Application of a percolation model to flow in fractured hard rocks

The "backbone' (ie, conducting part of the network) of a computer-generated two-dimensional percolation model of fractured formations is examined. The lengths of the conducting elements (line segments) are found to follow a power law distribution defined by N_l ∝ l^-1.9, where l is the length of the line segment sections, and N_l is the number of elements of length l in the backbone. The measured electrical resistivity of the model is found to yield a power law behavior defined by R ∝ (N/N_C - l) ^-1.3, where R is the overall resistance of the network, N_C is the threshold for the onset of electrical conduction, and N is the number of line segments in the system. An analysis of the effect of a distribution of fracture apertures in the network on its transport properties is also presented. -from Authors