Forward Modeling and validation of 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 establishing a 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 has been extended in the inertial laminar flow regime and to unsaturated conditions with applications to the vadose zone. 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 finite element simulations performed and field observations. Thus, this formulation could be useful for the inverse mapping of the geometry of groundwater flow from self-potential field measurements.

Estimation of the electrical potential distribution along metallic casing from surface self-potential profile

“…Numerous studies have been published during the two last decades about the use of the SP method for hydrological purposes (see for instance the reviews by Bolève et al, 2007;Jouniaux et al, 2009;Revil et al, 2012 and references therein). In particular, the SP method gave excellent results when applied to pumping tests.…”

Electrokinetic coupling in single phase flow in periodically changed capillary with a very small throat size

“…Wurmstich and Morgan [8] used a 3-D finite-difference algorithm to simulate streaming potential responses during oil pumping with the aim of using streaming potential as a tool to monitor subsurface flow. Other similar and relevant studies can also be found in [9][10][11][12][13][14][15] and references therein. These researches, however, usually neglect the effect of electrical potential on fluid flow and instead are focused on the characteristics of electrical potential distribution because the authors argue that the electrical potential have only negligible influences on fluid flow.…”

A review on electrokinetically induced seismo-electrics, electro-seismics, and seismo-magnetics for Earth sciences

“…The electric current density can also been expressed as a function of the volumetric charge density Q V and the Darcy velocity v. The volumetric charge density is sometimes expressed as a function of permeability, but this formula has not been validated using independent measurements of permeability and charge density deduced from the cation exchange capacity (CEC) measurements. Usually the volumetric charge density is deduced from streaming potential coefficient measurements using the following formula (Bolève et al, 2007):…”