Chapter 6 - Effective dielectric permittivity

Abstract

This chapter focuses on the determination of the effective permittivity of a heterogeneous medium. Starting with the example of a circuit with a capacitor, we first establish the relation between the effective permittivity, and the electric and displacement fields. A review is then made of the most popular models for predicting the complex effective permittivity of a heterogeneous medium. Some of them are at the core of the petrophysical models used in the interpretation of dielectric logging today. Most are generalizations to the case of the complex permittivity of the early model by Maxwell for estimating the effective conductivity of a medium made of spherical inclusions immersed in a host material. A fundamental model is given by the Maxwell–Garnett relation, which also extends to the case of ellipsoidal inclusions. A thorough review is made of the Hanai method, which, as considering infinitesimal increments of particles in a host material, is valid up to a higher concentration of particles than the above ones. Finally, other methods are reviewed, such as the ones from Bruggeman, Lichtenecker, of the popular CRIM method.