Part 1: Steady Radial Flow Questions

Question 1 (text book)

The initial piezometric surface in a confined aquifer of 20 m thickness is 34 m above the

bottom. After a long period of pumping, the piezometric surface stabilizes at 29.3 m above

the bottom. The hydraulic conductivity of the aquifer is 12.2 m/day. If the radius of the well

is 0.5 m and the radius of influence of the pumping is 500 m, what is the steady state well

discharge?

Islamic University of Gaza

Water Resources Management

EENV 4359

First Semester (2014-2015)

Instructors:

Dr. Yunes Mogheir

Eng. Wael Salem

Eng. Israa Abushaban

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Question 2

The following drawdowns were observed in a pump test. The drilling log indicated silty clay up to a

depth of 20 m underlain by a 25 m thickness of medium sand followed by fine sandy and clayey

sediment. The well screen was installed over the whole thickness of the aquifer (medium sand). A

discharge Q of 150 m3/hr was pumped for 15 hours till the drawdown became steady.

Dtermine the aquifer hydrulic conductivity K.

Oservation well at (m) 30 90

Drawdown (m) 0.64 0.20

Sol.

1- Steady Radial Flow (OR: Pumping for a long period).

2- Unconfined Aquifer (medium sand), H=25m.

3- Calculate K.

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Question 3 (text book)

After a long period of pumping from an unconfined aquifer at a constant rate of 850 m3/day, the cone

of depression reaches equilibrium. The aquifer has an initial saturated thickness of 20 m and a

hydraulic conductivity of 8.65 m/day. During the equilibrium, the water levels in an observation well

50 m away and in the pumping well are measured as 18.4 and 9.9 m. Determine:

1- The radius of influence of the pumping.

2- The radial distance where the steady drawdown is 5 cm.

3- The expected drawdown in the pumping well (rw = 0.4 m).

4- The total well losses.

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Question 4 (text book)

A well with a radius of 0.5 m pumps at the rate of 15 L/s from an unconfined aquifer that is

uniformly recharged at a rate of 0.6 m/day. Without pumping from the well, the water table is nearly

horizental and the aquifer thichness is 30 m. the hydrulic conductivity of the aquifer is 20 m/day.

Determine the radius of influence of the well and the approximate drawdown at the well location

near steady state condition.

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Question 5

A 30 cm diameter well fully penetrates an unconfined aquifer K is 10 m/day having a saturated

thickness of 30 m. Dtermine the discharge for a drawdown at the well of 5 m if rainfall penetration is

0.1 cm/hour. Assume steady state condition.

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Part 2: Unsteady Radial Flow Questions

Question 6

Drwadown in an observation well 100 meters away from a well fully penetrating a confined aquifer

of 20 m thickness and pumping at a steady rate of 30 m3 per hour are listed in the table below.

Determine the aquifer transmissivity and storativity using Theis, Jacob and chow method of solution

and compare between results.

t (min) s (m)

10 0.18

30 0.30

60 0.44

90 0.46

120 0.50

180 0.57

240 0.59

480 0.66

960 0.72

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Question 7

Assume that the pump of the well of Question 6 was stopped at 960 minutes. And residual

drawdowns were observed in an observation well 100 m from pumped well which are recorded in the

table below. Dtermine the Transmissivity of the aquifer. (Use Recovery method).

t’ (min) s’ (m)

0 1.10

10 1.00

15 0.95

10 0.91

25 0.86

40 0.78

60 0.69

90 0.62

110 0.53

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Question 8 (text book)

A fully penetrating production well pumps from a confined aquifer at a constant rate of 64 L/s. If the

coefficients of transmissiviy and storage of the aquifer are 1240 m2/day and 4 * 10

-4, respectively.

Estimate the drawdown at a distance of 200 m from the pumping well for pumping period of 8 hours,

30 days, and 6 months using:

1- Theis equation (Non-equilibrium equation).

2- Cooper-Jacob method of solution.

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Question 9

Calculate the drawdown in an observation well 100 m from a pumped well which completely

penetrates an unconfined aquifer. The aquifer properties are K = 20 m/day, H = 100 m, and S = 0.16.

The well is pumped at 5027 m3/day. Calculate s for t = 0.08, 0.32, 3.2, 8, 32, and 80 days.

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Question 10

An aquifer has been pumped for 240 min and at this time the drawdown was determined to be 0.878

m, Aquifer transmissivity is equal 1249.5 m2/day, and the aquifer was pumped at 1.895 m

3/min.

1- What should be the drawdown have been at 100 min of pumping.

2- At what time the drawdown of 0.61 m should been occur.

3- Find the aqufier storativity S if an observation well was at a distance of 50 m.

Hint: Use Cooper-Jacob method.

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Question 11

A completely penetrating well in an unconfined aquifer is pumped at a rate Q of 4000 m3/day. At

time t equal to 360 min the drawdown s was determined to be 0.9 m in an observation well at

distance r = 500 m. Also the aquifer transmissivity T is equal to 2000 m2/day.

4- Calculate the drawdown s for t = 160 min of pumping.

(Hint: Use Time-Drawdown (Cooper-Jacob) method)

5- Calculate the distance r of an observation well with a drawdown s equal to 1 m. (Hint:

Use Distance-Drawdown method)

Sol.

1- s = 0.77 m.

2- r = 266 m.

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Question 12

A completely penetrating well in an unconfined aquifer is pumped at a rate of 5072 m3/day. The

aquifer constants are T = 2000 m2/day and S = 0.16. Calculate the drawdown s in observation wells,

50, 100 and 200 m from the pumped well after 0.01, 0.025, 0.1, 0.25, 1, 2.5, 10, 25, and 100 days of

pumping.

Calculate the difference between drawdown s for the wells at 50 and 100 m from the pumped well,

and plot this difference against log t for the above t values.

Use the calculated s-vs-t data for observation well 100 m distance from pumped well to determine T

and S of the aquifer using Theis OR Jacob method. Compare calculated values of T and S with

“known” values of both.

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Question 13

You are asked to design a pump test for a confined aquifer in which the transmissivity is expected to

be about 1.4 * 10-2

m2/s and the storativity about 1.0 * 10

-4. What pumping rate would you

recommend for the test if it is desired that there be an easily measured drwadown of at least 1 m

during the first 6 h of the test in an observation well 150 m from the pumping well.

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Question 14

For transmissivity T = 2500 m2/day, storativity S = 1.0 *10

-3, and a pumping rate Q = 500 m

3/day,

calculate drawdowns in a confined aquifer for r = 10, 50, and 100 m at t = 150 min.

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Question 15

Values of drawdown and distance in a pumping test in a confined aquifer are listed in the following

table. Determine the hydrulic parameters of the aquifer using the distance straight-line technique.

Assume that t = 105 min, and Q = 10000 m3/day.

Distance

(m)

Drawdown

(m)

25 1.51

50 1.29

100 1.07

150 0.94