Calculation of effective permeability based on approximation of 3D renormalization

In this study, we derive the approximation of 3D renormalization based on that of 2D. First, we divide CT image into mesh grids according to the pore structure from samples. Next, effective permeabilities of each block are calculated from different equivalent medium models. Third, on the basis of the effective permeability of each grid cell, we apply the similarly analytic expression of the 2D electric network and the renormalization group formula for 2D CT image to derive the approximation equation of effective permeability in 3D media. The validity and accuracy of the proposed method are checked against known results of one idealized porous media models, which have analytic expressions and two rock samples which include both experimental permeability values and CT images. In addition, we apply the approximation of 3D renormalization to compute the effective permeabilities for three digital rocks from Imperial College London and then compare with absolute permeabilities calculated by the lattice Boltzmann method. Test results show that the relative errors deduced from the renormalization group method for simple models and the sandstone samples are within 10% and 25%, repsectivley.The magnitudes in three directions show weak anisotropy, and the effective permeabilities calculated by the approximation of 3D renormalization are in an acceptable range. © 2020, Periodical Office of China University of Petroleum. All right reserved.