xvEPA
United States
Environmental Protection
Agency EPA 510-R-13-002
3-D Modeling Of Aerobic Biodegradation Of
Petroleum Vapors: Effect Of Building Area Size On
Oxygen Concentration Below The Slab
U.S. Environmental Protection Agency
Office of Underground Storage Tanks
Washington, DC 20460
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11
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3-D Modeling Of Aerobic Biodegradation Of
Petroleum Vapors: Effect Of Building Area Size On Oxygen
Concentration Below The Slab
Prepared by
Lilian Abreu, PhD.
ArcadisU.S., Inc.
100 Montgomery Street
Suite 300
San Francisco, CA 94104
Christopher C. Lutes
ArcadisU.S., Inc.
4915 Prospectus Drive
Suite F
Durham, NC 27713
and
Eric M. Nichols, P.E.
ArcadisU.S., Inc.
78 Piscassic Road
Newfields,NH03856
Contract No. GS-23F-0339K
for
U.S. Environmental Protection Agency
Office of Underground Storage Tanks
Washington, DC 20460
June 2013
in
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IV
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Disclaimer
This document has been reviewed in accordance with U.S. Environmental Protection Agency
policy and approved for publication. Mention of trade names or commercial products does not
constitute endorsement or recommendation for use.
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Acknowledgements
Dr. Ian Hers and Dr. Parisa Jourabchi (Golder Associates, LTD); John A. Menatti (Utah
Department of Environmental Quality) and Dr. Eric M. Suuberg (Brown University) provided
technical peer reviews.
VI
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Table of Contents
Disclaimer v
Acknowledgements vi
List of Acronyms x
Executive Summary 1
1. Introduction 1
1.1 Background 1
1.2 Goal and Objectives 1
1.3 Document Development and EPA Peer Review 2
1.4 Document Organization 2
2. Methodology 5
2.1 Conceptualization of the Vapor Intrusion Process 5
2.2 Model Description 7
2.2.1 Model Capabilities 7
2.2.2 Model Limitations 8
2.3 Model Inputs 9
2.3.1 Building Footprint Size and Surrounding Land Cover 9
2.3.2 Source Depth and Concentration 11
2.3.3 Biodegradation Rate 12
2.3.4 Initial and Boundary Conditions for Petroleum Hydrocarbons and
Oxygen 14
2.3.5 Chemical Composition of Vapor Source 14
2.3.6 Model Input Parameters 15
2.4 Sensitivity Testing 15
2.5 Potentially Confounding Factors 17
3. Results and Discussion 19
3.1 Summary of Tabulated Results 19
3.2 Graphical Conventions Used in Figures 19
3.3 Results for a Homogeneous Sandy Soil and Square Buildings 23
3.4 Results for a Homogeneous Sandy Soil and Rectangular Buildings 31
3.5 Results for a Homogeneous Sandy Soil with an Overlying Silty Clay Layer at
Ground Surface 34
3.6 Results for Buildings with a Basement 36
4. Conclusions 40
5. References 42
Appendix A. Model Equations
Appendix B. Tabulated Simulation Results
vn
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List of Tables
Table 1. Theoretical Equivalent Units for Petroleum Hydrocarbon Vapor Concentrations
Represented as Benzene 12
Table 2. Model Input Parameters 16
List of Figures
Figure 1. Large U.S. building (Boeing Facility, Everett, WA) 10
Figure 2. Comparison of biodegradation rates found in the literature 13
Figure 3. Contours of simulated petroleum hydrocarbon vapors in the subsurface beneath a
building. Results for PHC source vapor concentration of 10,000,000 |ig/m3 at
depth of 15 ft (4.6 m) and building size of 2,073 ft x 2,073 ft (632 m x 632 m).
Initial oxygen concentration of 21 percent by volume and transport time of 20
days 20
Figure 4. Contours of simulated oxygen concentrations in the subsurface beneath a
building. Results for PHC source vapor concentration of 10,000,000 |ig/m3 at
depth of 15 ft (4.6 m) and building size of 2,073 ft x 2,073 ft (632 m x 632 m).
Initial oxygen concentration of 21 percent by volume and transport time of 20
days 21
Figure 5. Expanded view of portion of the 7 meter model domain outside the building
footprint. Results for source vapor concentration of 10,000,000 |ig/m3 at depth of
15 ft (4.6 m) and building size of 2,073 ft x 2,073 ft (632 m x 632 m). Initial
oxygen concentration of 21 percent by volume and transport time of 1 year 22
Figure 6. Concentration results for source vapor concentration of 10,000 |ig/m3 at depth of
5 ft (1.6 m) and building size of 2,073 ft x 2,073 ft (632 m x 632 m). Initial
oxygen concentration of 21 and 10.5 percent by volume and transport time of 20
years 24
Figure 7. Concentration results for source vapor concentration of 100,000 |ig/m3 at depth
of 5 ft (1.6 m) and building size of 2,073 ft x 2,073 ft (632 m x 632 m) over
sandy soil. Initial oxygen concentration of 21 and 10.5 percent by volume and
transport time of 20 years 25
Figure 8. Concentration results for source vapor concentration of 1,000,000 |ig/m3 at depth
of 5 ft (1.6 m) and building size of 2,073 ft x 2,073 ft (632 m x 632 m). Initial
oxygen concentration of 21 percent by volume and transport times of 3, 6 and 9
years 26
Figure 9. Concentration results for source vapor concentration of 1,000,000 |ig/m3 at depth
of 15 ft (4.6 m) and building size of 2,073 ft x 2,073 ft (632 m x 632 m) Initial
Vlll
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oxygen concentration of 21 percent by volume and transport times of 6, 9 and 20
years 27
Figure 10. Concentration results for source vapor concentration of 1,000,000 |ig/m3 at depth
of 15 ft (4.6 m) and building size of 2,073 ft x 2,073 ft (632 m x 632 m) for an
initial concentration of oxygen at 21 % and 10% and transport times of 8 and 9
years 28
Figure 11. Concentration results for source vapor concentration of 10,000,000 |ig/m3 at
depth of 15 ft (4.6 m) and building size of 2,073 ft x 2,073 ft (632 m x 632 m)
Initial oxygen concentration of 21 percent by volume. Three transport time: 20
days, 30 days and 1 year (steady state condition within one year of transport) 29
Figure 12. Concentration results for source vapor concentration of 10,000,000 |ig/m3 at
depth of 15 ft (4.6 m) and three building sizes: 98 ft x 98 ft, 66 ft x 66 ft and 33 ft
x 33 ft (30 m x 30 m, 20 m x 20 m, and 10 m x 10 m). Initial oxygen
concentration of 21 percent by volume and steady state condition within one year
of transport 30
Figure 13. Concentration results for source vapor concentration of 10,000,000 |ig/m3 at
depth of 30 ft (9 m) and three building sizes: 197 ft x 197 ft, 131 ft x 131 ft and
98 ft x 98 ft (60 m x 60 m, 40 m x 40 m, and 30 m x 30 m). Initial oxygen
concentration of 21 percent by volume and steady state condition within one year
of transport 33
Figure 14. Concentration results for a building with rectangular shape 2073 ft x 33 ft (632 m
x 10 m), source vapor concentration of 10,000,000 |ig/m at 15 ft (4.6 m), initial
oxygen concentration of 21 percent by volume and steady state condition. Results
viewed in two perpendicular cross sections by center of building 35
Figure 15. Concentration results for building 2,073 ft x 2,073 ft (632 m x 632 m), with full
6.6 ft (2 m) deep basement, source vapor concentration of 100,000 |ig/m3 at 5 ft
(1.6 m) below basement slab, transport time 9 years and initial oxygen
concentration of 21 percent by volume 37
Figure 16. Concentration results for building with full 2 m deep basement vs. building slab-
on-grade, for building area 2,073 ft x 2,073 ft (632 m x 632 m), source vapor
concentration of 100,000 |ig/m3 at 5 ft (1.6 m) below foundation slab, transport
time 9 years and initial oxygen concentration of 21 percent by volume 38
IX
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List of Acronyms
bgs Below ground surface
EPA U.S. Environmental Protection Agency
foc Mass fraction of organic carbon in soil
Koc Soil organic carbon
LNAPL Light non-aqueous phase liquid
NAPL Non-aqueous phase liquid
Pascal
Pa
PHC
PVI
psi
USGS
UST
VOC
Petroleum hydrocarbon
Petroleum vapor intrusion
Pounds per square inch
United States Geological Survey
Underground storage tank
Volatile organic compound
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Executive Summary
Vapor intrusion occurs when vapor-phase contaminants migrate from subsurface sources into
buildings. One broad sub-category of vapor intrusion is petroleum vapor intrusion (PVI), in
which vapors from petroleum hydrocarbons (PHCs) such as gasoline, diesel, or jet fuel enter a
building. The intrusion of contaminant vapors into indoor spaces is of concern due to potential
threats to safety (e.g., explosive concentrations of petroleum vapors or methane) and possible
adverse health effects from inhalation exposure to toxic chemicals.
Petroleum vapors have the potential to attenuate in the subsurface as a result of microbially-
mediated biodegradation. Aerobic biodegradation is typically the most significant process
affecting the attenuation of petroleum vapors in the subsurface. Sufficient oxygen must be
available beneath a building for rapid aerobic biodegradation of vapors from petroleum
hydrocarbons (and other biodegradable volatile organic compounds) to occur and thereby reduce
or eliminate the potential for PVI into overlying buildings.
The term oxygen shadow is qualitatively defined to mean existence of a concentration of oxygen
at which the availability of oxygen substantially limits the rate of aerobic biodegradation. A
generally accepted oxygen threshold in soil gas (and that which is used in this report) is 1 percent
by volume (Winegardener and Testa, 2002; Abreu and Johnson, 2006; Abreu et al., 2009a;
Ward, 1997; Davis, 2009).
ES.l Purpose and Document Focus
The purpose of this technical document is to report on 3-D finite difference vapor transport
modeling simulations designed to systematically assess the development of an oxygen shadow
beneath a building. These new simulation results are aimed at improving the understanding of
the impact of building footprint size on the oxygen shadow and will help to inform development
of guidance on petroleum vapor intrusion by the U.S. Environmental Protection Agency's (EPA)
Office of Underground Storage Tanks. These scenarios extend the simulations presented in
Abreu and Johnson (2005, 2006); Abreu et al. (2009a,b); and U.S. EPA (2012).
ES.2 Methodology
The work presented in this technical document features three-dimensional (3-D) mathematical
model simulations for a range of building sizes, source concentrations, and depths. The 3-D
model used in this work was developed by Abreu and Johnson (2005, 2006). Starting from a base
case model simulation, subsequent simulations were conducted to determine whether there are
size thresholds above which an oxygen shadow is always present, and below which an oxygen
shadow does not develop. Subsequent simulations were chosen based on the results of these
initial simulations and decreasing or increasing the building size. All other parameters were
reasonably representative of typical conditions and were held constant during the modeling
simulations. Soil properties for the base cases were for a homogeneous sandy soil and the
simulation was run for various durations to determine if quasi-steady state conditions had been
achieved or to verify the length of time before oxygen is depleted by aerobic biodegradation and
ES-1
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an oxygen shadow develops. Additional scenarios were run for a sandy soil overlain by a one
meter silty clay layer.
For the approximately 160 simulations in this report, only factors easily identified in the site
screening process (e.g., foundation dimensions and thickness of the vadose zone) were
considered. It is likely that results would change significantly if additional processes (e.g., high
permeability layers beneath building slabs, wind speed/direction variability and bi-directional
flow through foundation cracks and penetrations throughout the floor plan) were modeled.
ES.3 Findings and Conclusions
The results of this study may help practitioners identify situations where they should confirm
with field measurements the presence of oxygen necessary to support aerobic biodegradation of
petroleum hydrocarbons. Conversely, there are other situations where practitioners can
reasonably infer from site conditions the presence of a sufficient level of oxygen.
Simulation results indicate that the probability of an oxygen shadow developing increases with:
• Increasing building area (including surrounding pavement area)
• Increasing source vapor concentration
• Decreasing depth of vapor source beneath the building
• Increasing transport time for oxygen consumption under transient conditions
(assuming the source PHC vapor concentrations are stable)
ES-2
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1. Introduction
1.1 Background
Vapor intrusion occurs when vapor-phase contaminants migrate from subsurface sources into
buildings. Petroleum vapor intrusion (PVI) occurs when vapors from petroleum hydrocarbons
such as gasoline, diesel, or jet fuel enter a building. The intrusion of contaminant vapors into
indoor spaces is of concern due to potential threats to safety (e.g., explosive concentrations of
petroleum vapors or methane) and possible adverse health effects from inhalation exposure to
toxic chemicals.
Petroleum vapors have the potential to attenuate in the subsurface as a result of microbially-
mediated biodegradation. Aerobic biodegradation is typically the most significant process
affecting the attenuation of petroleum vapors in the subsurface. Sufficient oxygen must be
available beneath a building to support biodegradation of vapors from petroleum hydrocarbons
and other biodegradable volatile organic compounds (VOCs) and thus decrease or eliminate the
potential for PVI into overlying buildings.
