Investigating rough single fracture permeabilities with persistent homology

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.