Estimating the permeability of fractured rocks using topological characteristics of fracture network

The variability and inter-influence of individual geometric parameters make permeability evaluation of fractured rocks based on fracture geometric characteristics challenging. Therefore, three independent topological parameters, fracture mean density (εmean), network connectivity (nseg), and the average number of fractures intersecting with inlet and outlet boundaries per meter (Cmean) were proposed to describe the geometric characteristic of fractured rock, and a prediction model of permeability was established in terms of these topological parameters and fracture aperture. The relationship between topological parameters, aperture, and permeability was analyzed according to more than 300 models generated by the Monte Carlo method considering different fracture densities, lengths, and orientations. Fitting these results, a multivariate regression equation with a correlation coefficient larger than 0.91 was constructed for prediction permeability. We also found that nseg and e play a more important role in permeability when compared to εmean and Cmean. For fractured rocks of different topological sub-domains, a method physically simplifying them to a fracture of equivalent hydraulic conductivity is proposed, and then assembling them based on the mass conservation and compatible hydraulic pressure condition. The derivation between permeability obtained by prediction model and numerical simulation is less than 2%, verifying the prediction model.