Chap4 by jizhen1947

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									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.


Example Leaky Aquifer




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
             8) 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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