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Unit 04 : Advanced Hydrogeology

Hydraulic Testing


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Well Hydraulics

A water well is a hydraulic structure that is

designed and constructed to permit economic

withdrawal of water from an aquifer Water well construction includes:

Selection of appropriate drilling methods

Selection of appropriate completion materials

Analysis and interpretation of well and aquifer

performance


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Pumping Well Terminology

Static Water Level[SWL!ho" is the equili#rium waterle$el #efore pumpingcommences

Pumping Water Level[%WL !h" is the water le$elduring pumping

Drawdown!s & ho' h" is thedifference #etween SWL and%WL

Well ield!(" is the $olumeof water pumped per unittime

Speci!ic "apacity!()s" isthe yield per unit drawdown

ho

h

s

(


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"one o! Depression

A *one of low pressure is created centred on the pumping well

+rawdown is a ma,imum at the well and reduces radially

Head gradient decreases away from the well and the pattern

resem#les an in$erted cone called the cone o! depression

The cone e,pands o$er time until the inflows !from $arious

#oundaries" match the well e,traction

The shape of the equili#rium cone is controlled #y hydraulic

conducti$ity

Low -haquifer

High -haquifer

-h-$


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A#ui!er "$aracteristics

%ump tests allow estimation of transmission andstorage characteristics of aquifers

Transmissivity!T & -#" is the rate of flow through a

$ertical strip of aquifer !thic.ness #" of unit widthunder a unit hydraulic gradient

Storage "oe!!icient!S & Sy/ Ss#" is storage changeper unit $olume of aquifer per unit change in head

%adius o! &n!luence!0" for a well is the ma,imumhori*ontal e,tent of the cone of depression when thewell is in equili#rium with inflows


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Steady %adial "on!ined 'low Assumptions

1sotropic2 homogeneous2

infinite aquifer2 3'+ radial flow

&nitial "onditions

h!r24" & hofor all r (oundary"onditions

h!02t" & ho for all t

+arcy5s Law ( & '3r#-h)r

0earranging h & ' ( r3-# r

1ntegrating h & ' ( ln!r" / c

3-#

67 specifies h & hoat r & 0

8sing 67 ho& ' ( ln!0" / c

3-# 9liminating constant !c" gi$es

s & ho h & ( ln!r)0"

3-#

T$is is t$e T$iem )#uation

hoh

s

(

r

#


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Steady Uncon!ined %adial 'low Assumptions

1sotropic2 homogeneous2

infinite aquifer2 3'+ radial flow

&nitial "onditions

h!r24" & hofor all r (oundary "onditions

h!02t" & ho for all t

hoh

s

(

r

+arcy5s Law ( & '3rh-h)r

0earranging hh & ' ( r3- r

1ntegrating h3& ' ( ln!r" / c

3 3-

67 specifies h & hoat r & 0

8sing 67 ho3& ' ( ln!0" / c

- 9liminating constant !c" gi$es

ho3 h3& ( ln!r)0"

-

T$is is t$e T$iem )#uation


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T$iem )#uation Assumptions The equation for unconfined flow can #e rearranged to gi$e:

s & ho h & ( ln!r)0"

3- !ho/ h")3

7ompare this with the confined equation:

s & ho h & ( ln!r)0"

3-# 1t is clear than the only difference is that the aquifer thic.ness #

is replaced #y !ho/ h")3

The implicit assumption in the deri$ation !3'+ flow" implies thats is small compared with hoand that the !ho/ h")3 does not

de$iate significantly from ho

This assumption may not #e $alid in the immediate $icinity of a

pumping well in an unconfined aquifer


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T$iem )#uation Applications

The equation for unconfined flow can #e rearranged to gi$e:

- & ( ln!r)0"

!ho3' h3"

Similarly with the confined equation:

- & ( ln!r)0"

3# !ho h"

The radius of influence 0 is hard to estimate #ut any two wells at

different radial distance can #e used in the equations

- & ( ln!r3)r" and - & ( ln!r3)r"

!h33 h3" 3# !h3 h"

This means that for a well producing at a steady rate !(" with a

steady drawdown2 any pair of o#ser$ation points at different radial

distances can #e used to estimate -


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Speci!ic "apacity ;or a confined well producing at a steady rate !(" the specific capacity is

gi$en #y:

( & 3-#sw ln!rw)0"

This means that for a confined well producing at a steady rate !(" thespecific capacity is constant

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