Environ. Sci. Technol. 2007, 41, 3241-3248
Indoor Vapor Intrusion with Oxygen-Limited Biodegradation for a Subsurface Gasoline Source GEORGE E. DEVAULL* Shell Global Solution US Inc., Westhollow Technology Center, 3333 Highway Six South, Houston, Texas 77082
Development and results are presented for a subsurface soil to indoor air chemical vapor intrusion model that includes oxygen-limited biodegradation. The algebraic model incorporates a steady-state subsurface gasoline vapor source, diffusion-dominated soil vapor transport in a homogeneous subsurface soil layer, and mixing within a building enclosure. The soil is divided into a shallow aerobic layer including biodegradation and a deeper anaerobic layer in which biodegradation is neglected. Biodegradation of multiple chemicals is included, with aerobic firstorder reaction kinetics estimated from measured data. Oxygen is supplied at the soil surface below the building foundation. Oxygen demand is attributed to a sum of multiple biodegrading chemicals and to baseline respiration of native soil organic matter. The model is solved by iteratively varying the aerobic depth to match oxygen demand to oxygen supply. Model results are calculated for ranges of source concentrations, unsaturated soil characteristics, and building parameters. Results indicate vapor intrusion of petroleum hydrocarbons can be significantly less than indicated by estimates that neglect biodegradation.
This paper presents an algebraic model including aerobic biodegradation in coupled oxygen and multiple-chemical soil vapor transport. Oxygen demand is included for aerobic degradation of multiple gasoline constituent chemicals in soils and baseline soil oxygen respiration. Results have been calculated for representative parameter ranges. As with other vapor intrusion models, estimates are applicable for sites which have met a set of conditions establishing model validity, including checking for absence of direct groundwater or liquid hydrocarbon intrusion into buildings or direct contact with building foundations. This also includes checks for absence of potential preferential flow pathways, such as sewers and utility conduits, and for pressure-driven subsurface vapor flow, for example, in gas generation from municipal landfills.
Indoor Air Vapor Intrusion Model, No Degradation Before presenting the biodegradation model, the relevant mechanisms for chemical vapor transport with no biodegradation or other reaction are introduced. Steady-state conditions are presumed, with constant chemical source concentrations, homogeneous soil properties, and diffusiondominated soil vapor transport. No immiscible chemical phase is presumed within the modeled domain. Chemical vapor concentration, cv (mg/cm3-air), is therefore related to water-phase chemical concentration, cw (mg/cm3-water), within the soil matrix using a Henry Law coefficient, H.
cv ) Hcw
This assumption allows an immiscible chemical phase in a source zone at the modeled domain boundary. The effective diffusion coefficient through the porous soil media, Deff (cm2/ s), is estimated (14, 15).
Deff )
Introduction The potential for chemical vapor intrusion to indoor air from subsurface sources is of interest in evaluating risks and hazards at chemical impacted sites. Vapor intrusion may be estimated from measured indoor air and subsurface chemical vapor concentrations, but the range of direct measurement is limited by vapor saturation and chemical analysis detection limits, and is often confounded by other sources of identical chemicals affecting indoor air. Land use changes present an obstacle to direct measurement, for example, when no building is present to sample. Models help illuminate physical processes and extend the range of vapor intrusion estimates. Models for predicting chemical transport from subsurface soils to indoor air are included in guidance documents (1, 2) derived from Johnson and Ettinger (3). These models do not include attenuation due to chemical biodegradation. Aerobic biodegradation can significantly attenuate many petroleum chemical constituents in soil (4-10). An algebraic model incorporating chemical degradation is available (10), but it does not include oxygen-limited conditions. Multidimensional numerical models with oxygenlimited biodegradation are described (11-13). Results for the numerical models illustrate significant sensitivity to oxygen-limited biodegradation. * Corresponding author phone: 281-544-7430; fax: 281-544-8727; e-mail:
[email protected]. 10.1021/es060672a CCC: $37.00 Published on Web 04/04/2007
2007 American Chemical Society
(1)
(
θ10/3 v θT2
‚Dv +
)
θ10/3 Dw w ‚ 2 H θT
(2)
Molecular diffusion coefficients in vapor and water are, respectively, Dv and Dw (cm2/s). Soil porosity is θT (cm3void/ cm3-soil), soil moisture is θw (cm3-water/ cm3-soil), and θv (cm3-air/ cm3-soil) is vapor-filled soil porosity, equal to (θT - θw). Diffusive chemical flux, J (mg/cm2‚s), in a vertical coordinate direction, z (cm), is
∂cv ∂z
J ) -Deff‚
(3)
For chemical vapors located some distance, LT (cm), from a building foundation, with diffusive vapor transport dominant, the chemical vapor flux can be approximated as
J)
Deff ‚[c - ce] LT s
(4)
Chemical vapor concentration is indicated at the source, cs, and in indoor air, ce, and is presumed to be laterally extensive. Assuming no other chemical sources or sinks and a wellmixed building, chemical vapor flux is related to an indoor air concentration using a building air exchange rate, ER (s-1), as volume exchanges per unit time, and an indoor air mixing height (or building volume to foundation area ratio), Lmix (cm).
