Multi-capacitance electric relaxation model for complex electrical conductivity of sulphide ores

Many studies have been conducted to analyse dielectric polarisation and the complex electrical conductivity characteristics by the Cole-Cole type relaxation approximating rocks with a uniform material. That method has revealed the correlation between metal contents and chargeability, between the central relaxation time and the metallic particle size, and so on. Based on the model's success, such models have been extended to those with multiple capacitances. However, these models cannot represent the mechanism of electrical flow in rocks using equivalent circuits and cannot explain the electrical behaviour of rocks that deviates significantly from the assumptions of the models. Therefore, in this study, by re-evaluating Pelton's equation, we strove to formulate an appropriate multiple-capacitance model expressed by an equivalent circuit, with the aim of ascertaining electrical features more easily and properly than through the convolution of electrical response functions. We achieved theoretical expansion of Pelton-type formulae to multiple capacitances. Our Double-Pelton equivalent circuit model (DPM) was applied to the observed complex conductivity curves of artificial samples including pyrite. The obtained parameters of our DPM were found to have a good correlation to the rock features. We achieved to show that the conductive mechanism of the complex geometrical features of rock samples can be modelled simply and effectively. The continuous efficiency of sulphide particles in the direction of the electric field, and pyrite particles which can act as bottleneck conductors as in percolation theory, are found to be playing an important role in electric conduction.

Automated summary

Many studies have been conducted to analyze the electrical properties of rocks using the Cole-Cole relaxation model. However, these models have limitations in representing the electrical flow mechanism in rocks and explaining the real behavior of rocks. In this study, we proposed a multiple-capacitance model expressed by an equivalent circuit based on the re-evaluation of Pelton's equation. The model, called the Double-Pelton equivalent circuit model (DPM), was successfully applied to complex conductivity curves of artificial samples, revealing the conductive mechanism of rocks with complex geometrical features.