Chapter 15: Single Well tests
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Transcript Chapter 15: Single Well tests
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