Nuclear Britain
Posted by Chris Vernon on January 15, 2008 - 10:45am in The Oil Drum: Europe
Topic: Alternative energy
Tags: electricity, nuclear, united kingdom, uranium [list all tags]
The nameplate capacity of the UK nuclear fleet, stacked, from the peak capacity in the late nineties and following the published decommission schedule. Three life extensions are shown in red. Source: British Energy & Nuclear Decommissioning Agency
Background
The UK pioneered civilian nuclear power generation with a young Queen Elizabeth II opening the world's first public grid connected power station on 17th October 1956. Calder Hall's four 50MW reactors were finally shutdown in 2003 after generating 70TWh of electricity and more than two tonnes of weapons-grade plutonium over its 47 years of operation. Astonishingly by today's standards, Calder Hall was designed, constructed and commissioned in just three and a half years following Prime Minister Winston Churchill's order in 1952. Amazing how quickly you can get things done when you don't know what you're doing!Whilst this old power plant's electricity contribution was modest in the grand scheme of things its recent closure is representative of the fate facing the rest of the fleet in the near future.
Oldbury Nuclear Power Station
This photo is my local nuclear power station, Oldbury on the East bank of the Severn Estuary, 15 miles north of Bristol. Opened in 1968 it is scheduled to close during 2008 with the loss of 435MW from its two reactors.
An important thing to remember about nuclear power plants is that they share a lot in common with fossil fuel plants. They generate electricity by using the heat given off by radioactive fission to raise steam which is then used in normal steam turbines. In the photo the turbine building can be seen in front of the two reactors. Each of the reactors at Oldbury for example generate 815MW of thermal output, of which only some 218MW emerges as electricity indicating a thermal efficiency of 27%. This is an important point to be aware of when making primary energy comparisons. The primary, chemical, energy contained in coal, oil or gas should not be compared directly with the electrical output from a nuclear power station without first accounting for this thermal efficiency, something to remember when looking at how many nuclear power stations it takes to replace fossil fuel depletion.
The British nuclear fleet is now split into two categories. There are the nuclear legacy sites which are now under the control of the Nuclear Decommissioning Agency (NDA) and the eight modern sites which remain under the control of British Energy. The NDA have responsibility for 20 civil nuclear sites including decommissioned research facilities, fuel plants, fusion research, storage sites and the Magnox fleet. 15 of those sites are managed by British Nuclear Group and Westinghouse under NDA contracts. These were until recently both British Nuclear Fuels (BNFL) group companies but Westinghouse was recently sold to the Toshiba Corporation to the surprise of many outsiders considering the then uncertainly surrounding the nuclear industry in the UK.
Magnox Fleet
The nameplate capacity of the UK Magnox nuclear fleet, stacked, following their construction and decommission schedule.
Position mouse pointer over the chart to reveal power station breakdown.
Magnox is short for Magnesium non-oxidising and refers to the alloy of magnesium and aluminium used as a cladding for unenriched uranium metal fuel. The design was initially created to produce weapons-grade plutonium but later larger reactors were exclusively used for civilian electricity generation. It is said that North Korea used the Magnox design developed from the declassified blueprints of Calder Hall to generate plutonium for their nuclear weapons programme.
The decommission schedule is almost complete now with the end of the Magnox era clearly in sight, due significantly to the fact that the fuel assembly corrodes in water, limiting storage and the required fuel reprocessing plant is also at end of life. The decommissioning project is extremely complex since no consideration was given to decommissioning during the design and build in the 50's and 60's. This was a phase of nuclear R&D resulting in many one-off designs and very poor records of site inventories, how the site was used and in some cases a lack of design drawings! Such problems are not expected when the British Energy sites are decommissioned. A wealth of information is available at the above linked websites.
| Build Date | Capacity MW | Published Lifetime | Decommission Age | |
| Hunterston A | 1964 | 360 | 1989 | 25 |
| Berkeley | 1962 | 276 | 1989 | 27 |
| Trawsfynydd | 1965 | 390 | 1991 | 26 |
| Hinkley Point A | 1965 | 470 | 2000 | 35 |
| Bradwell | 1962 | 242 | 2002 | 40 |
| Calder Hall | 1956 | 194 | 2003 | 47 |
| Chapelcross | 1959 | 196 | 2005 | 46 |
| Sizewell A | 1966 | 420 | 2006 | 40 |
| Dungeness A | 1965 | 450 | 2006 | 41 |
| Oldbury | 1967 | 434 | 2008 | 41 |
| Wylfa | 1971 | 980 | 2010 | 39 |
The nameplate capacity and life of the UK Magnox nuclear fleet.
