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Solute Extraction in Variable Density Flow: Shock Wave Driven Transport Compared to Pumping Yuval Ohana and Shaul Sorek Blaustein Institutes for Desert Research Zuckerberg Institute for Water Research Department of Environmental Hydrology & Microbiology

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Original Theoretical Principle (Sorek 1996) Abrupt pressure change in saturated porous medium with non-dimensional investigation of balance equations for fluid mass & momentum and component mass. Model findings: Instantaneous fluid motion by Expansive/Compressive/Shock wave, displacing the component in the direction of wave propagation. Original theory

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Vertical one dimensional characteristic (analytical) solution (Burde & Sorek 2000) Solute displacement and its accumulation is more pronounced for a rigid matrix without adsorption. 1D solution

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Experimental studies (Gross et al. 2003) (1)High pressure chamber. (2)Low pressure chamber. (3)Fast electro-pneumatic valve. (4)Nitrogen gas container. (5)Collecting container. (6)Computerized pressure control system with probes. (A) Shock tube; Compression waves (1) (4) (3) (2) (5) Tube1

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Significant differences (0.3% - 26%) in solute concentration, compared with control levels. Tube2

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(B) X-Ray visualization; Compression wave X-Ray1

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C B A Direction of propagating shock wave Pre- application Post application Location of shock application X-Ray2

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Shockwave generator During shock application Pressure logging system (C) Field study; Compression waves Field1

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High decay of pressure from generator to location of application yet, Salt displacement in the direction of the propagating wave. Initial salinity at ~75 cm below surface sand layer Change in salinity post application of compaction waves. Percent change of salinity Field2

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Component Mass balance equation in ( ) f +( ) S * Adsorption Current Physical Macroscopic Model Total Variation Diminishing (TVD) Numerical (1D) Model Fluid ( ) f Mass Balance equation * Compressible, concentration dependent Momentum balance equation * Wave equation * Transfer of inertia to the solid * Newtonian fluid Gas/Liquid state relations; Definitions Solid porous matrix ( ) S Mass Balance equation * Incompressible (current); Deformable Momentum balance equation * Account for inertia * Gain of inertia from the fluid * Elastic Material constitutive relation; Definitions Input-Output

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Impulses Simulation of solute extraction by shockwaves Expansion waves by succession of abrupt pressure rise at the boundary (x=0) Pressure at x=0 reverts between pulses and assuming a large reservoir no effect on fluid and solute Schematic series of solute extraction due to cyclic emitting of pressure pulses

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Simulation of solute extraction by continuous pumping Constant pumping intensity at x=0, without gravitational body force Account for Darcy’s momentum using Hubbert’s potential and steady state extraction reached after very short transient stage Static matrix momentum balance equation Simulation conditions for comparing pumping and shockwave extraction: Slightly deformable matrix and almost incompressible fluid with density updated by concentration after each time increment {Wave, undisturbed domain properties at x L} {Pumping, boundary domain properties at x=0} { Wave pressure impulse at x=0} {Constant, continuous pumping pressure} Pumping

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(Extraction by pumping)/(Extraction by shockwaves) ImperviousSemi-PerviousPervious Unweathered Clay; Limestone; Dolomite Silt; Loess; layered clay; Oil Reservoir Rocks Sand & Gravel; Fractured Rocks 5.0*E-095.0*E-05 to 5.0*E-070.0630Water 2.0*E-102.0*E-06 to 2.0*E-080.00210Air Depth [m] Values of for typical reservoir matrix properties. Operation Matrix Fluid Comparison

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