Relating Electrical Resistivity to Permeability Using Resistor Networks

Abstract

We use resistor network models to explore the relationship between electrical resistivity and permeability in fractures filled with an electrically conductive fluid. The fracture aperture distribution is determined by generating fracture surface pairs that are constructed based on characteristics measured on rock samples. We use these to generate and solve resistor networks with variable hydraulic and electrical resistance. The aperture is incrementally increased, to analyse 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 four 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. The permeability increases at a greater rate than the conductivity, and therefore the percolation threshold can 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 but is always less than 10. Greater M values are associated with fractures above their percolation threshold and therefore open for fluid flow.