Numerical upscaling of multi-mineral digital rocks: Electrical conductivities of tight sandstones

Abstract

Tight sandstones usually present great variations in Archie's exponents due to their high clay contents and multi-scale pores. Conventional multi-scale digital rocks consider the effect of micro and macro pores but ignore the contribution of clay minerals to electrical conductivity, whereas traditional multi-mineral digital rocks cannot consider the contribution of micro pores. We propose an upscaling method to construct complex digital rocks for accurate estimation of electrical conductivities. Based on a 3-D grayscale image of a tight sandstone acquired by X-ray CT and a 2-D mineralogy slice imaged by energy-dispersive SEM (EDS-SEM), we reconstruct a 3-D multi-mineral digital rock that is composed of intergranular pores and mineral phases by image registration and multi-threshold segmentation. Fine mineral structures and micro pores are revealed by the multi-scale imaging technique. The effective conductivity of each mineral phase associated with a specific micro porosity is calculated by the Archie's equation or Waxman-Smits model. By assigning each voxel with the optimal conductivity according to its mineral phase, we estimate the bulk electrical conductivity of the entire digital rock by the finite element method. The contributions of fluids and clay minerals to the bulk electrical properties are implicitly incorporated into the numerical simulation without increasing computational cost. The upscaling method is validated by experimental measurements of formation factors. We investigate the effect of clay minerals and scanning resolutions on the calculated electrical conductivities with attempt to interpret variations in the cementation exponent.