pH-dependent surface charging and points of zero charge. IV. Update and new approach.

SUMMARY

The surface conductivity of porous rocks has two contributions: the first is associated with the diffuse layer coating the grains and is frequency-independent as long as the diffuse layer is above a percolation threshold. The second contribution is associated with the Stern layer of weakly sorbed counterions on the mineral surface and is frequency-dependent if the Stern layer is discontinuous at the scale of the representative elementary volume. In the frequency range 1 mHz–100 Hz, this second contribution is also associated with the main polarization mechanism observed by the spectral induced polarization method in granular media (neglecting the contribution of other polarization processes like those associated with redox processes and membrane polarization). At the macroscale, we connect the Stern layer contribution to the complex conductivity and to the expectation of the probability distribution of the inverse of the grain size. This is done by performing a convolution between the probability distribution of the inverse of the grain size and the surface conductivity response obtained when all the grains have the same size. Surface conductivity at the macroscopic scale is also connected to an effective pore size used to characterize permeability. From these relationships, a new equation is derived connecting this effective pore size, the electrical formation factor, and the expected value of the probability distribution for the inverse of the grain size, which is in turn related to the distribution of the relaxation times. These new relationships are consistent with various formula derived in the literature in the limit where the grain size distribution is given by the delta function or a log normal distribution and agree fairly well with various experimental data showing also some limitations of the induced polarization method to infer permeability. One of these limitations is the difficulty to detect the relaxation, in the phase, associated with the smaller grains, as this polarization may be hidden by the Maxwell–Wagner polarization at relatively high frequencies (>100 Hz). Also, cemented aggregates of grains can behave as coarser grains.

https://hal-insu.archives-ouvertes.fr/insu-00565026/document

Determination of permeability from spectral induced polarization in granular media

Complex conductivity of water-saturated packs of glass beads.

Low-frequency geoelectrical methods include mainly self-potential, resistivity, and induced polarization techniques, which have potential in many environmental and hydrogeological applications. They provide complementary information to each other and to in-situ measurements. The self-potential method is a passive measurement of the electrical response associated with the in-situ generation of electrical current due to the flow of pore water in porous media, a salinity gradient, and/or the concentration of redox-active species. Under some conditions, this method can be used to visualize groundwater flow, to determine permeability, and to detect preferential flow paths. Electrical resistivity is dependent on the water content, the temperature, the salinity of the pore water, and the clay content and mineralogy. Time-lapse resistivity can be used to assess the permeability and dispersivity distributions and to monitor contaminant plumes. Induced polarization characterizes the ability of rocks to reversibly store electrical energy. It can be used to image permeability and to monitor chemistry of the pore water–minerals interface. These geophysical methods, reviewed in this paper, should always be used in concert with additional in-situ measurements (e.g. in-situ pumping tests, chemical measurements of the pore water), for instance through joint inversion schemes, which is an area of fertile on-going research.

Review: Some low-frequency electrical methods for subsurface characterization and monitoring in hydrogeology

Electrical resistivity tomography technique for landslide investigation: A review

Laboratory experiments are performed to understand the controlling parameters of the electrical field associated with the seepage of water through a porous material. We use seven glass bead packs with varying mean grain size in an effort to obtain a standard material for the investigation of these electrical potentials. The mean grain size of these samples is in the range 56–3000 μm. We use pure NaCl electrolytes with conductivity in the range 10−4 to 10−1 S m−1 at 25°C. The flow conditions cover viscous and inertial laminar flow conditions but not turbulent flow. In the relationship between the streaming potential coupling coefficient and the grain size, three distinct domains are defined by the values of two dimensionless numbers, the Dukhin and the Reynolds numbers. The Dukhin number represents the ratio between the surface conductivity of the grains (due to conduction in the electrical double layer coating the surface of the grains) and the pore water electrical conductivity. At high Dukhin numbers (≫1) and low Reynolds numbers (≪1), the magnitude of the streaming potential coupling coefficient decreases with the increase of the Dukhin number and depends on the mean grain diameter (and therefore permeability) of the medium. At low Dukhin and Reynolds numbers (≪1), the streaming potential coupling coefficient becomes independent of the microstructure and is given by the well-known Helmholtz-Smoluchowski equation widely used in the literature. At high Reynolds numbers, the magnitude of the streaming potential coupling coefficient decreases with the increase of the Reynolds number in agreement with a new model developed in this paper. A numerical application is made illustrating the relation between the self-potential signal and the intensity of seepage through a leakage in an embankment.