The Magnox fleet
All the power stations are built approximately at sea-level on the coast, with the exception of Trawsfynydd located on lake in Wales. The long-term decommission schedule is unclear but over 100 years is not unreasonable. The Nuclear Decommissioning Authority currently have plans for 125 years. Any new build will most likely be on existing sites therefore maintaining operational power stations until at least 2080 followed by their decommission process. Placing such long lasting and potentially vulnerable assets at sea-level, given the current uncertainly surrounding ice-sheet melt sounds risky to me. If the main reason for reusing existing sites is public pressure this seems an unreasonable risk.
AGR and PWR Fleet
The nameplate capacity of the UK AGR and PWR nuclear fleet, stacked, following their construction and decommission schedule.
Position mouse pointer over the chart to reveal power station breakdown.
Whilst the Magnox fleet's time has all but passed the future of the more modern British Energy sites comprising of seven advanced gas-cooled reactor (AGR) power stations and one pressurised water reactor (PWR) is not quite as certain. British Energy was privatised in 1996 with what was then seen as the commercially viable British nuclear interests. The private venture didn’t turn out to be particularly viable though with the government forced to invest £3bn in 2004, assume liabilities worth between £150m and £200m p.a. over the next ten years and reclassify the company as a public body. The 1996 privatisation had netted just £2.1 billion.
The red areas in the chart above illustrate the recently granted extensions. Dungeness B's operation was extended by 10 years from 2008 to 2018 and more recently Hunterston B and Hinkley Point B were extended by 5 years from 2011 to 2016. The extension of the latter two, as well as only being 5 years came with a caveat. The output has been reduced to 70% of full power. The three that have been granted extensions were, by no coincidence I'm sure, the first three to face decommission in 2008, 2011 and 2011 respectively. Without any other information to hand it is probably reasonable to assume similar modest extension to the remaining four - something that might become critical as we will see later.
| Build Date | Capacity MW | Published Lifetime | Decommission Age | |
| Hinkley Point B | 1976 | 1220 | 2016 | 40 |
| Hunterston B | 1976 | 1190 | 2016 | 40 |
| Hartlepool | 1983 | 1210 | 2014 | 31 |
| Heysham 1 | 1983 | 1150 | 2014 | 31 |
| Dungeness B | 1983 | 1110 | 2018 | 35 |
| Heysham 2 | 1988 | 1250 | 2023 | 35 |
| Torness | 1988 | 1250 | 2023 | 35 |
| Sizewell B | 1995 | 1188 | 2035 | 40 |
The nameplate capacity and life of the UK AGR and PWR nuclear fleet. Includes extensions (Dungeness B 10yrs, Hinkley Point B 5yrs, Hunterston B 5yrs)
The AGR and PWR fleet
Again, sea level, coastal locations.
The UK Nuclear Fleet
The nameplate capacity of the UK nuclear fleet, stacked, following their construction and decommission schedule.
Position mouse pointer over the chart to reveal power station breakdown.
Combining all the power stations produces the above chart.
One interesting observation is that if we sum the annual nameplate capacity from the grid connection of Calder Hall in 1956 to 2007 to produce a total energy figure of 389 GWyears and similarly sum the capacity from 2008 to the decommission of Sizewell B in 2035 to produce 123 GWyears we can say we have depleted 76% of our installed capacity. This percentage assumes a constant load factor however the situation is probably worse as the load factor is decreasing as the infrastructure reaches end of life. The UK’s installed nuclear resource is as depleted as our North Sea oil and gas resource!
Load Factor
In 2006, in nameplate capacity terms the nuclear fleet represented 15% (DUKES 5.7) of grid connected capacity, this is slightly misleading as the load factors of generators vary with nuclear being higher than average, 69.3% opposed to 52.8% for the average load factor over all plant (DUKES 5.10). Despite its relatively low nameplate proportion nuclear managed to generate 19% (DUKES 5.1) of the UK’s electricity in 2006. As the fleet ages though, this high load factor can not be assumed to remain. The chart below shows how the nuclear fleet's load factor has declined over the last decade after a string of technical problems reduced the operation hours.
