Vapor Intrusion - Dealing with Contaminated Sites: From Theory Towards Practical Application - page 427

D eff ∂

C
∂

J =− (10.7)

z

where:

J is the vapor mass flux [M/L 2 -T]
C is the vapor concentration [M/L 3 ]
z is the distance over which the concentration change is measured [L]
∂

z is the concentration gradient [M/L 4 ],
D eff is the effective diffusion coefficient for the medium, [L 2 /T]

∂

C/

In porous media, the effective diffusion coefficient depends on the porosity and
water-filled porosity of the medium, as formulated by Millington and Quirk ( 1961 ).

/ /

10 3 10 3

D a θ

H θ

D w

a
θ

w
θ

= +

D eff (10.8)

2
T

2
T

where:

D a is the free-air diffusion coefficient [L 2 /T],
D w is the aqueous diffusion coefficient [L 2 /T],
θ a is the soil air filled porosity [volume vapor/total volume],
θ T is the soil total porosity [volume pores/ total volume],
θ w is the soil water-filled porosity [volume water/total volume], and
H is the dimensionless Henry's Law Constant [molar concentration in gas/
molar concentration in water].

10.4.1.3 Vapor Intrusion into Buildings

Calculating the flow rate for soil gas into buildings is challenging, because it
depends on the building pressure or vacuum relative to the pressure in the subsur-
face beneath the building, the permeability of the soil and fill materials beneath the
building, and the permeability of the foundation, all of which vary from building to
building and may also vary over time.
A conservative estimate of the potential for vapor intrusion can be developed
by assigning a value for the volumetric flow rate of soil gas into a building that is
sufficiently high to allow unrestricted entry of vapors diffusing upward to the sub-
floor region from a deeper source. For a typical residence, this is on the order of 1
to 10 L/min (Johnson 2002 ).

10.4.1.4 Attenuation Factors

Due to the complexity of the vapor intrusion pathway, some “models” of the path-
way use an attenuation factor (AF) approach, rather than the formulations described