Environ. Sci. Technol. 2007, 41, 4993-5001
Time-Variable Simulation of Soil Vapor Intrusion into a Building with a Combined Crawl Space and Basement W I L L I A M B . M I L L S , * ,† S A L L Y L I U , † M A R K C . R I G B Y , †,‡ A N D D A V I D B R E N N E R § Tetra Tech, Inc., 3746 Mt. Diablo Blvd., Suite 300, Lafayette, California 94549, Marine Science Institute, University of California, Santa Barbara, California 93106-6150, and Neptune and Company, Inc., 1505 15th St., Suite B, Los Alamos, New Mexico 87544.
A time-variable one-dimensional model (called ViM for Vapor Intrusion Model) to predict indoor vapor concentrations in a dwelling with a combined basement and crawl space has been developed. ViM predicts vapor concentrations in each of the three compartments. Volatile chemicals that intrude into the dwelling are assumed to originate from soil, groundwater (where an attenuating plume is simulated), or ambient air. Processes included in the model are advection, diffusion, biodecay, and adsorption in the soil column; transport by diffusion and advection into individual crawl space and basement compartments; advection from each compartment into an overlying dwelling space; and exchange of ambient air and indoor air. The timevariable concentration fields are solved by first transforming the partial and ordinary differential equations into Laplace space, solving the resulting ordinary differential equations or algebraic equations, and numerically inverting those equations. This approach was an expedient way of handling the coupling between the subsurface and the dwelling. ViM was applied to a building (Building 20) located at the former Moffett Field Naval Air Station, in Mountain View, CA. The building is a former bachelor officer’s quarters. The shallow groundwater beneath the building is contaminated with a number of volatile chemicals, including trichloroethene, cis-1,2-dichloroethene, and trans-1,2dichloroethene, all of which were simulated. Using indoor air data collected in 2003-2004, and other field data collected prior to that time, the accuracy of the model’s predictions was demonstrated. ViM’s results were also compared against a version of the steady-state Johnson and Ettinger model (1) that was modified to accommodate a dwelling with a combined crawl space and basement (called the JEM model in this paper). The predictions from the JEM model were consistently higher than the predictions from ViM, but still near the upper range of the observed data.
* Corresponding author phone: (925) 283-3771; fax: (925) 2830780; e-mail:
[email protected]. † Tetra Tech, Inc. ‡ University of California. § Neptune and Company, Inc. 10.1021/es061747d CCC: $37.00 Published on Web 06/15/2007
2007 American Chemical Society
Introduction Vapors in indoor air have long been a public health concern. Often, but not always, those vapors originate from an outside source, such as from the volatilization of chemicals in soil or groundwater that first migrate upward into a basement or crawl space and then into the space above where residents may live (i.e., the dwelling space). Most of the early efforts to model indoor vapor intrusion focused on the radioactive gas radon, which has been a concern in the United States for decades. This concern was engendered by such cases as a residence in Pennsylvania that was found to contain radon in indoor air at concentrations as high as 2500 pCi/L, nearly a thousand times above the U.S. Environmental Protection Agency’s (USEPA) action level of 4 pCi/L (2). Some of the first models for the intrusion of radon into indoor air were written by Scott (3) and Tanner (4), who described models for radon migration through the natural environment and into homes. Similarly, Nazaroff and Doyle (5) mathematically described several different mechanisms that can be used to model radon intrusion into homes. Shortly after the models for radon transport through soils and into homes were developed, concern turned to subsurface chemical contamination and models to simulate subsurface migration were developed (e.g., 6-9). The early models did not originally couple subsurface vapor transport with indoor vapor intrusion. That was first done by Johnson and Ettinger (1), although they used a relatively simple subsurface transport model. The Johnson and Ettinger (J&E) model is widely used today, especially by the regulatory community. The J&E model was developed primarily for residences with a cement foundation; i.e., either a single story slabon-grade residence or a single story residence with a basement. For residences with a basement, it was assumed that there is rapid mixing of the air in the dwelling space and the basement, leading to a uniform vapor concentration