Load factor of the UK nuclear fleet. Generated by dividing the nameplate capacity by the annual output.
I have no explanation for the low load factor in the late 70s and 80s. I can hypothesise that during this period the new AGRs were commissioned (two in ’76, three in ’83 and two in ’88) and that in the first few years, during their commissioning they were operating at significantly less than optimal load factors for tests and observations.
The data for 2007 is not available yet but given the increased level of closure last year I can only assume the figure will be significant lower, low 60s I expect. The power derating of the extended AGRs above is not the same as reducing load factor but is analogous in that less electricity will be produced in the future than the nameplate capacity would suggest.
Looking forward, assuming the current load factor of 69% can be maintained the output of the existing fleet will decline as shown below. Remember the 2006 data point was only 19% of the total supply.
UK nuclear output, forecast based on decommission schedule and 69% load factor.
New Nuclear Build
On Thursday 10th January 2006 the widely anticipated announcement came, the green light for new nuclear build in the UK. Business Secretary John Hutton announced to MPs:"The Government believes it is in the public interest that new nuclear power stations should have a role to play in this country's future energy mix alongside other low-carbon sources, that it would be in the public interest to allow energy companies the option of investing in new nuclear power stations and that the Government should take active steps to open up the way to the construction of new nuclear power stations."It has taken a long time and two consultations to reach this decision and it is important to note that this isn't the Government ordering power stations, they will be built with private money, Hutton confirming there would be no subsidies except in event of emergency at a nuclear plant."It will be for energy companies to fund, develop and build new nuclear power stations in the UK, including meeting the full costs of decommissioning and their full share of waste management costs,"
This 6 minute video package was broadcast by BBC's Newsnight programme on Tuesday 8th January 2008. It provides a good background and touches on many of the main points.
The clip reports the Government's consultation as saying even if the decision to build new power stations was taken today, would be 8 years before construction would begin, going on to add construction would take an optimistic 5 years meaning new power stations could not be online before 2021.
EDF Energy anticipated this decision and in September of 2007 submitted the plans for their 1.6GW EPR (Evolutionary Power Reactor) power station to the UK regulators for design assessment ( Press Release). Detailed information on this design is available from the EDF/AREVA website: www.epr-reactor.co.uk. This is the same design as is being built in Finland at Olkiluoto and in France at Flamanville.
The Finland build is the first one and has had some problems. Initially it was meant to cost 3.7bn euro and be complete in 2009, construction started in 2004. Since then there has been a 2 year slip and the cost increased by 1.5bn euros. So we're looking at 7 year build time and 5.2bn euro (£3.9bn).
What if the UK does manage to create the environment needed for EDF to build? Newsnight's 2021 figure assumed 5 years. If there's one thing that the UK doesn't have a good reputation for it's building large capital projects on schedule. 5 years is likely too optimistic, lets say 7 years but also cut a couple of years off the planning/regulatory approval stage bringing us back to 2021. Let's order 4.
The chart below shows what 4 new 1.6GW EPRs in 2021 do for the UK fleet. A sizeable gap remains and why some are calling the decision of new build too little, too late. The new capacity does not come online soon enough. However, Heysham 1 and Hartlepool have not yet been granted extensions, if like the three AGRs before them they are also granted extensions the gap closes up considerably. Position your mouse pointer over the chart to reveal the impact.
The nameplate capacity of the UK nuclear fleet, stacked, following their construction and decommission schedule and including 4 hypothetical 1.6GW EPRs in 2021.
Position mouse pointer over the chart to reveal impact of 6 year extensions to Heysham 1 and Hartlepool.
The extensions I've hypothetically added to Heysham 1 and Hartlepool are 6 years and derated to 70%, I don't think this is unreasonable and it does make a real difference. A sizeable gap still remains, capacity stands at a minimum of 5.3GW in 2019 and 2021, down from 10.9GW in 2008 representing a loss of 5.6GW. I think this is the best realistic scenario for future nuclear output (I don't think bringing on new generation before 2021 is realistic) so in that sense the decision has come too late - if the goal is to maintain >10GW of nuclear capacity. Of course this isn't a universal goal and some would be quite happy to see the back of nuclear altogether but this article is only considering the energy contribution of the nuclear fleet.
