Analytical model to determine the influence of building area size on subslab oxygen shadow by Prof....
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Transcript of Analytical model to determine the influence of building area size on subslab oxygen shadow by Prof....
Analytical model to determine the influence of building area size on subslab oxygen shadow
Yijun Yao
May 15, 2015 @ ZJU
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
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)
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
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
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
Conceptual scenario of petroleum vapor intrusion
Hydrocarbon vapor source
O2 diffusion from
open ground
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
EPA technical document in 2013
3D simulation results in EPA document
Conclusions given by EPA document
Those are absolutely right,
but they are common senses!
We need a simple and clear way to identify the
oxygen condition in the subslab zone!
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
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
Comparison with 3-D simulations for cases with different building footprint sizes
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
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
Limitations
This model does not work in the presence of
• significant advection
• transient transport
• soil heterogeneities
• preferential pathways
• non-uniform sources
谢谢!Thanks!