Three-dimensional flow characterization in a joint with plumose pattern

This work numerically simulates fracture flow in natural fractures, specifically in a joint with plumose pattern. A natural fracture surface, previously measured in the field using LiDAR scanning, was used to rebuild an open fracture geometry, assuming mode 1 fracture opening. Three-dimensional fracture flow was modeled by solving Stokes equation in a stationary regime using the finite element method. Three different pressure gradients and apertures were numerically investigated to better understand the impact of plumose patterns with different degrees of roughness. Resulting fracture flow fields were characterized by hydraulic aperture and by statistics on the directional components of the three-dimensional velocity vector. The results show that the hydraulic aperture and the longitudinal component of the velocity vector decrease with increasing roughness. Beyond this classical finding, the study shows that the variance of the longitudinal component of the flow velocity vector also decreases with increasing roughness. This behavior can be predicted based on variance estimates connected to the parabolic profile. The results further revealed that the variances of the transverse components of the velocity vector increase with fracture surface roughness. These findings suggest that the roughness-induced reduction in the mean and the variance of the longitudinal component of the velocity vector in joints with rough surfaces is accompanied with a simultaneous increase of the transverse components of the three-dimensional velocity vector.