Electrical and Petrophysical Modeling of Ferron Sandstone Data

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As part of the 3D characterization of a fluvial reservoir analog site in the Ferron Sandstone in east-central Utah, new lab measurements of porosity, permeability, water content, and complex dielectric permittivity are collected and analyzed. Petrographic analysis of thin sections extracted from the same samples produced data on bulk, macro- and microporosity, lithology, and cementation. Thus, we have an unusually comprehensive data base for analysis. Debye models of complex dielectric permittivities are fitted using three frequency-dependent Debye relaxation mechanisms. Most ambient and dry samples are dominated by low-frequency relaxation mechanisms. The average dielectric constant and electrical conductivity at the typical ground-penetrating radar (GPR) frequency of 75 MHz are directly related to volumetric water content and are 3.86 and 0.20 mS/m for oven-dried samples, 4.50 and 0.71 mS/m for ambient saturated sam-ples, and 15.42 and 13.11 mS/m for fully saturated samples. Electrical conductivity is poorly estimated from the oven-dried samples (for all clay content) because ion mobility is significantly reduced; thus, the dry conductivity is less useful for estimating petrophysical variations.Multivariate regressions with the petrophysical parameters estimate the electrical properties at 75 MHz and 1000 MHz with average correlation coefficients of ~0.921 and ~0.925, respectively. Empirically derived predictions of dielectric constant as a function of water content will always provide better fits to the observed values than either generic models (such as the CRIM model) or fits to other data sets (such as the Topp formula, which was derived for soils). The Topp model consistently underestimates the dielectric constant, while the CRIM model generally overestimates it, at both 75 and 1000 MHz. The overall regression procedures can be applied to data from other sites and potentially used as the basis of inversion of petrophysical properties from measurements of electric and dielectric properties.