The approach to modeling diffusivity in soils discussed in Chemical
Property Estimation, Chapter 12, differs slightly from that used to develop some
important diffusion models such as that of P.
C. Johnson and R. A. Ettinger (ES&T, 25, 1445-1452, 1991) widely used to predict the
intrusion rate of chemical vapors into buildings. For
instance, the effective diffusivity of a chemical in soil used in the Johnson and Ettinger
model is estimated from soil vapor concentrations of chemical while the apparent
diffusivity, defined in Section 12.2.2, is estimated from the chemicals bulk
concentration in soil. The Johnson and
Ettinger model is discussed here.
Johnson and Ettinger present an analytical solution for combined convective and diffusive transport of vapor-phase contaminants in a soil column. The transport equation is:
where:
ei = volume fraction of phase i, dimensionless (phase i is vapor (g), sorbed (s), condensed, and soil moisture(w))
Ci = chemical concentration in phase i, g/cm3
t = time, s
ui = Darcy velocity vector in phase i, cm/s
Dieff = effective diffusion coefficient in phase i, cm2/s
Ri = formation rate constant in phase i, g/cm3 s
where:
E = one-dimension mass transport rate, g/s
A = cross section area through which chemical is transported. cm2
C = concentration, g/cm3
DTeff = overall effective diffusion coefficient based on vapor concentration, cm2/s
LT = distance from source to receptor, cm.
and
.