well hydraulics

Well HydraulicsWell Hydraulics

Steady State AnalysisSteady State Analysis

Groundwater WellsGroundwater Wells

�� The groundwater is collected through the use of wellsThe groundwater is collected through the use of wells

�� Well systems usually have Well systems usually have –– well structure, pump and well structure, pump and

discharge pipesdischarge pipes

�� Well usually consists of perforated casing that allows water Well usually consists of perforated casing that allows water

to enter the well but prevents collapse of holeto enter the well but prevents collapse of holeto enter the well but prevents collapse of holeto enter the well but prevents collapse of hole

�� When waster is withdrawn, the flow becomes established to When waster is withdrawn, the flow becomes established to

compensate the withdrawlcompensate the withdrawl

�� Because of head loss, piezometric surface adjacent to well is Because of head loss, piezometric surface adjacent to well is

depressed; this is called ‘cone of depression’depressed; this is called ‘cone of depression’

�� Remember Darcy’s equation: Remember Darcy’s equation:

dx

dhKAQ −=

'' What is well hydraulics?What is well hydraulics?

To understand the processes in effect when one orTo understand the processes in effect when one or

more wells are pumping from an aquifer. This formore wells are pumping from an aquifer. This for

instance considers the analysis of drawdown due toinstance considers the analysis of drawdown due to

pumping with time and distancepumping with time and distance

'' Importance of well hydraulicsImportance of well hydraulics'' Importance of well hydraulicsImportance of well hydraulics

Groundwater withdrawal from aquifers are importantGroundwater withdrawal from aquifers are important

to meet the water demand. Therefore, we need toto meet the water demand. Therefore, we need to

understand well hydraulics to design a pumpingunderstand well hydraulics to design a pumping

strategy that is sufficient to furnish the adequatestrategy that is sufficient to furnish the adequate

amounts of wateramounts of water

Basic AssumptionsBasic Assumptions

�� The piezometric surface of the aquifer is The piezometric surface of the aquifer is horizontal prior to the start of the pumpinghorizontal prior to the start of the pumping

�� The aquifer is homogeneous and isotropic (same The aquifer is homogeneous and isotropic (same material with same properties in all directions)material with same properties in all directions)material with same properties in all directions)material with same properties in all directions)

�� All flow is radial toward the wellAll flow is radial toward the well

�� Groundwater flow is horizontalGroundwater flow is horizontal

�� Darcy’s law is validDarcy’s law is valid

�� The pumping well fully penetrates the aquiferThe pumping well fully penetrates the aquifer

Steady versus Transient (unsteady)Steady versus Transient (unsteady)

�� Steady state implies that the drawdown is a function ofSteady state implies that the drawdown is a function of

location onlylocation only

�� Transient state implies that the drawdown is a functionTransient state implies that the drawdown is a function

of location and timeof location and timeof location and timeof location and time

ThusThus

h = f(r) in case of steady stateh = f(r) in case of steady state

h = f(r,t) in case of transient stateh = f(r,t) in case of transient state

Steady Radial Flow to a Well in ConfinedSteady Radial Flow to a Well in Confined

AquifersAquifers


AquifersAquifers

�� When water is pumped from a confined aquifer,When water is pumped from a confined aquifer,

the pumpage creates a drawdown in thethe pumpage creates a drawdown in the

piezometric surface that induces hydraulicpiezometric surface that induces hydraulic

gradient toward the wellgradient toward the well

�� Drawdown at a given point is the distance byDrawdown at a given point is the distance by�� Drawdown at a given point is the distance byDrawdown at a given point is the distance by

which the water level is lowered. A drawdownwhich the water level is lowered. A drawdown

curve shows the variation of drawdown withcurve shows the variation of drawdown with

distance from the welldistance from the well

�� The induced flow moves horizontally toward theThe induced flow moves horizontally toward the

wellwell


AquifersAquifers

�� Apply Darcy’s law to derive the flow equation that relates Apply Darcy’s law to derive the flow equation that relates

drawdown with pumping:drawdown with pumping:


