Hard Energy Limits

[rufuspollock]

E.g. how much total energy is available from the sun?

MacKay covers these quite well as does #25 e.g. this chunk:

The sun deposits energy at Earth’s surface at a rate of about 1,000 W/m2(1,000 Watts per square meter; we’ll reach a better understanding for these units in Chapter 5). Ignoring clouds, the projected area intercepting the sun’s rays is justA�πR2⊕, whereR⊕is the radius of the earth, around 6,400 km. Roughly a quarter of the earth’s surface is land, and adding it all up we get about30×1015W hitting land. If we put solar panels on every square meter of land converting sunlight to electrical energy at 20% efficiency we keep 6×1015W. This is a little over 300 times the current global energy usage rate of 18 TW. What an encouraging number! Lots of margin. How long before our growth would get us there? After one century, we’re 10 times higher, and 100 times higher after two centuries. It would take about 2.5 centuries (250 years) to hit this limit. Then no more energy growth

[xyletto]

Nuclear energy:
Based on World Nuclear, uranium resources available:
6.078 M tonnes U (up to $160/kg U in extraction costs)
7.918 M tonnes U (up to $260/kg U in extraction costs)

Existing technology:
The world’s power reactors, with combined capacity of about 400 GWe and representing 9.18% of 2022 world's electricity generation(source) , requiring some 67,500 tonnes of uranium from mines or stockpiles each year. The vast majority of these reactors are "light water reactors", which generates electricity from fission of U-235 isotope, which is only present in 0.7% of naturally occurring uranium. The efficiency of this fuel is around 55 GWd/t for fuel enriched to 5% U-235. Using this technology, the uranium resources are expected to last around 100 years with our current usage rate, or about 10 years if a world that only uses nuclear reactors for electricity generation.

Breeder reactors;
Breeder reactors use abundant Thorium(Th-232) and U-238 which are fertile but not fissile isotopes. These isotopes do not readily fission to generate large amounts of heat, but can be transformed under the right conditions to become fissile isotopes, which then undergo fission to generate heat & electricity. These types of reactors are still experimental due to remaining technical challenges of scaling, reliability, safety and waste storage before widespread commercialisation can happen, and the political challenge of nuclear proliferation needs to be addressed before they can be implemented at all.

U-238 is the most abundant isotope (99.3%) and Thorium is estimated to be 3 times as abundant as Uranium in rocks & soil. With enrichment, U-238 and Th-232 can be consumed almost completely. Hence, this gives us a further 400x as much runway, lasting about 4000 years in a world that only runs on nuclear energy based on our current electricity consumption rate.

This analysis excludes less economical sources of uranium including lower grade ore and seawater (thorium does not dissolve in seawater), which may become more feasible with newer technologies.

[rufuspollock]

@xyletto thanks, that's a useful addition.