Preliminary modeling results (Abreu et al., 2009; Abreu and Johnson, 2005, 2006) indicate that
beneath buildings and other lower permeability ground covers, soil vapor may become depleted
of oxygen, forming an oxygen shadow. The term oxygen shadow refers to a concentration of
oxygen at which its availability substantially limits the rate of aerobic biodegradation. A
generally accepted oxygen threshold in soil gas used in this report is 1 percent by volume
(Winegardener and Testa, 2002; Abreu and Johnson, 2006; Abreu et al., 2009a; Ward, 1997;
Davis, 2009). Where an oxygen shadow occurs, the potential for PVI into buildings is increased.
This oxygen shadow is the result of an interrelationship among several factors including the
following:
• Building footprint
• Source concentration
• Depth of contamination
• Length of time for vapor and oxygen transport
• Underlying soil types and stratification
1.2 Goal and Objectives
The goal of this study was to determine whether there is a threshold building footprint size,
above which a permanent oxygen shadow may form beneath the center of an overlying building.
This was to be accomplished by using a 3-D mathematical model to simulate development of an
oxygen shadow beneath buildings of various sizes. These simulations expand upon those
presented in Abreu and Johnson (2005, 2006), Abreu et al. (2009a,b), and U.S.EPA (2012). This
report was prepared in support of EPA's Guidance For Addressing Petroleum Vapor Intrusion
At Leaking Underground Storage Tank Sites.
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1.3 Document Development and EPA Peer Review
A draft of the document was subjected to EPA's external peer review process from May to June
2012. The peer review contractor independently selected four experts not affiliated with EPA.
Dr. Ian Hers and Dr. Parisa Jourabchi (Golder Associates, LTD); John A. Menatti (Utah
Department of Environmental Quality) and Dr. Eric M. Suuberg (Brown University) provided
technical peer reviews. The expertise of the peer review panel includes:
• Practical and theoretical understanding of the petroleum vapor intrusion pathway,
including how volatile organic contaminants move and distribute in the subsurface
(soil gas), indoor air, and outdoor air from dissolved and nonaqueous phase liquid
sources
• Experience in planning and conducting site-specific vapor intrusion studies, including
developing and refining conceptual site models of the migration and distribution of
volatile contaminants
• Expertise in 3-D numerical modeling of vapor intrusion processes, applying and
calibrating models using site-specific data, and interpreting results to make decisions
at vapor intrusion sites
The peer reviewers were tasked to review the draft report and provide opinion and perspective
regarding the following:
• Whether the model and model runs are suitable and sufficient for the objectives of the
investigation
• The scientific appropriateness of using results from a numerical model for developing
screening criteria based on the dimensions of a building given the wide possibilities
for the foot print of a building that might be impacted by PVI, and given the relatively
limited empirical literature relating the dimensions of a building to the possibility for
vapor intrusion
• Whether the model inputs are reasonably representative of worst-case conditions for
oxygen depletion in the vadose zone immediately underlying a building
• Whether the reported conclusions are adequately supported by the simulation results
The document was then revised to address the comments of the peer reviewers. Additional
revisions to the final draft were made by EPA to conform to formatting standards.
1.4 Document Organization
This report is organized as follows:
• Section 2 - Methodology
• Section 3 - Results and Discussion
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Section 4 - Conclusions
Section 5 - References
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2. Methodology
2.1 Conceptualization of the Vapor Intrusion Process
Vapor intrusion occurs when VOCs from contaminated soils or groundwater migrate upwards
toward the ground surface and into overlying buildings through gaps and cracks in foundation
slabs or basement walls. This contaminant migration is driven by differences in concentrations
and air pressure between the contaminated subsurface regions and the affected buildings. The
vapor intrusion pathway is the route VOCs take from a source through the subsurface and
eventually intrude into a building. Entry routes into the building must exist for the vapors to
enter the building and driving forces must exist to cause the vapors to enter the building for the
pathway to be complete (U.S. EPA, 2012).
Some VOCs, especially petroleum hydrocarbon (PHC) vapors, readily biodegrade when
sufficient oxygen is present in soil gas. Biodegradation reduces the concentrations of PHCs in
soil gas as they migrate through the soil from the contaminant source into indoor air. This
reduction in concentration from a measurement point in the subsurface to indoor air is referred to
as attenuation. The extent of attenuation depends on the source concentration, the amount of
oxygen available for biodegradation, the biodegradation rate, soil moisture content, and the
length of time for vapor/gas transport (which is a function of the length of the transport
pathway). Subsurface transport of PHC vapors can be affected by the following:
• Subsurface features (e.g., fine-grained soils, soils with high-moisture content) that
may hinder the diffusion and advection of VOCs
• Biodegradation of contaminants
• Presence of entry routes through the building foundation and sub-grade walls
• Changes with time in groundwater level, source strength, and infiltration rates
• Pressurization of the building (under-pressurization draws soil gas into a building)
• Air exchange into a building, which brings fresh air into the enclosed space and
dilutes the concentration of VOCs that enter through the vapor intrusion pathway
(EPA, 2012)
Sources of subsurface PHC vapors include leaking gas pipes, leaking underground storage tanks
(USTs), aboveground spills, aboveground facilities that use PHCs during operations, historical
subsurface disposal of industrial wastes, and landfills. At leaking UST sites, the primary
contaminants of concern are petroleum fuels such as gasoline and diesel. When these substances
are released into the subsurface, they may partition into several phases:
• Residual phase non-aqueous phase liquid (NAPL) occurring as disconnected globules
trapped within soil pore spaces
• Mobile phase NAPL (i.e., free product)
• Aqueous phase dissolved in soil moisture and groundwater
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• Vapor phase in soil gas
NAPL masses comprised of substances less dense than water are light NAPLs or LNAPLs.
LNAPL sources are of particular concern because they typically create higher vapor
concentrations in soil gas and potentially greater mass flux than do dissolved groundwater
plumes containing the same chemicals. The simulations in this technical document assume a
vapor source in soil gas above the groundwater table; the vapors may originate from either
dissolved VOCs in groundwater at the top of the capillary fringe or LNAPL (residual or mobile)
accumulations near the water table.
Vapor transport in the subsurface may be controlled by four primary processes:
• Diffusion occurs when there are spatial differences in VOC concentrations in the
subsurface; vapors diffuse in the direction of lower concentrations.
• Advection occurs when there is bulk movement of soil gas induced by spatial
differences in soil gas pressure.
• Phase partitioning refers to the processes leading to VOC distribution between the
soil gas, the dissolved phase in soil pore water, and the sorbed phase on soil particle
surfaces. Phase partitioning will retard contaminant vapor transport in the subsurface
under transient conditions, but not under steady-state transport conditions, when the
mass transfer between phases approaches equilibrium.
• Degradation is usually associated with biodegradation, in which VOCs are converted
to other chemicals by microorganisms in the subsurface.
Vapor transport may occur under transient or steady state conditions. Under transient conditions,
concentrations are changing with time. Under steady state conditions, concentrations and
pressures are constant with time, although they may vary spatially. Under steady state conditions,
the parameters that influence transport by diffusion and advection:
• Soil porosity and moisture content
• Chemical diffusion coefficients in air and water
• Soil gas permeability
• Building pressurization relative to adjacent soil gas pressures
The Henry's law constant (which quantifies chemical partitioning between air and water) may
also influence transport when moisture content is high and Henry's law constant is very low. For
transient transport conditions, VOC transport may also be influenced by phase transfer to the
aqueous and solid phases, which depend on the VOC-specific Henry's law constant and sorption
coefficient to soil organic carbon (Koc), and on the mass fraction of organic carbon in soil (foc)
(EPA, 2012).
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2.2 Model Description
2.2.1 Model Capabilities
The vapor intrusion model developed by Abreu and Johnson (2005, 2006) and used during this
study is a three-dimensional, finite difference model. The Abreu-Johnson 3-D model (the 3-D
model) simultaneously solves transient transport equations (Appendix A) for the following:
• Soil-gas pressure field (from which the advective flow field is computed)
• Transient advective and diffusive transport and reaction of multiple chemicals
(including oxygen) in the subsurface
• Flow and chemical transport through foundation cracks
• Chemical mixing in indoor air
Starting from a base case comprised of a homogeneous sandy soil and a building of 33 ft x 33 ft
(10 m x 10 m), a series of model simulations were conducted by varying the building size and
geometry, source concentration, depth to the source, transport time, and initial oxygen
concentration. All other parameters were reasonably representative of typical conditions and
were held constant during the modeling simulations.
Although the model has the capability of simulating heterogeneous soil moisture distributions
beneath and adjacent to a building, formation of a moisture shadow1 beneath buildings (or the
increased infiltration of rain water below a roofs drip edge) was not simulated.
The soil gas concentration distribution in the subsurface is symmetrical to the center of the
building in the x and y dimensions for all scenarios simulated in this document. For
computational efficiency the model domain was set up to take advantage of this symmetry by
simulating vapor transport using only 1A of the building footprint. For example, for a 33 ft x 295
ft (10 m x 90 m) building, only 1A of its footprint area 15 ft x 148 ft (5 m x 45 m) is input into the
3-D model domain.
The numerical accuracy of the 3-D model has been previously demonstrated through the
comparison of model predictions with other analytical and numerical model results. The 3-D
model has been shown to be capable of fitting field measured vertical soil gas profiles. These
results are discussed in Abreu et al. (2009a,b and 2007) and Abreu and Johnson (2005, 2006).
The majority of the simulations presented in this report represent quasi-steady state transport
conditions; only a few transient transport scenarios are illustrated and discussed. Because the 3-D
model is a transient solution of the transport equations, the steady state scenarios presented in
this document were obtained by running simulations over a time period of sufficient length to
effectively represent steady state conditions (EPA, 2012). Verification that steady state
conditions had been reached was achieved by the following:
Soil moisture contents of 25 percent to 85 percent of field capacity are considered necessary for biodegradation to
occur in vadose zone soil (Ward, 1997).
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• Running the scenario for a given period of transport time
• Re-running the scenario for a longer transport time
• Comparing results of the two simulations to check whether additional simulation time
resulted in significant changes in concentration distribution in the subsurface or in the
indoor air concentration. If no significant changes were observed, it was assumed that
a quasi-steady state condition had been achieved.
2.2.2 Model Limitations
The 3-D model simulates the transport of contaminant vapors in the unsaturated soil zone; it does
not model the transport of dissolved contaminants via groundwater flow in the saturated zone.
The foundation floor and walls are simulated as impermeable barriers to the transport of vapors
from the subsurface to the indoors, except where there are cracks or openings in the foundation.
The baseline conditions for most simulations presented in this document assume:
• Slab-on-grade building
• Full-length perimeter crack shown in figure A-l of Appendix A
• Building with a steady under-pressurization of 7.3 x 10~4 psi (5 Pa)
• Relatively dry sandy soils
• Constant source concentration (i.e., no depletion of the source), and
• Infinite source footprint area covering the full extent of the building slab and beyond
The 3-D model simulates buildings with basement or slab-on-grade foundations; it does not
simulate buildings with a crawl space.
In actual foundations, the ability of concrete to transmit soil gas depends on the physical integrity
of the concrete and characteristics determined by cement mixtures, cement/water ratios, and
production processes (e.g., poured concrete vs. concrete block). Intact concrete is virtually
impermeable to advective air flow; however, in real settings volatile compounds from soil gas
may diffuse through a concrete slab and oxygen may also diffuse from indoor air toward soil gas
through a concrete slab.
In a site assessment for vapor intrusion, any relevant background VOC levels (i.e., contaminants
in indoor air that come from either indoor sources or from outdoor air) should be taken into
consideration. As a simplifying assumption, all VOCs in indoor air are the result of vapor
intrusion and that there are no background VOC contributions from either indoor or outdoor
sources. In addition, indoor air concentrations are assumed to be uninfluenced by sorption (or
desorption) to building materials (U.S EPA, 2012).
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2.3 Model Inputs
Inputs to the model include:
• Geometry descriptors (e.g., building footprint, foundation depth, crack locations and
widths, source depth, source footprint)
• Chemical properties
• Kinetic reaction rate parameters
• Indoor-outdoor pressure differential
• Oxygen concentration at the ground surface
• Chemical vapor concentrations at the vapor source
2.3.1 Building Footprint Size and Surrounding Land Cover
The goal of this study was to determine whether there is a threshold building footprint size,
above which a permanent oxygen shadow may form beneath the center of an overlying building.
This was to be accomplished by using a 3-D model to simulate development of an oxygen
shadow beneath buildings of various sizes. Building size parameters were selected based on a
review of published information. According to Census Bureau data from 2007, the majority of
the new single-family housing units sold in the U.S. between 1999 and 2007 have a floor area
that ranges between 1,000 and 5,000 ft2 (93 to 464 m2). Koomey (1990) reports the size
distribution of commercial buildings:
• 55 percent are from 1,001 to 5,000 ft2 (93 to 464 m2)
• 22 percent are from 5,001 to 10,000 ft2 (464 to 927 m2)
• 12 percent are from 10,001 to 25,000 ft2 (927 to 2,318 m2)
• 5.7 percent are from 25,001 to 50,000 ft2 (2,318 to 4,636 m2)
Starting from a base case model run (a square building 33 x 33 ft [10 x 10 m] overlying sandy
soil), a series of simulations were conducted to determine the building size threshold. The first
set of simulations used a building size of 295 ft x 295 ft (90 m x 90 m); a size chosen to
reasonably include building sizes within the distribution found in the USA. The largest footprint
modeled was a building with a footprint of 4.3 million ft2 (2,073 ft x 2,073 ft or 632 m x 632 m).
