Groundwater flow

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Groundwater flow

• General principles
• Important factors affecting flow
• Application for groundwater protection

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Gaining and losing streams

• Most observable flow in perennial streams
  (streams with constant flow) is baseflow
• Baseflow represents the discharge of groundwater
  along the stream channel
• Stream reaches may be gaining or losing
• Gaining streams receive groundwater flow
• Losing streams recharge groundwater

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Public and private water supply

• In Nevada, 99 of the public water supplies rely
  on groundwater
• 100 of private water supplies (for drinking
  water) rely on groundwater
• Groundwater also meets demand for irrigation and
  industrial uses

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Terminology

• Aquifer a water-bearing subsurface formation
  that can be used for water supply (10 gpm)
• Unconfined aquifer water-bearing subsurface
  formation that has the upper boundary at
  atmospheric pressure.
• Confined aquifer formation that is bounded
  above and below by formations that have
  significantly lower hydraulic conductivity

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Terminology

• Hydraulic conductivity a proportionality
  constant that represents physical characteristics
  of the geologic formation that are important
  determinants of water movement

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Aquifer materials

• Unconsolidated materials (sands, gravels, clays)
• Rock formations (sedimentary rocks)
• Igneous and metamorphic rocks
• Unconsolidated materials are the most exploited
  for water supply because of high yield,
  inexpensive drilling costs and adequate supply

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Confined and unconfined aquifers

• Confined aquifers also called artesian aquifers
  (Artois region of France)
• Recharge area is at a higher elevation than point
  at which water is extracted
• Elevation pressure head leads to water level in
  well being higher than in aquifer

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Unconfined aquifers

• Direct hydraulic connection with overlying
  recharge areas on soil surface
• Water table aquifers

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Darcys Law

• Background
• Named for Henri Darcy (1803-1858), chief engineer
  in Dijon, France
• Rapport à Le Maire et au Conseil Municipal, de
  Dijon, sur les Moyens de Fournir L'Eau Nécessaire
  à cette Ville, 1834
• Law was developed from studies of
  water-filtration to prevent cholera outbreaks

Saturated sand-filled column
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General principles Darcys law of saturated flow
in porous media

• The direction and amount of water flow in a
  porous medium is opposite the direction of the
  energy gradient and is determined by
  characteristics of the formation and the change
  in potential energy with distance

Change in energy that is creating flow with
distance
Proportionality constant that represents medium
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Schematic of System

• Head (h) consists of pressure and elevation head
• Dh/Dl represents change in head due to energy
  losses over horizontal distance

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Energy losses

• Due to friction effects in interaction with
  grains of porous medium
• Result leads to decreases in apparent head along
  the horizontal flow path

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Pressure head

• h zp/?
• Total pressure head (l) equals potential energy
  due to differences in elevation pressure
  applied (F/l2) /specific weight of water (g?,
  gravity?density (F/l3)
• z is always expressed with respect to a datum, or
  point of reference
• Water flows downhill and from areas of high
  pressure to low pressure

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Hydraulic conductivity (K)

• K (l/t)Ki(?/?)
• Ki (l2) intrinsic permeability, representative
  of the properties of the medium alone
• ? dynamic viscosity of the fluid (resistance of
  fluid to shearing ?ethanol 10-3 ltlt ?SAE30 oil
  10-1 Ns/m2)
• Hydraulic conductivity is equal to intrinsic
  permeability of the medium times properties of
  the fluid

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Focus on medium

• Assume fluid properties are constant
• The primary influence on flow is related to the
  medium and resistance and energy loss associated
  with fluid flow through the medium
• Ki represents the intrinsic permeability Cd2
• D mean pore diameter
• KC(D10)2 for grain sizes 0.1-3 mm, with D10
  mean grain diameter in cm

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Shape factor (C) Coefficient values
120ltClt150
40ltClt80
80ltClt120
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Hydraulic Conductivity and Texture
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Other important characteristics

• Specific yield (Sy) ratio of the total volume of
  water that drains from a saturated formation to
  the total volume of the formation
• Related to capillary effect because water is
  retained in pores by surface tension against
  gravitational drainage
• 0ltSylt1

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Specific yield

• Related to texture
• Importance relates to the amount of water that
  can be feasibly extracted from a formation

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Transmissivity

• Transmissivity indicator of the ability of
  formation to provide water
• TKb
• Transmissivity (l2/t) is the product of hydraulic
  conductivity and thickness of the aquifer (b)

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Drawdown curves

• Pumping creates a cone of depression, which
  represents the energy gradient created by
  lowering the water table
• The extent and shape of the cone may be measured
  with piezometers (observation wells)

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Assumptions inherent in Darcys Law

• Homogeneous (material is the same throughout the
  control volume)
• Isotropic (material has the same permeability in
  all directions within the control volume)
• Flow in pores is laminar (not turbulent)

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When Darcys Law is inapplicable (or hard to
apply)

• Flow with high velocitiesMacropore flow
  (fractures in rocks, large voids in soils or
  sediments)
• Media with very low permeabilityLow hydraulic
  gradient, low permeability environments (clays,
  solid rock)
• Heterogeneous, anisotropic and unsteady state
  conditions

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Application for groundwater protection

• Travel time estimation
• Darcys law represents flux through an area (Q/A
  discharge/area)
• Units are velocity units
• However, AltAvoid, in which Avoid represents the
  actual amount of space that water has to travel
  through
• Actual velocity q/?, with 0lt??1

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Example

• Two wells 780 meters apart in an unconfined
  aquifer have water levels of 1372.4 m and 1376.3
  m.
• The formation is composed of sand mixed with silt
• What is the average velocity of water in the
  formation?

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Solution

• q-K(Dh/Dl)
• K1 m/day (Fig 8-10)
• Dh/Dl (1372.4-1376.3)/780-.005
• q.005 m/day
• ?.44 (Tab 8-1)
• qe .01 m/day
• 10 yr travel distance41.5 m

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Travel time and risk management

• Many biological and chemical contaminants are
  unstable in the subsurface
• Biological and chemical contaminants are often
  released on the land surface as part of human
  existence (fuels, pesticides)
• Theory travel time from any influence lt time
  needed to dilute or degrade a potential
  contaminant

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Example Pesticides

• Degradation in soil and water occurs because
  chemicals are unstable broken down by microbes
• Degradation often represented as an exponential
  decay function
• Risks posed by pesticides are characterized by
  solubility, partitioning in soils (esp. organic
  matter), toxicity, half-life

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Concept of half-life

• Definition typical length of time needed for
  one half of the total mass of a pesticide to
  break-down to a non-toxic substance

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Example Oxamyl

• Carbamate pesticide
• Highly soluble in water (2000 mg/l)
• Half-life 1 day
• If we had water with a maximum concentration of
  2000 ppm and we waited for 1 day, we should find
  that the total mass of toxic material has
  decreased to 1000 mg (1000 ppm).

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Estimating fractional loss from half-life

• We want to know how long it would take for 99.99
  of Oxamyl dissolved in water to be degraded
• Half life 1 day
• C1 C0 ek(1)
• C1/ C0 0.5 ek(1)
• ln(C1/ C0) k(1) -.6931

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• (C1/ C0) ? .0001
• .0001 ? e-.6931(t)
• -9.2103 ? -.6931 (t)
• 13 days ? t
• Conclusion we should see 99.99 reduction in
  concentrations (mass/volume) after approximately
  13 days.
• Significance compare time needed for
  degradation to groundwater transport velocities
  to assess likelihood of contamination.

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Identifying zones of influence

• Conceptual application of representations of
  groundwater flow (extended to 2-3 dimensions)
• Use available information about formation
  characteristics, location and amount of
  discharge, general directions of groundwater flow

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Simple approach

• Fixed radius
• Requires minimal information about formation
  characteristics
• May or may not provide reasonable protection

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Parabolic capture zones

• Account for general directions of groundwater
  flow
• Require some information about piezometric
  surface elevations

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Analytic solutions

• Require more information about piezometric
  surface and formation characteristics
• Represent solutions to groundwater flow equations
• Based on computer simulations

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Summary

• Darcys law is a fundamental tool for analysis of
  groundwater flow
• Can be applied to estimate flow quantities and
  travel times
• Wellhead protection zones are based on
  multi-dimensional applications of groundwater
  flow models
• Wellhead protection assumes that dilution and
  chemical degradation occur before surface and
  subsurface sources influence water quality