Pore‐Scale Investigation of the Electrical Resistivity of Saturated Porous Media: Flow Patterns and Porosity Efficiency

Abstract

AbstractThe electrical resistivity‐porosity relationship of porous media is critical for reliable formation evaluation. Archie's equation is empirical, and uses only porosity as pore‐space property, neglecting the spatial variability of the pore space; its fitting parameters may have unclear physical meaning and be nonconstant over a wider porosity range or in spatially complex rocks. We use microfluidics augmented with pore‐network modeling to investigate the effects of pore‐space properties and their evolution processes on electrical resistivity‐porosity relationships. Both a flow‐pattern parameter and a measure of porosity efficiency are implemented to quantify the spatial variability of the flow field and the conduction efficiency of porous media. Results indicate that both pore‐size distribution and pore‐space evolution impact the electrical behavior considerably. In cases of unimodal pore‐size distributions, a larger pore‐size variation or a higher porosity reduction in small pores results in higher values of Archie's porosity exponent, m; the flow pattern becomes more heterogeneous, and the efficiency of porosity to conduct electricity decreases. For cases of bimodal pore‐size distributions, the formation factor‐porosity relationship is nonlinear in log–log plots; the flow behavior is primarily affected by the fraction and connectivity of large pores. Results suggest that using porosity alone as pore‐space characteristic is inadequate to describe the electrical behavior of complex porous media. Petrophysical classification based on flow patterns and porosity efficiency is an effective alternative to differentiate the results. We introduce the electrical quality index as an effective parameter for petrophysical classification, which is verified with core data for both Fontainebleau sandstones and carbonates.