Page 35 - Geothermal Energy Renewable Energy and The Environment

18 Geothermal Energy: Renewable Energy and the Environment

1.4

1.2 Less than 300 micron
grain size
Thermal conductivity (W/m–K) 0.8 Greater than 300 micron
1.0

0.6
grain size
0.4

0.2

0.0
0.0 2.0 4.0 6.0 8.0 10.0 12.0
Saturation (volume %)

FIGUre 2.3 Thermal conductivity as a function of saturation for sands of different grain size. (From
Manohar, K., Ramroop, K., and Kochhar, G., West Indian Journal of Engineering, 27, 2005.)

to a hundred times faster than a mineral. This also suggests that the rock enclosing a magma body
will behave as an insulating medium, transferring the heat away from the cooling molten rock at a
relatively slow rate.
Complicating these relationships is the fact that rocks and soils are porous materials. The
amount of porosity and its properties can vary significantly (see discussion in Chapter 4). In
general, the greater the porosity the lower the thermal conductivity. The extent to which thermal
conductivity and diffusivity are diminished by porosity will depend upon what fills the pore
space. Water and air are the most common pore-filling materials, and their respective thermal
conductivities (Figure 2.2) are significantly different. Thus, for two rocks or soil samples in which
all other things are equal, thermal conductivity will be higher in materials in which all of the pore
space is water-filled (saturated), compared to materials in which some or all of the pore space is
air-filled.
In Figure 2.3, the effect of saturation in quartz sand on the thermal conductivity is dramatically
apparent. There are several points relevant for geothermal considerations that emerge from
Figure 2.3. The first point is that the relationship between saturation and k is not linear. This results
th
from the fact that the surface tension of water causes it to distribute itself primarily along contact
points and junctions between sand grains, rather than evenly and uniformly within a pore space, in
contrast to what a gas would do. As a result, the ability of thermal energy to be transmitted at grain
contact points rapidly improves with the addition of a small amount of water. The rate at which
thermal transmissivity improves quickly falls between 10% and 20% saturation.
A second point evident from Figure 2.3 is that pore size also affects how saturation influences
k . This effect is a consequence of the fact that the number of contact points between grains, per
th
unit volume, depends directly on the size of the grains. Since there are more contact points per unit
volume for a smaller grain size, k will increase more rapidly with increasing saturation in fine sand
th
than coarse sand.
Both of these points make it clear that efficient use of geothermal energy must be based on thor-
ough knowledge of the properties of the geological materials at the site that will be developed. Such
knowledge should include thermal conductivity measurements that have been made in a laboratory
on material that is as little disturbed from its natural state as possible. This is true for applications