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Please Critique: Rough EROEI on nuclear enrichment processing in conventional plants

Just check out the file for now, folks.

Add comments as you come up with them.

Sheila Newman and Ilan Goldman


If this is a typical EROI study, they have left out the cost of commerce and the energy exxpenses of the workers that would not have occurred if they had not been employed in this industry. Therefore, the EROI is probably much lower than this very low EROI. I guess we can reject conventional plants out of hand.

Sheila and Ilan, Accepting the limited scope of this result, it still could benefit from substantial notes to explain the spreadsheet and how each number was derived. I see two columns, but no header atop the columns to explain what we are comparing. Based on the note at the bottom, I can guess it might be comparing gaseous diffusion vs. centrifuge enrichment processes. If that's the case, then the centrifuge process doesn't look too bad - but that's of course partly a consequence of the limited scope of the analysis. Do you plan to do more on this topic? I'm working with a collaborative of multiple universities and experts on ERoEI and a world energy modeling project is just getting started, so this will be of interest going forward. - Dick Lawrence ASPO-USA

The report by ISA of University of Sydney, "Life Cycle Energy Balance and Greenhouse Gas Emissions of Nuclear Energy in Australia" [ Download 2.75 MB PDF ] includes a full cycle energy analysis.
Their spreadsheet is available at

They have data for diffusion and centrifuge technology and they assume a mix of 30:70 for their base case, which represents the current state in the industry.

Diffussion:37,225 GWh(el) + 3,598 GWh(th) => 118,995 GWh
Centrifuge: 4,461 + 4,022 => 17,851
30:70 14,290 + 3,895 => 48,194

So ISA shows the electricity used in diffussion is 8.3 times that used in centrifuge, whereas your spreadsheet shows a ratio of 41.

Diffussion is clearly very inefficient technology and presumably will be phased out over time.

If only centrifuge technology is considered, the enrichment energy (electrical + thermal) is 12.6% of the full nuclear cycle's energy investment. The ERoEI of the full cycle is then 6.8 for ISA's base case.

Changing the Load factor from a very optimistic 85% to the world lifetime average load factor of 71.4%, and changing the uranium ore grade from the current 0.15% to the average of all Australian ores of 0.045%, the full cycle ERoEI drops to 5.3

A 1.3-GW power plant with 90 percent utilization produces 1.17 GW, i.e. 1.17 GJ per second, and the "Electricity Output" cell value, 1537380 GJ, is the amount it would produce in half a month.

(A year is 31,556,926 seconds. Dividing by 24 and multiplying by 1.17 we get 1538400. In a 365-day year, 31,536,000 s, the average half-month is 1,314,000 seconds, and this times 1.17 reproduces the "Electricity Output" cell value exactly.)

However, the "SWU (Separative Work Units)" cell contains 120000, and this seems closer to the annual separative work requirement of a nuclear power station that averages 1.17 GW*. The interval should be noted, and should be the same for both cells if they are to be compared.

*-- not to forget CANDU plants, about which there is nothing unconventional and whose uranium separative work requirement per year is zero.

I see both the cells in the "Electricity Output" row contain "*3600*365" in their formulae.

This suggests the factor-of-24 error is due not to mixing up years and half-months, but rather due to mixing up hours and days. There are 86400 seconds in a day, not 3600.

Sheila Newman, population sociologist
home page

Hi Tom,

Would you be able to rough in the cost of commerce and the energy expenses of the workers and deduct it?

Feel free to rough in your own theory as well. Although I have read it, since I'm trying to develop a working understanding of the basics of the various nuclear options, I'm not at this point taking a whole of society approach, but intend to later.

Hope that isn't too incomprehensible of me.


Sheila Newman, population sociologist
home page

Hi Dick,

Yes, we do plan doing more on this topic.
We are doing it in an ad hoc manner, as we want to compare notes, and here, for instance, to get sums terms etc critiqued.

I am interested in your collaborative of universities etc. This particular research of mine (basic as it is) which Ilan is helping with, is towards working up a new section on nuclear, either for a second edition of The Final Energy Crisis, or maybe for another book of articles on Energy and Post Oil Peak. Modelling energy really interests me, especially for particular regions/countries etc reflecting what they already have to work with, but a world energy project is of course of great energy.