Figure 1 presents a photograph of a building of this size. Approximately 160 simulations were
conducted; the results are tabulated in Tables B-l through B-5 in Appendix B.
In addition to reported building floor plan sizes, many U.S. buildings are surrounded by
parking lots, driveways, sidewalks, or roads. If the buildings and surrounding areas are in good
condition and not broken up by a significant number of cracks or expansion joints, they may
extend the effective footprint area subject to formation of an oxygen shadow. Parking lots
separated from buildings by planting beds and asphalt parking lots are less likely to contribute to
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Everett, Wash, factory building
Figure 1. Large U.S. building (Boeing Facility, Everett, WA). Image downloaded from
http://www. boeing. com/commercial/tours/images/K64532- 14_lg.jpg.
the formation of an oxygen shadow. Most asphalt pavements should have a permeability similar
to the hydraulic conductivity of fine silty sand (Shan, undated).
Subsurface vapor flow may differ for equal footprint sizes (smaller building surrounded by a
concrete parking lot equals the footprint of a larger building) due to the depressurization of the
interior space (assumed 5 Pa in these simulations). The air permeability of concrete increases
gradually with time, reaching a nearly stable value after 20 years that is similar to the
permeability of homogeneous clay (Nazaroff, 1988). The air permeability of soils modeled in
this study is greater than that of concrete.
The 3-D modeling simulations conducted by U.S. EPA (2012) used a 33 ft x 33 ft (10 m x 10 m)
square building. In a square building overlying a homogeneous and isotropic soil, oxygen
transport to the center of the building footprint would occur uniformly from all four directions. It
is reasonable to expect that in the case of a rectangular building, the magnitude of oxygen
transport along the long axis of the building would be lower relative to oxygen transport along
the short axis. Therefore, the simulations in Tables B-l through B-5 (Appendix B), include
some rectangular cases.
10
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2.3.2 Source Depth and Concentration
Simulations were repeated for three source depths: 5, 15 and 30 ft (1.6, 4.6, and 9 m,
respectively), and source vapor concentrations in the range of 10,000 |ig/m3 to 10,000,000
|ig/m3). In some cases, as many as six source vapor concentration increments were simulated:
10,000 |ig/m3, 100,000 |ig/m3, 1,000,000 |ig/m3, 2,000,000 |ig/m3, 5,000,000 |ig/m3 and
10,000,000 |ig/m3 in the soil vapor phase. This source strength range is reasonable for simulating
releases of petroleum fuels from leaking USTs because:
• Concentrations less than 10,000 |ig/m3 are very unlikely to exhibit an oxygen shadow
regardless of what values were selected for the other model parameters (see Section
2.3.6).
• EPA (2012, Section 5) presents results for scenarios using source strengths from
20,000,000 |ig/m3 through 200,000,000 |ig/m3 for a 33 ft x 33 ft (10 m x 10 m)
building. These results showed some instances where oxygen was depleted even for
such a relatively small building size. Abreu et al. (2009b) presents simulation results
using the same 3-D model and building size for source strengths of 4,000 |ig/m3,
40,000 |ig/m3, 400,000 |ig/m3, 1,000,000 |ig/m3, 4,000,000 |ig/m3, 10,000,000 |ig/m3,
40,000,000 |ig/m3, 100,000,000 |ig/m3, 200,000,000 |ig/m3 and 400,000,000 |ig/m3.
• Published estimates of soil gas concentrations in equilibrium with gasoline LNAPL
range from 220,000,000 |ig/m3 (220 mg/L) for weathered gasoline to 1,300,000,000
|ig/m3 (1,300 mg/L) for fresh gasoline (Johnson et al., 1990).
• The simulated range of source vapor concentrations corresponds approximately to a
range dissolved phase hydrocarbon concentrations from 0.01 mg/L to 10 mg/L, which
is a typical range for groundwater concentrations in equilibrium with older releases of
petroleum LNAPL (Lahvis et al., 2013; U.S. EPA, 2013).
• According to EPA (2012, p.66): "A hydrocarbon vapor source concentration of
20,000 mg/m3 (20,000,000 |ig/m3) might be encountered at sites where the vapor
source is gasoline or hydrocarbons dissolved in groundwater. A source vapor
concentration of 200,000 mg/m3 (200,000,000 |ig/m3) might be encountered at sites
where the source is weathered gasoline NAPL just above the water table."
The information in the preceding bullets is summarized in Table 1 to facilitate interpretation of
the magnitude of the vapor source concentrations used as input values in the 3-D model.
11
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Table 1. Theoretical Equivalent Units for Petroleum Hydrocarbon Vapor Concentrations
Represented as Benzene.
Liquid (Approximate Equivalent)
mg/L
0.01
0.1
1.0
10.0
220
1,300
U£/L
10
100
1,000
10,000
220,000
1,300,000
Vapor
ug/m3
10,000
100,000
1,000,000
10,000,000*
220,000,000
1,300,000,000
Type of
Vapor Source
A
Dissolved
Phase
?
|| LNAPL
*highest concentration simulated in the present study
2.3.3 Biodegradation Rate
The simulations reported here employ a first-order biodegradation model with a biodegradation
rate (X) of 0.79 h"1 for aromatic hydrocarbons, which is consistent with Abreu et al. (2009a, b)
and within the midrange of reasonably accepted values. This biodegradation rate is the average
reported for aromatic hydrocarbons in the analysis of DeVaull (2007), who compiled results
from 84 data sets of laboratory and field biodegradation rates for aromatic hydrocarbons
measured by multiple investigators. Figure 2 illustrates how the selected biodegradation rate
relates to other biodegradation rates that were tested in previous studies, which are summarized
later in this section. This biodegradation rate can also be compared to the values of 0.48 h"1 for
aromatic hydrocarbons summarized by DeVaull (2011). The sensitivity of the results of the 3-D
model to various biodegradation rates is presented in Abreu and Johnson (2006) and Abreu et al.
(2009a,b).
Abreu et al. (2009b, pp. 13-14) published additional simulations showing the oxygen distribution
at three somewhat different biodegradation rates (0.079 h"1, 0.79 h"1 and 2 h"1). They examined
slab-on-grade and basement scenarios with a 4,000,000 |ig/m3 vapor source at 13.2 ft (4 m) bgs
(a substantially lower concentration range then used in Abreu and Johnson [2006]). For these
lower source strengths, varying the biodegradation rate from 0.079 h"1 to 0.79 h"1 did not affect
the formation of an oxygen shadow. Ample oxygen is available for biodegradation under these
conditions, though subsurface oxygen concentrations decrease as X increases due to increasing
rates of oxygen utilization. The sensitivity of the modeled biodegradation in the 3-D model to
various biodegradation rates under various conditions of source concentration is shown as
Figures 30, 31, 33, 34 and 36 in U.S. EPA (2012) and Figures 5, 6, 12 and 13 in Abreu et al.
(2009b).
Biodegradation rates for aromatic hydrocarbons are not directly comparable to those for aliphatic
hydrocarbons. However, the ratio of oxygen to hydrocarbon consumed is typical of the
stoichiometric ratio for the complete mineralization of hydrocarbons to carbon dioxide (i.e., 3
kg-oxygen per 1 kg-hydrocarbon). More discussion of this is presented in Section 2.3.5.
12
-------
Simulations using individual properties of aromatic and aliphatic hydrocarbons with their
respective biodegradation rates show that oxygen consumption is equivalent, regardless of the
mixture of petroleum compounds being simulated as long as the total vapor concentration of the
source is the same (Abreu et al., 2009b).
Simulations published by Abreu and Johnson (2006, pp. 2309-2310) show the oxygen
distribution for three biodegradation rates (0.018, 0.18 and 1.8 h"1) slab-on-grade and basement
scenarios with 200,000,000 |ig/m3 vapor source strength at 16.5 ft (5 m) below ground surface
(bgs). In general, these results show that for high source concentrations (e.g., 200,000,000
|ig/m3) and depths of 16.5 ft (5 m) or less the biodegradation rate doesn't significantly affect the
size of the oxygen shadow. In these cases the simulated oxygen shadow extends across virtually
the entire building footprint regardless of the biodegradation rate selected (Abreu and Johnson,
2006). For these simulations, the observed oxygen penetration depth of about 8.25 ft (2.5 m) bgs
appeared to be relatively unaffected by first-order degradation rate for this source concentration
and depth. For all three degradation rates, simulated steady state soil gas profiles near the
foundation were influenced by the presence of the foundation for both basement and slab-on-
grade scenarios. In these simulations, oxygen is not present beneath the foundation at normalized
| Comparison of Biodegradation Rates
his study . onginaJy from DeVauN 20C7 for
Bromatics
DeVaull 2011 aromatics
X Abreu end Johnson 2006
t Abreu 2C09b
X 0.018
Lowrange Midrange (or only value) High-range
Figure 2. Comparison of biodegradation rates found in the literature.
13
-------
concentrations >0.05. Thus, these scenarios indicate that hydrocarbon vapor concentrations are
relatively unaffected by changes in first-order biodegradation rate when insufficient oxygen
concentrations exist beneath a foundation to support aerobic degradation.
From all of the simulations described in the preceding paragraphs, it is observed that for high
source strengths and low oxygen levels, soil gas concentration profiles for PHCs and oxygen are
insensitive to biodegradation rates. Conversely, for low source strengths and higher oxygen
levels, PHC vapor and oxygen concentration profiles are sensitive to biodegradation rates.
Specifically, in order for the biodegradation rate to influence development of an oxygen shadow
below a building, two conditions must be met:
• Oxygen concentration in soil gas must not be less than 2 percent by volume (i.e., there
must be sufficient oxygen available to support biodegradation), and
• Biodegradation rate must be greater than 2 h"1, which is in the high range of reported
values (see Figure 2) and higher than the values used in the studies discussed in this
section.
2.3.4 Initial and Boundary Conditions for Petroleum Hydrocarbons and Oxygen
The 3-D model was used to simulate the coupled transport and biodegradation of PHCs and
oxygen. The PHC source is assumed to be constant concentration and infinite extent located at
the lower boundary of the domain. At the upper boundary, the atmosphere is simulated as a
constant source of oxygen at 21 percent by volume. The oxygen influx is through the open
ground surface area next to the building. The initial concentration of oxygen in the subsurface
was assumed to be 21 percent by volume (the same as the atmospheric concentration). For some
simulations, the initial oxygen concentration in the subsurface was reduced to 10.5 percent by
volume; half of the oxygen concentration in the influx from the atmosphere at the open ground
(see Section 2.4 for more discussion).
In all simulations, the threshold oxygen concentration for biodegradation to occur was assumed
to be 1 percent by volume (which corresponds to a normalized oxygen concentration of 0.05 in
the contour plots) (Abreu and Johnson, 2006; Abreu et al., 2009a,b; Ward et al., 1997; Patterson
and Davis, 2009).
2.3.5 Chemical Composition of Vapor Source
Aerobically biodegradable chemicals (such as PHCs) simultaneously utilize oxygen and thus,
contribute to its depletion in the subsurface. Benzene is typically used as a surrogate for all
aerobically biodegradable PHCs and other VOCs of interest for PVI investigations.2 All
simulations presented in this report assume a single-component vapor source with physical-
2 When applying the results of this study to other sites, an equivalent benzene concentration should be calculated for
all degradable VOCs (i.e. total petroleum hydrocarbons plus methane) and the result used as the source vapor
concentration. Likewise, the biodegradation rate and other physical and chemical properties for benzene should be
used as model inputs.
14
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chemical properties for benzene. Abreu et al. (2009a,b) compared predicted VOC concentrations
and oxygen profiles for cases involving single and multicomponent sources with the same total
source concentration. For cases where oxygen is limiting and biodegradation rates are variable
(but fast compared with diffusive transport time scales), the vapor profiles of individual
components were similar. This behavior has been observed in the field and documented by
Roggemans et al. (2001). Abreu et al. (2009a,b) present simulation results using a higher
biodegradation rate of 71 hr"1 for aliphatic hydrocarbons. However, very similar oxygen profiles
were observed with the single-source benzene and multicomponent petroleum hydrocarbon
cases. Therefore, while the simulations presented in this report are for a single component
source, they are also applicable to a range of multicomponent sources involving aerobically
biodegradable chemicals (EPA, 2012).
As discussed in Section 3, for certain source concentrations and depths, the oxygen
concentrations in the subsurface may be depleted, creating anaerobic zones. Under these
conditions, incomplete degradation of hydrocarbons can result in the formation of methane gas.
