This study aims to present a simple method to calculate the permeability of porous materials using μ-CT images and an approximation based on the solution of Laplace's equation for pressure. For this purpose, an in-house computer program was developed based on finite difference method to determine the distribution of pressure in voxelated pore space. Afterwards, approximate permeability was obtained using Euclidean distance map of the pore space and a simple upscaling scheme for a range of porous media including idealized channels of elementary cross sections, Boolean models of spherical grains, bundles of capillary tubes and digital rocks obtained from μ-CT imaging. Next, a comparison was made between the Laplace permeability approximation and the analytical solutions of idealized microstructure and digitally-computed permeability of a number of rock samples using the Stokes solver and the lattice-Boltzmann method. It has been revealed that the estimated permeability values are in good agreement over the investigated range of porosity. The developed Laplace permeability solver was also well matched with the results of experimental measurement on a real rock sample. As an illustration of the applicability of the proposed method, the anisotropy of permeability at pore scale and the cross-correlation between permeability and connected macro-porosity was analyzed for the experimentally investigated rock sample. In conclusion, the results of this paper suggest that the proposed permeability solver is suitable for rough estimation of permeability and hence rough evaluation of heterogeneity/anisotropy from μ-CT images of rocks, particularly for large datasets with high number of pore voxels.

本研究旨在提出一种使用 μ-CT 图像和基于拉普拉斯压力方程解的近似值计算多孔材料渗透率的简单方法。为此，基于有限差分法开发了内部计算机程序，以确定体素化孔隙空间中的压力分布。然后，使用孔隙空间的欧几里德距离图和一系列多孔介质的简单放大方案获得近似渗透率，包括基本横截面的理想化通道、球形颗粒的布尔模型、毛细管束和从 μ- 获得的数字岩石。 CT成像。下一个，使用斯托克斯求解器和格子-玻尔兹曼方法对拉普拉斯渗透率近似与理想化微观结构的解析解和许多岩石样品的数字计算渗透率进行了比较。已经表明，估计的渗透率值在所研究的孔隙度范围内具有良好的一致性。开发的拉普拉斯渗透率求解器也与真实岩石样品的实验测量结果很好地匹配。为了说明所提出方法的适用性，对实验研究的岩石样品分析了孔隙尺度渗透率的各向异性以及渗透率与连通大孔隙度之间的互相关性。综上所述，