Effective permittivity of porous media: a critical analysis of the complex refractive index model

The availability of reliable constitutive models linking the bulk electric properties of porous media to their inner structure is a key requirement for useful quantitative applications of noninvasive methods. This study focuses on the use of dielectric measurements to monitor fluid saturation changes in porous materials. A number of empirical, semi-empirical and theoretical relationships currently exists that link the bulk dielectric constant with volumetric water content. One such relationship, named complex refractive index model or Lichteneker-Rother model has been extensively applied in recent years. Here we first analyse the characteristics of this Lichteneker-Rother model by means of theoretical considerations. This theoretical analysis indicates that the Lichteneker-Rother exponent is dependent upon the geometrical properties of the porous structure, as well as the permittivity contrast between the different phases. Pore-scale modelling and experimental data further support this result. The parameter estimation robustness in presence of synthetic data error is also assessed. This demonstrates that Lichteneker-Rother parameters cannot, in general, be independently identified on the basis of bulk dielectric constant versus moisture content data.