Journal of Petroleum Science and Engineering 36 (2002) 183 – 192
www.elsevier.com/locate/jpetscieng
Hydraulic versus pneumatic measurements of fractured
sandstone permeability
Salima Baraka-Lokmane *
Department of Geology and Geophysics, Grant Institute, University of Edinburgh, West Mains Road, Edinburgh EH9 3JW, UK
Received 22 November 2001; accepted 30 September 2002
Abstract
This paper investigates the issue of ascertaining whether gas can replace water for determining the flow parameters in
fractured porous media. This is accomplished by the determination of the hydraulic parameters using brine, the pneumatic
parameters using air, and the study of the correlation between these two parameters. The measurements are obtained for
fractured sandstone cores from the middle Stubensandstein unit in the Southwest German Trias. In most cases, the intrinsic
liquid permeability is lower than the intrinsic gas permeability. Intrinsic gas permeability (kg) ranged from 32 to 159 md, while
intrinsic liquid permeability (kl) ranged from 12 to 47 md. The ratio of intrinsic gas permeability to intrinsic liquid permeability
(kg/kl) shows two subgroups: (1) ratios ranging from 1 to 2 (62.5% of samples) and (2) ratios ranging from 4 to 5 (37.5% of
samples). The reduction in the intrinsic liquid permeability is governed by three phenomena: physicochemically, by the
migration of the clay particles which clog the pores, mechanically, by the breakdown of original fabrics caused by the passage
of wetting fronts across relatively delicate clay mineral complexes, and experimentally, by the undersaturation of samples
during liquid permeability measurements. This study concludes that gas permeability is more accurate than liquid permeability
because it measures more closely intrinsic permeability especially for clay-rich rocks. In addition, because gas experiments can
be conducted much faster than liquid flow experiments, gas is a desirable replacement fluid.
D 2002 Elsevier Science B.V. All rights reserved.
Keywords: Fractured sandstone; Liquid permeability; Gas permeability; Laboratory study
1. Introduction
In aquifers, where fractures make a significant
contribution to the transmissivity, the estimated
average permeability is some complex function of
fracture characteristics, e.g. fracture connectivity,
fracture aperture and spacing distributions (Bloom* Fax: +44-131-668-3184.
E-mail address: [email protected]
(S. Baraka-Lokmane).
field and Williams, 1995) as well as the matrix
properties of the aquifer material itself. In the field,
it is difficult to characterise fractures and to quantify
their contribution to the permeability of the medium
because the fracture geometry is generally complex
and unknown, especially in 3D. Laboratory permeability studies can contribute significantly to the
quantification of aquifer heterogeneity and to a
better understanding of the relationship between
flow properties and fracture geometry by means of
permeability measurements and determination of the
0920-4105/02/$ - see front matter D 2002 Elsevier Science B.V. All rights reserved.
PII: S 0 9 2 0 - 4 1 0 5 ( 0 2 ) 0 0 3 1 7 - 0
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S. Baraka-Lokmane / Journal of Petroleum Science and Engineering 36 (2002) 183–192
fracture geometry using resin impregnation techniques (Baraka-Lokmane, 2002). They can also help
to analyse the interaction between fracture and
matrix.
Much work has been carried out to study the
correlation between liquid and gas permeabilities in
sandstone (Lovelock, 1977; Sampath and Keighin,
1982; Rasmussen et al., 1993; Bloomfield and
Williams, 1995; Jaritz, 1998), but the comparison
between liquid and gas permeability has not yet
been determined for a fractured sandstone. In this
study, the intrinsic permeability is determined using
air and brine as the fluid medium. The measurements are obtained for 0.1 m diameter fractured
sandstone cores. The permeabilities derived using
these methods (kl for liquid, kg for gas) were then
compared. This study confirms the importance of
difference between gas and liquid permeabilities and
explains its causes in the case of fractured and
porous sedimentary rock.
Stubensandstein unit of the Middle Keuper succession
in the Southwest German Trias. The Stubensandstein
is characterised by a mixed mineralogy and high
matrix porosity. The mineralogical study showed that
the samples present well to poorly sorted grains.
