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

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 www.peakoil.org.au/isa.nuclear-calculator.xls 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.

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: • 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. • 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). • 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 Iraq’s nuclear program, but now outdated. • 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. • 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 field. 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 3.4).

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 http://www.cns-snc.ca/Bulletin/A_Miller_Heavy_Water.pdf 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: http://www.spacewar.com/2005/050111170915.f6e1tjsh.html

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 www.rertr.anl.gov 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:

0.0002806.

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. Sincerely, Sheila N