Nonlinear electrical response of saturated shaley sand reservoir and its asymptotic approximations

The quantitative interpretation of the electrical-resistivity log for reservoir characterization largely depends on a good understanding of the accurate relation between formation conductivity and rock constituents. This requires a mathematical model based on sound physical considerations. The models for the laws of physics are developed for electric conduction in linear conductors, so they can be extended easily to a homogeneous continuum. However, for further extension of these laws to a heterogeneous, porous medium, some approximations are needed. Using field equations designed for interpreting a homogeneous continuum to interpret a porous medium provides only a phenomenological description of the relations among macroscopic parameters of the porous medium.