John Hutton said in his speech that he hoped the first new reactors would be online by 2018. I'm of the opinion he's basing that hope more on the nuclear cliff graph than realistic analysis of how long it will actually take. He needs the first one in 2018. If it's taken this long to get this far, how long is it going to take to (a) choose a design and (b) create the commercial environment the manufactures will demand?
A loss of 5.6GW generating capacity doesn't sound awful until we consider the background against which it is likely to occur. UK gas production will be almost over by the end of the next decade leaving the country reliant on imports from Norway, Russia and beyond. This raises serious question marks over the long term viability of the 36% (2006 DUKES 5.1) electricity the country currently generates from gas. In addition to that approximately one third of the existing coal fleet is scheduled to close under the EU Large Combustion Plant Directive. In times of hardship EU directives will be the first thing to ignore but even the coal supply is questionable as the UK imports most of its coal and is now competing in an increasingly competitive market.
In 2006 the UK generated 394 TWh of electricity - what will the country generate in 2020?
Previously on The Oil Drum
Daddy, will the lights be on at Christmas?Offshore Wind
The European Gas Market
UK Energy Security
Energy: the fundamental unseriousness of Gordon Brown
CO2 capture and storage: The economic costs
Excellent and informative piece. Thank you very much.
It's really excellent.
But you can improve it in one way. You gave Sizewell B a 40 year life. But we aren't talking about a crappy old gas reactor from the 70's, so you could well increase the lifespan by 20 years, to 2055.
The scheduled decommission date is 2035 - I expect you're right and a significant extension will be possible. However our problems are sooner than that. The issue is what happens in the second half of the next decade - within 10 years.
And given that nuclear can't make any difference in that timescale, what "Plan B" would? i.e., how do we reduce our short-term future electricity demand (and/or increase supply) without increasing fossil fuel consumption?
This is the big question for the whole world not just the UK. Another question is ... how do we continue to grow our economies with rapidly declining fossil fuel consumption?
After reading the IPCC conclusions on Dangerous Antropogenic Climate Change the world's politicians have decided that CO2 emissions MUST fall to 80% of the 1990 levels by 2050 - however this assumes that the levels of CO2 start falling steadily from NOW.
If the 80% decline is to be met by 2050 then by 2020 we need to have reduced emissions by 30% or so - if we delay the decline then the deadline is not 2050 but some much sooner time - especially if we continue to actually increase emissions in the short term, or if the politicians are too optimistic with their 'best guess' as to what is safe.
So, what is the UK (and the world) to do? ... it looks like the UK can easily meet the 30% targets just by avoiding imports of coal, oil and gas ... a large number of new nukes may be out of the question as well, since they put a lot of CO2 into the air during the construction phase (just at the time we will be struggling to reduce the emissions).
It doesn't look like the UK has a coherent, adequate, timely plan 'A' let alone plan 'B' and we actually have oil, gas, and some coal - unlike most other European countries!
Does that mean we will get dangerous climate change because growth will be more important than climate change? ... if so forget about the nukes! ... we will need the money and declining energy earmarked for them to rebuild all our major coastal cities on higher ground.
Dear Xeroid,
This simple, harsh, and depressing answer to your last rhetorical question, 'Does that mean we will get dangerous climate change because growth will be more important than climate change?' is 'yes, 'we' will choose growth above any other consideration, until the bitter end!'
Anything else is unthinkable and unrealistic, regardless of the consequences. Putting ameliorating climate change would mean reversing, at the very least, as a timid start, the last thirty odd years of Western and now global economic policy, the so-called Reagan-Thatcher 'revolution' which has become the socio-economic paradigm of our age. The presumed foundation of our wealth and prosperity, though the model is now beginning to falter and totter. Such a reversal will not be easy or occure overnight. Too many people, though a minority, have benefitted and have never been richer or more powerful. One is almost talking about a social revolution and the resistance to this type of change will be dedicated, and red in tooth and claw.
The more I understand how the world all hangs together the more I'm sure you are correct, and therefore am basing my strategy on that basis!
That means the oil, gas and coal will not last anything like as long as they could ... no growth in primary energy = no growth in economy!
So, what do I advise my son or grandchildren to help them plan for the future ... their long term outlook is 80 years or so?
