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Three‐dimensional resistor network modeling of the resistivity and permeability of fractured rocks

The resistivity and permeability of 3‐D fracture networks have been modeled as the fractures within these networks are incrementally opened. In these models, the ratio of the rock resistivity to that of the fluid is 104, and the rock permeability is 1 × 10−18 m2. The changes in both resistivity and permeability depend on characteristics of the network itself such as fracture density, as well as the aperture distribution within individual fractures. In dense fracture networks where the density constant α is equal to 30, a percolation threshold can be defined in terms of mean fracture aperture, below which both resistivity and permeability are close to their matrix values. At the percolation threshold, a change in mean aperture of 0.02 mm can change the permeability by 4 orders of magnitude and resistivity by a factor of 4. The percolation threshold does not necessarily occur at the same aperture for different flow directions, so fracture networks near their percolation threshold commonly show anisotropy in both resistivity and permeability. Most sparse networks (α equal to 0.3 or less) do not percolate no matter how open the fractures are. On the other hand, many fracture networks with an intermediate value of α (equal to around 3) will percolate only in one or two directions. This can lead to very strong anisotropy in both resistivity and permeability (up to a factor of 160 and 109, respectively), with anisotropy increasing as the aperture of the fractures increases.