Permeability estimation from induced polarization (IP) measurements is based on a fundamental premise that the characteristic relaxation time τ is related to the effective hydraulic radius reff controlling fluid flow. The approach requires a reliable estimate of the diffusion coefficient of the ions in the electrical double layer. Others have assumed a value for the diffusion coefficient, or postulated different values for clay versus clay-free rocks. We have examined the link between a widely used single estimate of τ and reff for an extensive database of sandstone samples, in which mercury porosimetry data confirm that reff is reliably determined from a modification of the Hagen-Poiseuille equation assuming that the electrical tortuosity is equal to the hydraulic tortuosity. Our database does not support the existence of one or two distinct representative diffusion coefficients but instead demonstrates strong evidence for six orders of magnitude of variation in an apparent diffusion coefficient that is well-correlated with reff and the specific surface area per unit pore volume Spor. Two scenarios can explain our findings: (1) the length scale defined by τ is not equal to reff and is likely much longer due to the control of pore-surface roughness or (2) the range of diffusion coefficients is large and likely determined by the relative proportions of the different minerals (e.g., silica and clays) making up the rock. In either case, the estimation of reff (and hence permeability) is inherently uncertain from a single characteristic IP relaxation time as considered in this study.

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