# Peter Lux

## Mass and Volume of Spent Nuclear Fuel

I frequently hear comments about the amount of spent nuclear fuel for a certain amount of energy. One figure is that it is one pound coin for every household per year. Somewhere else I am told it is 0.3mg per KWh. Others will tell you that you could fit it into the Albert Hall – if you could you would soon not have an Albert Hall or a large part of central London.

Anyway, it is not too hard to get an estimate. Please note that this is based on what is really happening at the moment and not on some future sub-critical accelerator driven reactor in the future.

The amount of energy that you get from a given amount of nuclear fuel is called the burnup. The proposed new  EPRs at Hinkley and Sizewell are supposed to have a burnup of 60GWdays per tonne of Uranium. The mass of fuel changes very little so this is the amount of spent fuel that you have at the end.

This is 1,440,000 MWh/TU – we get 1,440,000 Mega Watt Hours per tonne of uranium.
This means that the count of spent Uranium is 6.94x 10-7 Kg(U)/KWh.
However the fuel is actually UO2 so mass of spent fuel is 7.88 x 10-7 Kg(UO2)/KWh
But only about 35% of this is turned into electricity so we have 2.25 x 10-6 Kg(UO2)/KWh – this is  2mg per KWh – so the figure of 0.3mg is a bit out.

The average household in the UK uses about 4170KWh per year (2013 figures). So this will result in 0.0094Kg (9.4g) of spent fuel per household which is about the mass of a pound coin – 9.5g. The actual volume (0.68 pound coins) is slightly smaller since the fuel is denser than the coin.

However, at least initially the spent fuel is kept in their fuel assembly. Each fuel assembly is .214 by .215 by 4.059 meters, has a mass of 657.9 Kg and contains 523.4Kg of UO21.

Therefore each fuel assembly can produce 232,529,173.33 KWh of electricity. Therefore the mass of spent fuel including the assembly now works out at 11.80g per household – 1.24 pound coins. However, the volume has greatly increased and is now 3.90 pound coins.

However, the bare assemblies are still producing a lot of heat and are highly radioactive. They therefore have to be stored in cooling ponds or later on in dry casks. Let us take the example of a dry cask.

Each cask (VSC-24) can hold 24 assemblies. Therefore it would have produced 24 times the energy of a single assembly. Each cask weighs 151T when loaded and is 3.3m in diameter and 5m heigh2. This works out at a mass of 11.88 pound coins per household and a volume of 25.51 pound coins. However, there must be gaps between the casks we have to multiply the volume a certain amount3 – lets say 5 so we get a volume of 127.56 pound coins.

However, the waste must be stored for hundreds of thousands of years. The thin concrete of the dry casks, exposed to the atmosphere would not last that long. There are plans to bury the waste in a geological disposal facility (gdf).

Working out the volume/mass of this is rather tricky – do you take into account the access tunnels and the rather complicated geometry. However, just to get an idea I have taken the distance between the casks as 6m and added 6m above and below the cask. I have also assumed a cubic packing arrangement when if reality it would be a network of tunnels which are at least 40m apart4. Each storage position can only hold 4 PWR assemblies however, note that this is for fuel which has a much lower burnup than the 60GWd/TU we are looking at here so the spacing may have to be increased or the number of assemblies per storage position decreased.

This works out at a mass of 181 coins per household and a volume of 2320 coins.

Don’t forget that the figures quoted here are for each household – don’t forget to multiply by the 26.4 million households in the UK5.

1 More on High Level Waste, Nuclear Tourist, (http://www.nucleartourist.com/basics/hlwaste.htm)

2 Concrete spent fuel storage casks dose rates (https://inis.iaea.org/search/search.aspx?orig_q=RN:32037391)

3 If we consider a square unit cell with the cask of radius r at the centre. For a gap the diameter of one flask between  reach cask then the unit cell must have dimensions of 4r x 4r. The ratio of the area of the flask to the area of the unit cell is therefore (4r)2r2 = 16/π = 5.09.

4 Long-term safety for the final repository for spent nuclear fuel at Forsmark, Svensk Kärnbränslehantering AB, March 2011 (https://www.stralsakerhetsmyndigheten.se/Global/Slutf%C3%B6rvar/KTL/KTL%203/01_vol1.pdf)

5 Families and Households, Office of National Statistics, 2013 (http://www.ons.gov.uk/ons/rel/family-demography/families-and-households/2013/stb-families.html)

### 20 Responses to “Mass and Volume of Spent Nuclear Fuel”

• Victor says:

Good calculations, but would be good to take into account possible spent nuclear fuel reprocessing option, when volume of radioactive waste increases some 100 times, according different estimates.

• There are other things to include as well, including all the waste generated in mining and refining the U, which is enormous, and includes masses of 238UF6 in gas cylinders, and the radwaste produced in decommissioning. It really would be interesting to compare this total volume to that of coal especially with the very low grade ores the industry is now turning to.

