From computed microtomography images to resistivity index calculations of heterogeneous carbonates using a dual-porosity pore-network approach: influence of percolation on the electrical transport properties.

Standard reservoir evaluations are based on Archie's law relating the average water saturation to the average electrical resistivity by R(ind) = S(w)(-2). However, especially in the case of complex heterogeneous carbonates, deviation from Archie's law is observed and generally attributed to factors affecting the percolation or disconnectedness of the different phases (wetting films, microporosity, macropores) assuring electrical conductance. Pore-network models (PNM's) in combination with high-resolution computed microtomography (µ-CT) constitute a very effective tool to investigate the influence of the geometry and topology of the porous media on the spatial distribution of the conductive phase, and therefore on the shape of the resistivity index curve. An extended version of the classical PNM applicable to dual-porosity systems is presented. It combines the classical pore-network modeling applied on the macroporous space with the macroscopic properties of the microporous phase, supposing that the two pore systems act in parallel. Three-dimensional images provide information on the connectedness of the microporous phase, which is then included in the simulations. Electrical behavior of sandstone and two carbonates presenting distinct resistivity index curves were simulated and compared to measurements. Both Archie and "non-Archie" behavior were correctly reproduced, and the curve shape was explained considering percolation of the different phases.

Geometrical and transport properties of random packings of polydisperse spheres.

Loose packings of spheres with bidisperse or log-normal distributions are generated by random sequential deposition. Porosity, conductivity, and permeability are determined. The porosities correspond to loose packings, but they follow the usual trends for bidisperse packings. The conductivity and permeability follow power laws as functions of the porosity of the packings. Several other quantities such as the classical Kozeny constant are successfully represented as functions of porosity. Some dimensionless representations gather the numerical data on curves valid for all particle distributions. Finally, comparisons with experimental data are satisfactory.

Capillary condensation in a fractal porous medium.

Small-angle x-ray and neutron scattering are used to characterize the surface roughness and porosity of a natural rock which are described over three decades in length scales and over nine decades in scattered intensities by a surface fractal dimension D = 2.68+/-0.03. When this porous medium is exposed to a vapor of a contrast-matched water, neutron scattering reveals that surface roughness disappears at small scales, where a Porod behavior typical of smooth interfaces is observed instead. Water-sorption measurements confirm that such interface smoothing is due predominantly to the water condensing in the most strongly curved asperities rather than covering the surface with a wetting film of uniform thickness.