Physicists love a good ‘back-of-the-envelope calculation’: a quick calculation that lets you roughly estimate something. The goal is not precision: you’re doing fine if you come within a factor of 10 of the right answer. Instead, the goal is a kind of rough preliminary insight. After all, if you can’t figure out the answer roughly, you probably shouldn’t charge ahead with calculations that claim to get the answer accurately.
Here’s a guest post by Charlie Clingen. It’s a 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?
His answer: 10 years.
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. Criticism is cheap: see if you can do better. I would love it if you did some more detailed and realistic calculations!
Indeed, I’m eager to get more ‘guest posts’ of many kinds here on Azimuth. The first, Terry Bollinger’s post on turning renewable energy into fuels, led to a great discussion that taught us a lot about this issue. Greg Egan’s Probability Puzzles were a fun way to sharpen our understanding of probability theory. Keep ’em coming!
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.
Assumptions
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:
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:
• Uranium 2005: Resources, Production and Demand.
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:
• Uranium 2007: Resources, Production and Demand.
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.
Hi, it’s John again. I don’t like “terawatt-hours per year” since this unit of power is not part of the standard metric system, like “watts” or “terawatts”. So let me express Clingen’s assumptions in metric:
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
By the way, because I spent a lot of time doing pure mathematics, you should not trust my ability to multiply numbers correctly. Check my work — and Charlie Clingen’s, too.
Azimuth 
You wrote: “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?”
It seems with “today’s uranium supply” you mean mostly uran 235 at a certain price.
As indicated in the source you were giving:
http://www.iaea.org/NewsCenter/News/2006/uranium_resources.html
the uranium supply per se may last much longer if one uses breeders. Breeders make the use of e.g. uran 238 possible, which is much more abundant than uran 235. Or in other words the more the price for uranium 235 is going up, the more it is likely that breeder technology will be used as means for the commercial use of nuclear energy.
A post on this is at:
http://www.randform.org/blog/?p=1336
The problem is that uranium breeder technology may fuel a plutonium market, since plutonium can also be used for breeding:
http://www.randform.org/blog/?p=1526
Likewise the current standards which are using thorium
for breeding are not much better:
http://www.randform.org/blog/?p=1841
And last but not least the waste problem is not so easy as Stewart Brand likes to see it according to your comment at:
https://johncarlosbaez.wordpress.com/2010/08/31/cap-and-trade-in-china/#comment-998
especially next to the known problems like leakages
http://www.randform.org/blog/?p=1888
http://www.randform.org/blog/?p=1875
and undercover military dumps sites:
http://www.randform.org/blog/?p=1832
There are new challenges posed by small reactors, while in the meantime the global documentation of big nuclear dump sites seems to be rather poor (especially if one keeps in mind that plutonium-239 (http://en.wikipedia.org/wiki/Plutonium-239) has a half life of 24,200 ys):
http://www.randform.org/blog/?p=2018
Quick points:
Included in E/U ought to be a factor for the amount of energy used in generating the output (building, decomissioning, mining, refining, etc), at least to show it’s negligable. This reference
http://nuclearinfo.net/Nuclearpower/WebHomeEnergyLifecycleOfNuclear_Power
appears to say on the order of 1 percent of the energy is used, although I’m unclear about that sites agenda and accuracy. So it looks like that factor should be indeed be negligable.
This reference
http://www.fraw.org.uk/mei/papers/oies_article.html
appears to say that 10 ppm of Uraninum is likely to be a floor on the “energy in/out break-even” point even with future technological developments, although they don’t explain what considerations go into this. (This appears to make using uranium in seawater at 0.003 ppmU not a net energy gain.)
AMOUNT OF URANIUM AVAILABLE FOR FUEL
John (B) pointed me to the following reference: Uranium Resources and Nuclear Energy:
Click to access EWG-paper_1-06_Uranium-Resources-Nuclear-Energy_03DEC2006.pdf
which was commissioned by a member of the German parliament and concludes that we are already almost out of usable uranium ore and the future for nuclear power so limited that we would best be served not to go down that road.
Bane references nuclearinfo.net:
http://nuclearinfo.net/Nuclearpower/WebHomeEnergyLifecycleOfNuclear_Power
which has an interesting analysis of the energy lifecycle of nuclear power, ending with a discussion of the amount of uranium available for future extraction and the costs associated with that extraction. Their projections indicate that nuclear fuel will be available at acceptable costs and in quantities so large as to eliminate any concerns about fuel being a bottleneck to future nuclear power production.
Just so we don’t get the idea that the amount of cost-effective, mineable uranium fuel is easy to assess, take a look at the back-and-forth rebuttals at the end of this report which deal in considerable detail with the various estimation methods under contention.
Maybe further work has been done to reconcile these vast differences. Does anyone out there know if a consensus regarding the amount of cost-effective uranium fuel has been reached? One has to assume that this situation must be well known by those in the business.
