"Geothermal power is considered to be renewable because any projected heat extraction is small compared to the Earth's heat content. The Earth has an internal heat content of 10^31 joules (3·10^15 TWh), approximately 100 billion times the 2010 worldwide annual energy consumption.[...] About 20% of this is residual heat from planetary accretion; the remainder is attributed to past and current radioactive decay of naturally occurring isotopes." -- https://en.wikipedia.org/wiki/Geothermal_energy#Renewability...
https://en.wikipedia.org/wiki/Earth%27s_energy_budget#Earth'...
One small nuance: the OP asked about the heat generated by Earth's mass. The 47TW is split between the original heat from the formation of the Earth and the nuclear decay of radioactive elements.
You have a bunch of bigger problems that come to roost much sooner than this if you're using that much geothermal though,
At the micro scale, that is, for an individual geothermal well or source, not so much. Single wells or geothermal fields may be depleted or degraded.
Because heat conductivity of rock is very limited, extraction of that heat by some mechanism will eventually cool that rock below viable levels for power generation. For enhanced intensive geothermal energy --- drilling holes in rock to depths of multiple kilometers and circulating a working fluid (typically water) through the substrate --- that is thought to be on the order of 1--3 decades. After which the borehole is no longer viable and must be left to recover for some period of time, perhaps centuries.
For conventional (geyser / steam vent) geothermal, the limiting factor tends to be groundwater. The instance I'm most familiar with is The Geysers powerplant in northern California, which saw a roughly 40% reduction in capacity over several decades as the groundwater feeding the geyser system was depleted. That would have to be restored by some means.
Note too that there may be contamination issues in repeatedly cycling deep-layer water to the surface, particularly of heavy metals or radioactive isotopes. These include "sulfur, vanadium, silica compounds, chlorides, arsenic, mercury, nickel, and other heavy metals".
<https://www.ucsusa.org/resources/environmental-impacts-geoth...>
Geothermal, you'd cool the crust and have to drill far deeper than is possible to exceed 50TW for long.
Wind, if you exceed somewhere in the 1-10W/m^2 you slow down the wind and create turbulence.
Solar, if you use more than ~1% of the land you're radically altering the albedo and habitat (so maybe up to 200TW).
Fossil fuels create GHG and run out quickly.
Nuclear creates enough waste heat in the 100-200TW range to cause as much radiative forcing as GHG does now.
We each get our 10-100kW and that's about it for living on a planet that isn't one giant factory/heatsink.
Both of these may actually turn out to be beneficial. Putting up solar panels above agricultural land ("Agri-PV") is not just avoiding clobbering up arable land with PV panels, but also has benefits for the plants [1]: they need less water because less sun directly hits the plants and heats up the soil which means both more resilience in drought periods and more capacity to regenerate groundwater planes, and the soil erosion from wind is reduced as well.
I wonder if putting up panels in the desert could help out de-desertification efforts as well for the same reasons.
As for albedo - given that we're already having issues with global warming, it is not that far-fetched to say that solar radiation being reflected off to space is a good thing overall.
[1] https://www.ise.fraunhofer.de/content/dam/ise/de/documents/i...
The albedo problem is the opposite of what your are thinking as it is another source of radiative forcing from putting a mostly black thing in the sun.
A Shockley-Queisser limited solar panel mostly only reflects IR. So where your plants/dirt might have an albedo of 0.3, the solar panel absorbs 80-95% of the light (albedo 0.05 to 0.2). 20-30% becomes electricity (and later thermalises when used).
This gives you a net forcing on the order of 100-250W or so _somewhere_ on earth for every m^2 of pv. If you cover too much land the radiative forcing is on the same order as GHG, hence the ~1% limit. 200-300W of work for 100-250W of new heat is a pretty fantastic deal compared to other options though.
Putting it above existing asphalt or a similar surface is 'free' because albedo is already 0.1 there. Similarly wind is free from a radiative forcing perspective.
Putting the panel in existing (light coloured) desert is much worse because deserts have an albedo around 0.4-0.6 so you are making 400-550W of new heat for your 200-300W of work.
This also leads to the interesting thought of placing bifacial tracking modules sparsely on low albedo dead surfaces and painting the surface white for a net reduction in thermal forcing (is there a 1000km patch of volcanic rock somewhere? Gobi desert?)
In the same framework, every joule of nuclear energy is a new watt of heating, and if it is from a steam engine, it's more like 3W (or even 5W once you include post-reactor heat as well as xW of heat for every 1W of pre-reactor work inputs of mining, milling, and enriching low quality ore).
Of course these all only become relevant if we slash carbon intensity to under 2% of what it is today and continue trying to grow our energy usage exponentially.
There are some ore bodies that are concentrated enough to fission faster, but they are rare (and not the uranium that is typically mined for fuel).
Yeah, but the heat doesn't penetrate to the ground any more, which should help with water retention?
You might make your desert nice, but you're still doing a climate change if you try to install more than a few hundred TW of solar panels.
Ideally you make the desert nice and then take a chill pill before covering all of the deserts and settle for somewhere in the range of 2-100kW per human as a steady state economy powered by a mix of wind, solar, geothermal, and maybe some nuclear.
How much heat is generated by Earth's gravity onto itself? How "renewable" is Geothermal energy, truly?