Methane is readily biodegradable aerobically, contributes to oxygen depletion, and may affect
the soil vapor profile of other hydrocarbons. Methane production and transport are not
specifically addressed in this document. However, if the methane concentrations (as part of the
overall hydrocarbon concentration) are within the range of simulated source concentrations and
pressure-driven advection of methane does not occur, then the model results presented in this
report should be generally applicable. It should be noted that methane may be the dominant
vapor component (present at 1 to 20 percent by volume) at some petroleum sites. These sites
may include ebullition of methane gas resulting in increased soil gas pressures with advective
flow of soil gas. The effect of methane gas generation on petroleum vapor intrusion was not
simulated in this study, but has been explored by Jourabchi et al. (2012).
2.3.6 Model Input Parameters
Model input parameters, including soil physical properties, are listed in Table 2. These
parameters are reasonably representative of typical conditions and were held constant during the
modeling runs. A homogeneous sandy soil was used for the base cases and simulations were run
for various lengths of time to determine if quasi-steady state conditions had been achieved or to
verify the time frame of transport time before oxygen is depleted. Additional scenarios were run
for a sandy soil overlain by a one meter thick layer of silty clay. All simulations were run with a
single fraction of recalcitrant organic carbon in the soil. Results under transient conditions
(including the time to reach a quasi-steady state condition) are affected by the fraction of
recalcitrant organic carbon due to its effect on transport of certain VOCs. However, the presence
or absence of an oxygen shadow in the sub slab would not be affected by the foc present in the
soil because the foc doesn't itself exert an oxygen demand.
2.4 Sensitivity Testing
To evaluate the sensitivity of the model to an initial condition where hydrocarbons are released
into a subsurface setting that contains less than atmospheric levels of oxygen, simulations were
performed with initial oxygen in soil gas at 10.5 percent by volume instead of 21 percent by
15
-------
volume. This value is in the range of background vadose zone soil oxygen content, which has
been reported in various sources as 5 to 18 percent3 and 15 to 21 percent4 by volume.
Table 2. Model Input Parameters
Building/foundation parameters
Length*: 10m to 632m
Width*: 10m to 632m
Depth in soil:
• 2.0 m (basement type)
• 0.2m (slab-on-grade type)
Foundation thickness: 0.15m
Enclosed space volume: (width x length x
2.44) m3
Indoor air mixing height: 2.44 m
Air exchange rate: 0.5 h"1
Crack width: 0.001 m
Crack location: Perimeter
Building depressurization: 5 Pa
Soil Properties
Sandy soil:
Soil bulk density: 1,660 kg/m3
Moisture-filled porosity: 0.054 m3water/m3soii
Total soil porosity: 0.375 m3Voids/m3soii
Soil gas permeability: 1E-11 m2
Benzene effective diffusion coefficient:
5.12E-3m2/h
Oxygen effective diffusion coefficient:
1.16E-2m2/h
Silty clay:
Soil bulk density: 1,380 kg/m3
Moisture-filled porosity: 0.216 m3water/m3soii
Total soil porosity: 0.481 m3voids/ni3Soii
Soil gas permeability: 1.5E-13 m2
Benzene effective diffusion coefficient:
1.65E-3m2/h
Oxygen effective diffusion coefficient:
3.74E-3m2/h
Foc= 0.001
Hydrocarbon vapor source properties
Location: base of vadose zone
Source size: entire domain footprint
Hydrocarbon properties
Overall effective diffusion coefficient for
transport in the porous media: 5.12E-3 m2/h
Overall effective diffusion coefficient for
9
transport in the crack: 3.17E-2 m /h
Atmospheric concentration: 0.0 mg/L
Henry's Law constant (Hi): 0.228 m3water/m3vapor
Sorption coefficient of hydrocarbon to organic
carbon (Koc,i): 61.7 kg/kg organic carbon
First order biodegradation rate = 0.79 h"1
Oxygen properties
Overall effective diffusion coefficient for
transport in porous media: 1.16E-2 m2/h
Overall effective diffusion coefficient for
9
transport in the crack: 7.2E-2 m /h
Henry's Law constant (H;): 31.6 m3water/m3vapor
Sorption coefficient of oxygen to organic carbon
(Koc,i): negligible, assumed 0 kg/kg oc
Ratio of oxygen to hydrocarbon consumed:
• 3 kg-oxygen/kg-hydrocarbon
Threshold concentration: 1% vol/vol
Atmospheric concentration: 21% vol/vol
Others
Dynamic viscosity of air: 0.0648 Kg/m/h
NOTE: model input parameters in this table are
provided in metric units only because the model
requires metric units.
3 http://www.colorado.edu/engineering/civil/CVEN4474/resources/Biovent.pdf
4 http://www.afcee.af.mil/resources/technologytransfer/programsandinitiatives/
bioventing/sitescreening/index.asp
16
-------
To evaluate the time frame before oxygen was depleted and to evaluate the oxygen conditions
when a quasi-steady transport condition was achieved, simulations were conducted with
increasing transport times.
Simulation results (see Tables B-l through B-5 in Appendix B) indicate that the probability of an
oxygen shadow developing increases with:
• Building size
• Source vapor strength
• Decreasing vadose zone thickness between source and building slab (source distance
from slab)
• Transport time for oxygen consumption under transient conditions
2.5 Potentially Confounding Factors
The following factors can increase the concentration of oxygen in the subsurface, but were not
included in the model simulations. As a result the model may overestimate the formation of an
oxygen shadow:
• Wind-induced advection. Wind impinging on buildings and topography can induce
pressure differences in soil gas, thus inducing a sub-horizontal flow of soil gas under
buildings, which may increase the rate of oxygen replenishment under a building, and
reduce the potential for shadow formation (Parker, 2003; Lundegard et al., 2008).
• Barometric-induced advection. Diurnal and longer-period barometric pressure
fluctuations can induce the flow of soil gas into and out of shallow soils. This
barometrically-induced advection may affect the rate of oxygen replenishment under
a building.
• Bi-directional soil gas exchange through foundation openings. Cracks and openings
in building foundations have been shown to have bidirectional flow, depending on the
differential pressure between the building and the adjacent soil gas (McHugh et al.,
2006). During periods of positive differential pressure, oxygen may enter the
subsurface through the foundation, thus increasing the rate of oxygen replenishment
and decreasing the tendency for shadow formation.
• Aerated foundation course. Many slab-on-grade buildings are constructed with a layer
of gravel or other coarse-grained material beneath the slab. This coarse-grained layer
may provide a conduit or plenum for enhanced advection of air under the building,
which may provide a protective blanket of oxygen-rich soil gas under the building
(Lundegard et al., 2008).
• Source depletion. The model assumes that the source does not deplete and has a
constant concentration beneath the full extent of the foundation.
• Permeable concrete. The model assumes the foundation concrete is impermeable and
doesn't account for the potential transport of oxygen through the foundation. In
17
-------
reality, concrete may allow slow diffusion of oxygen from the building into the
subsurface even in the absence of discrete openings or cracks.
• Moisture limitation under the building. As discussed in section 2.2, the model used
does not simulate water infiltration and associated effects the building may have on
limiting the infiltration of soil moisture beneath the slab. If moisture in the soils
immediately below the building fell to below 25 percent of field capacity, then
biodegradation in that area could be limited and the model may over predict the
consumption of oxygen. However, in cases where the petroleum hydrocarbon source
is associated with the groundwater table, a layer with both adequate moisture and
oxygen is likely to exist within the soil column.
In contrast, the following factors can decrease the concentration of oxygen in the subsurface, but
were not included in the model simulations. As a result the model may underestimate the
formation of an oxygen shadow.
• High natural oxygen consumption from unusually highly organic content soils (i.e.,
peat)
• The presence of high concentrations of other gases providing a carbon substrate for
microbial metabolism, such as methane, whether derived from the anaerobic
biodegradation of ethanol-blended gasoline or anaerobic degradation of conventional
petroleum fuels
• Shallow soil layers with high moisture content that restricts oxygen flux to the
subsurface (Lundegard et al., 2008)
• Regional coverage of a high percentage of the ground surface by impervious or lower
permeability materials, as may occur in major city centers. Information sources on
land cover derived from satellite or aerial photography data can be accessed from the
United States Geological Survey (USGS) Land Cover Institute
http://landcover.usgs.gov/index.php
• A vadose zone composed solely or principally of bedrock with little or no overlying
soils
Therefore, while these simulations may give an indication of the potential for oxygen shadow
formation under worst case conditions dominated by diffusive flow, they should not be regarded
as accurate predictions of actual performance at all field sites.
18
-------
3. Results and Discussion
3.1 Summary of Tabulated Results
The results from model simulations are summarized in Tables B-l through B-5 in Appendix B.
Tables B-l through B-4 present results for slab-on-grade buildings. Tables B-l through B-3
present results for a vadose zone consisting of a homogeneous sandy soil with vapor source
depths of the following:
• 5 ft (1.6m)-Table B-l
• 15 ft (4.6m)-Table B-2
• 30 ft (9 m) - Table B-3
In Tables B-l through B-3, the results for square building footprints are presented first, followed
by results for rectangular buildings. Within each group of building shape, the results are
presented in order of increasing source vapor concentration and foundation size.
Table B-4 presents the results for simulations run with a 3.3 ft (1 m) silty clay layer overlying
sand. Table B-5 presents results for buildings with a basement.
In the summary table, an oxygen shadow is qualitatively defined to occur when the predicted
oxygen content in soil gas beneath the slab is less than or equal to 1 percent by volume (Abreu
and Johnson, 2006; Abreu et al., 2009a,b; Ward et al., 1997; Patterson and Davis, 2009). The
minimum oxygen concentration immediately below the slab and 3.3 ft (1 m) below the slab is
also tabulated.
3.2 Graphical Conventions Used in Figures
The 3-D model calculates the chemical vapor concentration in the subsurface, the mass flow
rates into the building(s), and the indoor air concentration due to vapor intrusion. To facilitate the
discussion and the presentation of results, the model output has been normalized using the source
concentration (i.e., the predicted concentration is divided by the maximum vapor concentration
in the subsurface). The normalized concentrations shown in the figures can be multiplied by the
source concentration (or initial oxygen concentration, as appropriate) to convert into absolute
concentrations. The hydrocarbon concentration contour lines in most of the figures show these
normalized soil vapor concentrations, which are always dimensionless and range from 0 to 1,
with 1 being equal to the source concentration.
Since the simulations presented in this document assume a homogeneous soil system with an
infinite source footprint, there is symmetry in the soil gas concentration profile with relation to
the centerline of the building (Abreu and Johnson, 2006). Figures 3, 4, and 5 illustrate graphical
conventions used in analogous figures showing model results. Figure 3 shows a plot of the PHC
vapor profile beneath the full width of a large building as well as the corresponding half building
plot; notice that the contours are essentially identical. Figure 4 shows the corresponding oxygen
profiles beneath the full width of a large building and the corresponding half building. As with
Figure 3, the contours are essentially identical.
19
-------
Bui cirg di
- 632 meters
KTI-" :ui c rg dimension = 316 meters
.t
LJ-..
J=
:i
-1E-4-
-1E-5-
1E-6
-1E-7-
-1E-7-
1E-6
-Z
150 , . 200
x(m)
HYDROCARBON VFRTICAL PRQFII F
Since there is symmetry in the soil gas concentration profile in
relation la the center af the building, the concentration
results will be presented using only half of the bulding dimension
I Half bi. Idinq cirreis on - 316 mete's
ISO 200
x(m)
Figure 3. Contours of simulated petroleum hydrocarbon vapors in the subsurface beneath a building. Results for PHC source vapor
concentration of 10,000,000 ug/m3 at depth of 15 ft (4.6 m) and building size of 2,073 ft x 2,073 ft (632 m x 632 m). Initial
oxygen concentration of 21 percent by volume and transport time of 20 days.
20
-------
Building dimension = 632 meters
D)
J3 -2-
D.
to
Half bjj Id ing. c mersioi ~ 316 rre;ers
,&j
-------
HYDROCARBON
Ha f building dimension - 3' 6
OXYGEN
j Half building dimension = 316 metsrs
£OQ
-------
For both Figure 3 and Figure 4, the results are for a source with vapor concentration of
10,000,000 |ig/m3 and simulated transport time of 20 days; there is no oxygen shadow nor
hydrocarbon vapor build up below the slab. Figure 5 shows profiles for both PHC vapor and
oxygen concentrations beneath a building for the same scenario simulated in Figures 3 and 4 but
for a longer transport time (1 year), and the results show the oxygen shadow and hydrocarbon
vapor build up below the slab. Note that in all of the model scenarios, the model domain extends
horizontally beyond the building footprint for a distance of 23 ft (7 m). However, due to the scale
of the plot, the contours beyond the building are compressed and difficult to distinguish.
However, close up plots of this region (see the ovals drawn on Figure 5) reveal that at the far
boundary, the concentration isopleths are horizontal. This indicates that even under high source
vapor concentration conditions, the 7 m distance to the far boundary in the modeled domain
provides a sufficient surface area to allow for oxygen infiltration. Thus, the results are not
sensitive to further increases in the size of the modeled domain, and extension of the domain
(which would increase computational burden) is unnecessary.