J ) Lmix‚ER‚ce VOL. 41, NO. 9, 2007 / ENVIRONMENTAL SCIENCE & TECHNOLOGY
(5) 9
3241
Assuming in eq 4 that cs . ce, eq 4 and 5 yield
AF )
(
Deff/LT ce ) cs Lmix‚ER
)
(6)
The attenuation factor, AF, is the ratio of indoor air to subsurface soil vapor concentration. Combinations of parameters in eq 6 can yield estimates for which the assumption cs . ce is not met. In these cases, vapor transport is not limited by soil diffusion, but by resistance to chemical vapor transport within the building and through the building foundation. Including series terms for foundation and building transport resistance, the attenuation factor is
ce AF ) ) cs
1 Lmix‚ER
(
)
LT 1 1 + + Lmix‚ER h Deff
(7) FIGURE 1. Conceptual model diagram.
Representative values for the foundation mass transfer coefficient, h (cm/s), in eq 7 could be empirically estimated from data. Alternately, from Johnson and Ettinger (3), an estimate based on building and foundation physical characteristics is given by
h)
h)
( ) ηDcrk Lcrk
Qs ) 0
(8a)
Lmix‚ER LmixER‚Ab (exp(ξ) - 1) 1 -1 + ‚ Qs exp(ξ) exp(ξ) Qs > 0 (8b)
( ) (
)
Equation 8a applies for diffusion-dominated vapor flow through soil-filled cracks in a foundation of thickness Lcrk. The cracks cover an areal fraction, η (cm2/cm2), of the foundation area in contact with soil, Ab (cm2). The effective diffusivity in the foundation cracks, Dcrk, is estimated with eq 2. Equation 8b applies with convective volumetric airflow, Qs (cm3-air/s), entering the building through foundation cracks. Within eq 8b, ξ is
ξ)
QsLcrk AbDcrkη
of chemicals and oxygen in soils. A shallow aerobic layer, La, with biodegradation, and a deeper anaerobic layer, Lb, without biodegradation are included, as in Figure 1. Chemical vapor concentrations are indicated in the source zone, cs, at the anaerobic-aerobic interface, ct, and within indoor building enclosure air, ce. Chemical flux, J, are similarly defined. Chemical Vapor Transport with Biodegradation. For chemicals, an algebraic solution is first shown for a soil layer of depth, L, then applied for the layers La and Lb as in Figure 1. Aerobic chemical biodegradation is presumed to occur in the water-phase soil matrix as a source (+) or sink (-) per unit mass of soil, Λ (mg/g-soil‚s), specified by a first-order chemical degradation rate, kw (1/s).
Λ)-
∂J ) FsΛ ∂z
(11)
From eqs 3 and 11
Deff ‚
The prior development presents a vapor intrusion model without biodegradation. The next section shows a model which includes biodegradation, but which neglects the attenuating effects of a building and foundation on chemical vapor transport, that is, Lmix‚ER . Deff/LT and h . Deff/LT in eq 7. This yields estimates for building air concentration, ce, that are higher than the same scenario with resistance to chemical transport through the building and foundation included. Limited oxygen availability in the subsurface is included in the biodegradation model, based in part on the average volumetric airflow through the building foundation, Qs. The biodegradation model consists of a coupled set of conservation equations that include diffusion and reaction ENVIRONMENTAL SCIENCE & TECHNOLOGY / VOL. 41, NO. 9, 2007
∂2cv ∂z2
) -FsΛ
(12)
Using a reference chemical vapor concentration (at z ) 0) of c0, boundary conditions are specified as
( (
) )
c(z/L ) 1) )β c0
Indoor Air Vapor Intrusion with Biodegradation
9
(10)
The value Fs (g-soil /cm3-soil) is soil bulk density. The degradation term is included in chemical transport as
(9)
The Johnson and Ettinger model includes both diffusive and convective mass transfer across a building foundation. Further explanation is included in refs 3 and 16. Other estimates could include varied physical assumptions for the foundation, or could alternately be based on measured data sets for cs and ce, as in ref 1.
3242
θw ‚k c Fs H w v
c(z/L ) 0) )1 c0
(13)
A steady-state solution to eq 12 is given (17) by
( )
c(z) ) c0 (exp(-R) - β)‚exp(R‚z/L) + (β - exp(R))‚exp(-R‚z/L) exp(-R) - exp(R) R > 0 (14a)
( )
()
c(z) z )1‚(1 - β) c0 L
R)0
(14b)
with
From eqs 20, 21, and 23
R)
x
kwθwL2 DeffH
(15)
AF )
(
)
Deff ce ) ‚ cs LmixER 2Ra
(24)
Differentiating eq 14 and with eq 3
LbRa[exp(-Ra) + exp(Ra)] - La[exp(-Ra) - exp(Ra)]
LJ(z) ) Deffc0 (exp(-R) - β)exp(Rz/L) - (β - exp(R))exp(-Rz/L) R‚ exp(R) - exp(-R) R > 0 (16a)
Equations 10-24 have been presented for a single chemical. The equations apply for multiple chemicals using appropriate chemical-specific parameters. Oxygen Demand and Transport. Biodegradation within the aerobic soil layer, La, requires oxygen supplied from the soil surface. Oxygen respiration, ΛO2, is specified as a sum of oxygen demand in biodegradation of N individual chemicals plus a baseline soil oxygen respiration term, Λbase,O2.
