Question

A homogeneous isotropic confined aquifer of uniform thickness 30 m has hydraulic conductivity of 5 m/day and porosity of 0.3. There are two observation wells X and Y along a radial line from a fully penetrating pumping well at 100 m and 200 m distance, respectively. The well is pumped at a uniform rate to produce steady drawdown of 5 m at X and 3 m at Y. If a non-reactive pollutant enters at the observation well Y, then the time taken by the pollutant (under advection) to reach the observation well X is ________ days. (rounded off to two decimal places)

Hint:

In groundwater flow problems, always remember to use Darcy’s Law for calculating groundwater velocity, and consider the hydraulic gradient to determine the advection rate of pollutants.

Answer 1

Step 1: Use the Darcy’s Law to calculate the velocity of the pollutant.
The velocity of the non-reactive pollutant is the same as the groundwater velocity under advection, given by: \[ v = \frac{K \cdot h}{\phi} \] where:
\( K = 5 \, {m/day} \) (hydraulic conductivity)
\( h = {hydraulic gradient} \)
\( \phi = 0.3 \) (porosity)
We need to calculate the hydraulic gradient between the two wells. The drawdown at well X and well Y is provided as 5 m and 3 m, respectively, so the hydraulic gradient \( I \) between wells X and Y is: \[ I = \frac{h_X - h_Y}{d_X - d_Y} \] where \( h_X \) and \( h_Y \) are the drawdowns at X and Y, and \( d_X \) and \( d_Y \) are the distances from the pumping well. Thus, the hydraulic gradient is: \[ I = \frac{5 - 3}{200 - 100} = \frac{2}{100} = 0.02 \] Step 2: Calculate the velocity.
Now we can calculate the velocity using Darcy’s Law: \[ v = \frac{K \cdot I}{\phi} = \frac{5 \cdot 0.02}{0.3} = \frac{0.1}{0.3} = 0.333 \, {m/day} \] Step 3: Calculate the time taken by the pollutant.
The distance between well Y and well X is \( 200 \, {m} - 100 \, {m} = 100 \, {m} \). The time taken by the pollutant to travel from Y to X is given by: \[ t = \frac{{distance}}{{velocity}} = \frac{100}{0.333} \approx 300.3 \, {days} \] Step 4: Conclusion.
The time taken by the pollutant to reach observation well X is approximately: \[ \boxed{300.30} \, {days} \]