Within 10-15 years there will be various of short term fixes that will help alleviate the situation:
1) Electricity and NG imports. AFAIK France is building an EPR reactor on the other side of the channel specifically for exports to the UK
2) Conservation - I expect a huge amount of the electricity currently wasted for non-essential purposes (e.g. using A/C in the British climate) will be foregone once electricity rates double or triple
3) Coal - I don't think the plans of retiring the UK coal fleet will ever materialize, once the seriousness of the situation sinks in
4) Wind will add some help, but I expect its contribution to be much less material than expected, and to reach some point where not a lot more could be added - specifically the decline of NG powered generation will decrease the ability to absorb more wind in the UK grid.
Overall I think it is too early to press the panic button yet, which is not to say that the situation could become very dire. It all depends on the speed UK moves on building the nukes and implementing the measures listed above.
Current projections are based on Business As Usual. If shortages ever happen, IMO you will see how quickly you are able to proceed on things that used to take years. It's human nature to protract problems until they reach a crisis point.
Chris,
I think your information about costs is useful but incomplete. You give an estimate of 3.25 euro/Watt ($4.84/Watt) to build but with a subsidy to cover the risk of a nuclear accident. Do you know if Lloyd's was consulted to determine what the premium would be to cover a plant built on an inland site with a Chernobyl scale accident? Building on the Thames, for example, might run to $0.04-$0.10/kWh I think. Also, do you know if the EROEI was considered in this decision? I suspect that nuclear power can't approach even half of the EROEI of wind and thus would be more expensive.
Thanks,
Chris
Hi Chris (mdsolar),
Your blog on Nuclear EROI is really good. Do you have a reference for the French enrichment numbers that you quote? (only thing I see missing from your great article).
So, essentially, the nuclear EROI values have been skewed by inputs from the cold-war era. H.T. Odum supports your position of low nuke eroi. And I notice that C. Hall also puts the value at the near 10 mark. Without a high eroi, then uranium really will run out by 2050 or so.
The estimate for France is pretty crude since it only uses numbers of reactors. The three reactors used for diffusion are at Tricastin. I see now 59 power plants in 2002 in France. A more careful calculation would include the size of the reactors and the amount of enriched uranium France exports, but since the calculation only looks at enrichment, it should still give an idea. The main point of the post is that even using centrifuges, nuclear power does not compare well with renewable sources. This is shown using industry supplied numbers in the table. I don't think that cold war uranium skews EROEI as much as I originally thought, it should still be above one I now think. But, cold war weapons grade uranium, taken together with actual EROEI numbers that are lower than for coal, makes it painfully obvious that nuclear power is primarily about politics, especially non-proliferation, rather than about energy generation. We may be able to keep it limping along if we use higher quality energy sources for the majority of our energy generation, but increasing its fraction of the whole would be impoverishing. I think there is a risk that even maintaining the current fraction of nuclear power could lead to plants being shut down before the end of their design lifetime owing to lack of fuel. This would tend to reduce EROEI since the energy cost of construction would not be carried over the anticipated period of operation. Shifting the associated finacial risk to pivate investors, as the UK is proposing, is a wise move I think. Proposed federal loan guarantees in the US seem like a problem.
Chris
It's not even numerate. I went through this in the previous thread, but it's worth a repeat just to show the disappointingly dishonest arguments Chris seems to think he's somehow justified in making.
In his blog article Chris use this formula to calculate EROEI:
(1) EROEI = (Net Energy/Ein) + 1
where Net Energy = Eout - Ein
This is where alarm bells should first have started ringing. Why does Chris use a more complicated formula to calculate EROEI when it is easily computed with Eout/Ein? We shall see in a minute when we consider the example given on his blog (my original thought experiment from the other thread). But first let's show that equation (1) is equivalent to EROEI:
EROEI = (Net Energy/Ein) + 1
= (Eout - Ein)/Ein + 1 (step 1)
= (Eout/Ein) - (Ein/Ein) + 1 (step 2)
= (Eout/Ein) - 1 + 1 (step 3)
= Eout/Ein
Thus equation (1) does indeed calculate EROEI and Chris is within his rights to use it.
Now on to the example. We consider a country whose reactors use uranium with an energy equivalent to Eu each year. Their only energy input is for diffusion enrichment which takes half the output electricity of the reactors and hence half the input uranium. In such a situation you might think the EROEI would be 2 (and you'd be right) but Chris calculates a value of 1.5. How does he do this? Here's his formula with all values inputted:
EROEI = (Eu/2)/Eu + 1
For net energy he uses Eout = Eu and Ein = Eu/2 (Eout - Ein = Eu - Eu/2 = Eu/2).
