of the values available in literature4 (see Table 2). For this estimation, benzene was selected as the target compound, as commonly it is the main risk driver at petroleum sites. However, since in typical contamination scenarios it is more common to find a mixture of hydrocarbons that can simultaneously consume oxygen and thus contribute to its depletion in the subsurface, the simulations were carried out assuming that benzene is present in a TPH mixture. The vapor mass fraction, together with the main chemico-physical properties assumed for the different compounds of concern, are reported in Table 2. To calculate the acceptable benzene indoor concentration (eq 19) the following parameters were used: Target Risk, TR = 10−6, unit risk factor, URF = 7.8 × 10−6 (μg/m3)−1, Exposure Duration, ED = 25 y, Exposure Frequency, EF = 250 d/y and an averaging time, AT = 70 y. The other input parameters are reported in Table 1. It is 13269



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Figure 4. Results of Monte Carlo simulations carried out for dissolved phase (groundwater benzene concentration equal to 0.5 mg/L) and NAPL sources (groundwater benzene concentration equal to 15 mg/L): (a),(b) percentage frequency of the exclusion distance calculated with the developed model in the different simulations; (c),(d) cumulative frequency of the estimated exclusion distance; and (e),(f) Pearson correlation coefficients of the different input parameters.

worth pointing out that the convective flow rate, Qs, and the exposure parameters were selected in order to obtain a target concentration of benzene in the soil-gas at the bottom of the building (i.e., C = C0 at z = 0) equal to 100 μg/m3 that is one of the reference values used by U.S. EPA43 for the estimation of the vertical exclusion distances. Looking at Figure 3a, it can be noticed that an increase of the source concentration leads, as expected, to a corresponding increase of the safety vertical exclusion distance. In addition, the figure highlights the influence

of the biodegradation rate constant, λ, showing that an increase of λ leads, as expected, to a corresponding reduction of the minimum source depth required to obtain an acceptable indoor risk. In Figure 3a the vertical exclusion distances observed in more than one hundred sites and reported in the U.S. EPA database 47 are also reported. Making reference to this comparison, it can be noticed that all the field data fall below the line corresponding to the exclusion distances calculated by the model assuming a low biodegradation; most of them are also 13270



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below the model predictions obtained with a relatively high biodegradation rate. This confirms that the developed model correctly predicts the vertical exclusion distance, while keeping a simplified approach. A further evidence is reported in Figure 3b, where the model predictions are compared with the recent screening criteria defined through a statistical analysis of a large set of field data collected at petroleum hydrocarbon sites, by U.S. EPA,43 CRC care,41 and Lahvis et al.2 The obtained results suggest that the trend predicted by the model is in line with these empirical screening criteria. For example, Figure 3b shows that, considering a groundwater benzene source concentration of 0.5 mg/L and a moderate biodegradation rate, the vertical exclusion distance predicted by the model is 1.9 m against the 1.6 m vertical screening distance for dissolved phase sources set by U.S. EPA43 for UST sites, using the “clean soil method” (CS). In the case of residual LNAPL sources2 (groundwater benzene concentration equal to 15 mg/L), the model predicts a vertical distance of 4.9 m against a screening value of 4.1 m set by U.S. EPA43 for UST sites again using the “clean soil method” (CS). A good agreement is also observed with the values defined by CRC care,41 without considering the uncertainty factor of 1.5. Also, the values provided by Lahvis et al.2 are in line with the model predictions, except for the case of dissolved-phase sources, where the empirical screening distance was found to be negligible in 95% of the cases analyzed by these authors. These results show that for the contamination scenario described in Table 1, the developed model is consistent with the field data. However, the model results depend on the selected input parameters. Hence, to assess how the predicted screening criteria can change based on the assumed site parameters, a simplified Monte Carlo analysis was performed. Namely, 1000 simulations randomly varying the site parameters with a uniform distribution (i.e., each value is equally likely) in the ranges reported in Table 1 were carried out. Note that for these simulations, a 1% v/v was chosen as the maximum CH4 source concentration, which corresponds approximately to the 95th percentile of the values reported in the U.S. EPA database;47 this assumption may not apply to high ethanol content fuel releases that, as shown by Ma et al.,14,29 can be characterized by higher methane concentration (up to 75% v/v) that could lead to a further extension of the vertical distance required to attenuate vapors below screening levels. The obtained results, reported in Figure 4, show that for dissolved phase sources (groundwater benzene concentration of 0.5 mg/ L) most of the predicted exclusion distances fall within 0 and 1 m (Figure 4a) and nearly all are below 2 m (Figure 4c). This is in line with the vertical screening distance of 1.6 m fixed by U.S. EPA43 (using the clean soil method). For LNAPL sources (groundwater benzene concentration of 15 mg/L), in line with the screening criteria defined by U.S. EPA, the obtained results show that most of the vertical screening distances are within 1 and 5 m (Figure 4b). However, in some cases (approximately 10% of the simulations carried out, see Figure 4d) the model predictions suggest that higher vertical distances could be needed to reduce indoor benzene concentrations below acceptable riskbased levels. This is particularly true in cases of large buildings, low attenuation in the capillary fringe and high methane concentrations, which are the parameters that mostly influence the vertical screening distance when residual LNAPL sources are present (see Figure 4f). Hence, the developed model could support the site-generic screening empirical distance criteria, thus allowing to obtain a site-specific evaluation of the relevance of the volatilization pathway in the conceptual model of the site.

Article

ASSOCIATED CONTENT

S Supporting Information *

More details on the input parameters of the model and on the obtained results, as well as further comparison with literature data. This material is available free of charge via the Internet at http://pubs.acs.org.

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AUTHOR INFORMATION

Corresponding Author

*Tel.: +39 06 72597022; fax: +39 06 72597021; e-mail: [email protected]. Notes

The authors declare no competing financial interest.

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REFERENCES

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