Leaky Aquifers
-More likely to occur in the real-world than confined aquifers
-When a well in a leaky aquifer is pumped, it pulls water from the leaky aquifer
and from the aquifers above and below
When well is pumped, water from aquifer comes from storage, water is also supplied from storage in aquitard and water that leaks into it from the unpumped aquifer. Over time, more and more of the water pumped comes from storage in the unpumped aquifer until a steady state is reached.
Assumptions
-Overall 1) aquifer is leaky
2) aquifer and aquitard have an infinite areal extent
3) aquifer and aquitard are homogeneous, isotropic, and uniform thickness
4) prior to pumping, piezometric surface and water table are horizontal
5) aquifer is pumped at constant discharge rate
6) well is fully penetrating and receives water from horizontal flow
7) flow in aquitard is vertical
drawdown in unpumped aquifer is negligible
During unsteady state flow, storage capacity of the aquifer needs to be accounted for. If it is not, the following errors can occur:
-overestimation of K in leaky aquifer
-underestimation of K in aquitard
-false impression of inhomogeneity in leaky aquifer
Steady State Flow
Assumptions- 1) during pumping, the water table in the upper aquifer remains constant
2) the rate of leakage into the pumped aquifer is equal to the hydraulic gradient across the aquitard (ignores aquitard storage)
De Glee’s Method
Assumptions 1) flow to well is steady state
2) leakage factor is greater than 3 times the D (diffusivity? Or thickness?)
Example
Determine values for KD and c
-Plot values of drawdowns at piezometers at different distances away, make curve.
-Fit De Glee Type curve to plotted values, choose point where K0(r/L) =1 and r/L=1
Values of sm= 0.057m (drawdown) and r= 1100m (at well this far away)
Known Q of 761 m3/d
KD= Q x K0(r/L) = 761 x 1 = 2126m2/d
2π sm 2 x 3.14 x 0.057
c= r2/KD = (1100) 2 / 2126 = 569 d
Hantush- Jacob’s Method
Assumptions 1) flow to the well is steady state
2) L > 3D
3) r/L ≤ 0.05
sm~ 2.30Q x (log 1.12 (L/r))
2πKD
Example:
Plotted data from pump test and fit line to data points, sm versus r
Delta sm= 0.138m (from graph, one log cycle of r)
KD= 2.30 Q (Q is known, 761 m3/d)
2π Delta sm
KD= 2.30 x 761 = 2020 m2/d
2 x 3.14 x 0.138
C= (r0/1.12)2 r0 from graph
KD
C= (1100/1.12)2 = 982 m
2020
Unsteady State Flow
4 methods
- Walton curve-fitting and Hantush inflection point methods ignore aquitard storage
- Hantush Curve fitting and Neuman and Witherspoon ratio methods include aquitard storage
Assumptions
-Unsteady 1) water removed from storage in the aquifer and water supplied
State from leakage from aquitard is discharged instantaneously with
decline of head
2) storage in well can be ignored
Walton Curve Fitting Method
Assumptions 1) Aquitard is not compressible, so changes in aquitard storage are negligible
2) Flow to well is unsteady state
Similar to the Theis Method
s= Q x W(u, r/L)
4πKD
u= r2S
4KDt
Figure 4.5- Graph of various Walton’s type curves
Example:
-Plot values from pumping test on graph, s versus t
-Fit Walton’s type curve to plotted points to get values
KD= Q x W(u, r/L)
4πs
KD= 761 x 1 = 1731 m2/d
4 x 3.14 x 0.035
Hantush’s Inflection Point Method
Assumptions 1) aquitard is not compressible so aquitard storage is negligible
2) flow to the well is unsteady state
3) It must be possible to extrapolate the steady state drawdown for each piezometer
Can be used with a single piezometer or at least 2 piezometers
One piezometer method
-plot data from piezometer and extrapolate data to determine maximum drawdown
sp= half of maximum drawdown
delta sp comes from graph at log cycle
Hantush’s Curve Fitting Method
Includes aquitard storage
Assumptions 1) flow to the well is in an unsteady state
2) the aquitard is compressible
3) t < S’D’/10K’
-Uses type curves like the Walton and Theis methods
Example:
-Plot data from piezometer on graph, s versus t
-Fit Hantush’s type curve to plotted line to get values
Neuman-Witherspoon’s Method
Assumptions 1) Flow to the well is in unsteady state
2) the aquitard is compressible
3) radial distance from the well to the piezometer should be small (r < 100m)
4) t < S’D’/10K’
-Used for “slightly leaky” aquifers
Example:
Given values-
t= 4.58x10-2
sc= 0.009m
s= 0.171
KD= 1800 m2/d
S= 1.7x10-3
- now can use the graph to get values for 1/uc
Z=depth to bottom of aquitard
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