Relating permeability and electrical resistivity in fractures using random resistor network models

Abstract

We use random resistor network models to explore the relationship between electrical resistivity and permeability in a fracture filled with an electrically conductive fluid. Fluid flow and current are controlled by both the distribution and the volume of pore space. Therefore, the aperture distribution of fractures must be accurately modeled in order to realistically represent their hydraulic and electrical properties. We have constructed fracture surface pairs based on characteristics measured on rock samples. We use these to construct resistor networks with variable hydraulic and electrical resistance in order to investigate the changes in both properties as a fault is opened. At small apertures, electrical conductivity and permeability increase moderately with aperture until the fault reaches its percolation threshold. Above this point, the permeability increases by 4 orders of magnitude over a change in mean aperture of less than 0.1 mm, while the resistivity decreases by up to a factor of 10 over this aperture change. Because permeability increases at a greater rate than matrix to fracture resistivity ratio, the percolation threshold can also be defined in terms of the matrix to fracture resistivity ratio, M. The value of M at the percolation threshold, MPT, varies with the ratio of rock to fluid resistivity, the fault spacing, and the fault offset. However, MPT is almost always less than 10. Greater M values are associated with fractures above their percolation threshold. Therefore, if such M values are observed over fluid-filled fractures, it is likely that they are open for fluid flow.