Quartz is the dominant framework of the sandstone
samples (70 – 80%), with some feldspar (10 –25%),
and rare micas. The remaining fraction is cement, the
most common being clay minerals including kaolinite,
smectite and illite, carbonate (calcite or dolomite) and
quartz (in the form of overgrowths). Figs. 1 and 2
show examples of the coexistence of several types of
cements. The dominant cements of the different samples are listed in Table 1. The samples can be subdivided into three groups with respect to the dominant
cementing agent:
2. Characterization of samples
samples where carbonate is the dominant cement
(samples 4 and 5);
sample where kaolinite is the dominant cement
(sample 8);
samples where the dominant cements are clay
minerals and carbonate (samples 1, 2, 3, 6 and 7).
Eight core samples of 0.1 m in diameter chosen for
the present study were obtained from the middle
The samples contain fractures in the form of
opening-mode joints, with no appreciable shear off-
Fig. 1. SEM photo of cement containing kaolinite (K) and carbonate minerals (C).
S. Baraka-Lokmane / Journal of Petroleum Science and Engineering 36 (2002) 183–192
185
Fig. 2. SEM photo of cement containing smectite (S), kaolinite (K) and illite minerals (I).
set and no cataclastic deformation bands. The type,
nature and orientation of these fractures all have an
effect on the permeability of the sample. Poor
choice of sample could mean that the permeability
of the matrix would dominate the permeability of
the whole sample.
The samples were selected so that they contained
visible, open, unhealed and unfilled fractures that
could be cored roughly parallel to the axis of the
Table 1
Cement types and the dominant cement for the eight selected
samples
Sample
number
Type of cement
Dominant cement
1
2
3
kaolinite, carbonate, quartz
kaolinite, carbonate
carbonate, smectite, illite,
kaolinite, quartz
carbonate, kaolinite
carbonate, kaolinite
carbonate, quartz, smectite
carbonate, quartz, smectite
kaolinite, quartz, carbonate
kaolinite, carbonate
kaolinite, carbonate
carbonate, smectite
4
5
6
7
8
carbonate
carbonate
carbonate, smectite
carbonate, smectite
kaolinite
coring instrument. The sampling was carried out with
a special electric bore core drill with a diamonddrilling bit (Hilti, DD-160E).
3. Determination of the hydraulic and pneumatic
parameters
The air and brine permeability tests were conducted with eight samples. The permeability of clay
sandstones decreases rapidly and significantly when
the salt water present in the sandstone is replaced
by fresh water. The sensitivity of sandstone to fresh
water is primarily due to the blocking of pore passage by dispersed particles (Khilar et al., 1983), and
the permeability reduction due salinity changes
occurs regardless of the type of clay (Mungan, 1965).
It has been found that the permeability of the core
samples begins to decrease at a specific salt concentration. In the literature, this salt concentration has been
termed the critical salt concentration (CSC) (Rahman et
al., 1995). The CSC is defined as the minimum salinity
required protecting the formation from swelling clay
damage and mobilisation of clay fines. When the salt
concentration decreases below the critical value, the
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S. Baraka-Lokmane / Journal of Petroleum Science and Engineering 36 (2002) 183–192
double layer expands and the force of repulsion
between the clay particles increases, weakening the
bonds between them. The clay particles can then
separate more readily under the hydrodynamic shear
stress created by fluid flow, migrate and bridge at pore
constrictions, leading to pore plugging (Rahman et al.,
1995).
Much work has been carried out to study the
formation damage in sandstone (Mungan, 1965; Khilar et al., 1983; Khilar and Fogler, 1984; Mohan et al.,
1993; Rahman et al., 1995; Civan, 2000; De Lima and
Niwas, 2000). The experiments conducted by Mohan
et al. (1993) and Mohan and Fogler (1997) have
shown that the critical salt concentration (CSC) of
sodium chloride needed to prevent damage is between
4 and 5 M for Stevens sandstone and 0.07 M for Berea
sandstone. According to the studies reported above,
the brine used in the experiments was 9% NaCl brine,
with a density of 1.067 g/cm3 and a viscosity at 20 jC
of 1.31 cP.