I agree that the centrifuge process doesn't look too bad and that the reason is partly a consequence of the limited scope of the analysis.

Tom Wayburn will hopefully develop his comments but would you care to comment on what you think should be taken into account?

I have added those headers. You were right as to what they signified. I should probably synthesise the Wikipedia info more accessibly but won't spend time on it right away.

Glad you posted here, Dick.

Sheila N

Sheila Newman, population sociologist
home page

Hi Dave,

Thanks for this stuff, which I have downloaded to read. I think what Ilan and I are doing here is sort of building up basic models from scratch, one or two building blocks at a time. Possibly only when we have done a bit of this will we be able to evaluate the Melb Univ study.

I believe that Mike Stasse had a relevant comment to make about the Melbourne Univ study - that it anticipated a lot more fossil fuel use, i.e. a business as usual PLUS nuclear.

Is that so in your opinion?

Ilan wonders why certain technologies are chosen by some countries and others choose others. What was the reason for the assumption of the two different mixes in the Melbourne Univ study?

Sheila Newman, population sociologist
home page

Hi GRL Cowan boron combustion fan,

Thank you. We have now fixed the seconds and days confusion :-)

Thank you for assisting our humble beginnings.

We had not heard of the CANDO technology. Ilan has read about it now but we haven't had time to discuss it.

I will now go to your page and have a look.

What is your opinion as to why different technologies receive preference in different countries? Is there no outstanding technology?

Thanks very much.

Sheila N

The ISA team assumed a 3% per annum increase in our energy requirements, which over a long term can get really out of hand, and was looking at a scenario with a quarter being nuclear by 2050. These scenarios are totally unrealistic, of course. If the price of oil goes through the roof, the US economy will collapse, followed by everybody else, and no nuclear power stations will be built during a world depression.

I think diffusion technology was invented first and used to make weapons grade uranium in large quantities. It now makes 40% (and falling) of all power reactor fuel. Centrifuges are much more energy efficient and currently have 60% of the enriching market.

There are other methods of enrichment and background in the ISA report. Here are some clips:

3.4 Enrichment

At its natural concentration of 0.7%, 235U92 can be used as a reactor fuel only in
particular reactor types (heavy-water reactors and high-temperature reactors).

In order to be able to maintain a nuclear chain reaction in typical light water reactors, the
concentration of 235U92 in the uranium isotope mix has to be increased to about 3%.

At present there exist a range of enrichment methods using UF6 as feed. Since uranium
isotopes do not differ in their chemical behaviour, enrichment techniques exploit their
mass difference as a means for separating them [25].

These methods are:
â€¢ Gaseous diffusion: The heavier 238U92 isotope diffuses more slowly than the
lighter 235U92 : Enrichment from 0.7% to 3% 235U92 requires in the order of
1,000 consecutive separation cascades. In 2002, 40% of all enrichment plant
used gaseous diffusion (mostly France and USA). This percentage is
decreasing in favour of the centrifuge method.

â€¢ Gas centrifuge: The partial pressure of two gases (contained as a gas mixture
in a rotating cylinder) depends on their masses. Centrifugal forces cause a
radial concentration gradient, with the heavier isotope concentrated outside,
and the lighter isotope concentrated inside. Enrichment from 0.7% to 3% 235U92
requires in the order of 10 consecutive separation cascades. In 2002, 60% of
all enrichment plants used the centrifuge method (mostly Russia, Germany,
UK, Netherlands, China, and Japan).

â€¢ Electromagnetic Isotope Separation (EMIS): Uses the magnetic separation
principle of a mass spectrometer, albeit at a larger scale. Used for building the
Hiroshima bomb, and in Iraqâ€™s nuclear program, but now outdated.

â€¢ Aerodynamic (jet nozzle) method: Exploits the same physical principle as the
gas centrifuge, but creates a rotating gas mixture by injection into a circular jet.
Demonstration plants built in Brazil and South Africa.

