How long will Uranium and Thorium last?

Endliche und unendliche Ressourcen?

Distant future of the solar system: The sun has expanded into a red giant. (Wikimedia Commons)

During energy discussions, the terms “finite” and “infinite” are often mentioned, in the sense that sources of primary energy extracted from earth’s crust — fossil and nuclear fuels — are seen as limited and thus sooner or later exhaustable; solar irradiation, tidal energy from the moon and geothermal heat, on the other hand, are seen as inexhaustable.

This is, of course, untrue. The sun’s mass and lifespan is finite, much like the dissipation of geothermal heat slowly declines and tides diminish as the moon moves away from earth, transforming its orbit into doubly synchronous rotation (as with Pluto and Charon).

The question that needs to be asked is thus: How long will uranium and thorium last in comparison with solar energy; or, more precisely: with the timespan that will pass until earth in rendered uninhabitable by increasing solar luminosity (about 1 billion years).

Sources of Uranium

The only fissile nuclide naturally present on earth in substantial amounts is uranium 235. Constituting around 0.7% of natural uranium, nearly the entire rest is uranium 238, which cannot be fissioned easily. Neutron capture can transmute it into Pu-239, though, turning it into an energy source. This is what breeder reactors such as the DFR do, the more common light-water reactors only utilize a small part of it. The release about 0.7% of natural uranium’s heat content: Even this small yield can be economically useful — thanks to the incredibly amounts of energy in nuclei.

The following considerations will be based on the assumption that the DFR will be an essential foundation of energy supply — utilizing the complete heat content of uranium and thorium. A ton of heavy metal contains around 1 gigawatt-year of electricity or 3 gigawatt-years of heat. Let’s suppose generously that world population stabilizes in the future at 20 billion, with every person consuming on average 20 kW of primary energy (similar to the most energy-hungry countries of today, such as Saudi-Arabia). World consumption then clocks in at 4 * 1014 W or 400.000 gigawatts. This would mean that yearly 130.000 t of fission fuel need to be acquired. Which sources are accessible and how long will they last?

Conventional Resources

Two million tons of uranium are ready on hand as nuclear waste and depleted uranium: they will satisfy the energy consumption calculated above for 15 years.

The IAEA estimates the uranium resources accessible with current technology at a price of up to 260 Dollars per kg to be around 7 million tons (identified resources). Additionally, based on geological data, a further 10 mio. t are suspected to exist but have yet to be discovered (speculative resources).

One should realize that the price of nuclear electricity is a very weak funtion of uranium prices! Even if the “upper end” of the cost interval considered by the IAEA is assumed (260 Dollars per kg) and inefficient light-water reactors are used, the fuel price adds only half a cent to the price of each kWh; with the DFR, about 1/160 of this value — completely negligible. Thus, it presents no problem to include difficult to access resources of low concentration: the estimated 17 million t will last for 130 years. This is not the end of the road, though. Whether a certain mineral is considered an “ore” or just a “stone” depends simply on whether the concentration of the desired element is considered worthy of mining or not. In contrast to fossil fuels, which can only be found in certain locations, every cobble, every bucket of garden soil contains uranium and thorium. The low dependency of electricity prices on the fuel price allows us to utilize unconventional uranium sources with low concentration but huge total amount. The extration of uranium from phosphates was tested in the 1990s successfully on a large scale: In this form, 22 mio. t are accessible worldwide, stretching our resources for another 170 years. Adding it all up, we can last for 315, equal to the timespan from the early 18. century (before the industrial revolution) to today.

This is wholly sufficient to turn the DFR into a very useful energy source. The assumption that one and the same technology will be in use into the more distant future — in the sense of “sustainability”: being stuck on a certain techlevel without further development — is completely unrealistic! 315 years ago, there were no nuclear reactors, no airplanes, cars, trains, computers, spacecraft, even the steam engine was still an experimental technology waiting for its large-scale application. In the year 2333, the DFR will be considered old-fashioned; the power plants may be part of outdoor museums showing “life in old times”. Energy supply will be based on Palmstroem-Rienzi-Etymino-Amplifiers or some other future technology founded on natural laws which are unknown today.

