Physical Insights

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Funny Numbers.

with 4 comments

This is a chunk extracted from a recent post by Matt in the nuclear energy debate that is currently happening over at TalkClimateChange forums.

Rod Adams has already responded in the debate with his piece – but I was astonished by just how inaccurate these numbers are – so I wanted to have a look at these figures, and remind everyone exactly what the more correct figures are.

“Starting from this: A standard 100mw/eh nuclear reactor requires in the region of 160 tonnes of uranium fuel – processed from around 16 million tonnes of rock – each year.”

“100 mw/eh” ? Is that supposed to mean 100 MWe ? A standard nuclear power reactor, in the form in which they’re normally encountered, generates far more than 100 MWe – 1000 MWe is typical, for the standard currently popular designs of nuclear power reactors.

The amount of uranium required to fuel a nuclear power reactor, using currently widespread technology, i.e. LEU fuelled LWR, equates to about 200 metric tons of uranium oxide, before enrichment, per gigawatt-year of energy obtained.

Assuming 0.15% uranium oxide in the ore, that’s 133,300 tons of ore that needs to be processed per GW-yr.

“And knowing that An average [UK] home utilises 4700 kWh per year

The 100MW can provide 876,000,000 kWh. There are 25 million homes in the UK, or 117,500,000,000 kWh demand. Therefore to provide for just the electricity needs of the UK, requires 134 nuclear reactors.

(In reality, electricity demand is not 24/7. Since nuclear has to run continuously, you would need more fuel that the 134 x 160 = 21,440 tonnes of uranium per year.)”

Household electricity demand is estimated at 117.5 TWh. The actual total electricity consumption in the UK was 345.2 TWh as of 2004, according to the World Factbook – but this kind of estimate as made above isn’t too bad – it gives the correct order of magnitude.

Assuming that power reactors generate 1 GWe with a capacity factor of 90%:

345.2 TWh / (1 GW * 90% * 1 year) = 44 reactors needed to supply the UK’s electricity demand.

Obviously, it’s not entirely efficient if you somehow decide you want to use excess nuclear capacity to meet all the peak-load demand.

“(Note that this is also 134 x 16M = 2,144,000,000 or just over 2 billion tonnes of rock that need processing, transporting etc)”

133,300 tons of ore needs to be processed per GW-yr, assuming 0.15% uranium oxide content.

So, that’s 5.25 millon metric tons of uranium ore per year to supply the UK’s electricity.

The coal alternative is 177 million metric tons of coal.

“The McArthur River project is the world’s largest known high-grade uranium deposit. It is presently being developed to allow the start of production in late 1999. Located in northern Saskatchewan, Canada, the deposit is estimated to contain 416 million pounds of U3O8”

416 million pounds = 188 694.426 metric tonnes. Therefore the world’s largest known reserve of uranium has enough fuel to provide electricity to the UK domestic market – ignoring offices, industry, manufacturing and railways – for just under 9 years.”

Supplying the UK’s entire electricity needs from nuclear energy would consume about 8000 metric tons of uranium oxide per year.

That 416 million pounds of uranium oxide has an energy content corresponding to the UK’s total electricity consumption, at current levels, for 24,000 years.

I won’t really hold Matt responsible for such glaring inaccuracies, though – the bad data was taken straight from The Ecologist, here .


Written by Luke Weston

April 6, 2008 at 12:00 pm

4 Responses

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  1. Your figures are all over the lot. I understand that natural uranium is 0.7%, U-235, and that one, one-gig nuke (typical) uses 20 tons of fuel per year. The fuel is 5%, U-235, either diluted down from 90% weapons grade (US and Russian), or enriched from the 0.7% natural uranium. 5% of 20 tons enriched fuel, is one ton (1000 kg)of U-235, enriched from 1.4 X 1000, or 1400 tons of natural uranium. The amount of ore required to get this much natural uranium is more of a problem to figure. However, two processes, leaching uranium from ore in place, and more recent programs, essentially learning to filter it from the billions of tons of uranium in sea water, reduces the need to move mountains of ore.

    Richard Shaw

    April 7, 2008 at 5:19 pm

  2. The 200 tons of natural uranium number is about correct. Richard missed a decimal, and should have gotten 140 tons. With 0.2% 235U left in the tails, you get about 200 tons.

    But the 8000 tonnes per year figure is for U, not U3O8. That’s about 9500 tonnes of U3O8, meaning McArthur River is able to supply only 20,000 years of the UK’s present electricity consumption. There you go again, exaggerating the benefits of nuclear energy!

    Brad F

    April 8, 2008 at 4:50 am

  3. You’ve written “kilograms” in the article twice where you meant “tons”. Feel free to delete this comment after you correct, Luke


    April 10, 2008 at 3:09 pm

  4. I won’t delete the comment – I’ll take the opportunity to remind everyone that this kind of peer review is always appreciated, and very valuable.

    These sort of errors in specifying the units or whatever are easy enough for anybody to make – and really, the best way to defend the integrity of the information is to have it continually open to review and refinement from everyone.



    April 11, 2008 at 2:18 pm

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