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<p>In digital core studies, researchers usually use k<sub>g</sub>, 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<sub>x</sub>, k<sub>y</sub> and k<sub>z</sub>. In this paper, we selected 20 digital sub-samples with a uniform size of 1&#xa0;mm×1&#xa0;mm×1&#xa0;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<sub>k</sub> (permeability anisotropy coefficient) and A<sub>τ</sub> (tortuosity anisotropy coefficient). The A<sub>k</sub> 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<sub>max</sub> and k<sub>min</sub> 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<sub>k</sub> and k<sub>g</sub>, φ<sub>c</sub>, r<sub>t50</sub> 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<sub>k</sub> shows a moderate but statistically significant positive correlation with A<sub>τ</sub>, and this correlation remains statistically significant after controlling for k<sub>g</sub>, φ<sub>c</sub>, and the combination of k<sub>g</sub> and φ<sub>c</sub>. 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<sub>τ</sub> can more directly reflect the differences in flow path complexity across different directions. Therefore, A<sub>τ</sub> can be used as an important directional indicator for interpreting the directional permeability anisotropy of millimeter-scale sandstone digital sub-samples.</p>

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

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  • 发表日期：

    2026年7月17日

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  • Yibo Li

摘要

In digital core studies, researchers usually use kg, 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 kx, ky and kz. 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 Ak (permeability anisotropy coefficient) and Aτ (tortuosity anisotropy coefficient). The Ak 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 kmax and kmin 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 Ak and kg, φc, rt50 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, Ak shows a moderate but statistically significant positive correlation with Aτ, and this correlation remains statistically significant after controlling for kg, φc, and the combination of kg and φc. These findings demonstrate that, under the conditions of fixed field of view, identical sub-sample volume and consistent simulation procedure used in this study, Aτ can more directly reflect the differences in flow path complexity across different directions. Therefore, Aτ can be used as an important directional indicator for interpreting the directional permeability anisotropy of millimeter-scale sandstone digital sub-samples.