â€¢ Laser: The energy spectra, and therefore the ionisation energies of different
isotopes depend on their masses. Using mono-energetic laser beams, one
isotope can be preferentially ionised, and filtered out using an electrostatic

At the end of this stage, the enriched UF6 is converted into uranium oxide (UO2).

The energy needed for enrichment is partly dependent on the incremental enrichment
factor for one cascade, which in turn determines the number of cascades necessary to
achieve enrichment to around 3%.

Gaseous diffusion needs more cascades than the gas centrifuges, and additionally
requires the energy-intensive compression of UF6 at the entry point of each cascade (Table 3.4).

Gas centrifuges only require electrical energy for the rotation of the cylinders,
and some heat in order to maintain an axial convection of the UF6.

Atomic laser techniques require the normally metallic uranium
to be evaporated (using considerable heat energy), and then transferred into a vacuum,
so that ions can be electrostatically filtered [25].

The Australian laser technique is based on molecular rather than atomic laser separation.
Instead of having to maintain uranium atoms in a hot gas, the technique uses
the already gaseous UF6, and preferentially excites UF6 molecules.6

[ ... ]

The two tables above require an explanation of the unit SWU. Amounts of enriched
uranium are usually expressed as Separative Work Units (for example tonne SWU).8
There is a trade-off between the amount of natural uranium feed and the number of
SWUs needed to produce enriched uranium.

For example: in order to produce 10kg of
uranium at 4.5% 235U92 concentration while allowing a tails assay of 0.3% requires 100
kg of natural uranium and 62 SWU. Asking for the tails to have only 0.2% assay
limits the amount of natural uranium needed to 83 kg, but it also increases the
separative work to 76 SWU.

Hence, the optimal (tails assay) compromise between
uranium feed and separative work depends on the price of natural uranium versus the
cost of enrichment operating inputs. During times of cheap uranium, an enrichment
plant operator will probably choose to allow a higher 235U92 tails assay, and vice versa.

In terms of the energy balance of the nuclear fuel cycle this means that lower tails
assays mean that less energy is spent on mining, milling and conversion, and more on
enrichment, and vice versa ([17] pp. 26-36 & 43).

Storm van Leeuwen and Smith [18] summarise studies undertaken between 1974 and
2003, averaging 2,600 kWh/SWU for gas diffusion, and 290 kWh/SWU for gas
centrifuges.9 These values agree well with most of the additional references (Table

Some designers apparently have said, why not both? -- Magnox, RBMK. As far as I know none of these designs ever actually contributed plutonium to their countries' bomb collections, and all have since fallen by the wayside, also, as power producers. Some harder than others (Chernobyl was an RBMK).

There is a reactor type in which ordinary water boils right around the fuel rods, and the genesis of this type is obscure to me. It is of course known as the BWR, the Boiling Water Reactor. The world has, IIRC, something like 150 of them, and their number is increasing.

If you raise the rate of water injection into them, the boiling zone briefly moves higher up the rods, but this means there is more water around them, so power increases until the zone moves back down. So these reactors' power levels can be adjusted fairly quickly when demand changes, or as nuclear people say, they can load-follow.

The PWR was designed to produce motive power on board submarines*, and had to follow load nimbly there, but when it was adapted to work on shore, somehow that attribute was downgraded. More than half the world's power reactors are PWRs. The P stands for pressurized, which doesn't really distinguish it from the BWR except by implication: the PWR is more pressurized, enough that no boiling occurs. The very hot liquid water exiting the reactor goes through small pipes surrounded by other water elsewhere, and it is this other water that boils.

Like the BWR and PWR, the CANDU was designed strictly for power production, but has no naval ancestry, and might be hard to fit in a narrow hull. Its heavy water is, as with the other types, pressurized, and as with the PWR, pressurized enough that it doesn't boil, so that the class to which the CANDU belongs is the PHWR. (It is not, quite, the only member. There is a German variant and in India there are CANDU clones.)

Heavy water is a small fraction of natural water, but is easier to enrich than uranium. A technical discussion at gives the energy requirement rather vaguely ...

The G-S process was a triumph of engineering stubbornness: it uses large amounts of steam energy (>10 Mg/kg D2O); H2S is highly toxic ...