Bane’s reference is for 2004; the company does not have any data online for 2005,2006,2007,2008, or 2009…
Also, the data cited by Bane is only good for the Billiton Olympic Dam mine (in 2004) whereas the report cited by John (B) has worldwide scope and was published in 2006. Absent more recent work, I’d tend to give more credence to the German report.
http://en.wikipedia.org/wiki/Reprocessed_uranium
Whilst no numbers are talked about, there could be a *big* difference (orders of magnitude). Without some assumptions on future processes and technologies, these estimates could be quite unrealistic. On the other hand, I agree entirely with your analysis, as it pertains to current technologies.
Perhaps it would be worthwhile to extract an upper bound? After all, there is a definite upper bound to the energy to be had in fission of U-235, and the fudge factor of efficiency can be estimated from existing numbers (such as the ones you’ve provided) and might be easier to have some intuition about.
Incidentally, I suggest http://www.inference.phy.cam.ac.uk/withouthotair/c24/page_161.shtml as a good starting point.
From Wikipedia: “In 2008, total worldwide energy consumption was 474 exajoules (474×1018 J) with 80 to 90 percent derived from the combustion of fossil fuels. [1] This is equivalent to an average power consumption rate of 15 terawatts (1.504×1013 W)”
So another computation here (t = tonne):
E/U = 140 × 1013 J /t
In a year we use
E = 474×1018 J
That means that we would use 474×1018/140×1013 = 3×105 t of uranium per year to produce such amount of energy.
Then if we have X millions tonnes (X × 106 tonne) of uranium available, then we may produce energy E per year for a
E= X × 106 tonnes / 3 × 105 tonnes = X/3 × 10 per year.
Then if X = 5.5 we have similar result as you provide.
Thanks for your calculation, kakaz!
(Indeed, thanks to everyone for all the comments so far: I’m about to go shopping in Paya Lebar so it will take a while for me to respond to all these comments.)
I just want to note that you’re talking about total power usage while Charlie was talking about electrical power only. It’s good for us to get some sense of the relative magnitude of these quantities. Exajoules/year is not my favorite unit of power; I like pure metric units. But I have no desire to be dictatorial:
1 exajoule/year ∼ 31 gigawatts
total worldwide power consumption in 2008 ∼ 16 terawatts
total worldwide electrical power consumption in 2007 ∼ 1.9 terawatts.
If the idea is to replace fossil fuels as a primary source of energy for the planet, shouldn’t we use 16TW in the calculation ?
That would give us:
0.140*5e9/(16*3600*24*365)
ans = 1.3873
that’s one year and 4 months, not too much !!
Digression:
The most powerful wind turbine has a maximum output of 7MW, so assuming a capacity factor (http://www.awea.org/faq/wwt_basics.html) of 33%, it can generate on average 2.33MW. To produce 16TW we need to build almost 7 millions of them (16e12/2.3e6). Do we have enough materials to do it ?
Maintenance also worries me a little bit (average life span of a wind turbine is 30 years, but i imagine you don’t have to replace everything).
How about solar power, how much surface must be covered by PV panels to generate 16TW ?
Hi, Giampiero!
You wrote:
That’s an illuminating — and depressing! — calculation. But it’s even more unrealistic than the one Charlie Clingen did. It’s already unrealistic to imagine suddenly generating all our electrical power with nuclear reactors. It’s even more unrealistic to imagine suddenly equipping all cars, trains, and planes with electric or hydrogen-burning engines where the power is generated in nuclear reactors.
Try this webpage:
• Matthias Loster Total primary energy supply: from sunlight.
What’s clear is that project of switching to a carbon-neutral economy is incredibly ambitious. Consider Stewart Brand’s summary of Saul Griffith’s talk at the Long Now Seminar:
I urge everyone to watch the talk. Maybe Griffith is making some mistakes. If so, we need to catch them.
The Amory Lovins talk I posted a little earlier is a perfect complement to this. Lovins is not a theorist, he’s already doing “Renewistan” with dozens of major players. Business, industry, government, military. He argues that the transition is not only doable, it’s underway, doable entirely within a market framework, large parts of it can be done more cheaply than NOT doing it, most of it needs no subsidies, and the full transition can be made quickly. The talk is full of real-world examples.
His case on nuclear is unexpected. He argues (with lots of data) that it’s neither necessary nor economically viable. Lovins is one of the world’s leading energy experts. His position needs an answer from someone who’s been convinced by Stewart Brand. I don’t have enough perspective to judge … but given the costs and uncertainties of nuclear, I would prefer Lovins to be right.
The URL of the talk again is http://www.rmi.org/Default.aspx?Id=2318&vid=2437&cat=
(I’m an interested rank amateur, with a degree in environmental policy/politics/philosophy … a founder and former staff member (mid to late 1990s) of a Canadian community environmental action project focused on home energy assessments and energy efficiency retrofits … a curious generalist by nature, who likes the way John Baez communicates.)
Great talk indeed, and very interesting links. I knew about the clock but not about the seminars and foundation.
Yes, of course assuming an instant switch to all-electric transportation is unrealistic, but nevertheless it’s (i think) an interesting thought experiment to roughly assess the viability of nuclear power as primary energy source in the long run.
