CHAPTER 15: SINGLE WELL TESTSPresented 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!

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

IMPORTANT NOTE

RECOVERY TESTS

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

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

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 2: THE EQUATION

This method uses the following equation to generate a family of type curves:

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

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 2: EQUATION

The following ratio is used:

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

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 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

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 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

VARIABLE DISCHARGE METHODS

Confined Aquifers Birsoy-Summers’s method Jacob-Lohman’s free-flowing-well method

Leaky aquifers Hantush’s free flowing-well method

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

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 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 2 : EQUATION

RECOVERY TESTS

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

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

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 13.3.1 can be used

Provided that s’ is replaced by s’w

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