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