Loster’s web site is very interesting too. Leaving aside for now the issue of technical feasibility, i was thinking about “how much would it cost” to cover 170455 Km^2 with solar panels, and assuming 1W/$ (probably a little too good), 3TW would cost 3T$, which would be quite a stimulus package, since it’s 21% of the US GDP.
However, the good new is that the panels would last 20 years, so if we divide 3T$ by 20 years we get 150B$/year. This is not too bad considering the US is spending 400B$/year on imported oil, in order to cover for 0.8TW.
I have read that the cost for wind turbines is about 1M$/MW, not sure if this includes installation or if the MW is maximum or average power, but this would lead to the same figure of 1W/$, although for wind power i would expect larger economies of scale in the long run.
Thanks for the links again, i really liked them.
Your answer is reasonably consistent with the linked article below from Scientific American magazine (200 years at current consumption rates):
http://www.scientificamerican.com/article.cfm?id=how-long-will-global-uranium-deposits-last
There’s really important missing assumptions here, one of which is that mining uranium is done largely using vehicles and machinery powered using fossil fuels (diesel). See http://www.theoildrum.com/node/5060 “How Long Before Uranium Shortages”
That’s a very interesting aspect that has been mentioned before on this blog; this seems to be a blind spot of all discussion about alternative energy sources that I know. (As a physicist I would say it is a second order correction, but one that we definitely need to get a reasonable estimate
)
While I’m pretty sure that we can get small cars going using electric energy (from whatever source), there certainly are vital links in the resource chain that depend on a rather harmless, but very comprehensive energy source, like fossil fuels, that cannot be produced by known means (well, as far as I know).
This is definitely an aspect worthy of a wiki page :-)
Unfortunately I don’t have any data to add to this discussion, and even less time to think about it, but I’d like to mention, nevertheless, that Germany will definitely stop producing energy using any radioactive materials, within the next two decades. Don’t know about the French, though. Or the Russians.
Tim wrote:
By the way, the Azimuth Project wiki exists now; it’s just in too preliminary a form to show it to anyone. If you ever get enough time to help out, your help would be much appreciated.
Is this because of the influence of the Green Party?
If so, I’m afraid they’ll find themselves on the wrong end of history, at least in this one specific issue. And if you’re friends with any influential Green politicians, who might be persuadable, I’ll buy them a copy of Stewart Brand’s new book — he’s pretty eloquent on this subject.
In my opinion, keeping a wiki hidden until somehow it is ready goes against the whole idea of a wiki. You could end up putting a lot of effort into it and creating a lot of good content, but you may not develop a “community”. This is exactly the flawed strategy Joyal took with his wiki. Lots of good content that will never be quite ready and as such, lays dormant.
There’s not a single bloody bit of content in this wiki. Just a page that says “Hi, Welcome to Azimuth”. I was going to add links to this blog and stuff, but I was unable to for some reason, so I asked Andrew Stacey to help, but he hasn’t yet.
So fear not: there aren’t treasure troves of material lying dormant anywhere.
Hmm — but now I checked and I am able to make changes. So, okay, soon I’ll announce this to the world.
Thanks for the nudge, Eric.
Just let me know how I could help, and I’ll see if I can afford some time…(I did not have much free time during the last weeks due to a very time consuming task that I’ve been appointed to by my employer :-).
Yes, this decision was made by the last administration with the Green party participating, it has been one major goal of the party since it was founded. The current government is discussing if they prolong the time limit – but they won’t change the long term goal; paradoxically some members of the government claim that the companies running the nuclear power plants don’t intend to build new ones for economic reasons anyway.
I’ll definitely take a look at the book, but I doubt that any member of the Green party is susceptible to scientific arguments, if those challenge a core belief of the movement.
And no, I don’t know any politicians.
When I was in highschool, I did an internship in the chemistry lab of a hazardous waste deposit (where samples of the material to be deposited are examined, to determine if they are too toxic), when the minister of the environment of Lower Saxony visited. She was greeted by a group of neighbours with a hamper full of fruits and vegetables harvested from the nearby gardens and promised to make a salad out of it and serve it to her family (don’t know if she kept the promise, though, but the whole scenario was really funny anyway. I’m still laughing my head of).
That’s the closest I ever got to a member of any ministry of the environment. (BTW, she was a member of the social democrats, not of the Green party: Schröder, who later became chancellor, had achieved a coalition with the Green party where the only ministry that the Green party got was the ministry for family affairs, senior citizens, women and youth).
So how does this change when we add the more abundant thorium? How efficient is it compared to uranium? And how about reprocessing?
These are good questions, Aaron! See some of my preliminary fumbling attempts to discover answers here. It seems switching to thorium, or switching to reprocessing (a ‘breeder reactor’) could make a roughly order-of-magnitude difference. But those attempts don’t touch on how much energy you get from the thorium fuel cycle as opposed to the various fuel cycles involving uranium.
The other possible game-changer, much discussed here, is getting uranium out of sea water.
But surely someone has already done all these calculations! They’re important! I can’t believe the world has been waiting for us to do them!
