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Well Function Calculator
Enter u in the yellow cell and W(u) will be calculated in the adjacent collumn
Multiple u values can be enterred below
u W(u) 1/u W(u) Cooper-Jacob
1 0.2193839 4.558218918 -0.577215665
0.00001 10.93572 100000 10.9357098
0.00005 9.3263219 20000 9.326271888
0.0001 8.6332247 10000 8.633124707
0.0002 7.9401775 5000 7.9399775270.0002 7.9401775 5000 7.939977527
0.0005 7.0241867 2000 7.023686795
0.001 6.3315394 1000 6.330539614
0.002 5.6393914 500.0 5.637392434
0.004 4.9482413 250.0 4.944245253
0.007 4.3916172 142.9 4.384629465
0.01 4.0379296 100.0 4.027954521
0.015 3.6374333 66.67 3.622489413
0.02 3.3547078 50.00 3.3348073410.04 2.6812637 25.00 2.64166016
0.06 2.2953069 16.67 2.236195052
0.08 2.026941 12.50 1.948512979
0.1 1.822924 10.00 1.725369428
0.2 1.2226505 5.000 1.032222248
0.3 0.9056767 3.333 0.626757139
0.4 0.7023801 2.500 0.339075067
0.7 0.3737688 1.429 -0.2205407211 0.2193839 1.000 -0.577215665
1.2 0.1584084 0.8333 -0.759537222
1.6 0.0863083 0.6250 -1.047219294
2 0.0489005 0.5000 -1.270362845
2.4 0.0284403 0.4167 -1.452684402
2 7 0 0191819 0 3704 1 570467438
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u 1/u W(u) W(u) Coop %error Wu CJ
1.00E-05 100000 10.9357198 1.09E+01 -9.14E-05
2.00E-05 50000 10.24258262 10.24256 -0.000195
5.00E-05 20000 9.326321887 9.326272 -0.000536
7.00E-05 14285.71 8.98986965 8.9898 -0.000779
1.00E-04 10000 8.633224705 8.633125 -0.001158
2.00E-04 5000 7.940177517 7.939978 -0.002519
5.00E-04 2000 7.024186732 7.023687 -0.0071181.00E-03 1000 6.331539364 6.33054 -0.015792
2.00E-03 500 5.639391434 5.637392 -0.03546
4.00E-03 250 4.948241257 4.944245 -0.080821
7.00E-03 142.8571 4.391617234 4.384629 -0.15937
1.50E-02 66.66667 3.63743335 3.622489 -0.412532
3.00E-02 33.33333 2.959118724 2.929342 -1.016491
5.00E-02 20 2.467898489 2.418517 -2.041825
8.00E-02 12.5 2.026941003 1.948513 -4.025019
1.20E-01 8.333333 1.659541752 1.543048 -7.5495961.80E-01 5.555556 1.309796135 1.137583 -15.13854
2.50E-01 4 1.044282634 0.809079 -29.07059
3.50E-01 2.857143 0.794215435 0.472606 -68.05006
5.00E-01 2 0.559773595 0.115932 -382.8485
5.61E-01 1.783167 0.492204854 0.001175 -41779.85
1.00E+00 1 0.219383934 -0.57722 138.00727
1.40E+00 0.714286 0.116219313 -0.91369 112.7198
2.00E+00 0.5 0.048900511 -1.27036 103.849332.50E+00 0.4 0.024914918 -1.49351 101.66822
3.00E+00 0.333333 0.013048381 -1.67583 100.77862
3.50E+00 0.285714 0.00697014 -1.82998 100.38089
4.00E+00 0.25 0.003779352 -1.96351 100.19248
4.50E+00 0.222222 0.002073401 -2.08129 100.09962
5 00E 00 0 2 0 001148296 2 18665 100 05251
0.001
0.01
0.1
1
10
0 1
W(u)
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mult = mult * -1
uuu = uu / (x * Fact)
WF = WF + mult * uuuuu = u * uu
x = x + 1
Wend
WellFunc = WF
End Function
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1 10 100 1000 10000
Theis Type Curve
W(u)
C-J Approx.
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0.01
0.1
1
10
0.1 1 10 100 1000 10000
W(u)
.
1/u
Theis Type Curve
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0.01
0.1
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0.1 1 10 100 1000 10000
ho-h
.
