Environmental Engineering Reference
In-Depth Information
TABLE 3.26
Measured Fate and Transport Parameters of Selected Organic Compounds in Clay from
Soil Plug Diffusion Tests
Calculated
Aqueous Diffusion
Coeffi cient in Pure
Water
a
D
w
(cm
2
/s)
Relative
Concentration
C
/
C
0
after
14 days
Distribution
Coeffi cient
K
d
(mL/g)
Measured Effective
Aqueous Diffusion
Coeffi cient
b
D
e
(cm
2
/s)
Calculated
Retardation
Factor
c
R
f
Compound
Acetone
0.19
11.5 × 10
−6
5.6 × 10
−6
0.9
2.33
1,4-Dioxane
0.17
0.9
2.19
10.6 × 10
−6
4.0 × 10
−6
Aniline
1.3
0.7
10.1
9.8 × 10
−6
7.0 × 10
−6
Chloroform
4.5
0.5
43
10.6 × 10
−6
7.0 × 10
−6
Toluene
11
0.4
183
8.9 × 10
−6
5.8 × 10
−6
Source:
From Barone, F.S., Rowe, R.K., and Quigley, R.M., 1992,
Journal of Contaminant Hydrology
10(3): 225-250. With
permission.
a
Diffusion constants calculated by Barone et al. (1992) by using the Wilke-Chang equation for water at laboratory tempera-
ture, 22°C.
b
Barone et al. (1992) noted that the aqueous diffusion coefi cients i rst obtained for chloroform and toluene were unreason-
ably high owing to the role of nonsettling particles in the soil column.
c
Retardation factors calculated by the author using soil properties from Barone et al. and the familiar retardation equation
(Equation 3.32).
where
is porosity and
P
is an empirical factor selected for the geological medium under consid-
eration (Millington and Quirk, 1961; Parker et al., 1996). Tortuosity, sometimes represented with
the Greek letter
ϕ
, accounts for all factors that limit solute diffusion through the porous medium
such as the tortuous nature of the diffusion path, dead-end pores, and steric hindrance (Young
and Ball, 1998). Higher tortuosity factors indicate shorter l ow paths. Well-sorted sands (i.e.,
those that have essentially uniform grain size) have higher tortuosity factors because smaller
grains are not i lling pore spaces. Tortuosity factors in well-sorted, i ne-grained sands range from
0.6 to 0.8, whereas
χ
τ
in well-sorted, coarse-grained sands averages 0.4; for poorly sorted sands,
τ
ranges from 0.2 to 0.8 (Fetter, 1993; Hoffman et al., 1998). Barone et al. (1992) obtained tortuos-
ity factors for the subject Sarnia clay of 0.65 from the calculated and measured diffusivities of
chloroform and toluene. A theoretical estimate of tortuosity in unconsolidated materials is 0.67
(Bear, 1972).
Another approach to estimating the tortuosity of a soil involves contrasting measured diffu-
sion coefi cients of a compound of interest to the diffusion coefi cient of a nonretarded com-
pound such as 1,4-dioxane to obtain a relative approximation of tortuosity. This approach has
been used to compare carbon tetrachloride, perchloroethylene, and trichloroethylene to chloro-
form, whose retardation is considered negligible (Hoffman et al., 1998). Knowledge of the tor-
tuosity of a medium is useful for estimating the role of diffusion in retaining contaminants in
i ne-grained deposits.
Barone et al. (1992) estimated breakthrough times for vertical transport in clay soil. 1,4-Dioxane
was calculated to advance more than 5 m in 100 years, while toluene advanced less than 1 m in the
same time. The hypothetical calculation estimates that a leachate containing 1,4-dioxane at
300 mg/L discharged to the subject Sarnia clay would diffuse through a 1-m-thick clay landi ll liner
in 5 years and contaminate underlying groundwater to concentrations in excess of 30
μ
g/L (the
Canadian drinking water guidance in effect during the 1989 study).
To address the role of sorption in diffusive transport, scientists at Lawrence Livermore National
Laboratory (LLNL) developed a hybrid contaminant transport term that accounts for both tortuosity
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