3.1. Determination of the gas permeability
The gas permeability tests were measured using air
and were chosen for eight samples. The intrinsic matrix
permeability was measured from small bore cores with
volumes equal to approximately 50 cm3 (4 cm in length
and 4 cm in diameter), which did not contain visible
fractures.
The effective parameters of the matrix/fracture
system were estimated with a special tri-axial test
cell (Fig. 3). In contrast to the conventional procedures for the determination of the liquid permeability, because of the increase in the loss of the potential in the supply, the gas pressure was measured
directly between the sample input and output with
two potential probes, which were placed at each end
of the sample. The dried samples are sealed with a
flexible latex membrane to avoid leakage. The dry
air flows from the bottom (sample input) to the top.
Because of gas compressibility, flow through the
sample is allowed to stabilize before measuring
permeability. The pressure difference can be regulated in a short time using the pressure difference
adjuster, where the permeability is higher than 1 md,
steady state is achieved within 1 min. The apparatus
allows the mean sample pressure to be increased
without increasing the pressure gradients. Thus, the
rate of flow remains low avoiding turbulent conditions. Two parameters are measured: pressure difference (Dp) and the flow rate of air ( Qpo) using a flow
meter. The flow rate of air ranged from 0.3 to 3 cm3/
s and the pressure difference ranged from 7.20 102
to 8.37 103 Pa.
Fig. 3. Equipment for the measurement of gas permeability ( p1 [Pa]: input pressure, p2 [Pa]: output pressure, pz [Pa]: confining pressure, Dp
[Pa]: pressure difference, Qpo [m3/s]: flow rate of air.
S. Baraka-Lokmane / Journal of Petroleum Science and Engineering 36 (2002) 183–192
187
Fig. 4. Klinkenberg correction of the apparent permeability (ka) for sample 3.
The differential gas pressure is made as small as
possible to provide a suitable rate of air flow. The
permeability is determined by means of a multiplepoint gas flow test. The permeability of air, ka, as
calculated from Darcy’s law (Klinkenberg, 1941) is
plotted against the inverse of the mean absolute air
pressure on the sample, 1/p̄ (Fig. 4). The permeability
is evaluated by extrapolation
k ¼ limka as p̄ ! l
Compressibility of the gas, the effect of Klinkenberg
slip flow as well as the effect of the turbulence was
taken into consideration (Bloomfield and Williams,
1995).
To avoid turbulent conditions, low gas pressure
gradients were used. To insure that turbulent flow did
not occur, the flow rates for each sample were
measured using a range of pressure differences. The
resulting gas flow rate versus gas pressure for sample
5 is shown in Fig. 5; the linear function demonstrates
laminar flow. The calculated Reynolds numbers
ranged from 5.10 10 7 to 3.85 10 5 confirming
that the permeability tests were conducted under
laminar flow conditions, and that Darcy’s law is valid
over the range of pressure gradients used.
The gas permeability values (kg) for the eight core
samples varied between 30 and 180 md, while matrix
gas permeability values (kgm) varied between 1 and 4
md (Table 2).
3.2. Determination of the liquid permeability
The intrinsic permeability was measured using 9%
NaCl brine (saturated under vacuum) and small bore
cores of a volume of 50 cm3 (4 cm in length and 4 cm
Fig. 5. Correlation between hydraulic gradient and gas flow rate for sample 5.
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S. Baraka-Lokmane / Journal of Petroleum Science and Engineering 36 (2002) 183–192
Table 2
The hydraulic, pneumatic and physical parameters of the eight selected samples
Sample
number
kg
(md)
kl
(md)
kg/kl
Porosity,
/ (%)
Saturation,
Sr (%)
1
159
38.6
4.12
21.54
95.89
2
125
27.9
4.48
25.69
3
4
5
6
7
8
44.2
56.7
55.1
33.4
31.9
130
17.3
43.2
46.9
12.3
15.1
25.2
2.55
1.31
1.17
2.72
2.11
5.16
21.31
21.85
21.19
20.52
20.17
17.89
klm
(md)
kgm/klm
Characteristics
33.26
13.50
2.46
. more than one fracture
. large fracture aperture
. presence of clay nodules
91.37
123.49
26.60
4.64
91.01
93.27
93.27
98.21
90.22
76.69
31.74
34.05
31.22
28.34
26.84
24.90
12.45
25.99
26.68
10.42
12.72
7.48
2.55
1.31
1.17
2.72
2.11
3.33
.