3.3 Results for a Homogeneous Sandy Soil and Square Buildings
Results for simulations for homogeneous sandy soil are presented in Appendix B, Tables B-l
through B-3. As shown in Figure 6 and Figure 7, no oxygen shadow develops beneath the largest
building simulated (2,073 ft x 2,073 ft [632 m x 632 m]) with relatively low source vapor
concentrations (10,000 |ig/m3 and 100,000 |ig/m3) even when the source is shallow (5 ft [1.6 m])
and the transport time is long (50 years). Therefore, it can be inferred that no oxygen shadow
would develop if the source vapor concentration is at or below 100,000 |ig/m3 and with a thicker
vadose zone. However, as shown in Figure 8, when the source vapor concentration is increased
to 1,000,000 |ig/m3 and the source depth is only 5 ft (1.6 m), an oxygen shadow develops after a
period of 6 to 9 years under the same large building. Figure 9 shows that when the source depth
is increased to 15 ft (4.6 m) and the source concentration is held at 1,000,000 |ig/m3, no oxygen
shadow forms even after 20 years. If the initial oxygen concentration in the soil gas is reduced to
10.5 percent by volume then an oxygen shadow does develop (Figure 10). Extending the
transport time to 50 years has a similar effect. As shown in Figure 11, with the highest source
vapor concentration modeled (10,000,000 |ig/m3), an oxygen shadow develops in less than one
year after release for the 15 ft (4.6m) vadose zone thickness combined with the largest modeled
building size 2,073 ft x 2,073 ft (632 m x 632 m). Therefore, it can be inferred that an oxygen
shadow has a greater potential to occur when the vadose zone is thinner than 15 ft (4.6 m) and
the source vapor concentrations are in the range of 10,000,000 |ig/m3. In fact, under these
conditions, an oxygen shadow develops in less than one year beneath a building with dimensions
of 98 ft x 98 ft (30 m x 30 m); no oxygen shadow developed for buildings with a smaller
footprint (Figure 12 and Table B-2).
For a small building with dimensions of 33 ft x 33 ft (10 m xlO m) underlain by the highest
source vapor concentration modeled (10,000,0
an oxygen shadow forms rapidly (Table B-l).
source vapor concentration modeled (10,000,000 |ig/m3) and a shallow 5 ft (1.6 m) vadose zone,
23
-------
HYDROCARBON
,i Half build ng dirrnora on - 316 iru:o-'£
OXYGEN
Initial Oxygen Concentration = 21%
I Hnll hi.i riirn <\ rwisiiir = !i'i.i Titters
?JtJtJW3tJtJtJt3tJl£J9^^
1SQ 200
x(m)
15D 200
x(m)
aso
iUt
Initial Oxygen Concentration = 10,5%
17
-O.DG1
0.01
ex;
7
/
i
oooooc
r
!
xxxxxxxxxxxxx
1 — 1
1
xxxxx>
[
0<>C>O
1 1
1 1
S^2G<
0.!
XXX
Os
},9
150 2J'J
X (-11)
:>uc
1CW
(m)
Figure 6. Concentration results for source vapor concentration of 10,000 jng/mj at depth of 5 ft (1.6 m) and building size of 2,073 ft x
2,073 ft (632 m x 632 m). Initial oxygen concentration of 21 and 10.5 percent by volume and transport time of 20 years.
24
-------
HYDROCARBON
i H.-i I bu Id ing rliTmrHinn = HIT;. n
7
1SD 2DO
(rn)
OXYGEN
Initial Oxygen Concentration = 21%
I Half tiLii circi d moisior - 3' 6 ivo'.crs
Initial Oxygon Concentration = 10.5%
i'
7
150 200
>: ;rn)
vv
7
/
CKXXXX
xxxxxxxxxxxxx
1 — '
>C*XK>0<
xxxxxxxxxxxx>
1 — '
>o
-------
HYDROCARBON
OXYGEN
3 Years of Vapor Transport
Hal"' auildinq cirrensicr - 316 motors
Half build rg diners on ~ 3' 6
,^<>C>OOC>CC>OC'
150 200
x (m)
x(m)
6 Years of Vapor Transport
15Q 2CX)
>: I 11)
:;: ii i 0
11:::
160 x (m) 2DO
9 Years of Vapar Transport
x
x fm)
*~- 0-
E
£ **~
S -1-
y-J/yyJ/yyy>yy y fSJ^fffJ SSSSSSSS S SS S S S S f J S jV S S S S S S y'yyj— I
0,001
JJJJ1
-
-
rj,yyjjyyy>yyyyyyyyyyyyyyylyy,yyyyy>y^j/yvyy>xyyyyy
0
^
•
1
~T~
0.9
t|
Figure 8. Concentration results for source vapor concentration of 1,000,000 jig/m at depth of 5 ft (1.6 m) and building size of 2,073 ft x
2,073 ft (632 m x 632 m). Initial oxygen concentration of 21 percent by volume and transport times of 3, 6 and 9 years.
26
-------
HYDROCARBON
OXYGEN
. H:H|! ::nil:!inci riimension =316 meters
6 Years of Vapor Transport
- j Hal'' ajilding dirio-isicr - 31 S i
•
7
/ 1—
1- ^
^ ^.J L.
I
CJ
7
150 200 250 300
X (rn)
TOO 160 2OO 250
9 Years of Vapor Transport
E
f
JZ -2-
n
--
1E-7
1F-fi
-Iff-K
/-— "N
\
n 7
(
\
\
\
\
\
\
= ::
150 200
x(rn)
Z5D 300 a 5D
20 Years of Vapor Transport
0.4
1
(m)
Figure 9. Concentration results for source vapor concentration of 1,000,000 jig/m at depth of 15 ft (4.6 m) and building size of 2,073 ft
x 2,073 ft (632 m x 632 m) Initial oxygen concentration of 21 percent by volume and transport times of 6, 9 and 20 years.
27
-------
HYDROCARBON
OXYGEN
9 Years of Vapor Transport
Initial Oxygen Concentration = 21%
Half build! rta dimension = 316 meters
"f
1
r
•2-
-•'
n
0
-2
7
^
— 1E-8— — ^
3
a
i
) mo
150
X
rrrrrj
-
t
I
; '
1
/
I I
200 30*> C SO 1OD
(m)
8 Years of Vapor Transport
Initial Oxygen Concentration = 1D%
1E-7
1F^
1E-S
1
15D
X
^
Jl R
2DD 250
(m)
O.B
i
0.2
\
N
11
) Mill 1
- nn
1511
?nn
xfm)
:,nn
Figure 10. Concentration results for source vapor concentration of 1,000,000 jig/m at depth of 15 ft (4.6 m) and building size of 2,073 ft
x 2,073 ft (632 m x 632 m) for an initial concentration of oxygen at 21% and 10% and transport times of 8 and 9 years.
28
-------
HYDROCARBON
1 HaH buitdmo dirnansion = 316
7
VI
s
L
I-
C:
-te-7-
•:•
1E-7
TD-6
1E-5-
-1E-4-
• Source
KIO
-1E-5-
X (m)
x (m)
OXYGEN
20 Days of Vapor Transport
h.i f rjtj d ng d
7
-o.a-
30 Days of Vapor Transporl
300 Q SO
par of Vapor Transporl
•fl.1-
150 200
x(mj
x fm)
x(rn>
•3 '35,
Figure 11. Concentration results for source vapor concentration of 10,000,000 figlm at depth of 15 ft (4.6 m) and building size of 2,073
ft x 2,073 ft (632 m x 632 m) Initial oxygen concentration of 21 percent by volume. Three transport time: 20 days, 30 days and
1 year (steady state condition within one year of transport).
29
-------
HYDROCARBON
OXYGEN
Building dimensions: 30 m .x 30 m
10 12 16 18 20 22 0 t
Building dimensions: 20 m x 20 m
10 12 14
x(m)
16
Building dimensions; 10 m x 10 m
J_
c_
1E-7
10 12
10 12
Figure 12. Concentration results for source vapor concentration of 10,000,000 figlm at depth of 15 ft (4.6 m) and three building sizes:
98 ft x 98 ft, 66 ft x 66 ft and 33 ft x 33 ft (30 m x 30 m, 20 m x 20 m, and 10 m x 10 m). Initial oxygen concentration of 21
percent by volume and steady state condition within one year of transport.
30
-------
For the highest source vapor concentration modeled (10,000,000 |ig/m3) and a relatively large
vadose zone thickness (30 ft: 9 m) only a limited number of simulations were run. The results
show that oxygen is substantially depleted and rapidly comes to a steady state condition.
However, the oxygen does not quite reach the operational definition of an oxygen shadow for
buildings between 98 ft x 98 ft (30 m x 30 m) and 131 ft x 131 ft (40 m x 40 m) (Figure 13 and
Table B-3). An oxygen shadow does form beneath a building of 197 ft x 197 ft (60 m x 60 m).
Results for higher source vapor concentrations and small 33 ftx33 ft(10mx 10m) buildings
are shown in EPA (2012, Section 5), and Abreu and Johnson (2006). U.S EPA 2012 summarizes
for sources at 26 ft (8 m) bgs in a uniform sand:
"The concentration profiles for the basement scenario . . . show that for source vapor
concentrations of 100,000,000 and 200,000,000 \\.g/m (representative of weathered gasoline
NAPL sources), oxygen is consumed before it can penetrate beneath the foundation. Thus, no
biodegradation is occurring beneath the foundation in the region below the 0.05 oxygen contour
line, because of limited oxygen availability and supply. In this region, the vapor transport is not
attenuated by biodegradation. As a result, the hydrocarbon concentration is higher below the
foundation compared with similar depths away from the building with sufficient oxygen for
biodegradation. For a source vapor concentration of 20,000,000 \\.g/m , oxygen penetrates
beneath the entire foundation. The vapor transport is attenuated by biodegradation throughout
much of the subsurface, and the vertical profile of the hydrocarbon concentration is similar
beneath the building and aw ay from the building. The concentration profiles for the slab-on-
grade scenario show an increased oxygen supply beneath the foundation relative to the basement
scenario, and the vapor transport is therefore attenuated by biodegradation beneath the entire
building footprint, even for the highest source concentrations simulated. The differences in the
aerobic zone (oxygen) distribution beneath the slab-on-grade foundation compared with the
basement foundation are due to the combination of a smaller distance for oxygen transport from
the atmosphere and an increased distance for hydrocarbon transport from the source to
locations immediately beneath the slab. The concentration profiles in the subsurface away from
the foundation are identical for both scenarios (basement and slab-on-grade). " (U.S. EPA,
2012). Note: units converted from the original for compatibility with this report).
3.4 Results for a Homogeneous Sandy Soil and Rectangular Buildings
Several rectangular building simulations were performed for shallow vapor sources at 5 ft (1.6
m). Three simulations were performed for a very thin building footprint 33 ft x 2,073 ft (10 m x
632 m) with a source vapor concentration of 1,000,000 |ig/m . These simulations came to quasi-
steady state with a stable concentration of oxygen at 15.6 percent by volume. This oxygen
concentration is substantially higher in comparison to the scenario with a very large square
building (2,073 ft x 2,073 ft: 632 m x 632 m) that resulted in development of an oxygen shadow
beneath the building. In contrast, this result is similar to the base case where the building was
square with dimensions of 33 ft x 33 ft (10 m x 10 m) that resulted in only a slight decrease
(from 21 percent to 17.8 percent) in the oxygen concentration beneath the building (Table B-l).
This result is consistent with the expectation for rectangular buildings discussed in Section 2.3.1.
-------
Additional simulations with rectangular buildings were also performed at the depth of 15 ft (4.6
m) with a long, thin 33 ft x 295 ft (10 m x 90 m) building. With the highest source vapor
concentration of 10,000,000 |ig/m3 quasi-equilibrium was reached with a stable oxygen
concentration of 4 percent by volume. These results are comparable to those (6.1 percent
oxygen) for a square building of 33 ft x 33 ft (10 m x 10 m). Even when the extreme bounding
case of a 33 ft x 2,073 ft (10 m x 632 m) building shape was simulated, quasi-equilibrium was
reached with a stable oxygen concentration of 4.1 percent by volume (Figure 14 and Table B-2).
These results provide further support for the expectation for rectangular building discussed in
Section 2.3.1.
32
-------
HYDROCARBON
OXYGEN
Building dimensions: 60 m x 60 m
duildincj dintp-isiurs <1U ir- :«: -Id ir
Building dimensions' 30 m x 30 m
x(m)
Figure 13. Concentration results for source vapor concentration of 10,000,000 jig/mj at depth of 30 ft (9 m) and three building sizes: 197
ft x 197 ft, 131 ft x 131 ft and 98 ft x 98 ft (60 m x 60 m, 40 m x 40 m, and 30 m x 30 m). Initial oxygen concentration of 21
percent by volume and steady state condition within one year of transport.
33
-------
Thus, the depletion of oxygen beneath a rectangular building is controlled primarily by the
dimension of the short side of the floor plan (i.e., the shortest distance from the slab center to the
edge of the building) (see Figure 14). The minimum oxygen concentration in the rectangular
buildings will be slightly lower than would be expected for a square building with the same
length as the smaller side of the rectangular building.
