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Revista Română de Materiale / Romanian Journal of Materials 2014, 44 (2), 147 – 152 147
POROZITATEA, PERMEABILITATEA ŞI DENSITATEA ÎN VRAC A ROCILOR
ŞI RELAŢIILE ACESTORA BAZATE PE MĂSURĂTORI DE LABORATOR
POROSITY, PERMEABILITY AND BULK DENSITY OF ROCKS AND
THEIR RELATIONSHIPS BASED ON LABORATORY MEASUREMENTS
ABDELAALI RAHMOUNI1∗, ABDERRAHIM BOULANOUAR1, MOHAMED BOUKALOUCH1,
ABDERRAHIM SAMAOUALI1, YVES GERAUD2, JAMAL SEBBANI1
1Laboratory of Thermodynamics, Department of Physics, Faculty of Science, Mohammed V University Agdal, P.O. Box 1014,Rabat, Morocco.
2University of Lorraine, ENSG, UMR 7359-GeoRessources, Nancy Cedex, France.
Physical properties of rocks are measured and analyzed, and their relationships are discussed in this paper. Permeability
and mercury porosimetry methods, porosity, and pore size distribution are determined. Furthermore, bulk and particle densities
of rocks are determined. The morphology of the porous medium has been approached by mercury porosimetry which gives an
appearance to the pore distribution of the material. The permeability of a variety of natural materials is characterized using a
relatively new laboratory apparatus. Permeability and porosity are in close relation, and it could be assumed that its relationship
is linear, i.e., with increasing porosity, permeability increases as well. This relationship is influenced by other rock properties,
such as the amount of open and closed pores within the rock sample, size, and distribution of pores. From this point of view, it
is necessary to study these physical properties of natural materials as well, because this enables an overall analysis of rocks
and their possible use for construction.
Keywords: rocks, permeability, porosity, mercury porosimetry, bulk density, TinyPerm II
1. Introduction
The fluid transport into porous materials is an
area of study relevant to many scientific and
engineering fields such as hydrogeology, physics,
and geo-environmental, petroleum, and chemical
engineering. Knowledge of permeability and
porosity is critical to accurately predicting fluid
transport. As a result, there is a great interest
among scientists and engineers in quantifying
permeability characteristics, porosity of natural and
manmade materials for many practical applications
related to oil extraction, groundwater flow and
contaminant transport [1,2].
Permeability and porosity are two of the
primary properties that control the movement and
storage of fluids in rocks. They represent an
important characteristic of materials. On the basis
of the known permeability and porosity, possible
influences of water on an engineering construction
are considered.
Furthermore, knowledge of permeability and
porosity is necessary at water leakages, at the
structural foundation in order to evaluate affluent to
a foundation pit, and in terms of the design of
waterproofing of buildings. Permeability and
porosity are also very important indicators for the
utilization of various kinds of rocks [3].
Mainly calcarenite rocks are used for various
purposes in the building industry, for the renovation
of historical monuments, stonework, and
sculptures, etc. The use of marbles and granites is
related to the architecture: floor coverings and
facades, decorated as columns, and balusters; but
also with planning the manufacture of street
furniture: benches. Permeability and porosity have
an impact on rock weathering, which affects the
field of engineering utilization.
Permeability is one of the rock properties that
are necessary for considering the solving of
hydrological and hydrogeological problems by
methods of numerical and physical modelling [4, 5].
Devices such as surface gas permeameters
provide reliable measurements and may be used to
determine other material properties. These
permeameters, however, are only capable of
material testing at single points in time, and
establishing a large, high density map can be
extremely time consuming. As a result, it would be
both critical and helpful to know the extent
(minimum distance) between sampling points
needed to “accurately” predict material properties
for natural and manmade materials with varying
levels of heterogeneity.
A surface permeability probing method,
developed by Valek, et al. [6], demonstrated the
applicability of using a surface gas permeameter
for historic conservation including: the weathering
and decay process associated with masonry
materials, characterization of existing materials to
∗ Autor corespondent/Corresponding author,
e-mail: a.rahmouni@yahoo.fr
148 A.Rahmouni, A. Boulanouar, M. Boukalouch, A. Samaouali, Y. Geraud, J. Sebbani / Porosity, permeability and bulk density of
rocks and their relationships based on laboratory measurements
seek compatible replacement material, and
investigation of the carbonation process in lime
mortars in historic and modern masonry. While this
method was highlighted as being non-destructive
and able to measure a wide range of permeability
values, it was found that measuring low
permeability material was seldom non-destructive.
