The Influence of Pore Geometry on the Dielectric Dispersion of Clean Sandstones

In an idealized description a clean sandstone is an isotropic two-component medium consisting of a solid with dielectric constant ∈1and a pore fluid (brine) with dielectric constant e2 and conductivity σ2. On the basis of D. Bergman's work [Ann. Phys. 138, 78 (1982)] the dielectric response of such a medium is expressed in terms of the dc conductivity and of a real, positive and bounded function, defined in <1, 0> and independent of ∈¹, ∈2, and σ2. This function is restricted by three relations which express weighted averages of it in terms of the asymptotic value of the dielectric response at high frequency, the porosity, and the dc conductivity. The formalism is exact for two-component media of the type specified. It supplements an approximate treatment by Lysne (1983) and can, without much difficulty, be generalized to any isotropic two-component composites.