Summary 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.

Recent advances in micro-CT techniques allow imaging heterogeneous carbonates at multiple scales and including voxel-wise registration of images at different resolution or in different saturation states. This enables characterising such carbonates at the pore-scale targeting the optimizing of hydrocarbon recovery in the face of structural heterogeneity, resulting in complex spatial fluid distributions. Here we determine effective and total porosity for different pore-types in a complex carbonate and apply this knowledge to improve our understanding of electrical properties by integrating experiment and simulation in a consistent manner via integrated core analysis. We consider Indiana Limestone as a surrogate for complex carbonate rock and type porosity in terms of macro- and micro-porosity using micro-CT images recorded at different resolution. Effective and total porosity fields are derived and partitioned into regions of macro-porosity, micro-porosity belonging to oolithes, and micro-porosity excluding oolithes’ rims. In a second step we use the partitioning of the micro-porosity to model the electrical conductivity of the limestone, matching experimental measurements by finding appropriate cementation exponents for the two different micro-porosity regions. We compare these calculations with calculations using a single cementation exponent for the full micro-porosity range. The comparison is extended to resistivity index at partial saturation, further testing the assignment of Archie parameters, providing insights into the regional connectivity of the different pore types.

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.