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

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

Foreword Preface 1. Fundamentals of the self-potential method 2. Development of a fundamental theory 3. Laboratory investigations 4. Forward and inverse modeling 5. Applications to geohazards 6. Application to water resources 7. Application to hydrothermal systems 8. Seismoelectric coupling Appendix A: a simple model of the Stern layer Appendix B: the u-p formulation of poroelasticity References Index.

The Self-Potential Method: Theory and Applications in Environmental Geosciences

In hard-rock aquifers, fractured zones constitute adequate drinking water exploitation areas but also potential contamination paths. One critical issue in hydrogeological research is to identify, characterize, and monitor such fractured zones at a representative scale. A tracer test monitored with surface electrical resistivity tomography (ERT) could help by delineating such preferential flow paths and estimating dynamic properties of the aquifer. However, multiple challenges exist including the lower resolution of surface ERT compared with crosshole ERT, the finite time that is needed to complete an entire data acquisition, and the strong dilution effects. We conducted a natural gradient salt tracer test in fractured limestones. To account for the high transport velocity, we injected the salt tracer continuously for four hours at a depth of 18 m. We monitored its propagation with two parallel ERT profiles perpendicular to the groundwater flow direction. Concerning the data acquisition, we always focused ...

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A salt tracer test monitored with surface ERT to detect preferential flow and transport paths in fractured/karstified limestones

Assessing the contribution of electrical resistivity tomography (ERT) and self-potential (SP) methods for a water well drilling program in fractured/karstified limestones

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.

J.-J. Fry

Papers

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