### Analysis of the movement of a tracer

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Environmental engineering

Question 1: Analysis of the movement of a tracer in a contaminated aquifer indicates that the local Darcy velocity is 1.2 m/d. The aquifer has a hydraulic conductivity of 14.0 m/d, a depth of 11 m, and a porosity of 0.3. How long will it take a contaminant with a retardation factor of 3.0 to travel 50 m? For approximately what fraction of that time do you think the contaminant will be adsorbed to solids in the aquifer, as opposed to being dissolved in the moving water?

Question 2: Sometimes pump-and-treat systems use a combination of injection wells and withdrawal wells to simultaneously “push” and “pull” contaminated groundwater toward the locations where it is drawn to the surface for treatment. Consider a system in which a straight line of injection 2.0-m-diameter wells has been constructed on one side of a contaminated site, and a parallel line of identical withdrawal wells has been constructed on the other side. The two lines of wells are separated by 100 m, and the wells are spaced at 10-m intervals in each line. Before pumping is initiated, the water layer in the unconfined aquifer is 40 m thick. The hydraulic conductivity in the aquifer is 5 x 10 -4 m/s .

Note that, in this system, near the injection wells, the water level will be higher when the wells are pumped than when they are not pumped. That is, the wells will generate a “drawup” rather than a drawdown. One of the convenient generalizations of groundwater flow is that the drawdown of the piezometric head at any location when multiple wells are present is simply the sum of the drawdowns that would develop at that location from each well operating independently. Similarly, the ‘draw-up’ of an injection well with flow rate Q is equal in magnitude (but opposite in direction) to the drawdown that would be induced if the well were withdrawing water from the aquifer at a flow rate of Q.

(a) Derive equation for the water depth as a function of distance from the withdrawal wells if only those wells are operating. To simplify the analysis, assume that the system can be modeled as though water withdrawal occurs uniformly along the whole line of wells, rather than at specific points.

(b) When only the withdrawal wells are operating, as in the scenario in part (a), the drawdown at the perimeter of the withdrawal wells is 12 m. If both sets of wells are turned on and all the wells operate with flow rates of 0.25 m3/min, plot the height of the piezometric surface between the two lines of wells, as a function of distance from the line of withdrawal wells. (Hint: Use the information for drawdown caused by the withdrawal wells to compute the draw-up caused by the injection wells, and then add the drawdown and draw-up at each location to find the net change in the water table at that location.)

Question 3: A pump-and-treat system has been installed at a Superfund site to capture a deep plume of contaminated groundwater, and the water that has been pumped out is being stored in a fiberglass tank for subsequent treatment. The water contains a mixture of chloride and the solvent trichloroethylene (TCE). However, the tank has been ruptured by an over-aggressive fork-lift driver, allowing the liquid to leak into a shallow groundwater system. The porosity of the soil is approximately 0.2 and the density of the soil grains is 2.8 g/cm3.

After 100 days, the chloride plume is approximately 190 m long, and the TCE plume is only 26 m long. Treating the spill as an instantaneous point-source, and assuming that the chloride behaves as a conservative solute and that biodegradation is  negligible, estimate the retardation factor, R, for TCE in the aquifer.

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