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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

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chapter 15 single well tests

Chapter 15: Single Well tests

Presented by: Lauren Cameron

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?
methods to analyze single well tests
Constant Discharge

Variable-Discharge

Confined Aquifers

Birsoy-Summers’s method

Jacob-Lohman’s free-flowing-well method

Leaky aquifers

Hantush’s free flowing-well method

  • Confined aquifers
    • Papadopulous-Cooper Method
    • Rushton-Singh’s ratio method
  • Confined and Leaky aquifers
    • Jacob’s Straight-Line method
    • Hurr-Worthington’s method
Methods to analyze Single-well tests
recovery tests

Theis’s Recovery Method

  • Birsoy-Summer’s’ recovery method
  • Eden-Hazel’s recovery Method
Recovery Tests
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
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
papadopulos cooper s method 3 remarks

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
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
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
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
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
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
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 Uwdecreases

  • 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
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
birsory summers s method

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 :
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
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
recovery tests1

Theis’s Recovery Method

  • Birsoy-Summer’s’ recovery method
  • Eden-Hazel’s recovery Method
Recovery Tests
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 13.3.1 can be used
    • Provided that s’ is replaced by s’w
Birsoy-Summers’s Recovery Method
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