AquifersAquifers

Rearranging and integrating for the boundaryRearranging and integrating for the boundary

conditions at the well h = hconditions at the well h = hww and r = rand r = rww

andand

at the edge of the aquifer h = hat the edge of the aquifer h = h and r = rand r = rat the edge of the aquifer h = hat the edge of the aquifer h = h00 and r = rand r = r00

yields (with the negative sign neglected):yields (with the negative sign neglected):


AquifersAquifers


AquifersAquifers

�� Thiem equationThiem equation

where rwhere r11 and rand r22 are the distances and hare the distances and h11 andand

hh2 2 are the heads of the respective observationare the heads of the respective observation

wellswells

Textbook formTextbook form

where Q is in gallons per minute, Kwhere Q is in gallons per minute, K is the is the

( )12

1

2log528

hhm

rr

Q

K f−

=

where Q is in gallons per minute, Kwhere Q is in gallons per minute, Kff is the is the permeability in gallons per day per square foot permeability in gallons per day per square foot and r and h are measured in feet. m is the and r and h are measured in feet. m is the thickness of aquifer (same as b in previous case)thickness of aquifer (same as b in previous case)


AquifersAquifers

From a practical standpoint, the drawdown From a practical standpoint, the drawdown ss

rather than the head rather than the head hh is measured so:is measured so:

Example [1] Example [1] –– Steady State ConfinedSteady State Confined

AquiferAquifer

A well in a confined aquifer is pumped at a rate of 220A well in a confined aquifer is pumped at a rate of 220

gal/mingal/min

Measurement of drawdown in two observation wellsMeasurement of drawdown in two observation wells

shows that after 1,270 min of pumping, no furthershows that after 1,270 min of pumping, no further

drawdown is occurringdrawdown is occurringdrawdown is occurringdrawdown is occurring

Well 1 is 26 ft from the pumping well and has a head ofWell 1 is 26 ft from the pumping well and has a head of

29.34 ft above the top of the aquifer29.34 ft above the top of the aquifer

Well 2 is 73 ft from the pumping well and has a head ofWell 2 is 73 ft from the pumping well and has a head of

32.56 ft above the top of the aquifer.32.56 ft above the top of the aquifer.

Use the Thiem equation to find the aquifer transmissivityUse the Thiem equation to find the aquifer transmissivity

Solution [1]Solution [1]

�� We must first convert the pumping rate of 220 gal/min to an We must first convert the pumping rate of 220 gal/min to an

equivalent rate in cubic feet per dayequivalent rate in cubic feet per day

�� Now we substitute the given values into Thiem equation:Now we substitute the given values into Thiem equation:

Steady Radial Flow to a Well inSteady Radial Flow to a Well in

Unconfined AquifersUnconfined Aquifers

Confined versus UnconfinedConfined versus Unconfined



The flow equation is similar for that of confined The flow equation is similar for that of confined

aquifers except we use aquifers except we use hh instead of instead of bb



Rearranging and integrating for the boundaryRearranging and integrating for the boundary

conditions at the well, h = hconditions at the well, h = hww and r = rand r = rww, and at the, and at the

edge of the aquifer, h = hedge of the aquifer, h = h00 and r = rand r = r00, yields:, yields:



Converting to heads (hConverting to heads (h11 and hand h22) and radii at two) and radii at two

observation wells at locations robservation wells at locations r11 and rand r22::



�� Rearranging to solve for the hydraulic conductivity:Rearranging to solve for the hydraulic conductivity:

Textbook form of unconfined aquiferTextbook form of unconfined aquifer

�� Where Q is in gallons per minute, KWhere Q is in gallons per minute, Kff is in is in gallons per day per square foot and r and h are gallons per day per square foot and r and h are measured in feet.measured in feet.

well hydraulics

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