• Pete says:

Thanks for the comment. I have covered some of these issues in my post on Energy Density of Uranium. I did not consider the overburden of mining (i.e. the rock you have to dig out before getting to the ore) or several other factors since these are about the same for coal and uranium. However, the mill tailings from uranium mining still contains 85% of the radioactivity of the original ore and should be counted as low level radioactive waste.
Having said this my post was trying to unwind some of the spin about nuclear power given by the pro-nuclear lobby. My main objection to nuclear power is that it is not needed, is too expensive and too risky – economically, environmentally and in terms of security of supply.

• Robertok06 says:

@
‘My main objection to nuclear power is that it is not needed, is too expensive and too risky – economically, environmentally and in terms of security of supply.’

Unsubstantiated statement!… For a substantiated one you can always read this… third time I bring it to your attention… confirmation bias anyone?

‘Using historical production data, we calculate that global nuclear power has prevented an average of 1.84 million air pollution-related deaths and 64 gigatonnes of CO2-equivalent (GtCO2-eq) greenhouse gas (GHG) emissions that would have resulted from fossil fuel burning. On the basis of global projection data that take into account the effects of the Fukushima accident, we find that nuclear power could additionally prevent an average of 420,000-7.04 million deaths and 80-240 GtCO2-eq emissions due to fossil fuels by midcentury, depending on which fuel it replaces. By contrast, we assess that large-scale expansion of unconstrained natural gas use would not mitigate the climate problem and would cause far more deaths than expansion of nuclear power.’

• Pete says:

I was merely stating what my opinion is. I don’t think that Hansen discusses anywhere in his paper what my opinion is. I am not sure how I would substantiate what my opinion is except state it – of course I could be lying.
It is based on evidence – some of which I have already written about in previous posts. I will get back in more detail on the Hansen paper which compares nuclear to fossil fuels – not energy efficiency or renewables.

• robertok06 says:

@pete

” I will get back in more detail on the Hansen paper which compares nuclear to fossil fuels – not energy efficiency or renewables.”

I take the liberty to write a LONG post here, because the point you rise is worth it… hope you don’t mind.
Don’t waste your time any further, there is NO comparison possible with renewables!… and, again, the reason is that you can’t possibly compare the lowest energy density sources (wind and PV) with the highest density nuclear and thermal (coal, gas)… just read the paper, published in Energy Policy by Weissbach et al… you can find a pre-print with no pay-per-view fees here:

“Energy intensities, EROIs, and energy payback times of electricity generating power plants”

The conclusions are: intermittent renewables, after the NECESSARY and MANDATORY storage requirements are taken into account, have an ‘un-buffered EROEI’ which is too low to even make them economical. That’s why even if the pro-renewables claim that “grid parity” is reached, as soon as the feed-in triffs or substantial incentives are trimmed or removed the installation of new turbines and PV panels drops dead… see Spain, Italy as two major examples.
The paper also dispels some of the usual “tricks” used by pro-renewbles, who, for instance, often assume a 3x bigger “final energy” factor for the electricity-generating intermittent sources, but the exergy analysis of Weissbach et al puts that in the right context…

Once you have read that you can try with De Castro et al, again published in Energy Policy in 2013 (or 2012?)… also this one has a pre-print version… on the physical impossibility to employ intermittent renewables on a scale large enough to substitute the thermal power stations.

If these two are not enough to convince you, then try to get a copy of Vaclav Smil’s paper on energy density… there are some nice comparison relevant to your country.

Cheers,

R.

• robertok06 says:

@pete

” I am not sure how I would substantiate what my opinion is except state it – of course I could be lying.”

ow!…. c’mon!… an un-subtantiated opinion is valid if it is in the form of “I prefer the smell of roses to that of cynnamon”… or “Liverpool is a much better football team than MUtd”… but physics and technology ARE NOT “opinions”!… there are things in this world that have a validity BEYOND opinions!… they simply are “true” in the mathematical/boolean sense… no possibility to change their status.

R.

• Robertok06 says:

Oliver:

As I already tried to explain to Pete, the…

‘masses of 238UF6 in gas cylinders’

ARE NOT WASTE!, they are resources, depleted uranium which can and will be used one day as fuel again.

R.

• Robertok06 says:

@Oliver

Forgot this… You may want to try and find out about ‘co-extraction’ (like at Olympic Dam), and on-site leaching.

There’s no substitute to study, none!

• Robertok06 says:

In-situ leaching… Of course

• Pete says:

How is this relevant to the amount of spent fuel are you sure that you are posting on the correct post? You have now posted 5 comments on my blog in the last 50 minutes.

• robertok06 says:

@pete

Yes it is relevant!… Oliver has mentioned the steriles left on the surface after mining… if one adopts the in-situ leaching technique there’s no sterile left on the surface and the amount of the terribly dangerous waste is not increased.

R.