I don’t know if this is what you want, but I compared fission energy produced by an atomic fission. Uranium-233 yields 197.9 MeV. Uranium-235 yields 202.5 MeV. Plutonium-239 yields 207.1 MeV.
The Uranium-235 path is in common use today because it was the technology development that led to the bomb. The Uranium-233 path was not taken during 1960-1070 because it was harder to make a bomb using Uranium-233. The Plutonium-239 path was discouraged because it was too easy to make a bomb out of it. The bomb played a big role in our selection of nuclear power plant technologies.
Thanks for the info! It’s good to give links for all figures of this sort, since otherwise when I get around to using them I either need to dig up the sources or just say “Hybrid Moiety claims…” It’s a cool name, but it would raise eyebrows in the bibliography of a scientific paper.
True! And I guess it still does, since some argue that breeder reactors are bad because they can help nasty guys make nukes.
(I would rather stay out of that political discussion right here, because I find that bringing in politics seriously degrades the level of scientific thought in a group discussion. But obviously at some point that discussion would need to occur.)
How about: Kaye & Laby Online, Table of Physical and Chemical Constants, Sec 4.7.1: Nuclear Fission.
Allow me to compare with chapter 24 of David MacKay’s Sustainable Energy without the Hot Air (SEWTHA), previously linked to on this blog:
He has the same U = 4.7e9 kg as baseline, but also mentions 22e9 kg of uranium in phosphate deposits and 4.5e12 kg in seawater.
David estimates that an affluent person on average consumes 195 kWh/d, which is about 8 kW of total power from all energy sources combined (Americans use a bit more than that). With a world population of 7 billion, that gives E/T = 56e12 W. That’s 25 times more than Charlie’s number, but remember that not all people on the planet are affluent (unfortunately), and that David includes non-electric power usage as well.
Now, I think the major assumption in Charlie’s analysis is the use of once-through reactors. David says they give 1 GW for 162 tonnes of uranium pr year, which gives E/U = 194 GJ/kg (I wonder why that differs from Charlie’s 140 GJ/kg; did I multiply incorrectly? I’m a general nonsense mathematician too, so you shouldn’t trust my numbers).
However, a fast-breeder reactor is 60 times more efficient than a once-through reactor, giving E/U = 12 TJ/kg.
Summary of numbers:
U = 4.7e9 kg (conservative), 27e9 kg (with phosphate deposits), 4.5e12 kg (in seawater).
E/T = 2.1e12 W (just electric), 56e12 W (all included, everyone living like a European).
E/U = 194e9 J/kg (once-through), 12e12 (fast-breeder).
Range of results (everyone affluent, all power nuclear): from
T = 4.7e9 * 194e9 / 56e12 s = 188 days, through
T = 27e9 * 12e12 / 56e12 s = 183 years, all the way to
T = 4.5e12 * 12e12 / 56e12 s = 30,500 years (using seawater sources).
Range of results (current electricity usage from nuclear): from
T = 4.7e9 * 194e9 / 2.1e12 s = 14 years, through
T = 27e9 * 12e12 / 2.1e12 s = 5,000 years, all the way to
T = 4.5e12 * 12e12 / 2.1e12 s = 0.8 million years (using seawater).
Next question: Redo the calculation for fusion (assuming we can it to work) using the various fusion fuels (D+D, D+T, p+B11, He3, …).
(PS. Why is there no preview for comments here?)
I’ve been trying to find some concrete figure for the energy that would be used “making” reactor-suitable uranium by extracting it from seawater. Unfortunately, the web is littered with sites that claim some detailed papers are “a complete joke” and replace them with a 2 line calculation giving a number more to their liking (rather than writing a full, detailed rebuttal paper), making me doubt everybody :-( . So the academic paper here:
http://www.mdpi.com/2071-1050/2/4/980/
estimates the EROEI (energy return on energy invested) for the cutting edge passive adsorbption in compound-specific absorbing mats at around 2.5. If this is roughly correct, that would mean that at equilibrium 40 percent of the generated energy is used to extract the “next lot of fuel” (possibly more depending on energy conversion losses). This drops the time including seawater extraction to 0.48 million years.
Other people appear to claim much higher EROEI for seawater extraction, but I genuinely lack the expertise to know which figure is most likely to match reality.
bane says:
The “academic paper” link times out. However, some other papers that were recent two years ago are mentioned in this slideshow (PDF).
The way I look at it is, the polymer they soak in the ocean has combustion energy nearly equal to its weight in oil, and — p. 17 — it is repeatedly used to fish, typically, 0.004 times its own mass of uranium out of the sea. On each run, then, it delivers 0.004*14000, i.e. 56, times its combustion energy.
This is consistent with the estimated price on that page: $260/kg, $2.6 per barrel-oil-equivalent. Not competitive with land-based mining operations that now are getting $134/kg, and in some cases spending much less, but a lot closer to competitiveness than used to be the case.
Maybe someone has information more recent than 2009.
