The use of topology in fracture network characterization

In two-dimensions, a fracture network consist of a system of branches and nodes that can be used to define both geometrical features, such as length and orientation, and the relationship between elements of the network – topology. Branch lengths are preferred to trace lengths as they can be uniquely defined, have less censoring and are more clustered around a mean value. Many important properties of networks are more related to topology than geometry. oportions of isolated (I), abutting (Y) and crossing (X) nodes provide a basis for describing the topology that can be easily applied, even with limited access to the network as a whole. Node counting also provides an unbiased estimate of frequency and can be used in conjunction with fracture intensity to estimate the characteristic length and dimensionless intensity of the fractures. The nodes can be used to classify branches into three types – those with two I-nodes, one I-node and no I-nodes (or two connected nodes). The average number of connections per branch provides a measure of connectivity that is almost completely independent of the topology. We briefly discuss the extension of topological concepts to 3-dimensions.