In this paper, we characterize the permeability of a
variety of natural materials using a relatively new
laboratory apparatus. The apparatus is unique in
that it is non-destructive and capable of measuring
a wide range of surface gas permeability on
building materials. Discussion of the laboratory
methods used for measuring permeability and
porosity and their relationship is carried out in this
paper.
2. Materials and methods
The study includes 13 varieties of building
stone extracted from different regions of Morocco,
deliberately varied. The geographical distribution of
selected samples is shown in Figure 1.
Measurements of permeability and porosity are
performed on 13 samples. These measures will
help to better understand and identify the
characteristics of the porous network of materials
used in the construction.
Porosity of porous medium describes the
fraction of the void space in the rock, where the
voids may contain air or water. The porosity is
defined as the ratio of the volume of voids
expressed as a percentage of the total (bulk)
volume of a rock, including the solid and void
components. Porosity is calculated from the
derived formula:
1001 ×
⎟
⎟
⎠
⎞
⎜
⎜
⎝
⎛−=
ρ
ρ
d
N (1)
where ρd is bulk density of the dry specimen
and ρ is particle density.
Bulk density can be determined from a
regular specimen by a stereo-metric method. Our
tests are carried out on 13 samples. Particle
density, an average mass per unit volume of the
solid particles in a rock sample, is usually
determined by applying the mercury intrusion [7]
Permeability and porosity depend on pores
in the rock. There are two discerned typologies of
pores in rocks: closed and open pores. Closed
pores are completely isolated from the external
surface, not allowing the access of external fluids
in either the liquid or gaseous phase. Closed pores
influence parameters such as density and
mechanical and thermal properties. Open pores
are connected to the external surface and are
therefore accessible to fluids, depending on the
pore characteristics/size and the nature of fluid.
Open pores can be further divided into dead-end
or interconnected pores. The percentage of
interconnected pores within the rock is known as
effective porosity. Effective porosity excludes
isolated pores and the pore volume occupied by
water that is adsorbed on clay minerals or other
grains. Total porosity, determined from formula (1),
is the total void space in the rock, whether or not it
contributes to fluid flow.
Effective porosity is typically less than total
porosity. The character of porosity alters with the
genesis of rocks and strongly determines its
physical properties, e.g., permeability, adsorption
properties, mechanical strength, or durability. On
Fig. 1 - Geographical distribution of studied rocks.
A.Rahmouni, A. Boulanouar, M. Boukalouch, A. Samaouali, Y. Geraud, J. Sebbani / Porozitatea, permeabilitatea şi densitatea 149
în vrac a rocilor şi relaţiile acestora bazate pe măsurători de laborator
the basis of the known character of porosity,
predicting rock behaviour under different
environmental conditions and its usage are
considered.
One of the most important parameters is
the pore size and pore size distribution. Pores are
classified according to four groups depending on
the access size: micropores, with a size less than 2
nm diameter; mesopores, ranging between 2 and
50 nm diameter; macropores, which are in range
from 50 nm to 7500 nm diameter and rough pores
in size over 7500 nm [8].
2.1. Mercury porosimetry
This technique consists in injecting the non-
wetting fluid (mercury), under various pressures in
previously desiccated and degassed samples [9]. It
allows porosity and pore size to be estimated by
measuring the volume of injected mercury and the
injection pressure. The applied pressure is
connected to the threshold access of the pore by
the Young- Laplace equation:
R
P
ϕ
σ
cos2
= (2)
where P [Pa] is an actual pressure, R [nm] half-
length distance of two opposite walls of a pore
expressed by an effective radius, σ surface tension
of mercury [480·10-3 N·m-1] and ϕ contact angle
[141.3°].
