# Contents

## Idea

Peak uranium refers to the theory that uranium production will follow a roughly bell-shaped curve, whose peak is imminent. This is an example of a peak theory. Also see Nuclear power.

## A back-of-the-envelope calculation

For now, we begin with Charlie Clingen’s back-of-the-envelope calculation that tackles this question:

If we kept using electricity at a constant rate, how long would today’s uranium supply last if the world switched overnight to generating all electrical power with today’s nuclear technology?

Your first reaction may be a howl of indignation. After all, you’ve probably seen drastically longer times mentioned as answers to this question… or… umm… at least similar-sounding questions. For example, read:

• Martin Sevior, Is nuclear power a viable option for our energy needs?, The Oil Drum, March 1, 2007.

He says “unlike conventional oil, uranium resource exhaustion will not be an issue for the foreseeable future”. And he shows a truly heart-warming graph by M. King Hubbert, who is famous for his 'peak oil' theory:

So maybe Clingen’s answer is way off. It certainly involves a lot of simplifying assumptions that are clearly unrealistic. But because these assumptions are clearly stated, we can change them and see how the answer changes.

For example, his calculation assumes that the world has about 5 million tonnes of uranium ready and waiting to be mined and refined for a reasonable cost. This comes from the Red Book, put out by the International Atomic Energy Agency. But the Red Book also says that over 35 million tons could be lurking around somewhere if we’re clever enough to find it. If you’re willing to go with that higher figure, just multiply Charlie’s answer by 7. The new answer: 70 years. Of course, this neglects the fact that electricity usage may go up.

So, please take this in the right spirit: it’s not supposed to be a definitive answer, just a starting-point for more detailed work. There is already more to see on the Azimuth blog.

But on with the show…

### Question

If we kept using electricity at a constant rate, how long would today’s uranium supply last if the world switched overnight to generating all electrical power with today’s nuclear technology?

### Objective

The goal is to get a rough estimate of how long currently known reserves of uranium will suffice to provide nuclear power, using today’s technologies, to satisfy all electrical power requirements, worldwide, at today’s level of consumption.

We consider a highly simplified base case using as inputs today’s known uranium reserves, today’s nuclear power technologies, and today’s total world-wide power requirements. This base case, although totally unrealistic, can be refined in a controlled, step-by-step fashion by easing restrictions and revising assumptions in ways that highlight major areas needing further investigation. Because this toy model requires only four inputs and yields a single output, it is easy to quickly test various hypothetical situations with mental or back-of-the-envelope computations, thereby easily achieving an intuitive understanding of the various critical assumptions, requirements, and issues involved.

The framework used here could easily be refined and extended to build a more useful model with multiple input parameters providing realistic and useful outputs.

There are two kinds of assumptions and restrictions recognized here:

1) Known assumptions and restrictions used to compute this rough estimate. These will be listed.

2) Unknown assumptions that are hidden in data taken from various sources. It is best to assume that all input data are inaccurate. Whenever possible, assumptions used to compute the values of input data should be discovered and stated.

All the technology, estimation, science, costing etc. details are hidden in the assumptions. The real difficulties in achieving a reasonable understanding of this problem are all buried in the assumptions.

When possible, the sensitivity of the results upon various assumptions should be made explicit.

### Results

Under the assumptions stated below, using the most conservative values and assuming that cited inputs are reasonably accurate, the current uranium supply would be depleted in about ten years (9.6 – 11.2 years).

Using a less conservative estimate for the known world-wide uranium reserve, the current uranium supply would be depleted in about 70 years.

### Asssumptions

There are many known assumptions underlying the calculation:

1. It is assumed that the changeover to nuclear power, supplying the total world-wide requirements for electrical power, will occur instantaneously — instant power plant construction, instant fuel availability, etc. Nuclear power replaces carbon-based power generation, hydroelectric power, wind power, etcetera. This is the most extreme assumption.

