The Role of Pore‐Shape and Pore‐Space Heterogeneity in Non‐Archie Behavior of Resistivity Index Curves

Abstract

AbstractResistivity index curves describe the relationship between electrical resistivity and water saturation of porous media and are critical in formation evaluation and for the geophysical monitoring of subsurface processes. Archie's second equation enforces a linear relationship between resistivity index and water saturation in log‐log plots which has been widely used for the assessment of in situ hydrocarbon saturation. However, resistivity index curves that deviate from Archie's equation are ubiquitous in subsurface reservoirs, especially complex carbonates exhibiting bimodal pore‐size distributions, where the effects of pore‐scale controlling factors on rock resistivity remain unclear. We implement pore‐network models built under controlled conditions of pore shapes, bimodal pore‐size distributions, pore connectivity, micropore fractions, and anisotropy to investigate the effects of pore shapes and pore‐space heterogeneity on resistivity index curves. Results indicate that percolating wetting films associated with pore shapes decrease the resistivity index at low values of water saturation and cause a decrease in saturation exponent. In cases of bimodal pore‐size distributions, micropore fractions control the connectivity between macropores, thus affecting water drainage and resistivity index curves. At low fractions of micropores, the resistivity index curve is governed by the connected macropore system at high values of water saturation and is then determined by micropores, thereby resulting in non‐Archie behavior. Pore‐size distributions and spatial anisotropy also affect the resistivity index curves. We summarize the observed pore‐space heterogeneity effects on resistivity index curves and compare model predictions to numerical simulations; both the geometric mean model and effective medium theory provide acceptable estimates of the electrical properties of bimodal porous media.