in the dwelling space and basement. However, for buildings with crawl spaces, USEPA (10) has recognized that the J&E model (as implemented by the USEPA) is of limited applicability. With that limitation as a motivation, the model described in this paper (named the Vapor Intrusion Model, or ViM) was developed to simulate soil vapor intrusion into homes with crawl spaces. Other capabilities were also added to ViM that are not present in the USEPA (10) version of the J&E model, including (a) time-dependent predicted indoor air concentrations. (This allows indoor air concentrations to be simulated over a variety of exposure periods, from years to days); (b) Simulation of three different source terms: (i) a time-dependent groundwater plume, where the contaminant plume can either attenuate or intensify over time, (ii) a time-dependent source of contaminated soil in the unsaturated zone, and (iii) ambient air (i.e., ambient or background outdoor air is not assumed to be free of contaminants); (c)Solution of differential equations by numerically inverting Laplace transforms. (This allows ViM to execute very quickly; i.e., typically on the order of seconds for a 70 year simulation); (d) Simulation of crawl spaces by assuming a porous medium beneath the home, rather than a basement that may have a concrete floor and walls; (e) Simulation of basements and crawl spaces as separate compartments from the dwelling space; (f) Simulation of buildings with both a crawl space and a basement. (The motivation for simulating a building with a combined basement and crawl space originated from the case study examined in this paper; i.e., Building 20, which is a bachelor’s officers quarters on a former military base that has both a VOL. 41, NO. 14, 2007 / ENVIRONMENTAL SCIENCE & TECHNOLOGY
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FIGURE 1. ViM conceptual model for vapor transport from a groundwater plume into a three-compartment building. Note: abbreviations are defined in the Glossary in the Supporting Information. crawl space and a basement); (g) Monte Carlo simulation. This allows uncertainties in multiple variables to be examined simultaneously.
ViM Model Development Rationale for Model Development. Since indoor vapor intrusion has been recognized as an environmental problem for decades, and since vapor intrusion modeling has been preformed for decades, a reasonable question to ask is why develop a model such as ViM? The primary motivation for developing ViM was to provide a model that can simulate vapor intrusion into buildings with crawl spaces. As will be shown in this paper, a building with a crawl space may be much more prone to vapor intrusion into the dwelling space than a building with a cement foundation. Thus, using an indoor vapor intrusion model that assumes a foundation is present to model a dwelling with a crawl space may produce inaccurate results. Also, since a number of houses have more than one foundation type (statistics are provided below), a model that can simulate such situations may be useful. In 1995, the Department of Energy (11) surveyed over 7000 households across the entire United States and found that 31, 45, and 34% had slabs, basements, and crawl spaces, respectively. Therefore, the number of homes with crawl spaces in the United States appears to be a significant fraction of the total. Further, the percentages of foundation types in the Department of Energy (11) study add up to approximately 110%, indicating that approximately 10% of the houses surveyed had more than one foundation type. 4994
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Of the models described in Table S-1 of the Supporting Information, those most similar to ViM are the indoor vapor intrusion models by Sanders and Talimcioglu (12) and Turczynowicz and Robinson (T&R) (13). Both models are time-variable and simulate diffusion and advection through a one-dimensional soil column, as does ViM. However, in those two models, soil is the source term, while ViM can simulate groundwater, soil, and/or ambient air source terms. ViM can simulate a building with a crawl space and/or basement, and intrusion into the dwelling space from both a crawl space and/or basement. The T&R model simulates only a crawl space, while the Sanders and Talimcioglu (12) model simulates only a well-mixed space, and does not distinguish the basement from the dwelling space. The Sanders and Talimcioglu (12) model also assumes that the basement is essentially decoupled from the unsaturated zone. Both the T&R model and ViM do not make this assumption, but couple the indoor subsurface compartment with the soil column, thus requiring simultaneous solution of those equations. The simultaneous equations, after evaluating the spatial derivatives, are efficiently solved by numerically inverting Laplace transforms. Conceptual Model and Assumptions. The ViM conceptual model is illustrated in Figure 1. The contamination in this figure is assumed to originate from volatile organic chemicals in an attenuating groundwater trichloroethene (TCE) plume beneath the site. The plume also contains cis-1,2-dichloroethene (cis-1,2-DCE) and trans-1,2-dichloroethene (trans-
