Question

A water well of diameter 100 mm has been bored into a horizontal confined aquifer of thickness b = 9.5 m and is fully penetrating (i.e. can take water from all levels within the aquifer). The water table is initially 24.2 m above the bottom of the well (lower confining layer). When the well is pumped at 150 litres per minute the draw-down is 1.6 m in a monitoring well r = 3.0 m away from the well. The hydraulic conductivity is K = 8.5 m/day.

Estimate:
the draw-down at r = 9.1 m from the well.
Answer: m (3 marks)

Answer 1

To estimate the drawdown at a distance of r = 9.1 m from the well, we can use the Theis equation for confined aquifers:

S = (Q / (4 * π * T)) * W(u)

Where:

S = Drawdown at the monitoring well (m)

Q = Pumping rate (m³/s)

T = Transmissivity of the aquifer (m²/s)

W(u) = Well function, which is a function of u = r² * S / (4 * K * t)

Given:

Q = 150 liters/minute = (150/1000) m³/60 s ≈ 0.0025 m³/s

T = 8.5 m/day = 8.5 / 86400 m²/s (convert to m²/s)

r = 3.0 m (distance to monitoring well)

S = 1.6 m (drawdown in the monitoring well)

K = 8.5 m/day = 8.5 / 86400 m/s (convert to m/s)

First, calculate u using the given values:

u = r² * S / (4 * K * t)

Now, calculate W(u) using the calculated u:

W(u) = -expint(-u)

Finally, estimate the drawdown at r = 9.1 m using the Theis equation:

S_estimated = (Q / (4 * π * T)) * W(u)

Plug in the values and calculate S_estimated.

Keep in mind that this calculation involves iterative methods for evaluating the well function. The result may vary slightly based on the method used.