Relaxation time distribution obtained from a Debye decomposition of spectral induced polarization data

Abstract

We have developed an alternative formulation for Debye decomposition of complex electric conductivity spectra, by recasting it into a new set of parameters with a close relationship to the continuous formulation for the complex conductivity method. The procedure determines a relaxation time distribution (RTD) and two frequency-independent parameters that modulate the complex conductivity spectra. These two parameters represent (1) the direct current contribution and (2) the conductivity range spanned by the low- and high-frequency limits. The distribution of relaxation times quantifies the contribution of each distinct relaxation process. Assuming that characteristic times with insignificant contributions can be ignored, a minimum set of characteristic relaxation times is determined. Each contribution can then be associated with specific polarization processes that can be interpreted in terms of electrochemical or interfacial parameters of mechanistic models derived from inverted parameters obtained from the proposed approach. Synthetic tests show that the procedure can fit spectral induced polarization (SIP) data and successfully retrieve the RTD. We have applied the procedure to laboratory SIP data from experiments with sand and oil mixtures undergoing microbial degradation of hydrocarbons. The RTD reveals evidence of a length scale at which a new polarization process takes place as a result of the biodegradation process.