title: Deviation from Archie's law in partially saturated porous media: Wetting film versus disconnectedness of the conducting phase.
abstract: We experimentally study the electrical transport in partially water-saturated pore network. The porous medium under investigation is a Fontainebleau sandstone, characterized by x-ray tomography. We show the existence of two electrical conductivity regimes. At high water saturation, the electric resistivity follows a well-known Archie law. Below a water saturation S_{w} approximately 0.2 , a strong negative deviation from this Archie law is observed. We attribute this transition to the existence of "a thick liquid film," assuring the ionic conduction in the low saturation regime. A numerical simulation is proposed to confirm this scenario. Two possible protocols are used to distribute the brine phase in the pore network of a three-dimensional microtomography image. The first one is based on a minimization of the interfacial energy. The second takes into account a quasistatic capillary displacement. The classical random-walk algorithm is used to compute the electric conductivity at various water saturations. Without the "thick film," both of the two fluid-placing protocols show a disconnectedness transition of the brine phase when S_{w}<0.2 . Adding this "film" to solid surface, the electrical continuity is maintained. The bending down trend is correctly reproduced, showing that in this range, the electric response cannot be described by a power law as usual.
authors.affiliation: Physique de la Matière Condensée, Ecole Polytechnique, CNRS, 91128 Palaiseau, France and IFP, Rueil Malmaison 92852, France.
authors.forename: M
authors.initials: M
authors.lastname: Han
authors.forename: S
authors.initials: S
authors.lastname: Youssef
authors.forename: E
authors.initials: E
authors.lastname: Rosenberg
authors.forename: M
authors.initials: M
authors.lastname: Fleury
authors.forename: P
authors.initials: P
authors.lastname: Levitz