Question

Cone of Depression – determini

ng the maximum pumping rate fo

r a specified draw down.

(+20)

A consulting company decides to u

se Pump & Treat to remove the

TCE plume from the aquifer. For an

unconfined aquifer such as this, t

here is a possibility that dr

awdown during the Pump & Treat operation will

lower the water table to the

bottom of the well and that the wa

ter will stop flowing (thi

s is bad). Suppose a 6

inch diameter well is installed

which fully penetrates the 15-m

thick aquifer which has a hydraulic

conductivity of 0.001 m/s. Deter

mine the maximum pumping rate

(in gallons per minute, gpm) that can be

sustained indefinitely if the dr

awdown at an observation well 5

00 m from the pumped well is 12 m and the

drawdown at the pumped well is

limited by the depth of the aqui

fer and the height of the submersible pump,

which you may estimate at 0.3 m

(i.e., drawdown in the pumping

well may not exceed 14.7 m).

Answer: Q = 50.5 gpm.

Answer 1

Cone of Depression – determining the maximum pumping rate for a specified draw down.(+20) A consulting company decides to use Pump & Treat to remove the TCE plume from the aquifer. For an unconfined aquifer such as this, there is a possibility that drawdown during the Pump & Treat operation will lower the water table to the bottom of the well and that the water will stop flowing (this is bad). Suppose a 6 inch diameter well is installed which fully penetrates the 15-m thick aquifer which has a hydraulic conductivity of 0.001 m/s. Determine the maximum pumping rate (in gallons per minute, gpm) that can be sustained indefinitely if the drawdown at an observation well 500 m from the pumped well is 12 m and the drawdown at the pumped well is limited by the depth of the aquifer and the height of the submersible pump, which you may estimate at 0.3 m (i.e., drawdown in the pumping well may not exceed 14.7 m).

Solution –

For the ease in looking for the data the question has been formatted again as shown below.

Given data –

Unconfined aquifer

Depth of aquifer = 15 m

Diameter of pumping well = 6 inch = 0.1524 m

Radius of pumping well = half of diameter of well = 0.0762 m

Allowable drawdown in pumping well = 14.7 m

Height (H₂) = 15 – 14.7 = 0.3 m

Hydraulic conductivity (K) = 0.001 m/s

Discharge rate (Q) = unknown

Radius of observation well = 500 m

Drawdown in observation well = 12 m

Height (H₁) = 15 – 12 = 3 m

For unconfined aquifer we use dupit’s formula

Where symbols have their usual meaning

Putting the values in the equation above we will get

Q = 0.003184843 m³/s

= 3.184843 l/s

= 0.841346 gal/s

Q = 50.4807795 gal/min

So, the maximum pumping rate will be 50.5 gpm.

A feedback is highly appreciated.