These porosimetry measurements are
performed using an apparatus Micromeritics Pore
Sizer 9320 which makes it possible to inject
mercury with pressures ranging between 0.001 and
300 MPa. So the access threshold ranges between
400 and 0.003 µm. This technique determines the
connected porous volume and its distribution
according to the injection pressure and the
thresholds access.
Cylindrical samples, of 25 mm length and 20
mm in diameter, are dried at 60°C, weighed and
placed in an injection cell. After a degasification
step under a 50 µm mercury depression, the
injection cell is filled with mercury, and then the
vacuum is broken gradually until atmospheric
pressure. The intrusion measurement, i.e., the
volume of mercury injected into the sample, is
made for low pressures (between 0.001 and 0.15
MPa) and for high pressures (between 0.15 and
300 MPa). The pressure rises are carried out in
stages; after each stage, the injected mercury
volume is measured. From these data, it is
possible to determine the saturation curve
according to the injection pressure.
2.2. Permeability
We have used a relatively new surface gas
permeameter for making gas permeability
measurements on the surface of the substrate
specimens described above. The permeameter,
TinyPerm-II, made by New England Research,
Inc.. It is a unique hand-held device that can
characterize the permeability of rocks and soils or
the effective hydraulic aperture of fractures in situ
on outcrops as well as on laboratory specimens
[10]. The apparatus is capable of making
permeability measurements ranging from 0.01 to
10 darcies for matrices and 10 µm to 2 mm
fracture apertures [10]. Although the
measurements could have been made in the field,
all measurements reported here are made on the
specimens in a laboratory.
This device uses Darcy’s law to compute the
permeability. Brown and Smith [11] show the
permeability can be determined using the following
relationship:
L
kA
P
Q
µ
−=
0
(3)
where Q is the net air flow into the piston syringe,
P0 is the applied pressure which remains constant,
A is the inlet area for air flow, µ is the viscosity of
the gas (air), and L is the length. Since the values
of A, L and µ are known; and Q and P0 are
measured, equation (3) may be solved for
permeability, k.
The testing procedure is straightforward; the
operator presses a rubber nozzle against the
specimen and withdraws air from it with a single
stroke of a syringe. As air is pulled from the
sample, a microcontroller unit simultaneously
monitors the syringe volume and the transient
vacuum pulse is created at the sample surface.
Using signal processing algorithms, the micro-
controller computes the response function of the
sample/instrument system. Key characteristics of
this response are displayed on the liquid crystal
display (LCD) screen. Theory shows a relationship
between the response function and permeability;
and either matrix permeability or effective fracture
flow aperture may be determined from the
calibration charts and tables provided [10, 11].
The response function is related to
permeability K:
8737.12)(log8206.0 10 +
−
=
KT (4)
where T is the value of the response function and
the recorded output from the mini-permeameter.
For each sample point 3–6 measurements are
made in order to ensure the quality of the data. For
each sample point, an average of the
measurements is calculated and used as the
representative value for that point.
In total, 13 various rock samples are tested,
and values of the permeability, particle and bulk
densities, and porosity are listed in Table 1. The
values of the presented rock properties are
predominantly determined as an arithmetic
average of rock specimen tests. For each
specimen, the permeability, particle, and bulk
150 A.Rahmouni, A. Boulanouar, M. Boukalouch, A. Samaouali, Y. Geraud, J. Sebbani / Porosity, permeability and bulk density of
rocks and their relationships based on laboratory measurements
Table 1
Physical properties of rocks
Rock class
Types of rock
Location
Rock code
Permeability
K
(m2)
Bulk
density
ρd
(g/cm3)
Particle
density
ρ
(g/cm3)
Porosity
N
(%)
Biocalcarenite Rabat-Salé 1 2.28E-11 1.64
2.38 31.07
Biocalcarenite Rabat-Salé 2 3.34E-11 1.59
2.38 33.15
Biocalcarenite Rabat-Salé 3 1.74E-11 1.68
2.39 29.82
Biocalcarenite Rabat-Salé 4 5.04E-11 1.60
2.49 35.83
Sedimentary Calcarenite Ben Slimane 5 2.2E-15 2.45 2.72 9.84
Calcarenite Ben Slimane 6 1.8E-15 2.55
2.76 7.61
Biocalcarenite Bouskoura 7 1.46E-11 2.25
2.81 19.89
Travertin Meknès 8 3.13E-16 2.34
2.47 5.26
Calcarenite Taza 9 8.01E-14 2.54
2.96 14.08
Marble (Black) Khenifra 10 1.24E-19 2.71 2.72 0.3
Metamorphic Marble Bou Acila 11 3.72E-18 2.72 2.73 0.39
Marble Bou Acila 12 2.14E-18 2.74
2.75 0.26
Magmatic Granite Agadir 13 5.08E-17 2.69 2.71 0.59
densities are measured, and porosity calculated.
