Page 30 - Geothermal Energy Systems Exploration, Development, and Utilization

6 1 Reservoir Definition

−2
Mantle heat flow (mW m )
300

50

15
Ocean
Continent
Mid-oceanic
Continental ridge
margin
Heat production
High Low

Figure 1.2 Sketch of mantle heat flow variations from con-
tinental center to mid-oceanic ridge, emphasizing a low sub-
continental heat flow with a localized increase at continental
margin, corresponding to a lateral decrease in crustal heat
production.

continental margin areas (Lenardic et al., 2000). In other words, the low and con-
stant heat flow beneath the continent can be considered as the dominant large-scale
thermal boundary condition applying above the subcontinental mantle (Figure 1.2).

1.1.4
Fourier’ Law and Crustal Geotherms

Heat transfer within the continental crust occurs mainly through heat conduction.
Heat advection may occur during magmatism episodes (arrival of hot magma at
shallow depths enhancing local temperatures), intense erosion episodes (uplift of
isotherms), and periods of hydrothermal convection. All these phenomena can
be considered as short-lived processes when equilibrium thermal regime of the
crust is considered. In steady state and without advective processes, the simplest
form of Fourier law, with a constant thermal conductivity, a depth-dependent
temperature field, and with appropriate boundary conditions for continental crust,
canbewrittenas


2
 k d T + A = 0


 dz 2

(1.1)
T(z = 0) = T 0



 dT
k (z = h) = Q m

dz
where k is the crustal thermal conductivity, A heat production, T 0 surface tem-
perature, h the thickness of the crust, and Q m the mantle heat flow. Temperature
profile within the crust thus can be written as

−A 2 Q m + Ah
T(z) = z + z + T 0 (1.2)
2k k