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Permeability estimation from spectral induced
polarization (SIP) measurements is based on a
fundamental premise that the characteristic relaxation
time (t) 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 examine the link between
t and reff for an extensive database of sandstone samples
where 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 1 or 2 distinct representative
diffusion coefficients but instead demonstrates strong
evidence for 6 orders of magnitude of variation in an
apparent diffusion coefficient that is well correlated with
both reff and the specific surface area per unit pore
volume (Spor). Two scenarios can explain our findings:
(1) the length-scale defined by t is not equal to reff and is
likely much longer due to the control of pore surface
roughness; (2) the range of diffusion coefficients is large
and likely determined by the relative proportions of the
different minerals (e.g. silica, clays) making up the rock.
In either case, the estimation of reff (and hence
permeability) is inherently uncertain from SIP relaxation
time.
Within this study we have shown, that spectral induced polarization is a reliable method for the enhanced characterization of the Fontainebleau sandstone in general, and for its related stratigraphical units in particular. Due to its high sensitivity towards pore network and pore surface changes, different stratigraphical units can be clearly differentiated and
probably even classified. We have observed a good correlation between the maximum of the SIP phase shift and the dominant pore throat radius for this rock type, as it has been reported for others sandstones before [20].
We investigate the pore space of rock samples with respect to different petrophysical parameters using various methods, which provide data upon pore size distributions, including micro computed tomography (μ-CT), mercury intrusion porosimetry (MIP), nuclear magnetic resonance (NMR), and spectral induced polarization (SIP). The resulting cumulative distributions of pore volume as a function of pore size are compared. Considering that the methods differ with regard to their limits of resolution, a multiple length scale characterization of the pore space geometry is proposed, that is based on a combination of the results from all of these methods. The findings of this approach are compared and discussed by using Bentheimer sandstone. Additionally, we compare the potential of SIP to provide a pore size distribution with other commonly used methods (MIP, NMR). The limits of resolution of SIP depend on the usable frequency range (between 0.002 and 100 Hz). The methods with similar resolution show a similar behavior of the cumulative pore volume distribution in the overlapping pore size range. The methods μ-CT and NMR provide the pore body size while MIP and SIP characterize the pore throat size. Using this difference, the average pore body to throat ratio is determined to be about three for the Bentheimer sandstone.
Our study shows that a good agreement between the pore radii distributions can only be achieved if the curves are adjusted considering the resolution and pore volume in the relevant range of pore radii. The MIP curve with the widest range in resolution should be used as reference
Other than commonly assumed the relaxation times observed in the electrical low-frequency range (1 mHz – 40 kHz) of natural porous media like sandstones and tuff stones cannot be directly related to the dominant (modal) pore throat sizes, measured (e.g.) with mercury intrusion porosimetry (MIP). Working with a great variety of sandstones from very different origins and featuring great variations in textural and chemical compositions as well as in geometrical pore space properties, it was observed that particularly samples with narrow pore throats were characterized by long (low-frequency) relaxations. These, however, can (following the current theories) be rather explained by long “characteristic length scales” in these media or low diffusion coefficients along the electrical double layer. However, there is no straightforward way (or single approved method) of getting reliable numbers for properties such as the lengths of pore throats, the diameter and length of the wide pores and their respective distributions. Consequently we follow a multi-methodical approach and combine the benefits of MIP, micro-computed tomography (μ-CT) and nuclear magnetic resonance (NMR) to achieve much deeper insight due to the different resolutions and sensitivities to either pore constrictions (throats) or wide pores. This helps us to understand, whether the observed electrical relaxation phenomena actually depend on geometric length scales or rather on other properties such as chemical composition, clay content, clay type or cation exchange capacity. In this paper, we showcase selected results of a systematic study of a total of 16 sandstones and three tuffs. Findings and the particular advantage of the used method combination are discussed and shown in detail for a representative sample selection.