2. All costs are assumed to be unchanging and irrelevant. One exception: the total known uranium reserves estimates of 4.7 – 5.5 million tonnes are those that can now be mined at a price of US$130 per kilogram. 3. Total known reserves of uranium are assumed to be fixed. Even the “currently known” values which were used are dependent on numerous assumptions and predictions. 4. Mining and processing (cost, capacity, and time) of uranium is assumed not to be a limiting factor. Processed uranium fuel is assumed to be available as soon as needed. 5. Annual worldwide consumption of electrical power is assumed to be fixed at “today’s” rate. No population growth, no increased power requirements. 6. Power generation technology and efficiency are assumed to be fixed at today’s levels. 7. Note also that the calculation only concerns uranium, not thorium. There are also unknown assumptions: 1. The estimates for total known uranium reserves world-wide are highly variable and based on assumptions that are not evaluated here. 2. The estimates of power production efficiency are also based on assumptions not evaluated here. Breeder reactor technology, if feasible for wide-scale deployment, might vastly improve efficiency. 3. The estimate of current-day worldwide total electricity consumption is also based on assumptions not evaluated here. 4. There must be further implicit assumptions that we have overlooked. ### Analysis The number of years that available reserves of uranium will support “today’s” worldwide electric power consumption is given by: T = U × (E/U) / (E/T) where T = time for which world-wide supply of uranium will last U = total known reserves of uranium E/U = terawatt-hours of electricity generated per (metric) tonne of uranium E/T = terawatt-hours of electricity consumed per year world-wide This gives: T = (4.7 – 5.5 million tonnes) × (38,750 TWh/million tonnes) / (19,000 TWh/year) = 9.6 – 11.2 years Note. To get a less conservative estimate, using the value of 35 million tonnes for the total uranium reserve, as opposed to the 4.7 – 5.5 million tonne value, we can simply multiply our result by 7. Then T = 10 years × 7 = 70 years Similarly, if average power generation efficiency were assumed to double (instantaneously) we could multiply the result by 2; if world-wide power demand were to double, we could divide the result by 2. And if we were to ramp up any or all of the factors over a period of time — for example, if power production were to ramp up linearly over a period of 50 years, rather than instantaneously — a simple multiplicative factor can be computed to adjust the final result, D. In short, it is quite easy to do simple sensitivity analyses and to adjust results based on changes to input assumptions. #### Estimates for U, E/U, and E/T U: total uranium reserves, in tonnes Here we have two different estimates: U = 4.7 – 5.5 million tonnes, or 35 million tonnes. Sources: an International Atomic Energy Agency report from June, 2006: also called the “Red Book”, estimates the total identified amount of conventional uranium stock, which can be mined for less than USD 130 per kg, to be about 4.7 million tonnes. This number was made for 2005; underlying assumptions unknown. The 2007 Red Book estimate was 5.5 million tonnes: This book estimates the identified amount of conventional uranium resources which can be mined for less than US$ 130/kg to be about 5.5 million tonnes, up from the 4.7 million tonnes reported in 2005. Undiscovered resources, i.e. uranium deposits that can be expected to be found based on the geological characteristics of already discovered resources, have also risen to 10.5 million tonnes. This is an increase of 0.5 million tonnes compared to the previous edition of the report. The increases are due to both new discoveries and re-evaluations of known resources, encouraged by higher prices.

It’s worth noting that the 2006 Red Book says: “However, world uranium resources in total are considered to be much higher. Based on geological evidence and knowledge of uranium in phosphates the study considers more than 35 million tonnes is available for exploitation.”

E/U: energy per tonne of uranium

Estimate:

E/U = (2,558 TWh/year) / (0.066 million tonnes/year) = 38,760 TWh/million tonnes

Source:

Press release by OECD Nuclear Energy Agency, June 3, 2008.

which says:

At the end of 2006, world uranium production (39 603 tonnes) provided about 60% of world reactor requirements (66 500 tonnes) for the 435 commercial nuclear reactors in operation. The gap between production and requirements was made up by secondary sources drawn from government and commercial inventories (such as the dismantling of over 12 000 nuclear warheads and the re-enrichment of uranium tails). Most secondary resources are now in decline and the gap will increasingly need to be closed by new production.

