Saturation dependence of the quadrature conductivity of oil‐bearing sands

We have investigated the complex conductivity of oil‐bearing sands with six distinct oil types including sunflower oil, silicone oil, gum rosin, paraffin, engine oil, and an industrial oil of complex composition. In all these experiments, the oil was the non‐wetting phase. The in‐phase (real) conductivity follows a power law relationship with the saturation (also known as the second Archie's law) but with a saturation exponentn raging from 1.1 to 3.1. In most experiments, the quadrature conductivity follows also a power law relationship with the water saturation but with a power law exponent p can be either positive or negative. For some samples, the quadrature conductivity first increases with saturation and then decreases indicating that two processes compete in controlling the quadrature conductivity. One is related to the insulating nature of the oil phase and a second could be associated with the surface area of the oil / water interface. The quadrature conductivity seems to be influenced not only by the value of the saturation exponent n (according to the Vinegar and Waxman model, p = n− 1), but also by the surface area between the oil phase and the water phase especially for very water‐repellent oil having a fractal oil–water interface.