1,2-DCE), which are TCE breakdown products. The plume is assumed to cover an area larger than the dwelling space so that one-dimensional transport through the soil column is an appropriate assumption. In the unsaturated zone, processes that are simulated include diffusion, advection, adsorption, decay, and a finite availability of contaminants in the attenuating plume. Advection can occur throughout the soil column (e.g., from infiltrating soil moisture) or near the base of the building foundation due to pressure differentials between indoor and outdoor air (typically, such pressure differentials are between 2 and 10 Pa). Soil heterogeneities are assumed to be manifested through multiple homogeneous layers, including a capillary fringe, that are assimilated into one equivalent layer. The basement is assumed to have a solid foundation. Cracks may exist within the foundation or at the perimeter (i.e., in a manner similar to the J&E model). The crawl space is assumed to have a natural soil base (i.e., a porous medium) and, therefore, soil gas intrusion into the crawl space could be greater than into the basement. Both types of subsurface spaces are assumed to be ventilated with outdoor air, as is the dwelling space. Once vapors have intruded into the dwelling’s subsurface, they further migrate into the dwelling space. Once in the dwelling space, the model assumes that internal air flow is sufficient to mix the vapors and produce a single indoor vapor concentration that is time dependent. The outdoor (i.e., background) concentration can be nonzero, so that the indoor air concentrations could increase to elevated levels during active vapor intrusion, and return to background levels subsequent to source depletion. The vapor concentrations in each of the three compartments are allowed to differ. The model’s predictions were not only compared against available site specific data for the dwelling and crawl spaces, but also against a modified version of the J&E model (called JEM in this paper) to account for the dual basement-crawl space configuration. Figure S-4 in the Supporting Information shows the JEM conceptual model. The basic assumptions of the original J&E model (1) were retained, except that a nonzero background concentration and first-order biodegradation rate were added to JEM, in addition to the dual crawl space-basement configuration. As shown in Figure S-4 of the Supporting Information, the steady-state vapor concentrations in the crawl space, basement, and dwelling spaces are all assumed to be equal. Mathematical Model. The mathematical development of ViM is provided below, while the mathematical development of JEM is contained in the Supporting Information. The mass balance equations for this one-dimensional quasi-analytical model are all expressed in terms of vapor-phase concentrations. Both aqueous and adsorbed phase concentrations are also represented in ViM, but not a NAPL (nonaqeous phase liquid) phase. Indoor air contamination is assumed to originate from chemicals that volatilize from groundwater or soils, from nonzero outdoor air concentrations, or from elevated indoor air concentrations that may be present at the beginning of the simulation. Subsurface porous media are treated as a single equivalent layer of homogeneous sublayers. Thus, the model derivation builds on the concepts of the USEPA model (10), which are not repeated here. Figure 1 illustrates the ViM conceptual model. The building consists of three compartments: a crawl space, a basement, and a dwelling space. Time-variable vapor-phase concentrations are predicted separately for each compartment. The vapors that migrate through the soil are not assumed to interact with each other until they mix in the dwelling space. Beginning with the porous media beneath the crawl space, the vapor-phase mass transport equation can be written as follows (all symbols are defined in the Glossary in the Supporting Information):
(
)
∂Cg θgVg θwVw ∂Cg + + ) ∂t Rg RgKh ∂z
(
(θw)
10/3
DH2O
Khθ2Rg
+
(
)
(θg)10/3 ∂2 C g D air θ2Rg ∂z2
)
kadsKpFb Cg kwθw + kgθg + (1) Kh Kh Rg
where
Rg )
θw KpFb + + θg Kh Kh
(2)