However, the value he uses for Ein in the denominator is Eu, the entire energy value of the uranium used by the reactors, not just that used to power the enrichment process. Thus he is using a different value of Ein in the denominator than in his calculation of net energy in the numerator. As can be seen above in step 2, this means that Ein/Ein does not equal 1 and therefore equation (1) is not equal to EROEI.
I pointed this out to Chris in this post and yet he repeats the same flawed argument here. Either he cannot comprehend simple mathematics or is blatantly attempting to deceive.
I think you need to read the blog again. For net energy I use Eu/2, the energy that can be converted to electricity for use by society. For Ein I use Eu, the energy that is expended. I think you have your ins and outs confused.
Chris
Chris:
And net energy = Eout - Ein, so if Eout = Eu then your Ein must logically be Eu/2.
Chris:
So you admit your Ein's are inconsistent leading to an incorrect calculation of EROEI?
Seriously, Chris, this is getting ridiculous. I'm a proponent of nuclear power, believing it vitally necessary to help us cope with climate change and fossil fuel depletion. However, I can honestly say that in all the words I've written about nuclear and renewables I've never knowingly tried to deceive anyone with a lie. Anyone with even small mathematical ability can see that your calculation of EROEI is flawed, designed to produce an artificially low value that tells you nothing about its energetic sustainability. Did you really expect to get away with this on TOD where there are lots of people far brighter than either of us?
Your really are confusing yourself I think. Ein is Eu, not Eout. If Eout were Eu, then EROEI(thermal)=1 not 1.5. Obviously Eout is Eu/2 to be converted to electricity for use by society plus Eu to be used for the process next year, just as you originally proposed. Thus, EROEI(thermal)=1.5. If you take Eout to be Eu then you have not bothered to enrich any uranium.
Chris
If Eout = Eu/2 and Ein = Eu then
Net Energy = Eout - Ein = Eu/2 - Eu = -Eu/2
and
EROEI = Eout/Ein = (Eu/2)/Eu = 1/2
The reason we get these nonsensical values is that you include all the energy of the uranium as an input. If we were talking about oil, for example, were you got a 100 barrels back for every one you invested, it would be like pretending that Ein was 100 instead of 1. This is why you use this equation:
EROEI = Net Energy/Ein + 1
in order to hide the fact that you are using different values of Ein to suit your purposes. However, as I've shown above, when doing so, this equation no longer calculates EROEI.
Read what I wrote again. Eout is both the energy going to society and the energy in the enriched uranium to be used during the next refueling. The net energy is what is available to convert to electricity for use by society. You seem to be confusing yourself by not reading carefully.
Chris
Chris:
I've read everything you've written very carefully, Chris, and the fact that you can't admit your mistake and stop trying to deceive is increasingly painful.
EROEI = Eout/Ein
and also
EROEI = Net Energy/Ein + 1
If you are correct, Chris, then you should be able to explicitly state your Eout and Ein and get the same value of EROEI using either equation. We both know you can't do that.
Better read again. I've stated what Eout in both my last two posts since this seems to be where you are getting stuck. Divide that by Eu and you'll get 1.5. I thought your example would give two before converting to electricity by analogy with oil but it doesn't. I tried rather hard to make it come out to two because I was somewhat surprised. Perhaps it would help you to try to carry out the calculation yourself.
Chris
Chris:
Very well.
Thought Experiment
A country has nuclear reactors and uses half the output to enrich the uranium for next year. The other half is used to power factories, homes, etc. There is no other energy input but that used to power the enrichment process. The energy used to mine the uranium, build the reactors, deal with the waste, etc, is assumed to be zero.
Energy Content of Uranium = Eout = Eu
Energy required to Enrich uranium = Ein = Eu/2
Net Energy = Eu - Eu/2 = Eu/2
EROEI = Net Energy/Ein + 1 = (Eu/2)/(Eu/2) + 1 = 1 + 1 = 2
Thus giving the obviously correct answer. This would be the same for oil, gas, coal, etc if half the output were used to mine/refine the input. It is no different for uranium.
