2D pore-scale simulation of wide-band electromagnetic dispersion of saturated rocks

摘要

Effective medium theories (EMTs) are invoked routinely to interpret multifrequency dispersions of dielectric permittivity and electrical conductivity of saturated rocks. However, EMTs exhibit limitations that substantially restrict their validity for petrophysical interpretation. For instance, pore connectivity is of significant interest in the study of subsurface reservoirs, but no existing EMT includes it as an explicit property in the analysis of kilohertz- to gigahertz-range dielectric measurements. We introduce a new approach to quantify the effects of pore geometry and connectivity on the kilohertz-gigahertz frequency dispersion of dielectric permittivity and electrical conductivity of clay-free porous rocks. This approach is based on the numerical solution of the internal electric fields within submicron-resolution pore maps constructed with grain and rock pixels. The discrepancy between the internal fields and electrical currents calculated for a homogeneous scatterer and those calculated for a given pore map is minimized to yield the effective electrical conductivity and dielectric constant for that pore map. This minimization is performed independently for each frequency and is verified to agree implicitly with Kramers-Kronig's causality relationships. We show that EMTs only predict an average dispersion for given microscopic geometrical parameters (e.g., porosity, pore eccentricity), whereas individual realizations honoring the same parameters are associated with dispersion about average values predicted by EMTs. Unlike any EMT prediction, we show that pore connectivity plays a major role in both the shape and amplitude of wide-band electromagnetic property dispersions. The simulation procedure introduced in this paper provides a systematic method to assess the sensitivity of a multitude of pore-scale properties on the macroscopic wide-band dielectric dispersion of saturated rocks.