Page 27 - Geothermal Energy Systems Exploration, Development, and Utilization

1.1 Expressions of Earth’s Heat Sources 3
separation of the inner core, and possibly radiogenic heat generation within
the core yield estimates of core heat loss ranging from 4 to 12 TW (Jaupart,
Labrosse, and Mareschal, 2007). Precise determinations of ohmic dissipation and
radiogenic heat production should improve this estimate. Independent studies
based on core–mantle interactions tend to favor large values (Labrosse, 2002),
while according to Roberts, Jones, and Calderwood (2003), ohmic dissipation
in the earth’s core would involve between 5 and 10 TW of heat loss across the
core–mantle boundary. The averaged value of 8 TW (Jaupart, Labrosse, and
Mareschal, 2007) is proposed in Figure 1.1.

Total heat loss = 46 TW

Heat production within the crust and mantle lithosphere = 7 TW
Heat loss from the mantle = 39 TW

Heating from Heating source
the core within the mantle Mantle cooling
8 TW 13 TW 18 TW
Figure 1.1 Heat sources and losses in the earth’s core and
mantle. (After Jaupart, Labrosse, and Mareschal, 2007.)

The earth’s mantle releases heat at the base of the crust. Radiogenic heat
production can be estimated through chemical analyses of either meteorites,
considered as the starting material, or samples of present-day mantle rocks.
Different methods have been used; the objective being to determine uranium,
thorium, and potassium concentrations. Applying radioactive decay constants
for these elements, the total rate of heat production for the bulk silicate earth
(thus including the continental crust) equals 20 TW, among which 7 TW comes
from the continental crust. Thus, heat production within the mantle amounts
to 13 TW (Figure 1.1, Jaupart, Labrosse, and Mareschal, 2007). Since total heat
loss from the mantle is larger than heat input from the core and heat generation
within it, the remaining heat content stands for mantle cooling through earth’s
history.
Mantle cooling corresponds to the difference between total heat loss from the
mantle (39 TW) and heat input (from the core, 8 TW) plus internal generation
(13 TW). This 18 TW difference can be converted into an averaged mantle cooling
◦
−1
of 120 CGy , but over long timescales, geological constraints favor lower values
◦
−1
of about 50 CGy . Knowledge of the cooling rate enables one to draw a more
accurate radial temperature profile through the earth (Jaupart, Labrosse, and
Mareschal, 2007). However, as it is shown below, precise temperature profile
within the deep earth does not necessarily constrain shallow temperature profiles
within the continental crust.