Calculating the electrical conductivity of digital rocks based on two-dimensional images

Abstract

Summary In order to calculate the electrical conductivity conveniently and quickly by digital rock physics (DRP), the conductivity relationship between two-dimensional (2D) and three-dimensional (3D) digital rocks is studied in this work. Based on the 3D microstructure of 3 sandstones obtained by micro X-ray computer tomography, we have established the digital rocks. New 3D digital rocks with larger porosity are generated by expanding the pores digitally. The electrical conductivity of the 3D and 2D digital rocks are calculated by finite element method, and we characterize the conductivity-porosity relationship by Archie equation, and cementation coefficients are obtained. With the connection between 2D and 3D cementation coefficient as a link, the conductivity-porosity relationship of 3D digital rocks can be determined through the conductivity-porosity relationship obtained from fast calculation of 2D images, and the conductivity of 3D digital rocks can then be calculated. We predicted the 3D digital rocks conductivity-porosity relationship of a synthetic sandstone sample, and the electrical conductivity of the 3D digital rocks shows great correlation (correlation coefficient better than 96%) with that calculated from 3D images using finite element method, which verifies the validity of the proposed calculation method of digital rock electrical conductivity based on 2D images.