Fractal Features of Fracture Networks and Key Attributes of Their Models

This work is devoted to the modeling of fracture networks. The main attention is focused on the fractal features of the fracture systems in geological formations and reservoirs. Two new kinds of fracture network models are introduced. The first is based on the Bernoulli percolation of straight slots in regular lattices. The second explores the site percolation in scale-free networks embedded in the two- and three-dimensional lattices. The key attributes of the model fracture networks are sketched. Surprisingly, we found that the number of effective spatial degrees of freedom of the scale-free fracture network models is determined by the network embedding dimension and does not depend on the degree distribution. The effects of degree distribution on the other fractal features of the model fracture networks are scrutinized.