Page 118 - Materials Chemistry, Second Edition

Plume Migration in Aquifer and Soil 101

where

R =+ ρ b K p (3.33)
1
φ

The parameter, R, is often called the retardation factor (dimensionless) and
has a value ≥ 1. Equation (3.32) is essentially the same as Equation (3.22),
except that the reaction term in Equation (3.22) is taken care of by R (Equation
3.33). The retardation factor reduces the impact of dispersion and migration
velocity by a factor of R. All of the mathematical solutions that are used to
solve the transport of inert tracers can be used for the transport of the COCs
if the groundwater velocity and the dispersion coefficient are divided by the
retardation factor. From the definition of R, we can tell that R is a function
of ρ , ϕ, and K . For a given aquifer, ρ and ϕ would be the same for differ-
b
b
p
ent COCs. Consequently, the larger the partition coefficient, the larger is the
retardation factor.
Example 3.19: Determination of the Retardation Factor
The aquifer underneath a site is impacted by several organic compounds,
including benzene, 1,2-dichloroethane (DCA), and pyrene. Estimate their
retardation factors using the following data from the site assessment:

• Effective aquifer porosity = 0.40
• Dry bulk density of the aquifer materials = 1.6 g/cm 3
• Fraction of organic carbon of the aquifer materials = 0.015
• K = 0.63 K ow
oc
Solution:
(a) From Table 2.5,
Log(K ) = 2.13 for benzene → K = 135
ow
ow
Log(K ) = 1.53 for 1,2-DCA → K = 34
ow
ow
Log(K ) = 4.88 for pyrene → K = 75,900
ow
ow
(b) Using the given relationship, K = 0.63K , we obtain:
ow
oc
K = (0.63)(135) = 85 (benzene)
oc
K = (0.63)(34) = 22 (1,2-DCA)
oc
K = (0.63)(75,900) = 47,800 (pyrene)
oc
(c) Using Equation (2.26), K = f K , and f = 0.015, we obtain:
oc
oc
oc
p
K = (0.015)(85) = 1.275 (benzene)
p
K = (0.015)(22) = 0.32 (1,2-DCA)
p
K = (0.015)(47,800) = 717 (pyrene)
p