Influence of Local Aperture Heterogeneity on Invading Fluid Connectivity During Rough Fracture Drainage

Determining the (in)efficiency of wetting phase displacement by an invading non-wetting phase (drainage) in a single fracture is key to modelling upscaled properties such as relative permeability and capillary pressure. These constitutive relationships are fundamental to quantifying the contribution, or lack thereof, of conductive fracture systems to long-term leakage rates. Single-fracture-scale modelling and experimental studies have investigated this process, however, a lack of visualization of drainage in a truly representative sample at sufficient spatial and temporal resolution limits their predictive insights. Here, we used fast synchrotron X-ray tomography to image drainage in a natural geological fracture by capturing consecutive 2.75 μm voxel images with a 1 s scan time. Drainage was conducted under capillary-dominated conditions, where percolation-type patterns are expected. We observe this continuously connected invasion (capillary fingering) only to be valid in local regions with relative roughness, λ_b ≤ 0.56. Fractal dimension analysis of these invasion patterns strongly aligns with capillary fingering patterns previously reported in low λ_b fractures and porous media. Connected invasion is prevented from being the dominant invasion mechanism globally due to high aperture heterogeneity, where we observe disconnected invasion (snap-off, fragmented clusters) to be pervasive in local regions where λ_b ≥ 0.67. Our results indicate that relative roughness has significant control on flow as it influences fluid conductivity and thus provides an important metric to predict invasion dynamics during slow drainage.