This is helpful because it shows where you are confused. The energy expended is obviously Eu rather than Eu/2. The energy produced is also clearly Eu in enriched uranium plus Eu/2 in thermal energy that can be used elsewhere. You are undercounting both the input and the output. The net energy is indeed Eu/2, but you must calculate this as (Eu+Eu/2)-Eu rather than the way you have done. You don't get that net thermal energy unless you use the whole system. Confining your analysis to half the system is what is steering you wrong.
Chris
And this is helpful in showing where you are 'confused'.
Chris:
No, the energy produced by the inputted uranium Eu is Eu/2 to enrich next years uranium, Eu/2 thermal energy to be used elsewhere, and Eu embodied in next years uranium. This sums to 2Eu, hence net energy is Eu and EROEI = Eu/Eu + 1 = 2.
Your mistake, Chris, is in ignoring the energy used to enrich the uranium as an output. You seem to be conflating net energy and gross energy. You do have a penchant for apples/oranges comparisons. They're seldom valid, you know.
Before you were undercounting, but now you are overcounting. The energy used to enrich uranium is used up. All you get is the enriched uranium as an output. You are kind of wanting to keep your cake and eat it at the same time. Hope this clears things up for you now.
Chris
Oh things are now very clear. Let's recap:
The Mdsolar Patented Way to Calculate Nuclear EROEI
1) Take as Ein all uranium used Eu, not just that for enrichment.
2) Eout is now the energy in next years enriched uranium, Eu, plus the thermal energy not used for enrichment.
3) EROEI can now be calculated with Net Energy/Ein + 1.
This accurately describes the method you use to calculate EROEI in my original thought experiment, in which half the reactors were powering the enrichment process, leading to a value of 1.5.
Okay, now the fun part: we vary the original assumption of the thought experiment and see what happens.
Enrichment uses only 1/10th reactors output
Ein must still be Eu
Eout is now the energy is the enriched uranium, Eu, plus the thermal energy not used for enrichment, 9Eu/10.
Therefore Net Energy = 9Eu/10
and EROEI = Net Energy/Ein + 1 = (9Eu/10)/Eu + 1 = 1.9
Hmmm, very strange. We've reduced the power needed to enrich the uranium by 5 times, and yet our mdsolar approved EROEI has only increased from 1.5 to 1.9.
Okay, let's really go mad:
Enrichment uses only 1/1000th reactors output
Ein = Eu (of course!!)
Eout = Eu + 999Eu/1000
Net Energy = Eout - Ein = 999Eu/1000
Therefore EROEI = Net Energy/Ein + 1 = 1.999
Curiouser and curiouser. Only one fivehundredth of the original energy is used for enrichment but our EROEI still hasn't breached 2.
Hmm, wonder what would happen in the case were no energy at all was used in the nuclear lifecycle. Surely Chris's foolproof method will give us an infinity for EROEI, as it must. Let's see:
Enrichment uses none of reactors output
Ein = Eu
Eout = Eu + Eu = 2Eu
Net Energy = Eout - Ein = Eu
Therefore EROEI = Net Energy/Ein + 1 = 2
That's right, Chris, in the event were there are no energy inputs your method calculates an EROEI of 2. May I humbly suggest you are mistaken.
Reductio ad absurdum. I was puzzled by that result. Thanks.
Chris
And if I weren't so dense that I actually read what you wrote rather than assuming, we'd have got to this point ages ago.
I've corrected the blog and added an acknowledgement as a comment. I think you'll agree that the thermal/actual terms help to clarify what we were discussing in a previous thread, but let me know it you disagree.
Chris
mdsolar:
I know you'll be just delighted to find out I have other problems with the blog entry, Chris. I'll concentrate on the next one.
We've finally come to an agreement that in the thought experiment were half a country's reactors are used to enrich their uranium - and there are no other inputs - then EROEI = 2 in terms of primary energy input to output.
You then go on to calculate EROEI in terms of electrical output to primary energy input using this formula:
EROEI = (0.3*(Eu/2))/Eu/2) + 1 = 1.3
However, this is incorrect. The point I was erroneously making in our discussion above about inconsistent Ein's is ironically valid when discussing this calculation. Essentially you're multiplying the net energy by 0.3, which leads to a different Ein in the numerator than in the denominator. If we multiply the equation out we shall see that it does not equal the traditional definition of EROEI:
If EROEI = (0.3*Net Energy)/Ein + 1
then EROEI = (0.3Eout - 0.3Ein)/Ein + 1 = 0.3Eout/Ein - 0.3 + 1 = 0.3Eout/Ein + 0.7
If your equation was truly calculating EROEI(electric) then it would simplify to 0.3Eout/Ein. Also, reductio ad absurdum, if Eout = 0, EROEI = 0.7 not zero.
