CLEEN's MMEA program organised an international seminar on cleaner air - Outdoor and indoor air quality together with Zhejiang University and assistant organizer Insigma group. This is one of the keynote presentations in the seminar. More info in www.mmea.fi The cleantech field is expanding rapidly and Finnish companies are committed to working for a better environment in the fields of energy efficiency, air quality and monitoring. The world-class Cleantech know-how from Finland and the cooperation with Chinese partners and the results were highlighted in the MMEA seminar. Some of the leading Finnish cleantech companies together with Finnish and Chinese research institutions were present at the event. The seminars focused on cooperation between Finland and China concerning indoor and outdoor air quality and solutions to make them better.

1. Analytical model to determine the influence of
building area size on subslab oxygen shadow
Yijun Yao
May 15, 2015 @ ZJU

2. 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

3. 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）

4. 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

5. 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

6. 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

7. Conceptual scenario of petroleum vapor intrusion
Hydrocarbon vapor source
O2 diffusion from
open ground

8. 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

9. EPA technical document in 2013

10. 3D simulation results in EPA document

11. Conclusions given by EPA document
Those are absolutely right,
but they are common senses!

12. We need a simple and clear way to identify the
oxygen condition in the subslab zone!

13. 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 slab0 =
𝐷ℎ∇2 𝑐ℎ − 𝑅
𝐷 𝑜∇2co − 𝛽𝑅
⇒ 0 = ∇2 𝑐ℎ −
𝐷 𝑜
𝐷ℎ 𝛽
𝑐 𝑜
Harmonic/Laplace equation
𝑅 =
𝑘𝑐ℎ, 𝑐 𝑜 > 1%
0, 𝑐 𝑜 ≤ 1%
Coupled 2-D contaminant-oxygen
diffusion/reaction
𝑤 = 𝑐ℎ −
𝐷 𝑜
𝐷ℎ 𝛽
𝑐 𝑜
Define a new variable
1% is the reaction threshold of oxygen
and 0 = ∇2
w

14. 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
x
z = 0
x = Lslab/2x = 0
constant vapor source
x  ∞
Conformal transform: Schwarz–Christoffel mapping
Carslaw and Jaeger, 1959, conduction of heat in solids

15. Comparison with 3-D simulations for cases
with different building footprint sizes

16. 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
Normalizedaerobicdepth(La/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
Normalizedaerobicdepth(La/L)
Csource (g/m3)
Lslab/L = 12345678910
Basement
(df = 0.25 ds)
fully aerobic
oxygen shadow

17. The critical building footprint size
 ,
2 2
ln
1 cos 
 
     
slab c
a
L
L
w
0.01
0.1
1
10
100
1000
0 1 2 3 4 5 6 7
Vaporsourceconcentration
Csource(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 source
a amb
h source O
D C
w
O
D C D



 

18. Limitations
This model does not work in the presence of
• significant advection
• transient transport
• soil heterogeneities
• preferential pathways
• non-uniform sources

19. 谢谢!
Thanks!