LJ(z) )1-β Deffc0
R)0
(16b)
N
The chemical flux solutions of eq 16 are applied with subscripts to designate aerobic (a) and anaerobic (b) soil layers. In the aerobic zone with chemical degradation (Ra > 0), a conservative overestimate of chemical flux from subsurface soil to indoor air at za ) La is made presuming ct . ce, or approximately, βa ) 0 in eq 16a.
ΛO2 )
N
1
∑ φ ‚(J
Je,O2 - Jt,O2 )
(18)
i)1
e,i
- Jt,i) + FsLaΛbase,O2
N
(19)
∑
Deff,ict,i
i)1
‚
x
kw,iθw
‚
Deff,iHi
φi
2 - exp(-Ra,i) - exp(Ra,i)
+ exp(Ra,i) - exp(-Ra,i) FsLaΛbase,O2 (27)
For oxygen concentration, substitution of eq 12 into eq 25 and integrating (0 to La) yields
ce,O2 - ct,O2 )
with
N
()
exp(-Ra) + exp(Ra) Lb 1 )1‚ Ra ‚ βb La exp(-Ra) - exp(Ra)
i)1
(21)
(22)
With eq 5, eq 22 yields
(
)
1
‚
Deff,O2
φi
‚ [ct,i - ce,i] -
(
)
FsΛbase,O2La2 2Deff,O2
(28)
)
Deff,O2ce,O2 N
∑ i)1
ce 2Ra Deff/La ) ‚ ct LmixER exp(Ra) - exp(-Ra)
( ) Deff,i
Oxygen concentration at the aerobic to anaerobic interface, ct,O2, is zero. For a conservative overestimate of oxygen demand, ce,i is presumed zero in eq 28. With the applied zero concentration conditions, eqs 27 and 28 yield Je,O2La
For za ) La in the aerobic zone, from eq 17
LaJe 2Ra ) Deffct exp(Ra) - exp(-Ra)
∑
(20)
Equating eqs 18 and 19 and solving for 1/βb
()
(26)
i
Je,O2 )
In the anaerobic zone with no degradation, flux is constant (Js ) Jt). At the aerobic-anaerobic interface, from eq 16b
ct βb ) cs
(25)
base,O2
i
Oxygen flux at the aerobic to anaerobic interface Jt,O2 is zero. Substituting eqs 18, 22, and 15 into eq 26 yields
At the aerobic-anaerobic interface, at za ) 0, eq 17 is
LbJt ) 1 - βb Deffcs
i)1
The value φi (mg-chemical /mg-oxygen) is a chemical-specific mass ratio of oxygen to chemical consumption. Equations 11 and 12 apply for oxygen with Λ ) ΛO2. Substituting eq 11 into eq 25 and integrating (0 to La) yields
LaJ(za) ) Deffct exp(-Ra)exp(Raza/La) + exp(Ra)exp(-Raza/La) Ra‚ (17) exp(Ra) - exp(-Ra)
LaJt exp(-Ra) + exp(Ra) ) Ra ‚ Deffct exp(Ra) - exp(-Ra)
Λi
∑φ +Λ
Deff,ict,i φi
‚
x
kw,iθw
Deff,iHi N
(23)
Where the assumption ct . ce is not met, attenuation across the neglected building foundation may be significant. In these conditions, the Johnson and Ettinger (3) model of eqs 7 and 8 may yield more applicable results.
‚
∑ i)1
2 - exp(-Ra,i) - exp(Ra,i) exp(Ra,i) - exp(-Ra,i)
( )( Deff,ict,i φi L a
-
+ FsLaΛbase,O2
)
FsΛbase,O2La 2
(29)
Biodegradation Model Solution. The biodegradation model includes chemical and oxygen transport equations for concentration and flux and a set of intermediate parameter calculations. This equation set is solved either by specifying VOL. 41, NO. 9, 2007 / ENVIRONMENTAL SCIENCE & TECHNOLOGY
9
3243
TABLE 1. Saturated Vapor Concentrations; Effective Diffusion Coefficient, Deff,i, Henry’s Law Coefficient, Hi, and Diffusive Attenuation Distance, LR,i in Aerobic Soils for Gasoline Component Chemicals and Surrogatesa saturated vapor concentration (mg/m3-air)
Deff,i effective diffusion coefficient (cm2/s) [range]
Hi Henry’s law coefficient (cm3/cm3)
LR,i aerobic diffusive reaction length (cm) [range]
10 800 14 700 980 3760 117 1140 12.5 1.4
0.00097-0.026 0.00096-0.026 0.00083-0.022 0.00079-0.021 0.0011-0.029 0.0011-0.029 0.0011-0.029 0.00067-0.017
0.23 0.28 0.33 0.22 0.56 0.33 0.19 0.020
2.1-26 2.3-29 2.4-29 1.9-23 3.6-43 2.7-33 2.1-26 0.53-6.3
553 000 78 200 11 600 2360
0.0011-0.029 0.0011-0.029 0.0011-0.029 0.0011-0.029 0.0019-0.051
51 54 56 59 45
3.6-44 3.7-45 3.8-46 3.9-47
aromatic hydrocarbons benzene toluene ethyl benzene xylenes (mixed isomers) EC >8-9 aromatic EC >9-10 aromatic EC >10-11 aromatic napthalene aliphatic hydrocarbons EC >5-6 aliphatic EC >6-7 aliphatic EC >7-8 aliphatic EC >8-9 aliphatic oxygen a
Applied soil properties include θT from 0.36 to 0.49 cm3-void/cm3-soil and θw from 0.039 to 0.22 cm3-water/cm3-soil.
