GROUNDWATER - Water Quality Engineering in Natural Systems - page 197

5.13. Seepage velocities surrounding a municipal well
field are on the order of 5 m/day, the well field is
approximately circular with a radius of 70 m, and
the longitudinal dispersion coefficient is on the
order of 50 m 2 /day. Determine whether contami-
nant transport from the boundary of the well field
is advection or dispersion dominated.

(b) Estimate the range of aqueous concentrations
for which the linear isotherm deviates by less
than 10% from the Langmuir isotherm. Given
that the Langmuir isotherm provides a more
realistic representation of the sorption process,
what is the advantage to using the linear iso-
therm in practice?

5.18. The concentration of TCE in a groundwater is
measured as 100 mg/L, the fraction of organic
carbon in the solid matrix is estimated as 1.5%,
and the bulk density of the aquifer is approxi-
mately 1800 kg/m 3 . Estimate the mass of TCE
sorbed per unit volume of the aquifer.

5.14. A contaminant spill in an aquifer has resulted in
a pollutant cloud that is 11 m long, 5 m wide, and
2 m deep. The pore sizes in the aquifer are on the
order of 2 mm, the molecular diffusion coefficient
is 10 −9 m 2 is the tortuosity is 1.3, and the mean
seepage velocity is 0.1 m/day. Estimate the com-
ponents of the dispersion coefficient that should
be used in modeling plume transport.

5.19. Three kilograms of tetrachloroethylene is spilled
over a 1.2-m depth of groundwater and spreads
laterally as the groundwater moves with an
average velocity of 0.2 m/day. The longitudinal
and transverse dispersion coefficients are 0.05 and
0.005 m 2 /d, respectively; the porosity is 0.15; the
density of the aquifer material is 2.65 g/cm 3 ; log K oc
is 2.42 ( K oc in cm 3 /g); and the organic carbon frac-
tion in the soil is 8%. Calculate the concentration
at the spill location after 1 hour, 1 day, and 1 week.
Compare these values with the concentration
obtained by neglecting sorption.

5.15. The seepage velocity, v , surrounding a well is
described by the relation

Q
rbn

v =

2π

where Q is the pumping rate at the well, r is
the radial distance from the well, b is the aquifer
thickness, and n is the effective porosity of the
aquifer. At a particular well, the pumping rate is
20,000 L/min, the thickness of the saturated zone
is 15 m, and the effective porosity is 0.15. Estimate
the extent of the region surrounding the well
where advection transport dominates macrodis-
persion. (Hint: Use the Péclet number vr / D L as a
basis for your analysis.)

5.20. Use all the empirical relationships in Table 5.7 to
estimate the organic carbon sorption coefficient
of TCE. Assume that log K ow of TCE is 2.29 (as
shown in Table 5.8). Verify the claim that the
actual value of log K oc , given in Appendix B, is
within 1 standard deviation of the mean of the
predictions given by the empirical equations listed
in Table 5.7.

5.16. Determine whether the dispersivities given by
Equation (5.41) are consistent with the values
given in Table 5.5. 5.21. An aquifer contains a contaminant spread over a

500-m 3 volume of the aquifer. The porosity of the
aquifer is 0.15, and the retardation factor of the
contaminant is 10. Estimate the volume of pore
water that must be removed to reduce the mass of
contaminant in the aquifer by 99%.

5.17. Sorption onto a soil matrix can be described by
the Langmuir isotherm given by

K Sc
K c

l aq

F =

1 +

l aq

5.22. A buried drum containing 10 kg of a contami-
nant suddenly ruptures and spills all of its con-
tents into the groundwater over a 1-m depth. The
mean seepage velocity in the aquifer is 0.5 m/day,
the porosity is 0.2, the longitudinal dispersion
coefficient is 1 m 2 /d, the horizontal-transverse
dispersion coefficient is 0.1 m 2 /d, vertical mixing
is negligible, and the first-order decay constant
of the contaminant is 0.02 d −1 . Determine the
maximum concentration in the groundwater after
100 days. Compare this concentration to the
maximum concentration without decay.

where F is the mass of tracer sorbed per unit mass
of the solid phase, c aq is the aqueo u is concentration,
K l is the Langmuir constant, and S is the maximum
sorption capacity of the soil matrix.

(a) If the sorption capacity of the soil matrix is
5000 mg/kg and the linear isotherm distribu-
tion coefficient at low aqueous concentrations
is 60 L/kg, estimate the Langmuir constant
and express the Langmuir isotherm as a rela-
tionship between F and c aq only.