The Permeability Calculation of the Digital Rock by a New Finite Difference Method

Digital rock images may capture more detailed pore structure than the traditional laboratory methods. No explicit function can correlate permeability accurately for flow within the pore space. This has motivated researchers to predict permeability through the application of numerical techniques, e.g., finite difference method (FDM). However, in order to get better permeability calculation results, the grid refinement was needed for the traditional FDM. And the accuracy of this method decreased in pores with elongated cross sections. The goal of this study is to develop a new FDM to calculated the permeabilities of digital rocks with complex pore space. An elliptical pore approximation method is invoked to describe the complex pore space. The permeabilities of the digital rock images after grid coarsening are calculated by the new FDM in three orthogonal directions. These results are compared with the previously validated lattice-Boltzmann method (LBM), which indicates that the predicted permeabilities calculated by the new FDM usually agree with permeabilities calculated by LBM. We conclude that the presented new FDM is suitable for complex pore space.