Multiscale relationships between fracture length, aperture, density and permeability

Fractured rocks exhibit a hierarchical structure which renders their attributes scale-dependent. In particular available data indicate a tendency for fracture length scales to be distributed according to a power law, average fracture aperture to be given by a power of the fracture length scale, and fracture density as well as log permeability to behave as random fractals. To date, no consistent theoretical relationship has been developed between fracture type (as categorized, for example, by length scale and/or aperture) and corresponding fractal attributes (such as density and log permeability). We develop and explore multiscale relationships between these fracture categories and attributes on the basis of a theory recently proposed by the author, which allows linking them in a formal way.