Time
Data Plot
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Theis type curve matching (Match point method)
To minimize the Average % difference between the data and the Theis equation calculation
Use the arrows on the data plot to match the type curve to the data
(or use the solver tool)Minimize Type curve shifting
r = 32.5 ft Av. % difference course fine
Q= 163 ft /hr 60.32423 233 50
233 50
Field Data Theis eq. for comparison
t (hr) ho-h (ft) ho-h calcul %diff
0.01 0.867 0.043113 95.026780.02 1.879 0.239983 87.22767
0.05 3.657 0.885563 75.78671
0.1 5.193 1.629527 68.61979
0.2 6.811 2.512471 63.11318
0.5 9.013 3.79485 57.89696
0.7 9.831 4.283794 56.42646
1 10.701 4.808308 55.06838
2 12.398 5.839437 52.901945 14.648 7.215452 50.74222
7 15.475 7.722653 50.09751
10 16.353 8.260949 49.48236
20 18.058 9.308256 48.45287
50 20.312 10.69403 47.35246
100 22.018 11.74279 46.66823
1
10
100
ho-h(ft)
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Match Point Calculationsump = 1
W(u)mp = 1
tmp = 0.023988 S = 7.79E-04
(ho-h)mp = 1.513561 T = 8.57 ft /hr
u
3.3333332
1.2
0.72
0.432
0.2592
0.15552
0.093312
0.055987
0.033592
0.020155
0.012093
0.007256
0.004354
0.002612
0.001567
0.00094
0.0005640.000339
0.000203
0.000122
7.31E-05
4.39E-05
ata Plot and Theis Type Curve Match
Field Data
Type Curve
7.79E-04S=
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To minimize the Average % difference between the data and the modelUse the arrows on the data plot or enter values in the green cells or
Use the solver tool
Shifted Type Curve
Type Curve 4 2.2
1/u W(u) 1/u shift W(u) Shift
0.3 0.00857445 0.007196499 0.0129780.5 0.04890051 0.011994165 0.074014 0.001 0.001
0.833333 0.15840844 0.019990274 0.239761 0.002 0.002
1.388889 0.35991791 0.033317124 0.544758
2.314815 0.65159785 0.05552854 0.986233
3.858025 1.01626581 0.092547566 1.538181
6.430041 1.43344168 0.154245944 2.169602
10.71674 1.88577047 0.257076573 2.854229
17.86123 2.36062973 0.428460955 3.572958
29.76871 2.84955445 0.714101592 4.312975
49.61452 3.34712205 1.19016932 5.066074
82.69086 3.84995016 1.983615533 5.827135
137.8181 4.35596182 3.306025889 6.593015
229.6968 4.86389347 5.510043148 7.361801
382.828 5.3729807 9.183405247 8.132335
638.0467 5.88276256 15.30567541 8.903921
1063.411 6.39296166 25.50945902 9.676139
1772.352 6.90341128 42.51576503 10.448742953.92 7.41401126 70.85960838 11.22156
4923.2 7.92470149 118.0993473 11.99452
8205.334 8.43544587 196.8322455 12.76756
13675.56 8.94622275 328.0537425 13.54066
22792.59 9.45701913 546.7562375 14.31378
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Increment
Minimize S = 1.45E-04 S*10 =
r = 32.5 m Av. % difference Increment
Q= 163 ft3/hr 0.249225 T = 5.27 ft
2/hr
Field Data Model for comparison Model Fit (solid line on graph)
t (hr) ho-h (ft) ho-h calcul %diff t (hr) ho-h (ft)
0.01 0.867 0.875061 0.941271 0.01 0.87506077
0.02 1.879 1.890675 0.625295 0.015 1.4255805
0.05 3.657 3.671962 0.399774 0.02 1.89067489
0.1 5.193 5.208577 0.302856 0.03 2.631445330.2 6.811 6.827608 0.239465 0.05 3.67196174
0.5 9.013 9.029915 0.184964 0.07 4.40404463
0.7 9.831 9.847924 0.170283 0.1 5.20857652
1 10.701 10.71818 0.156925 0.15 6.14871312
2 12.398 12.41532 0.13594 0.2 6.82760751
5 14.648 14.66524 0.115312 0.3 7.79622684
7 15.475 15.49238 0.109194 0.5 9.02991533
10 16.353 16.36951 0.103369 0.7 9.84792406
20 18.058 18.07467 0.093642 1 10.71818350 20.312 20.32941 0.083266 1.5 11.7102173
100 22.018 22.03528 0.07682 2 12.4153192
3 13.4103205
5 14.6652409
7 15.4923837
10 16.3695069
15 17.3668881
20 18.0746662
30 19.0723453
50 20.3294095
70 21.1574713
100 22.0352839
150 23.0332014
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1.00E-06 To minimize the Average % difference between the data and the model
145 Change T and S using the arrows or entering values in the yellow cells or
0.01 Use the solver tool
599
0.001 0.001
0.002 0.002
0.1
1
10
100
0 01 0 1 1 10 100
ho-h(ft)
.
