Page 112 - Materials Chemistry, Second Edition

Plume Migration in Aquifer and Soil 95

dispersion dominates). The dispersion coefficient can be written as the sum
of two terms: effective molecular diffusion coefficient, D , and hydraulic dis-
d
persion coefficient, D :
h
D = D + D h (3.23)
d
The effective molecular diffusion coefficient can be obtained from molecu-
lar diffusion coefficient, D , as
0
D = (ξ)(D ) (3.24)
0
d
where ξ is the tortuosity factor that accounts for the increased distance that
COCs need to travel to get around the soil grains. Typical ξ values are in the
range of 0.6 to 0.7 [7].
The hydraulic dispersion coefficient is proportional to the groundwater
flow velocity as

D = (α)(v) (3.25)
h
where α is the dispersivity. The hydraulic dispersion coefficient is scale
dependent; its value has been observed to increase with increasing trans-
port distance. The longitudinal dispersivity values from field tracer tests
and model calibration of COC plumes are found to be in the range of 10
to 100 m, which is much higher than that from column studies in the
laboratories.
The molecular diffusion coefficients of COCs in dilute aqueous solutions
are very much smaller than in gases at atmospheric pressure, usually rang-
ing from 0.5 to 2 × 10 cm /s at 25°C (compared with typical values of 0.05 to
2
−5
0.5 cm /s in the gaseous phase, as shown in Table 2.5). Values of molecular
2
diffusion coefficients of selected compounds are shown in Table 3.6.

TABLE 3.6
Values of Diffusion Coefficients of Selected
Compounds in Water
Compound Temperature Diffusion Coefficient
(°C) (cm /s)
2
Acetone 25 1.28 × 10 −5
Acetonitrile 15 1.26 × 10 −5
Benzene 20 1.02 × 10 −5
Benzoic acid 25 1.00 × 10 −5
Butanol 15 0.77 × 10 −5
Ethylene glycol 25 1.16 × 10 −5
Propanol 15 0.87 × 10 −5
Source: [8].