Application of a percolation model to flow in fractured hard rocks

The “backbone” (i.e., 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 N1 ∝ 1−1.9, where 1 is the length of the line segment sections, and N1 is the number of elements of length 1 in the backbone. The measured electrical resistivity of the model is found to yield a power law behavior defined by R ∝ (N/Nc − 1)−1.3, where R is the overall resistance of the network, Nc is the threshold for the onset of electrical conduction, and N is the number of line segments in the system. Both the threshold and the electrical resistivity exponent are in agreement with the theoretical values expected for percolation systems in the continuum. Examination of available geological data supports these results, although additional field data are required. The model presented here provides a useful reference for comparison and suggests the nature of geological‐geophysical data that should be obtained in future field studies. An analysis of the effect of a distribution of fracture apertures in the network on its transport properties is also presented. Based on the limited data available, it is suggested that the so‐called universal behavior predicted by percolation theory is in general to be expected for both the fluid hydraulic conductivity and the electrical conductivity in common systems of fractures.