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!