Electrical conductivity in shaly sands with geophysical applications

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Abstract
We develop a new electrical conductivity equation based on Bussian's model and accounting for the different behavior of ions in the pore space. The tortuosity of the transport of anions is independent of the salinity and corresponds to the bulk tortuosity of the pore space which is given by the product of the electrical formation factor F and the porosity ϕ. For the cations, the situation is different. At high salinities, the dominant paths for the electromigration of the cations are located in the interconnected pore space, and the tortuosity for the transport of cations is therefore the bulk tortuosity. As the salinity decreases, the dominant paths for transport of the cations shift from the pore space to the mineral water interface and consequently are subject to different tortuosities. This shift occurs at salinities corresponding to ξ/t(+)f ∼ 1, where ξ is the ratio between the surface conductivity of the grains and the electrolyte conductivity, and t(+)f is the Hittorf transport number for cations in the electrolyte. The electrical conductivity of granular porous media is determined as a function of pore fluid salinity, temperature, water and gas saturations, shale content, and porosity. The model provides a very good explanation for the variation of electrical conductivity with these parameters. Surface conduction at the mineral water interface is described with the Stern theory of the electrical double layer and is shown to be independent of the salinity in shaly sands above 10−3 mol L−1. The model is applied to in situ salinity determination in the Gulf Coast, and it provides realistic salinity profiles in agreement with sampled pore water. The results clearly demonstrate the applicability of the equations to well log interpretation of shaly sands.