Page 36 - Geothermal Energy Renewable Energy and The Environment

Sources of Geothermal Heat: Earth as a Heat Engine 19

that are dependent on the thermal properties of near-surface materials (e.g., ground source heat
pump installations; discussed in Chapter 11), as well as for applications involving power generation
using geothermal energy from deep bedrock sources.
Although the thermal conductivity of minerals is not insignificant, minerals are poor con-
ductors of heat compared to metals. Aluminum, for example, has a thermal conductivity of
about 210 W/m-K at room temperature and iron has a thermal conductivity of about 73 W/m-K.
Minerals conduct heat at rates that are, in general, one to two orders of magnitude less than those
for common metals (Table 2.3). Although thermal conductivity has a strong influence on the local
thermal properties of a geothermal site, the amount of heat available at a site is a reflection of
another heat transfer process in the Earth that derives from the relatively low thermal conduc-
tivity of minerals. That heat transfer process is convection, which is the dominant mode of heat
transfer in the Earth.

convecTion
Conductive heat transfer occurs without movement of mass. However, a warm mass of any material
flowing into a cooler region is also a means for accomplishing heat transfer. If, for some physical
reason, the flow of the heated mass into the cooler region is not accompanied by any heat conduc-
tion, the process is called advection. Under most circumstances in the Earth, however, the move-
ment of the mass will occur as heat is simultaneously being conducted away. This combined process
of heat being transferred by both mass movement and heat conduction is called convection.
In the presence of gravity, materials that have a lower density will tend to rise above materials of a
higher density. In a planetary body composed of randomly distributed materials of differing density,
an equilibrium state will eventually be achieved when all of the materials are ordered sequentially
from the highest density material in the center of the body to the lowest density material at the outer
edge of the body. This arrangement of densities is called density stratification. Density stratification
will occur spontaneously over time provided some or all of the materials are capable of flow. The
rate at which this will occur depends upon the viscosities and density differences of the materials
involved. The early Earth achieved this state of density stratification within a few tens of millions
of years, as previously discussed. However, this condition did not result in a static planet because it
was not a stable configuration.
Viscosity is the resistance of a material to flow when stressed. Materials with a high viscosity
are materials that, because of their molecular structure, possess high internal friction. Fluids, such
as cold honey or molasses, have a high viscosity, compared to water or air. The resistance to flow is
3
measured in units of Pascal-seconds (Pa × s). One Pa × s is equivalent to 1 m × kg × s /m , which is
2
a measure of applied stress and the resulting deformation (or strain) it experiences. The range of vis-
cosities materials possess is shown in Table 2.4. Note that many materials that seem incapable of flow
at room temperature conditions (such as portions of the solid mantle of the Earth) do, in fact, have
high but significant viscosities at high temperatures and pressures that are important over geological
time scales.
In the absence of an energy source, a density-stratified Earth is a stable configuration for the
distribution of materials that compose the Earth. However, the hot, molten outer core is a very large
energy source that continuously heats the base of the mantle. As previously noted, the minerals
that compose the Earth are poor thermal conductors. The mantle, therefore, is essentially a thermal
insulator surrounding the core. As the base of the mantle heats, the minerals immediately adjacent
to the core expand, thus becoming less dense. In addition, they also become less viscous. As this
happens, portions of the thermally perturbed lower mantle begin to experience gravitational insta-
bility since they become relatively buoyant compared to the overlying, cooler and denser mantle.
Eventually, the combined effect of decreasing density and viscosity overcomes the resistance to
flow and the heated lower mantle begins to rise buoyantly toward the surface. It is at this point that
convection starts.