True groundwater velocity

Groundwater flows from a well toward a river in a confined aquifer that is 20 meters thick (see picture). The hydraulic conductivity is 10-4m/s, the head at the well is 50m and the head at the river is 40m, the distance between the river and the well is 1km. Assume a porosity of 0.35, effective porosity of 0.3 and that the aquifer is 150m wide.
(10pts) What is the volumetric flow rate (Q) of water flowing in the aquifer?
(5pts) What is the Darcy velocity (q)?
(5 pts) What is the true groundwater velocity (v’)?
(20pts) Your neighbor and you each have groundwater wells that you use to irrigate your fields. You both draw from an unconfined aquifer. Your well has a radius of 0.05m, your neighbor’s well is located 50m away. The hydraulic conductivity of the soil is
Perchloroethylene (PCE) is dumped into a pond. PCE that has a retardation factor (R) of 5.9. The PCE seeps down into the unconfined aquifer below the pond. There is a well 50m away. How long it will take the PCE in the groundwater below the pond to reach the well if the well pumping causes a hydraulic gradient of 0.025. Assume a porosity of 0.18 and a K of 0.04m/d.
Assume there is a plume of Trichloroethylene (TCE) heading toward a towns drinking water well in a confined aquifer. Building a physical containment unit is decided to be too expensive so hydrodynamic containment is considered. The plume is estimated to be 15m wide. The city can afford to install one well and plan to pump at a rate of 0.05m3/s. The hydraulic gradient in the region is 0.004, the hydraulic conductivity is 5.5×10-3m/s. The aquifer has a consistent thickness of 25m.
(25pts) Calculate key points of the capture zone assuming the planned pumping rate. Key points should include your well location, the leading edge of your capture zone (y=0), the width of your capture zone at the well location (x=0), and the maximum width of the capture zone (x -> ∞). Mark the values on the capture zone diagram.
(5pts) Will this single well pumping at this rate be enough to capture the plume?
(5pts) What do you propose the pumping rate should be in order to capture the plume?
10-3m/d. Assuming you pump at a rate of 3m3/day and measure the head in your well to be 15m, what will be the steady-state head of the water in your neighbors well?

(10pts) Draw a cross-sectional diagram of the situation
(5pts) Use the hydraulic gradient to find the true velocity of the water
(5pts) Calculate the velocity of the PCE using R
(5 pts) Calculate the time it would take the PCE to travel from the pond to the well.

Sample Solution