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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.
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.
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
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 on 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 is proposed, that is based on a combination of the results from all of these methods.
The approach is demonstrated using samples of Bentheimer and Röttbacher 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 verlapping pore size range. We assume that µ-CT and NMR provide the pore body size while MIP and SIP characterize the pore throat size. Our study Shows that a good agreement between the pore radius 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.