Equation 1 assumes equilibrium between phases, all coefficients are constant, and layer-equivalent values. Note that an advection term is included for generality to simulate processes such as infiltration. Equation 2, with appropriate values of coefficients, is used for each of the two unsaturated zone columns beneath the crawl space and beneath the basement. For convenience, the three coefficients in eq 1 can be written as V/T, D/T, and k/T:
∂Cg ∂Cg ∂2 C g + VT/ ) DT/ 2 - kT/ Cg ∂t ∂z ∂z
(3)
When vapor intrusion is modeled from only a groundwater source, the soil column is assumed to initially be free of contamination, and is expressed by
Cg(z,t ) 0) ) 0
(4)
If a soil source is also modeled, contamination in the soil column in expressed by
Cg(z,t ) 0) ) f(z)
(5)
where f(z) is a user-specified profile of soil column contamination. At the water table, the vapor concentration is assumed to be dominated by a groundwater plume that has a timevariable concentration beneath the building, as given by
Cg(z ) Lcs,t) ) KhCgw(t) ) KhCgwo exp(-kgwt)
(6)
The general form of eq 6 is a groundwater plume with contaminant concentrations either decreasing (i.e., when kgw > 0) or increasing over time (i.e., when kgw < 0). At the soil-crawl space interface, a flux boundary condition is specified such that the flux at the top of the soil column is equal to the flux across a thin diffusive layer at the base of the crawl space:
AcsRgDT/
∂Cg (z ) 0,t) - AcsRgVT/ Cg (z ) 0,t) ) ∂z AcsDair {Cg(z ) 0,t) - Ccs(t)} (7) dair
For the basement scenario, the same equations apply as eqs 1-6, but with appropriate changes in the definitions and values of parameters. The development of that equation is not shown. Within the crawl space, the following mass balance equation applies:
(
) (
)
∂Ccs Qscs AcsDair Ca - Xcs + C + ) Xcs ∂t Vcs Vcsdair cs
(
Qscs Vcs
+
)
AcsDair C (z ) 0,t) (8) Vcsdair g
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subject to
Ccs(t ) 0) ) Ccso
(9)
The mass continuity equation for the dwelling space considers fluxes from both the crawl space and basement:
(
)
∂Cd Qcd Qbd Ca + ) -XdCd + Xd ∂t Vd Vd Qcd Qbd Ccs + C (10) Vd Vd b subject to
Cd(t ) 0) ) Cdo
(11)
The steps required to solve the simultaneous differential equations for Cd (t), Ccs (t), Cb (t), and Cg (z,t) are to first transform each differential equation into Laplace space to produce a set of equations with the unknowns C h d, C h cs, C h b, and C h g(z,s) (the overbar denotes variables in Laplace space). The first three equations are algebraic, while the equation for C h g(z,s) is an ordinary differential equation. The differential equation is then converted into an algebraic equation by assuming an appropriate solution form, as discussed below. The resulting equations are linear and are solved simultaneously, still in Laplace space. The equations are numerically inverted to obtain Cd (t), Ccs (t), Cb (t), and Cg (z,t). We illustrate the major steps in the solution by taking the Laplace transforms for the equation for Cd (t), Ccs (t), and Cg (z,t) and applying the initial conditions and transformed boundary conditions:
(
(s + Xd)C h d ) Cdo + Xd -
(
s + Xcs +
)
)
Qcd Qbd Ca + Vd Vd s Qcd Qbd C h + C h (12) Vd cs Vd b
(
)
AcsDair Qcs Ca + C h ) Ccso + Xcs dairVcs cs Vcs s Qcs AcsDair + C h (z ) 0,s) (13) Vcs Vcsdair g
(
)
and
dC hg d 2C hg (s + kT/) C h g + VT/ ) DT/ dz dz2
(14)
Equations 12-14 are the Laplace transformed equations for the three mass balance equations for Cd (t), Ccs (t), and Cg (z,t), respectively. Equation 14 is still an ordinary differential equation. To solve eq 14, the transformed boundary conditions at z ) 0, and z ) Lcs are needed. They come from eqs 6 and 4, which are respectively: -AcsRgDT/
(
)
dC hg AcsDair (z ) 0,s) + AcsRgVT/ + C h g(z ) 0,s) dz dair AcsDair C h cs ) 0 (15) dair
and
C h g(z ) Lcs,s) ) 4996
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(16)
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Thus, eqs 15 and 16 are the two boundary conditions needed for eq 14. A general solution of the following form is assumed for eq 14:
C h g(z,s)) ) Aebz + K
(4-f)
where A, b, and K are determined by substituting into 14, 15, and 16. Those steps require significant amounts of algebra, and are not shown here. The Laplace space solutions were inverted and have been tested using three alternative algorithms: Gaver-Stehfest (14), Gaver-Wynn rho (15), and DeHoog (16). The DeHoog algorithm was applied to the verification tests reported in this paper, while the GaverStehfest algorithm was used for Building 20 calibration and validation applications. A Monte Carlo approach was implemented to evaluate the effect of uncertainties in input data on model predictions. While many alternative input distributions are available for use, the results presented in this paper are based on uniform distributions with uncorrelated variables.
