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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

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Chapter 15: Single Well tests

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

  2. 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. 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

  4. Important note

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

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

  9. 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

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

  12. 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. 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. 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. 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. 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

  19. 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. 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 :

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

  26. 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

  27. Theis’sRecovery Method 2: Remarks

  28. 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

  29. 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

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