Mechanisms of Confining Pressure Dependence of Resistivity Index for Tight Sandstones
Authors: Dai Hongyi , Shikhov Igor , Arns Ji-Youn , Li Rupeng , Arns Christoph Hermann 
Published: November 2020

Abstract
Resistivity measurements are a major input into hydrocarbon reserve estimation and are usually described by Archie's laws. In this study digital rock physics (DRP) is utilized to analyse the mechanisms of non-Archie and Archie behaviour of formation factor (FF) and resistivity index (RI) of low porosity Fontainebleau sandstone for ambient conditions and under high confining pressure, respectively.
Fontainebleau sandstone was imaged by micro-CT at a resolution of one micron and sub-resolution details of grain contact width distribution along with their length, extracted from a set of scanning electron microscope (SEM) images. The nano-scale aperture of grain contacts, which is below image 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 function of applied confining pressure is introduced, capturing the pressure dependence. The concept was implemented by grain-contact labelling and introducing an additional phase derived from a Euclidean distance transform. Sub-voxel 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 effective rock resistivity and resistivity index directly on the segmented image using the finite element method (FEM).
For the numerically modelling of Formation Factor and Resistivity Index of low porosity Fontainebleau sandstone as a function of confining pressure, which depends on sub-resolution features, a set of hypotheses were tested: (1) two segmentation scenarios based on the measured contact aperture distribution from SEM analysis – a homogeneous grain contact aperture based segmentation (single grain contact network) by assuming all grain contacts as a average constant value and a heterogeneous grain contact aperture based segmentation (dual grain contact network) by assigning two groups of grain contact aperture (wide and narrow); (2) homogeneous and heterogeneous morphological change of grain contacts due to confining pressure effect; (3) partial saturation of grain contacts. In all cases strong water-wetness was assumed and discretization effects were analysed carefully.
The numerical results highlight the relative contribution of each of two conductive components of Fontainebleau 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 formation factor, but small effect on resistivity index. Grain contacts and confining pressure are found to have a significant impact on RI behaviour of low-porosity Fontainebleau 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 experiment.