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A Sandbox Experiment of Self-Potential Signals Associated with a Pumping Test

CNRS-CEREGE, University of Aix-Marseille III, Dep. of Hydrogeophysics and Porous Media, BP 80, 13545 Aix-en-Provence, Cedex 4, France

View larger version (51K): [in a new window]   Fig. 1. Sketch indicating the position of the observation station P, the position of the source point M, the source region i in which fluid flow takes place. The source region is bounded by the interface . The region e corresponds to the vadose zone. The vectors n and nS represent the outward unit vectors perpendicular to the top surface and the phreatic surface, respectively.

View larger version (85K): [in a new window]   Fig. 2. Picture of the Plexiglas tank. All the electrodes are connected to a multichannel multimeter interfaced to a laptop computer. One electrode is used as a reference (here located on the right side of the picture) for the measurements.

View larger version (56K): [in a new window]   Fig. 3. Position of the electrodes (1–27 plus a reference electrode) and piezometers (P1–P6) and geometry of the tank. The pumping well is placed in the middle of the tank (H = 0M 35 cm). We note Q the volumetric pumping rate. The pumped water is injected at the two end-members of the tank.

View larger version (26K): [in a new window]   Fig. 4. Laboratory measurements of the electrokinetic coupling coefficient. (a) Sketch of the experimental setup (ZetaCad) showing pore fluid reservoirs R1 and R2 (1), sample tube (2), pressure sensors (3), voltage electrodes connected to an impedance meter (4), and measurements of the electrical conductivity of the electrolyte (5). The pressure level in the reservoirs is controlled by adjusting the pressure with N2 gas. (b) Laboratory measurement of the electrokinetic coupling coefficient of the sand used in the sandbox experiment with tapwater.

View larger version (27K): [in a new window]   Fig. 5. Snapshot of the distribution of the electrical potential at the shutdown of the pump. The line results from a best fit of the theoretical model: Exp. 1, Q = 60 cL min–1 (1.0 x 10–5 m3 s–1); Exp. 2, Q = 255 cL min–1 (4.25 x 10–5 m3 s–1).

View larger version (21K): [in a new window]   Fig. 6. Distribution of the piezometric head in the steady-state conditions of pumping for Exp. 1 (filled circles) and 2 (crosses). The filled squares represent the piezometric levels at the shutdown of the pump and at the end of the relaxation of the depression cone. The lines correspond to a parabolic fit of the measurements.

View larger version (21K): [in a new window]   Fig. 7. Variation of the piezometric level vs. time in Piezometer P6 in the vicinity of the reference electrode. This variation h0 (6 cm) is smaller than the piezometric level variations recorded in the vicinity of the pumping well.

View larger version (30K): [in a new window]   Fig. 8. (a, b) Variation of the piezometric levels vs. time in the vicinity of the pumping well. (c, d) Variation of the electrical potentials vs. time in the vicinity of the pumping well. In both cases, the fit corresponds to a decreasing exponential function exp(–t/), where t is time and is a relaxation time (see main text). Note that the relaxation time is the same for both the electrical and the hydraulic signals in the vicinity of the pumping well (results from Exp. 1).

View larger version (23K): [in a new window]   Fig. 9. Variation of the piezometric levels vs. time in the vicinity of the pumping well. (a) Variation of the hydraulic head vs. time in the vicinity of the pumping well. (b) Variation of the electrical potential vs. time (results from Exp. 2).

View larger version (21K): [in a new window]   Fig. 10. (a) Variation of the electrical potentials at Electrode E16 vs. the piezometric levels recorded in Piezometer P4. (b) Predicted variation of the electrical potentials at Electrodes E16 vs. the piezometric levels recorded in Piezometer P4 (results from Exp. 1).

View larger version (26K): [in a new window]   Fig. 11. Electrical potential change vs. piezometric level change (the piezometric levels are interpolated from the values measured in the piezometers) between t = 3.5 min and the end of the experiment (35 min later). The error bar on the electrical potentials is about 0.2 mV, and the error bar on the piezometric head change is 0.05 m. The same trend is obtained in Exp. 2 (not shown here).