a maximum downward oxygen flux, Je,O2, or a maximum oxygen concentration, ce,O2 at the upper soil boundary.Iteration within the range 0 e La e LT yields an aerobic depth La, using either eqs 27 or 28 to check convergence to the specified oxygen criteria. A monotonic relation exists between La, Je,O2, andce,O2. Ambient oxygen concentration in air, camb,O2 (0.279 mg/ cm3-air), is an upper limit for ce,O2 in eq 28. This is equivalent to a bare soil floor in a building. Measured oxygen concentration below a building foundation could also be specified as an upper limit for ce,O2. A mass flow limit on available oxygen below a building foundation can be estimated from studies of air intrusion through building foundations. Hers et al. (4) suggest a measured range for convective airflow, Qs, entering a building through the subsurface foundation in a range of 1-10 L-air /min. Additional convective airflow will also pass under a building without entering the building. Therefore, the range of Qs through a building foundation defines a lower limit for the total airflow under a building. With a building foundation area, Ab, downward mass flux of oxygen into soil below a building foundation for eq 27 is
|Je,O2| e
Qs ‚c Ab amb,O2
(30)
Model Parameters Solutions for the biodegradation model and the Johnson and Ettinger model have been calculated using representative parameter ranges and values, which are discussed as follows. Source Parameters. The source composition is based on a representative unweathered hydrocarbon gasoline (18) and includes individual chemicals and surrogate fractions. Saturated vapor concentrations based on Raoult law partitioning and specified water to gasoline volume ratio of 10 are included in Table 1. In model calculations the source concentration, cs, is specified as the saturated concentration times a multiplied factor ranging from 1 to 10-5. Chemical-Specific Physical Parameters. Physical properties for gasoline chemical components, surrogate petroleum fractions, and oxygen are included in the Supporting Information. These include molecular weight, molecular diffusivity in air and water, Henry’s law coefficient, pure chemical aqueous solubility, and vapor pressure. 3244
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ENVIRONMENTAL SCIENCE & TECHNOLOGY / VOL. 41, NO. 9, 2007
The mass ratio of oxygen to chemical consumption, φi, presumes complete aerobic reaction of hydrocarbon constituents to carbon dioxide and water on a mass basis
φi )
MWi
(
MWO2‚ n +
m 4
)
(31)
with MWi as molecular weight (g/g ‚ mole) and hydrocarbon chemical formula defined by
(
CnHm + n +
m m ‚ O2 f ‚ H2O + n‚CO2 4 2
)
Chemical Degradation Rate. Aerobic degradation of petroleum chemicals in soils is pervasive. Petroleum hydrocarbons are readily biodegradable in soils under aerobic conditions (19) with degradation observed after initial exposures of hours or days. Given that aerobic biodegradation occurs, a range of empirical degradation rates has been estimated. These rates are applicable if specified criteria are met (20), including that inorganic nutrients are available, soil moisture is present at levels sufficient to support biological activity, and oxygen is present. Inorganic mineral nutrients are present in native soils at levels sufficient to maintain existing soil biomass. Soils with moisture above the plant wilting point (21) meet the water criterion. Bordon and Bedient (22) present a value of 0.1 mg/L oxygen in water, above which aerobic degradation is observed. While the biodegradation rates depend on multiple conditional factors and are not strictly first-order, they can be presumed to exhibit first-order behavior if these limiting conditions are met. The biodegradation rate is an average over a representative volume larger than the soil pore scale and smaller than observed macroscopic soil heterogeneities. First-order kinetics are presumed, with the specific rate proportional to waterphase chemical concentration, as in eq 10. Data are included for soils with no nutrient amendments, and if supporting information allows determination of a rate consistent with eq 10. Empirical rates have been defined for two chemical classes, aromatic and aliphatic hydrocarbons, based on reported measurements by multiple investigators. Apparatus includes microcosms in which the disappearance of a chemical is monitored over time and measurement of steadystate concentration profiles in laboratory soil columns under
An analysis for a range of straight- and branched- aliphatic hydrocarbons includes values from 17 data sets (32-34). Chemicals include C6-C12 -range normal paraffins and isomers of dimethylpentane, dimethylhexane, trimethylpentane, and trimethylhexane. Figure 2 shows data for the aliphatic hydrocarbons, including a geometric mean rate of kw ) 71 h-1. The mean water-phase degradation rate for these aliphatic hydrocarbons is greater than indicated for aromatic hydrocarbons. The confidence interval on the mean is wider than for the aromatic data set, which may be due to limited data, or due to the much lower water-phase partitioning in soil for aliphatic hydrocarbons relative to aromatic hydrocarbons. More complex models for biodegradation kinetics are not considered either because they do not improve on estimates within the observed confidence intervals, or because they require calibration parameters that are not readily available. Dependence that may be apparent in individual test series (temperature for example) is not included, as the variability in rates between different data sets is greater than the indicated dependence in specific investigations. Higher chemical concentrations may increase the likelihood of local anaerobic zones within the aerobic averaging volume, or that available nutrients may be limited and may, therefore, limit maximum biomass growth and the observed degradation rate for some soils. Anaerobic degradation, which may contribute to additional attenuation for some chemicals, is neglected. Empirical rate estimates for kw,i would be required to include additional chemicals in the model. Based on eq 15, as a measure of biodegradation relative to diffusion, we define a diffusive reaction length, LR,i, by setting Ri ) 1.
