Not in the rock that geothermal can access. That rock is recharged by heat flow from below on a shorter timescale than that (but much longer than geothermal would extract the heat.)
As I understand it, most of the heat that was deposited by radioactive decay in the crust three billion years is still in the crust, not having had time to conduct its way to the surface, and most of heat deposited in the crust even today is from radioactive decay in rocks in the crust itself.
https://en.wikipedia.org/wiki/Geothermal_energy#Resources says 20% of the Earth's internal heat content is residual heat from planetary accretion 4.5 billion years ago, but of course that's mostly not in the crust. It also says, "the conductive heat flux averages 0.1MW/km²."
At the given thermal gradient of about 28°/km, a nominal thermal conductivity of 3.3W/m/K for granite (https://www.sciencedirect.com/science/article/abs/pii/S00137...), we can derive a heat flow rate. By dividing by a nominal specific heat of 0.7J/g/K and some density estimate like 2.4g/cc, we ought to be able to get a speed in meters per second. Let's see...
Not in the rock that geothermal can access. That rock is recharged by heat flow from below on a shorter timescale than that (but much longer than geothermal would extract the heat.)
As I understand it, most of the heat that was deposited by radioactive decay in the crust three billion years is still in the crust, not having had time to conduct its way to the surface, and most of heat deposited in the crust even today is from radioactive decay in rocks in the crust itself.
https://en.wikipedia.org/wiki/Geothermal_energy#Resources says 20% of the Earth's internal heat content is residual heat from planetary accretion 4.5 billion years ago, but of course that's mostly not in the crust. It also says, "the conductive heat flux averages 0.1MW/km²."
At the given thermal gradient of about 28°/km, a nominal thermal conductivity of 3.3W/m/K for granite (https://www.sciencedirect.com/science/article/abs/pii/S00137...), we can derive a heat flow rate. By dividing by a nominal specific heat of 0.7J/g/K and some density estimate like 2.4g/cc, we ought to be able to get a speed in meters per second. Let's see...