https://agupubs.onlinelibrary.wiley.com/doi/pdf/10.1029/2006JB004673

Streaming potentials of granular media: Influence of the Dukhin and Reynolds numbers

We propose an algorithm to invert self-potential signals measured at the ground surface of the Earth to localize hydromechanical disturbances or to the pattern of groundwater flow in geothermal systems. The self-potential signals result from the divergence of the streaming current density. Groundwater flow can be either driven by topography of the water table, free convection, or deformation of the medium. The algorithm includes the electrical resistivity distribution of the medium obtained independently by DC resistance tomography or electromagnetic methods or by coding the assumed geology in terms of distribution of the electrical resistivity accounting for the effect of the temperature and salinity distributions and possibly constraints from borehole measurements. Inversion of the distribution of the source current density from ground surface and borehole self-potential measurements is achieved by solving the inverse problem using Tikhonov regularization solutions that are compatible with the physics of the primary flow problem. By introducing assumptions regarding the smoothness or the compactness of the source and the three-dimensional distribution of the electrical resistivity of the system, the inverse problem can be solved in obtaining the three-dimensional distribution of the current source density in the ground. However, an annihilator can be added to the inverted source geometry without affecting the measured self-potential field. Annihilators can be obtained from boundary conditions. Synthetic models and a sandbox experiment are discussed to demonstrate the validity of the algorithm. An application is presented to the geothermal field of Cerro Prieto, Baja California, Mexico, using literature data. Inversion of the self-potential and resistivity data allows observing a plume of hot groundwater rising to the ground surface in the central part of the investigated area and discharging to the ground surface in the southwest part. The temperature anomaly associated with the existence of this plume is independently observed by interpolating borehole temperature measurements. We found a good agreement between the distribution of the temperature and the inverted source current density. The proposed method appears therefore as a noninvasive method for remote detection and three-dimensional mapping of subsurface groundwater flow.

https://agupubs.onlinelibrary.wiley.com/doi/pdf/10.1029/2007JB005302

Three-dimensional inversion of self-potential data used to constrain the pattern of groundwater flow in geothermal fields

We invert self-potential data in order to locate anomalous water flow pathways in dams and embankments and to estimate the seepage velocity. The inversion of the self-potential data is performed
using the modified singular value decomposition for the inverse problem using a linear formulation of the forward problem. The kernel is solved numerically accounting for the topography of the system and the resistivity distribution, which is independently obtained through electrical resistance tomography. A prior constraint based on finite element modelling of ground water flow can also be used to provide a prior source current density model if needed. This self-potential tomography
approach is first validated with a synthetic case study showing how the position of a preferential
fluid flow pathway can be retrieved from self-potential and resistivity data and how the seepage velocity can be obtained inside one order of magnitude. This methodology is then applied to a test site corresponding to a portion of an embankment dam along the Rhone River in France. Two self-potential maps (with 1169 and 2076 measurements, respectively) and four resistivity tomograms are used to locate a leak. One self-potential profile and one resistivity profile are used together to perform the 2D inversion of the self-potential data to locate the anomalous leakage at depth and to estimate the flow rate. The depth at which the preferential fluid flow pathway is located, according to self-potential tomography, agrees with an independent geotechnical test using the Permeafor. This demonstrates the usefulness of this methodology to detect preferential water channels inside the body of a dam.

A. Bolève

Papers

Streaming potentials of granular media: Influence of the Dukhin and Reynolds numbers

Three-dimensional inversion of self-potential data used to constrain the pattern of groundwater flow in geothermal fields

Preferential fluid flow pathways in embankment dams imaged by self-potential tomography

Localization and quantification of leakages in dams using time-lapse self-potential measurements associated with salt tracer injection

Influence of the Dukhin and Reynolds numbers on the apparent zeta potential of granular porous media.