Directional permeability anisotropy of 1 mm³ sandstone digital sub-samples under fixed micro-CT field of view and its...

In digital core studies, researchers usually use k_g, the geometric mean of absolute permeabilities in three orthogonal directions, to describe the overall seepage capacity of a rock sample. However, this common practice tends to mask the directional differences hidden in k_x, k_y and k_z. In this paper, we selected 20 digital sub-samples with a uniform size of 1 mm×1 mm×1 mm, which were cut from the fixed micro-CT (micro X-ray computed tomography) field of view of 5 parent sandstone samples. Based on pore space reconstruction and single-phase steady-state seepage simulation, we calculated the permeability and tortuosity in each of the three directions separately, and then defined A_k (permeability anisotropy coefficient) and A_τ (tortuosity anisotropy coefficient). The A_k values of these 20 sub-samples range from 1.044 to 1.770, with an average of 1.270 and a median of 1.252, indicating that the overall directional anisotropy is at a low to moderate level. The frequencies of k_max and k_min appearing in x, y and z directions were not concentrated on a single coordinate axis, and chi-square goodness-of-fit tests detected no statistically significant preferential or restricted flow direction in the coordinate system used in this study. We found no significant statistical correlation between A_k and k_g, φ_c, r_t50 or Euler number. This result suggests that directional permeability anisotropy cannot be simply represented by the overall seepage capacity, the volume of effective flow-contributing pores, the dominant throat size, or the global topological characteristics of the pore space. In contrast, A_k shows a moderate but statistically significant positive correlation with A_τ, and this correlation remains statistically significant after controlling for k_g, φ_c, and the combination of k_g and φ_c. These findings demonstrate that, under the conditions of fixed field of view, identical sub-sample volume and consistent simulation procedure used in this study, A_τ can more directly reflect the differences in flow path complexity across different directions. Therefore, A_τ can be used as an important directional indicator for interpreting the directional permeability anisotropy of millimeter-scale sandstone digital sub-samples.