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- Consolidated materials (1)
- Membrane polarization (1)
- Mercury intrusion (1)
- Permeability (1)
- Pore radius (1)
- Pore throat size (1)
- Relaxation time (1)
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- Spectral induced polarization (1)
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There is currently a debate within the SIP community about the characteristic textural length scale controlling relaxation time of consolidated porousmedia.One idea is that the relaxation time is dominated by the pore throat size distribution or more specifically the modal pore throat size as determined in mercury intrusion capillary pressure tests. Recently new studies on inverting pore size distributions from SIP data were published implying that the relaxation mechanisms and controlling length scale are well understood. In contrast new analytical model studies based on the Marshall-Madden membrane polarization theory suggested that two relaxation processes might compete: the one along the short narrow pore (the throat) with one across the wider pore in case the narrow pores become relatively long.
This paper presents a first systematically focused study into the relationship of pore throat sizes and SIP relaxation times. The generality of predicted trends is investigated across a wide range of materials differing considerably in chemical composition, specific surface and pore space characteristics. Three different groups of relaxation behaviors can be clearly distinguished. The different behaviors are related to clay content and type, carbonate content, size of the grains and the wide pores in the samples.
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.