Water and Rocks

But lets continue our extrapolation as a mental exercise, even if they may make us feel like a Roman economist calculating that in the year 2000 firewood and horse feed will run low, dooming civilization…

Average crust rock contains uranium at a concentration of 1-3 ppm: 1 to 3 gram per ton of gravel, dirt or garden soil. This corresponds to a releasable thermal energy of 80-240 MJ per kilogram. This gives average rocks eight times the heat content of hard coal! If the melting heat of silicon (after oxygen the second most common element in earth’s crust) of 1.8 MJ/kg is taken as an approximation of the energy needed to extract the uranium, an energy excess of up to 100 can be achieved. Even if the isolation of uranium from the melt consumes considerable additional energy amounts, running the entire process exothermally should present no problem — most of all if thorium, which is four times more common than uranium, is also utilized, ramping the the ratio of releasable nuclear energy to melting heat up to about 500.

With 10 g of actinide per ton of mineral on average, 1.3 * 1010 t of crust rock need to be mined per year, equal to 400 tons per second, similar to current coal mining. The mass of the continental crust is estimated to be 1.6 * 1019>/sup> t — a resource for 1 billion years.

Of course, one would not wish to scrape up the entire land surface with bucket excavators, most of all, because nature has already prepared efficient excavators powered by solar energy: they are called rivers, grinding off 30.000 t uranium per year and flooding them into the sea, in which the balance of illuviation and sedimentation has stabilized at a concentration of 0.003 ppm (3 milligrams of uranium per ton of water), or 4.5 billion tons in the entire ocean. Thorium is not to be found in the sea, as its compounds are not water-soluble.

Japanese scientists have developed promising technologies to extract the highly dilute uranium with fibers based on amidoxime.

In the first experiment, three absorber beds, containing 350 kg of absorber material together, were suspended on top of each other at 20 m of depth (7 km from Mutsu-Sekine in Aomori Prefecture). The absorbers extracted 0.5 g of uranium per kg of absorber material over 30 days. Over the entire experiment, running for 240 days, around 1 kg of uranium could be recovered.

This technology could still be improved substantially: To design the process in a simpler and more efficient fashion, the absorber material was fashioned into ribbons, which were anchored on the sea floor standing upright like water plants while being washed around by the currents. In that way, an extraction of 1.5 — 2 g of uranium per kg of absorber within 30 days was achieved: This was possible due to the improved contact between absorber and water, but also because of higher water temperatures at the experiment’s location off the coast of Okinawa, which increases uptake efficiency.

Can this process be scaled up to industrial dimensions? An experimental setup of this kind is already planned: A rectangle of ocean floor of 1000 square kilometers (15.2 km x 67.8 km) is to be “planted” with the ribbons standing upright underwater — each 60 m in length, with 8 m distance between the ribbons — creating an uranium farm collecting 1200 t per year.

If the uranium is extracted at a slower rate than the rivers wash it in, the concentration stabilizes at a lower value and the process can be kept up for eons, until the entire uranium in earth’s crust has been used up. If the extration rate is larger than 30.000 t/year, the concentration in the sea slowly declines to zero. At 130.000 t/year, this energy source can be used for 36.000 years — similar to the timespan from the paleolithic age up to today.

These are nice mathematical exercises, but for future energy supply they are probably irrelevant. Neither acquisition of fission fuels from other celestial bodies (e.g. the moon could be a good thorium mining field) nor technological innovations and inventions of coming centuries were taken into account. It suffices to point out: The DFR can supply energy over timespans surpassing the age of human civilization multiple times! Its role will not be to stay in use forever, but to massively boost the EROI and thus the productivity of our industries, enabling further developments, towards new energy sources with an even higher EROI, new discoveries and possibilities.