Page 31 - Geothermal Energy Renewable Energy and The Environment

14 Geothermal Energy: Renewable Energy and the Environment

Table 2.2
heat production from radioactivity, in J/kg-s
material k U Th Total
Upper continental crust 9.29 × 10 –11 2.45 × 10 –10 2.77 × 10 –10 6.16 × 10 –10
Average continental crust 4.38 × 10 –11 9.82 × 10 –11 6.63 × 10 –11 2.07 × 10 –10
Oceanic crust 1.46 × 10 –11 4.91 × 10 –11 2.39 × 10 –11 8.76 × 10 –11
Mantle 3.98 × 10 –14 4.91 × 10 –13 2.65 × 10 –13 7.96 × 10 –13
Bulk Earth 6.90 × 10 –13 1.96 × 10 –12 1.95 × 10 –12 4.60 × 10 –12

Source: Van Schmus, W. R., Global Earth Physics, Washington, DC: American Geophysical Union,
283–91, 1995.

where q is the heat flow at the surface, q is an initial value for heat flow unrelated to the specific decay
0
of radioactive elements at the current time, D is the thickness of crust over which the distribution
of radioactive elements is more or less homogeneous (for a general model of the crust this value is
usually taken as 10 to 20 km), and A is the heat production rate per volume of rock. The variable A
can be recast as

A = h × e , (2.2)
-λt
0
where h is the initial heat production, λ is the decay constant (which is equal to 0.693/t ) for the
0
1/2
isotope of interest, and t is time.
Table 2.2 provides a summary of heat production in various parts of the crust and mantle.
Using the values for the upper crust and assuming that the background heat flow is approximately
40 mW/m (based on the heat from the cooling core), the average heat flow at the surface of the
2
continental crust would be approximately

2
q = 0.04 W/m + 10,000 m × 1.35e-6 W/m = 54.0 mW/m ,
3
2
3
assuming an average rock density of 2200 kg/m . If the average heat flow for the planet is 87 mW/m ,
2
why is this result so low? The answer lies in how heat is transferred in the Earth.
TransFer oF heaT In The earTh
It is common experience that heat does not stay where it is generated—heat obviously and always
moves from a warm body or region to a cooler body or region. That simple observation gave rise
to one of sciences most fundamental breakthroughs, the principles of thermodynamics, which
will be discussed quantitatively in Chapter 3. At this point, what we will consider are the primary
mechanisms (radiation, conduction, and convection) whereby heat transfer takes place, and how
those mechanisms influence the availability of geothermal energy. Heat transfer mechanisms will
be revisited in Chapter 11, where its role in direct use geothermal applications is considered in
detail.

radiaTion
Heat can be transferred radiatively by the emission and absorption of thermal photons. Thermal
photons are similar to light photons (380–750 nanometers), but fall at the longer wavelength
(approximately 700 to beyond 15,000 nanometers) infrared portion of the electromagnetic spectrum.
Most Earth materials are relatively opaque to infrared radiation, so the primary role radiation plays