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