P.S.: I’ve posted 5 messages, very short ones. The other day you have objected/complained that they were too long… you should make up your mind, Pete!… do you want readers to read your blog and comment it or do you not want that to happen? I understand that my comments, coming to conclusions diametrically opposite to yours are not what you’d like to have in here, but in that case you are the owner of the blog… do the right thing… censure me…. I’m used to that, it happens on all “evironmentally sensitive” blogs I go… you guys don’t want any real discussion based on FACTS and DATA, you can’t take that.

• roberto kersevan says:

“As I make very clear at the top of this post it would be impossible to put all the waste in one lump the size of a football field 20 feet high – it would explode and burn releasing vast amounts of radioactivity a long time before you actually filled it.”

Voila’… here it is…

…page 13:

“If all the 160,000 spent fuel assemblies currently in storage were assembled in one place, they would only cover a football field about 5 1/2 yards high.”

Is this true? It comes from the NRC, so I assume they know what they are talking about.

Cheers.

• Pete says:

@roberto kersevan
A ‘football’ field -assuming American football rather than ‘soccer’ is 120yrds by 53.3yrds. Total volume if it is 5.5yrds high is 26895.51m3. This can hold 160,000 assemblies each of which has a volume of 0.168m3. This gives 7.23×10-10m3/KWh which is about 3.014×10-6m3 per household. My figure is 3.33×10-6. So their number are not that far out. However, I have assumed a much higher burnup. The difference may be due to the different sizes of BWR and PWR fuel assemblies, however, the difference is so small that I am not going to worry about it. So yes the NRC basically agree with my figures.

• Pete says:

P.S. Note however, that you could not place fuel assemblies that close without ‘criticality issues’ (i.e. a nuclear explosion – low yield but still significant) and difficulties in dissipating the decay heat (i.e.a meltdown)- I could reference loads of NRC documents stating this. This is the main point of my post. I shall inform the NRC of their error and will post it when/if I get a reply

• robertok06 says:

@pete

‘P.S. Note however, that you could not place fuel assemblies that close without ‘criticality issues’ (i.e. a nuclear explosion – low yield but still significant) ‘

The criticality issue is valid only for a limited amount of time, after a while (depending on the burn-up of the fuel) one can store the fuel assemblies rather close, and they can be air-cooled… or one could alternate neutron-absorbing materials between rows of fuel ass’ys. It is not usually done because, as we have seen here, the amount of such assemblies is ridiculously small, any country other than the Vatican City and possibly Andorra and Luxembourg would not have any problem finding a surface of few-football-fields-equivalent on which to build a above-surface storage.
That’s a fact, not my opinion.

• roberto kersevan says:

The amount of high-level long-lived (HLLL) waste (the depleted uranium is a RESOURCE!) in a light water reactor is of the order of 0.3 mg/kWh, as referenced here…

… by no less than nuclear-fobic WWF Espana.

Look at any of the pdf’s on the list… last page (usually)… 0.236 mg/kWh for RAA (high-activity waste), and a volume of the order of 2 mm3/kWh for “RBMA”, which stands for low-to-medium activity waste, which can be compacted and most of it released as regular waste after temporary storage of few years.

So, weight-wise the HLLL waste of a family consuming 5000 kWh/y for 70 years amounts to a total of about 105 grams, and the volume to be stored temporarily as compacted low-medium activity waste is of the order of 700-1050 cm3… 1 liter!

This is why all the waste generated so far by the more than 100 civil reactors in the USA occupies the volume of a football field 20 feet high… no more no less (trying to find the DoE document where I read this).

Cheers,

R.

• Pete says:

Hi Roberto
I am beginning to wonder if you actually read my posts let alone try to understand them (e.g. http://www.plux.co.uk/energy-density-of-uranium/#comment-2212).
First of all I have provided my calculations as an Excel spread sheet – I do get a slightly different value for the amount of waste per KWh than that provided in the reference. However, my main point is that the total volume of waste is different from the volume it actually takes up since you have to avoid excessing heat production (fire) and recriticality (explosion).
As I make very clear at the top of this post it would be impossible to put all the waste in one lump the size of a football field 20 feet high – it would explode and burn releasing vast amounts of radioactivity a long time before you actually filled it.
Pete

• roberto kersevan says:

I also begin to wonder whether you understand that I was not questioning your calculations, and, yes, I am aware that there are criticality issues… I just wanted to add some info, like the spanish web page on the amount of waste in that country.
Nowhere in my message I was questioning your data/calculations… only thing you and I disagree, clearly, is the relevance of the mentioned volumes and, probably, associated costs.

This document from IAEA (pardon me if you already mentioned/linked somewhere else on your blog pages…. can’t read all of them)

…clearly states the amount of metric tons of heavy metal for the world reactors. Figure 4 shows that in 2020 we’ll have between 300 and 350 thousand tons of HM, and about 100kT reprocessed.

Is it an overwhelming amount of material, everything included? Not at all, in my opinion, at least not compared to the tens of millions of metric tons of toxis industrial waste, which is the real problem, nuclear, thanks to its highest energy density compared to all other technologies, is the least of the problems for mankind.