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The pore size distribution provides a suitable description of the pore space geometry that can be used to investigate the fractal nature of the pore space or to determine a fractal dimension. Fractal dimension describes the size of geometric objects as a function of resolution. It can be integrated into models of permeability prediction. We investigated the fractal dimension of the pore volume of 11 Eocene sandstone samples from China. This study describes an approach to use spectral induced polarisation spectra to estimate the pore size distribution and to determine the fractal dimension of the pore volume. Additionally, the fractal dimension was derived from data of the capillary pressure curves from mercury intrusion and the transversal relaxation time distribution of nuclear magnetic resonance. For samples with an effective pore radius larger than 1 μm, good agreement exists between the values of fractal dimension derived from the three different methods, which implies the identification of similar pore structures. Spectral induced polarisation can be a non-invasive laboratory technique for the estimation of the pore size distribution, but the application of the methodology for field measurements remains a challenging problem considering the limited frequency range.
In der Vergangenheit wurde immer wieder diskutiert, ob die Porenhalsverteilung poröser silikatischer Medien maßgeblich die Relaxationszeit in Messergebnissen der Spektralen Induzierten Polarisation (SIP) bestimmt und dementsprechend auch neuere Ansätze, Porenweitenverteilungen aus diesen Daten abzuleiten, zuverlässig sein können. Systematische Studien an Gesteinen mit sehr unterschiedlichen Porenverteilungen zeigten, dass in Materialien mit engen Porenhälsen (z.B. < 5 μm) vor allem oder zusätzlich zum vermuteten Porenhalspeak niederfrequente Relaxationen zu beobachten sind, deren Ursache noch unklar ist.
Unter Einbeziehung der Methoden Röntgen-Computertomografie (μ-CT), Quecksilberporosimetrie (MIP), Stickstoffabsortion, Nukleare Magnetische Resonanz, SIP und Auflichtmikroskopie untersuchen wir den Porenraum hinsichtlich der Parameter Porosität, Permeabilität und innere Oberfläche und bestimmen die geometrischen Eigenschaften wie Porenweitenverteilungen oder fraktale Dimension durch verschiedene Algorithmen. Dabei ist zu berücksichtigen, dass sich die Methoden hinsichtlich der Grenzen ihres Auflösungsvermögens unterscheiden. Mit einer Zusammenführung der Ergebnisse aller Methoden kann eine mehrere Längenskalen überdeckende Charakterisierung der Porenraumgeometrie erfolgen.
Die Anwendung und Auswertung der verschiedenen Methoden werden am Beispiel von Baumberger Kalksandstein und Bentheimer Sandstein verglichen und diskutiert.
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
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.