# Chapter 15: Single Well tests

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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 Papadopulous-Cooper Method Rushton-Singh’s ratio method Confined and Leaky aquifers Jacob’s Straight-Line method Hurr-Worthington’s method Confined Aquifers Birsoy-Summers’s method Jacob-Lohman’s free-flowing-well method Leaky aquifers Hantush’s free flowing-well method Methods to analyze Single-well tests

Important note

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

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

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

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 1: assumptions/Uses continued

Hurr-Worthington’s Method 2: The Equation

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 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 can be used for variable discharges Parameters s and r should be replaced by Sw and rew Same assumptions as Birsory-Summers’s method in 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

Jacob-Lohman’s free flowing-well method 2: Equation

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

Leaky aquifters, Hantush’s free-flowing well method 2 : Equation

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

Theis’s Recovery Method 1: Assumptions
Theis recovery method, , 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

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 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