LR,i )
FIGURE 2. Aerobic biodegradation rates for (a) aromatic hydrocarbons and (b) straight chain and branched aliphatic hydrocarbons with geometric mean first-order rates of 0.79 and 71 h-1 respectively. A 95% confidence interval on the geometric mean value and the geometric standard deviation of the data are shown in each plot.
both diffusive and convective vapor flow conditions, in field lysimeters, and in vadose zone field data. A range of conditions (temperatures, moisture levels, soil types, etc.) is included. DeVaull (20) discusses data analysis for the measurement systems. The compilation for aromatic hydrocarbons includes a total of 84 data sets (20, 23-33). Individual chemicals include benzene, toluene, ethylbenzene, and xylenes (BTEX); trimethylbenzene, and naphthalene. Rates for mixed BTEX chemicals are included. Figure 2 shows water-phase concentration versus degradation rate, a geometric mean rate of kw ) 0.79 h-1, a 95% confidence interval on the mean, and the geometric standard deviation of the data.
x
Deff,iHi kw,iθw
(32)
Calculated ranges of Deff,i and LR,i using geometric mean biodegradation rates, kw,i, and tabulated Henry’s law coefficients, Hi, are included in Table 1. These ranges have been applied in the model calculations. Baseline Soil Respiration. Oxygen respiration occurs in soils without chemical contamination, and is included as an added term in eq 25. Neale (35) reported on oxygen utilization rates in soil microcosms for nine soil types, with each soil at three moisture levels. Hendry (36) measured carbon dioxide generation for a sandy soil in an unsaturated soil layer, with respiration rates estimated through a diffusion model fit. In addition the author has measured oxygen respiration rates in a range of soil media, with data analysis methods comparable to the cited studies. From these data for moist soils, a correlation of baseline oxygen respiration rate, Λbase,O2, to soil organic carbon level, foc (g-oc/g-soil), is found.
(
Λbase,O2 ) - 1.69
)
mg - O2 ‚f g - oc‚day oc
(33)
For the range 0.0004 < foc < 0.4, errors in the oxygen respiration estimate are within a factor of approximately 10 of the correlation at a 95% confidence level. Dependence of respiration rate on soil moisture levels was reported (35, 36) but is not included in eq 33 as the variability between data sets is greater than the indicated dependence for specific soils. Dry soils with moisture levels below the plant wilting point (21) are not included. Variability in soil oxygen respiration may be due to experimental methods, variations in the biological availability and types of soil organic carbon, diffusion limitations within soil layers and within the soil matrix, temperature, moisture levels, and soil heterogeneity. At very low organic carbon concentrations, random meaVOL. 41, NO. 9, 2007 / ENVIRONMENTAL SCIENCE & TECHNOLOGY
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3245
surement error in organic carbon concentration contributes to the measured data variability. In biodegradation model calculations, baseline soil respiration is applied as a function of soil organic carbon fraction for foc from 0.0004 to 0.05 g-oc/g-soil. Soil Parameters. A soil bulk density, Fs, of 1.7 g-soil/cm3soil is specified (2). The biodegradation model includes soil bulk density only as a product of soil bulk density and baseline oxygen respiration, as in eqs 26-29. The soil bulk density is presumed constant as the nominal variation in soil bulk density is less than the variability in the baseline oxygen respiration rate of eq 33 and the associated data sets. Ranges for soil porosity, θT from 0.36 to 0.49 cm3-void/ cm3-soil and soil moisture θw from 0.039 to 0.22 cm3-water/ cm3-soil are specified. Vapor-filled soil porosity, θv, is calculated by difference. These values encompass ranges typical for unsaturated soils (1, 21). Building Parameters. Nominally building parameters in the biodegradation model include ER ) 6 /day, Lmix ) 240 cm, and Ab ) 100 m2. For the Johnson and Ettinger model (3), upper and lower limiting ranges for the building parameters and foundation parameters are specified (7) that encompass ranges from other sources (1, 2). This include Qs from 1 to 10 L-air/min; ER from 6 to 24 d-1; Lcrk from 10 to 15 cm; η from 0.00005 to 0.001 cm2/cm2; Lmix from 240 to 480 cm; and Ab equal to 100 m2. In an alternate approach, a range of building attenuation factors could be developed based on an empirical analysis of measured data (1). Oxygen Boundary Condition. Two oxygen boundary conditions have been applied. Maximum oxygen concentration levels are specified at values ranging from 0.279 to 0.000279 mg/cm3. For a mass flow limited oxygen boundary, Qs is specified at maximum values ranging from 1 to 10 L-air/ min (4), with an applied upper bound oxygen concentration of 0.279 mg/cm3-air. Oxygen Demand to Availability Ratio. Ratios of maximum oxygen demand relative to oxygen availability are defined to aid interpretation of model results. Maximum oxygen demand is estimated presuming the soil layer LT is aerobic. For oxygen flux, based on eqs 27 and 32 we define a ratio of maximum oxygen demand relative to oxygen availability, Yf. N
∑ Yf )
i)1
(
)
Deff,ics,i 2 - exp(-RT,i) - exp(RT,i) ‚ φiLR,i exp(RT,i) - exp(-RT,i) Je,O2
(
+
)
LTFsΛbase,O2 Je,O2
(34)
and RT,i ) LT/LR,i. Similarly, for an oxygen concentration boundary condition, based on eq 28 we define a ratio of maximum oxygen demand relative to oxygen availability, Yc.
