Page 116 - Materials Chemistry, Second Edition

Plume Migration in Aquifer and Soil 99

the molecular diffusion for the dispersion of the benzene plume in the fol-
lowing two cases:
1. The hydraulic gradient = 0.01
2. The hydraulic gradient = 0.0005

Solution:
(a) The hydraulic conductivity of the aquifer = 500 gpd/ft 2
= (500)(4.73 × 10 ) = 0.024 cm/s (Use the conversion factor in
−5
Table 3.1.)
Use Equations (3.1) and (3.2) to find out the groundwater velocity
(for gradient = 0.01)
(0.024)(0.01)
v s = = 610× − 4 cm/s
0.4
The molecular diffusion coefficient of benzene (at 20°C) = 1.02 ×
10 cm /s (Table 3.6).
-5
2
From Equation (3.23), D = D + D h
d
The effective molecular diffusion coefficient can be obtained as
(Equation 3.24):
D = ξ(D ) = (0.65)(1.02 × 10 ) = 0.66 × 10 cm /s
2
−5
−5
d
0
The hydraulic dispersion coefficient can be determined as
(Equation 3.25):
D = α(v) = (200 cm)(6 × 10 cm/s) = 12,000 × 10 cm /s
2
−4
−5
h
The hydraulic dispersion coefficient is much larger than the dif-
fusion coefficient. Therefore, the hydraulic dispersion will be
the dominant mechanism for the dispersion of COCs.
(b) For a smaller gradient, the groundwater will move more slowly,
and the dispersion coefficient will be proportionally smaller.
The effective molecular diffusion coefficient will be the same as
0.66 × 10 cm /s.
2
−5
Use Equations (3.1) and (3.2) to find the groundwater velocity (for
gradient = 0.0005):
(0.024)(0.0005)
v s = = 3.0 10 cm/s× − 5
0.4
The hydraulic dispersion coefficient can then be determined as
(Equation 3.25):
D = α(v) = (200 cm)(3.0 × 10 cm/s) = 600 × 10 cm /s
2
-5
-5
h
The hydraulic dispersion coefficient is still much larger than the
diffusion coefficient at this relatively flat gradient of 0.0005.