insu-00565026
https://insu.hal.science/insu-00565026
https://insu.hal.science/insu-00565026/document
https://insu.hal.science/insu-00565026/file/181-3-1480.pdf
doi:10.1111/J.1365-246X.2010.04573.X
[IRD] IRD - Institut de recherche pour le développement
[SDE] Sciences De l'Environnement
[INSU] INSU - Institut National des Sciences de l'Univers
[UNIV-SAVOIE] Université Savoie Mont Blanc
[UPMC] Université Pierre et Marie Curie
[AFRIQ] HAL-Francophonie, Afrique et océan indien
[UGA] HAL Grenoble Alpes
[CNRS] CNRS - Centre national de la recherche scientifique
[UNIV-GRENOBLE1] Université Joseph Fourier - Grenoble I
[INPG] Institut polytechnique de Grenoble
[IRSTEA] IRSTEA - Institut national de recherche en sciences et technologies pour l'environnement et l'agriculture (<b>anciennement Cemagref</b>)
[GIP-BE] GIP Bretagne Environnement
[IFSTTAR] Ifsttar
[UMMISCO] Unité de Modélisation Mathématique et Informatique de Systèmes COmplexes
[AGREENIUM] Archive ouverte en agrobiosciences
[SORBONNE-UNIVERSITE] Sorbonne Université
[SU-SCIENCES] Faculté des Sciences de Sorbonne Université
[SU-SCI] Sciences - Sorbonne Université
[UMI-209] Unité de modélisation mathématique et informatique des systèmes complexes
[INRAE] Institut National de Recherche en Agriculture, Alimentation et Environnement
[USMB-COMUE] Université Savoie Mont Blanc - UGA [* - 2019]
[SU-TI] Sorbonne Université - Texte Intégral
[ALLIANCE-SU] Alliance Sorbonne Université
[UNIV-EIFFEL] Université Gustave Eiffel
[IFSTTAR-UNIVEIFFEL] Institut Français des Sciences et Technologies des Transports, de l'Aménagement et des Réseaux
Determination of permeability from spectral induced polarization in granular media
Revil, A.
Florsch, Nicolas
[SDU.STU.GP] Sciences of the Universe [physics]/Earth Sciences/Geophysics [physics.geo-ph]
[PHYS.PHYS.PHYS-GEO-PH] Physics [physics]/Physics [physics]/Geophysics [physics.geo-ph]
[SDE.MCG] Environmental Sciences/Global Changes
ART
Probability distributions
Electrical properties
Hydrogeophysics
Permeability and porosity
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.
2010-06
2021-03-03
en
Geophysical Journal International
Oxford University Press (OUP)