&EPA
United States
Environmental Protection
Agency
Environmental Monitoring
Systems Laboratory
Las Vegas NV 13027
Research and Development
EPA/600/S4-84/089 Aug. 1985
An Investigation of Electrical
Properties of Porous Media
Stephen W. Wheatcraft, Kendrick C. Taylor, and John G. Haggard
The problem of ground-water con-
tamination has generated a need for de-
tailed information on ground-water
quality. The information derived from
well drilling and sampling is limited, es-
pecially for delineating a ground-water
contamination plume. DC electrical
geophysical methods are increasingly
used to help delineate contaminated
ground water, but these methods pro-
vide only resistivity data. Because sim-
ple resistivity is affected by many differ-
ent parameters, it is often impossible to
develop a unique interpretation of the
data. Complex resistivity (CR) supplies
considerably more information about
the saturated porous medium, thus in-
troducing the possibility of reducing
the number of unknown parameters af-
fecting the electrical response of the
porous medium.
The CR method provides two fre-
quency dependent curves: impedance
amplitude (related to resistivity) and
phase shift (related to capacitive ef-
fects). Although CR offers much more
information than a single resistivity
measurement, there is not much
known about how the CR responses are
affected by pore geometry, pore fluid
chemistry and clay content.
In this study, a laboratory measure-
ment system is set up to allow system-
atic variation of parameters of interest,
in order to determine their effect on
amplitude and phase data. The labora-
tory apparatus consists of a sample
holder, appropriate electrodes, and a
data collection and analysis system. Ex-
periments were conducted to vary
grain size, concentration of NaCI and
clay content.
Results indicate that grain size has
little to no effect on amplitude or phase
at any frequency for clay-free samples.
Phase-shift becomes increasingly nega-
tive over the range of frequencies inves-
tigated for a clay-bearing sample (3%
clay content). The amplitude also be-
comes increasingly smaller with in-
creased frequency for a clay-bearing
sample.
Comparison of amplitude versus
salinity for the clay and nonclay sam-
ples show that it may be possible to
develop a modified version of Archie's
Law for low salinity samples that con-
tain clay.
This Project Summary was devel-
oped by EPA's Environmental Monitor-
ing Systems Laboratory, Las Vegas,
NV, to announce key findings of the re-
search project that is fully documented
in a separate report of the same title
(see Project Report ordering informa-
tion at back).
Introduction
Geophysical techniques are com-
monly used in investigations of the
character and extent of the ground-
water resource. This is especially true
with respect to electrical methods. In
general, these techniques rely on de-
tecting the electrical response of sub-
surface units and then correlating this
response with other geologic informa-
tion so that estimates of hydrogeologic
parameters can be made.
Traditional DC resistivity techniques
used in conjunction with other methods
usually provide adequate information
about ground-water levels. However,
DC methods are inadequate for many
problems in which the contaminant
plume location, distribution, and chemi-
cal nature are of interest because so
many unknown parameters are gener-
ally involved in determining the DC re-
sistivity. (For instance, a relatively low
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resistivity value can be indicative of
high salinity and/or high moisture con-
tent.)
Complex resistivity (CR) investiga-
tions conceptually could reduce the un-
knowns and therefore the ambiguity in-
herent in traditional DC methods. This
potential advantage of CR exists be-
cause two sets of numbers, impedance
and phase shift, for a suite of frequen-
cies are generated for a particular
porous medium, instead of a single
value of resistivity obtained with DC
techniques. With this additional infor-
mation, it may be possible to obtain ac-
tual concentration values and/or type of
chemical species present in a contami-
nated ground-water system.
This study is an effort to characterize
the complex, frequency dependent elec-
trical response of a saturated porous
medium when certain parameters are
varied. The parameters to be varied in
these experiments are grain size, salin-
ity and clay content.
Procedure
To determine the complex impedance
of the sample, the voltage waveforms
across a known resistance (Vr) and
across the sample (Vs) are digitized. By
measuring the voltage drop across the
known resistance (Rr), the current can
be determined utilizing Ohm's law. To
characterize the sample impedance in-
dependent of sample geometry, it is
necessary to multiply by the sample
length (L) and divide by the sample
cross section (A). This is referred to as
the intrinsic impedance of the material.
To obtain the complex electrical re-
sponse of the sample, a sine wave was
used as an input and the digitized volt-
ages were recorded and analyzed for up
to 10 harmonics. This was repeated
until the frequency range of interest was
covered. Measurement of voltage
waveforms across the sample and resis-
tor were facilitated by digital recording.
