Groundwater Plume Travel Time
A town pumps 1,200 m³/day from a well field in a sandy aquifer. Water-table elevations are 42.0 m at pumping well A, 48.0 m at monitoring well B located 600 m directly upgradient from A, and 47.5 m at well C located 300 m from B and 300 m from A, offset 200 m from the straight B-A line. Hydraulic conductivity is 10 m/day and porosity is 0.25. A chloride plume is detected at B at 20 mg/L; background is 5 mg/L. A clay lens 2 m thick lies between B and A but pinches out 100 m from A. The pumping well is screened in the lower sand. A resident says the plume will take decades to reach A because groundwater moves slowly.
1. Calculate the hydraulic gradient and the average linear groundwater velocity between B and A. Show units and state the flow direction.
Read the worked answer
The hydraulic gradient is the head difference divided by distance: i = (48.0 m - 42.0 m) / 600 m = 6.0 m / 600 m = 0.010 m/m. The Darcy velocity is q = K × i = 10 m/day × 0.010 = 0.10 m/day. The average linear velocity, or seepage velocity, is v = q / porosity = 0.10 m/day / 0.25 = 0.40 m/day. Groundwater flows from higher head to lower head, so the direction is from B toward A. At 0.40 m/day, the calculated travel time over 600 m is 600 m / 0.40 m/day = 1,500 days, or about 4.1 years, not decades.
2. The resident's claim that the plume will take decades is not supported by the calculation. Explain two aquifer features that could make the actual arrival time longer or shorter than about 4 years.
Read the worked answer
One feature that could lengthen arrival is the clay lens. Clay has low permeability and can adsorb or retard chloride, so flow may be slowed or diverted around it. Adsorption and dispersion in the sand can also dilute and spread the plume, delaying the first arrival at A. A feature that could shorten arrival is the pumping well itself. Pumping lowers the water table near A and steepens the gradient close to the well, increasing velocity there. Fractures or coarser lenses in the lower sand could also provide fast paths. Because these effects act in opposite directions, the calculated 4-year time is an average estimate, not a precise prediction.
3. Determine whether the plume at B is likely to move toward C or toward A, and explain how you used the water-table data.
Read the worked answer
Groundwater flows from higher head to lower head. Well B has a head of 48.0 m; C has 47.5 m; A has 42.0 m. Both C and A are downgradient from B. The gradient from B to C is (48.0 - 47.5) / 300 m = 0.0017, while the gradient from B to A is (48.0 - 42.0) / 600 m = 0.010. The B-to-A gradient is about six times steeper, so the dominant flow is toward A. Some plume may move toward C because C is slightly lower, but the stronger gradient and the pumping at A should draw most of the plume toward A. The clay lens could deflect part of the flow, so the answer is a likely direction, not a guarantee.