Upgrading of aperture model based on surface geometry of natural fracture for evaluating channeling flow

In order to evaluate scale dependency in fracture flow under confining pressure, measurements of fracture surface topography at the atmospheric pressure and permeability at 30 MPa were conducted on granite samples containing different scaled fractures of 5 × 7.5 (37.5) cm², 10 × 15 (150) cm², and 20 × 30 (600) cm². Two kinds of fractures, mated and sheared fractures, were prepared for each scale. Moreover, fluid flows within aperture distributions of the fractures at the confining pressure were numerically determined using the data of fracture surface topography by matching numerical and experimental permeabilities. Based on the evaluation, scale-dependency was predicted as follows. Regardless of the fracture scale, the fluid flow is always characterized by channeling flow within an aperture distribution with a significant number of the contact points (zero-aperture) and a log-normal like distribution of the aperture. Since the surface roughness increases and the contact point does not change significantly with fracture scale, aperture for both mated and sheared fractures increases with fracture scale, where the relationship between the geometric mean of aperture and fracture scale (area or length of the fracture) is linear on log-log plot, with the slope of less than unity. The geometric standard deviation of aperture has no scale dependency. Despite of the scale dependency in aperture, permeability of mated fracture does not increase clearly with fracture scale, probably due to a small connectivity of the aperture. In contrast, permeability of sheared fracture increases with fracture scale, due to a large connectivity of the aperture that increases with fracture scale. Moreover, in case of a sheared fracture, the relationship between the permeability and fracture scale (area or length of the fracture) is linear on log-log plot, where the slope is less than unity.