flow to wells - 1 groundwater hydraulics daene c. mckinney
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Steady Flow to a Well in a Confined AquiferTRANSCRIPT
Flow to Wells - 1Groundwater Hydraulics
Daene C. McKinney
Summary
• Steady flow to a well in a – confined aquifer– to a well in an unconfined aquifer– 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
• Q = 400 m3/hr• b = 40 m• Two observation wells,
1. h1 = 85.3 m (@ r1 = 25 m)
2. h2 = 89.6 m (@ r2 = 75 m)
• 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
• Head
• Drawdown
h(r = R) = h0
Example - Steady Flow to a Well in a Confined Aquifer
• 1-m diameter well • Q = 113 m3/hr • b = 30 m• h0= 40 m • Two observation wells,
h1 = 38.2 m (@ r1 = 15 m)h2 = 39.5 m (@ r2 = 50 m)
• 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=h1𝑎𝑡 𝑟=𝑟1
h=h2𝑎𝑡 𝑟=𝑟2
• Given: – Q = 300 m3/hr – Unconfined aquifer – 2 observation wells, h = 40 m (@ r1 = 50 m)
h = 43 m (@ r2 = 100 m) • Find: K
Example – 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
𝑑𝑄=2𝜋𝑟𝑑𝑟𝑊𝑄=2𝜋𝑟 2𝑊+𝐶
a 𝑠𝑟→0 ,𝑄→𝑄𝑤
𝑄=𝜋𝑟 2𝑊+𝑄𝑤
2𝜋 h𝑟 𝐾 h𝑑𝑑𝑟 =𝜋𝑟 2𝑊+𝑄𝑤
h02−h2= 𝑊
2𝐾 (𝑟 2−𝑟02 )+
𝑄𝑤
𝜋 𝐾 𝑙𝑛 ( 𝑟0
𝑟 )
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
h02−h2= 𝑊
2𝐾 (𝑟 2−𝑟02 )+
𝑄𝑤
𝜋 𝐾 𝑙𝑛( 𝑟0
𝑟 )𝑄=𝜋𝑟 2𝑊+𝑄𝑤 h𝑤 𝑒𝑛𝑟=𝑟0 ,𝑄=0 𝑄𝑤=𝜋𝑟0
2𝑊
(19 )2− (16 )2= 0.062(0.864 )
( (35.35 )2−𝑟 02 )+ 0.06𝜋𝑟0
2
𝜋 (0,864)𝑙𝑛 ( 𝑟 0
35.35 )
r=35.35 m
Solve by iteration: r0 = 70 m, Qw = 924 m3/d
Capture Zones
Well Pumping in Uniform Flow
• “capture zone” = zone from which a well is drawing water in an aquifer
• 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
• “groundwater divide” = boundary of the region providing inflow to the well
− 𝑦𝑥 =tan ( 2𝜋 𝐾𝑏𝑖𝑄 𝑦 )
− 2𝜋 𝐾𝑏𝑖𝑄 𝑦=𝑡𝑎𝑛−1( 𝑦𝑥 )=𝜃
𝑦=−𝑄
2𝜋 𝐾𝑏𝑖 𝜃
𝑦=± 𝑄2𝐾𝑏𝑖
𝑎𝑠 𝑥→∞,𝜃→𝜋
𝑥𝐿=−𝑄
2𝜋 𝐾𝑏𝑖
Example – 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.
𝑖= ∆h∆𝑥=3𝑚
1000𝑚=0.003
𝑦=± 𝑄2𝐾𝑏𝑖=±
1296𝑚3/𝑑𝑎𝑦2(20𝑚/𝑑)(35𝑚)(0.003)
=±308𝑚
𝑥𝐿=−𝑄
2𝜋 𝐾𝑏𝑖=−1296 𝑚3
𝑑𝑎𝑦
2𝜋 (20𝑚𝑑 ) (35𝑚 ) (0.003 )=-98.2 m
Summary
• Steady flow to a well in a – confined aquifer– to a well in an unconfined aquifer– capture zones