.
.
.
.
.
.
.
.
in diameter) without visible fractures, taken from each
of the previously described eight samples.
Determination of permeability using brine was
conducted with the equipment shown in Fig. 6.
The sample was sealed in a latex membrane to
avoid leakage and a confining pressure of at least
3 105 Pa was applied. The brine present in the
storage container is injected into a saturated sample
and the volumes of the brine flow (input and output)
were measured with burettes. The effluent brine
flowed into a closed storage container where a constant pneumatic pressure was used to maintain a
saturation pressure. To insure that the samples were
kgm
(md)
in the matrix
one fracture
large fracture aperture
more than one fracture
more than one fracture
one fracture
more than one fracture
more than one fracture
one fracture
large fracture aperture
completely saturated, the measurements of liquid
permeability were carried out at high saturation pressures ranging from 2 105 to 5 105 Pa; any residual
air in the core would be and rendered negligible.
Pressure differences (Dp) across the samples were
ranged from 1 104 to 7 104 Pa and flow rates
( Q) from about 0.02 to 0.1 cm3/s.
The intrinsic permeability value (kl) are listed in
Table 2 along with the matrix permeabilities (klm). The
intrinsic permeability values (kl) measured for the
eight samples vary between 14 and 50 md. Intrinsic
matrix permeability values (klm) vary between 7 and
26 md. They are given in Table 2.
Fig. 6. Equipment for the measurement of liquid permeability ( p1 [Pa]: input pressure, p2 [Pa]: output pressure, pz [Pa]: confining pressure, Q1
[m3/s]: water input volumetric rate of flow, Q2 [m3/s]: water output volumetric rate of flow).
S. Baraka-Lokmane / Journal of Petroleum Science and Engineering 36 (2002) 183–192
189
Fig. 7. Correlation between hydraulic gradient and brine flow rate for sample 3.
To check whether the assumption that laminar flow
was valid in the presence of fractures, the flow rate
was measured at different pressure differences for
each sample.
The calculated Reynolds numbers
range from
pffiffiffi
4 10 7 to 2 10 6 ðRe ¼ qu k =lÞ. This is significantly less than the critical Reynolds number of 1,
which indicates incipient turbulent flow. Fig. 7 shows
a linear dependency between brine flow rate and the
hydraulic gradient for sample 3, demonstrating that
Darcy’s law is valid over the range of pressure
gradients studied. Therefore, the permeability tests
were conducted at laminar flow condition.
4. Correlation between liquid and gas permeability
The liquid and gas permeability tests were conducted under laminar flow conditions. The intrinsic
gas permeability (kg) ranged from 31.9 to 159 md,
while intrinsic liquid permeability (kl) ranged from
12.3 to 46.9 md. The degrees of correlation between
the two permeability measurements are analysed on
the basis of kg/kl ratios, Table 1. Two tendencies in the
distribution of kg/kl were observed. (1) Ratios ranging
from 1 to 2 (samples 3, 4, 5, 6, and 7), and (2) ratios
ranging from 4 to 5 (samples 1, 2, and 8).
Scatter between liquid –gas permeabilities are also
reported in the literature (Lovelock, 1977; Sampath and
Keighin, 1982; Rasmussen et al., 1993; Bloomfield and
Williams, 1995; Jaritz, 1998) with a tendency for liquid
permeability to be lower than gas permeability. The
ratio of gas permeability to liquid permeability for
sandstone cores ranges from 1 to 30 (Table 3).
The sandstone used in this study is from the same
outcrop used by Jaritz (1998). The ratio between
intrinsic gas and liquid permeabilities is between 1
and 3, for the sandstone cores and between 1 and 5 for
the fractured sandstone cores (reported in Table 2).
There are several reasons for the scatter of liquid –gas
permeabilities.
4.1. Migration of clay particles
Three types of clays are present in the cement of
the measured samples: kaolinite, illite and smectite.
