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A water budget perspective of leaky aquifer response
to pumping
David Scott1 and Bruce Hunt2
1Environment Canterbury2University of Canterbury (Retired)
Characterizing leaky aquifers
Standard measures– Leakance - units of length– K’/B’ - units of 1/time
Alternative measure– t50 - units of time
More general applicability
Hypothetical example
Water table aquifer (B = 5m)
Pumped aquifer (B = 10m)
Aquitard (B = 5m)
200 m
Q = 50 L/s
Vertical drainage after 0.1 days
1 mm drawdown, 1 km radius circle
Specific yield 0.1
Volume = 314 m3, Qavg = 36 L/s
Qavg = 72% of pumping rate
Drainage rate
0
12.5
25
37.5
50
0.001 0.01 0.1 1 10 100 1000
Time (days)
Flo
w r
ate
(l/s
) Instantaneous drainage rate
Average drainage rate
Drainage rate
0
12.5
25
37.5
50
0.001 0.01 0.1 1 10 100 1000
Time (days)
Flo
w r
ate
(l/s
)
Instantaneous Drainage rate
Numerical model
0
10
20
30
40
50
0.001 0.01 0.1 1 10 100 1000
Time (days)
Flo
w r
ate
(l/s
)
0
0.4
0.8
1.2
1.6
2
Dra
wd
ow
n (
m)
Drainage rate
Water table drawdownPumped aquifer drawdown
Drainage rate & drawdown
Sensitivity of t50 to Sy, T0 & K’/B’
0
0.05
0.1
0.15
1 10 100 1000 10000
Sy/S
t 50
(day
s)
Sy
0
0.005
0.01
0.015
0.02
0.025
0.03
1 10 100 1000 10000
T0 (m2/day)
t 50
(day
s)T0
0.001
0.01
0.1
1
10
100
0.000001 0.00001 0.0001 0.001 0.01 0.1
K'/B' (1/days)
t 50
(da
ys
)
K'/B'
Clay
Silt, sandy silt
Modflow solution
● Independent check● Allows consideration of less
idealised cases● Underlying layer● Sloping aquifer● Alternative boundary conditions
● Zone budget● Modpath - visualisation
Effect of an underlying layer?
0
12.5
25
37.5
50
0.001 0.01 0.1 1 10 100 1000
Time (days)
Flo
w r
ate
(l/s
) 2 aquifer case
3 layer case
from lower aquiferr
Pumping from the lower layer…
0
12.5
25
37.5
50
0.001 0.01 0.1 1 10 100 1000
Time (days)
Flo
w r
ate
(l/s
)
2 aquifer case
3 layer case
pumping from lower layer
Effects of adjacent boundary
0
12.5
25
37.5
50
0.001 0.01 0.1 1 10 100 1000
Time (days)
Flo
w r
ate
(l/s
) 5 km from boundary
2 aquifer case
2 km from boundary
Sloping aquifer (1:1000)
0
10
20
30
40
50
0.001 0.01 0.1 1 10 100 1000 10000
Time (days)
Flo
w r
ate
(l/s
)
2 aquifer case
sloping
Conclusions
Vertical drainage can develop to become a significant proportion of the pumping rate in a relatively short time
t50 value provides a useful measure of aquifer leakiness
Water budget perspective provides a parallel to Theis’s analysis of the “source of water derived from wells”
Leaky aquifers leak!
0
10
20
30
40
50
0.001 0.01 0.1 1 10 100 1000
Time (days)
Flo
w r
ate
(l/
s)
2 aquifer case
drainage from shallow aquifer
total vertical drainage through aquitard
released from aquitard storage
Aquitard storativity
Empirical expression for t50
y = 0.697x
0.0001
0.001
0.01
0.1
1
10
100
1000
0.0001 0.001 0.01 0.1 1 10 100 1000
S/(K'/B') (days)
t 50 (
day
s)
“. . . the term aquitard has been coined to describe the less-permeable beds in a stratigraphic sequence. These beds may be permeable enough to transmit water in quantities that are significant in the study of regional ground-water flow, but their permeability is not sufficient to allow the completion of production wells within them.”
—Freeze and Cherry,1979