Chapter 5 Solutions to Odd Numbered Problems
These
solutions were provided by Todd Rayne of Hamilton College
5.1. A community
is installing a new well in a regionally confined aquifer with a transmissivity
of 1589 ft2/day and a storativity of 0.0005. The planned pumping
rate is 325 gal/min. There are several nearby
wells tapping the same aquifer, and the project manager needs to know if the
new well will cause significant interference with these wells. Compute the
theoretical drawdown caused by the new well after 30 days of continuous pumping
at the following distances: 50, 150, 250, 500, 1000, 3000, 6000, and 10,000 ft.
(This problem and the following problem can readily be solved using Excel with
the algorithm that is suggested in Analysis K. The repetitive nature of the
calculations is especially suited to a spreadsheet solution.)
Using
Excel, enter radius values manually, compute u values, look up W(u) values and enter them manually, and
compute 
values. The first line in the spreadsheet shown below gives
the formula for calculating u and
drawdown for the first r value. Use
the copy and paste commands to fill the spreadsheet. Q must be converted from gpm to 
.
|
r (ft) |
u |
W(u) |
|
|
entered
manually |
|
entered
manually from table |
|
|
50 |
6.56E-06 |
11.351 |
35.56 |
|
150 |
5.90E-05 |
9.161 |
28.70 |
|
250 |
1.64E-04 |
8.163 |
25.58 |
|
500 |
6.56E-04 |
6.747 |
21.14 |
|
1000 |
2.62E-03 |
5.378 |
16.85 |
|
3000 |
2.36E-02 |
3.21 |
10.06 |
|
6000 |
9.44E-02 |
1.875 |
5.87 |
|
10000 |
2.62E-01 |
1.014 |
3.18 |
5.3. Plot the
distance-drawdown data from Problem 1 on semilog paper (or on Excel).
The answer is on page 564 of the textbook.
5.5. Plot the
distance-drawdown data from Problem 2 on semilog paper (or on Excel).
The answer is on page 565 of the textbook.
5.7. If the aquifer in Problem 1 is not fully
confined, but is overlain by a 13.7-ft-thick confining layer with a vertical
hydraulic conductivity of 0.13 ft/day and no storativity, what would be the
drawdown values after 30 days of pumping at 325 gal/min at the indicated
distances?
|
A r (ft) entered manually |
B |
C |
D |
E |
F
|
|
50 |
409.214 |
0.122 |
0.000007 |
4.56 |
14.29 |
|
150 |
409.214 |
0.367 |
0.000059 |
2.44 |
7.64 |
|
250 |
409.214 |
0.611 |
0.000164 |
1.53 |
4.79 |
|
500 |
409.214 |
1.222 |
0.000656 |
0.71 |
2.22 |
|
1000 |
409.214 |
2.444 |
0.002622 |
0.18 |
0.56 |
|
3000 |
409.214 |
7.331 |
0.023600 |
0.001 |
0.003 |
|
6000 |
409.214 |
14.662 |
0.094399 |
0 |
Nil |
|
10000 |
409.214 |
24.437 |
0.262219 |
0 |
Nil |
This
problem was solved in Excel using given values of 
, and 
and 
were calculated, 
values were read from
Appendix 3, and 
values were
calculated in Excel.
5.9. With reference to the well
and aquifer system in Problem 1, compute the drawdown at a distance of
250 ft at the following times: 1, 2, 5, 10, 15, 30, and 60 min; 2, 5, and 12 h;
and 1, 5, 10, 20, and 30 days.
|
time
entered manually |
time
(days) convert time days |
|
W (u)
entered manually from table |
|
|
1
min |
0.000694444 |
7.08E+00 |
0.0001 |
0.00 |
|
2
min |
0.001388889 |
3.54E+00 |
0.008 |
0.03 |
|
5
min |
0.003472222 |
1.42E+00 |
0.148 |
0.46 |
|
10
min |
0.006944444 |
7.08E-01 |
0.369 |
1.16 |
|
15
min |
0.010416667 |
4.72E-01 |
0.598 |
1.87 |
|
30
min |
0.020833333 |
2.36E-01 |
1.080 |
3.40 |
|
60
min |
0.041666667 |
1.18E-01 |
1.660 |
5.20 |
|
2 hr |
0.083333333 |
5.90E-02 |
2.311 |
7.24 |
|
5 hr |
0.208333333 |
2.36E-02 |
3.195 |
10.01 |
|
12
hr |
0.5 |
9.83E-03 |
4.058 |
12.71 |
|
1
day |
1 |
4.92E-03 |
4.746 |
14.87 |
|
5
days |
5 |
9.83E-04 |
6.352 |
19.90 |
|
10
days |
10 |
4.92E-04 |
7.044 |
22.07 |
|
20
days |
20 |
2.46E-04 |
7.733 |
24.23 |
|
30 days |
30 |
1.64E-04 |
8.132 |
25.48 |
5.11. Plot the time-drawdown data
from Problem 9 on semilog paper.
The
graph is on page 566 of the textbook.
5.13. A well that pumps at a
constant rate of 78,000 ft3/day has achieved equilibrium so that
there is no change in the drawdown with time. (The cone of depression has
expanded to include a recharge zone equal to the amount of water being pumped.)
