Developments in a model to describe low-frequency electrical polarization of rocks

The author reworks his total current conductivity function introduced in a previous paper, related to electrical polarization of rocks in the frequenc y range of 1 MHz to 10(-3) Hz. The original five parameters in this functio n are replaced by new ones. which from the beginning have cleat petrophysic al and electrochemical meanings and well-defined ranges of variation. Some classical models are derived as particular cases of it. The main existing m odels proposed to describe induced polarization (IP) are analyzed, and most of them are grouped together under a common circuit analog representation and a respective generating function. A circuit analog is assigned to each model. The multi-Cole-Cole model circuit analog reveals intrinsic constrain ts involving the values of its circuit elements. Because of these constrain t relations and the relaxation times ratio (tau(1)/tau(2))-usually many ord ers of magnitude from unity-the model has no physical validation to represe nt single-phase material systems tin the sense of the polarization). The pe rformance and analysis of the various models to describe a few well-selecte d experimental data show that only two of the models, the multi-Cole-Cole a nd Dias models, can provide a function structure capable of fitting these d ata. This fact, the associated petrophysical interpretation consistency, an d the basic characteristics of these two models, such as the way they were derived (empirically, the former; phenomenologically, the latter) and the n umber of coefficients in the function (directly related to the degree of am biguity of their determination), make the author's model attractive and pro mising.