1. 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

2. 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

3. 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

4. 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

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

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

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

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

9. 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

10. 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

11. 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

12. 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

13. (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