(
∑
Yc )
) ( ))
1/2
N
Deff,i‚[cs,i/φi]
i)1
Deff,O2‚ce,O2
2
-
LT Fs Λbase,O2 2Deff,O2‚ce,O2
(35)
For both Yc and Yf, the soil layer is entirely aerobic for Y < 1, partially anaerobic for Y > 1, and for Y ) 1, entirely aerobic with oxygen consumption equal to oxygen demand.
Model Results BTEX Chemicals. Calculated biodegradation model results are shown for BTEX chemicals in Figure 3. All of the BTEX biodegradation results are similar and, therefore, plotted as composite median values. For equal values of Yc and Yf the 3246
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ENVIRONMENTAL SCIENCE & TECHNOLOGY / VOL. 41, NO. 9, 2007
FIGURE 3. Median attenuation factors for BTEX chemicals in a gasoline source zone. Both oxygen concentration and flux boundary conditions are included, with values of Y as indicated. Comparison is made to the eq 6 “bare soil floor” and eqs 7 and 8 “foundation” model using high and low parameter ranges. The confidence intervals apply for the biodegradation model results at AF ) 10-8, and include 90% of model predictions. specific results for AF are not necessarily equal but the composite median results are equivalent and, therefore, plotted as a single curve for specified integer values of Y. The vertical and horizontal confidence intervals in Figure 3 apply for each of the median values at AF ) 10-8 and include 90% of calculated results. The no-biodegradation estimates of eqs 6-8 are included using maximum and minimum foundation parameters consistent with (7). The biodegradation model results of Figure 3 indicate values of AF that are always less than the estimates of eq 6. With greater biodegradation (larger values of Ra,i) or greater oxygen availability (lower values of Y), the biodegradation model predictions for AF are increasingly less than the nobiodegradation estimates. The confidence intervals in Figure 3 are significantly greater for AF than for (Deff,i /LT)/(LmixER), principally due to the slope of the plotted lines. For example, in the biodegradation model an increase in the vapor source to building separation distance LT by a factor of 2 at AF ) 10-8 and Y ) 1 decreases AF by a factor of 8 × 106. The same change in LT (at AF ) 10-8) for the no-biodegradation models decreases AF by a factor of 2. This result implies that in interpreting vapor intrusion for biodegrading petroleum chemicals, much greater confidence may be assigned to parameters dependent on the Figure 3 horizontal axis (for example, an exclusion distance based on LT), rather than on the attenuation factor AF. For cases in which the soil zone, LT, is entirely aerobic (Y e 1), an explicit solution for AF is given by eq 23. An approximate relation based on eq 23 for Y g 1 illustrates the sensitivity of the biodegradation model results of Figure 3 to key parameter groups.
AF )
(
)
2RT,i Deff/LT ‚Y ‚ LmixER exp(RT,i) - exp(-RT,i)
(36)
Equation 36 includes terms for the ratio of maximum oxygen demand to oxygen availability (as either Yc or Yf), and a
chemical properties; baseline soil oxygen respiration data and analysis; a discussion of the Yc and Yf relationship; and a summary of the model parameters. This material is available free of charge via the Internet at http://pubs.acs.org.
