28 Aug 2023
 | 28 Aug 2023
Status: this preprint is open for discussion.

Investigating rough single fracture permeabilities with persistent homology

Marco Fuchs, Anna Suzuki, Togo Hasumi, and Philipp Blum

Abstract. The permeability of rock fractures is a crucial parameter for flow processes in the subsurface. In the last decades different methods were developed to investigate on permeability in fractures, such as flow through experiments, numerical flow simulations or empirical equations. In recent years, the topological method persistent homology was also used to estimate permeability in fracture networks and porous rocks, but not for rough single fractures. Hence, we apply persistent homology analysis on a decimeter-scale, rough sandstone bedding joint. To investigate on the influence of roughness, three different data sets are created to perform the analysis: (1) 200 µm resolution, (2) 100 µm resolution and (3) 50 µm resolution. All estimated permeabilities were then compared to values derived by experimental air permeameter measurements and numerical flow simulation. The results reveal that persistent homology analysis is able to estimate the permeability of a single fracture even if it tends to slightly overestimate permeabilities compared to conventional methods. Previous studies using porous media showed the same overestimation trend. Furthermore, expenditure of time for persistent homology analysis as well as air permeameter measurements and numerical flow simulation was compared which showed that persistent homology analysis can be also an acceptable alternative for conventional methods in this regard.

Marco Fuchs et al.

Status: open (until 20 Oct 2023)

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  • RC1: 'Comment on egusphere-2023-1855', Anonymous Referee #1, 22 Sep 2023 reply

Marco Fuchs et al.

Marco Fuchs et al.


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Short summary
In this study, the permeability of a natural fracture in sandstone is estimated based only on its geometry. For this purpose, the topological method of persistent homology is applied to three geometric data sets with different resolutions for the first time. The results of all data sets compare well with conventional experimental and numerical methods. Since the analysis takes less to the same amount of time, it seems to be a good alternative to conventional methods.