Data Plot
Field Data
Model Fit
1.45E-04
5.27
S=
T= m2/hr
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0.1
1
10
100
0.01 0.1 1 10 100
ho-h(ft)
.
time (hr)
Data Plot
Field Data
Model Fit
1.45E-04
5.27
S=
T= m2/hr
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Cooper-Jacob Analysis
Minimize S =
r = 32.5 m Av. % difference
Q= 163 ft3/hr 3.676333 T =
Field Data Model for comparison Theis Fit
t (hr) ho-h (ft) ln(t) ho-h calcul %diff t (hr)
0.01 0.867 -4.605 0.849334 2.026345 0.01
0.02 1.879 -3.912 1.886668 0.412061 0.015
0.05 3.657 -2.996 3.737431 2.189861 0.02
0.1 5.193 -2.303 5.3467 2.962727 0.030.2 6.811 -1.609 7.047699 3.47074 0.05
0.5 9.013 -0.693 9.365557 3.908835 0.07
0.7 9.831 -0.357 10.22709 4.027017 0.1
1 10.701 0.000 11.14385 4.134597 0.15
2 12.398 0.693 12.93206 4.303693 0.2
5 14.648 1.609 15.30313 4.469985 0.3
7 15.475 1.946 16.17487 4.519315 0.5
10 16.353 2.303 17.09931 4.566284 0.7
20 18.058 2.996 18.89649 4.644727 150 20.312 3.912 21.27295 4.728413 1.5
100 22.018 4.605 23.07093 4.780397 2
3
5
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10
15
20
30
50
70
100
150
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Set the data range of Slope and Intercept for the log-linear p
1.46E-04 S*10 = 146 If you change the range of the data plotted the log-linear tren
The T and S will be calculated below using the Slope and Int
5 ft2/hr
thin line on C-J Fit to = 0.012352 Slope of h 2.4428729 Intercept of
ho-h (m) D(ho-h) = T= 5.31 m2/hr S=
0.8493345 -0.51593
1.4089027 0.474574 0.001 0.001
1.8866684 1.177345 0.002 0.002
2.6533427 2.1678453.7374313 3.415727
4.5032422 4.237685
5.3466996 5.108997
6.333987 6.099497
7.0476993 6.802267
8.0667585 7.792767
9.3655569 9.040649
10.227087 9.862608
11.143849 10.7339212.189071 11.72442
12.932057 12.42719
13.980596 13.41769
15.303129 14.66557
16.174871 15.48753
17.09931 16.35884
18.150511 17.34934
18.89649 18.05211
19.948025 19.04261
21.272955 20.29049
22.145725 21.11245
23.070935 21.98376
24.122736 22.97426
y = 2.4428729ln(x) + 10.7338813
0
5
10
15
20
25
30
0.01 0.1 1 10
ho-h(ft)
.
time (hr)
Data Plot
Field Data
C-J Fit0.000139
5.31
Theis Fit
Log (Field Data)
S=
T= m2/hr
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rtion of the data
d line formula should match the Slope and Intercept calsulated
rcept, respectively.
10.7338813
0.000139
S=
T= m2/hr
100 1000
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y = 2.4428729ln(x) + 10.7338813
0
5
10
15
20
25
30
35
0.01 0.1 1 10 100 1000
ho-h(ft)
.
time (hr)
Data Plot
Field Data
Theis Fit
0.000139
5.31
Log. (Field Data)