1. Chapter 15: Single Well tests
Presented by: Lauren Cameron

2. What is a Single Well Test?
A single-well test is a test in which no piezometers are used
Water-level changes are measured in the well
Influenced by well losses and bore-storage
Must be considered
Decreases with time and is negligible at t > 25r,2/KD
To determine if early-time drawdown data are dominated by well- bore storage:
Plot log-log of drawdown s vs. pumping time
Early time drawdown = unit–slope straight line = SIGNIFICANT bore storage effect
Recovery test is important to do!
What is a Single Well Test?

3. Methods to analyze Single-well tests
Constant Discharge
Variable-Discharge
Confined aquifers
Papadopulous-Cooper Method
Rushton-Singh’s ratio method
Confined and Leaky aquifers
Jacob’s Straight-Line method
Hurr-Worthington’s method
Confined Aquifers
Birsoy-Summers’s method
Jacob-Lohman’s free-flowing-well method
Leaky aquifers
Hantush’s free flowing-well method
Methods to analyze Single-well tests

4. Important note

5. Recovery Tests Theis’s Recovery Method
Birsoy-Summer’s’ recovery method
Eden-Hazel’s recovery Method
Recovery Tests

6. Constant Discharge Methods
Confined aquifers
Papadopulous-Cooper Method
Rushton-Singh’s ratio method
Confined and Leaky aquifers
Jacob’s Straight-Line method
Hurr-Worthington’s method
Constant Discharge Methods

7. Papadopulos-Cooper’s Method 1: assumptions
Curve Fitting Method
Constant Discharge
Fully Penetrating Well
Confined Aquifer
Takes Storage capacity of well into account
Assumptions:
Chapter 3 assumptions, Except that storage cannot be neglected
Added: Flow to the well is in UNSTEADY state
Skin effects are negligible
Papadopulos-Cooper’s Method 1: assumptions

8. Papadopulos-Cooper’s Method 2: The Equation
This method uses the following equation to generate a family of type curves:
Papadopulos-Cooper’s Method 2: The Equation

9. Papadopulos-Cooper’s Method 3: remarks
The early-time = water comes from inside well
Points on data curve that coincide with early time part of type curve, do not adequately represent aquifer
If the skin factor or linear well loss coefficient is known
S CAN be calculated via equations or 15.3
S is questionable
Papadopulos-Cooper’s Method 3: remarks

10. Rushton-Singh’s ratio Method 1: Assumpions/uses
Confined aquifers
Papadopulos-Cooper type curves = similar
Difficult to match data to (enter Rushton-Sing’s Ratio method)
More sensitive curve-fitting method
Changes in well drawdown with time are examined (ratio)
Assumptions
Papadopulos-Cooper’s Method
Rushton-Singh’s ratio Method 1: Assumpions/uses

11. Rushton-Singh’s ratio Method 2: Equation
The following ratio is used:
Rushton-Singh’s ratio Method 2: Equation

12. Rushton-Singh’s ratio Method 3: Remarks
Values of ratio are between 2.5 and 1.0
Upper value = beginning of (constant discharge) test
Type curves are derived from numerical model
Annex 15.2
Rushton-Singh’s ratio Method 3: Remarks

13. Jacob’s Straight Line Method 1: Uses/Assumptions
Confined AND Leaky aquifers
Can also be used to estimate aquifer transmissivity.
Single well tests
Not all assumptions are met so additional assumptions are added
Jacob’s Straight Line Method 1: Uses/Assumptions

14. Jacob’s Straight Line Method 2: Remarks
Drawdown in well reacts strongly to even minor variations in discharge rate
CONSTANT DISCHARGE
No need to correct observed drawdowns for well losses
In theory:
Works for partially penetrating well (LATE TIME DATA ONLY!)
Use the “1 ½ log cycle rule of thumb” to determine is well-bore storage can be neglected
Jacob’s Straight Line Method 2: Remarks

15. Hurr-Worthington’s Method 1: assumptions/Uses
Confined and Leaky Aquifers
Unsteady-State flow
Small-Diameter well
Chapter 3 assumptions Except
Aquifer is confined or leakey
Storage in the well cannot be neglected
Added conditions
Flow the well is UNSTEADY STATE
Skin effect is neglegable
Storativity is known or can be estimated
Hurr-Worthington’s Method 1: assumptions/Uses

16. Hurr-Worthington’s Method 1: assumptions/Uses continued

17. Hurr-Worthington’s Method 2: The Equation

18. Hurr-Worthington’s Method 3: Remarks
Procedure permits the calculation of (pseudo) transmissivity from a single drawdown observation in the pumped well. The accuracy decreases as Uw decreases
If skin effect losses are not negligible, the observed unsteady- state drawdowns should be corrected before this method is applied
Hurr-Worthington’s Method 3: Remarks

19. Variable Discharge Methods
Confined Aquifers
Birsoy-Summers’s method
Jacob-Lohman’s free-flowing-well method
Leaky aquifers
Hantush’s free flowing-well method
Variable Discharge Methods

20. Birsory-Summers’s Method :
The Birsory-Summers’s method from can be used for variable discharges
Parameters s and r should be replaced by Sw and rew
Same assumptions as Birsory-Summers’s method in
Birsory-Summers’s Method :

21. Jacob-Lohman’s free flowing-well method 1: Assumptions
Confined Aquifers
Chapte 3 assumptions
Except:
At the begging of the test, the water level in the free-flowing well is lowered instantaneously. At t>0, the drawdown in the well is constant and its discharge is variable.
Additionally:
Flow in the well is an unsteady state
Uw is < 0.01
Remark: if t value of rew is not known, S cannot be determined by this method
Jacob-Lohman’s free flowing-well method 1: Assumptions

22. Jacob-Lohman’s free flowing-well method 2: Equation

23. Leaky aquifters, Hantush’s free-flowing well method 1 : Assumptions
Variable discharge
Free-flowing
Leaky aquifer
Assumptions in Chapter 4
Except
At the begging of the test, the water level in the free-flowing well is lowered instantaneously. At t>0, the drawdown in the well is constant and its discharge is variable.
Additionally:
Flow is in unsteady state
Aquitard is incompressible, changes in aquitard storage are neglegable
Remark: if effective well radius is not known, values of S and c cannot be obtained
Leaky aquifters, Hantush’s free-flowing well method 1 : Assumptions

24. Leaky aquifters, Hantush’s free-flowing well method 2 : Equation

25. Recovery Tests Theis’s Recovery Method
Birsoy-Summer’s’ recovery method
Eden-Hazel’s recovery Method
Recovery Tests

26. Theis’s Recovery Method 1: Assumptions
Theis recovery method, , is also applicable to data from single-well
For
Confined, leaky, or unconfined aquifers
Theis’s Recovery Method 1: Assumptions

27. Theis’s Recovery Method 2: Remarks

28. Birsoy-Summers’s Recovery Method
Data type
R esidual drawdown data from the recovery phase of single-well variable-discharge tests conducted in confined aquifers
Birsoy-Summers’s Recovery Method in can be used
Provided that s’ is replaced by s’w
Birsoy-Summers’s Recovery Method

29. Eden-Hazel Method : uses/Assumptions
For Step-drawdown tests (14.1.2) is applicable to data from the recovery phase of such a test
Assumptions in Chapter 3 (adjusted for recovery test:s)
Except:
Prior the recovery test, the aquifer is pumped stepwise
Additionally
Flow in the well is in unsteady state
u < 0.01
u’ < 0.01
Eden-Hazel Method : uses/Assumptions