Permeability from Complex Conductivity: An Evaluation of Polarization Magnitude versus Relaxation Time Based Geophysical Length Scales

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Geophysical length scales determined from complex conductivity (CC) measurements can be used to estimate permeability k when the electrical formation factor F describing the ratio between tortuosity and porosity is known. Two geophysical length scales have been proposed: [1] the imaginary conductivity σ" normalized by the specific polarizability cp; [2] the time constant τ multiplied by a diffusion coefficient D+. The parameters cp 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 recently presented CC permeability models: [1] an empirical formulation based on σ"; [2] a mechanistic formulation based on τ;. The performance of the CC models was evaluated against measured permeability; this performance was also compared against that of well-established k estimation equations that use geometric length scales to represent the pore scale properties controlling fluid flow. Both CC models predict permeability within one order of magnitude for a database of 58 sandstone samples, with the exception of those samples characterized by high pore volume normalized surface area Spor and more complex mineralogy including significant dolomite. Variations in cp and D+ likely contribute to the poor performance of the models for these high Spor samples. The ultimate value of such geophysical models for permeability prediction lies in their application to field scale geophysical datasets. Two observations favor the implementation of the σ" based model over the τ based model for field-scale estimation: [1] the limited range of variation in cp relative to D+; [2] σ" is readily measured using field geophysical instrumentation (at a single frequency) whereas τ requires broadband spectral measurements that are extremely challenging and time consuming to accurately measure in the field. However, the need for a reliable estimate of F remains a major obstacle to the field-scale implementation of either of the CC permeability models for kestimation.

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Presented at the AGU Fall Meeting on December 13, 2017 in New Orleans, LA