GROUNDWATER - Water Quality Engineering in Natural Systems - page 196

Available irrigation water and effective rainfall
combined has a TDS content of 90 mg/L, soil
evaporation during the spring planting season is
35 cm, and the effective rainfall is 20 cm.

5.7. Repeat Problem 5.6 for the case in which the con-
taminant undergoes biodegradation with a decay
rate of 0.01 d −1 . Assess whether biodegradation
has a significant effect on the downstream
concentration.

(a) Estimate the amount of irrigation water
required and the expected TDS concentration
in the root zone.
(b) Determine the LR, leaching ratio, and
minimum requirement for irrigation plus rain-
fall to avoid excessive TDS in the root zone.

5.8. Pure TCE exists at the residual saturation level in
a portion of an aquifer that is 10 m long, 5 m wide,
and 2 m deep. This volume is called the source
zone of TCE in the aquifer. As groundwater flows
through the source zone, TCE is dissolved in the
groundwater, and the groundwater exits the source
zone with TCE at the solubility concentration. The
groundwater flow is normal to the width of the
source zone, the first-order decay coefficient of
TCE in groundwater is 0.02 d −1 , the seepage veloc-
ity is 0.3 m/d, the longitudinal dispersivity is 10 m,
the horizontal-transverse dispersivity is 1 m, and
the vertical-transverse dispersivity is 0.1 m. A
small water-supply well is located 200 m down-
stream of the source zone. Determine whether the
water-quality criterion of 5 µ g/L for TCE will be
exceeded at the well intake.

5.2. Five kilograms of a conservative contaminant is
spilled into the groundwater and is well mixed
over the top 1 m. The longitudinal and (horizon-
tal) transverse dispersion coefficients are 0.5 and
0.05 m 2 /d, respectively; vertical mixing is negligi-
ble; the mean seepage velocity is 0.3 m/day; and
the porosity of the aquifer is 0.2. Determine the
concentrations at the spill location for the first 7
days after the spill. How are your calculated con-
centrations affected by the assumed depth of the
spill?

5.3. Determine the maximum contaminant concentra-
tions in Problem 5.2 for the first 7 days after the
spill.

5.9. Hydraulic conductivity measurements (in m/d)
on 50-cm core samples taken from an isotropic
aquifer indicate a variable log-hydraulic conduc-
tivity that can be described by a mean of 3.2, a
variance of 1.6, and a correlation length scale of
1.3 m.

5.4. A contaminant is injected continuously over a
depth of 3 m into an aquifer with a mean seepage
velocity of 0.45 m/day and longitudinal and trans-
verse dispersion coefficients of 1 and 0.1 m 2 /d,
respectively. The injection rate is 0.4 m 3 /d with a
concentration of 130 mg/L. Estimate the steady-
state contaminant concentration 30 m down-
stream of the injection location.

(a) Estimate the effective hydraulic conductivity
and macrodispersivity of the aquifer.
(b) If the mean hydraulic gradient in the aquifer
is 0.005 and the effective porosity is 0.15, esti-
mate the components of the macrodispersion
coefficient.

5.5. For the case described in Problem 5.4, determine
the distance from the injection location to the
point where the contaminant concentration is 1%
of the injection concentration.

5.10. The piezometric heads measured at three loca-
tions in an aquifer are 3.62, 2.20, and 2.10 m. The
coordinates of the measurement locations are
(1 km, 2.5 km), (2.3 km, 1.4 km), and (1.7 km,
1.3 km), respectively. Determine the hydraulic
gradient in the aquifer.

5.6. A contaminant source is 5 m wide × 2 m deep and
continuously releases a conservative contaminant
at a concentration of 70 mg/L. The mean seepage
velocity in the aquifer is 0.1 m/day, the aquifer
is 10 m deep, and the longitudinal, horizontal-
transverse, and vertical dispersivities are 1, 0.1,
and 0.01 m, respectively.

5.11. How would your dispersivity estimates change in
Problem 5.9 if the aquifer were anisotropic with a
horizontal correlation length scale of 1.3 m and an
anisotropy ratio of 0.1?

(a) Determine the downstream location at which
the plume will be fully mixed over the depth
of the aquifer.
(b) Estimate the contaminant concentrations at
the water table 200 m downstream of the
source after 5 years of operation.

5.12. The mean seepage velocity in an aquifer is
1 m/day, the mean pore size is 3 mm, and the
molecular diffusion coefficient of a toxic contami-
nant in the groundwater is 2 × 10 −9 m 2 is Should
molecular diffusion be considered in a pore-scale
contaminant transport model?