1. Chapter 4- Leaky Aquifers
Analysis and Evaluation of Pumping Test Data, Revised Second Edition

2. 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.

3. Example
A deep sedimentary basin where an interbedded system of permeable and less permeable layers form a multi-layered aquifer system.

4. 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.

5. What Happens When We Start to Pump the Well?
The piezometric surface in the lower confined will drop.
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.
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.

6. 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.

7. Assumptions 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.

8. Additional Assumptions for Unsteady State Conditions
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

9. Pumping Test “Dalem”

10. 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.

11. 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

12. 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:

13. De Glee’s Method (cont’d)
Analysis of data from pump test with De Glee Method

14. 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:

15. 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:

16. 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.

17. 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.

18. Walton’s Method (cont’d)
Walton uses a type curve for each value of r/L to produce a family of type curves.

19. Walton’s Method (cont’d)
After data acquisition, we can fit the type curve to the observed data curve:

20. 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

21. 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:

22. 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:

23. 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:

24. Hantush’s Curve-Fitting Method (cont’d)
Analysis of pumping test data:

25. 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:

26. 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: