Well Hydraulics

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Well Hydraulics

• Steady State Analysis

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Groundwater Wells

• The groundwater is collected through the use of
  wells
• Well systems usually have well structure, pump
  and discharge pipes
• Well usually consists of perforated casing that
  allows water to enter the well but prevents
  collapse of hole
• When waster is withdrawn, the flow becomes
  established to compensate the withdrawl
• Because of head loss, piezometric surface
  adjacent to well is depressed this is called
  cone of depression
• Remember Darcys equation

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• ?? What is well hydraulics?
• To understand the processes in effect when one or
• more wells are pumping from an aquifer. This for
• instance considers the analysis of drawdown due
  to
• pumping with time and distance
• ?? Importance of well hydraulics
• Groundwater withdrawal from aquifers are
  important
• to meet the water demand. Therefore, we need to
• understand well hydraulics to design a pumping
• strategy that is sufficient to furnish the
  adequate
• amounts of water

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Basic Assumptions

• The piezometric surface of the aquifer is
  horizontal prior to the start of the pumping
• The aquifer is homogeneous and isotropic (same
  material with same properties in all directions)
• All flow is radial toward the well
• Groundwater flow is horizontal
• Darcys law is valid
• The pumping well fully penetrates the aquifer

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Steady versus Transient (unsteady)

• Steady state implies that the drawdown is a
  function of
• location only
• Transient state implies that the drawdown is a
  function
• of location and time
• Thus
• h f(r) in case of steady state
• h f(r,t) in case of transient state

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Steady Radial Flow to a Well in ConfinedAquifers
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Steady Radial Flow to a Well in ConfinedAquifers

• When water is pumped from a confined aquifer,
• the pumpage creates a drawdown in the
• piezometric surface that induces hydraulic
• gradient toward the well
• Drawdown at a given point is the distance by
• which the water level is lowered. A drawdown
• curve shows the variation of drawdown with
• distance from the well
• The induced flow moves horizontally toward the
• well

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Steady Radial Flow to a Well in ConfinedAquifers

• Apply Darcys law to derive the flow equation
  that relates drawdown with pumping

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Steady Radial Flow to a Well in ConfinedAquifers

• Rearranging and integrating for the boundary
• conditions at the well h hw and r rw
• and
• at the edge of the aquifer h h0 and r r0
• yields (with the negative sign neglected)

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Steady Radial Flow to a Well in ConfinedAquifers
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Steady Radial Flow to a Well in ConfinedAquifers

• Thiem equation
• where r1 and r2 are the distances and h1 and
• h2 are the heads of the respective observation
• wells

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Textbook form

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

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Steady Radial Flow to a Well in ConfinedAquifers

• From a practical standpoint, the drawdown s
• rather than the head h is measured so

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Example 1 Steady State ConfinedAquifer

• A well in a confined aquifer is pumped at a rate
  of 220
• gal/min
• Measurement of drawdown in two observation wells
• shows that after 1,270 min of pumping, no further
• drawdown is occurring
• Well 1 is 26 ft from the pumping well and has a
  head of
• 29.34 ft above the top of the aquifer
• Well 2 is 73 ft from the pumping well and has a
  head of
• 32.56 ft above the top of the aquifer.
• Use the Thiem equation to find the aquifer
  transmissivity

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Solution 1

• We must first convert the pumping rate of 220
  gal/min to an equivalent rate in cubic feet per
  day
• Now we substitute the given values into Thiem
  equation

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Steady Radial Flow to a Well inUnconfined
Aquifers
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Confined versus Unconfined
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Steady Radial Flow to a Well inUnconfined
Aquifers

• The flow equation is similar for that of
  confined aquifers except we use h instead of b

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Steady Radial Flow to a Well inUnconfined
Aquifers

• Rearranging and integrating for the boundary
• conditions at the well, h hw and r rw, and at
  the
• edge of the aquifer, h h0 and r r0, yields

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Steady Radial Flow to a Well inUnconfined
Aquifers

• Converting to heads (h1 and h2) and radii at two
• observation wells at locations r1 and r2

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Steady Radial Flow to a Well inUnconfined
Aquifers

• Rearranging to solve for the hydraulic
  conductivity

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Textbook form of unconfined aquifer

• Where Q is in gallons per minute, Kf is in
  gallons per day per square foot and r and h are
  measured in feet.

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