Effective aperture and orientation of fractal fracture network

Distribution of fracture length has been shown to exhibit fractal characteristics. In this study, we proposed a new idea of effective fracture in terms of aperture and orientation for a fractal fracture network and developed solutions of effective aperture in relation to fractal characteristics, flow behavior and hydraulic gradient. Another main point is that the use of Darcy's law is not required. The effective fracture approach takes into account the scenario that the entire fractal fracture network may effectively behave similarly to a bundle of fractures where flows may be non-linear. The effective fracture approach explicitly distinguishes laminar and turbulent flows based on the size of effective fracture. To do so, an iterative procedure is developed to determine the effective fracture aperture. Results demonstrate that the effective aperture only slightly varies with hydraulic gradient, which illustrates that the idea of effective aperture can be used in the mixture of laminar and turbulent flows. The effective aperture decreases with the scaling exponent, increases linearly with the maximum fracture length, increases significantly with the minimum over maximum fracture length ratio, and increases with the scaling coefficient. The effective orientation shows expected decrease as the precision parameter of the fracture orientation increases.