3.5 Results for a Homogeneous Sandy Soil with an Overlying Silty Clay Layer at
Ground Surface
Approximately thirty simulations were conducted with a 3 ft (1 m) thick silty clay layer acting as
a capping layer on top of an underlying homogeneous sandy soil (Table B-4). For simulations
with the source at a depth of 5 ft (1.6 m), the silty clay layer comprises the majority of the
simulated vadose zone. Thus, the resulting oxygen transport is substantially lower than the base
case where sandy soil comprised the entire thickness of the vadose zone. For example, beneath
the largest building 2,073 ft x 2,073 ft (632 m x 632 m) and with the source vapor concentration
of 100,000 |ig/m3, a minimum oxygen concentration of 1 percent by volume is reached beneath
the slab in 20 years, although depletion of oxygen began within only 9 years (Table B-4). This
stands in contrast to the corresponding scenario for a sandy soil, which still had an oxygen
concentration of 17.9 percent by volume beneath the slab after 20 years of simulated transport
(Table B-l).
Similarly, for a medium sized square building (98 ft: 30 m on a side) with a source vapor
concentration of 1,000,000 |ig/m3 at a depth of 5 ft (1.6 m) and beneath the shallow silty clay
layer, an oxygen shadows forms within 9 years (Table B-4). This stands in contrast to the
corresponding all-sand condition, where the oxygen was 12.3 percent by volume after 9 years
had elapsed (Table B-l).
At the vadose zone thickness of 15 ft (4.6 m) with the 3.2 ft (1 m) silty clay layer at the surface
and a source vapor concentration of 1,000,000 |ig/m3 an oxygen shadow forms in 9 years (Table
B-4). Without the silty clay layer, the corresponding simulations do not reach oxygen
concentration of 1 percent by volume until between 20 and 50 years had elapsed.
With the largest vadose zone thickness modeled (30 ft: 9 meters) and a source vapor
concentration of 10,000,000 |ig/m3 the overlying clay layer still reduces the oxygen flux to the
subsurface. For example, with the 98 ft x 98 ft (30 m x 30 m) building footprint the oxygen
concentration beneath the building is reduced from 2.9 to 1.9 percent by volume. With a 131 ft x
131 ft (40 m x 40 m) building footprint, an oxygen shadow forms after 6 years (Tables B-3 and
B-4).
34
-------
Cross section through Center of BuMIng on x direction
Building dimansinri on x direction: 632 nwtare
'
\ \ "— '
HYDROCARBON
•
1 ' — '
if YYYYYVYYYYYYYYYYYYYYYYYYYYYYYY^ L
1 1 1 1
,M
; ^>_
Cross section through Cental at Building on y direction
Building dimension on y diredion: 10 meters
s
I
HYDROCARBON
•
3
1E-7
_ »c.c
I _»-, - •
I I •— '
! / OXYGEN
j
i
V
2; ^
I a
n a
I* i
UOE
xxxxxxxxxxxx>
a 3
o! i
1
^
\^
V
Figure 14. Concentration results for a building with rectangular shape 2,073 ft x 33 ft (632 m x 10 m), source vapor concentration of
10,000,000 ug/m3 at 15 ft (4.6 m), initial oxygen concentration of 21 percent by volume and steady state condition. Results
viewed in two perpendicular cross sections by center of building.
35
-------
3.6 Results for Buildings with a Basement
Five simulations were performed for a very large building 2,073 ft x 2,073 ft (632 m x 632 m)
with a 6.6 ft (2 m) deep basement (Table B-5 and Figure 15) and the source located 5 ft (1.6 m)
below the basement slab. The results are essentially the same as those for the corresponding slab-
on-grade scenario with a source located 5 ft (1.6 m) below the slab (Table B-l). The results
presented in Table B-l for slab-on-grade and source at 5 ft (1.6 m) bgs are applicable to
basement scenarios with a basement depth of 6.6 ft (2 m) and source depth of 12 ft (3.6 m) bgs.
Although there may be some slight differences (due to the atmospheric ground surface boundary
being further away in the basement scenario) the overall results are essentially the same.
Abreu and Johnson (2006), Abreu et al. (2009a,b) and EPA (2012) presented a significant
number of biodegradation scenarios that compared soil vapor and oxygen profiles for buildings
with a basement versus slab-on-grade. The results in all four of these investigations are
consistent and indicate that the primary controlling factor is the separation distance between the
vapor source and the overlying foundation slab, and not the particular construction of the
foundation (i.e., slab versus basement).
Figure 16 shows the results of a basement scenario and the corresponding slab-on-grade scenario
for a very large building (2,073 ft x 2,073 ft: 632 m by 632 m) with a full basement.
36
-------
Hydrocarbon
t Half building dimension = 316 meters
.^kXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX?g^ .£xxxx xxx xxx xxx xxx xxx xxx >0OOOOOCOOC&
Oxygen
Ha f bu i;hq JiriBriiibn = 316 miners
f s t f s i t f s e t f / t t f f t //,',-
f / t t f / t t f
0.001
-Q.D1 •
*M
0.9
' 'i:'i
200
Figure 15. Concentration results for building 2,073 ft x 2,073 ft (632 m x 632 m), with full 6.6 ft (2 m) deep basement, source vapor
concentration of 100,000 ug/m3 at 5 ft (1.6 m) below basement slab, transport time 9 years and initial oxygen concentration of
21 percent by volume.
37
-------
Basement
I I U.ll bu Icr-ig -j •iii.-fjiL>ii - 31K • i:
t>
n
hydrocarbon
-0.001 •
-0.01
150
x(m)
Basement
; I k I" bu
7
a -0.5-
.Q
Hydrocarbon
Slab on grade
-O.KJ1-
-001-
160 2CO
Mm)
iJC
H-.l'' bu lt:ir'q cringns '.:•'! = ^ 1 r>
£ -1-1
W1
C.-
~. -,
&
-3-
Ocygwi
150 2DD
0,9
i Half building dimension = 316 meters
/
? o-
$.0.5-
£• -
-5-1 a-
:
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^S,
7j
^
1=1
Oxygen p
K
100
1SD
2CB 25C
a
MO
x(m)
Figure 16. Concentration results for building with full 2 m deep basement vs. building slab-on-grade, for building area 2,073 ft x 2,073 ft
(632 m x 632 m), source vapor concentration of 100,000 ug/m3 at 5 ft (1.6 m) below foundation slab, transport time 9 years
and initial oxygen = 21 percent by volume..
38
-------
[This page intentionally left blank.]
39
-------
4. Conclusions
The results of this study may help practitioners identify situations where they should confirm
with field measurements the presence of oxygen necessary to support aerobic biodegradation of
petroleum hydrocarbons. Conversely, there are other situations where practitioners can
reasonably infer from site conditions the presence of oxygen.
The results of approximately 160 simulations (see Tables B-l through B-5 in Appendix B) show
that the presence or absence of an oxygen shadow is dependent on the following:
• Increasing building area (including surrounding pavement area)
• Increasing source vapor concentration
• Decreasing depth of vapor source beneath the building
• Increasing transport time for oxygen consumption under transient conditions
(assuming the source PHC vapor concentrations are stable)
At lower source vapor concentrations (up to 100,000 |ig/m3) an oxygen shadow does not develop
even beneath very large buildings (tested cases ranged up to 2,073 ft x 2,073 ft: 632 m x 632 m)
with shallow 5 ft (1.6 m) vadose zone, after a long simulated transport time (50 years).
At the intermediate vapor concentration modeled in this report (1,000,000 |ig/m3):
• An oxygen shadow did not form beneath a medium size building, 98 ft x 98 ft
(30 m x 30 m) with a shallow 5 ft (1.6 m ) vadose zone after a simulated transport
time of 9 years
• An oxygen shadow did develop under a building with dimensions of 131 ft x 131 ft
(40 m x 40 m) with a shallow 5 ft (1.6 m ) vadose zone after a simulated transport
time of 9 years
• An oxygen shadow did not form beneath the largest building simulated,
2,073 ft x 2,073 ft (632 m x 632 m) with a moderate thickness vadose zone 15 ft (4.6
m) after a simulated transport time of 20 years
At the highest vapor concentration modeled in this report (10,000,000 |ig/m3):
• An oxygen shadow developed within one year beneath a small building 33 ft x 33 ft
(10 m x 10 m) with a shallow 5 ft (1.6 m) vadose zone
• An oxygen shadow developed within one year beneath a medium size building
98 ft x 98 ft (30 m x 30 m) with a moderate thickness vadose zone 15 ft (4.6 m)
• An oxygen shadow did not develop under a building with dimensions of 66 ft x 66 ft
(20 m x 20 m) with a moderate thickness vadose zone 15 ft (4.6 m) even after a
simulated transport time of 20 years
40
-------
At source vapor concentrations of 1,000,000 |ig/m3, the simulations indicated that a longer
transport time is required for the concentrations to reach quasi-steady state, and oxygen
concentrations are still above the threshold for a period of time before it is eventually depleted.
This may be interpreted as the result of a flux balance. If diffusion is the dominant transport
mechanism, then the following two processes are finely balanced:
• Upward diffusion of hydrocarbons
• Downward and lateral diffusion of oxygen
It is very likely that the modeled results would change significantly if additional processes were
modeled, such as high permeability layers beneath building slabs, wind speed/direction
variability and bi-directional flow through foundation cracks and penetrations throughout the
floor plan. However those factors may be more difficult to identify during a site screening
process than the inputs in the current modeling (such as foundation dimensions and thickness of
the vadose zone).
The depletion of oxygen beneath a rectangular building is controlled primarily by the dimension
of the shorter side of the floor plan.
41
-------
5. References
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Biodegradation on Soil Vapor Intrusion into Buildings: Evaluation of Low Strength
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Abreu, L.D.V. 2005. A Transient Three-dimensional Numerical Model to Simulate Vapor
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45
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Appendix A. Model Equations
Table A-l. Equations Solved by the Numerical Code
Parameter
Equation
Soil gas disturbance
pressure field
rfri
Soil gas flow field
rm
Chemical transport:
advection, diffusion,
and aerobic
biodegradation
5C;
where
a =
4>w Koc,i "foe "Pb
Hi Hi
10/3
,10/3
JW Cog"""
JJ (^oxygen < Cog
The reaction rate for oxygen (R0) is determined stoichiometrically:
m
R0=
Indoor air
concentration
i indoor
where
'i,amb
Qs =
and
i Qck-
Lck
exp
Qck
wck.Dck
dck
ck
-C
indoor
exp
Qck
T-V
wck-Dck
-1
A-l
-------
Definitions of Symbols Used in Table A-l
p: disturbance pressure (absolute atmospheric pressure minus absolute soil gas pressure at
a point) [M/L/T2]
t: time [T]
P : mean soil gas pressure (approximated by the atmospheric pressure for the problems of
interest here) [M/L/T2]
fa: gas-filled porosity [L3gas/L3soii]
jUg : soil gas dynamic viscosity [M/L/T]
I_L ,
[VI: vector del operator [L" ]
Kg. soil permeability to soil gas flow [L2]
rffo: soil gas discharge vector [L3gas/L2area/T]
/': chemical-specific subscript
Cig: gas-phase concentration of chemical /' [M;/L3gas]
pjji^j: soil moisture specific discharge vector [L3flUid/L2area/T]
Ri: net loss rate of chemical / due to reaction [M;/L3soii/T]
fa : moisture-filled porosity [L3water/L3soii]
Pb'. soil bulk density [Msoii/L3soii]
foe'. mass fraction of organic carbon in the soil [Moc/Msoii]
Koc.i : sorption coefficient of chemical / to organic carbon [(Mi/M0c)/(Mi/L3water)]
Hi. Henry's law constant for chemical / [(Mi/L3gas)/ (Mi/L3water)]
Dig. effective porous media diffusion coefficients for chemical / in soil gas [L2/T]
Diw: effective porous media diffusion coefficients for chemical /' in soil moisture [L2/T]
df: molecular diffusion coefficient of chemical / in air [L /T]
dCf: molecular diffusion coefficient of chemical /' in water [L2/T]
fa : total soil porosity (= g + fa) [L3pores/L3soii]
AJ: first-order reaction rate [1/T]
Coxygen'- oxygen soil gas concentration [M/L3-vapor]
rk0 : ratio of oxygen to hydrocarbon consumed [M0/M;]
m: total number of aerobically degrading chemicals
Es: emission rate of chemical /' to enclosed space [M/T]
Aex: enclosed space air exchange rate [1/T]
Vb : enclosed space volume [L3] where indoor air is assumed fully mixed
Ci,amb: concentration of chemical / in ambient air [M/L3]
Qs: soil gas flow rate to the enclosed space [L3/T]
Cogmm: threshold oxygen concentration for aerobic biodegradation to occur.
A-2
-------
Table A-2. Boundary Conditions
Boundaries
Boundary Condition(s)
All vertical plane-of-symmetry, all lateral
boundaries, solid foundation sections,
and the lower model domain boundary
Vp- n=0
V C[K • n = 0 (except at the vapor source boundary)
Vapor source boundary
Soil-atmosphere interface
natm(t\ = 0
^ ^' for steady atmospheric pressure, otherwise
patm (t) = Al • sin(^ • t + 9l) + A2 • sin(^2 • t + 92)
clg = o
Coxygen = C
(0.28 mg/cm)
Disturbance pressure within the
building
Foundation crack-soil interface.
