Chapter 3 – Porous Media Introduction Here we will discuss the subsurface rock /reservoirs through which the water flows which includ: - Porosity - Permeability and hydraulic conductivity of porous media - Variability of these parameters with respect to location and direction - Measurement of these parameters
Porosity All geologic materials have some amount of pore space, or empty space, in them. The term porosity (φ) refers to the fraction of the total volume of a rock or sediment that is pore space. In other words, it is defined as the volume of the voids divided by the total volume, or
3.1
Where: Vvoids = volume of the voids [L 3] Vtotal = total volume of the sample [L 3] Please note the variable
n
is sometimes used as a variable for porosity.
Porosity can also be expressed as a percentage (simply multiply the ratio by 100). Note that porosity is dimensionless. We can also identify a quantity called the Void
Ratio (e), which is defined as the volume of voids divided by the volume of solids, or
3.2
Where: Vsolids = volume of the solids [L 3]
Geologic materials are never completely dry; there is always some volume of water in them. We can think about geologic materials as composed of multiple phases – a solid phase, a water phase, and a gas phase (Figure 3-1). In turn, the solid phase can be further divided into its individual mineral phases (Figure 3-2).
Figure 3-1. Porosity in a rock (© Uliana, 2001, 2012).
Figure 3-2. Moisture content (by volume) (© Uliana, 2001, 2012).
Each of the mineral phases in a rock or sediment sample has a volume and mass associated with it. Every fluid and every mineral has a density associated with it.
Density Density has units of [M·L -3] and is defined as the ratio of an object's mass to its volume. We can express it mathematically as:
3.3
Often, we use the symbol ρ (rho) for density. Table 3-1 lists densities of some common substances.
Air Water
0.0012 1.0
Quartz
2.65
Aluminum
2.70
Iron
7.86
Gold
19.3
Table 3-1. Densities of some common substances in g/cm3 at room
Density is not a constant; it varies with temperature (generally higher temp = lower density; lower temp = higher density) and pressure (higher pressure = higher density; lower pressure = lower density). Therefore, when density is reported, it is usually accompanied by a temperature and a pressure. If no temperature or pressure is given, it is usually implied that the density value is at ‘standard temperature and pressure’ (STP), which is 25ºC and 1 atmosphere.
The density of water behaves differently than most other substances. As liquid water cools, the density increases as expected. However, when water hits about 4ºC, it reaches maximum density (1.000 g/cm 3), then as it cools further, the density goes down. That is why ice floats on water (whereas the solid form of most other substances would be denser than the liquid form and would therefore sink.)
We can also express density as the unit weight of a substance, where unit weight is equal to the density of a substance times gravitational acceleration (9.8 m/s 2). Unit weight is simply a way of expressing density in terms of weights that we
actually measure in the lab. Density can also be expressed in a non-dimensional way (i.e., without units) by taking the ratio of the density of the substance to the density of water. This non dimensional ratio is called the specific gravity ( γ ), and is expressed mathematically as:
3.4
Specific gravity allows us to record density data in a way that is independent of units. We can convert specific gravity values to density values in whatever units we want simply by multiplying by the density of water. Since the density of water is approximately 1 g/cm 3, specific gravity is basically equivalent to density in g/cm 3. Table 3-2 lists the specific gravities of some common rock forming minerals.
Mineral Name
Specific gravity
Quartz
2.65
Calcite
2.71
Dolomite
2.85
Na-feldspar
2.62
K-feldspar
2.57
Muscovite mica
~2.80
Clay (kaolinite)
2.60
Table 3-2. Specific gravities of some common rock-forming minerals.
We can see from the table that the majority of the rock-forming minerals that we are likely to encounter have a specific gravity of about 2.65-2.7. Since most rocks that we find are made of minerals with specific gravities of about 2.7, we can usually use a specific gravity of 2.7 when estimating the density of rocks. However, all rocks have some amount of void (i.e., empty) space in them, and a certain percentage of this void space contains water. When determining the density of a sample of rock or soil, we need to take into account the percentage of void space in the rock, and the percentage of that void space that contains water, in order to determine the bulk density of the sample. The bulk density is defined as the
overall density of a sample of rock (including the void spaces, any water in the void spaces, and any other substances that might be incorporated into the rock, such as organic material i.e. oil and gas), as opposed to the density of the individual minerals that make up the rock.
For example: if we consider a 1 cm 3 piece of solid quartz, we know that quartz has a specific gravity of 2.65 and a density of 2.65 g/cm 3, therefore the piece of solid quartz will have a mass of 2.65 grams. However, if we consider a 1 cm 3 piece of quartz sandstone, the quartz sandstone will contain a certain percentage volume of quartz grains, a percentage volume of empty space in between the quartz grains, and a percentage volume of water in the empty spaces. Since water has a specific gravity of 1.0 (at STP), and the mass of air is so small that it is negligible, the overall density (i.e., bulk density) of the sample of sandstone will be less than 2.65 g/cm 3, and the mass of the sample will be less than 2.65 grams. Or, if our sandstone contains a large percentage of a heavier mineral, like magnetite ( γ =5.2) or galena (γ =7.5), the sample may have a density greater than 2.65 g/cm 3. When calculating the mass of a sample, we need to first determine the bulk density of the sample, and then use that instead of the density of the minerals that make up the rock to calculate mass.
As previously stated, there is usually some measurable quantity of water in the pore spaces of any rock or sediment sample. We have a number of ways of quantifying the moisture content of geologic materials.
