Nuclear fuel will last us for 4 billion years

Nick Touran, Ph.D. (nuclear engineering), 2020-10-28. Reading time: 6 minutes

As shown in our energy flow diagram, our energy resource options are derived either directly from sunlight (solar, wind, hydro, biofuel), by digging up fossilized organic matter (coal, oil, gas), or from accessing primordial energy (nuclear fission, geothermal, tidal, fusion). These are all limited in quantity. Some will last us about as long as the sun, while others may run out soon and are thus not sustainable.

How does nuclear fission perform in the sustainability question? This question has been answered quite skillfully by the legendary David MacKay in Sustainable Energy Without the Hot Air, but we figured we could add our own version as well. Here is the result:

Nuclear sustainability plot

Breeder reactors can power all of humanity for more than 4 billion years. By any reasonable definition, nuclear breeder reactors are indeed renewable. However, billion-year sustainability does require advances in seawater uranium extraction, reactor construction performance, and public acceptance. We have developed breeder reactors in the past, but they remain a small minority of our current fleet.

We are talking about all primary energy here rather than just electricity. In most parts of the world, electricity is about 40% of total energy. The rest is for transportation, industrial heat, etc.

The basis facts:

  • Total world energy consumption of primary energy in 2019 was about 584 exajoules (BP Statistical Review of World Energy 2020)
  • A modern light-water reactor can pull an average of 60 MWd/kg out of its 4.8% enriched nuclear fuel (AP1000 docs)
  • One kg of 4.8% enriched uranium requires 9.5 kgU natural uranium input to the enrichment plant (and 7.8 SWU) (any old SWU calculator)
  • A breeder reactor with a recycling fuel cycle can pull about 900 MWd/kg out of non-enriched nuclear fuel (natural or depleted uranium or thorium)
  • There are 6.1 million tonnes of uranium in reasonably assured deposits (World Nuclear Uranium)
  • There are 6.3 million tonnes of thorium in reasonably assured deposits (World Nuclear Thorium)
  • Uranium exists in seawater at an average concentration of 0.003 ppm (also World Nuclear Uranium)
  • There are about 332 million cubic miles of water on Earth, 96.5% of it is in the ocean (USGS). At a density of 1 gram/cm\(^3\), this comes out to 1.4 yottagrams of water, or 1.4e21 kg)
  • At 0.003 ppm, this means there are about 4000 million tonnes of uranium in seawater
  • The average crustal concentration of uranium is about 2.8 ppm (World Nuclear Uranium)
  • There are about 6.5 million million tonnes (6.5e13 tonnes) of uranium in the crust, which continuously replenishes the uranium in seawater through erosion, runoff, and plate tectonics.
  • Thorium requires the use of a breeder reactor so it is to be included only once breeder reactors are assumed

The math

It’s convenient to use the GNU units program to do these kinds of comparisons quickly. This is available for free on Windows, Linux, and Mac.

For mined uranium and non-breeders, we use

$ units "6.1 million tonnes*60 MW*day/kg/9.5/(584 exajoules/year)"  "years"
5.6997837

For seawater uranium and non-breeders, it’s

$ units "4000 million tonnes*60 MW*day/kg/9.5/(584 exajoules/year)"  "years"
3737.5631

Because non-breeders are 140x less fuel efficient than breeders, it has long been considered impractical to use low-grade uranium resources like seawater or crustal nuclear fuel in non-breeders. The energy to get the material out is too high given the return.

Breeders with mined uranium:

$ units "6.1 million tonnes*900 MW*day/kg/(584 exajoules/year)"  "years"
812.21918

Breeders with mined uranium and thorium:

$ units "(6.1 million tonnes+6.3 million tonnes)*900 MW*day/kg/(584 exajoules/year)"  "years"
1651.0685

Breeders with mined and seawater resources:

$ units "(6.1e6 tonnes+6.3e6 tonnes+4000e6 tonnes)*900 MW*day/kg/(584 exajoules/year)" "years"
534253.81

Breeders with mined, seawater, and erosion resources, assuming about half the erosion resource will reach the sea:

$ units "(6.1e6 tonnes+6.3e6 tonnes+4000e6 tonnes+6.5e13 tonnes* 0.5)*900 MW*day/kg/(584 exajoules/year)"  "years"
4.3279315e+09

As a bonus, let’s compute how many reactors we’d need to make 100% of the primary world energy. Assuming big gigawatt-scale reactors, we find:

$ units "584 exajoules/yr /(3300 MW)"
5607.9511

We have about 450 reactors in the world today, so we’d need to build about 5100 more large reactors to produce all our energy with low-carbon nuclear.

Another nearly unbelievable fact (HT reddit user paulfdietz) is that if you dig up an average crustal rock, it will have 20x more nuclear energy in it than a piece of pure coal of the same mass. With crustal abundances of 2.8 and 6 ppm for uranium and thorium, and a chemical energy density of 33 MJ/kg for coal, the math here is:

$ units "(2.8e-6 + 6e-6) * 900 MW*day/kg / (33 MJ/kg)" 
20.736

😲

More thoughts

Of course, no serious energy planners propose using 100% of anything, so this will be mixed with other low-carbon energy sources like wind, solar, hydro, geothermal, etc. as appropriate on a regional basis.

The mined uranium and thorium values are very likely to increase if demand increases. As with most minerals, as demand goes up, people prospect more and find more. The numbers here are expected to be conservative for the mined resources.

Critiques

For a robust analysis, the energy required to extract the resources needed to generate power must be considered. The concept of Energy Return on Investment (EROI) formalizes this. Some studies, like Bardi, 2010, attempt to do this for seawater uranium extraction, but only consider non-breeder reactors (long considered impractical) and assume uranium extraction will require as much power as reverse osmosis desalination, which is likely a strong overestimate considering the more recent research. Even if seawater uranium extraction is hard, the fact that each average crustal rock has 20x more nuclear energy than an equal mass of coal validates the true practicality of billion-year nuclear resources.

See Also