The effect of grain anisotropy on the electrical properties of sedimentary rocks

Abstract

We have examined the effect of particulate anisotropy on the electrical properties of sedimentary rocks by generalizing the treatment of Sen et al (1981) to the case of ellipsoidal grains with a distribution of orientations and depolarizing factors. Two distributions in orientation have been treated in detail—randomly oriented grains in three dimensions and grains with aligned principal axes in two dimensions. In the former case the conductivity is a scalar satisfying Archie’s law, [Formula: see text], with [Formula: see text] the conductivity of the pore fluid and ϕ the porosity. The exponent m has a minimum of 1.5 for spherical grains. The presence of highly oblate (disk shaped) grains raises m significantly. As long as grains with extremely large eccentricities (≳15) are not present, the exponent falls in the observed range [Formula: see text]. For aligned grains the conductivity is a tensor with principal values that satisfy a generalized Archie’s law of the form [Formula: see text], where [Formula: see text] is the jth principal value of the conductivity and [Formula: see text] can be expanded as a power series in ϕ with a constant leading term. For grain eccentricities in the range 0–0.95, the coefficients [Formula: see text] fall in the range 0.1–4. The exponent m has a minimum value of 2 for two dimensions, independent of grain shape, if all grains have the same shape, and it is larger for any distribution of grain shapes. If the distribution of grain shapes is chosen so that the rock is isotropic, m and a have the same values as for isotropic rock composed of grains with the same distribution of shapes but with random orientations. Since different distributions of grain orientation can lead to the same effective conductivity, it is clear that measurements of dc conductivity are not sufficient to determine the grain distribution. The model is also used to obtain the complex dielectric constant. If the dielectric constant of solid rock is small compared to the real part of the dielectric constant of water, the complex dielectric constant has the same dependence on porosity as the dc conductivity except at very small porosities.