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Steady Flow to a Well in a Confined Aquifer
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Flow to Wells - 1Groundwater Hydraulics
Daene C. McKinney
Summary
โข Steady flow to a well in a โ confined aquiferโ to a well in an unconfined aquiferโ capture zones
Steady Flow to a Well in a Confined Aquifer
Flow to a Well in a Confined Aquifer
Flow to a Partially Penetrating Well in a Confined Aquifer
Steady Flow to a Well in a Confined Aquifer
2rw
Ground surface
Bedrock
Confined aquifer
Q
h0
Pre-pumping head
Confining Layer
br1
r2
h2h1
hw
Observation wells
Drawdown curve
Q
Pumping well
Example - Steady Flow to a Well in a Confined Aquifer
โข Q = 400 m3/hrโข b = 40 mโข Two observation wells,
1. h1 = 85.3 m (@ r1 = 25 m)
2. h2 = 89.6 m (@ r2 = 75 m)
โข Find: Transmissivity (T)
2rw
Ground surface
Bedrock
Confined aquifer
Q
h0
Confining Layer
br1
r2
h2
h1
hw
Q
Pumping well
Steady Flow to a Well in a Confined Aquifer
โข Head
โข Drawdown
h(r = R) = h0
Example - Steady Flow to a Well in a Confined Aquifer
โข 1-m diameter well โข Q = 113 m3/hr โข b = 30 mโข h0= 40 m โข Two observation wells,
h1 = 38.2 m (@ r1 = 15 m)h2 = 39.5 m (@ r2 = 50 m)
โข Find: Head and drawdown in the well
2rw
Ground surface
Bedrock
Confined aquifer
Q
h0
Confining Layer
br1
r2
h2
h1
hw
Q
Pumping well
Drawdown
Example - Steady Flow to a Well in a Confined Aquifer
2rw
Ground surface
Bedrock
Confined aquifer
Q
h0
Confining Layer
br1
r2
h2
h1
hw
Q
Drawdown @ well
Drawdown at the well
Steady Flow to a Well in a Confined Aquifer
2rw
Ground surface
Bedrock
Confined aquifer
Q
h0
Pre-pumping head
Confining Layer
br1
r2
h2h1
hw
Observation wells
Drawdown curve
Q
Pumping well
Steady Flow to a Well in a Unconfined Aquifer
Flow to a Well in an Unconfined Aquifer
Steady Flow to a Well in an Unconfined Aquifer
2rw
Ground surface
Bedrock
Unconfined aquifer
Q
h0
Pre-pumping Water level
r1
r2
h2h1
hw
Observation wells
Water Table
Q
Pumping well
h=h1๐๐ก ๐=๐1
h=h2๐๐ก ๐=๐2
โข Given: โ Q = 300 m3/hr โ Unconfined aquifer โ 2 observation wells, h = 40 m (@ r1 = 50 m)
h = 43 m (@ r2 = 100 m) โข Find: K
Example โ Steady Flow to a Well in an Unconfined Aquifer
2rw
Ground surface
Bedrock
Unconfined aquifer
Q
h0
Prepumping Water level
r1
r2
h2
h1
hw
Observation wells
Water Table
Q
Pumping well
Steady flow to a Well in an Unconfined Aquifer with Recharge
Recharge rate = WFlow to well increases
๐๐=2๐๐๐๐๐๐=2๐๐ 2๐+๐ถ
a ๐ ๐โ0 ,๐โ๐๐ค
๐=๐๐ 2๐+๐๐ค
2๐ h๐ ๐พ h๐๐๐ =๐๐ 2๐+๐๐ค
h02โh2= ๐
2๐พ (๐ 2โ๐02 )+
๐๐ค
๐ ๐พ ๐๐ ( ๐0
๐ )
Example - Steady flow to a Well in an Unconfined Aquifer with Recharge
r
50 m25 cm diameter well to maintain lowered water tableK = 1x10-5 m/s (0.864 m/d)Bottom of aquifer is horizontal at 20 m bgsWater table is 1 m bgsUnconfined aquifer is recharged at W = 0.06 m/dWater table must be lowered 3 m over site
Drawdown at corners must be at least 3 m
h02โh2= ๐
2๐พ (๐ 2โ๐02 )+
๐๐ค
๐ ๐พ ๐๐( ๐0
๐ )๐=๐๐ 2๐+๐๐ค h๐ค ๐๐๐=๐0 ,๐=0 ๐๐ค=๐๐0
2๐
(19 )2โ (16 )2= 0.062(0.864 )
( (35.35 )2โ๐ 02 )+ 0.06๐๐0
2
๐ (0,864)๐๐ ( ๐ 0
35.35 )
r=35.35 m
Solve by iteration: r0 = 70 m, Qw = 924 m3/d
Capture Zones
Well Pumping in Uniform Flow
โข โcapture zoneโ = zone from which a well is drawing water in an aquifer
โข When a well is in an aquifer with a uniform regional flow, we can calculate the capture zone by superposing the uniform flow on the well flow
โข โgroundwater divideโ = boundary of the region providing inflow to the well
โ ๐ฆ๐ฅ =tan ( 2๐ ๐พ๐๐๐ ๐ฆ )
โ 2๐ ๐พ๐๐๐ ๐ฆ=๐ก๐๐โ1( ๐ฆ๐ฅ )=๐
๐ฆ=โ๐
2๐ ๐พ๐๐ ๐
๐ฆ=ยฑ ๐2๐พ๐๐
๐๐ ๐ฅโโ,๐โ๐
๐ฅ๐ฟ=โ๐
2๐ ๐พ๐๐
Example โ Capture Zone).5 m radius well pumps at 15 L/s from a 35 m thick confined aquifer with a hydraulic conductivity of 20 m/d. Distance and head drop between 2 well are 1000 m and 3 m before the well.Find: longitudinal and transverse limits of water entering the well.
๐= โhโ๐ฅ=3๐
1000๐=0.003
๐ฆ=ยฑ ๐2๐พ๐๐=ยฑ
1296๐3/๐๐๐ฆ2(20๐/๐)(35๐)(0.003)
=ยฑ308๐
๐ฅ๐ฟ=โ๐
2๐ ๐พ๐๐=โ1296 ๐3
๐๐๐ฆ
2๐ (20๐๐ ) (35๐ ) (0.003 )=-98.2 m
Summary
โข Steady flow to a well in a โ confined aquiferโ to a well in an unconfined aquiferโ capture zones