Advection, diffusion, and reaction in a channel Approximately 50 m3 of an agricultural pesticide with an initial concentration of 1.6 × 105 mol/m3 have been spilled into a stream following a train derailment. You have been called in to predict the aqueous concentrations of this pesticide at various points along the stream, and the mass that will be delivered to a lake with critical habitat 70 km downstream. You look up the main component of the pesticide and see that it degrades in water (due to hydrolysis reaction) with a half-life of 1.9 h. The discharge rate of the stream is 75,000 L/min. It has an average depth of 0.3 m and an average width of 1.2 m.
Advection, diffusion, and reaction in a channel
Approximately 50 m3 of an agricultural pesticide with an initial concentration of 1.6 × 105
mol/m3 have been spilled into a stream following a train derailment. You have been called in
to predict the aqueous concentrations of this pesticide at various points along the stream, and
the mass that will be delivered to a lake with critical habitat 70 km downstream. You look up
the main component of the pesticide and see that it degrades in water (due to hydrolysis
reaction) with a half-life of 1.9 h. The discharge rate of the stream is 75,000 L/min. It has an
average depth of 0.3 m and an average width of 1.2 m.
a. Calculate the maximum concentration (in mol/L) of the pesticide that will
be observed at a town 10 km downstream and at the point where the stream
reaches the lake, 70 km downstream. Assume a sheer velocity of 0.40 m/s.
b. Plot the concentration of this pesticide entering the town and the lake with
time. Care should be taken when selecting time steps so that features contaminant
peak are observable. If your time step is too large, you may miss the top of the
peak.
c. How important are the processes of longitudinal dispersion and hydrolysis
in attenuating the peak concentration between the town and the lake? (quantify
your answer) You can answer this question using the spreadsheet or
computational tool you used for part b, adjusting for parameters controlling
dispersion and reaction.
d. Estimate the total mass of this pesticide that will be transported into the
lake.
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