The basic electrical measurement
system used in this study is shown in
Figure 1. To determine complex imped-
ance, it is necessary to provide a current
of the desired frequency in the sample.
This is done by connecting a function
generator to the current electrodes in
the sample holder.
A function generator was employed
as the voltage source. A decade resistor
box was constructed which contains
values from 10 ohm to 1 x 106 ohms.
Because the current density had to be
kept low to ensure a linear electrical re-
sponse, the resulting voltage drops
were too small to be accurately deter-
mined using the. A/D converter. This
was especially pronounced for samples
with low impedances and at low fre-
quencies. To overcome this problem, a
preamp was used.
After the voltage waveforms are am-
plified, they are digitized and recorded
with a resolution of 0.002 volts. The A/D
converter is interfaced to a computer
that controls the sampling and record-
ing.
An important feature of the system is
the sample holder (Figure 2) and its four
electrode arrangement. The unit con-
sists of two plexiglass reservoirs that
are connected by a cylindrical plexi-
glass sample tube. The sample is held in
place by plexiglass plates. The cylinder
and sample can be removed from the
reservoirs without disturbing the
sample.
The sample was saturated by filling
the fluid reservoirs. Saturation was con-{
sidered to be complete when the reser-
voir level remained constant and the
pore fluid conductivity, temperature,
and pH were constant in both reser-
voirs.
Results
Four different porous medium sam-
ples were prepared. The first three
porous medium samples were pure
glass beads of different grain sizes. The
size distribution within each sample
varied slightly, but the variation was
limited enough so that each sample
could be considered uniform in size.
The fourth sample was prepared as a
clay-bearing porous medium contain-
ing 3% Na-Montmorillonite by weight
mixed uniformly with large (2.2-2.8
mm) glass beads. A number of different
Frequency Generator
n\
5
i
Freq.
Cont.
i
/?,
Sample W/
f1
f'W
U- £ (t)
- f)
Pre-
Amp
Pre-
Amp
Clock
k,
Q
*.
h.
<
c
c
C
«J
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Computer
Figure 1. Experimental setup.
Fluid Reservoir
Fluid Reservoir
Current
Electrode
Figure 2. Sample holder.
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experiments were run on each sample,
varying the salinity concentrations, as
shown in Table 1.
Induction effects were observed at
frequencies greater than 100 Hz in low
salinity samples (<0.001 molarity). The
phase increase at higher frequencies
was expected because the calibration
showed similar phase increases. These
phase increases are caused by inductive
coupling within the equipment and
should not be attributed to true sample
response.
Small differences in amplitude oc-
curred in the three clay free samples
above 1000 Hz but are within the ex-
pected errors of the experiment. It may
be concluded that there is no effect of
grain size on the phase shift in clay-free
samples. This is an expected result,
since the phase shift should always be
zero in a clay-free sample.
. Figure 3 compares the phase shift re-
sponse of two samples of the same
grain size, one of which contained 3%
clay. The results are shown for runs of
three different salinites. The clean sam-
ples have essentially zero phase shift.
whereas the clay samples have nega-
tive shifts.
Figure 4 relates amplitude to salinity
for samples of the same pore size. Be-
cause the effect of frequency on ampli-
tude is small, only one frequency was
used (10 Hz). The clean sample plots as
a straight line on the log-log plot, in
agreement with Archie's Law. The clay-
bearing sample also plots as a straight
line, but with a smaller slope. Run CG4
falls above the straight line, however it
is believed that about one-half of the
clay was lost from the sample between
run CG3 and CG4, thus causing the shift.
The smaller slope associated with CG4
implies that a new form of Archie's Law
can be developed for porous media con-
taining clay with pore fluid of low salin-
ity. This form of Archie's Law would
have the form:
pB = ac|> -mpfn
Table 1. Summary of the Samples Used
Experiment
Run
GB1
GB2
GB3
GB4
GB5
GB6
GB7
GB8
GB9
GB10
GB11
GB12
GB13
GB14
GB15
GB16
GB18
GBW
GB20
CG1
CG2
CG3
CG4
CG5
CG6
greater than one for
pies. Because there
Glass Bead
dia. (mm)
2.8-2.0
2.8-2.0
2.8-2.0
2.8-2.0
2.8-2.0
2.8-2.0
2.8-2.0
2.8-2.0
0.85-0.60.
