Landfill Plume in a Sand Aquifer
A closed municipal landfill overlies a 12-m-thick sand aquifer. Monitoring wells show a leachate plume whose leading edge for a conservative chloride tracer is 600 m downgradient after 25 years of leakage; a reactive contaminant of concern has a retardation factor of 3. Aquifer tests give hydraulic conductivity 20 m/day, porosity 0.30, and the water-table gradient is 0.003. A community well is 1,200 m downgradient from the landfill. The landfill has no engineered liner, and the water table is 3 m below the waste. State regulators must decide whether to require a pump-and-treat system at the landfill, an alternative water supply for the community, or both. The consultant’s report claims the plume is moving at 0.2 m/day and will reach the well in about 16 years; the community group argues that the reactive contaminant will arrive much sooner because retardation is irrelevant when the source is continuous.
1. Calculate the Darcy flux, seepage velocity, and retarded front velocity. Use them to evaluate both the consultant’s and the community group’s claims.
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Darcy flux q = K i = 20 × 0.003 = 0.06 m/day. Seepage velocity v = q/n = 0.06/0.30 = 0.20 m/day (about 73 m/yr). That is the velocity of a conservative tracer such as chloride. For the reactive contaminant, the retarded velocity is v/R = 0.20/3 = 0.067 m/day (about 24 m/yr). The observed chloride front, 600 m in 25 years, gives 24 m/yr-not 73 m/yr-so the aquifer is more heterogeneous or the source has not been continuous at full strength; the calculation is an upper bound, not a prediction. The consultant’s 0.2 m/day is the unretarded seepage velocity; using it to forecast the reactive contaminant overstates its speed and gives a 16-year arrival, which is inconsistent with R = 3. The community group is also wrong: retardation slows the front; a continuous source affects concentration, not the front’s speed. The retarded travel time from landfill to well is 1,200/0.067 ≈ 18,000 days ≈ 49 years, so about 24 years remain after 25 years.
2. Assess the risk to the community well and recommend a management strategy, including monitoring.
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The well is 1.2 km downgradient and the retarded front needs roughly another 24 years to reach it under the simple calculation, but uncertainty is large: preferential flow paths, pumping, and a fluctuating water table could accelerate arrival. Chloride is already 600 m out, so the source is active. A pump-and-treat system at the landfill can contain the plume if wells are placed downgradient and pumped at a rate that captures or reverses the flow; it will not clean the aquifer quickly because contaminants sorb to sand. Alternative water supply is the more reliable near-term protection for the community. I would recommend both: install sentinel monitoring wells between the plume and the community well, sample for the contaminant of concern and chloride quarterly, and define a trigger concentration for switching the well or providing bottled water. Model capture zones with the measured gradient and pumping. Also control the source by capping the landfill.
3. Explain why the observed chloride front (600 m in 25 years) differs from the calculated 73 m/yr seepage velocity, and what that means for predicting arrival.
Read the worked answer
The calculated 0.20 m/day is a Darcy seepage velocity assuming uniform sand, steady flow, and a continuous source. The observed average is 600/25 = 24 m/yr, about one-third of the calculated value. Possible reasons: the source did not leak at full strength for the entire period; the plume has spread and diluted, so the detectable edge is not the advective front; the aquifer has lower-conductivity zones or the gradient is smaller than 0.003; and retardation or anion exclusion affects chloride slightly. Heterogeneity is the main issue-preferential paths can move contaminants faster than the average, while fine layers slow them. Therefore the observed front should be used to calibrate a transport model, not simply the Darcy calculation. Predictions should be given as a range, with monitoring triggers, because a single arrival date implies false precision.