Mechanisms of Confining Pressure Dependence of Resistivity Index for Tight Sandstones by Digital Core Analysis
Authors: Dai Hongyi , Shikhov Igor , Li Rupeng , Arns Ji-Youn , Arns Christoph H. 
Published: February 2021

Resistivity measurements are a major input into hydrocarbon reserve estimation and are usually described by Archie’s laws. In this study, we use digital rock physics to analyze the mechanisms of non-Archie and Archie behavior of formation factor (FF) and resistivity index (RI) of low-porosity Fontainebleau (FB) sandstone for ambient conditions and under high confining pressure, respectively.

FB sandstone was imaged by micro-X-ray computed tomography (micro-CT) at a resolution of 1 µm. Subresolution details of the grain contact width distribution along with their length were extracted from a set of scanning electron microscope (SEM) images. The nanoscale aperture of grain contacts, which is below tomogram resolution, is accounted for in micro-CT-based numerical calculations by assigning effective porosity and conductivity to individual voxels of the extracted grain contact network. A porosity reduction of grain contacts and open pore space as a function of applied confining pressure is introduced, capturing the pressure dependence. The concept was implemented by grain contact labeling, introducing an additional phase derived from a Euclidean distance transform (EDT). Subvoxel stress-strain effects were incorporated by attributing all compressibility effects to the pore space (open pore space and grain contacts), treating the solid phase as perfectly rigid. Voxel-scale input conductivities are assigned using Archie’s law followed by solving the Laplace equation for sample-scale rock resistivity and RI directly on the segmented image using the finite element method.

For the numerical modeling of the FF and RI of low-porosity FB sandstone as a function of confining pressure, which depends on subresolution features, a set of hypotheses were tested. These are based on two segmentation scenarios incorporating the measured contact aperture distribution from SEM analysis—a homogeneous aperture-based segmentation by assuming all grain contacts as an average constant value and a heterogeneous aperture-based segmentation assigning two groups of grain contact apertures. The segmentation scenarios enable homogeneous and heterogeneous morphological change of grain contacts due to confining pressure effects. Furthermore, partial saturation of grain contacts is considered. In all cases, strong water-wetness was assumed, and discretization effects were analyzed carefully.

The numerical results highlight the relative contribution of each of two conductive components of FB sandstone (open pores vs. grain contacts) over the full range of partial saturations. Of importance is the connectivity of the system, with discretization effects having a significant effect on FF, but a small effect on the RI. Grain contacts and confining pressure are found to have a significant impact on RI behavior of low-porosity FB sandstone. Both the grain contact network with homogeneous aperture and the heterogeneous grain contact network are able to describe experimental observations. However, it is not sufficient to assume a homogeneous change in contact area, and an inhomogeneous deformation of grain contact zones is required to match the experiment.