I am writing this because it is mentioned in many children’s science books and on the Internet. This is the fact that one kilogram of Uranium can produce millions of times more energy than something like coal (83,140,000 MJ/Kg for Uranium 235 compared with 24MJ/Kg for coal). However, this is very misleading.
I will be comparing it to fossil fuels, but this does not mean that I am in favour of fossil fuel plants, but it is a good comparison to get things in perspective.
Too Much Power
For building a nuclear bomb the enormous amounts of energy are great – you can produce a very big explosion and kill millions of people. However, this is not good in a power plant. You need to ‘burn’ the Uranium a lot slower – in fact some coal and gas power plants produce a lot more power. It is also necessary to be able to remove the heat generated so that you do not get excessive temperatures. There is nothing special about nuclear power – it is just another way of boiling water.
Batch Process
Nuclear power generation is a batch process. With fossil fuel plants the fuel is feed in a bit at a time to be burnt. With nuclear several years supply of fuel is present in the reactor at any one time and is slowly ‘burnt’. This constrains the operating temperature that the plant can run at since too high a temperature will damage the fuel rods. The nuclear reaction isร inherently a batch process since you need a critical mass of fuel to sustain the nuclear reaction. However, the critical mass is still enough to cause a massive nuclear explosion if not controlled carefully.
Theร operating temperature for a gas plant (over 900รยบC) is much higher than that of a nuclear plant (320รยบC) which means that a gas plant can have a much greater thermal efficiency2.
Amount of Fuel
What is important is that you need less fuel to produce the same amount of power. However, just taking the energy density of Uranium 235 is very misleading.
The fuel used in a nuclear power plant is only slightly enriched with Uranium 235 (let us say 4%). We could do a calculation on how much energy per kilogram this would produce but there are other factors – e.g. some of the Uranium 238 is converted to plutonium which is then fissioned. So let us take the expected burnup rate for the proposed new reactors – 60 GWdays/ Tonne, which is 60MWdays/Kg or 5,184,000MJ/Kg. This is already a lot lower than the 83,140,000 MJ/Kg which is often quoted.
Now we have to take into account that the Uranium has been enriched from 0.711% U-235 to 4% U-235. So we actually need 7.31Kg of natural uranium to produce this3. So the energy density of natural uranium is 83,140,000/7.31 = 709,166 MJ/Kg.
But we also have to take into account the amount of energy needed for fuel fabrication. Figures vary considerably but let us take 2000MJ/Kg4.
There is also the energy needed to enrich the uranium to 4%. This takes about 7.69 SWU with each SWU requiring 187KWh/SWU4 which is 5177MJ/Kg.
Taking these into account we now have an energy density of 701,988 MJ/Kg.
Unlike coal, uranium has to be extracted from an ore. The quality of the ores varies but let us say it is 0.2% which is typical. Therefore, the energy density of the ore isย 701,988 x 0.2% = 1404 MJ/Kg.
Although this is still a very large amount, it is 60,000 times less than the 83,140,000 MJ/Kg we started with. With lower burnup and lower quality ore (say 40GWday/Tonne and 0.02%) then we are down to an energy density of 93 MJ/Kg for uranium ore.
The last factor, which is true of any thermal plant, is that only a portion of the thermal energy can be converted into electricity – about 33% for nuclear, 40% for coal and over 55% for modern gas plants. However, the efficiency of energy use can be massively improved by using Combined Heat and Power (CHP)
This is not a full energy analysis. It does not take into account the energy needed to mine the uranium ore, construct the nuclear power plant etc. However, I hope it does put the arguments about the massive energy density of Uranium compared with fossil fuels into perspective.
My workings can be found in this spread sheet
1 Energy Density, Wikipedia (http://en.wikipedia.org/wiki/Energy_density)
2 There are lots of discussion about the ‘Carnot Cycle’ on the web but Feynman gives a very general derivation of the efficiency rather than just for an ideal gas. R Feynman Lectures in Physics Chapter 44 (http://www.feynmanlectures.caltech.edu/I_44.html)
3 See the table at the end of mu post on Uranium Enrichment (http://www.plux.co.uk/uranium-enrichment-formula/)
4 Lenzen, M. (2008) Life cycle energy and greenhouse gas emissions of nuclear
energy: A review. Energy Conversion and Management 49, 2178-2199.(http://www.isa.org.usyd.edu.au/publications/documents/ISA_Nuclear_Report.pdf)
Leave a Reply