PREDICTING HYDRAULIC PROPERTIES THROUGH MEASURMENT OF
SPECTRAL INDUCED POLARIZATION (SIP)
Ingham, M.1, Joseph, S.1, Gouws, G.2.
1
School of Chemical and Physical Sciences, Victoria University of Wellington
2
School of Engineering and Computer Science, Victoria University of Wellington
Introduction
Theory predicts that the permeability of an aquifer material should be related to the predominant
grain diameter (e.g. Revil & Glover, 1997). It can also be derived that the relaxation time
associated with polarization processes taking place in the electrical double layer that forms at the
boundaries of pores is similarly dependent on grain size (Revil & Florsch, 2010). This leads to the
implication that measurements of relaxation time through the frequency dependence of the
electrical conductivity of an unconsolidated material may be used as a proxy for measurement of
permeability. Such measurements are normally referred to as spectral induced polarization (SIP).
Here we present the results of laboratory measurements that demonstrate that SIP
measurements may indeed be used to predict the permeability of sands typical of those found in
many New Zealand coastal aquifers.
Methods
The procedure for laboratory measurements has previously been described by Joseph et al.
(2015) who also demonstrated that the relaxation time associated with the polarization processes
measured by SIP is independent of the pore fluid conductivity. In the present study the
permeability and SIP response of samples of sands of different grain sizes has been measured,
along with the permeability and electrical formation factor.
Results
Typical measurements of the SIP response are shown in Figure 1. The phase peak is a result of
the frequency dependence of surface conduction that takes place in the electrical double layer as
a result of charge separation induced by the applied electric field. At low frequencies the
0.06
0.00
0.05
0.25
-Phase (rads)
0.50
0.04
0.75
1.00
1.25
0.03
1.50
1.75
0.02
2.00
2.25
0.01
2.50
0
0.001
2.75
0.01
0.1
1
10
Frequency (Hz)
100
1000
3.00
Figure 1: Example of measurements of SIP phase for sands of different grain size as indicated by the
Krumbein number.
conduction process is able to readily respond to the applied field and the phase lag of the
response is small. With increasing frequency there is an increasing time lag in the conductive
response with a concomitant increase in phase. At sufficiently high frequency the phase
decreases again as conduction can no longer respond to the rapidly changing field direction. It
can be seen from Figure 1 that the characteristic low frequency peak in the phase response
occurs at progressively lower frequencies as the grain size increases (Krumbein number
decreases). Modelling of such curves using a Cole-Cole model (Cole & Cole, 1941) allows the
relaxation time (  CC ) to be determined and theoretical relationships such as
kA
 CCDi
(1)
4m 2F (F  1)2
which predicts the permeability from  CC , the formation factor (F), the cementation exponent (m)
and the ionic diffusion coefficient (Di), to be tested. A is a simple multiplicative constant arising
from approximations made in the theoretical developments. Figure 2 shows how measured
values of permeability compare to values predicted by equation (1) with a best fitting value of A of
2.49.
1E-08
kmeas (m2)
1E-09
1E-10
1E-11
1E-12
1E-13
1E-13
1E-12
1E-11
1E-10
kpred (m2)
1E-09
1E-08
Figure 2: Comparison of measured permeability and permeability predicted by equation (1) for samples in
this study, with a value of the multiplicative constant of 2.49.
Summary
Laboratory measurements conclusively demonstrate a relationship between SIP measurements
and permeability for sands typical of New Zealand coastal aquifers. It is clear that field SIP
measurements may be a viable geophysical proxy for hydraulic properties. If logistical challenges
involved in such measurements can be overcome this will allow the measurement of permeability
cheaply and over wide spatial areas.
References
Cole, K.S. & Cole , R.H. (1941) Dispersion and absorption in dielectrics. Journal of Chemical Physics, 9,
341–351.
Joseph, S., Ingham, M. & Gouws, G. (2015) Spectral induced polarization measurements on New Zealand
sands – dependence on fluid conductivity. Near Surface Geophysics, 13, 169-177, doi: 10.3997/18730604.2014043.
Revil, A. & Florsch, N. (2010) Determination of permeability from spectral induced polarization data in
granular media. Geophysical Journal International, 181, 1480-1498, doi: 10.1111/j.1365-246X.2010.04573.x.
Revil, A. & Glover, P.W.J. (1997) Nature of surface electrical conductivity in natural sands, sandstones and
clays. Geophysical Research Letters, 25, 691-694.