The 2009 estimate for nuclear power generation is given as 2,558 TWh (terawatt-hours) (see below).

Comparison: an unsourced webpage at the Argonne National Labs says: “One ton of natural uranium can produce more than 40 million kilowatt-hours of electricity.”

This is roughly consistent with the 38,760 TWh/million tons used here.

E/T: Worldwide electrical power usage, in terawatt-hours/year

Estimate:

E/T = 19,000 TWh/year

Source:

World Nuclear News, May 5, 2010.

states that last year, nuclear power generated 2,558 TWh of electricity, comprising 13-14% of the world’s electricity demand. This suggests an annual world-wide rate of total electricity consumption in 2009 of around 19,000 TWh.

Thus the total world-wide electrical energy consumption for 2009 was estimated (by this source) at 19,000 terrawatt-hours, corresponding to a power consumption rate of 19,000 terrawatt-hours/year.

Also, the nuclear power generated in 2009 was estimated at 2,558 TWh (terawatt-hours).

Comparison: Wikipedia lists information from the US Energy Information Administration saying the total electrical power usage in 2007 was 17,100 TWh/year. This is roughly consistent with the above value of 19,000 TWh.

### Units

You may not like “terawatt-hours per year” since this unit of power is not part of the standard metric system, like “watts” or “terawatts”. So, here are the numbers in different units:

U = 4.7 – 5.5 million tonnes, or 35 million tonnes, depending on assumptions.

E/T = 2.1 terawatts

E/U = 140 terajoules / tonne = 140 gigajoules / kilogram

## Alternative calculations

### David MacKay

On page 161 of his book Without the Hot Air, David MacKay estimates how much power could be generated per person, with a world population of 6 billion, if all available uranium were to be consumed steadily over the next 1,000 years. (1 kWh/d for each of 6 billion people corresponds to about 2,200 TWh/year.)

Using mined uranium, including that available in phosphate deposits, he reckons that conventional ‘once-through’ reactors would provide 0.55 kWh/d. With an average consumption of 8.7 kWh/d, that is 19,000 TWh/year shared between 6 billion, his 1,000 year target would fall to 63 years.

But if fast reactors were to be used, burning almost all the uranium and most of the radioactive by-products too, the conversion goes up by a factor of about 60, thus allowing 33 kWh/d per person.

He goes on to point out that the oceans contains about 4.5 billion tons of uranium, though the extraction rate is limited by the very slow rate at which the water circulates. With extraction of 10% of the available uranium over a period of 1,600 years, the circulation period, he estimates that 280,000 tons per year would be available. This, using fast reactors, would allow a per capita generation of 420 kWh/d. (For an overview of seawater extraction see, e.g., Masao Tamada, 2009.)

That is about 50 times current electricity production for the next 1,000 years.

His calculation changes if thorium rather than uranium is used. Estimating that the available amount of mined thorium is 4 times the amount in presently known reserves, MacKay reckons that conventional reactors would provide 4 kWh/d. Using the Carlo Rubbia’s ‘accelerator-driven system’, output would be about 6 times greater, or 24 kWh/d per person. This is almost 3 times current worldwide production for the next 1,000 years.

The estimated factor 60 mentioned above is data from the World Nuclear Association—see page 171 of MacKay’s book Without the Hot Air. This estimate is also used in a short calculation in an essay on the blog randform by Nadja Kutz. This calculation is an introduction to the problems of nuclear power generation and the question of peak uranium.

### Barry Brook

Another analysis has been presented by Barry Brook:

This is very detailed and deserves to be presented carefully here.

### Rowan Eisner

If we’re looking at substituting uranium for oil, we should be looking at total energy use for how long it will last, rather than just electricity. My back of the envelope calculation gives 42 days (U reserve -> power generation with current technology/global energy consumption).

I tried to check against the proportion of world energy which is consumed as electricity, which, if the wikipedia figures are to be believed, would give about 1 day for the above 70 year electricity alone calculation (5TW out of 150PW). So I’m not sure why there’s more than an order of magnitude difference, but either way, it’s not a very useful strategy for energy security.