analytical model to determine the influence of building area size on subslab oxygen shadow by prof....
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Analytical model to determine the influence of building area size on subslab oxygen shadow
Yijun Yao
May 15, 2015 @ ZJU
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Conceptual scenario of vapor intrusion
Factors
• Soil
• Groundwater
• Building
• Atmosphere
Processes
• Advection
• Diffusion
• Degradation
• Absorption
Attenuation
• Source-subslab
• Subslab-Indoor
http://www.epa.gov/oswer/vaporintrusion/basic.html
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Contaminant types
• US EPA, Office of Solid Waste and Emergency Response (OSWER)
Chlorinated chemicals, such as PCE and TCE (Mostly chemical solvents and dry cleaning detergent, usually difficult for biodegradation)
• US EPA, Office of underground storage tank
Petroleum products
(From the leakage of gas tanks, and aerobically biodegradable)
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Models for risk assessment--numerical
Abreu and Johnson, Environ. Sci. Technol. 2006
• Study complicated scenarios;
• Requiring relevant software and technical skills;
• Research purposes
Basement Basement
Basement Basement
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Models for risk assessment--analytical• Mass transfer equations;
• Simple for screening purposes;
• Convenient to use and widely distributed
Spreadsheet of the Johnson-Ettinger model
http://www.epa.gov/oswer/riskassessment/airmodel/johnson_ettinger.htm
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Aerobic biodegradation of petroleum products in soil
US EPA, 2013, Evaluation Of Empirical Data To Support Soil Vapor Intrusion Screening Criteria For Petroleum Hydrocarbon Compounds, http://www.epa.gov/OUST/cat/pvi/PVI_Database_Report.pdf
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Conceptual scenario of petroleum vapor intrusion
Hydrocarbon vapor source
O2 diffusion from
open ground
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Building footprint size
Koomey, 1990, Energy Efficiency in New Office Buildings: An Investigation of Market Failures and Corrective Policies
Large building (Boeing Facility, Everett, WA)
http://www.boeing.com/commercial/tours/images/K64532-14_lg.jpg
US commercial building
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EPA technical document in 2013
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3D simulation results in EPA document
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Conclusions given by EPA document
Those are absolutely right,
but they are common senses!
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We need a simple and clear way to identify the
oxygen condition in the subslab zone!
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2D coupled contaminant-oxygen transport/reaction model
Hydrocarbon vapor source
Anaerobic zone
(Vapors diffusing from the source)
Aerobic to anaerobic interface
Aerobic zone
(O2 diffusion from open ground)
Open Ground surface
Impervious slab 0 = 𝐷ℎ∇
2𝑐ℎ − 𝑅
𝐷𝑜∇2co − 𝛽𝑅
⇒ 0 = ∇2 𝑐ℎ −𝐷𝑜
𝐷ℎ𝛽𝑐𝑜
Harmonic/Laplace equation
𝑅 = 𝑘𝑐ℎ, 𝑐𝑜 > 1%0, 𝑐𝑜 ≤ 1%
Coupled 2-D contaminant-oxygen
diffusion/reaction
𝑤 = 𝑐ℎ −𝐷𝑜
𝐷ℎ𝛽𝑐𝑜
Define a new variable
1% is the reaction threshold of oxygen
and 0 = ∇2w
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2D coupled contaminant-oxygen transport/reaction model
z
x
z = L
z = 0
x = Lslab/2
B.C.: ∂w/∂z = 0
x = 0
Open Ground surface
Impervious slab
constant vapor source
x ∞
B.C.: ∂w/∂x = 0
constant O2 source
Aerobic to anaerobic interface
B.C.: w (x, za) = wa
(c) Combined variable (w)
B.C.: w (x, L) = 1
B.C.: w (x, 0) = 0
z
x
z = L
z = 0
x = Lslab/2
B.C.: ∂Cv/∂z = 0
x = 0
Open Ground surface
Impervious slab
constant vapor source
x ∞
B.C.: ∂Cv/∂x = 0
constant O2 source
B.C.: Cv (x, 0) = Csource
Aerobic to anaerobic interface
B.C.: Cv (x, za) = 0
(a) Hydrocarbon vapors
z
x
z = L
z = 0
x = Lslab/2
B.C.: ∂CO/∂z = 0
x = 0
Open Ground surface
Impervious slab
constant vapor source
x ∞
B.C.: ∂CO/∂x = 0
constant O2 source
Aerobic to anaerobic interface
B.C.: CO (x, za) = 0
(b) Oxygen
B.C.: CO (x, L) = O2amb
Conformal transform: Schwarz–Christoffel mapping
Carslaw and Jaeger, 1959, conduction of heat in solids
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Comparison with 3-D simulations for cases with different building footprint sizes
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The role of building size on subslab oxygen shadow
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
0.01 0.1 1 10 100 1000
No
rma
lize
d a
ero
bic
de
pth
(L
a/L
)
Csource (g/m3)
Slab-on-grade(df =0)
Lslab/L = 12345678910
fully aerobic
oxygen shadow
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
0.01 0.1 1 10 100 1000
No
rma
lize
d a
ero
bic
de
pth
(L
a/L
)
Csource (g/m3)
Lslab/L = 12345678910
Basement(df = 0.25 ds)
fully aerobic
oxygen shadow
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The critical building footprint size
,
2 2ln
1 cos
slab c
a
LL
w
0.01
0.1
1
10
100
1000
0 1 2 3 4 5 6 7
Va
po
r s
ou
rce
co
nc
en
tra
tio
nC
so
urc
e(g
/m3)
Slab half width as a ratio to depth to the source (0.5Lslab,c/L)
Knight and Davis (2013)
This work (slab-on-grade)
This work (basement)
2
h sourcea amb
h source O
D Cw
OD C D
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Limitations
This model does not work in the presence of
• significant advection
• transient transport
• soil heterogeneities
• preferential pathways
• non-uniform sources
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谢谢!Thanks!