The actual calculation of EROEI(electric) is:
(Using a factor of 1/3 to account for conversion to electricity and make the maths prettier)
Net Energy = Eout - Ein = (1/3)*Eu - Eu/2 = Eu/3 - Eu/2 = -Eu/6
Therefore EROEI = Net Energy/Ein + 1 = (-Eu/6)/(Eu/2) + 1 = -1/3 + 1 = 2/3
Which brings us right back to the motivation for the original thought experiment: to show that EROEI(electric) is a poor measure of energetic sustainability, giving a value of < 1 for a process that produces an energy profit.
I want to consider two cases. The issue we are dealing with here is scope because I want to compare what it takes to run an electric toaster given EROEIs in various forms. So, how do we handle scope?
Let us say we have an oil well with EROEI(well head) =2 and a refinery at some distance. The oil company has two choices on how to transport the oil. It can use a sail boat with the strange property that 70% of the oil transported during the journey evaporates, or it can use a tanker that burns 70% of the oil. To calculate EROEI at the refinery terminal rather than the well head the way I am doing it, I want the evaporation case so net energy is 0.3*(net energy at the well head) and I get EROEI(terminal)=0.3*1/1+1=1.3. You object to this because you want to retain the difference in the net energy calculation and apply the conversion also to oil that was used to pump I think. In the case of the tanker I think we would both say that Eout=2 and Ein=1.7 so that EROEI=1.176. Net energy is the same in both cases, 0.3, but in one case we just lost the oil while in the second case we used it so that it affects the denominator.
Based on this, we might account for waste in conversion as though that energy were actually used as an input. So, if X is a reported thermal EROEI and Y is the conversion efficiency then 1-Y is the fractional loss which is applied to the original net energy. This is (X-1)*Ein. So, we write (1-Y)*(X-1)*Ein as the additional term for the denominator. X=Eout/Ein and without loss of generality we can set Ein=1 so that Eout=X. This then gives:
X'=X/(1+(1-Y)*(X-1))
Where X' is the desired effective EROEI for X greater than 1.
If Y=0 then X'=1. If Y=1 then X'=X. If Y=0.5 and X=1.05 then X'=1.024. If X=10 and Y=0.5 then X'=1.8 and at higher X we approach 2, just as you pointed out to me earlier. In the case of actually burning the oil, this would make sense since we are seeing the limiting case of the tanker using half the oil it transports. When Y=0.3 then X' approaches 1.43 (1/(1-y)).
But this is not really sensible when we are considering losses because we do expect improvements in X to lead to improvements in X' that are quasi-linear.
So, I think that we need to work on the numerator.
I am indeed multiplying net energy by 0.3, so now X'=Y*(X-1)+1. If X=1 then X'=1, if X=0 the X'=0, If Y=0, then X'=1 and if Y=1 then X'=X. If X=10 and Y=0.5 then X'=5.5. Now, I think you criticism is not so strong because I am looking for a way to carry forward from the net energy, and what it's composition was beforehand does not seem to me to be all that important. It is the net energy which undergoes a loss. But I do notice is that taking X to the limit gives an asymptotic behavior with successively lower X' going to a limit of 5 for Y=0.5 and this is not transmitting improve initial EROEI.
So, I think that there is a way to compare thermal sources with those that provide electricity directly and it looks something like 0.3*Eout/Ein in its behavior, but I'm not sure yet what it is.
Chris
Oh dear, you have constructed a house of cards, Chris. You concoct this oil analogy and consider it to be essentially equivalent to our earlier uranium thought experiment, only it isn't. In our earlier discussion all the uranium - i.e. the gross Eu - was converted to electricity at an efficiency of 0.3. In this example only the net energy is subject to conversion.
Also the EROEI in your example is 1.3 regardless of whether the tanker or sail boat is used. Why?
Beginning of Process:
Ein = 1 unit of oil
End of Process:
Eout = 1 unit of oil at well head + 0.3 units at terminal = 1.3
Therefore EROEI = Eout/Ein = 1.3/1 = 1.3
This is true for both transport methods.