Approximate determination of surface conductivity in porous media

We have studied the fluid permeability and the electrical conduction in artificially made impregnated sandstones in order to determine the surface conductivity approximately. The electrical conductivity of the impregnated porous medium is not proportional to the conductivity of the impregnation liquid, but a linear dependence is found which permits us to calculate an electrical formation factor, F, and an intercept with the ordinate axis. We propose that 'Archie's law' for the formation factor's porosity-dependence is composed of two factors: a factor inversely proportional to the porosity and a tortuosity factor. The tortuosity factor is dependent on the grain size distribution of the sandstone. The formation factor has been shown to relate to the permeability, k, in two ways: either as k alpha F^-1 or as k alpha F^-2, where the proportionality factors are different geometrical properties of the porous medium. We also show that it is possible to calculate the surface conductivity from a theoretical relation between the conductivity intercept and the permeability.