Literature Cited
FIGURE 4. Normalized oxygen flux versus a ratio dependent on terms for baseline soil oxygen respiration and chemical oxygen demand. This is a plot of eq 29. The value A is given by eq 37. chemical-specific kinetic biodegradation rate. For RT,i ) LT/ LR,i, and LR,i ) 9 cm, eq 36 matches the median BTEX biodegradation model results in Figure 3. The confidence bounds in Figure 3 correspond to a range of LR,i from 4.9 to 15 cm. Values of LR,i between approximately 2 and 21 cm bound the extreme BTEX results for the biodegradation model and compare with the range of BTEX values for LR,i in Table 1. The biodegradation model and the terms identified in eq 36 may prove useful in indoor vapor intrusion validation efforts for biodegrading chemicals. This may include further investigation of chemical-specific diffusive reaction lengths and of oxygen demand relative to oxygen availability. The biodegradation model may also be of use in practical screening applications, for example in estimating ranges of site conditions that may or may not be of further potential concern. Oxygen. Oxygen demand in the biodegradation model is limited to the aerobic soil layer and is described by eq 29, from which we define N
∑ A)
i)1
Deff,ict,i φi
‚ Ra,i ‚
2 - exp(-Ra,i) - exp(Ra,i) exp(Ra,i) - exp(-Ra,i) N
Deff,ict,i
i)1
φi
∑
(37)
Figure 4 includes a plot of eq 29, for specified values of A. This figure indicates the relative contribution to oxygen demand from either baseline soil oxygen respiration or chemical biodegradation, and the effects of chemical biodegradation kinetics on oxygen demand as a function of A. Both baseline soil oxygen respiration and chemical biodegradation may contribute to total oxygen demand, or one or the other may be dominant, depending on the specific model scenario parameters.
Acknowledgments This work was completed with the support of Royal Dutch Shell PLC. The author gratefully acknowledges the experimental laboratory work of H. L. Wisniewski and E. M. Hinojosa. The useful suggestions of several anonymous reviewers are gratefully acknowledged.
Supporting Information Available Information on a compiled set of building characteristic parameters; gasoline mixture composition and component
(1) Guidance for Evaluating the Vapor Intrusion to Indoor Air Pathway from Groundwater and Soils (Subsurface Vapor Intrusion Guidance); Draft, November 2002 EPA530-D-02-004; United States Environmental Protection Agency, Office of Solid Waste and Emergency Response: Washington, DC, 2002. (2) ASTM E 1739-95. Standard Guide for Risk-Based Corrective Action Applied at Petroleum Release Sites; American Society for Testing and Materials: West Conshohocken, PA, 2002. (3) 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. (4) 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. (5) Fitzpatrick, N.; Fitzgerald, J. J. An Evaluation of vapor intrusion into buildings through a study of field data. Soil Sediment Contam. 2002, 11 (4), 603-623. (6) 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. (7) Hers, I.; Zapf-Gilje, R.; Li, L.; Atwater, J. The use of indoor air measurements to evaluate intrusion of subsurface VOC vapors into buildings. J. Air Waste Manage. Assoc. 2001, 51 (3), 13181331. (8) Roggemans, S.; Bruce, C. L.; Johnson, P. C.; Johnson, R. L. 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, 2001. (9) Fischer, M. L.; Bentley, A. J.; Dunkin, K. A.; Hodgson, A. T.; Nazaroff, W. W.; Sextro, R. G.; Daisey, J. M. Factors affecting indoor air concentrations of volatile organic compounds at a site of subsurface gasoline contamination. Environ. Sci. Technol. 1996, 30 (10), 2948-2957. (10) Johnson, P. C.; Kemblowski, M. W.; Johnson, R. L. Assessing the significance of subsurface contaminant migration to enclosed spaces: Site-specific alternatives to generic estimates. J. Soil Contam. 1999, 8, 389-421. (11) Lahvis, M. A.; Baehr, A. L. Documentation of R-UNSAT, a Computer Model for the Simulation of Reactive, Multispecies Transport in the Unsaturated Zone; U.S. Geological Survey OpenFile Report 97-630; U.S. Geological Survey: Reston, VA, 1997. (12) Abreu, L. D. V.; Johnson, P. C. Simulating the effect of aerobic biodegradation on soil vapor intrusion into buildings: Influence of degradation rate, source concentration, and depth. Environ. Sci. Technol. 2006, 40 (7), 2304-2315. (13) Abreu, L. D. V.; Johnson, P. C. Effect of vapor source-building separation and building construction on soil vapor intrusion as studied with a three-dimensional numerical model. Environ. Sci. Technol. 