Hindawi Publishing Corporation
International Journal of Geophysics
Volume 2012, Article ID 728495, 17 pages
doi:10.1155/2012/728495
Research Article
Frequency-Dependent Streaming Potential
of Porous Media—Part 2: Experimental Measurement of
Unconsolidated Materials
P. W. J. Glover,
1
E. Walker,
1
J. Ruel,
2
and E. Tardif
2
1
Department of Geology and Engineering Geology, Laval University, Qu´ ebec City, QC, Canada G1K 7P4
2
Department of Mechanical Engineering, Laval University, Qu´ ebec City, QC, Canada G1K 7P4
Correspondence should be addressed to P. W. J. Glover, paglover@ggl.ulaval.ca
Received 3 June 2011; Revised 1 November 2011; Accepted 12 December 2011
Academic Editor: Tsuneo Ishido
Copyright © 2012 P. W. J. Glover et al. This is an open access article distributed under the Creative Commons Attribution License,
which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Frequency-dependent streaming potential coefficient measurements have been made upon Ottawa sand and glass bead packs
using a new apparatus that is based on an electromagnetic drive. The apparatus operates in the range 1 Hz to 1 kHz with samples
of 25.4 mm diameter up to 150 mm long. The results have been analysed using theoretical models that are either (i) based upon
vibrational mechanics, (ii) treat the geological material as a bundle of capillary tubes, or (iii) treat the material as a porous medium.
The best fit was provided by the Pride model and its simplification, which is satisfying as this model was conceived for porous media
rather than capillary tube bundles. Values for the transition frequency were derived from each of the models for each sample and
were found to be in good agreement with those expected from the independently measured effective pore radius of each material.
The fit to the Pride model for all four samples was also found to be consistent with the independently measured steady-state
permeability, while the value of the streaming potential coefficient in the low-frequency limit was found to be in good agreement
with other steady-state streaming potential coefficient data.
1. Introduction
There have only been 10 measurements of the frequency-
dependent streaming potential coefficient of porous geolog-
ical and engineering materials. A review of the existing mea-
surements was carried out by Glover et al. [1]. These previous
measurements can be divided into two groups: (i) transient
measurements with a percussive source and (ii) harmonic
measurements with a vibrating source.
While the first of these approaches mimics many of the
possible applications more closely [2–4], it cannot provide
the streaming potential coupling coefficient as a function of
frequency without using the frequency domain filtering and
Fourier techniques. Such techniques can only be used in a
linear system. Although the equations that describe the
streaming potential coefficient are linear below the transition
frequency and there is no evidence that they become non-
linear above that frequency, it has not yet been shown that
such an approach can be made to work for streaming po-
tential coupling coefficient measurements on rocks. The
processing of such data has, however, been discussed at
length in Reppert and Morgan [5]; they mention that inertial
effects may be seen if the transient signal has strong enough
high-frequency components.
The second approach is capable of providing the stream-
ing potential coupling coefficient at each frequency directly.
Its disadvantage is that a high-quality harmonic driving pres-
sure is required to create the time-varying flow. Various
authors have shown that measurements on a range of ma-
terials are possible in the range 1 Hz to 600 Hz [6–10], but
before the recent paper of Tardif et al. [11] only one meas-
urement had been made on a geological material [10].
This paper reports research that uses the electromagnetic
drive concept proposed by Glover et al. [1] to create an
apparatus for measuring the frequency-dependent streaming
potential coupling coefficient of unconsolidated materials
such as sands, gravels, and soils. Unconsolidated materials
were chosen because it is easier to arrange a sample holder