Guest post by Roger Andrews:

Lulled by the power of e=mc2 I had always assumed that the world had enough uranium to support almost any level of nuclear power expansion. I mean, when one miserly kilogram of U generates 37 MWh of electricity, resources must be effectively inexhaustible, right?

Recently it occurred to me that it might be a good idea to confirm that this is in fact the case, so I ran some numbers – and found to my surprise that in fact it may not be the case. Sure, we have enough uranium to last for many decades at modest rates of growth and every prospect of finding more. But what if the world suddenly decided to decarbonize global electricity generation by expanding nuclear, which may indeed be the only way of doing it within the time-frames specified by the present generation of emissions reduction plans? Do we have enough uranium to support the massive increase in demand this would entail?

To answer this question I needed a nuclear decarbonization scenario, and here’s what I concocted:

Replace all the world’s coal-fired plants with nuclear plants by 2050. Assuming no change in the relative contributions of other generation sources this gives a 2050 generation mix of ~55% nuclear, ~25% gas and ~20% hydro and other.

Allow for global electricity demand growth of 1.5%/year through 2050.

Assume that the amount of uranium consumed per unit of electricity generated remains the same as it is now.

This scenario decarbonizes global electricity generation by 75% by 2050 and cuts global carbon emissions by about 30% below what they otherwise would have been. (100% decarbonization would require the conversion of gas as well as coal to nuclear, but this removes a lot of useful load-following capacity, gives less bang-for-the-buck – gas emits only about half as much carbon as coal – and puts too many electric eggs in the nuclear basket. It’s impossible to meet 80% emissions-reduction targets by decarbonizing electricity generation anyway because it contributes only about 40% of total global carbon emissions, a fact that seems to have escaped the attention of the emissions-cutters, but I digress.)

The scenario calls for installed global nuclear capacity to increase from 364GW at present to 2,820GW by 2050, which should be achievable. Assuming a six-year lead time – the average in France – the first nuclear plants come on line in 2020 and in each of the following 30 years another 79.2GW of nuclear capacity is added, which is not out of reach (75GW of wind and solar alone was added globally in 2013). Costs also shouldn’t be prohibitive. At an assumed average installed cost of $5,000/KW they total $US400 billion/year, about equal to worldwide investment in power generation facilities in 2013.

It also calls for a corresponding increase in uranium production from 68,000 tons/year to 527,000 tons/year, representing an annual increase of 15,300 tons/year in each of the 30 years between 2020 and 2050 (again assuming a six-year discovery and development lead time). Is this achievable? For the purposes of analysis I have assumed it is, but it may not be. The largest annual production increase so far registered is ~10,000 tons (in 1958) and even the $20 billion planned expansion at the supergiant Olympic Dam deposit, which hosts maybe a third of the world’s presently-known uranium resources, would add only about 20,000 tons/year if and when it goes ahead. If the 15,000 tons/year expansion rate isn’t achieved resource life will be lengthened but the decarbonization target won’t be met.

Anayway, having thus established what uranium demand is going to be, the question becomes, is there enough uranium to fill it? Let’s see what we can rustle up in the way of resources:

Known Resources:

According to the OECD Nuclear Energy Agency, arguably the most authoritative source, the world has 5,327,000 tons of uranium resources in the reasonably assured and inferred categories at prices up to $US50/lb U and 7,096,600 tons in these categories at prices up to $100/lb. I use the higher number, rounded off to 7.1 million tons, because increased demand would almost certainly drive uranium prices to $100/lb. (Higher prices would liberate yet more resources, but offsetting this is the fact that the OECD estimates include inferred resources, at least some of which will not be there. I’ve treated this as a “wash”.)

To this we can add the ~600,000 tons of uranium in civil and military uranium/plutonium stockpiles and in nuclear weapons scheduled for decommissioning, plus 300,000 tons (a guesstimate) extractable from the 1.5 million tons of depleted uranium contained in low-grade tailings (more details on stockpiles here). This increases known resources from 7.1 to 8.0 million tons.

We can also add phosphate rock uranium. At higher prices uranium can be profitably extracted as a byproduct of phosphoric acid production. Production is, however, limited by the rate at which phosphate rock is mined and by its low average uranium concentration (~100 ppm). I’ve assumed an average annual production of 200 million tons of phosphate rock and recovery of half of the total contained uranium. This yields 10,000 tons of uranium per year, adds another ~0.9 million tons of uranium between now and the end of the 21st century and increases known resources from 8.0 to 8.9 million tons.

Then I’ve added 200,000 tons from recycling of spent uranium and plutonium, which presently supplements global uranium supply by 2-3%. This increases known resources to 9.1 million tons.

Finally I add a nominal 100,000 tons from sea water uranium, which despite the ~4 billion tons of uranium the oceans reportedly contain is unlikely ever to contribute much because of the enormous volumes of sea water that must be processed to extract it. (Over 20 trillion tons would have to be processed to produce the 68,000 tons of uranium consumed worldwide in 2013.)

Known uranium resources therefore top out at 9.2 million tons. How long do they last under the nuclear decarbonization scenario?

Until 2048. They will in fact be exhausted before the decarbonization target is met.

Undiscovered Resources:

Higher uranium prices will of course stimulate exploration and lead to the discovery of more uranium. As to how much more, OECD/NEA estimates that there are 10,400,500 tons of undiscovered uranium resources in the world, calculated as the sum of “prognosticated” resources in uranium-producing areas and “speculative” resources in non-producing areas potentially prospective for uranium, and I have accepted this as the best available estimate and assumed that all of it will be discovered and produced. Adding it to the 9.2 million tons of known resources yields 19,600,500 tons of uranium, which I’ve rounded up to 20 million tons for convenience.

And how long does this last-squeal-out-of-the-pig resource last? Until 2069. The 2050 decarbonization target is met, but 19 years later the world runs out of uranium.

Resource changes with time are summarized graphically below. I’ve assumed that the 10.8 million tons of undiscovered resources is added to inventory at the rate of 200,000 tons/year beginning in 2015 and ending in 2068:

The spreadsheet calculations used to generate the data used in the graphic are here.

The above estimates are of course subject to large uncertainties, but the implications are clear. There’s a very real possibility that the world does not have enough uranium to “go nuclear”, or at least not on a scale large enough to have a significant and lasting impact on global carbon emissions.

So long as it continues to build conventional pressurised water and boiling water reactors, that is.

Breeder reactors, anyone?