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CHAPTER 15: SINGLE WELL TESTS Presented by: Lauren Cameron

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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!

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METHODS TO ANALYZE SINGLE-WELL TESTS Constant Discharge Confined aquifers Papadopulous-Cooper Method Rushton-Singh’s ratio method Confined and Leaky aquifers Jacob’s Straight-Line method Hurr-Worthington’s method Variable-Discharge Confined Aquifers Birsoy-Summers’s method Jacob-Lohman’s free-flowing-well method Leaky aquifers Hantush’s free flowing-well method

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IMPORTANT NOTE

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RECOVERY TESTS Theis’s Recovery Method Birsoy-Summer’s’ recovery method Eden-Hazel’s recovery Method

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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

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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

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PAPADOPULOS-COOPER’S METHOD 2: THE EQUATION This method uses the following equation to generate a family of type curves:

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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

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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

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RUSHTON-SINGH’S RATIO METHOD 2: EQUATION The following ratio is used:

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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

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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

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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

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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

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HURR-WORTHINGTON’S METHOD 1: ASSUMPTIONS/USES CONTINUED

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HURR-WORTHINGTON’S METHOD 2: THE EQUATION

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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

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VARIABLE DISCHARGE METHODS Confined Aquifers Birsoy-Summers’s method Jacob-Lohman’s free-flowing-well method Leaky aquifers Hantush’s free flowing-well method

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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

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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

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JACOB-LOHMAN’S FREE FLOWING- WELL METHOD 2: EQUATION

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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

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LEAKY AQUIFTERS, HANTUSH’S FREE- FLOWING WELL METHOD 2 : EQUATION

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RECOVERY TESTS Theis’s Recovery Method Birsoy-Summer’s’ recovery method Eden-Hazel’s recovery Method

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THEIS’S RECOVERY METHOD 1: ASSUMPTIONS Theis recovery method, 13.1.1, is also applicable to data from single-well For Confined, leaky, or unconfined aquifers

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THEIS’S RECOVERY METHOD 2: REMARKS

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BIRSOY-SUMMERS’S RECOVERY METHOD Data type Residual 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

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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

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