Equations for the electrical conductivity, the electrochemical potential, and the streaming potential of a clay-lined, brine-filled capillary tube have been developed from fundamental principles of irreversible thermodynamics and electrochemistry following the work of Gross and Osterle. Use of the equations gives insight into the role of clay in determining the electrical conductivity as well as the electrochemical and streaming potentials in shaly sand reservoir rocks. The variation in these electrical properties with the magnitude of the electrical potential of the pore lining clay, the radius of the capillary, and the concentration and composition of the saturating brine is investigated. A constant value of surface potential is shown to yield plots which exhibit good qualitative agreement with the experimental shaly sand data of Waxman and Smits and Hill and Milburn. By contrast, a constant value of surface charge density is shown to yield plots of brine saturated capillary conductivity which exhibit good qualitative correlation to the experimental shaly sand data of Schon and Borner. The electrochemical potential is shown to vary smoothly from the diffusion potential to the theoretical limit of the Nernst potential as either the surface charge or the capillary radius is changed. The streaming potential of a clay-lined capillary tube is directly proportional to the surface potential of the tube at sufficiently large values of tube radius and brine concentration. This is consistent with Smoluchowski's equation.

Incorporation of the clay-lined capillary tube model into a 3-dimensional network model allows for study of the variation of resistivity index with water saturation in water-wet shaly sand formations. The effects of brine concentration, ion radii, and clay distribution on the magnitude of the Archie saturation exponent, n, are investigated. Relative changes in n are shown to be consistent with experimental results of Waxman and Thomas. The distribution of clays in the rock is shown to significantly alter the resistivity index-saturation plots.