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Surface Conduction Model for Fractal Porous Media
Author(s) -
Wang Hongtao,
Revil André
Publication year - 2020
Publication title -
geophysical research letters
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.007
H-Index - 273
eISSN - 1944-8007
pISSN - 0094-8276
DOI - 10.1029/2020gl087553
Subject(s) - fractal , thermal conduction , fractal dimension , porosity , exponent , power law , porous medium , materials science , surface conductivity , conductivity , surface (topology) , permeability (electromagnetism) , texture (cosmology) , mineralogy , geology , geometry , physics , composite material , mathematics , mathematical analysis , chemistry , philosophy , linguistics , biochemistry , statistics , artificial intelligence , image (mathematics) , computer science , membrane , quantum mechanics
The electrical conductivity of natural water‐saturated porous materials has two contributions, one associated with conduction in the pore network and a second one associated with the electrical double layer coating the surface of the mineral grains, and called surface conductivity. We model the effect of material texture on surface conductivity based on fractal theory. We demonstrate that surface conductivity obeys a power‐law dependence (that we called surface Archie's law) on the specific surface area. The power exponent is theoretically related to the porosity exponent entering Archie's law and to the fractal dimension of the pore network. A permeability model is derived by combining the new surface Archie's law and the Kozeny‐Carman model. We show that our model is consistent with both numerical finite element simulations on synthetic porous media and experimental data.