Size effect on the hydraulic behavior of fluid flow through a single rough-walled fracture

Abstract

This study provides a numerical approach to evaluate the effect of sample sizes on fluid flow through a single rough-walled fracture. The rough-walled fracture was generated by using mathematical statistics. Its aperture follows a normal distribution along a large-size plane of dimensions 20 m × 20 m, and from this large-size fracture plane, a series of fractures with different sizes were extracted. Then, a two-dimensional (2D) Reynolds equation was solved to simulate fluid flow through these rough-walled fractures with different mean fracture apertures and roughness. The impact of normal stress on the hydraulic properties was introduced by using a hyperbolic function. The simulated results show a positive correlation between hydraulic conductivity and fracture sizes. In fact, hydraulic conductivity of the fluid flow through a single rough-walled fracture increases with the increment of the fracture size until a given size from which it stays constant. The hydraulic conductivity for this given size can then be considered as a representative of that in larger sample sizes. This given size resulted to range from 12 m to 16 m, due to the variations in mean fracture apertures, roughness and normal stress. In addition, it was also found that this representative size tends to decrease with an increase in the mean fracture apertures, while tends to increase as the fracture roughness or the normal stress increases, since those variables affect the fracture topology and contact areas, which play an important role in controlling the tortuosity and connectivity of fluid flow through a rough fracture.