CHAPTER 15: SINGLE WELL
TESTS
Presented by: Lauren Cameron

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 wellbore 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?
Constant Discharge


Confined aquifers
Variable-Discharge

Confined Aquifers

Papadopulous-Cooper Method

Birsoy-Summers’s method

Rushton-Singh’s ratio method

Jacob-Lohman’s free-flowing-well
method
Confined and Leaky aquifers

Jacob’s Straight-Line method

Hurr-Worthington’s method

Leaky aquifers

Hantush’s free flowing-well method
METHODS TO ANALYZE SINGLE-WELL
TESTS
IMPORTANT NOTE
 Theis’s
Recovery Method
 Birsoy-Summer’s’
 Eden-Hazel’s
recovery method
recovery Method
RECOVERY TESTS


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

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

This method uses the following equation to generate a family of
type curves:
PAPADOPULOS-COOPER’S METHOD
2: THE EQUATION

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 15.2 or 15.3

S is questionable
PAPADOPULOS-COOPER’S METHOD
3: REMARKS

Confined aquifers

Papadopulos-Cooper type curves = similar


More sensitive curve-fitting method


Difficult to match data to (enter Rushton-Sing’s Ratio method)
Changes in well drawdown with time are examined (ratio)
Assumptions

Papadopulos-Cooper’s Method
RUSHTON-SINGH’S RATIO METHOD 1:
ASSUMPIONS/USES

The following ratio is used:
RUSHTON-SINGH’S RATIO METHOD 2:
EQUATION

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

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

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



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
HURR-WORTHINGTON’S METHOD 1:
ASSUMPTIONS/USES CONTINUED
HURR-WORTHINGTON’S METHOD 2:
THE EQUATION

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 unsteadystate drawdowns should be corrected before this method is
applied
HURR-WORTHINGTON’S METHOD 3:
REMARKS


Confined Aquifers

Birsoy-Summers’s method

Jacob-Lohman’s free-flowing-well method
Leaky aquifers

Hantush’s free flowing-well method
VARIABLE DISCHARGE METHODS

The Birsory-Summers’s method from 12.1.1can be used for
variable discharges


Parameters s and r should be replaced by Sw and rew
Same assumptions as Birsory-Summers’s method in 12.1.1
BIRSORY-SUMMERS’S METHOD :

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 FLOWINGWELL METHOD 1: ASSUMPTIONS
JACOB-LOHMAN’S FREE FLOWINGWELL METHOD 2: EQUATION

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 FREEFLOWING WELL METHOD 1 : ASSUMPTIONS
LEAKY AQUIFTERS, HANTUSH’S FREEFLOWING WELL METHOD 2 : EQUATION
 Theis’s
Recovery Method
 Birsoy-Summer’s’
 Eden-Hazel’s
recovery method
recovery Method
RECOVERY TESTS

Theis recovery method, 13.1.1, is also applicable to data from
single-well

For

Confined, leaky, or unconfined aquifers
THEIS’S RECOVERY METHOD 1:
ASSUMPTIONS
THEIS’S RECOVERY METHOD 2:
REMARKS

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 13.3.1 can be used

Provided that s’ is replaced by s’w
BIRSOY-SUMMERS’S RECOVERY
METHOD

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