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Environmental Modeling
Fluid flow model for predicting the intrusion rate of subsurface contaminant vapors into buildings Todd Arthur McAlary, John Gallinatti, Gordon Thrupp, William Wertz, Darius Mali, and Helen Dawson Environ. Sci. Technol., Just Accepted Manuscript • DOI: 10.1021/acs.est.8b01106 • Publication Date (Web): 25 Jun 2018 Downloaded from http://pubs.acs.org on June 28, 2018
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Fluid Flow Model for Predicting the Intrusion Rate
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of Subsurface Contaminant Vapors into Buildings
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Todd A. McAlary**1, John Gallinatti2, Gordon Thrupp2, William Wertz3, Darius Mali4 and Helen
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Dawson5
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Geosyntec Consultants, Inc., Toronto, ON
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Geosyntec Consultants, Inc., Oakland, CA
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Geosyntec Consultants, Inc., Albany, NY
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Geosyntec Consultants, Inc., Guelph, ON
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Geosyntec Consultants, Inc. Washington, D.C.
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Abstract
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A new method is presented for calculating a building-specific subslab to indoor air attenuation
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factor for use in assessing subsurface vapor intrusion to indoor air. The technique includes: 1)
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subslab gas extraction with flow and vacuum measurements and mathematical modeling to
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characterize the bulk average vertical gas conductivity of the floor slab, 2) monitoring of the
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ambient pressure gradient across the floor slab with a micromanometer, 3) calculating the *
Corresponding author – Geosyntec Consultants, Inc., 3250 Bloor Street West, Suite 600, Toronto, ON M8X 2X9; phone (905) 339-7066; e-mail:
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volumetric flow of soil gas into the building (Qsoil), and 4) dividing Qsoil by the building
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ventilation rate (Qbuilding) to calculate a building-specific attenuation factor.
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calculations using order statistics from 121 individual tests are comparable to the U.S. EPA
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empirical attenuation factors for residential buildings and the U.S. Navy empirical attenuation
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factors for commercial/industrial buildings. A case study of a commercial building shows
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encouraging agreement between the attenuation factors calculated via this method and via
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conventional subslab and indoor air sampling.
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Introduction
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Risk assessments typically assume that people breathe an average of 20,000 L of air per day and
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drink about 2 L of water per day (1). As a result, the concentrations of chemicals in air must be
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much lower than in water to yield the same exposure, so subsurface vapor intrusion to indoor air
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is often the pathway posing the greatest potential risk at sites contaminated with VOCs(2).
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Radon exposure is estimated to result in about 20,000 deaths per year in the United States
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alone(3).
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Regulatory guidance for assessing VOC vapor intrusion (2) and radon (3) has been developed to
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protect human health in the United States, and some other countries have similar programs.
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Nazaroff et al. conducted early research into radon intrusion, including a five-month study of a
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detached house with a basement (4) which concluded that pressure-driven flow is an important
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mechanism for radon entry.
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temperature differences, wind loads, barometric pressure changes, and mechanical fans. Gas
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entry typically occurs at discontinuities in the foundation that are irregular and difficult to
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characterize or predict. For VOCs, the source of vapors is often at depth below the building and
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Soil gas entry to buildings is therefore an important concern for human health.
Building pressure gradients can be caused by indoor-outdoor
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vertical diffusion to the region just below the foundation is also an important mechanism, which
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is often simulated using some form of the Jury model (5).
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Several attempts have been made to mathematically model soil gas or vapor intrusion over the
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past few decades. Radon models (6-9) and VOC models (10) have been developed for decades
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by researchers around the world, which is a testament to the importance and difficulty of this
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task (see also additional citations in the Supporting Information). The more detailed models are
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limited by availability of data for important parameters and the simpler models are limited by
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their ability to simulate all the processes involved. As a result, building-specific modeling of
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indoor air concentrations attributable to VOC vapor or radon gas intrusion has been elusive.
