Chapter 4- Leaky Aquifers
Analysis and Evaluation of Pumping
Test Data, Revised Second Edition
Definition
A leaky aquifer, also known as a semi-confined aquifer, is an aquifer whose
upper and lower boundaries are aquitards, or one boundary is an aquitard
and the other is an aquiclude.
An aquitard is a geological unit that is permeable enough to transmit water in
significant quantities when viewed over large areas and long periods, but its
permeability is not sufficient to justify production wells being placed in it.
Clays, loams, and shales are typical aquitards.
Example
A deep sedimentary basin where an interbedded system of permeable and
less permeable layers form a multi-layered aquifer system.
Description of Aquifer Considered in
Chapter 4 Solutions
The system consists of two aquifers separated by an aquitard. The lower
aquifer rests on an aquiclude. A well fully penetrates the lower aquifer and is
screened over the total thickness of the aquifer. The well is not screened in
the upper unconfined aquifer.
What Happens When We Start to
Pump the Well?
1.
The piezometric surface in the lower confined will drop.
2.
The water that the pumped aquifer contributes to the well discharge
comes from storage within the confined aquifer. The water contributed
by the aquitard comes from storage within the aquitard and leakage
through it from the overlying unpumped, unconfined aquifer.
3.
As pumping continues, more of the water comes from leakage from the
unconfined aquifer and relatively less from aquitard storage.
• The flow induced by the pumping is assumed to be vertical in the aquitard
and horizontal in the pumped aquifer.
Important Note
For a proper analysis of a pumping test in a leaky
aquifer, piezometers are required in the leaky confined
aquifer, in the aquitard, and in the upper unconfined
aquifer.
Assumptions
1.
2.
3.
4.
5.
6.
7.
8.
The aquifer is leaky (surprise, surprise)
The aquifer and the aquitard have a seemingly infinite areal extent
The aquifer and the aquitard are homogeneous, isotrpic, and of uniform
thickness over the area influenced by the pump test
Prior to pumping, the piezometric surface and the water table are
horizontal over the area that will be 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
The flow in the aquitard is vertical
The drawdown in the unpumped aquifer (or in the aquitard if there is no
unpumped aquifer) is neglible.
Additional Assumptions for Unsteady
State Conditions
1.
The water removed from storage in the aquifer and the water supplied by
leakage from the aquitard is discharged instantaneously with decline in
the piezometric surface
2.
The diameter of the well is so small that the storage in the well can be
neglected
Pumping Test “Dalem”
Steady State Flow
After a certain time, the well discharge comes into equilibrium with the
leakage through the aquitard, and a steady-state flow is attained.
Solutions to the steady state flow problem are found on these assumptions:
• During pumping, the water table in the upper unconfined aquifer remain
constant
• The rate of leakage from the upper unconfined aquifer into the leaky
aquifer is proportional to the hydraulic gradient across the aquitard.
The assumption of a constant water table will only be satisfied if the upper
unconfined aquifer is recharged by an outside source. Without recharge, the
water table will drop due to its water leakance through the aquitard into the
pumped, confined aquifer.
The second assumption completely ignores the storage capacity of the
aquitard. This is justified when the flow to the well has become steady and
the amount of water supplied from storage in the aquitard has become
negligibly small.
De Glee’s Method
This method uses steady state drawdown data and allows the characteristics
of the aquifer and the aquitard to be determined.
Can be used if all the assumptions listed at the beginning are met and these
conditions are met:
• The flow to the well is in steady state
• Leakage factor is greater than three times the saturated thickness of the
aquitard
De Glee’s Method (cont’d)
• For the steady state drawdown in an aquifer with leakage from an
aquitard proportional to the hydraulic gradient across the aquitard, this
solution is used:
De Glee’s Method (cont’d)
• Analysis of data from pump test with De Glee Method
Hantush-Jacob’s Method
This method uses steady state drawdown data and allows the characteristics
of the aquifer and the aquitard to be determined.
Can be used if all the assumptions listed at the beginning are met and these
conditions are met:
• The flow to the well is in steady state
• Leakage factor is greater than three times the saturated thickness of the
aquitard
• r/L < or = 0.05 (distance of piezometer from well / leakance factor)
The formula for this method is an approximation of De Glee’s solution:
Hantush-Jacob’s Method (cont’d)
The extended straight line portion of the curve intercepts the r axis where the
drawdown is zero (sm = 0 and r = r0), which reduces the equation to:
Unsteady State Flow
The additional assumptions for unsteady state flow are:
• The water removed from storage in the aquifer and the water supplied by
leakage from the aquitard is discharged instantaneously with decline in
the piezometric surface
• The diameter of the well is so small that the storage in the well can be
neglected
Two of the solutions for unsteady flow neglect the effect of aquitard storage,
which may result in:
• An overestimation of the leaky aquifer K
• An underestimation of the aquitard K
• A false impression of heterogeneity in the leaky aquifer.
Walton’s Method
Walton’s method can be applied if the following assumptions and conditions
are satisfied:
• All assumptions listed at the beginning of the chapter
• The aquitard is incompressible (the changes in aquitard storage are
neglible)
• The flow to the well is in unsteady state
This solution has the same form as the Theis well function, but there are two
parameters in the integral: u and r/L.
Walton’s Method (cont’d)
Walton uses a type curve for each value of r/L to produce a family of type
curves.
Walton’s Method (cont’d)
After data acquisition, we can fit the type curve to the observed data curve:
Hantush’s Inflection-Point Method
Hantush developed several procedures for the analysis of pumping test data
in leaky aquifers, all of them based on this equation:
One of the procedures uses drawdown data from a single piezometer, while
the other uses drawdown data from at least two piezometers.
Either of Hantush’s procedures of the inflection-point method can be used if
the following assumptions and conditions are satisfied:
• All the assumptions listed at the beginning of the chapter
• The aquitard is incompressible (the changes in aquitard storage are
negligle)
• The flow to the well is in unsteady state
• It must be possible to extrapolate the steady state drawdown for each
piezometer
Hantush’s Inflection-Point Method
(cont’d)
This is the graph of the Hantush Inflection Point Method procedure that uses the
drawdown data from a single piezometer:
Hantush’s Inflection-Point Method
(cont’d)
This is the graph of the Hantush Inflection Point Method procedure that uses
the drawdown data from 4 piezometers:
Hantush’s Curve-Fitting Method
Hantush’s curve-fitting method can be used if the following assumptions and
conditions are satisfied:
• The assumptions listed at the beginning of this chapter
• The flow to the well is in an unsteady state
• The aquitard is compressible (the changes in aquitard storage are significant)
• t < S’D’ / 10K’
Drawdown equation for unsteady flow:
Hantush’s Curve-Fitting Method
(cont’d)
Analysis of pumping test data:
Neuman-Witherspoon’s Method
The Neuman-Witherspoon Ratio Method can be applied if the following assumptions
and conditions are met:
• The assumptions listed at the beginning of the chapter
• The flow to the well is in an unsteady state
• The aquitard is compressible (the changes in aquitard storage are significant)
• The radial distance from the well to the piezometers should be small (<100m)
• t < S’D’ / 10K’
This is based on a theory for a “slightly leaking aquifer” where the drawdown in the
pumped aquifer is given by the Theis equation and the drawdown in the aquitard of
very low permeability is described by:
Summary
This chapter illustrates the methods of analyzing steady and unsteady flow to
a well in a leaky aquifer.
This table summarizes the values obtained from the different methods: