Tracer vs. Pressure Wave Velocities Through Unsaturated Saprolite

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Tracer vs. Pressure Wave VelocitiesThrough
Unsaturated Saprolite

• Todd C. Rasmussen
• Associate Professor of Hydrology
• The University of Georgia, Athens
• www.hydrology.uga.edu

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Configuration for Intact Saprolite Column

• Depth (cm)
• Saprolite surface 0
• TDR probe 4
• Tensiometer 7
• TDR probe 10
• Suction lysimeter 13
• TDR probe 16
• Tensiometer 19
• TDR probe 22
• Suction lysimeter 25
• TDR probe 28
• Tensiometer 31
• TDR probe 34
• Ceramic plate 38

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Representative Saprolite Properties

• Particle sizes sand 0.66 g/g
• silt 0.21 g/g
• clay 0.13 g/g
• Bulk density 1.25 g/cm3
• Porosity 0.5283 cm3/cm3
• Field saturated K 25.1 cm/day
• Lab saturated K 27.3 cm/day

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Chloride Tracer Responses- Columns 1 and 2 -

• z ? v ne
• cm days cm/d
• 1 13 2.17 6.00 3.8
• 25 7.99 3.13 7.3
• 2 13 3.50 3.72 5.9
• 25 9.89 2.53 8.7
• 38 18.64 2.04 10.8

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Possible Explanations for Rapid Unsaturated
Transport

• Preferential flow
• Bypass flow
• Macropore flow
• Fracture flow
• Boundary layer flow
• Mobile zone flow

• Finger flow
• Funnel flow
• Media heterogeneities
• Ion exclusion
• Colloid transport

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Experimental Findings

• A large saprolite core was used for an
  unsaturated flow and Cl- tracer experiment
• The tracer traveled four times more quickly than
  homogeneous flow predicts
• Unsaturated conditions were maintained using
  short irrigation pulses, 0.6 cm3/s
• The pressure pulses traveled 1000 times more
  rapidly than expected.

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Irrigation Schedules

• ID Spray Interval
  Duration Flux
• sec min hours
  cm/day
• 1 A 5 40 9 6 0.229
• B 5 20 18 6
• 2 A 5 40 18 12 0.221
• B 5 20 29 9.67

Spray rate 0.6 cm3/s
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• ID Duration Interval Duration Flux
• sec min hours cm/day
• 3 A1 2 10 6 1 0.071
• A2 2 20 3 1
• A3 2 30 2 1
• A4 2 60 1 1
• A5 2 120 1 2
• B1 1 10 6 1
• B2 1 20 3 1
• B3 1 30 2 1
• B4 1 60 1 1
• B5 1 120 1 2
• C1 3 20 3 1
• C2 3 40 3 2
• C3 3 60 1 1
• C4 3 120 1 2

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Types of Velocities

• Darcian flux (velocity)
• q - K ?h
• Fluid (transport) velocity
• v q / ?
• Kinematic (pressure wave) velocity
• c dq / d?

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Unit Gradient Formulation ?h 0, 0, -1

• Darcian flux q K
• Fluid velocity v K / ?
• Kinematic velocity c dK / d?
• Kinematic ratio k c / v
• d (ln K) / d (ln ?)

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Moisture Characteristic Curves

• Brooks - Corey ? 0.6465 ? 6
• van Genuchten ? 0.6465 1 - (1 - ?7)0.14302
• Broadbridge-White
• ? 52 1 - 1/? - ln (10.3 - ?) / ? (10.3 -
  1) / 10.3
• where ? (? - ?r ) / (?s - ?r ) is the
  relative saturation

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Advection Dispersion Equation for Pressure Waves

• ? is the fluid pressure head
• c dK / d? is the kinematic wave velocity
• D K / Cp is the hydraulic diffusivity
• Cp d?/d? is the specific water capacity

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Pressure Response to Spike Input

• Co is the magnitude of the input

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Peak Wave Velocity

• w is the wave peak velocity
• tp is the time of peak at depth z
• ? c z / D is the hydraulic Peclet Number

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Effect of Hydraulic Peclet Number

• ? ltlt 1 is dominated by diffusion
• ? gtgt 1 is dominated by a kinematic wave

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Fluid Pressure Responses- Column 3 -

• z ?p tp w D Cp
• cm cm min cm/d cm2/d cm-1
• 7 15.28 5.08 1,983 2,314 30.7e-6
• 17 9.91 6.75 3,627 10,276 6.9e-6
• 24 5.94 9.42 3,670 14,680 4.8e-6
• 34 2.35 18.17 2,695 15,272 4.6e-6

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Conclusions

• The effective transport porosity of saprolite is
  less than the total porosity
• This leads to at least a four-fold increase in
  the solute velocity relative to that predicted by
  homogeneous flow
• The pressure wave velocity is even faster, about
  1000 times greater than the darcian flux
• A hydraulic advection-diffusion equation closely
  predicts observed pressure responses
• The best fit occurs with a small specific water
  capacity, Cp d? / d?

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Implications

• Solute Transport
• Consistent with other studies, saprolite from the
  Georgia Piedmont shows preferential solute
  transport
• Use of the total porosity to predict solute
  transport underestimates solute travel times
• Fluid Pressure
• Rapid pressure waves are associated with surface
  perturbations
• These have attributes of displacement (piston)
  flow
• Use of pressure responses overestimates solute
  travel times

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Unsaturated Fractured Rock Hydraulic Properties
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Galileo Number

• Dimensionless number, ratio of two forces

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Hydraulic Conductivity

• The unsaturated hydraulic conductivity is
• and the saturated hydraulic conductivity is
• which is just the Kozeny-Carman Equation