Strongly hydrophilic minerals, particularly swelling
clays can be important in controlling the liquid permeability (Mungan, 1965; Sampath and Keighin,
1982; Khilar et al., 1983; Khilar and Fogler, 1984;
Bitton and Gerba, 1984; Appelo and Postma, 1993;
Mohan et al., 1993; Rahman et al., 1995; Bloomfield
and Williams, 1995; De Lima and Niwas, 2000; Civan,
2000). Smectites can swell with changing ionic conditions and eventually disperse and migrate with the
Table 3
Scatter of liquid – gas permeability data from the literature
kg/kl
Nature of
samples
Number of
samples
Authors
1!5
1 ! 10
sandstone
sandstone
1155
10
2!4
fractured tuff
1 ! 30
sandstone
55
1!3
sandstone
15
Lovelock, 1977
Sampath and
Keighin, 1982
Rasmussen
et al., 1993
Bloomfield and
Williams, 1995
Jaritz, 1998
105
190
S. Baraka-Lokmane / Journal of Petroleum Science and Engineering 36 (2002) 183–192
flowing fluid. Swelling alone reduces the effective area
for flow and causes reduction in permeability. Kaolinites and illites are non-swelling clays that tend to
detach from the rock surface and migrate when the
colloidal conditions are conducive for release. The
migrating particles can get trapped in pore throats,
thus causing a reduction in permeability (Mohan et al.,
1993).
This is generally observed for the samples with a
large fracture apertures (greater than 40 Am) (BarakaLokmane, 2002), where the values of liquid permeability are lower than the values of the gas permeability; this is explained by the presence of the clay
minerals within the fracture aperture, which are
responsible for the reduction of the water flow rate.
The presence of clay minerals within the fracture
aperture was verified by independent methods (resin
casting and magnetic resonance imaging techniques)
(Baraka-Lokmane, 1999, 2002; Baraka-Lokmane et
al., 2001).
4.2. Breakdown of original fabrics
The passage of wetting fronts across relatively
delicate clay mineral complexes can breakdown the
original fabrics and may physically alter the geometry
of some of the flow channels, causing irreversible
changes in the permeability of the medium and therefore modifying liquid permeabilities in a complex
manner (Lovelock, 1977; Bloomfield and Williams,
1995).
4.3. Undersaturation of samples
Undersaturation of samples during liquid permeability measurement may cause a systematic underestimation of liquid permeability. It results liquid
permeability values consistently lower than the gas
permeability values. It may not be possible to fill all
of the pore space with brine during the liquid permeability measurement, particularly in finer grained
sandstones (Lovelock, 1977).
To determine the reasons for the scatter of liquid
and gas permeability data, physical parameters such
as: matrix porosity (/), and the degree of saturation
(Sr), matrix gas (kgm) and liquid permeability (klm)
tests were conducted for the eight samples whose
characteristics are presented in Table 1.
The matrix porosity measured with the help of a
Helium Pycnometer, as well as the matrix gas and
liquid permeability were measured from small bore
cores with volumes equal to approximately 50 cm3 (4
cm in length and 4 cm in diameter), which did not
contain visible fractures. During the liquid permeability measurements, the saturation degree Sr is calculated
as follows: Sr = 1 + po/p̄(Sro 1), where p̄ is the mean
absolute air pressure on the sample during the liquid
permeability test, po is the atmospheric pressure, and
Sro is the degree of saturation at atmospheric pressure.
The saturation degrees were measured from the previously described fractured bore cores.
5. Discussion
The ratio between matrix gas permeability (kgm)
and liquid permeability (klm) for sample 2 is equal to
2.46 (Table 2). The high value of the ratio is due to the
presence of clay nodules in the matrix (Baraka-Lokmane, 1999). In addition, the scatter between the
liquid and the gas permeability is particularly high
for the samples where a large fracture aperture is
observed (43.6 Am for sample 1 and 43.6 Am for
sample 8) (Baraka-Lokmane, 2002). In these samples,
the two first processes cited above (migration of clay
particles and the breakdown of original fabrics caused
by the passage of wetting fronts across relatively
delicate clay minerals complexes) are probably due
to the presence of clay minerals within the relatively
large fracture aperture. The mineralogical study shows
that the clay minerals are the dominant cement of
these samples. For sample 8, the scatter between
matrix gas and liquid permeability is also explained
by undersaturation of this sample during liquid permeability measurements; indeed, the degree of saturation is lower than 80% (Baraka-Lokmane, 1999).