Model Verification Tests A series of ViM tests were performed to verify the model code. Verification is intended to show that when ViM is compared against a well-tested model for the same problem, the results match closely. Verification tests are important in helping to establish model credibility. Once verification is completed, then model validation can proceed, where the model is applied to a field site with enough data to validate model predictions. The verification test results are included in the Supporting Information.
Case Study Calibration and Validation Setting. ViM was applied to a site located in Mountain View (CA) (Figure 2a). The building simulated is located at Moffett Field Naval Air Station, and is a former bachelor’s officers quarters (Building 20). Figure 2b shows a plan view of Building 20 and indoor sampling locations. Beneath Building 20, TCE concentrations in the shallow groundwater were between 100 and 200 µg/L during 2002-2003. Groundwater TCE contours are shown in Supporting Information Figure S-5. Data to characterize TCE concentrations beneath Building 20 extend back to 1990, and show that concentrations have been slowly decreasing over that time period. Evidence associated with TCE disposal activities at the upgradient sources suggest that the plume originated around 1970. Most of Building 20 has two stories and a crawl space beneath, and the remainder is one story with a basement. Dwelling space vapor concentrations of multiple chemicals were measured at locations 20-1 and 20-2 over a portion of the years 2003 and 2004, and in the crawl space (i.e., location 20-3) three times in 2004. No data were collected from the basement. Five liters (L) of vapor were collected using 6 L Summa canisters with flow controllers set at 3.5 mL/min over 24 h for indoor, crawl space, and background air samples. Outdoor air samples collected over the plume represent both 8 (at 10.4 mL/min) and 24 h integrated samples. A single-use Teflon tube was attached to each Summa cannister to collect vapor samples at 4-5 feet above the ground surface. All vapor samples were analyzed by a commercial analytical laboratory using USEPA Method TO-15A SIM. Both indoor air and outdoor air TCE data are shown as time series in Figure 3a. For most of the period with overlapping background data and indoor air data, the indoor air data are 1 to 2 orders of magnitude greater than background air, with the exception of September and December 2003, when some of the background samples approached concentrations similar to the indoor air samples collected from location 20-2; however,
FIGURE 2. Location and plan view of Building 20 and TCE plume based on 2002-2003 data.
the reason for this is unknown. The three crawl space samples are nearly an order of magnitude greater than the indoor concentrations, and were nearly constant over the sampling period of about 3 months. Figure 3b examines the spatial variability of indoor vapor concentrations at locations 20-1 and 20-2, and the data in the figure are compared to the 1:1 line. If all data points fell perfectly along the 1:1 line, then the building would be wellmixed. However, the data for each of the three chemicals are biased toward higher concentrations at location 20-2 (for trans-1,2-DCE and TCE) or higher concentrations at 20-1 (for cis-1,2-DCE). Thus, even though ViM makes the assumption of well-mixed concentrations within the dwelling, some departure from this ideal behavior is evident in the data. One reason for this departure is the relatively low air exchange rate for this currently unused building. A second reason could be limitations on the accuracy of the data that would help explain the bias of two of the chemicals toward higher concentrations of location 20-2, and a bias for lower concentrations at the third chemical at the same location. The Mountain View area experiences a Mediterranean climate with air temperatures only infrequently below 40 °F (4.5 °C) or above 90 °F (32 °C). Supporting Information Figure S-6 shows a time series of hourly temperature data for 20032004, a period that corresponds to the indoor air data collected at the site. Also shown in Supporting Information Figure S-6 are hourly precipitation data that depict a dry season (summer to fall) and wet season (winter to spring) each year, which are typical of this area. Annual precipitation is approximately 50 cm. It is emphasized that all of the data used for the Building 20 calibration and validation analysis were collected prior to the development of ViM, and none of the data collected were done so with future modeling in mind. The Building 20 site was chosen for this modeling exercise because, after reviewing the available historical data (which includes indoor air concentration data collected over a period of 3-6 months, meteorological data, soil property data, among other data types), we concluded that enough data were available to conduct the model validation. While some data types were not collected (such as basement air chemical concentrations), discussion of model parametrization is provided (i.e., either by prior data collection or estimation methods applied herein) in the following section and in Supporting Information Table S-3.