0.85-0.60
0.85-0.60
0.85-0.60
0,85-0.60
0.85-0.60
0. 15-0. 106
0. 15-0. 106
0. 15-0. 106
0. 15-0. 106
0. 15-0. 106
2.8-2.0
2.8-2.0
2.8-2.0
2.8-2.0
2.8-2.0
2.8-2.0
clay-bearing sam-
were only three
% Na-Mont
by Weight
0
0
0
0
0
0
Q
0
0
0
0
0
0
0
0
0
0
0
0
3.0
3.0
3.0
3.0
3.0
3.0
These results indicate
influence this effect.
Molarity of
NaCI Sat. Sol.
0.0001
0.0005
0.001
0.005
0.01
0.05
n 1
V. 1
0.5
0.0005
0.001
0.005
0.01
0.005
0.1
0.0005
0.001
0.01
0.05
0.1
0.1
0.05
0.01
0.005
0.001
0.0005
that salinity may
where:
a = empirical constant
4> = porosity
m = cementation factor
PB = bulk (formation) resistivity
pf = fluid resistivity
n = constant which depends on the
formation clay content
The data from these results suggest that
he fluid resistivity has an exponent
valid data points, no attempt was made
to calculate a value for n.
Another significant result is that the
samples have nearly identical response
when the pore fluid has 0.1 molarity
NaCI. Unfortunately, there are no data
beyond where the curves meet, so it is
impossible to determine what will hap-
pen at higher NaCI concentrations. It is
generally assumed that clay-containing
formations will have a lower resistivity
than clean formations due to the addi-
tional surface conductance on the clay.
Conclusions
Amplitude/phase data are not af-
fected by variation in grain size for
clay-free samples. This result implies
that hydraulic conductivity cannot be
determined by amplitude/phase data
because hydraulic conductivity is a
function of porosity and grain size.
Clay-free samples-have zero phase
shift over the range of frequency mea-
surement, whereas the clay-bearing
sample showed increasingly negative
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I
I
2 0
2 S 8 8 gfc DSJB
10
1
.c
tt
to
<0
-10
Symbol
D
0
Pun
CBS
GB12'
GB 18
Grain Size
2.8-2.0 mm
0.85-0.80 mm
0.1 5-0 108 mm,
o
00
O o
"
0
e
1
Log Frequency
Figure 3. Effect of grain size on phase and amplitude (without clay).
\og\c investigations ignore or avoid this
problem, thus making the interpreta- ,
tions subject to significant error. The
electrical effects of clay on a saturated
porous medium need to be understood
so that clay content and variation can be
determined. Amplitude/phase data
taken over a range of frequencies show
promise for enabling these determina-
tions. Further quantitative laboratory
work needs to be done to understand
more fully the relationships between
amplitude/phase information and clay
content.
Clay content information can be de-
rived from nuclear logging techniques.
However, to apply this information in
interpreting the electrical response re-
quires an indirect relationship involving
the cation exchange capacity of the clay.
A model accounting for the effect of clay
on amplitude that is based on phase in-
formation may be more direct. An addi-
tional advantage of CR over techniques
using active sources is the elimination
of the logistical problems associated
with the radioactive source. The poten-
tial advantages to downhole CR over
other methods may lend further weight
to the recommendation to develop a
better understanding of the relationship
between amplitude/phase information
and clay content.
The insensitivity of amplitude and
phase to grain size variation provides a
strong indication that further research
in this area will not be necessary. It does
not seem likely that hydraulic conduc-
tivity variations resulting purely from
grain size variations will be detectable
with downhole CR methods. Informa-
tion on grain size variation is very im-
portant for the determination of hy-
draulic conductivity variations, and it is
recommended that other downhole
methods be examined to determine
their potential in this area.
phase shifts from about 10 Hz through
3500 Hz. The amount of clay in the sam-
ple was only 3%, which is an indication
that CR measurements may be quite
sensitive to clay content and therefore
useful for detecting changes in hy-
draulic conductivity that are due to the
presence of clay. Downhole CR data
would be more useful than surface CR
for clay-content determination for two
reasons: a) the vertical changes in hy-
draulic conductivity are very useful in
determining contaminant migration in
ground water, and b) surface measure-
ments cannot provide the detailed reso-
lution necessary to delineate thin but
important changes in hydraulic conduc-
tivity.
The results of this study show that the
presence of clay has a large effect on
the frequency dependent electrical
properties of a saturated porous
medium. Most well log interpretation
strategies that have been used in hydro-
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10.000
o
1
.S 1000
100
,CG1
.001
Concentration NaCI (Molarity)
Figure 4. Effect of clay content on the impedance vs. salinity relationship.
0 U.S.GOVfRNMENTPRINTlNOOFFICE:18e5 559-111/20444
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