GROUNDWATER - Water Quality Engineering in Natural Systems - page 198

5.23. If the decay factor in Problem 5.22 could be
increased by adding nutrients to the groundwater,
determine the required decay rate for the calcu-
lated maximum concentration to be reduced by
90%.

(a) If the mean seepage velocity is 1 m/d, the
porosity is 0.2, and the bulk density of the
aquifer matrix is 1.8 g/cm 3 , estimate the dis-
persion coefficient that should be used to
model contaminant dispersion in the aquifer.
neglect pore-scale molecular diffusion.
(b) A degreasing shop spills 50 kg of trichloro-
ethylene (C 2 HCL 3 ) over the top 2 m of the
aquifer. If the aquifer matrix contains 2%
organic carbon, and the first-order decay coef-
ficient is 0.02 d −1 , estimate the maximum con-
centration of TCE in the aquifer after 100
days. Assuming that the spill occurs over 10
minutes, use the solubility of TCE to deter-
mine whether TCE will exist as a nAPL in the
vicinity of the spill.

5.24. Five kilograms of TCE is spilled over a 0.8-m
depth of groundwater that moves with an average
seepage velocity of 0.2 m/day. The porosity of the
aquifer is 0.2, vertical dispersion is negligible, and
the longitudinal and transverse dispersion coeffi-
cients are 0.1 and 0.01 m 2 /d, respectively. If the
retardation factor is equal to 15 and the first-order
decay factor is 1 d −1 , calculate the concentration at
the spill location after 1 day and 1 week.

5.25. Industrial wastewater is to be pumped into an
aquifer at a rate of 35 m 3 /d, and the wastewater is
to be discharged uniformly over the 12-m satu-
rated thickness of the aquifer. Field measurements
indicate that the seepage velocity in the aquifer is
1 m/d, the porosity is 0.2, and the bulk density is
1600 kg/m 3 . Existing technical literature indicates
that the contaminant could have a half-life of 200
days and a distribution coefficient of 0.1 cm 3 /g.
Regulatory requirements are that the area sur-
rounding the injection well have restricted access
to allow for the groundwater concentration to at
least decrease to 10% of the injection concentra-
tion. How far downstream of the well should have
restricted access by assuming: (1) the contaminant
is conservative; (2) the contaminant decays; (3)
the contaminant sorbs; and (4) the contaminant
sorbs and decays? Given all these results, which
distance would you select for your restricted
access area?

5.27. What residual mass fraction can be expected when
spills of fuel oil in fine sands are cleaned up by
pumping free product from the groundwater?
How does this residual mass fraction compare
with fuel oil spills in coarse sands? Assume that
the porosity is 0.20 for coarse sand, 0.30 for fine
sand, and the density of sand grains is 2650 kg/m 3 .

5.28. A 2 × 2 × 3 m (deep) portion of an aquifer con-
tains chlorobenzene at a residual saturation of
15%. If the porosity of the contaminated portion
of the aquifer is 0.17, the density of chlorobenzene
is 1110 kg/m 3 , the solubility of chlorobenzene in
water is 500 mg/L, and the mean seepage velocity
of the ambient groundwater is 0.05 m/d, estimate
the time it would take for the chlorobenzene to be
removed by dissolution.

5.29. A portion of a 500 × 500 m industrial site has been
contaminated by spillage of a 50:50 mixture (by
volume) of ethylbenzene and benzene. The con-
taminated area is at the center of the site, has
dimensions 20 × 20 m, and the contamination
extends to a depth of 2 m into the saturated zone.
The thickness of the saturated zone is 25 m, the
estimated hydraulic conductivity of the aquifer is
15 m/d, the effective porosity is 0.19, and the
hydraulic gradient is estimated as 0.5%.

5.26. Six pumping tests have been conducted in an iso-
tropic aquifer, and the hydraulic conductivities
calculated from these tests are 512, 253, 487, 619,
320, and 402 m/d. It is estimated that each of these
hydraulic conductivities is characteristic of a cyl-
inder of radius 100 m, and the correlation length
scale of the hydraulic conductivities is on the
order of 50 m. The temperature of the groundwa-
ter is 25°C, and the characteristic pore size, d , of
the aquifer can be related to the effective hydrau-
lic conductivity, K eff , of the aquifer by the Hazen
formula

(a) If the contaminated area within the saturated
zone contains ethylbenzene and benzene
at a 25% residual saturation, estimate the
steady-state concentrations of ethlybenzene
and benzene on the site boundary.
(b) Is decay a significant factor in calculating the
concentrations on the boundary?
(c) Estimate the time required to remove benzene
from the nAPL residual by dissolution.

γ
µ

K

eff =

1 02 10 3 . ×

−

d

2

where γ is the specific weight of the groundwater,
and µ is the dynamic viscosity.