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Tracer vs. Pressure Wave Velocities Through Unsaturated Saprolite

Tracer vs. Pressure Wave Velocities Through Unsaturated Saprolite. Todd C. Rasmussen Associate Professor of Hydrology The University of Georgia, Athens www.hydrology.uga.edu. Configuration for Intact Saprolite Column. Depth (cm) Saprolite surface 0 TDR probe 4 Tensiometer 7

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Tracer vs. Pressure Wave Velocities Through Unsaturated Saprolite

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  1. Tracer vs. Pressure Wave VelocitiesThrough Unsaturated Saprolite Todd C. Rasmussen Associate Professor of Hydrology The University of Georgia, Athens www.hydrology.uga.edu

  2. 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

  3. 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

  4. Chloride Tracer Responses- Columns 1 and 2 - z vne 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

  5. 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

  6. 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.

  7. 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

  8. 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

  9. Types of Velocities • Darcian flux (velocity) • q = - K h • Fluid (transport) velocity • v = q /  • Kinematic (pressure wave) velocity • c = dq / d

  10. 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 )

  11. Moisture Characteristic Curves Brooks - Corey  = 0.6465  6 van Genuchten  = 0.6465 [ 1 - (1 - 7)0.1430]2 Broadbridge-White  = 52 { 1 - 1/ - ln [ (10.3 - ) /  (10.3 - 1) ] / 10.3 } where  = ( - r ) / (s - r ) is the relative saturation

  12. 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

  13. Pressure Response to Spike Input • Co is the magnitude of the input

  14. 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

  15. Effect of Hydraulic Peclet Number •  << 1 is dominated by diffusion •  >> 1 is dominated by a kinematic wave

  16. 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

  17. 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

  18. 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

  19. Unsaturated Fractured Rock Hydraulic Properties

  20. Galileo Number • Dimensionless number, ratio of two forces:

  21. Hydraulic Conductivity • The unsaturated hydraulic conductivity is: • and the saturated hydraulic conductivity is: • which is just the Kozeny-Carman Equation

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