The Sun and the wind, we are told, will last forever. Also tides, rivers, and the heat of the earth. So energy based on those sources will last forever too: that's renewable energy.
Now that's not literally true, of course: In a billion years or less, the Sun, expanding to its red giant stage, will strip the Earth of its atmosphere. After that, no more wind power, no more rain, and no more rivers as the oceans boil away. And no more people either, at least on this planet. So a "renewable" resource won't literally last forever; but if it lasts a billion years or so, that will suffice for the lifetime of human civilization here on Planet A. (There is no Planet B. At least not currently.)
Fossil fuels are not renewable. There is a fixed amount in the ground, and we are digging them up and pumping them up at ever-increasing rates. This is clearly unsustainable, for more reasons than one.
And then there's nuclear power, based on uranium resources. Many people believe that we're running out of uranium, that global resources will soon be depleted, and for that reason it makes no sense to use nuclear power in the long term.
But follow below the orange atom as we discover why we will never run out of nuclear fuel, not even in a billion years, and why it will always be cheap, even in the End Times.
The World Nuclear Association estimates current global uranium reserves at a shade under 6 million tonnes, and we are currently using uranium at at rate of about 60,000 tonnes per year. So we do that division and discover (gasp) less than 100 years of uranium left!
But there is a hidden assumption in reserve computations that most people aren't aware of, and that is the price. Uranium is traded on world markets as "yellowcake", which is uranium oxide (U3O8). The current price of yellowcake is about $35/lb. If you do the math, you find that the amount of uranium required to produce 1 kWh of electricity at that price is just 0.2 cents, a trivial amount: about 2% of the total cost of electricity. (The remaining 98% is the cost to build and run the power plant, and for fuel processing.)
Let's assume for the moment that nobody ever does any more exploration for uranium, and that what we've discovered so far is all we will ever have. As we deplete our existing known resources, the price of yellowcake will rise due to the law of supply and demand. Because the amount of uranium used to produce electricity is so low, even if the price of yellowcake doubles, triples, or quadruples, it will have almost no effect on the price of electricity at the back end.
But an increasing price of yellowcake will have a dramatic impact on the amount of uranium reserves, even without further prospecting. That's because of the hidden price assumption in the reserve calculation. It takes a certain amount of money to extract yellowcake from uranium ore, and the lower the grade of ore, the greater the cost to extract. So if the current price of yellowcake is $35/lb, and it costs $45/lb to extract yellowcake from a certain low-grade deposit, that is not an economical deposit to mine. Even though we know it's there, it's not counted as a reserve, because nobody will touch it.
But if the price of yellowcake doubles to $70/lb, that formerly uneconomic deposit suddenly becomes economically viable. Thus every reserve estimate is based on an assumption of a specific price for the commodity. And if the price changes, the reserve estimate will change too -- and dramatically so.
Let's see how this works in practice. Here is a summary of US uranium reserves at various prices, as they were estimated by the US Atomic Energy Comission and the US Geological Survey in the mid 1960's.
Yellowcake price /lb |
Reasonably assured (million tons) |
With additions (million tons) |
AEC |
USGS |
AEC |
USGS |
$7 |
- |
- |
.1 |
- |
$8 |
.15 |
- |
.43 |
- |
$10 |
.21 |
.19 |
.56 |
1.1 |
$15 |
.46 |
- |
1 |
- |
$30 |
.66 |
.36 |
1.6 |
1.9 |
$50 |
6 |
- |
10 |
- |
$100 |
11 |
15 |
25 |
40 |
$500 |
500 |
- |
2000 |
4700 |
The higher the price, the greater the reserves available at that price. Let's look at the AEC numbers (the third column above, with additions, i.e., assuming future additions to reserves from future prospecting.) Here they are on a graph, using logarithmic axes:
Here we see that reserves (both assured reserves and additional reserves) are roughly proportional to the square of the price. If the price doubles, reserves increase by a factor of four; if the price goes up tenfold, reserves increase a hundredfold. These prices are in mid-1960's dollars; at that time yellowcake was about $7/lb, and although the price has bounced around since then (including one big spike in 2007), overall the price of yellowcake hasn't changed much in 50 years after allowing for inflation. These AEC estimates are deliberately conservative; the USGS reserve estimates are roughly twice as high at all prices; and global reserves are about 25 times higher than US reserves.
Most importantly, note that at the high end of the graph, the curve is bending flatter instead of steeper: there is no "bottom" of reserves seen by the AEC at those prices. That's because at those prices, we are using granite as ore, an essentially inexhaustible resource.
Keep that in mind as we consider the other major effect of increasing uranium prices: fuel efficiency.
As the price of uranium rises, another economic effect will take hold: fuel efficiency for nuclear reactors will become a more important consideration. The current fuel cycle for nearly all reactors is a "once through" fuel cycle: the fuel is put into a reactor for 12 to 18 months, after which it is removed. That lightly-used fuel is then known as "spent fuel", but the truth is that it's hardly spent at all: nearly all the original energy that was in it at the beginning still remains.
