Environmental Engineering Reference
In-Depth Information
TABLE 5.2. Well Function for Leaky Aquifer,
W
(
α
,
β
)
β
α
0.00
0.002
0.004
0.007
0.01
0.02
0.04
0.06
0.08
0.10
0.00
12.6611
11.2748
10.1557
9.4425
8.0569
6.6731
5.8456
5.2950
4.8541
1 × 10
−6
13.2383
12.4417
11.2711
10.1557
·
·
·
·
·
·
2 × 10
−6
12.5451
12.1013
11.2259
10.1554
·
·
·
·
·
·
5 × 10
−6
11.6289
11.4384
10.9642
10.1290
9.4425
·
·
·
·
·
8 × 10
−6
11.1589
11.0377
10.7151
10.0602
9.4313
·
·
·
·
·
1 × 10
−5
10.9357
10.8382
10.5725
10.0034
9.4176
8.0569
·
·
·
·
2 × 10
−5
10.2426
10.1932
10.0522
9.7126
9.2961
8.0558
·
·
·
·
5 × 10
−5
9.3263
9.3064
9.2480
9.0957
8.8827
8.0080
6.6730
·
·
·
7 × 10
−5
8.9899
8.9756
8.9336
8.8224
8.6625
7.9456
6.6726
·
·
·
1 × 10
−4
8.6332
8.6233
8.5937
8.5145
8.3983
7.8375
6.6693
5.8658
5.2950
4.8541
2 × 10
−4
7.9402
7.9352
7.9203
7.8800
7.8192
7.4472
6.6242
5.8637
5.2949
4.8541
5 × 10
−4
7.0242
7.0222
7.0163
6.9999
6.9750
6.8346
6.3626
5.8011
5.2848
4.8530
7 × 10
−4
6.6879
6.6865
6.6823
6.6706
6.6527
6.5508
6.1917
5.7274
5.2618
4.8478
1 × 10
−3
6.3315
6.3305
6.3276
6.3194
6.3069
6.2347
5.9711
5.6058
5.2087
4.8292
2 × 10
−3
5.6394
5.6389
5.6374
5.6334
5.6271
5.5907
5.4516
5.2411
4.9848
4.7079
5 × 10
−3
4.7261
4.7259
4.7253
4.7237
4.7212
4.7068
4.6499
4.5590
4.4389
4.2990
7 × 10
−3
4.3916
4.3915
4.3910
4.3899
4.3882
4.3779
4.3374
4.2719
4.1839
4.0771
1 × 10
−2
4.0379
4.0378
4.0375
4.0368
4.0351
4.0285
4.0003
3.9544
3.8920
3.8190
2 × 10
−2
3.3547
3.3547
3.3545
3.3542
3.3536
3.3502
3.3365
3.3141
3.2832
3.2442
5 × 10
−2
2.4679
2.4679
2.4678
2.4677
2.4675
2.4662
2.4613
2.4531
2.4416
2.4271
7 × 10
−2
2.1508
2.1508
2.1508
2.1507
2.1506
2.1497
2.1464
2.1408
2.1331
2.1232
1 × 10
−1
1.8229
1.8229
1.8229
1.8228
1.8227
1.8222
1.8220
1.8164
1.8114
1.8050
2 × 10
−1
1.2227
1.2226
1.2226
1.2226
1.2226
1.2224
1.2215
1.2201
1.2181
1.2155
5 × 10
−1
0.5598
0.5598
0.5598
0.5598
0.5598
0.5597
0.5595
0.5592
0.5587
0.5581
7 × 10
−1
0.3738
0.3738
0.3738
0.3738
0.3738
0.3737
0.3736
0.3734
0.3732
0.3729
1.00
0.2194
0.2194
0.2194
0.2194
0.2194
0.2194
0.2193
0.2192
0.2191
0.2190
2.00
0.0489
0.0489
0.0489
0.0489
0.0489
0.0489
0.0489
0.0489
0.0489
0.0488
5.00
0.0011
0.0011
0.0011
0.0011
0.0011
0.0011
0.0011
0.0011
0.0011
0.0011
7.00
0.0001
0.0001
0.0001
0.0001
0.0001
0.0001
0.0001
0.0001
0.0001
0.0001
8.00
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
where
K
0
is the modified Bessel function of the second
kind of order zero (described in Appendix D.2).
0.1 kg/m
3
. The steady-state concentration is given by
Equation (5.24) as
=
Qc
H D D
Vx
D
EXAMPLE 5.3
o
c x y
( ,
)
exp
1 2
/
2
π
(
)
2
L
T
L
A conservative contaminant is injected continuously
through a 4-m-deep perforated well into an aquifer with
a mean seepage velocity of 0.8 m/day and longitudinal
and transverse dispersion coefficients of 2 and 0.2 m
2
/d,
respectively. If the injection rate of the contaminated
water is 0.7 m
3
/d, with a contaminant concentration of
100 mg/L, estimate the steady-state contaminant con-
centrations at locations 1, 10, 100, and 1000 m down-
stream of the injection well. neglect vertical diffusion.
1
2
V
D
2
x
D
2
y
D
2
K
+
0
4
L
L
T
which yields
( . )( . )
( )(
0 7 0 1
( . )
( )
0 8
2 2
x
c x
( , )
0
=
exp
2
π
4 2 0 2
×
. )
1 2
/
1
2
Solution
2
2
0 8
4 2
.
x
K
0
×
2
From the data given,
H
= 4 m,
V
= 0.8 m/d,
D
L
= 2 m
2
/d,
D
T
= 0.2 m
2
/d,
Q
= 0.7 m
3
/d,
and
c
o
= 100 mg/L =
=
0 00440
.
exp( .
0 2
x K
)
( .
0 2
x
) kg/m
3
0
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