Geometrical constraints for membrane polarization
Authors:
A. Hördt, K. Bairlein, M. Bücker and H. Stebner
Journal name: Near Surface Geophysics
Issue: Vol 15, No 6, December 2017 pp. 579 - 592
DOI: 10.3997/1873-0604.2017053
Language: English
Info: Article, PDF ( 1.27Mb )
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Summary:
Membrane polarization is one process that might describe the causes of induced polarization in sediments
at the pore scale. Here, we investigate the practical relevance of one particular model, which
consists of two cylindrical pores with different radii r and lengths L, for which the impedance can be
calculated analytically. We derive approximate equations that relate polarizabilities and relaxation
times directly to r and L. Based on these relations and on a systematic exploration of the parameter
space, we investigate under which conditions membrane polarization is relevant in the sense that it
produces measurable phase shifts in the frequency range typically observed in the laboratory or at the
field scale.
In principle, a wide range of spectra can be obtained. Maximum phase shifts up to hundreds of
milliradian can be simulated, and the characteristic time scales cover the entire range typically
measured in the laboratory. We discuss some specific constraints in the context of results from
mercury injection porosimetry and recently published laboratory data and show that the required
geometries are not unrealistic, even if a moderate ratio between pore length and width is included
as an additional condition. We conclude that membrane polarization as a possible mechanism is not
limited to a particular frequency range. We also provide evidence that the pore length of the wide
pore is likely to control the measured relaxation times in practical situations. The results encourage
further attempts to combine impedances of two-pore systems to approach the simulation of real
sediments, with the aim to extract pore space parameters from measured data.
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