Of particular interest is how Qcd and Qbd (i.e., the flow rate from the crawl space to the dwelling, and from the basement to the dwelling, respectively) have been calculated. ViM assumes these values are positive (i.e., flow into the residence). To make these calculations, eq 10 was used, along with mean values of model variables, and mean values of measured concentrations Cd and Ccs. The last term on the right-hand side of eq 10 was ignored because that term is much smaller than other terms. This is because (a) Qbd is much smaller than Qd, as shown below, and (b) predicted values of Cb are several orders of magnitude less than Ccs (see Figure 4a). Also, the time derivative was ignored because it is also small, since Cd remains nearly constant over the period of data collection. Finally, Qbd and Qcd are related by the known area ratio of the basement and crawl space. By making these assumptions, only one unknown remains in eq 10, and thus Qbd and Qcd can be solved from eq 10 and the known ratio between the two unknowns. The air flow rates for Qbd and Qcd were determined using eq 10 to be 690 m3/day and 2700 m3/day, respectively. Since the two air flow rates are related by the areas of the basement and crawl space, and since chemical data were not available for the basement, the driving force for air leakage was assumed to be the same for both basement and crawl space. A site visit and examination of the basement and crawl space supported this assertion.
Model Application ViM simulated the site from 1970 to 2040, or a 70-year period (i.e., a typical lifetime). While air exchange rates in the past, when the building was operational, may have been higher than today, specific information about building ventilation was not available, and air exchange rates were assumed to be the same as today. The building has not been used since the late 1990s, which is at least 4 years before indoor air sampling was performed. Groundwater contamination was first/assumed to occur beneath the site in 1970 based on a review of past reports. Calculations were performed for 76 irregularly spaced time values, with a higher density of values within the first 10 years to capture the period when indoor vapor concentrations were most rapidly changing. Since the equations are solved analytically (vs numerically), the concept of a time step is not necessary. Since numerical inversion of Laplace transforms was used (Gaver-Stehfest (GS) (14)), the accuracy of VOL. 41, NO. 14, 2007 / ENVIRONMENTAL SCIENCE & TECHNOLOGY
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FIGURE 3. Vapor-phase concentrations associated with Building 20.
the solutions depends on the number of terms used in the GS algorithm. It was found that typically 14-18 terms in the GS algorithm were sufficient for this application. These results were favorably compared to symbolically generated solutions that used 48, or more, terms. Tools such as Mathematica (17) and Matlab (18) could be used for this purpose, and Matlab was selected for this work. Computational times increased significantly using symbolic mathematics. Figure 4a shows 70 years of ViM and JEM generated predictions for TCE in indoor air. The ViM model predicts TCE concentrations in the basement, crawl space, and dwelling space, while JEM assumes that the entire building is a single compartment. Using Monte Carlo techniques, multiple predictive traces (i.e., 40 in the Figure 4a) were generated by ViM. Forty simulations were selected to illustrate the approximate range of predictions based on the specified uncertainty assigned to each variable. Test cases with up to 5000 simulations have been performed and the range expanded only slightly when compared to Figure 4a. The 4998
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observed data points are more clearly shown in Figure 4b, which shows only the years 2003-2004. The ambient air concentrations used for the simulation were based on 20032004 data. The ambient air concentration (assumed to be 0.08 µg/m3 for TCE, the average of the measured data) is small relative to most of the predicted values, except near the beginning of the simulation. At the end of the simulation, TCE concentrations in the basement approach background, while crawl space and dwelling space concentrations are still well above background, but decreasing. While ViM predictions and observations shown in Figure 4b are generally in agreement, it is noted that the temporal extent of the observed data (i.e., 3-6 months) is short compared to the period simulated (i.e., 70 years). While a longer period of historical data would have been desirable for comparing model predictions during 1970-2000, indoor vapor-phase data are not typically available for such lengthy periods (and were not at this site). However, model predictions for the future could be examined by revisiting the site
FIGURE 4. Predicted TCE concentrations in Building 20. and collecting indoor air samples, say over 5 year intervals beginning around 2010.
