Drawdown versus time data for an observation well 100 ft from the pumping well a
ID: 1761643 • Letter: D
Question
Drawdown versus time data for an observation well 100 ft from the pumping well are tabulated below. Identify the type of boundary and determine the radius of the image well from the observation well. What additional information would you need to locate the Time after Pumping Drawdown (ft) Started (minute 5 10 15 20 25 30 40 50 60 70 80 90 100 110 120 180 240 300 360 420 480 540 600 660 720 840 960 0.08 0.22 0.32 0.41 0.49 0.56 0.67 0.77 0.85 0.95 1.01 1.08 1.14 1.20 1.25 1.51 1.70 1.87 1.99 2.10 2.20 2.28 2.36 2.46 2.50 2.63 2.77Explanation / Answer
Radius of the image well,
The Theis equation follows:
S = 114.6 Q W(u)
Tt
S = drawdown (feet)
Q = pumping rate (gpm)
T = transmissivity (gpd/ft)
W(u) = is read “well function of u” and represents an exponential integral
u = 1.87 r2 s
Tt
r = radius (ft) from center of pumped well to point where drawdown is computed
s = storage coefficient (dimensionless)
t = time since pumping started (days)
Assumption
T = 50000 gpd / ft (621 m2 / day)
Storage Coefficient s = 5 x 10-4
Q = 500 gpm (2730 m3 / day)
Solution :
Radius of image well, r =
r =
S = 0.08, t = 5 min [(5/(24*60)) in days] {24 hours, 60 minutes}
r = = 0.50916 ft = say as 0.51 ft
Based on this formula, remaining radius calculated,
Time after Pumping Started (Minute)
Drawdown (ft)
radius of image well (r) in feet
5
0.08
0.51
10
0.22
1.19
15
0.32
1.76
20
0.41
2.31
25
0.49
2.82
30
0.56
3.30
40
0.67
4.17
50
0.77
5.00
60
0.85
5.75
70
0.95
6.56
80
1.01
7.24
90
1.08
7.94
100
1.14
8.60
110
1.2
9.25
120
1.25
9.86
180
1.51
13.27
240
1.7
16.26
300
1.87
19.07
360
1.99
21.55
420
2.1
23.91
480
2.2
26.16
540
2.28
28.25
600
2.36
30.29
660
2.46
32.44
720
2.5
34.16
840
2.63
37.84
960
2.77
41.51
Boundary Location :
The previous equation can be integrated with the following boundary conditions:
1 At distance rw (well radius) the head in a well is hw,
2 At distance R from well (Radius of influence), the head is H (which is the undisturbed
head and equal to initial head before pumping)
The equation can be integrated with the following boundary conditions:
1. At distance rw (well radius) the head in a well is hw,
2. At distance R from well (Radius of influence), the head is H (which is the undisturbed
head and equal to initial head before pumping)
3. So, the equation can be written as:
Sw = H-hw = (Q/2*3.14*T)ln(R/rw)
R & rw details required for finding boundaries
Refer the details in below following link :
http://www.ose.state.nm.us/Pub/HydrologyReports/Hydrology%20Training%20Report052106.pdf
Time after Pumping Started (Minute)
Drawdown (ft)
radius of image well (r) in feet
5
0.08
0.51
10
0.22
1.19
15
0.32
1.76
20
0.41
2.31
25
0.49
2.82
30
0.56
3.30
40
0.67
4.17
50
0.77
5.00
60
0.85
5.75
70
0.95
6.56
80
1.01
7.24
90
1.08
7.94
100
1.14
8.60
110
1.2
9.25
120
1.25
9.86
180
1.51
13.27
240
1.7
16.26
300
1.87
19.07
360
1.99
21.55
420
2.1
23.91
480
2.2
26.16
540
2.28
28.25
600
2.36
30.29
660
2.46
32.44
720
2.5
34.16
840
2.63
37.84
960
2.77
41.51
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