Influence of Grain Size and Shape on the Performance of Dielectric Permittivity-Based Water Saturation Assessment Models
Authors:   The University of Texas at Austin, Azizoglu Zulkuf , Heidari Zoya ,   The University of Texas at Austin
Published: September 2024

Dielectric permittivity mixture models commonly assume simple geometries for the constituting rock components, which affect their reliability in rocks with complex pore geometry and rock fabric such as carbonates. The combined influence of pore geometry, grain shape, and grain size on the performance of those models in water saturation assessment remains to be tested. Frequency-domain dielectric permittivity simulations can model the influence of pore and grain geometries on dielectric permittivity without a need for explicitly defining those parameters. Individual impacts of the aforementioned properties can be quantified and separated in the pore-scale domain via dielectric permittivity simulations. Therefore, the objectives of this paper are to (a) design pore-scale rock samples with different grain shapes and sizes, (b) investigate the influence of grain shape, grain size, and pore connectivity on the dielectric permittivity of the pore-scale rock samples as well as rock images from carbonate and sandstone formations, and (c) evaluate the performance of multiple dielectric permittivity mixture models in the quantification of water saturation. We construct three-dimensional (3D) synthetic rock models with spheroidal grains. We use different aspect ratios (i.e., the ratio of the radius of the major axis to the radius of the minor axis) and grain sizes for spheroids. Next, we numerically alter the water saturation. We perform frequency-domain dielectric permittivity simulations (through the solution of Maxwell’s equations in the frequency domain) in actual and synthetic samples in the frequency range of 100 Hz to 5 GHz. Finally, we test the performance of multiple dielectric permittivity mixture models (e.g., Maxwell-Garnett, Hanai-Bruggeman, CRIM, etc.) in the estimation of water saturation from dielectric permittivity measurements. We observed that the relative permittivity (i.e., the real part of the dielectric permittivity) increased with an increase in the aspect ratio of the spheroid grains. The electrical conductivity (which is associated with the imaginary part of the dielectric permittivity) decreased as the grains became flatter, which is due to the decreasing efficiency in electrical current flow. The dielectric permittivity dispersion is much less significant for rounder spheroid grains. The dispersion and absolute values of the relative permittivity and electrical conductivity decreased with the decreasing water saturation. We documented that overlooking the influence of pore and grain geometries can lead to average relative errors in water saturation up to 100% in the sandstone and carbonate samples. Taking into account the grain geometry and using Maxwell-Garnett formulation with the background medium properties estimated with the CRIM equation resulted in the lowest average relative errors (10%) in water saturation quantification. The documented results quantified the impacts of grain size, grain shape, and pore connectivity on dielectric permittivity. This analysis was possible through pore-scale modeling of dielectric permittivity dispersion. The outcomes demonstrate the limitations of the current dielectric permittivity mixture models in the calculation of dielectric permittivity and assessment of water saturation under different conditions. Therefore, the results of this work can help in quantifying the uncertainty associated with the use of existing dielectric permittivity mixture models depending on the pore and grain geometry of any given rock.