Page 201 - Geothermal Energy Renewable Energy and The Environment

188 Geothermal Energy: Renewable Energy and the Environment

radioactive decay in the crust. In deep mines around the world, temperatures at depths of 1 km to
2 km can be as high as 60°C (140°F) and with local thermal gradients as high as 0.5°C to 1.5°C per
100 feet. Such gradients would result in a surface temperature of between 5°C and 42°C (40°F and
107°F), in the absence of an atmosphere or sun. Other regions have lower heat flows and would be
cooler. Hence, solely on the basis of heat flow, there would be a wide range of temperatures in the
shallow subsurface, with local hot spots and cold spots.

solar insolaTion
The atmosphere and solar insolation mitigate that extreme temperature variability at the surface.
2
The average daily influx of solar energy that reaches the surface is about 200 W/m for the Earth
as a whole (Wolfson 2008). This energy input, along with that which interacts with the atmosphere
to generate weather patterns, moderates the variation in surface temperature throughout the world.
This effect heats the top tens of centimeters of the land surface during the day and allows it to slowly
cool at night, all within a restricted temperature range that is strongly dependent upon latitude. This
diurnal effect slowly propagates into the subsurface.
Added to this is the effect of precipitation that, when coupled with the diurnal effect of solar inso-
lation, significantly adds to the thermal energy content of the subsurface. As rainfall occurs (or snow
melts), the fate of the resulting meteoric water is complex. Some of the water immediately returns
to the atmosphere via evaporation, some is taken up by plants and either incorporated into the plant
material or respired back into the atmosphere, some runs over the surface to local drainage systems,
and some percolates into the ground where it slowly flows in the subsurface to the local water table
and enters the aquifer system. The percolating water most significantly impacts the subsurface ther-
mal reservoir by absorbing heat from the surface solar energy and transporting it to deeper levels in
the soil and rock. The high heat capacity of water assures that solar energy is relatively efficiently
transported to the subsurface. The result is that the energy content of the subsurface reflects the
sum of both solar and geothermal energy inputs, with the former dramatically moderating the geo-
thermal variability. Figure 10.5 shows the soil thermal regimes of the United States. Note how the
temperatures strongly correlate with latitude as well as regional climate patterns.

soil characTerisTics
Figure 10.6 shows idealized and observed temperature variability as a function of moisture content,
depth, and season. There are two idealized curves (thinnest lines) for each season shown. The outer
curves represent temperature variation with depth for wet soils, while the inner curves are for dry
soils. The difference between these curves is due to the fact that, for a given heat flow over a speci-
fied distance, the temperature gradient will be a direct inverse function of the thermal conductivity.
This is apparent by rearranging Equation 2.1:

(∇x × q )/∇T = k . (10.1)
th
th
As the thermal conductivity decreases, as it must if the saturation in a rock decreases, the ther-
mal gradient must increase.
The idealized curves in Figure 10.6 are drawn for the case where the annual surface temperature
swing is about 10°C about the local mean temperature. However, the behavior of real systems is
more complex. Note that the summer swing from the mean in the Finland observations shown in the
figure is about 14°C, but the winter swing is about half that amount, reflecting the effects of local
weather patterns and latitude. At lower latitudes the swing is likely to be more symmetrically distrib-
uted about the mean annual soil temperature. Adding to this complexity is the fact that temperature
swings can range from as little as 5°C to values exceeding 20°C, depending upon local weather and
seasonal variability.