"Mg" means megagram, i.e. 1,000 kg, so more than 10,000 kg of (ordinary) steam per kg of (heavy) water separated. But how much more? Twice more?

Let's assume twice more. Then a CANDU that starts life with 360 tonnes of heavy water and after 40 years leaves 300 tonnes to its successor --

... designers of thermal reactors have a fundamental choice: either, isotopically enrich the uranium fuel in fissile atoms; or, isotopically enrich the moderator in deuterium. The first option is an ongoing requirement. The second ... is close to being a one-time operation since only around 0.5%/a of the heavy water is lost from a CANDU...

-- will need 7200000000 kg of steam, 7.2 million tonnes, for that initial 360-tonne allotment. But a CANDU that powers a 600-electric-MW steam turbine/dynamo set does so by putting ~1875 thermal MW into steam production. (The very hot heavy water exits the reactor and flows as liquid through pipes surrounded by ordinary water; the latter boils.) That will be around 0.75 tonnes of (ordinary) steam per second.

So the steam-raising a CANDU must do to power the heavy water extraction process for its twin requires its first nine million seconds of full power operation, or thereabouts. Its first ~100 days, out of probably 30 full power years in service; and at the end, most of the heavy water can be bequeathed to a successor. That probably is why Miller isn't very precise.

This has taken some time, but I didn't know this stuff, so I've gained.

* Two years ago, an event showing that it does this very well:

Sheila and James,

I didn't find a URL to Sheila's Excel file although I certainly found it earlier; but, I found the ISA file, which is good enough to use as an example of the problem I am referring to. All of this data is too vast for me in the time I have to study it; but, I can make my points by discussing just one number, for example, the energy costs associated with mining. I would like to understand what is included in that figure.

In, I defined five EROIs (0 - 4) rather than six because I didn't think it was fair to include over-consumption in sectors other than energy due to the payment of a manager or commissar class more than the workers were paid, although, clearly, if workers could live on their salaries, managers could live on a worker's salary too. The five EROIs corresponded to the following investment costs - and, when I say costs, I always mean energy costs, or, rather, the consumption of stockpiles of Helmholtz available energy (U - ToS) produced earlier. U is internal energy; To is the temperature of the coldest reservoir to which heat can be dumped, and S is entropy.

1. EROIo. The energy invested (EIo) is the direct energy overhead of the energy sector.

2. EROI1. EI1 includes, in addition to the direct energy overhead, the indirect energy costs associated with the energy overhead of the manufacturing and transportation portions of the overhead of the energy sector but not the overhead due to commerce.

3. EROI2. EI2 includes, in addition, the overhead due to the activities of commerce in connection with the sale of energy.

4. EROI3. EI3 includes, in addition, the consumption of energy associated with that portion of the salaries paid to the energy sector in excess of what they would have been if no one earned more than the workers do. This is thought to account for over-consumption associated with profit taking in connection with the sale of energy.

5. EROI4. EI4 includes, in addition, the consumption of energy by the workers in the energy sector and the pro-rata shares of the energy expenses of the workers and managers in other sectors insofar as they support the energy sector.

What is included in, for example, the total energy cost of mining? Or, if you wish, enrichment?

Tom Wayburn, Houston, Texas

something like, "Man, I guess I showed what I'm made of, gleefully saying Reject conventional plants out of hand when it was the too-good-to-be-true result that needed to be rejected, not out of hand, but via a minute's arithmetic", you're instead introducing a whole shovelful of new EROIs.

What would your proper course of action be if you were unalterably convinced that nuclear energy had much higher EROI than fossil fuel energy?

"What are the maths of dilution of radioactive material collecting above ground", is the title of Yahoo energy resources post. They're somewhat difficult, and I am not entirely on top of them yet, but I found this pdf document at enlightening.

Its Figure 2, shows how the radioactivity, measured as a proportion of a fission reactor's heat production, varies with time after the reactor is shut down. At the left side the graph cuts off at 200 days post-shutdown, i.e., doesn't show the heat production fraction for earlier times.

