Groundwater flow

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Groundwater flow
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Basic principles of GW Flow

• Porosity and effective porosity
• Total porosity is defined as the part of rock
  that's void space
• nT Vv/VT (VT Vs)/VT
• Vv void volume,
• VT total volume
• Vs solid volume
• void ratio
• e Vv/Vs
• Primary porosity interstitial porosity (original
  in the rock)
• Secondary porosity fracture or solution porosity
• Primary porosity range from 26 to 47 (using
  different arrangements and packing of ideal
  spheres).

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Porosity of Sediments and Rocks

• Depending on grain size, particle shape and
  arrangement, diagenetic features, actual values
  of porosity can range from zero or near zero to
  more than 60.
• In general, for sedimentary rocks, the smaller
  the particle size, the higher the porosity.
• Total porosity amount of pore space (does not
  require pore connection)
• Effective porosity percentage of interconnected
  pore space available for groundwater flow.
• Effective porosity can be one order of magnitude
  smaller than total porosity (difference greatest
  in fractured rocks).

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Measurement of porosity

• In the lab, porosity is measured by taking a
  sample of known volume (V),
• sample is dried in an oven at 105oC until it
  reaches a constant weight (expelling moisture).
• Dried sample is then submerged in a known volume
  of water and allowed to remain in a sealed
  chamber until saturated
• Volume of voids is equal to original water volume
  minus volume in the chamber after saturated
  sample is removed. Result is effective porosity.

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• Total porosity is found from
• bulk density is mass of sample after dried
  divided by original sample volume, particle
  density is oven-dried mass divided by volume of
  solid determined from water-displacement test.
• In most rocks and soils, particle density is
  about 2.65g/cc (2650kg/m3).

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n 47.65
n 25.95

1. Cubic packing of spheres
2. Rhombohedral packing

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• Darcys Experimental Law
• Darcy's Experimental Law
• water was passed through a sand column and the
  volumetric flow rate Q was measured at the outlet
• The cross-sectional area of the sand column was
  known, as was the length of the sand in the
  column. During the experiment, Darcy measured
  the distance between the water levels in the two
  manometers at various flow rates.
• He tabulated Q, A, L , and (h1 - h2). He
  calculated Q/A and (h1-h2)/L. Q/A is a
  volumetric flow rate per unit surface area and is
  termed specific discharge.

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Darcys Experimental Law (contd.)

• Darcy's law is stated as
• The velocity of flow is proportional to hydraulic
  gradient
• Darcy's law is valid for flow through most
  granular material.
• The law holds as long as flow is laminar.
• In turbulent flow, water particles take more
  circuitous paths.
• Darcy's velocity (q)
• Darcy's q is a "superficial" velocity.
• Actual velocity v is the volumetric flow rate per
  unit area of connected pore space.
• Therefore, v q/ne (Ki/ne) , where neA is the
  effective area of flow and ne is the effective
  porosity. v is the linear velocity of
  groundwater. v is always larger than the
  superficial velocity and increases with
  decreasing effective porosity.

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Henry Darcy
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Other forms of Darcy's law

• q Ki
• Q KiA
• v Ki/ne
• v q/ne
• v and q are both vector quantities (with
  magnitude and direction).

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Darcys experiment
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Darcys Law, contd.

• Actual velocity (linear gw velocity)
• v q / ne
• ne effective porosity
• Applicability of Darcys Law
• Laminar flow

• Turbulent flow

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Applications of Darcys Law

• Predict groundwater flow to a well
• Predict rate and direction of contaminants
  movement
• Estimate hydraulic head for different locations
  in an aquifer

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Hydraulic Head

• wl's are measured with reference to a common
  datum, taken arbitrarily at the base of the
  sample. Absolute values of wl elevations were of
  no concern to Darcy (only the difference between
  them). We are concerned here with the actual
  water level elevations and what they mean.
• Manometers
• devices to measure wl elevations in the lab
• Piezometers
• a tube or a pipe to measure wl elevations in
  field. It's open at top where measurements are
  taken, and open at bottom to facilitate entrance
  of water.
• A common datum is sea level (elevation zero).

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Hydraulic Head (contd.)

• Total head is a function of
• pressure head,
• elevation head,
• velocity head.
• Bernoulli equation.
• under conditions of steady flow, total energy of
  an incompressible fluid is constant at all
  positions along a flow path in a closed system.
  This may be written as

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Hydraulic Head (contd.)

• (total energy contained in the water)
• g acceleration due to gravity
• z elevation of base of piezometer
• P pressure exerted by water column,
• ? fluid (water) density
• v velocity
• Divide through by g to get (next slide)

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Hydraulic Head (contd.)

• Equation above describes total energy contained
  by the fluid.
• 1st term energy of position
• 2nd term energy due to sustained fluid pressure
• 3rd term energy due to fluid movement

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• elevation head, pressure head, velocity head
• velocity head is ignored (slow movement)
• Stated simply
• total head (h) is the sum of elevation of the
  base of piezometer and length of water column in
  piezometer

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Example 3.1

• gs elevation 1000 m
• DTW 25 m
• peizometer 50 m
• Water density 1000 kg/m3
• Find
• Hydraulic head
• Pressure head
• pressure

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Example 3.1

• Solution
• Hydraulic head
• Pressure head
• pressure

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Hydraulic Gradient

• Total head h hp z
• Gradient change in head with distance
• i dh / dx
• in vector form, gradient may be written as
• grad h ?h

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Hydraulic gradient (contd)

• Equipotential lines
• Lines of equal hh
• Gradient contour interval/horizontal distance

h 120m
h 100m
h 80m
Direction of groundwater flow
Angle 90
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3-point problem
B
A
E
C
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Hydraulic conductivity and permeability

• Hydraulic conductivity (K) is constant of
  proportionality in Darcys Experimnet
• HC ease with which groundwater flows through the
  porous medium
• Sands gravels high K
• Clay shales low K
• Units L/T e.g. m/d, ft/d, gpd/ft2

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Example 3.3

• Groundwater flows through a buried valley aquifer
  with a cross sectional area of 1 x 106 ft2,and a
  length of 2x 104 ft.
• Hydraulic head at gw entry 1000 ft
• Hydraulic head at gw exit 960 ft
• Groundwater discharge 1 x 105 ft3/day
• whats HC of aquifer in ft/day, m/d.
• If effective porosity 0.3, find the linear
  groundwater velocity.

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Intrinsic Permeability

• ?w density of water kg/m3
• g accelration of gravity m/sec2
• ? viscosity kg/(m.sec)
• k intrinsic permeability m2
• K hydraulic conductivity m/sec
• 1 m2 104 cm2 1.013x1012 Darcy

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Intrinsic Permeability

• Example 3.4

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Empirical Approaches for estimation

• Hazen
• Harleman

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Grain-Size Distribution
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Laboratory Measurements of K

• Field Tests
• Empirical relations
• Lab measurements
• Whats the most reliable?

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Laboratory Measurements of K

• Constant-head test
• Falling-head test

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Constant-Head Teast
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Mapping Flow in Geological Systems
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Mapping Flow in Geological Systems
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Mapping Flow in Geological Systems
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Mapping Flow in Geological Systems
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