Ulrik says:
Now, I think the major assumption in Charlie’s analysis is the use of once-through reactors. David says they give 1 GW for 162 tonnes of uranium pr year, which gives E/U = 194 GJ/kg (I wonder why that differs from Charlie’s 140 GJ/kg; did I multiply incorrectly?
Hmmm… I used an E/U of 38, 760 TWh/million tonnes, which equals 38,760 MWh/tonne; but 1 GW/162 tonnes/year seems to have a units problem. If we assume it is 1GWh/162 tonnes/year, that is only around 6.2 MWh/tonne, right? What did I miss?
If 1000 kg of Uranium produces 40 million kWh, then 1 kg produces 40,000 kWh, and costs (according to the assumption above) $130. Hence the contribution of the fuel to the price of the energy is 130/40,000 = 0.325 cents per kWh.
Would it be safe to say that the cost of the fuel is not the limiting factor, and that if the price were to rise five-fold it probably wouldn’t affect the economic viability significantly?
Extraction from seawater is reckoned to be a little over five times the price of mining conventional ores – and since supply is sufficient to meet current demand, nobody has put much money into making it cheaper. (Seawater extraction has apparently already been demonstrated at lab scale.)
It’s fair enough – for the sake of this argument – to use only current demonstrated technology. (Even though that’s obviously unrealistic as a prediction.) But the assumed ceiling on the price of Uranium has a big impact on the result – especially considering that it’s not an actual economic or technological limitation, unlike some of the issues that have been neglected. Does such a limit comply with the spirit in which the question is asked?
I had a look at streamfortyseven’s link, and noticed the following comment on that page by Bill Hannahan.
http://www.theoildrum.com/node/5060#comment-473446
“Reports in the 1970’s estimated the cost of extracting uranium from sea water at $1,500 to $2,000 per pound. R&D has reduced that to less than $150 per pound, of uranium.
http://www.taka.jaea.go.jp/eimr_div/j637/theme3%20sea_e.html
http://jolisfukyu.tokai-sc.jaea.go.jp/fukyu/mirai-en/2006/4_5.html
The oceans contain 4.6 billion tons of uranium, half of which is sufficient to support 10 billion people at the U.S. level for 400 years using first generation reactors and over 30,000 years with breeders. In reality the oceans are continuously supplied with uranium by the erosion of land, so the uranium supply is effectively unlimited.
We do not need breeders for a long time but we should move forward with breeder R&D to reduce mining and waste volumes.
Why are there no sea water uranium extraction plants?”
world-nuclear.org (a rather pro-nuclear society) says on
http://www.world-nuclear.org/info/inf75.html
On this webpage they also say:
However if I understood correctly breeder technology is still considered to be cheaper than seawater extraction:
Last but not least breeders may in prinicple mitigate the waste problem (the current standards however don’t do that, but are rather
creating a plutonium market and it is quite likely that that this won’t get better):
From http://www.world-nuclear.org/info/inf69.html
(see also http://www.randform.org/blog/?p=1840)
and the links I gave in the above comment
ah, I see, that all seems quite logical then. I particularly liked the observation via your first link that, on balance, a resource in an economy will roughly maintain the same current reserve future (of economically accessible orebodies) given current consumption over time, assuming that the total supply is effectively unlimited.
I suppose one probably needs other assumptions on the distribution of accessibility of orebodies per capital expenditure for this statement to hold, ie, whether the access to resources always grows exponentially (or at least faster than polynomial), with linear increase in R&D expenditure.
your comment about breeder reactors was quite surprising, however. I had heard of them (but only quite recently, in particular, the Traveling Wave Reactor from Bill Gate’s TED talk) but was not aware that they can potentially be 50 to 60 times more efficient. certainly 500 years of supply via the above conservative estimate sounds pretty good to me.
For more on breeders, I gave these two links on a previous post. You may find them of interest.
http://www.nationalcenter.org/NPA378.html
http://www.skirsch.com/politics/globalwarming/ifrQandA.htm
I don’t understand what you mean with “current reserve future”.
The breeder technology only “looks” promising, however it is not in my point of view.
It is more dangerous than current reactor types, where apart from the reprocessing problems (-> also the IFR needs reprocessing http://www.world-nuclear.org/info/default.aspx?id=540&terms=IFR) the danger of an unwanted prompt criticality http://en.wikipedia.org/wiki/Prompt_critical and a nuclear meltdown is higher.
It is usually claimed that a fast reactor can burn in principle “all” actinides (and in particular the long-lived plutonium) however I haven’t found a good overview about how much remnants will be left (even in a closed fuel cycle).
Moreover it seems to me to be a naive assumption to assume that fast breeders would only be used for getting rid of plutonium. Since they can also breed plutonium and since there is an economic interest they will be used for breeding and thus will most likely fuel the plutonium market.
One should also remark that usually also U-235 is used in breeders, I don’t know how well or whether at all the processes works without it, so the question of Uran 235 abundance seems to be not as urgent as for the non-breeders but still important enough.