The morphology of the porous medium has been
approached by mercury porosimetry which gives
an appearance to the pore distribution of the
material. The samples have a sufficient volume to
be representative of the material. The results are
shown in Figures 2, 3, 4 and Table 2.
3. Results and discussion
The results of the permeability tests are
analysed using the method of least-squares
regression. The correlation coefficient (R2) is
determined for this regression.
The permeability is correlated with porosity.
The plot indicating the correlation is shown in
Figure 2. It is seen that there is a linear relation
between permeability and porosity. The correlation
coefficient is acceptably high, suggesting a
sufficient correlation between the two variables for
engineering use.
0 5 10 15 20 25 30 35 40
1E-20
1E-18
1E-16
1E-14
1E-12
1E-10
1E-8
11
10
13
12
8
65
9
7
3
124
y=0.21123x-17.11285
R
2
=0.96016
Permeability (m
2
)
Porosity (%)
Fig. 2 - Relationship between permeability and porosity of
rocks.
Permeability and porosity are in a close
relationship that depends on the amount of the
void space in the tested material. It is widely
accepted that permeability is determined by
microstructure, which is, in this context, defined in
terms of pore and crack structures. So it could be
supposed that with increasing porosity, the
permeability should increase as well. But there are
some other facts to note when speaking about this
relationship. Therefore, permeability of porous
material is influenced not only by porosity, but also
by shape and the arrangement of pores, or by the
amount of clayey component [8, 12].
Firstly, it is necessary to distinguish between
total and effective porosity. We are not able to
make assumptions on permeability of tested
material from values of total porosity, due to the
fact that it is the total void space in the rock. A rock
may be highly porous, but if the voids are not
interconnected, fluids within the closed (isolated)
pores cannot leak.
Secondly, pore size distribution is important.
To clarify the relationship between permeability
and porosity, pore size and pore size distribution
are determined for selected rock samples. Pore
dimensions cover a very wide range. Within our
research, two samples of calcarenite, which have
approximately the same order values of
permeability, but different porosities, are tested by
mercury porosimetry for pore size distribution.
Results are shown in Figures 3 and 4.
As we can see from Figures 3 and 4, sample
2 has a more uniform distribution in the range of
pore size. The rough pores of this sample should
not exceed 70% in total. It has a very broad
spectrum of porosity with significant mesoporosity
(pore diameter access between 1 and 100 µm).
The prevailing part of pores belongs to the rough
A.Rahmouni, A. Boulanouar, M. Boukalouch, A. Samaouali, Y. Geraud, J. Sebbani / Porozitatea, permeabilitatea şi densitatea 151
în vrac a rocilor şi relaţiile acestora bazate pe măsurători de laborator
pores, which can create main transporting ways for
liquid. In the case of sample 7, the distribution of
pore size is different. The rough pores of this
sample about 30 % in total. The dominant part of
pore belongs to the mesoporosity, and
microporosity, which is also very important.
0.01 0.1 1 10 100 1000
0.00
0.05
0.10
0.15
0.20
Cumulative Pore Volume
Incremental Pore Volume
Pore Diameter (µm)
Cumulative Pore Volume (mL/g)
0.0
0.1
0.2
0.3
0.4
0.5
Incremental Pore Volume (mL/g)
Fig. 3 - Pore size distribution of calcarenite from Rabat-Salé
(sample 2).
0.01 0.1 1 10 100
0.00
0.01
0.02
0.03
0.04
0.05
0.06
0.07
Cumulative Pore Volume
Incremental Pore Volume
Pore Diameter (µm)
Cumulative Pore Volume (mL/g)
0.00
0.02
0.04
0.06
0.08
Incremental Pore Volume (mL/g)
Fig. 4 - Pore size distribution of calcarenite from Bouskoura
(sample 7).
