Fig. 1. Half-space heterogeneous model with water pumping well. (a) is plan view of model and (b) is cross-section of the model. Background of the model is silty sand and that has physical properties of K(1×10-6
Fig. 2. Vertical cross-sections of streaming current source density about homogeneous and heterogeneous models. (a) is streaming current source density about water pumping when the physical properties are same within whole model (K = 1×10-6
Fig. 3. Surface plan map of SP about homogeneous and heterogeneous pumping models. (a) homogeneous half-space model, (b) heterogeneous K half-space model, (c) heterogeneous K and L halfspace model and (d) heterogeneous K, L and σ half-space model (Sheffer and Oldenburg, 2007).
Fig. 4. Surface profiles of SP at y = 500 m. (a) homogeneous halfspace model, (b) heterogeneous K half-space model, (c) heterogeneous K and L half-space model and (d) heterogeneous K, L and σ half-space model (Sheffer and Oldenburg, 2007).
Fig. 5. SP anomaly and resistivity profiling to compare results at fracture zones in a hard rock. Resistivity survey was conducted to use Wenner configuration with 150 m current electrode separation (i.e. a = 50 m) and SP response was measured along the same profile line with a 10 m potential electrode separation. Positive SP anomaly is interpreted to show groundwater flow in the fractured formation (Pozdnyakova et al., 2001; Sharma and Baranwal, 2005).
Fig. 6. SP distributions with 5 different time steps of water (white) moving model toward the production well, which is located at 0 m on the horizontal axis. (a) shows 2 snapshots of 231 days and 463 days of the saturation distribution within the reservoir layer. (b) is SP about 1D horizontal section per different times. The peak of the SP curve per each time is located at the water front of same time (Saunders et al., 2008).
Fig. 7. Vertical sections of 3 models containing shale (black) with different percent; (a) 17%, (b) 35% and (c) 50% randomly. From the different contents of the model, conductivity structure of the reservoir is changed (Saunders et al., 2008).
Fig. 8. Maximum SP measured at the well versus time for models with varying contents of shale. SP increases in early time about the model of higher shale content while the water front is far away from the well. And increased conductivity by shale content makes potential reduced when the water front is close to the well (Saunders et al., 2008).
Fig. A-1. Examples about three types of electrical double layer:(a), (b) and (c). (a) is Helmholtz double layer that surface ofcolloid is charged with negative ions and positive ions areabsorbed to negative ions symmetrically consisting layer. (b) isGouy-Chapman double layer. In this layer model, ions havingsame charge with charge on the surface of colloid also consist ofdiffuse layer. (c) is stern double layer. This system consists of twolayers of stern layer and Gouy layer. Stern layer is fixed and Gouylayer is diffuse layer that can be moved. Three types of electricaldouble layer are all electrical equilibrium state as long as therearen't any external current sources or any other forces.
Fig. A-2. 4 types of electrokinetic phenomena are all connectedeach other. These phenomena can be divided into two groups; oneis under being in the given electric field and the other is if electricfield. Electrophoresis and electro-osmosis have complementaryrelation under the electric field.
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