The TWR (Travelling wave reactor) is a certain concept for using nuclear fission as means of power generation which according to the New York Times recently received 35 million $ in funding. It was even promoted by Bill Gates in a TED talk
http://www.ted.com/talks/lang/eng/bill_gates.html and thus received a considerable amount of media attention.
http://www.nytimes.com/2010/06/15/business/energy-environment/15nuke.html?_r=1
However despite the media attention I found it quite hard to get technical details on the proposed reactor design, a quick literature search for the
http://en.wikipedia.org/wiki/Traveling_wave_reactor
didn’t reveal much.
The pdf at http://www.nuc.berkeley.edu/files/TerraPowerGilleland.pdf
on the website of Berkeley nuclear engineering department:
http://www.nuc.berkeley.edu/node/1077
is more adressed to a broad public than it would contain technical details, Bill Gates TED talk is not very technical either.
Openly available and cited at Wikipedia is a Ph.D. thesis in nuclear engineeering from 1980:
http://dspace.mit.edu/handle/1721.1/54273
An evaluation of the breed/burn fast reactor concept by Atefi, Bahman (1980)
(Advisor: Michael J. Driscoll and David D. Lanning)
Department: Massachusetts Institute of Technology. Dept. of Nuclear Engineering.
Furthermore the english Wikipedia entry mentiones (6.9.10)
“The behavior of the reactor power vs. time represents a soliton. This is contrary to many media reports[15] , which are still discussing a candle-like reactor with a power region that moves down a stick of fuel. The standing-wave or soliton behavior maintains most of the benefits of the traditional view of a TWR, giving up stagnant fuel while adding simplicity in cooling.”
The TWR concept relies according to the above informations a lot on computer simulations, however I couldn’t even find information on which solitonic model is used for the simulations – maybe a cylindrical KP equation? Neither could I find any reliable assessment on how realistic the transition from simulation to experiment is. Solitonic behaviour is often highly dependent on the given initial conditions and the involved geometric shapes and thus not so easy implementable in an experiment.
Apart from the basic technical questions I also couldn’t find an assessment of the percentage of actinides, which will remain as a left-over after the burn process had terminated.
All in all it seems to me the whole TWR-concept is – politely speaking – rather futuristic. In principle it is good to invest in research, however I would prefer that such an amount of money would go into research which has no apriori commercial interest and especially into less dangerous technologies like for example into basic research and the simulation of solid state physics.
(see e.g.http://www.randform.org/blog/?p=1479
http://www.randform.org/blog/?p=1127)
The traditional light water reactor leaves 50% of fissile Uranium and Plutonium unburned in the waste. If we switch to a molten salt design we should be able to double the Uranium life. A molten salt reactor can burn Uranium 235 or Plutonium just as well as Uranium 233. If we counted the Thorium as well then that should put another 4x in the time estimate.
Hybrid: I am very ignorant of reactor design, so please don’t be offended by all my questions.
1) When you refer to “molten salt design” do you mean molten salt cooled reactors or molten salt fueled reactors?
2) You write:
Why does the Wikipedia article on breeder reactors say “a normal reactor is able to consume less than 1% of the natural uranium that begins the fuel cycle”?
The chance to improve efficiency by a factor of 2 would be nice, but a factor of 100 would be really nice.
Actually that Wikipedia article suggests that breeder reactors beat ‘traditional’ ones by a factor of 33:
3) Why do you say thorium gives just a factor of 4? I read in Wikipedia that “thorium is at least four times as abundant as uranium in the Earth’s crust and at least 500 times as abundant as uranium-235”. Isn’t 500 the more relevant number?
Or are you comparing a breeder reactor that uses thorium to one that uses uranium-238, the most common isotope of uranium?
I probably have a lot more questions, but that’s enough for now!
I was talking about molten salt fueled reactors where the fissile materials are dissolved in fluoride salt. According to Robert Hargraves’ July 2010 article in American Scientist, 1.15 tons or uranium-235 in solid oxide fuel is consumed in light water reactor, and ends up at the end of its service life 0.3 tons of uranium-235 and 0.3 tons of plutonium remaining. That is wasting about 50% of the fuel.
Your quote about uranium breeder reactor being more efficient compared to light water reactor probably refers to the ratio of uranium-238 to uranium-235 in uranium ore, plus not having to waste uranium in the enrichment process to make uranium solid oxide fuel.
I said thorium would bring about 4x longer time because I was already assuming breeding technology. If you just compare to uranium-235, then the ratio is at least 500.
Let me try to post two links in this reply. The first link points to Liquid Fluoride Thorium Reactors article written by Hargraves and Moir.
The second link points to Wikipedia’s page on Molten-Salt Reactor Experiment.
Charlie C says:
David says that a 1 GW plant consumes 162 tonnes in one year, so, fully parenthesized, I mean:
E/U = (1 GW)/((162e3 kg)/(1 year)) = (31.6e6 s)*(1e9 W)/(162e3 kg) = 195 GJ/kg. Hopefully it’s clear now.
Got it! Thanks. Sorry for being so dense. I was thinking in terms of ENERGY generated in one year (TWh) per million tonnes, and your expression is POWER (GW) per million tonnes consumed in a year, which of course are equivalent. I haven’t done these power/energy conversions in a LONG time and I’m still pretty rusty.
