CE 473/573 Groundwater
Fall 2011
Homework 6
Due Friday December 9
*39. (Only part c is required) Heavy rainfall causes a river next to a confined aquifer to
rise 50 cm. The aquifer has a transmissivity of 30 m2 /d and a storativity of 5 × 10−4 ,
and initially the head in the aquifer was uniform. The rise in the river causes the head
in the aquifer to rise by the same amount at the stream.
a. When will the head be 25 cm larger than the initial value 100 m away from the
river?
b. When will the head be 25 cm larger than the initial value 200 m away from the
river?
c. Compute the ratio of times from parts a and b and explain how you can compute
the ratio without solving parts a and b.
*40. During a tracer study in a river, dye is injected steadily at a concentration of 50 ppb.
The researchers estimate that the dispersion coefficient D is about 80 m2 /s. When
will the concentration be 25 ppb at a station 1000 m from the injection site?
*41. A mass of 0.25 kg of dye is injected over a very short period into an aquifer with
hydraulic conductivity 50 m/d, hydraulic gradient 0.001, and porosity 18%.
a. What is the peak concentration 10 m from the injection?
b. When will the peak concentration occur?
42. Leaking gasoline tanks are a source of the BTEX compounds: benzene, toluene, ethylbenzene, and xylene. Rank them in order of increasing solute velocity if all experience
the same average linear velocity of groundwater flow.
*43. Approximate half-lives for the benzene, toluene, ethylbenzene, and xylene are 300, 20,
120, and 190 days, respectively. The EPA maximum contaminant levels for these compounds are 5, 1000, 700, and 10, 000 µg/L, respectively. Suppose the concentrations
of all four in a leaking tank is 30 mg/L and use an average linear velocity of 2 m/d,
a bulk density of 2 g/cm3 , a soil organic fraction of 0.5%, and an effective porosity of
22%.
a. Compute the plume lengths assuming steady flow and no dispersion.
b. Compute the plume lengths assuming steady flow. Include dispersion.
c. Compute the plume lengths after 1, 5, 10, 50, and 100 years.
d. Compare the estimates from parts a, b, and c.
e. Estimate the ratios of the terms in the full transport equation. Explain how these
ratios indicate the important processes in the transport of the four compounds.
44. (Old exam problem) A manufacturing plant has been leaking 1,1-dichloroethane into
a confined aquifer of thickness 13 m since the 1960s. The aquifer has hydraulic conductivity 5 m/d, effective porosity 21%, soil organic carbon content 0.4%, bulk density
2.4 g/cm3 , and hydraulic gradient with a magnitude of 0.01. Studies nearby show the
dispersivity to be about 5 m. The contaminant 1,1-dichloroethane has a solubility of
5500 ppm, a half-life of about 110 days, a value of Koc of 45 mL/g, and a maximum
contaminant level (MCL) of 7 µg/L.
a. If the concentration of 1,1-dichloroethane at the source of the leak is 25 mg/L,
how long is the plume—that is, how far downgradient is the concentration above
the MCL?
b. A well is to be installed so that the contaminated water can be pumped and
treated. However, it cannot be placed downgradient of the source because of a
parking lot. If it is placed 50 m upgradient of the source, what flowrate would
you recommend using?
c. Would the required flowrate from part b increase or decrease if the following
parameters increase? Briefly explain why.
i.
ii.
iii.
iv.
v.
Half-life
Soil-water partition coefficient Koc
Hydraulic gradient
Aquifer thickness
Source concentration
Groundwater flow
Parking lot
Proposed well
Leak source
50 m
Building
45. (Old exam problem) As part of a remediation project, you must determine the extent
of contamination from an underground storage tank that has been leaking benzene
for many years. The aquifer, which is confined has a hydraulic conductivity of 1 m/d,
effective porosity of 23%, soil organic carbon content of 0.3%, bulk density of 2 g/cm3 ,
and hydraulic gradient with a magnitude of 0.008. The half-life of benzene is 300 days,
and the maximum contaminant level (MCL) is 0.005 mg/L. The concentration in the
leaking tank is 18 mg/L.
a. Compute the length of the plume by assuming steady state and ignoring dispersion. Define the end of the plume to be the point at which the concentration
equals the MCL.
b. Estimate the dispersivity.
c. Compute the length of the plume by assuming steady state and including dispersion.
46. Solve problem 2 of the final exam of 2008.
47. Solve problem 3 of the final exam of 2008.
48. Solve problem 4 of the final exam of 2008.
49. Solve problem 5 of the final exam of 2008.
50. Solve problem 2 of the final exam of 2009.
51. Solve problem 3 of the final exam of 2009.
52. Solve problem 4 of the final exam of 2009.
53. Solve problem 5 of the final exam of 2009.
54. Solve problem 2 of the final exam of 2010.
55. Solve problem 3 of the final exam of 2010.
56. Solve problem 4 of the final exam of 2010.
57. Solve problem 5 of the final exam of 2010.