The well taps a confined aquifer that is 18 ft thick. An observation well 125
ft away has a head of 277 ft above sea level; another observation well 385 ft
away has a head of 291 ft. Compute the value of aquifer transmissivity using
the Thiem equation.
Using
Eqn. 5-44:
where 
5.15. A slug test was
performed on a monitoring well with a radius of 2 in and a sand pack radius of
5 in. The aquifer thickness was 8 ft and the initial height of the water column
in the casing above the top of the screen was 51 ft. The following data showing
the change in the elevation of the water in the casing with time were collected
following the lowering of a solid slug into the water. Find the aquifer
transmissivity of you assume a storativity of 0.001.
Time (s) Head (ft) Time
(s) Head (ft)
0 2.67 10 0.33
0.1 2.38 12 0.60
0.2 2.13 14 0.28
0.4 1.83 16 0.42
0.8 1.34 18 0.22
1.2 0.65 20 0.30
1.6 0.02 22 0.20
2.0 0.55 24 0.21
2.4 0.96 26 0.16
2.8 1.26 28 0.15
3.2 1.45 30 0.14
3.6 1.47 32 0.10
4.0 1.36 34 0.10
4.4 1.14 36 0.08
4.8 0.84 38 0.09
5.2 0.49 40 0.05
5.6 0.12 42 0.07
6.0 0.23 44 0.04
6.2 0.53 46 0.05
6.6 0.75 48 0.02
8.0 0.89 60 0.01
The
following values are obtained from the data plot:
t1 = 3.5 s Ht1 = - 1.46 ft
t2 = 12.2 s Ht2 = - 0.65 ft
Using
equations in Sec. 5.6.3.1:
and from the graph of head vs. time:
1. Calculate 
(Eqn. 5-101)
2. Calculate 
(Eqn. 5-100)
3. Calculate damping factor (Eqn. 5-102)
4. Rearrange Eqn. 5-99 to calculate 
5. Calculate d (Eqn. 5-98)
6.
Calculate a (Eqn. 5-97)
7. Calculate c (Eqn. 5-96)
8. Calculate 1st estimate of T (Eqn. 5-95)
9. Calculate second estimate of T (Eqn. 5-95)
10. Calculate third estimate of T (Eqn. 5-95)
11. Repeat step 10 until a closure criterion
is met. This can easily be done in Excel.
12. Now check the solution by comparing values
of L from Eqn. 5-103 and 5-99.
a. From Eqn. 5-103
b. From Eqn. 5-99
The
two L values are within 20%.
5.17. A test well was drilled to a total depth of 117 ft with the
following geologists log:
073 ft Coarse sand
7382 ft Clayey sand
82117 ft Coarse sand
117 ft Crystalline bedrock
The depth to water was 55 ft. The test
well was screened from 82 to 117 ft. It was pumped at a rate of 560 gal/min.
Drawdown was measured in an observation well that was also screened from 82 to
117 ft and was located 82 ft away from the pumping well. The following
time-drawdown data were obtained:
Elapsed Time (min) Drawdown (ft)
0 0.00
1 0.90
2 2.15
3 3.05
4 3.64
5 4.07
6 4.52
7 4.74
8 5.02
9 5.21
10 5.53
15 5.72
20 5.97
30 6.12
40 6.20
50 6.25
60 6.27
90 6.29
120 6.29
(A) Plot the time-drawdown data on 3 x 5 cycle
logarithmic paper. Compute the value of the storativity and transmissivity of
the aquifer using the graphical method for leaky aquifers. Find the vertical
hydraulic conductivity of the confining layer.
(B) Compute the value of aquifer storativity and
transmissivity of the aquifer using the Hantush inflection-point method.
A.
Using
AQTESOLV one can find the following values of T, S and r/B:
T = 1.477 ft2/min
S = 0.0008
r/B = 0.6026
Vertical
hydraulic conductivity of the confining unit: (assume clayey sand is confining
unit), using Equation 5.63:
B.
Time-drawdown graph is:
The
following values are found from a time-drawdown graph:
from
Appendix 5: 
from Equation
5-17:
from
Equation 5-72
5.19. A well in a water-table aquifer was pumped at a rate of 873 m3/day.
Drawdown was measured in a fully penetrating observation well located 90 m
away. The following data were obtained (Kruseman & deRitter 1991):
Find the transmissivity,
storativity, and specific yield of the aquifer.
Time Drawdown Time Drawdown Time Drawdown
(min)
(m) (min) (m) (min) (m)
0 0 18 0.098 300 0.173
1.17 0.004 21 0.103 370 0.173
1.34 0.009 26 0.110 430 0.179
1.7 0.015 31 0.115 485 0.183
2.5 0.030 41 0.128 665 0.182
4.0 0.047 51 0.133 1340 0.200
5.0 0.054 65 0.141 1490 0.203
6.0 0.061 85 0.146 1520 0.204
7.5 0.068 115 0.161
9.0 0.064 175 0.161
14 0.090 260 0.172
The
best match for the Type A curve and the early drawdown data is with the 
curve. At the match
point 
m and 
Substitute these
values into Equation 5-78 and 5-79.
given 
Given 
The
Type B curve for 
is matched to the
late drawdown data. The match point values are 
and 