If the missing trace from 200 days to zero days were there, it would require a screen or a piece of paper 140 times taller, because at the instant of shutdown the fraction, I happen to know, is 0.07, not 0.0005. But in those early days it's also dropping very fast, so to plot them, we would make the divisions hours or days rather than the hundreds of days in the chart we have, and we would make the vertical units larger. What this, I think, means is that the chart would look the same.

Three equations are plotted; they all give close-enough results. The one that I find useful, although I recognize that it doesn't look very nice, is the one labelled U. & W., Untermyer and Weills:

Delayed power/in-service power =
   0.1*{ (t+10)^(-0.2) - (t + T_0 + 10)^(-0.2) -0.87*[(t + 20000000)^(-0.2) - (t + 20000000 + T_0)^(-0.2)] }

... where 'T_0' is how long the reactor was on and 't' is how long ago it shut down, both in seconds. This can be simplified if we approximate the time the reactor is on. 'T_0', as infinity; this causes the "^(-0.2)" terms that include it to become zero, so we can cross them out:

Delayed power/in-service power =
   0.1*{ (t+10)^(-0.2) - xxxxxxxxxxxxxxxxxxxx -0.87*[(t + 20000000)^(-0.2) - xxxxxxxxxxxxxxxxxxxxxxxxxxx] }

... and get this:

Delayed power/in-service power =
   0.1*{ (t+10)^(-0.2) -0.87*(t + 20000000)^(-0.2) }

What good is that?

Well, we can interpret the post-shutdown time in seconds 't' as the time a man-made radioactive nucleus takes to escape and become diluted. Suppose it takes ten years, i.e. 316 million seconds. Then the delayed power in the escaped, diluted man-made radioactive material is this fraction of the power of the reactor that we suppose to have been running, and leaking, forever:

0.1*{ (316,000,000+10)^(-0.2) -0.87*(316,000,000 + 20,000,000)^(-0.2) }

... and that's:

0.1 * {0.0199555 0.87*0.0197121}

... and that's:


If you are able to put the whole equation, with a finite value for 'T_0', into a spreadsheet you will find that reactors that have run less than forever will have built up slightly less ten-years-delayed leakage. After infinite time, the radioactive nuclei that have escaped to the wild are decaying, and emitting their radiation, exactly as fast as new leakage replaces them; after long but finite times, they are decaying almost as fast, and therefore their activity is building up slowly.

So, for a collection of reactors that over many decades averages 1 trillion watts of total heat production, and have spent fuel pools that are only big enough for ten years' accumulation, and spent fuel older than that is all totally leaked and dispersed, we know the environmental radioactivity due to them will asymptotically approach 0.00028 trillion watts, 280 megawatts. It will forever get closer but never quite there.

To decide whether that can be "put safely into the world system on a dilute basis", you could compare it to the megawattage of radioactivity naturally dilute in, um, nature. That's actually the easy part because the dilute radioactivity in nature doesn't noticeably vary in a human lifetime. I'll return to this if there is some interest.

Dear Boron Combustion fan,
(Original question was actually "What are the maths of dilution of radioactive material collecting above ground" (meaning material which has been brought to the surface and thus artificially increases the ambient above ground radioactivity).

Thanks a lot for your contribution here, which I have just read with interest and mathematical incompetence, interpreting it with the help of James Sinnamon, the website editor, who is now reformatting your contribution.

I will ponder and discuss your response so that I can come up with some useful remarks and I will email it to a few lists in the hope of stimulating some reactions.

So please take this as positive encouragement to continue in this vein.


Sheila N

Dear contributors on the 'rough EROEI' of nuclear,

It may not look as if much was achieved here, but in fact it was enough to set off contacts and networks for other investigations, culminating in a long chapter on nuclear energy which will be published in Sheila Newman (ed), The Final Energy Crisis, (2nd Edition) Pluto Press, UK, 2008, which is due out in September and will cost something like AUD$31. The new book also contains a fascinating analysis by Swiss particle physicist, Michael Dittmar, of the $10 billion euro ITER project for nuclear fusion. There are articles by Colin Campbell and 8 others.

Sheila Newman, population sociologist
home page
Copyright to the author. Please contact if you wish to make substantial reproduction or republish or contact the editor at jaymz@bi