But there are other ways to use uranium that are much, much more efficient than the current once-through fuel cycle: you can use a "fast spectrum" reactor, or you can use a liquid fuel reactor. Both of these methods can extract all, or nearly all of the energy in the uranium fuel, which sharply reduces the amount of uranium needed to produce energy. These fuel cycles work by fissioning all of the uranium atoms in the reactor, leaving nothing left as "spent" fuel. If fully used, yellowcake contains 160 times more energy than typically extracted in the once-through fuel cycle.
Admittedly those full-use fuel cycle reactors are decades away from full exploitation. But since we're thinking in billion-year timeframes here, a few decades is small beans in context. Those reactors will come, sooner or later. And when they do, we will be able to use (a) all existing "spent fuel" (aka long-lived waste) as fuel; and (b) all existing stockpiles of "depleted" uranium as fuel, thus making more efficient use of all uranium that has already been mined. When those stocks are gone, we will be able to use newly-mined uranium with that same high fuel efficiency, and leave no long-term waste behind.
That means that instead of spending 0.2 cents on the uranium fuel for one kWh of electricity, we will only be spending about .00125 cents (in current dollars) for the uranium fuel for a kWh. And that will allow yellowcake prices to rise 10 times, 100 times, or 1000 times higher than they are today, without substantially increasing the cost of electricity.
And since reserves increase with the square of the price, increasing the price of yellowcake by 1000 times would increase global reserves by a million times, without raising the price of electricity. So instead of 100 years of reserves, we would have millions of years of reserves.
The worst-case scenario
Let's assume that we completely decarbonize the global energy supply, and that we accomplish that by using only uranium as a fuel. Currently, nuclear power accounts for just 2.5% of the world's primary energy supply, but that could be increased to 100% by going to more electric vehicles, by synthesizing liquid fuels, and by using nuclear power for industrial process heat. In that world, we would be using 40 times the amount of nuclear energy we use today.
Let's also assume that world population doubles from current levels before stabilizing, and that the average person in the future will use twice as much energy as the current average world citizen. So let's multiply that 40 times by another factor of 4 to account for that, giving us 160 times as much nuclear power as we use today.
But let's also assume full-use fuel cycles, which would decrease the amount of uranium used by a factor of 160. So the total amount of uranium needed every year in that future would be about the same as today, 60,000 tonnes per year. Over a billion years, the world would need 60 trillion tonnes of uranium. That is about 10 million times current world reserves at the current price. Since reserves increase with the square of the price, we would reach those levels of uranium reserves when the price increases by a factor of about 3200. At those prices, a kWh of electricity would have about 4 cents in uranium costs -- an increase from today, but not a huge one.
It would also mean that an average cubic meter of rock, anywhere on earth, would contain $860 worth of uranium. Mining anything would be economic at those prices. (This assumes 1 part per million U and 3.5 tonnes of rock per cubic meter.)
The likely-case scenario
Uranium isn't the only fuel we can use for nuclear power. We can also use thorium, another heavy element, in a full-use fuel cycle reactor. And thorium is more than three times more common in the Earth's crust than uranium is. Beyond that, thorium is a lot cheaper than uranium. In fact, thorium is so cheap that it's current price might actually be negative: some people would pay you to haul it away and get rid of it. Thorium is considered a nuisance because it's lightly radioactive and the NRC requires that you have a license to handle it.
Thorium reserves follow the same math as uranium reserves: reserves approximately increase with the square of the price. With a price of $500/lb for thorium, the AEC in 1967 put Reasonably Available reserves of thorium at 3000 million tons, about six times the uranium reserves at the same price. Those prices imply we would be processing raw granite for the heavy elements within them; we will be "burning the rocks", in Alvin Weinberg's apt phrase, and there are enough rocks to last well over a billion years. So the time will come when most of the nuclear fuel we use will be thorium, and only a fraction will be uranium. If the AEC's 6:1 high-price reserve fraction holds, after a billion years uranium prices would have to rise by a factor of 1200 from current prices, when Earth becomes breakfast toast. The cost of uranium in one kWh would then be 1.5 cents, which again would not raise the price of electricity much from today's prices, even at the end of civilization.
But that's not likely to happen either. Why not? For two reasons: first, because at some point we might actually figure out how to make nuclear fusion work, and work cheaply. That might be centuries away at our current pace -- the ITER facility in France is costing tens of billions and will not produce a single Watt of electricity. But the possibility is out there.
The other possibility is mining the Moon. Obviously such an enterprise would cost a lot of money up front, but once you have all the equipment in place (likely robotic), sending raw materials back to Earth for processing is surprisingly cheap from the Moon, because of the Moon's low gravity. An electric mass driver could manage it easily without chemical rockets. And on the Moon, you can mine forever without the slightest environmental damage to good old Planet A.
Further reading
Lightfoot, H. D., Manheimer, W., Meneley, D. A., Pendergast, D., & Stanford, G. S. (2006, May). Nuclear fission fuel is inexhaustible. In EIC Climate Change Technology, 2006 IEEE (pp. 1-8). IEEE.