This phenomenon occurs for finer grained sandstone,
which is the case for this sample. For sample 2, there
is no difference between matrix and the sample gas
and liquid permeability ratio. The fracture of this
sample does not run right through the core sample
(Baraka-Lokmane, 2002); thus, the contribution of
hydraulic conductivity of the fracture to the total
hydraulic conductivity of the sample is negligible.
The gas permeability is about 4.5 times higher than
the liquid permeability; therefore, the clay minerals
S. Baraka-Lokmane / Journal of Petroleum Science and Engineering 36 (2002) 183–192
present (as cement in the matrix) seem to be responsible for the scatter between gas and liquid permeability values. This study has shown that the gas
permeability is carried out much faster than liquid
permeability technique and is less prone to experimental problems and errors. Gas permeability technique measures more closely the intrinsic permeability,
therefore it is to be recommended especially for clayrich fractured porous rocks.
6. Conclusions
Both liquid and gas permeability tests were performed under conditions that insure laminar flow.
Intrinsic gas permeability (kg) ranged from 32 to 159
md, while intrinsic liquid permeability (kl) ranged from
12 to 47 md. There is a general tendency for intrinsic
liquid permeability to be lower than intrinsic gas
permeability. For fractured sandstone cores, there are
two tendencies in the distribution of the ratio of
intrinsic gas permeability to intrinsic liquid permeability (kg/kl): (1) ratios ranging from 1 to 2 (62.5% of the
samples), and (2) ratios ranging from 4 to 5 (37.5% of
the samples).
Three samples (1, 2 and 8) differed from the remaining five samples. These three samples exhibit
ratios of intrinsic gas permeability to intrinsic liquid
permeability ranging between 4 and 5. The factors
reducing the liquid permeability are governed by three
phenomena: (1) physicochemically, by the migration of
the clay particles which clog the pores, (2) mechanically, by the breakdown of original fabrics caused by
the passage of wetting fronts across relatively delicate
clay mineral complexes, and (3) experimentally, by
undersaturation of samples during water permeability
measurements.
It has been recognised that liquid permeability tests
are very time consuming and because gas permeability
measures more closely intrinsic permeability especially
for clay-rich rocks, gas is a desirable replacement fluid.
List of symbols
k
ka
kg
Intrinsic rock permeability, L2
Apparent permeability using air pressure
gradient, L2
Intrinsic gas permeability, L2
kgm
kl
klm
p
p̄
p1
p2
po
pz
Q
Qg
Qpo
Q1
Q2
Re
Sr
Sro
u
Dp
l
q
/
191
Intrinsic matrix gas permeability, L2
Intrinsic liquid permeability, L2
Intrinsic matrix liquid permeability, L2
Pressure, Pa
Mean absolute air pressure on the sample, Pa
Input pressure or the pressure at x1, Pa
Output pressure or the pressure at x2, Pa
Atmospheric pressure (101325 Pa)
Confining pressure, Pa
Liquid volumetric rate of flow, L3/T
Gas volumetric rate of flow, L3/T
Flow rate of air, L3/T
Liquid input volumetric rate of flow, L3/T
Liquid output volumetric rate of flow, L3/T
Reynolds number
Saturation degree
Saturation degree at atmospheric pressure
Darcy’s velocity or filtration velocity, L/T
Pressure difference, Pa
Dynamic viscosity of fluid, M/LT
Density of fluid, M/L3
Matrix porosity
Acknowledgements
This work was conducted as part of the project
‘‘Festgesteins-Aquiferanalog: Experimente und Modellierung’’, funded by Deutsche Forschungsgemeinschaft (DFG), Germany. The author thanks Prof. Dr.
Georg Teutsch and Dr. Bryne Ngwenya for their
constructive comments on drafts of the manuscript, as
well as the managing editor and the two anonymous
reviewers for their constructive critical review of the
manuscript.
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