Isotope Hydrology HW-3, answer key
1) (12
points) Br push/pull experiment
In 2007,
we performed the following push/pull experiment in
Bangladesh. We injected 540 L of water with a Br- concentration of
120mg/L into the aquifer. In the end we added another 80 L of water
without tracer. After letting the tracer solution rest in the ground,
we recovered about 900 L of water. The Br- concentrations as a function
of pumped volume of water are given in this spreadsheet
and we looked
at the Br curve in class (Fig).
a) Assuming
a porosity of 0.3, what is the radius of the volume around
the injection well that is affected by the experiment?
b) Fit the
observed Br- data with a model given in equation (11) in the
paper by Schroth
et al., 2000. You will not be
able to fit the first 80L of fresh
water recovery, just try to match the plateau and the right side of the
curve. Determine the dispersivity in cm of the aquifer . What
dispersivity would you expect? See Fig we discussed in
class
and
compare with your answer (Hint: our experiment is fairly consistent
with the literature data).
There is a
problem in Excel using the erfc, it is not defined for
negative numbers. See Excel spreadsheet that you downloaded for how to
work around this.
If a sphere is assumed as a zone of influence, the volume is ~900/0.3 =
3m3, equivalent to a radius of 0.9m.
See spreadsheet for
answer. The data are fit best if we assume a dispersivity of about 5mm.
The fit is even improved if we assume that the total injected volume
was 640 instead of 620L not required to answer the question correctly
though). This discrepancy is easily accomodated by the
measureemnt uncertainty of the total flow.
Resources:
M.
H. Schroth, J. D. Istok and R. Haggerty (
2000) In situ evaluation of solute retardation using single-well
push–pull tests Advances in Water Resources Volume 24, Issue 1, October
2000,
Pages 105-117
2) (14 points) Isotope enrichment
The stable
istope composition of a pond in Bangladesh was monitored
for a year. Data are included in the spreadsheet you donwloaded above.
a) Plot the d18O
in the pond and in precipitatoin, as well as (monthly) precipitation
amount as a function of time. How do you interpret the change over time
in d18O?
Again,
see spreadsheet downloaded
above for the plot. It appears that the pond becomes isotopically
heavier as the dry season progresses until (isotopically light)
precipitation kicks in and pulls the pond back to lighter values. The
effects of the one major rain event end of September are
particularly impressive.
b) Assume
that during times of no precipitation you have evaporation
only affecting the ponds. Use the Rayleigh equation with an
equilibrium fractionation factor for 25oC to and a
kinetic fractionation for a relative humidity of 0.8 and estimate how
much of the original water you lost during the evaporation process.
Again see spreadsheet downloaded
above for the answer. The fractionation factors for the paramers given
in the question are: ee (18O)
=
9.4
‰, ek (18O)
= -1.2 ‰
for the liquid: R/Ro = f -(ee + ek)
d18O became heavier during the evaporation process by
7‰, i.e. R/Ro = 1.003 = f -(9.4‰
-1.2)‰
f the can be calculated as f = 1.007 -1000/8.2= 0.69.
So the fraction of water that remained was 0.69.