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µg/m3 within a short period of time. ViM nearly captures the range of variability using Monte Carlo simulations and allowing each of 25 input variables to be random with a range of 10% around the mean. However, no single ViM trace captures the variability of the individual concentrations. Although the reasons for this rapid variability in dwelling space concentrations are unknown, several possibilities include (a) Changes in air exchange rates in response to changing meteorological patterns; (b) Changes in TCE flux rates into the building over time; (c) Limitations on the accuracy of indoor air vapor samples. Since the JEM model is steady-state, TCE concentrations in the groundwater plume were approximated by a single date; i.e., mid-2004 conditions were used to coincide with the availability of indoor air data. Figure 4b compares the JEM and ViM model results to the observed data for each of the 40 traces generated. In general, the JEM model predictions were above the ViM dwelling space predictions, but at the upper end of the observed data. The variability of the JEM predictions is noticeably less than the variability of the ViM predictions. This is because ViM requires more input variables than JEM, and the number of variables treated as random was larger. The ViM predictions shown in Figure 4 are best interpreted as model calibration results, since the soil moisture content was adjusted within a plausible range (final calibration value of 0.22). The rationale for adjusting soil moisture was that data for soil moisture at Building 20 were not available. To test the robustness of the calibration, simulations were performed for cis-1,2-DCE and trans-1,2-DCE, as shown in Figure S-7 in the Supporting Information. Only the chemical characteristics were changed relative to the TCE simulation previously shown. Although the concentrations are 1-2 orders of magnitude below the TCE concentrations, the patterns of the traces are very similar, and the placement of the JEM predictions is relatively similar. It is noted that the chemical characteristics of the three chemicals simulated do not vary greatly, and model validation would have been more robust if chemicals with widely differing properties were used. However, no such data for other chemicals were available. Summary. This paper has described a dynamic model that is capable of simulating vapor intrusion into a dwelling with a combined crawl space and basement. Unlike previous models that simulate buildings as a single well-mixed compartment, ViM simulates indoor vapor concentrations in the crawl space, basement, and dwelling space separately. The time period of simulations can be long (e.g., 70 years) but the model can perform such simulations expediently due to the use of Laplace transforms and inverse transform techniques. This technique accommodates the linkage between the contamination migrating through the soil column and into the dwelling, and therefore, no assumptions have to be made that crawl space concentrations are negligible compared to vapor-phase concentrations at the top of the soil column beneath the subsurface compartments. The analysis of Building 20 has demonstrated that ViM can make plausible predictions of indoor vapor concentrations. However, ViM does need additional data that steady-state models, such as the JEM, do not need. A further limitation of ViM is that it is one-dimensional, and is applicable to contaminant scenarios that are spatially large compared to the building that is simulated, although this is a limitation shared by the J&E model (1, 10). For Building 20, vapor-phase concentrations in the crawl space were predicted to be 100 times higher than in the basement (Figure S-11). Vapor concentrations in the dwelling space are well above concentrations in the basement, indicating that the crawl space is the primary source of vapor intrusion. If Building 20 is simulated as having only a 5000
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basement (Figure S-12), it is immediately apparent that the dwelling space concentration would be much lower (i.e., over 30 times lower) than if the building is simulated as having both a crawl space and a basement. Thus, simulating a crawl space as a basement would not be appropriate as indoor vapor concentrations, and associated health risks, could be significantly underpredicted.
Acknowledgments We acknowledge Amber Genteman and Dana Constance for their expert assistance in preparing this paper, and Tetra Tech Research and Development for their support in undertaking this research. We also acknowledge Sandy Olliges and Tom Anderson, NASA Ames Research Center, for providing the Moffett Field data used in this paper. Finally, we are grateful to three anonymous reviewers who offered many constructive comments. The paper has been greatly improved because of them.
Supporting Information Available A database review of both vapor intrusion models and other models that simulate airflow patterns and the evolution of contaminants that originate in indoor air (e.g., smoke from cigarettes). ViM verification test results based on comparison with two existing models. A derivation of the JEM model that expands the J&E model capabilities to include a crawl space, biodecay, and nonzero ambient concentrations. Plume attenuation analysis that illustrates time-variability. Model sensitivity analysis for the Building 20 application. A detailed table of input data used for the Building 20 calibration and validation. Additional figures that show additional site information and ViM predictions. This material is available free of charge via the Internet at http://pubs.acs.org.
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Received for review July 21, 2006. Revised manuscript received April 30, 2007. Accepted May 14, 2007. ES061747D
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