Page 235 - Soil and water contamination, 2nd edition

222 Soil and Water Contamination

Example 11.8 Residual concentration
A spill of one barrel (= 159 l) of a DNAPL spreads slowly in a shallow aquifer with a
porosity of 28 percent. The residual concentration of the DNAPL in the aquifer material
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is 18 percent. Calculate the maximum aquifer volume in m that will be contaminated by
the DNAPL.
Solution
The proportion of the maximum contaminated aquifer volume that will be occupied by
the DNAPL equals 0.18 × 0.28 = 0.0505. Thus, the maximum contaminated aquifer
3
3
volume is 0.159 m /0.0505 = 3.15 m .

EXERCISES
1. In a small river with an average width of 3 m and an average depth of 0.75 m the stream
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flow velocity is 6.5 cm s and the phosphate (PO ) concentration is 0.23 mg l .
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Calculate the inorganic phosphorus (P) load of this river in tonnes y .
2. Explain why numerical environmental models are often preferable to analytical solutions.
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2
3. The discharge of a river with a cross-sectional area of 10 m is 2 m s . At time t = 0
a dye tracer is released into the river. Calculate the time needed for the tracer to reach
a measurement location 500 m downstream from the release point, assuming that the
tracer is subject only to advection.
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4. A river has a discharge of 16 m s and a sodium concentration of 44.5 mg l . A
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tributary discharges into this river at a rate of 3 m s . The sodium concentration in the
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tributary is 16 mg l . Calculate the sodium concentration in the river downstream from
the inflow of the tributary.
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5. A flow reactor with a cross-sectional area of 0.8 m is filled with sandy sediment
with a dispersivity α of 0.01 m. The sediment is fully saturated with water with
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a Cl concentration of 0 mg l . At time t = 0 a continuous inflow of water with a Cl
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concentration of 250 mg l is started with a flow velocity of 1 m d .
a. Calculate the dispersion coefficient.
b. Does this coefficient refer to longitudinal or to transverse dispersion? Give reasons for
your answer.
c. Calculate the Cl concentration at x = 1.0 m after 18 hours, using Equation (11.32).
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The experiment is repeated with a water flow velocity of 0.5 m d .
d. Calculate the Cl concentration at x = 1.0 m after 36 hours.
e. Compare the answers of questions c) and d) and explain the outcomes.
f. Explain why dispersion is linearly related to the groundwater flow velocity (see also
Figure 11.4).
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6. In the same flow reactor as in question 5, in which the flow velocity was set at 0.75 m d ,
a mass of 1 g of an inert tracer is released instantaneously.
a. Sketch the concentration field in the flow reactor as function of distance after 1 day.
b. Calculate the maximum concentration after 1 day.
c. Sketch the concentration evolution as function of time at x = 1.0 m
d. Calculate the maximum concentration at x = 1.0 m.

10/1/2013 6:45:03 PM
Soil and Water.indd 234
Soil and Water.indd 234 10/1/2013 6:45:03 PM