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The most commonly-used model for VOC vapor intrusion has been the Johnson and Ettinger
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Model (11), a 1-dimensional, steady-state model that provides an algebraic expression for the
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attenuation factor (AF), defined as the indoor air concentration (Cindoor) divided by the
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subsurface vapor concentration at a specified depth (Csource):
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AF=(Cindoor/Csource)
(1)
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For the special condition of a source directly beneath the foundation (i.e., the source-building
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separation distance → 0) and advection is the dominant mechanism of transport across the floor
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slab, AF→Qsoil/Qbuilding, where Qsoil is the volumetric flow rate of soil gas into the building
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and Qbuilding is the total volumetric flow rate of air through the building or basement (i.e., the
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ventilation rate, which equals the interior volume multiplied by the air exchange rate). The
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building volume is easily measured or estimated. The air exchange rate can usually be estimated
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within a factor of about three for a typical residence: the mean air exchange rate for residences is
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0.45 /hr and the 10th percentile is 0.18 /hr, according to the U.S. EPA Exposure Factors
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Handbook (1). Chan et al. (12) analyzed a database of 70,000 residential building leakage tests
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and showed comparable results. Qbuilding can be measured using blower door tests(13) and
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tracer tests(14,15). The air exchange rates for commercial buildings tend to be higher (mean =
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1.5 /hr(1)) and sometimes are available from mechanical engineers responsible for the heating,
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ventilating and air conditioning (HVAC) systems. Qsoil is more difficult to estimate. Nazaroff
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(6) developed an equation assuming that flow to the expansion joint between the floor and the
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wall of a building is similar to a line-sink at the bottom of the slab:
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Qsoil = 2 π k ∆P Xcrack µ ln(2Zcrack/Rcrack)
(2)
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where:
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k = the shallow soil or granular fill permeability to air flow [L2]
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∆P = the indoor-outdoor pressure difference [M/L-T2]
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µ = the viscosity of air [M/L-T]
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Xcrack = the total length of cracks through which soil gas vapors are flowing [L]
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Rcrack = the effective crack width [L]
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Zcrack = the crack opening depth below grade, or thickness of the floor slab [L]
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∆P can be measured with a pressure transducer/datalogger and Zcrack is seldom much different
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than 0.1 to 0.15 m.
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practically impossible to accurately measure Xcrack and Rcrack on a building-specific basis, so the
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Nazaroff model is not very useful for building-specific calculations of Qsoil.
However, direct measurements of k are seldom available and it may be
Johnson (16)
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argued that because of challenges estimating Qsoil, it would be preferable to combine
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Qsoil/Qbuilding, which can be reasonably estimated (from mass balance principles) to be equal
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to the ratio of the indoor air concentrations divided by subslab concentrations (i.e., the subslab-
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to-indoor air AF).
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As an alternative to mathematical modeling, the U.S. EPA (17) compiled and analyzed a
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database of indoor air and subslab sampling results, primarily for residential structures and
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chlorinated compounds to better understand the degree to which subslab VOC concentrations are
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attenuated as soil gas entering the building is diluted by the ventilation of the building (i.e., the
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subslab-to-indoor air AF).
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concentrations high enough to minimize bias from background sources, they calculated a 95th
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percentile value of 0.03 for the subslab-to-indoor air AF.
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adopted 0.03 as a default AF for development of subslab screening levels (SSSL = Cindoor/AF).
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Considering this is a 95th percentile AF, it would be expected to be overly protective for 19 of 20
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residential buildings and Song et al. (18) and Yao et al. (19) provide arguments that the EPA
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database analysis may result in a high bias in the AF values. Furthermore, higher ceilings and
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higher air exchange rates for commercial buildings tend to result in lower AFs than residential
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buildings, but agencies are often reluctant to adopt lower default AFs for commercial/industrial
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buildings despite available empirical subslab and indoor air data that indicates this would be
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appropriate (20). Regulators usually recommend additional sampling if subslab concentrations
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exceed the conservative screening levels and some recommend mitigation if subslab vapor
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concentrations exceed screening levels by a relatively modest factor (e.g., 10x) (e.g., 21,22).
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Considering the U.S. EPA empirical database shows almost 5 orders of magnitude range in the
After filtering the database to focus on buildings with subslab
Many regulatory agencies have
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subslab AFs, using a default of 0.03 for all buildings is overly protective by a wide margin for
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most buildings.
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There is a distinct need for better methods to determine the susceptibility of specific buildings to
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VOC vapor and radon gas intrusion.
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temporal variability (23,24) and bias from background sources (25), and subslab samples are
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subject to uncertainties from spatial variability, so empirical AF values derived from the EPA
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database are unavoidably imperfect. The purpose of this article is to develop and demonstrate a
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method to calculate building-specific attenuation factors using subslab flow and vacuum
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measurements, building pressure and building ventilation rates, which will provide an
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independent line of evidence to augment empirical attenuation factors.
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Conceptual Model
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In the field of hydrogeology, aquifer discharge (Qaq) is calculated using (26):
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Indoor air samples are subject to uncertainties from
Qaq = K i A
(3)
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where:
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K = hydraulic conductivity [L/T]
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i = hydraulic gradient [L/L], and
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A = cross-sectional area perpendicular to flow (L2)
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Equation 3 can be applied to calculating Qsoil where A is the footprint of the building, i is the
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pressure gradient across the floor slab and K is the bulk average vertical gas conductivity of the
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floor slab. Groundwater models can be applied to soil gas flow as long as the pressure gradients
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are small enough that the gas behaves similar to an incompressible fluid (27). Subslab venting
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systems typically operate with applied vacuum
