Large-scale effects on resistivity index of porous media

The estimation of humidity in the unsaturated zone of soils and NAPL saturation in contaminated aquifers may be based on the interpretation of electrical resistivity index logs. In the present work, concepts of the theory of the two-phase flow in pore networks are employed to interpret the form of the equilibrium and dynamic resistivity index curves of large porous samples. A resistivity cell is constructed to measure the capillary and electrical properties of large samples of unconsolidated porous media. The drainage capillary pressure and resistivity index curves of a sand column are measured by using the micropore membrane (porous plate) method, where a 0.5% wt/vol NaCl aqueous solution is displaced by n-dodecane. The dynamic resistivity index curves are measured by using the continuous injection technique for various orientations of the sand column. Based on concepts of the two-phase flow theory, concerning the dominant displacement growth pattern in a pore network and arising from the cooperative effects of capillary, buoyancy, and viscous forces, approximate relationships are developed for the resistivity index and saturation exponent as functions of the water saturation. The saturation exponent decreases as the displacement advances and the fluid distribution across the sand column tends to be homogenized after oil breakthrough. Both the resistivity index and saturation exponent increase as the displacement pattern tends to become compact and stable. In the destabilized flow pattern, as the Bond number decreases, the resistivity index may increase respectably within a narrow range of values of the Bond number. This happens when the thickness of the unstable capillary finger exceeds the lateral dimension of the porous sample and becomes a fractal percolation cluster. The saturation exponent becomes almost constant and independent of water saturation only over the destabilized displacement pattern at high values of the Bond number.