Three-dimensional images of fractured rocks can be acquired by an X-ray micro-CT scanning technique, which allows researchers to investigate the ‘true’ inner void structure of a natural fracture without destroying the core. The 3D fractures in images can be characterised by measuring morphological properties on both fracture apertures and its trend surface, like the medial surface, that reveals the undulation of fracture planes. In a previous paper, we have proposed a novel method to generate fracture models stochastically. Based on a large number of such fracture models, in this work a modified factor was proposed for improving the performance of the cubic law by incorporating the flow-dominant characteristics, including two parameters (aperture roughness and spatial correlation length) for fracture apertures and two (surface undulation coefficient and spatial correlation length) for fracture trend-surface. We assess and validate the modified cubic law by applying it to natural fractures in images that have varying apertures and extremely bended trend-surfaces, with the permeabilities calculated by a Lattice Boltzmann Method as ‘ground truths’.
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