Ock = \ -•
Wck~
12 jil -dak
exp
=w
v^~r
~^
K
S j
exp
d
-1
C
'g\
ve
A-3
-------
Definitions of Symbols Used in Table A-2
—>
n : unit vector normal to the surface of interest
patm(i): disturbance pressure at the soil-atmosphere interface [M/L/T2]
p'"door(i): disturbance pressure within the building [M/L/T2]
Aps(0: pressure difference between the indoor air and the atmospheric air (or gauge pressure)
A: user-defined amplitudes [M/L/T2]
cp: user-defined frequencies [radians/T]
6: user-defined phases [radians]
Qck: soil gas flow rate per unit length of crack [(L3gas/T)/L]
wck: crack width [L]
dck: foundation thickness [L]
C^T : oxygen atmospheric concentration [M/L3-vapor]
9
Dck: effective diffusion coefficient for transport in the crack [L /T].
Revision of the Indoor Air Mixing Equation Assumption
The indoor air concentration equation presented in Table A-l was derived by assuming an
instantaneous steady-state condition on the enclosed space mass balance. This assumption did
not hold true for high frequency barometric pressure fluctuations; therefore, a revised indoor air
mixing equation was derived to properly account for an accumulation term in simulations with
transient pressure fluctuations. The revised equation is as follows:
_
f-iindoor -rr , ( 77 _i_ 77 A (~< \ (f _ f \\
^ig,m-\ ' y b T^s ~^y b ' -"-ex '^i.ambj'y-m lm-\)\
Where m is the time step index and all other variables are as defined for Table A-l.
A-4
-------
10m
9.75m
9.75 m
10 m
(b)
Figure A-l. Plan view of the foundation crack distribution (dashed lines) used in the
simulations for perimeter cracks illustrated for the 10m x 10m case.
Note that as the building dimensions increase the length of the perimeter cracks also increase and
they retain the same distance of 0.25 m from the exterior walls.
A-5
-------
[This page intentionally left blank.]
A-6
-------
Appendix B. Tabulated Simulation Results
B-l
-------
Table B-l. Matrix Summarizing Simulations Run with Source at 5 ft (1.6 m)
Full Domain Scale (International Units)
Geology: Homogeneous Sand
Source Vapor
Concentration
|jg/m3
Foundation
Dimensions
(mx m)
Initial Oxygen
Concentration
(%)
Simulated
Transport Time
with
Biodegradation
Years
Oxygen
Shadow?
Minimum Oxygen
Concentration Directly
Beneath the Slab
C/Catm (%)
Minimum Oxygen
Concentration 1 m (3 ft)
Beneath the Slab
C/Catm (%)
Slab-on-grade Building Square Shape (meters x meters)
10,000
10,000
10,000
10,000
10,000
10,000
10,000
10,000
10,000
10,000
10,000
10,000
10,000
10x10
10x10
10x10
10x10
90x90
90x90
90x90
90x90
90x90
90x90
120x120
120x120
120x120
21
21
21
21
21
10.5
21
10.5
21
10.5
21
10.5
21
0.5
1
9
50
1
1
9
9
50
50
9
9
50
no
no
no
no
no
no
no
no
no
no
no
no
no
0.99
0.99
0.99
0.99
0.99
0.50
0.97
0.48
0.87
0.48
0.98
0.49
0.9
20.8
20.8
20.8
20.8
20.8
10.4
20.4
10.1
18.3
10.1
20.6
10.2
18.9
0.99
0.99
0.99
0.99
0.99
0.50
0.97
0.48
0.87
0.48
0.98
0.49
0.9
20.8
20.8
20.8
20.8
20.8
10.4
20.4
10.1
18.3
10.1
20.6
10.2
18.9
B-2
-------
Table B-l. Matrix Summarizing Simulations Run with Source at 5 ft (1.6 m)
Full Domain Scale (International Units)
Geology: Homogeneous Sand
Source Vapor
Concentration
|jg/m3
10,000
10,000
10,000
10,000
10,000
10,000
10,000
Foundation
Dimensions
(mx m)
120x120
240 x 240
632 x 632
632 x 632
632 x 632
632 x 632
632 x 632
Initial Oxygen
Concentration
(%)
10.5
21
21
21
21
10.5
10.5
Simulated
Transport Time
with
Biodegradation
Years
50
0.8
9
20
50
20
50
Oxygen
Shadow?
no
no
no
no
no
no
no
Minimum Oxygen
Concentration Directly
Beneath the Slab
C/Catm (%)
0.44
0.99
0.99
0.99
0.96
0.49
0.46
9.2
20.8
20.8
20.7
20.2
10.2
9.7
Minimum Oxygen
Concentration 1 m (3 ft)
Beneath the Slab
C/Catm (%)
0.44
0.99
0.99
0.99
0.96
0.49
0.46
9.2
20.8
20.8
20.7
20.2
10.2
9.7
100,000
100,000
100,000
100,000
100,000
100,000
100,000
100,000
100,000
10x10
10x10
10x10
90x90
90x90
90x90
90x90
90x90
90x90
21
21
21
21
10.5
21
10.5
21
10.5
1
9
50
1
1
9
9
50
50
no
no
no
no
no
no
no
no
no
0.99
0.98
0.98
0.99
0.48
0.91
0.42
0.57
0.17
20.8
20.6
20.6
20.7
10.1
19.2
8.7
11.9
3.5
0.99
0.98
0.98
0.99
0.48
0.91
0.42
0.57
0.17
20.8
20.6
20.6
20.7
10.1
19.2
8.7
11.9
3.5
B-3
-------
Table B-l. Matrix Summarizing Simulations Run with Source at 5 ft (1.6 m)
Full Domain Scale (International Units)
Geology: Homogeneous Sand
Source Vapor
Concentration
|jg/m3
100,000
100,000
100,000
100,000
100,000
100,000
100,000
100,000
100,000
Foundation
Dimensions
(mx m)
120x120
120x120
120x120
120x120
632 x 632
632 x 632
632 x 632
632 x 632
632 x 632
Initial Oxygen
Concentration
(%)
21
10.5
21
10.5
21
21
10.5
21
10.5
Simulated
Transport Time
with
Biodegradation
Years
9
9
50
50
9
20
20
50
50
Oxygen
Shadow?
no
no
no
no
no
no
no
no
no
Minimum Oxygen
Concentration Directly
Beneath the Slab
C/Catm (%)
0.92
0.42
0.58
0.11
0.93
0.85
0.35
0.63
0.12
19.3
8.7
12.1
2.3
19.6
17.9
7.2
13.2
2.5
Minimum Oxygen
Concentration 1 m (3 ft)
Beneath the Slab
C/Catm (%)
0.92
0.42
0.58
0.11
0.93
0.85
0.35
0.63
0.12
19.3
8.7
12.1
2.3
19.6
17.9
7.2
13.2
2.5
1,000,000
1,000,000
1,000,000
1,000,000
1,000,000
1,000,000
1,000,000
10x10
10x10
10x10
30x30
40x40
40x40
40x40
21
21
21
21
21
10.5
21
1
9
50
9
9
9
20
no
no
no
no
no
yes
yes
0.93
0.85
0.85
0.59
0.59
0.05
0.05
19.5
17.8
17.8
12.3
12.4
1.0
1.0
0.92
0.85
0.85
0.58
0.59
0.05
0.05
19.3
17.7
17.7
12.2
12.3
1.0
1.0
B-4
-------
Table B-l. Matrix Summarizing Simulations Run with Source at 5 ft (1.6 m)
Full Domain Scale (International Units)
Geology: Homogeneous Sand
Source Vapor
Concentration
|jg/m3
1,000,000
1,000,000
1,000,000
1,000,000
1,000,000
1,000,000
1,000,000
1,000,000
1,000,000
1,000,000
1,000,000
1,000,000
1,000,000
1,000,000
1,000,000
1,000,000
1,000,000
Foundation
Dimensions
(mx m)
60x60
90x90
90x90
90x90
90x90
90x90
90x90
120x120
120x120
120x120
120x120
632 x 632
632 x 632
632 x 632
632 x 632
632 x 632
632 x 632
Initial Oxygen
Concentration
(%)
21
21
10.5
21
10.5
21
10.5
21
10.5
21
10.5
21
21
10.5
21
10.5
21
Simulated
Transport Time
with
Biodegradation
Years
9
1
1
9
9
50
50
9
9
50
50
1
3.0
3.0
6.0
6.0
9
Oxygen
Shadow?
yes
no
no
yes
yes
yes
yes
yes
yes
yes
yes
no
no
yes
no
yes
yes
Minimum Oxygen
Concentration Directly
Beneath the Slab
C/Catm (%)
0.05
0.93
0.16
0.05
0.04
0.04
0.04
0.05
0.04
0.04
0.04
0.93
0.78
0.05
0.56
0.05
0.05
1.0
19.5
3.4
0.9
0.9
0.9
0.9
1.0
0.8
0.8
0.8
19.5
16.4
1.0
11.8
1.0
1.0
Minimum Oxygen
Concentration 1 m (3 ft)
Beneath the Slab
C/Catm (%)
0.05
0.93
0.15
0.05
0.04
0.04
0.04
0.05
0.04
0.04
0.04
0.92
0.78
0.05
0.56
0.05
0.05
1.0
19.5
3.2
0.9
0.9
0.9
0.9
1.0
0.8
0.8
0.8
19.4
16.3
1.0
11.7
1.0
1.0
B-5
-------
Table B-l. Matrix Summarizing Simulations Run with Source at 5 ft (1.6 m)
Full Domain Scale (International Units)
Geology: Homogeneous Sand
Source Vapor
Concentration
|jg/m3
Foundation
Dimensions
(mx m)
Initial Oxygen
Concentration
(%)
Simulated
Transport Time
with
Biodegradation
Years
Oxygen
Shadow?
Minimum Oxygen
Concentration Directly
Beneath the Slab
C/Catm (%)
Minimum Oxygen
Concentration 1 m (3 ft)
Beneath the Slab
C/Catm (%)
2,000,000
10x10
21
0.5
no
0.86 18.1
0.85 17.9
5,000,000
5,000,000
5,000,000
5,000,000
10x10
120x120
240 x 240
632 x 632
21
21
21
21
0.5
0.8
0.8
0.8
no
yes
yes
yes
0.32 6.7
0.05 1.0
0.05 1.0
0.05 1.0
0.29 6.1
0.05 1.0
0.05 1.0
0.05 1.0
10,000,000
10,000,000
10,000,000
10,000,000
10x10
20x20
30x30
90x90
21
21
21
21
0.5
0.5
0.5
0.8
yes
yes (X)
yes (X)
yes
0.05 1.0
0.05 1.0
See simulation with dimensions 10x10 above
0.05 1.0
0.05 1.0
Slab-on-grade Building Rectangular Shape (meters x meters)
10,000
10,000
10,000
10x90
30x90
60x90
-
-
-
-
-
-
no(X)
no(X)
no(X)
See simulations with dimensions 90 x 90 above
B-6
-------
Table B-l. Matrix Summarizing Simulations Run with Source at 5 ft (1.6 m)
Full Domain Scale (International Units)
Geology: Homogeneous Sand
Source Vapor
Concentration
|jg/m3
1,000,000
1,000,000
1,000,000
Foundation
Dimensions
(mx m)
10x632
10x632
10x632
Initial Oxygen
Concentration
(%)
21
21
21
Simulated
Transport Time
with
Biodegradation
Years
6
9
20
Oxygen
Shadow?
no
no
no
Minimum Oxygen
Concentration Directly
Beneath the Slab
C/Catm (%)
0.78
0.76
0.75
10,000,000
10,000,000
10,000,000
10,000,000
10x90
20x90
30x90
60x90
21
21
21
21
0.8
0.8
0.8
0.8
yes
yes (X)
yes (X)
yes (X)
0.05
16.3
15.9
15.6
Minimum Oxygen
Concentration 1 m (3 ft)
Beneath the Slab
C/Catm (%)
0.77
0.75
0.74
1.0
0.05
16.2
15.8
15.5
1.0
See simulation with dimensions 1 0 x 90 above
See simulation with dimensions 1 0 x 90 above
(X) means the simulation was not run separately, but the qualitative result was obvious by inspection based on results of other simulations.
B-7
-------
Table B-2. Matrix Summarizing Simulations Run with Source at 15 ft (4.6 m)
Full Domain Scale (International Units)
Geology: Homogeneous Sand
Source Vapor
Concentration
|jg/m3
Foundation
Dimensions
(m x m)
Initial Oxygen
Concentration
(%)
Simulated
Transport Time
with
Biodegradation
Years
Oxygen
Shadow?
