On Permeability Prediction From Complex Conductivity Measurements Using Polarization Magnitude and Relaxation Time

Geophysical length scales determined from complex conductivity (CC) measurements can be used to estimate permeability k when the electrical formation factor F is known. Two geophysical length scales have been proposed: (1) the specific polarizability c(p) normalized by the imaginary conductivity sigma and (2) the time constant tau multiplied by a diffusion coefficient D+. The parameters c(p) and D+ account for the control of fluid chemistry and/or varying minerology on the geophysical length scale. We evaluated the predictive capability of two CC permeability models: (1) an empirical formulation based on sigma or normalized chargeability m(n) and (2) a mechanistic formulation based on tau. The performance of the CC models was evaluated against measured k; and further compared against that of well-established k estimation equations that use geometric length scales. Both CC models predict permeability within one order of magnitude for a database of 58 sandstone samples, with the exception of samples characterized by high pore volume normalized surface area S-por. Variations in c(p) and D+ likely contribute to the poor model performance for the high S-por samples, which contain significant dolomite. Two observations favor the implementation of the sigma-based model over the tau-based model for field-scale k estimation: (1) a limited range of variation in c(p) relative to D+ and (2) sigma field measurements are less time consuming to acquire relative to s. The need for a reliable field-estimate of F limits application of either model, in particular the sigma model due to a high power law exponent associated with F.