The distribution of pore volumes of sample 2
is unimodal (a single dominant family of pores
resulting in a single point of inflection in the curve
of injection). It is possible to determine a radius
access or threshold pore: it corresponds to the
radius access of pore that to a low pressure
increment provides access to a large pore volume.
It is graphically determined on the first injection
curve as the radius corresponding to the inflection
point of the curve or by the method of tangents [7,
13]. The threshold pore can also be viewed on the
curves representing the increment of mercury
injected for each access radius. The injection
curves with multiple turning points illustrate
y = -27.94 8x + 78.557
R
2
= 0.974
0
5
10
15
20
25
30
35
40
1.2 1.7 2.2 2.7 3.2
Bulk dens ity (g/cm
3
)
Poro sity (%)
4
1
2
3
8
5
9
7
6
1210
11
Fig. 5 - Relationship between bulk density and porosity of
rocks.
multimodal porous networks where several
families ray access to the pores coexists.
Average pore diameter is usually used as a
representative parameter of the pore size
distribution. In case of sample 2, average pore size
diameter is 1.96 µm; for sample 7, average pore
size diameter is 0.57 µm (Table 2).
It is well known that mineral admixtures
affect permeability. The basis for this effect can be
understood in terms of the formation of a large
amount of porosity in the mesopore range. This
assertion requires further experimental verification.
Finally, there are some other characteristics
of samples we have observed, such as the
relationship between bulk density and porosity. We
have obtained the generally known fact from rock
samples. The relationship between bulk density
and porosity of all the 13 tested samples can be
seen in Figure 5. We can clearly identify that with
decreasing bulk density, the porosity of the sample
increases. It is due to the small differences in
particle densities, which are not dependent on
porosity, but only on modal composition. The
modal compositions of calcarenite samples are
assumed to be approximately the same.
The relationship between bulk density and
porosity of all tested samples is shown in Figure 5.
Calcarenite has high porosity. The
permeability of the rocks above depends on the
structured nature of minerals forming the solid
matrix. The permeability of these rocks is in the
range of 10-11.
Tested samples of granite and marble are
fine-grained rocks, so they have low porosity, and
this fact causes a low permeability as well.
Table 2
Physical properties of tow samples calcarenite.
Types of rock
location
Rock
code
Permeability
k
(m2)
Bulk density
ρd
(g/cm3)
Particle density
ρ
(g/cm3)
Porosity
N
(%)
Average pore
size diameter
(µm)
Calcarenite Rabat-Salé 2 3.34E-11 1.59 2.38 33.15 1.96
Calcarenite Bouskoura 7 1.46E-11 2.25 2.81 19.89 0.57
152 A.Rahmouni, A. Boulanouar, M. Boukalouch, A. Samaouali, Y. Geraud, J. Sebbani / Porosity, permeability and bulk density of
rocks and their relationships based on laboratory measurements
4. Conclusion
Physical properties of 13 rock samples are
measured and analyzed in an integrated manner.
Laboratory measurements have been carried out
on the following physical properties: permeability,
porosity, pore size distributions and bulk density.
The graphs of permeability against porosity have
been presented. From the graphs it can be seen
that, permeability of the rocks is directly
proportional to porosity.
The interest of this study is focused on
samples of rocks extracted from different regions of
Morocco to pick up the physical properties of rocks
that experienced a rarity of technical studies. It
provides results on the permeability and porosity
for these well-characterized rocks. The results
obtained show that the permeability of porous
material is influenced not only by porosity, but also
by the shape and arrangement of pores, or by the
amount of clayey component. Only effective
porosity can influence permeability, because only
open pores are interconnected and allow leaking
water through. Another important factor is pore size
distribution. By evaluating the relationship between
porosity and permeability, it is also necessary to
take into account rock bulk and particle density.
Acknowledgements
This work is performed in the Project Integrated Action Franco-
Moroccan No.MA/07/168, between University of Strasbourg and
Mohammed V University- Agdal of Rabat, Morocco.
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