Minimurr
Concentrat
Beneath
C/Catm
i Oxygen
ion Directly
the Slab
(%)
Minimurr
Concentrati
Beneath
C/Catm
i Oxygen
on 1 m (3 ft)
the Slab
(%)
Slab-on-grade Building Square Shape (meters x meters)
1,000,000
1,000,000
1,000,000
1,000,000
1,000,000
1,000,000
1,000,000
1,000,000
1,000,000
1,000,000
1,000,000
1,000,000
1,000,000
90x90
90x90
90x90
120x120
120x120
120x120
200 x 200
200 x 200
200 x 200
200 x 200
200 x 200
240 x 240
240 x 240
21
10.5
21
21
21
21
10.5
21
10.5
21
10.5
10.5
21
9
9
20
9
20
50
8
9
9
20
20
8
9
no
yes
no
no
no
yes
no
no
yes
no
yes
no
no
0.59
0.05
0.23
0.70
0.34
0.05
0.23
0.71
0.05
0.36
0.04
0.22
0.71
12.3
1.0
4.9
14.7
7.1
1.0
4.8
14.9
1.0
7.6
0.9
4.6
14.9
0.58
0.05
0.23
0.70
0.34
0.05
0.22
0.71
0.05
0.36
0.04
0.22
0.71
12.3
1.0
4.8
14.7
7.1
1.0
4.6
14.9
1.0
7.6
0.9
4.6
14.9
B-S
-------
Table B-2. Matrix Summarizing Simulations Run with Source at 15 ft (4.6 m)
Full Domain Scale (International Units)
Geology: Homogeneous Sand
Source Vapor
Concentration
|jg/m3
1,000,000
1,000,000
1,000,000
1,000,000
1,000,000
1,000,000
1,000,000
Foundation
Dimensions
(m x m)
240 x 240
240 x 240
632 x 632
632 x 632
632 x 632
632 x 632
632 x 632
Initial Oxygen
Concentration
(%)
10.5
21
21
10.5
21
10.5
21
Simulated
Transport Time
with
Biodegradation
Years
9
20
6
8
9
9
20
Oxygen
Shadow?
yes
no
no
no
no
yes
no
Minimurr
Concentrat
Beneath
C/Catm
0.05
0.36
0.81
0.20
0.71
0.05
0.36
i Oxygen
ion Directly
the Slab
(%)
1.0
7.6
17.0
4.2
14.9
1.0
7.6
Minimurr
Concentrati
Beneath
C/Catm
0.05
0.35
0.81
0.20
0.71
0.05
0.36
i Oxygen
on 1 m (3 ft)
the Slab
(%)
1.0
7.4
17.0
4.2
14.9
1.0
7.6
5,000,000
90x90
21
9
yes
0.05
0.9
0.05
0.9
10,000,000
10,000,000
10,000,000
10,000,000
10,000,000
10,000,000
10x10
10x10
10x10
10x10
10x10
20x20
21
21
21
21
10.5
21
0.5
1
9
50
50
1
no
no
no
no
no
no
0.29
0.29
0.29
0.29
0.29
0.06
6.1
6.1
6.1
6.1
6.1
1.3
0.28
0.28
0.28
0.28
0.28
0.06
5.9
5.9
5.9
5.9
5.9
1.3
B-9
-------
Table B-2. Matrix Summarizing Simulations Run with Source at 15 ft (4.6 m)
Full Domain Scale (International Units)
Geology: Homogeneous Sand
Source Vapor
Concentration
|jg/m3
10,000,000
10,000,000
10,000,000
10,000,000
10,000,000
10,000,000
10,000,000
10,000,000
Foundation
Dimensions
(m x m)
20x20
20x20
30x30
90x90
90x90
632 x 632
632 x 632
632 x 632
Initial Oxygen
Concentration
(%)
21
21
21
21
21
21
21
21
Simulated
Transport Time
with
Biodegradation
Years
9
20
0.8
0.8
9
0.05
0.08
1
Oxygen
Shadow?
no
no
yes
yes
yes
no
no
yes
Minimurr
Concentrat
Beneath
C/Catm
0.06
0.06
0.05
0.05
0.04
0.42
0.14
0.05
i Oxygen
ion Directly
the Slab
(%)
1.3
1.3
1.0
1.0
0.9
8.8
2.9
1.0
Minimurr
Concentrati
Beneath
C/Catm
0.06
0.06
0.05
0.05
0.04
0.42
0.13
0.05
i Oxygen
on 1 m (3 ft)
the Slab
(%)
1.3
1.3
1.0
1.0
0.9
8.8
2.7
1.0
Slab-on-grade Building Rectangular Shape (meters x meters)
10,000,000
10,000,000
10,000,000
10,000,000
10,000,000
10,000,000
10x90
10x90
10x90
10x90
20x90
30x90
21
21
10.5
21
21
21
0.8
9
20
50
0.8
0.8
no
no
no
no
yes
yes
0.20
0.19
0.19
0.19
0.05
0.05
4.1
4.0
4.0
4.0
1.0
1.0
0.19
0.19
0.19
0.19
0.05
0.05
3.9
4.0
4.0
4.0
1.0
1.0
B-10
-------
Table B-2. Matrix Summarizing Simulations Run with Source at 15 ft (4.6 m)
Full Domain Scale (International Units)
Geology: Homogeneous Sand
Source Vapor
Concentration
|jg/m3
10,000,000
10,000,000
10,000,000
10,000,000
10,000,000
Foundation
Dimensions
(m x m)
60x90
10x632
10x632
10x632
10x632
Initial Oxygen
Concentration
(%)
21
21
21
21
21
Simulated
Transport Time
with
Biodegradation
Years
0.8
1
6
9
20
Oxygen
Shadow?
yes
no
no
no
no
Minimurr
Concentrat
Beneath
C/Catm
0.05
0.20
0.20
0.20
0.20
i Oxygen
ion Directly
the Slab
(%)
1.0
4.1
4.1
4.1
4.1
Minimurr
Concentrati
Beneath
C/Catm
0.05
0.20
0.20
0.20
0.20
i Oxygen
on 1 m (3 ft)
the Slab
(%)
1.0
4.1
4.1
4.1
4.1
B-ll
-------
Table B-3. Matrix Summarizing Simulations Run with Source at 30 ft (9 m)
Full Domain Scale (International Units)
Geology: Homogeneous Sand
Source Vapor
Concentration
|jg/m3
Foundation
Dimensions
(mx m)
Initial Oxygen
Concentration
(%)
Simulated
Transport Time
with
Biodegradation
Years
Oxygen
Shadow?
Minimurr
Concentrat
Beneath
C/Catm
i Oxygen
ion Directly
the Slab
(%)
Minimurr
Concentrati
Beneath
C/Catm
I
i Oxygen
on 1 m (3 ft)
the Slab
(%)
Slab-on-grade Building Square Shape (meters x meters)
10,000,000
10,000,000
10,000,000
10,000,000
10,000,000
10,000,000
10,000,000
10,000,000
10,000,000
30x30
30x30
30x30
30x30
40x40
40x40
40x40
60x60
60x60
21
21
21
21
21
21
21
21
21
1
6
9
20
1
9
20
1
9
no
no
no
no
no
no
no
no
no
0.14
0.14
0.14
0.14
0.062
0.062
0.062
0.06
0.06
2.9
2.9
2.9
2.9
1.3
1.3
1.3
1.3
1.3
0.14
0.14
0.14
0.14
0.06
0.06
0.06
0.06
0.06
2.9
2.9
2.9
2.9
1.3
1.3
1.3
1.3
1.3
Slab-on-grade Building Rectangular Shape (meters x meters)
10,000,000
10,000,000
10x632
10x632
21
21
1
6
no
no
0.47
0.47
9.9
9.9
0.46
0.46
9.7
9.7
B-12
-------
Table B-4. Matrix Summarizing Simulations Run with a Silty Clay Layer on Ground Surface
Full Domain Scale (International Units)
Geology: silty clay on top (1 m thick) and Sand Below
Source Vapor
Concentration
|jg/m3
Source
Depth
(m)
Foundation
Dimensions
(m x m)
Initial Oxygen
Concentration
(%)
Simulated Transport
Time with
Biodegradation
Years
Oxygen
shadow?
Minimum (
Concent
Directly B
the SI
C/Catm
Dxygen
ration
eneath
ab
(%)
Minimum O;
Concentratic
(3 ft) Beneal
Slab
C/Catm
cygen
>n 1 m
hthe
(%)
Slab-on-grade Building Square Shape (meters x meters)
100,000
100,000
1.6
1.6
632 x 632
632 x 632
21
21
9
20
no
yes
0.47
0.049
9.9
1.0
0.47
0.05
9.9
1.0
1,000,000
1,000,000
1,000,000
1,000,000
1,000,000
1,000,000
1,000,000
1,000,000
1,000,000
1,000,000
1.6
1.6
1.6
1.6
4.6
4.6
4.6
4.6
4.6
4.6
30x30
30x30
40x40
40x40
120x120
120x120
200 x 200
200 x 200
240 x 240
240 x 240
21
21
21
21
21
21
21
21
21
21
1
9
1
9
4
9
4
9
4
9
no
yes
no
yes
no
yes
no
yes
no
yes
0.44
0.05
0.32
0.05
0.24
0.05
0.24
0.05
0.24
0.05
9.2
1.0
6.7
1.0
5.0
1.0
5.0
1.0
5.0
1.0
0.44
0.05
0.32
0.05
0.24
0.05
0.24
0.05
0.24
0.05
9.2
1.0
6.7
1.0
5.0
1.0
5.0
1.0
5.0
1.0
B-13
-------
Table B-4. Matrix Summarizing Simulations Run with a Silty Clay Layer on Ground Surface
Full Domain Scale (International Units)
Geology: silty clay on top (1 m thick) and Sand Below
Source Vapor
Concentration
|jg/m3
10,000,000
10,000,000
10,000,000
10,000,000
Source
Depth
(m)
4.6
9
9
9
Foundation
Dimensions
(m x m)
632 x 632
30x30
30x30
40x40
Initial Oxygen
Concentration
(%)
21
21
21
21
Simulated Transport
Time with
Biodegradation
Years
4
6
9
6
Oxygen
shadow?
no
no
no
yes
Minimum (
Concent
Directly B
the SI
C/Catm
0.24
0.09
0.09
0.05
Dxygen
ration
eneath
ab
(%)
5.0
1.9
1.9
1.0
Minimum O;
Concentratic
(3 ft) Beneal
Slab
C/Catm
0.24
0.09
0.09
0.05
cygen
>n 1 m
hthe
(%)
5.0
1.9
1.9
1.0
Slab-on-grade Building Rectangular Shape (meters x meters)
1,000,000
1,000,000
1,000,000
1.6
1.6
1.6
10x632
10x632
10x632
21
21
21
1
9
20
no
no
no
0.66
0.53
0.52
13.9
11.1
10.9
0.65
0.52
0.52
13.7
10.9
10.9
10,000,000
10,000,000
10,000,000
10,000,000
10,000,000
10,000,000
10,000,000
4.6
4.6
4.6
4.6
4.6
4.6
4.6
10x60
10x60
10x60
10x90
10x90
10x632
10x632
21
21
21
21
21
21
21
1
9
20
1
9
1
6
no
no
no
no
no
no
no
0.10
0.10
0.10
0.10
0.10
0.10
0.10
2.1
2.1
2.1
2.1
2.1
2.1
2.1
0.10
0.10
0.10
0.10
0.10
0.10
0.10
2.0
2.0
2.0
2.0
2.0
2.0
2.0
B-14
-------
Table B-4. Matrix Summarizing Simulations Run with a Silty Clay Layer on Ground Surface
Full Domain Scale (International Units)
Geology: silty clay on top (1 m thick) and Sand Below
Source Vapor
Concentration
|jg/m3
10,000,000
Source
Depth
(m)
4.6
Foundation
Dimensions
(m x m)
10x632
Initial Oxygen
Concentration
(%)
21
Simulated Transport
Time with
Biodegradation
Years
9
Oxygen
shadow?
no
Minimum (
Concent
Directly B
the SI
C/Catm
0.10
Dxygen
ration
eneath
ab
(%)
2.1
Minimum O;
Concentratic
(3 ft) Beneal
Slab
C/Catm
0.10
cygen
>n 1 m
hthe
(%)
2.0
10,000,000
10,000,000
9
9
10x632
10x632
21
21
1
9
no
no
0.33
0.33
6.9
6.9
0.33
0.33
6.9
6.9
B-15
-------
Table B-5. Matrix Summarizing Simulations Run with Source at 5 ft (1.6 m) Below a Basement
Full Domain Scale (International Units)
Geology: Homogeneous Sand
Building With Full Basement Square Shape (meters x meters)
Basement Depth of 2 m bgs
Source Vapor
Concentration
|jg/m3
10,000
Foundation
Dimensions
(mx m)
632 x 632
Initial Oxygen
Concentration
(%)
21
Simulated
Transport Time
with
Biodegradation
Years
9
Oxygen
shadow?
no
Minimurr
Concentrat
Beneath
C/Catm
0.99
i Oxygen
ion Directly
the Slab
(%)
20.8
Minimurr
Concentrati
Beneath
C/Catm
0.99
i Oxygen
on 1 m (3 ft)
the Slab
(%)
20.8
100,000
632 x 632
21
9
no
0.88
18.4
0.88
18.4
1,000,000
1,000,000
1,000,000
632 x 632
632 x 632
632 x 632
21
21
21
1.0
3.0
9
no
no
yes
0.87
0.60
0.05
18.2
12.5
1.0
0.86
0.59
0.05
18.0
12.4
1.0
B-16
------- |