John, I highly recommend adding this video presentation by Amory Lovins to the discussion on nuclear energy. It’s the most information-filled and thought-provoking presentation on energy I’ve seen this year, and is full of (to me) unexpected reasons for optimism. I had no clear opinion on nuclear before watching it.
http://www.rmi.org/Default.aspx?Id=2318&vid=2437&cat=
Kirk Sorensen has a proposal to build a small number of fast chloride molten salt reactors to burn up de-commissioned weapons fuel and trans-uranic waste. These reactors have enough neutron productions to convert thorium to uranium-233, which would tap a resource that lasts at least 500 times longer compared to uranium-235 alone.
He said these plants should allow a ramp up of eventually up to 1000 liquid fluoride molten salt reactors. That would put a serious dent in carbon emissions!
You can’t be shy when trying to tackle a problem as big as Global Warming!
Amory Lovins is an anti-nuclear activist and alternative energy salesman, and calling him an expert on energy is a joke. His predictions have failed repeatedly and his nuclear pieces have been debunked completely.
A great article on expertise:
Nuclear Expertise: The Amory Lovins Charade
A detailed series of articles responding to a nuclear-bashing paper by Lovins. It’s a devastating critique:
Amory Lovins and His Nuclear Illusion – Part One (The Art of Deception)
Amory Lovins and His Nuclear Illusion – Part Two (Big Plants vs. Small Plants)>
Amory Lovins and His Nuclear Illusion – Part Three (Energy Efficiency and “Negawatts”)
Amory Lovins and His Nuclear Illusion – Part Four (Costs of New Nuclear Plants)
Amory Lovins and His Nuclear Illusion – Part Five (Nuclear Plant Reliability)
I think scientists are at a distinct disadvantage in the energy debate. In scientific debates you assume that your opponent is rational, honest and willing to change his/her mind (well, maybe I’m being a little optimistic). But like climate change, the subject of energy brings in ideologues, politicians and activists. Facts mean nothing to these people.
It would be little short of disastrous for us to discover a source of clean, cheap, abundant energy because of what we might do with it. — Amory Lovins.
Thanks for the links. If you’re interested in why Amory Lovins thinks what he thinks, you’d enjoy the remarks in Stewart Brand’s book Whole Earth Discipline. They’re old friends, but Brand has come to disagree with Lovins on nuclear power, so he spends a fair amount of time analyzing Lovins’ views.
However: I want to avoid debates focused on the merits of particular people. Somehow this brings out the worst in everyone — as in, you’re with us or against us. One great thing about science is that — when it’s working well — it can break down big problems into dozens of tiny little problems that are sufficiently dry and technical that people can argue about them without the emotional attachment that forms ‘parties’. When it’s working well, people get more status from being right than from being on the winning team.
But as you say, scientists are at a disadvantage when it comes to everything-goes political struggles.
Here’s a summary version of Lovins’ critique of Brand, in his own words: http://www.grist.org/article/2009-10-13-stewart-brands-nuclear-enthusiasm-falls-short-on-facts-and-logic
Lovins speaks of Brand with friendship and respect, and gets quickly to the core of why they disagree: he sees Brand’s economics as simply wrong, and explains why in some detail. I find his argument convincing. If he’s right, the technical (and safety) issues about nuclear are simply irrelevant. There’s lots of useful data from both sides in the extended discussion at the end of this article.
To Ijon Tichy: the pretence that Lovins is some kind of crank only discredits your own views. Here’s his bio, from his MacArthur Fellowship through four decades of work in 50 countries, and projects with many Fortune 500 companies, the UN, OECD, Congress, and the U.S. Energy and Defense Departments. http://www.rmi.org/Content/Files/Acorpbio_16i10.pdf
Thanks, it’s nice to hear both sides of the issue from the people themselves.
I already scolded Ijon for turning up the rhetorical heat. But he never said Lovins was a “crank”; he said Lovins was a “anti-nuclear activist and alternative energy salesman”, which is nowhere near as bad. Notice how the argument is ratcheting up, just as I feared.
Please, folks: let’s focus on facts, theories, and ideas — not whether particular people are “good” or “bad”.
Thanks; Ui, quite a lot of material to digest in this thread.
I’m reading Whole Earth Discipline right now and will take a look at Lovin’s response after I have finished.
Steward Brand lists “green Germany” as an example of a country that is advocating nuclear power since “they did not shut down their nuclear reactors”: That’s not quite right: The administration of the social democrats and the green party stopped the building of new reactors and announced not to prolong the already guaranteed run-time of existing power plants. The Merkel administration of conservatives and liberals decided yesterday to extend the lifespans somewhat.
Bernard L. Cohen wrote a paper in the American Journal of Physics arguing that uranium breeder reactors are effectively a renewable energy source able to meet all of our energy needs. It’s a one-page paper, so it’ll be a quick read:
Breeder reactors: A renewable energy source
Two breeder reactor designs I like:
Liquid-Fluoride Thorium Reactor
Integral Fast Reactor (also Q&A)
Thanks for the link to Cohen’s paper!
