EAS 44600 Groundwater Hydrology
Lecture 4: Porosity and Permeability
Dr. Pengfei Zhang
Porosity of Earth Materials
The porosity of earth materials is defined as the part of rock or soil that is void space, often
expressed as a percentage:
V
n= v
(4-1)
VT
where n is the porosity, Vv is the void volume, and VT is the total volume. Porosity has the units
L3
of 3voids .
LR. E .V .
To describe porosity, or any other aquifer parameter, it is useful to first define the concept of
representative elementary volume (R.E.V.). The R.E.V. is a volume of aquifer over which the
porosity, for example, is describable by a single value. This concept is necessary because a
volume smaller than the volume that fits the definition of a representative elementary volume
will yield different aquifer parameters depending upon where one “places” the R.E.V on the
sample. To illustrate, let us take a look at Figure 4-1. Both diagrams represent the same porous
media. In the diagram on the left, the squares, which represent a poor choice for a R.E.V.,
delineate volumes for which very large differences in porosity would be obtained. In the
diagram on the right, the R.E.V.’s are sufficiently large that an equivalent porosity is obtained
for both of the R.E.V.s.
Figure 4-1. Representative elementary volume (R.E.V.).
Some typical kinds of porosity associated with various rocks are shown in Figure 4-2. The
interstitial porosity of rocks (Figure 4-2 a through d) is referred to as primary porosity, whereas
the fracture or solution porosity (Figure 4-2 e and f) is called secondary porosity.
4-1
Figure 4-2. Relation between texture and porosity. (a) Well-sorted sedimentary deposit having
high porosity; (b) poorly sorted sedimentary deposit having low porosity; (c) well-sorted
sedimentary deposit consisting of pebbles that are themselves porous, so that the deposit as a
whole has a very high porosity; (d) well-sorted sedimentary deposit whose porosity has been
diminished by the deposition of mineral matter in the interstices; (e) rock rendered porous by
solution; (f) rock rendered porous by fracturing (Meinzer, 1923).
Porosity can be determined in a couple of ways in laboratory. One method is to take a known
volume of sediment and dry it in an oven at 105 °C until it reaches a constant weight. This
removes moisture in the sample, but not water in the mineral structure. The dried sample is then
added to a known volume of water, and the resulting increase in volume as determined by the
increased water level represents the volume of the sediment itself (no voids). The volume of
sediment plus voids is determined from the height of the sediment and the cross-sectional area of
the chamber to which the sediment is added in the previous step. The volume of the voids is then
found by difference. This method of determining porosity is called volumetric method.
Alternatively, if one determines the bulk density of the sediment, one can calculate its porosity.
The bulk density (ρb) represents the density of the sediment including its voids. Recall that
density is mass over volume, and the volume used in bulk density is the volume of sediment plus
voids, or R.E.V.:
M
ρb = 3 sed
(4-2)
LR.E .V
In contrast, the particle density (ρs) does not include the voids, but represents the density of the
rock itself:
M
ρ s = 3sed
(4-3)
Lsed
For most rock and soil, the particle density is 2.65 g⋅cm-3.
Looking at the units above, one can see that ρb/ρs gives the volume of sediment per volume of
R.E.V.:
4-2
ρb
M sed L3sed
L3sed
=
⋅
=
ρ s L3R.E .V . M sed L3R.E .V .
(4-4)
Therefore, the porosity (n) is easily calculated:
n = 1−
ρ b L3R.E .V .
L3
L3
= 3
− 3 sed = 3voids
ρ s LR.E .V . LR. E .V . LR. E .V .
(4-5)
This method of determining porosity is called gravimetric method.
The porosity of a sediment depends on a number of factors including the roundness of the grains,
the packing of the grains, and the size distribution of the grains. For a sediment of perfectly
round grains of a single diameter (an impossibly narrow size distribution), the porosity will
depend only on the packing, with n= 0.48 for cubic packing, and n= 0.26 for rhombohedral
packing. For sediments consisting of a number of differently sized grains (wider size
distribution), the smaller grains will sit in the pores between the larger grains, and so the porosity
will be lower than it would be in a sand made of only one of the grain sizes. Likewise,
angularity of the grains will tend to cause them to pack less efficiently, and so will increase the
porosity of the sediment. Typical ranges in porosity for a variety of earth materials are given in
Table 4-1 below.
Table 4-1. Range in values of porosity.
Material
Porosity (%)
SEDIMENTARY
Gravel, coarse
24-36
Gravel, fine
25-38
Sand, coarse
31-46
Sand, fine
26-53
Silt
34-61
Clay
34-60
SEDIMENTARY ROCKS
Sandstone
Siltstone
Limestone, dolomite
Karst limestone
Shale
5-30
21-41
0-40
0-40
0-40
CRYSTALLINE ROCKS
Fractured crystalline rocks
Dense crystalline rocks
Basalt
Weathered granite
Weathered gabbro
0-10
0-5
3-35
34-57
42-45
4-3
Grain-Size Distribution
The grain-size distribution expresses the percent of the sediment mass that is finer than a given
grain size, as shown in Figure 4-3 below.
Figure 4-3. Grain-size distribution curve of a silty fine to medium sand.
Hence, in the format shown above, the less steeply the curve drops, the greater the grain size
distribution, and the wider the variety of grain sizes in the sediment. An important parameter
used to describe the grain size distribution is the uniformity coefficient, Cu, which is the ratio of
the grain size for which 60% of the sediment is finer by weight, to the grain size for which 10%
of the sediment is finer by weight.
Cu =
d60
d10
(4-6)
A sediment with Cu less than 4 is well sorted. If Cu is more than 6, the sediment is poorly
sorted.
Specific Yield
Specific yield (Sy) is the volume of water that drains from a saturated rock or sediment by
gravity, relative to the total volume of the rock:
4-4
Sy =
L3yield
L3R. E .V .
(4-7)
The water retained by the rock or sediment is called pendular water, and the ratio of this
volume to the total volume of the rock is called the specific retention (Sr).
L3yield
L3pendular
L3voids
Sr = n − S y = 3
−
= 3
LR. E .V . L3R. E .V .
LR. E .V .
(4-8)
Greater specific yields are obtained from medium to coarse sediments. Ranges of specific yield
for a variety of sedimentary rocks are given in Table 4-2 below.
Table 4-2. Specific yields in percent for sedimentary rocks.
Specific Yield
Material
Maximum
Minimum
Average
Clay
5
0
2
Sandy clay
12
3
7
Silt
19
3
18
Fine sand
28
10
21
Medium sand
32
15
26
Coarse sand
35
20
27
Gravelly sand
35
20
25
Fine gravel
35
21
25
Medium gravel
26
13
23
Coarse gravel
26
12
22
Permeability
The porosity of earth materials is known to vary, for example, clays have high porosity relative
to mixtures of sand and gravel (Table 4-1). Although porosity is an important parameter in terms
of characterizing void space in an earth material, the porosity does not describe the ability of the
rock or sediment to transmit water.
The ability of water to be transmitted through a rock or sediment is termed permeability.
Permeability depends on the interconnectedness of the pore spaces rather than the porosity
itself. For example, clays have high porosity, but the pores in clays are not well connected. As a
result, clays do not transmit water well, and hence have low permeability. In contrast, sand and
gravel mixtures may have lower porosity than clays, but the pores in the mixtures are well
connected and can transmit water easily. Therefore, sand and gravel mixtures have high
permeability.
4-5