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 ͑DEMA͒ is used to develop a dielectric permittivity model for clean ͑i.e., clay free͒ media that divides the pore spaces into elements corresponding to three categories of relative size scale: microscopic porosity ͑e.g., intergranular cracks͒, mesoscopic porosity ͑e.g., main pore volumes͒, and macroscopic porosity ͑e.g., vugs and fractures͒. 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.

Backfill Impacts on Moisture Measurements in Fractured Rock

“…To improve estimates of water content made by the TDR method, much effort in recent years has been spent in studying the dielectric behavior of rocks and soil (e.g., Sakaki and Rajaram, 2006; Endres and Bertrand, 2006; Knight and Abad, 1995; Rothe et al, 1997) and the design of TDR probes (e.g., Souto et al, 2008; Sakaki and Rajaram, 2006; Ferré et al, 1996; Selker et al, 1993). However, three important challenges—the proper installation of probes, gap effects, and K a − θ calibrations for specific rock types (Sakaki and Rajaram, 2006)—remain unresolved.…”

Comparison of Petrophysical Relationships for Soil Moisture Estimation using GPR Ground Waves

“…In contrast, effective medium approximations (e.g., the differential effective medium method) use microscale geometric models to explicitly incorporate textural and structural information about the heterogeneous system into the prediction of dielectric properties. Various geometric models have been developed that incorporate pore structure or geometry (e.g., Endres and Bertrand, 2006), grain shape (e.g., Sen, 1984; Kenyon, 1984; Tyč et al, 1988; Jones and Friedman, 2000), and pore‐scale fluid distribution (e.g., Endres and Redman, 1996; Friedman, 1998; Cosenza et al, 2003; Chen and Or, 2006); these studies have demonstrated that the dielectric property of the medium is not solely a function of porosity and water content, which is the primary assumption of volumetric mixing formulae.…”

“…The differential effective medium (DEM) approach (Norris et al, 1985) for deriving petrophysical relationships based on geometric models has been extensively used to examine the dielectric properties of rocks and soils (e.g., Sen, 1984; Cosenza et al, 2003; Endres and Bertrand, 2006). The DEM method is based on an iterative inclusion embedding process where infinitesimally small volumes of the inclusions are sequentially embedded into the heterogeneous system; the electrical property of the effective medium that results from a given embedding constitute the electrical property of the background material for the next embedding step.…”

“…The DEM method is based on an iterative inclusion embedding process where infinitesimally small volumes of the inclusions are sequentially embedded into the heterogeneous system; the electrical property of the effective medium that results from a given embedding constitute the electrical property of the background material for the next embedding step. The mathematical description of the embedding process (e.g., Endres and Bertrand, 2006) is parameterized in terms of a homogenization variable p that monotonically increases from 0 at the start to 1 when the embedding process is completed. In this study, we considered three DEM‐type geometric models that were applied in Endres and Redman (1996) to examine the permittivity dependence on the soil water content.…”

Study of the properties of non-gas dielectric capacitors in porous media

“…The conductive paths of these charges are usually continuous in relatively high porosity and high permeability reservoirs, but in most occasions, they are discontinuous in tight oil and shale gas zones, or in the low porosity and low permeability reservoirs (Gasparrini et al 2014;Ghanizadeh et al 2014). Therefore, the electric properties of rocks include two major aspects: one is the conductive capability of free positive and negative charges in the water solution through the paths formed by pores and throats which connected with each other; the other is the dielectric capability of the bound charges of the non-conductive substances and particles, including rock matrix particles, oil or gas molecules, and pure water molecules (Freedman and Vogiatzis 1979;Jonscher 1983;Endres and Bertrand 2006). Nevertheless, whether conductive or dielectric, the current paths in the formation are influenced by the geometric pore structure of rocks.…”