Here is a quote from Cohen’s paper containing some claims that deserve to be checked, not just accepted at face value:
Check away, folks! He gives references for some of these figures.
I’m always a little dubious about looking at feasibility in terms of costs in dollars per unit, because monetary costs munge together so many contributions (energy, potentially rare chemicals, raw materials, raw human work, human creativity, asset depreciation, etc) so that it’s difficult to separate the assumptions that go into a given price. I’d think that it’d be more enlightening to tabulate in terms of uranium availability at an EROEI of at least 20, at least 10, at least 5, etc, along with the other “constraints” like asset depreciation, etc, explicitly.
There’s a claim of an EROEI of large scale industrial uranium from seawater extraction being about 2.5 linked to
here, although I’m not sure how accurate that figure is likely to be.
[…] facts about climate science. It is supposedly going to be opened on Sep. 27. I was commenting on a blog post on Azimuth where guest blogger Charlie Clingen explained how one could find ways to answer the […]
A more detailed summary than the one given in the
comment at:
https://johncarlosbaez.wordpress.com/2010/09/03/how-long-would-uranium-last/#comment-1003
is meanwhile at:
http://www.randform.org/blog/?p=3249
Perhaps a related question you might be interested in is ‘how much CO2 would nuclear power emit?’ It’s commonly assumed to be zero of course, but when mining uranium, milling, construction and decommissioning of power plants etc is taken into account it can be quite significant. Dr Mark Diesendorf has looked into this question:
http://www.ies.unsw.edu.au/staff/mark.html
Click to access Nukes&CO2.pdf
fyi
[…] didn’t write that “Bill Gates investment in TWR technology is probably critical” but that – […]
Yay! It looks like Barry Brook is doing a detailed analysis of various scenarios for nuclear power over on his blog BraveNewClimate! This should really help us figure things out.
Here are the posts so far:
Scenarios for nuclear power to 2060
SNE 2060 – thermal reactor build rates, uranium use and cost
SNE 2060 – are uranium resources sufficient?
He’s studying four scenarios, two previously considered by the World Nuclear Association in their report called the “Nuclear Century Outlook” (or “NCO”). But he doesn’t buy all their assumptions. He considers the fourth of his scenarios most plausible:
1. NCOL: NCO Low Scenario (anchoring to 602 GW in 2030 and 1140 GW in 2060)
2. NCOH: NCO High scenario (1350 GW in 2030, 3688 GW in 2060)
3. TR1: A mid-growth scenario that tracks between NCO Low and High, but which peaks at around 2050 and slowly declines thereafter
4. TR2: A high-growth scenario that is identical to NCO High through to 2030, after which the relative growth rate slows only gradually (absolute number of GW per year continues to increase).
Looks good! It seems that some serious “systems analysis” of the total problem is getting done. Data sources and effective analytical approaches are becoming more and more apparent. Pretty soon, finding ways to clearly yet accurately integrate and present the relevant analyses and results in ways that busy non-specialists can understand will become a significant challenge for this topic and all the other Azimuth topics as well. That could be a major contribution of Azimuth.
Dr. Brook has linked back here.
Too many comments, but Ctrl+F doesn’t show me any mention of Alberta or the tarsands.
They are useful as an existence proof: about 80 percent net energy can be had from tarsands that are six mass percent tar. Or six percent oil, if you prefer to call them oilsands, as I think they who work there do.
Approximating tar’s energy as 40 MJ/kg, that tells us 2.4 MJ/kg, two-thirds of a kilowatt-hour, of fuel energy in a fuel ore is enough for an adequately high fraction to be net.
Now, in CANDU reactors, natural uranium typically yields 164 thermal MWh/kg (so said a leaflet I was given when I visited the Darlington station near me a few years ago). So we can estimate how much extractable uranium an ore must contain to be as good as the tarsands, net-energy-wise: two-thirds over 164000. Four ppm.
That’s a little higher than uranium abundance’s 2.2-to-2.8-ppm range in upper continental crust, but probably not so much as to disqualify average crust as a net-energy-yielding uranium ore. After all, some older CANDUs burned their natural UO2 longer, up to ~250 thermal MWh/kg, back when commercial uranium ore grades were not so high as they are today.
Another way to test the potential, as uranium ore, of average stuff underfoot is to compare its (Darlington-relative) U energy content, 2.2e(-6) times 164 thermal MWh/kg, 360 thermal Wh/kg, with the comminution energy cost of hard rock, ~25 electrical Wh, ~75 thermal Wh, per kg. This gives the same sort of net fraction, (360-75)/360, 0.8.
(How fire can be domesticated)
[…] my comment on Azimuth to the previous concept may give some hints why they may have wanted to change their reactor […]
Who is Charlie Clingen?
Here is some information about Charles Clingen.
Thanks!
Thanks, John, for replying. I had forgotten about that mini-autobiography I wrote for your online Category Theory Course. Hope that is satisfactory for Sara.