Chapter 3: Confined Aquifers
Draw a Confined Aquifer: (an aquifer bounded above and below by an aquiclude)
Aquiclude
Aquifer
Flow
Aquiclude
When a confined aquifer is pumped, the loss of hydraulic head happens rapidly because
the release of the water from storage is entirely due to the compressibility of the aquifer
material and the water. This means that the drawdown will be measurable at great
distances from the pumping well.
Because the pumped water must come from reduction of storage within the aquifer,
theoretically, only unsteady-state flow can exist. However, in practice, if the change in
drawdown has become negligibly small with time, it is considered to be in a steady-state.
Therefore there are methods for evaluating both steady-state flow and unsteady-state flow
pump tests.
Assumptions
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The aquifer is confined
The aquifer has a seemingly infinite areal extent
The aquifer is homogeneous, isotropic, and of uniform thickness over the area
influenced by the test
Prior to pumping, the piezometric surface is horizontal (or nearly so) over the area
influenced by the test
The aquifer is pumped at a constant discharge rate
The well penetrates the entire thickness of the aquifer and thus receives water by
horizontal flow
Additional assumptions for unsteady-state methods:
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The water removed from storage is discharged instantaneously with decline of head
The diameter of the well is small (i.e. the storage in the well can be neglected)
Confined Aquifer Example: Oude Korendijk
Steady-State Flow
 Thiem’s Method
(uses two or more piezometers)
Q= 2πT(sm1- sm2)
2.30 log (r2/r1)
or
T = 2.30 Q_ log r2/r1
2π(sm1- sm2)
Q= well discharge in m3/d
T= transmissivity in m2/d
r1 and r2= respective distances of the piezometers from the pumping well in m
sm1 and sm2= respective steady-state drawdowns in the piezometers in m
(note: there is an additional equation you can use if only one piezometer is available,
but it is of limited use, and should only be used when other methods can not be applied.
See pg. 57 equation 3.3 for more details)
There are two procedures that can be used to determine the transmissivity. Using semilog paper, the first method plots the drawdown of each piezometer against time (draw
in curve, Figure 3.3), and the other plots the drawdowns against the distance between
the well and the piezometer (draw in best-fitting straight line, Figure 3.4).
The first method uses the original equation, and the second uses a slightly reduced
equation: Q = 2πT Δsm (the slope of the line) or T= 2.30 Q
2.30
2πΔs
Note: The water level dropped in all piezometers throughout pumping, but it dropped
uniformly in H30 and H90 after a short amount of time, meaning that the hydraulic
gradient between these two wells was constant. Thiem’s method works under this
condition, which is called “transient steady-state flow”.
Unsteady-State Flow
 Theis Method
(introduces the time factor and Storativity)
s = Q_ W(u)
4πT
or T= QW(u)
4πs
Where:
u = r2S_ and consequently S= _4Tut_
4Tt
r2
t= time since pumping started
W(u) = - 0.577261 – ln u + u – _u2 + _u3 ……. (values can be found in Annex 3.1)
2x2! 3x3!
After plotting the observed drawdown versus time on log-log paper, you can superimpose the Theis curve on the data curve to find where they match (Figure 3.6). Then
choose an arbitrary point, and read it’s coordinates for W(u), 1/u, s, and t. (Calculations
can be simplified if you choose the point where W(u) = 1 and 1/u = 1.)
When using the Theis method and all curve-fitting methods, you should give less weight
to the early data because they may not closely represent the theoretical drawdown
equation on which the type curve is based.

Jacob’s Method
This method is based on the Theis equation, and is only valid when u ≤ 0.01
To achieve small values of u the piezometers needs to be close to the pumping well, and
the test needs to be performed over longer periods of time.
s = 2.3Q log 2.25Tt
4πT
r2S
There are three applications for Jacob’s Approximation:
1. s versus log t for one piezometer, at various times (r is constant)
2. s versus log r for several piezometers, at one time (t is constant)
3. s versus log t/r2 for several observation wells, at various times
For method 1 (Figure 3.7):
T= 2.3Q
4πΔs
and
S= 2.25Tt0
r2
For method 2: (you need at least 3 piezometers for reliable results)
T= -2.3Q and S= 2.25Tt
2πΔs
r0 2
For method 3:
T= 2.3Q
and
4πΔs
S= 2.25T (t/r2)0