A new formulation to compute self-potential signals associated with ground water flow

Abstract

Abstract. The classical formulation of the coupled hydroelectrical flow in porous media is based on a linear formulation of two coupled constitutive equations for the electrical current density and the seepage velocity of the water phase and obeying Onsager's reciprocity. This formulation shows that the streaming current density is controlled by the gradient of the fluid pressure of the water phase and a streaming current coupling coefficient that depends on the so-called zeta potential. Recently a new formulation has been introduced in which the streaming current density is directly connected to the seepage velocity of the water phase and to the excess of electrical charge per unit pore volume in the porous material. The advantages of this formulation are numerous. First this new formulation is more intuitive not only in terms of constitutive equation for the generalized Ohm's law but also in specifying boundary conditions for the influence of the flow field upon the streaming potential. With the new formulation, the streaming potential coupling coefficient shows a decrease of its magnitude with permeability in agreement with published results. The new formulation is also easily extendable to non-viscous laminar flow problems (high Reynolds number ground water flow in cracks for example) and to unsaturated conditions with applications to the vadose zone. We demonstrate here that this formulation is suitable to model self-potential signals in the field. We investigate infiltration of water from an agricultural ditch, vertical infiltration of water into a sinkhole, and preferential horizontal flow of ground water in a paleochannel. For the three cases reported in the present study, a good match is obtained between the finite element simulations performed with the finite element code Comsol Multiphysics 3.3 and field observations. Finally, this formulation seems also very promising for the inversion of the geometry of ground water flow from the monitoring of self-potential signals.

Tomography of the Darcy velocity from self‐potential measurements

“…Self‐potential signals of electrokinetic nature are due to the drag of the excess of electrical charge contained in the pore water and resulting from the existence of the electrical diffuse layer at the pore water/mineral interface. In an isotropic but possibly heterogeneous medium, the total current density is given by [ Revil et al , 2007; Bolève et al , 2007b] where θ s is the porosity, θ is the water content, j is the electrical current density (in A m −2 ), u is the Darcy velocity (in m s −1 ), ϕ is the SP (in V), σ is the electrical conductivity of the porous material (in S m −1 ) [see Revil et al , 1998], and V is the excess charge (of the diffuse layer) of the pore water per unit pore volume (in C m −3 ), which depends mainly on the permeability of the porous material (Figure 1). The continuity equation for the electrical charge is ∇ · j = 0.…”

The self potential method

“…Wanfang et al (1999) attempt separating the SP response from karstic features from that due to topographic effect and noise. A negative self-potential anomaly is associated with the presence of palaeo-channel because of the horizontal flow of ground water (Bol'eve et al, 2007). Since the flow of current and hence equipotential line is also dependent of subsurface resistivity distribution, the variations in resistivity will modify the SP anomalies.…”

“…The SP anomalies can be modeled, e.g., vertical lithological contacts or structural discontinuities give steep, asymmetrical anomaly with its amplitude depending on resistivity ratio (Fitterman, 1979;Corwin and Hoover, 1979). It helps to understand the pattern of ground water flow in the subsurface, identify preferential flow path and also variations in permeability (Minsley, 2007;Jardani et al, 2007;Bol'eve et al, 2007). The inversion of self-potential signals has significant applications.…”

Distribution of Vapor and Condensate in a Hydrothermal System: Insights From Self‐Potential Inversion at Mount Tongariro, New Zealand

“…Here ψ is the SP in V, and σ is the electrical conductivity (S/m) of the rock. Assuming fully saturated rock, the streaming current density is where is the excess charge per unit pore volume (C/m 3 ) of the electrical double layer at the solid‐fluid interface that is effectively dragged by the water flowing at Darcy velocity, u (Bolève et al, ). The movement of the excess charge due to the water flow in turn generates electrical potentials that can be measured at the surface as the SP data.…”