A pore-size scale model for the dielectric properties of water-saturated clean rocks and soils

Abstract

The dielectric properties of water-saturated rock and soils are strongly dependent on the amount and nature of their porosity; interpretation of these geophysical data requires petrophysical models that incorporate both of these elements. The differential effective medium approximation (DEMA) is used to develop a dielectric permittivity model for clean (i.e., clay free) media that divides the pore spaces into elements corresponding to three categories of relative size scale: microscopic porosity (e.g., intergranular cracks), mesoscopic porosity (e.g., main pore volumes), and macroscopic porosity (e.g., vugs and fractures). The hierarchical size-scale structure imposed by the DEMA iterative embedding process is used to assign each pore space category its role in model construction. Use of this model demonstrates that the relationship between dielectric permittivity and porosity is significantly affected by the size scales of pores present in the rock models. A region of realizable permittivity-porosity values is obtained by varying the pore structure in the scaled-porosity model. The bounds of this region correspond to end-member porosity models. Analysis of experimental permittivity data for water-saturated sandstones and carbonates that cover a substantial range of porosity values found that the scaled-porosity models account for a significant part of the variability in experimental data.