2005, 39 (12), 4550-4561. (14) Jury, W. A.; Spencer, W. F.; Farmer, W. J. Behavior assessment model for trace organics in soil: I. Model description. J. Environ. Qual. 1983, 12, 558-564. (15) Bruell, C. J.; Hoag, G. E. The diffusion of gasoline-range hydrocarbon vapors in porous media, experimental methodologies, In Proceedings of the NWWA/API Conference on Petroleum Hydrocarbons and Organic Chemicals in Groundwater: Prevention, Detection, and Restoration, 1986, November 1214, Houston. (16) Johnson, P. C. Identification of application-specific critical inputs for the 1991 Johnson and Ettinger vapor intrusion algorithm. Ground Water Monit. Rem. 2005, 25 (1), 63-78. (17) Cussler, E. L. Diffusion-Mass Transfer in Fluid Systems, 2nd ed.; Cambridge University Press: Cambridge, UK, 1997. (18) Potter, T. L.; Simmons, K. E. Total Petroleum Hydrocarbon Criteria Working Group Series, Volume 2: Composition of Petroleum Mixtures; Amherst Scientific Publishers: Amherst, MA, 1998. (19) Ollivier, B.; Magot, M., Eds. Petroleum Microbiology; ASM Press: Washington, DC, 2005. (20) DeVaull, G. E.; Ettinger, R. A.; Salanitro, J. P.; Gustafson, J. B. Benzene, toluene, ethylbenzene, and xylenes [BTEX] degradation in vadose zone soils during vapor transport: First-order rate constants, In Proceedings of the Petroleum Hydrocarbons and VOL. 41, NO. 9, 2007 / ENVIRONMENTAL SCIENCE & TECHNOLOGY
9
3247
(21) (22) (23)
(24) (25) (26) (27)
(28)
(29)
Organic Chemicals in Ground Water - Prevention, Detection, and Remediation Conference, API/NGWA, 1997, November 1214; Ground Water Publishing Company: Westerville, OH, 365379. Guymon, G. L. Unsaturated Zone Hydrogeology; Prentice Hall: Englewood Cliffs, NJ, 1994. Bordon, R. C.; Bedient, P. B. Transport of dissolved hydrocarbons influenced by oxygen-limited biodegradation, 1. theoretical development. Water Resour. Res. 1986, 22 (13), 1973-1982. Holman, H. Y.; Tsang, Y. W. Effects of Soil Moisture on Biodegradation of Petroleum Hydrocarbons in In Situ Aeration: Air Sparging, Bioventing, and Related Bioremediation Processes; Hinchee, R. E., Miller, R. N., Johnson, P. C., Eds.; Battelle Press: Columbus, OH, 1995; pp 323-332. Jin, Y.; Streck, T.; Jury, W. A. Transport and biodegradation of toluene in unsaturated soil. J. Contam. Hydrol. 1994, 17, 111127. Karlson, U.; Frankenberger, W. T., Jr. Microbial degradation of benzene and toluene in groundwater. Bull. Environ. Contam. Toxicol. 1989, 43, 505-510. Ostendorf, D. W.; Kampbell, D. H. Biodegradation of hydrocarbon vapors in the unsaturated zone. Water Resour. Res. 1991, 27, 453-462. Ostendorf, D. W.; Kampbell, D. H. Vertical profiles and near surface traps for field measurement of volatile pollution in the subsurface environment. In Proceedings of the National Water Well Association Conference on New Technologies for Quantifying the Physical and Chemical Properties of Heterogeneous Aquifers; Dallas, TX, 1989. Salanitro, J. P.; Western, M. M.; Kemblowski, M. W. Biodegradation of aromatic hydrocarbons in unsaturated soil microcosms. In Fourth National Conference on Petroleum Contaminated Soils, September 25-28; University of Massachusetts: Amherst, 1989. Salanitro, J. P.; Diaz, L. A.; Williams, M. P.; Wisniewski, H. L. Simple methods to estimate aromatic hydrocarbon degrading
3248
9
ENVIRONMENTAL SCIENCE & TECHNOLOGY / VOL. 41, NO. 9, 2007
(30)
(31) (32)
(33)
(34) (35) (36)
units (microbes) in soil and ground water. In International Symposium on Subsurface Microbiology (ISSM-93), 19-24 September; Bath, UK, 1993. Lahvis, M. A.; Baehr, A. L.; Baker, R. J. Quantification of aerobic biodegradation and volatilization rates of gasoline hydrocarbons near the water table under natural attenuation conditions. Water Resour. Res. 1999, 35 (3), 753-765. March. Hers, I.; Atwater, J.; Li, L.; Zapf-Gilje, R. Evaluation of vadose zone biodegradation of BTX vapors. J. Contam. Hydrol. 2000, 46, 233-264. Hohener, P.; Duwig, C.; Pasteris, G.; Kaufmann, K.; Dakhel, N.; Harms, H. Biodegradation of petroleum hydrocarbon vapors: Laboratory studies on rates and kinetics in unsaturated alluvial sand. J. Contam. Hydrol. 2003, 66, 93-115. Pasteris, G.; Werner, D.; Kaufmann, K.; Hohener, P. Vapor phase transport and biodegradation of volatile fuel compounds in the unsaturated zone: A large scale lysimeter experiment. Environ. Sci. Technol. 2002, 36, 30-39. Moyer, E. E. Investigation of diffusion and biodegradation of vapor phase petroleum hydrocarbons, Ph.D. Thesis, University of Massachusetts, 1993. Neale, C. N.; Hughes, J. B.; Ward, C. H. Impacts of unsaturated zone properties on oxygen transport and aquifer reaeration. Groundwater 2000, 38, 784-794. Hendry, M. J.; Mendoza, C. A.; Kirkland, R.; Lawrence, J. R. An Assessment of a mesocosm approach to the study of microbial respiration in a sandy unsaturated zone. Groundwater 2001, 39, 391-400.
Received for review March 21, 2006. Revised manuscript received February 14, 2007. Accepted February 19, 2007. ES060672A
