What is the typical quantity (in kg) of uranium-235 present at a given moment in a working nuclear plant?
How does this compare to the typical amount of uranium-235 in a typical nuclear bomb (typically one kg of uranium-235)
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$\begingroup$ In one specific location or on the whole site ie at various locations? $\endgroup$– Solar MikeNov 8 '20 at 13:13
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$\begingroup$ In one specific location $\endgroup$– Mathieu KrisztianNov 8 '20 at 13:15
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$\begingroup$ See burnup, then you can calculate the amount of fuel from the capacity and typical burnup for the type of reactor. Then the amount of U235 from the the fuel composition of the reactor. $\endgroup$– Phil SweetJan 27 at 3:24
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Atomic Weapons
The critical mass of metallic U-235 is about 50 kg[1] and the only U-235-based fission weapon deployed in combat--the Little Boy weapon--had about 64 kg of U-235[2]; there's more U-235 than that in nuclear power plants.
Why this is not a good comparison
Weapons-grade U-235 is highly enriched (think 80%+), meaning it contains mostly U-235 and correspondingly less U-238. A typical commercial nuclear reactor is running fuel with enrichments of up to 5%, which is far too low for weapons use. Of course, fresh fuel (fuel that hasn't been in the reactor) could be converted back into UF6 and further enriched if one had the capability.
However, once fuel has been irradiated in the reactor, fissions and neutron capture change the composition of the fuel. Neutron-absorbing U-236 is formed in the fuel and it becomes impractical to extract and further enrich just the U-235 from this fuel, which would be required constructing a fission weapon (there are, on the other hand, proliferation concerns surrounding reprocessing spent fuel related to the extraction of Pu-239). So even if there was enough mass of U-235 in a nuclear power plant to meet the required U-235 mass for a fission weapon, the composition of depleted fuel makes it unusable for this purpose.
Nuclear Power Plants
Nonetheless, to actually answer the question, let's estimate how much U-235 a typical PWR unit has.
Mass of U-235 in the Plant's Core
Let's assume we have a generic PWR plant with 157 fuel assemblies at an average enrichment of 3%, and with solid 0.3225" diameter pellets in a 17x17 assembly with 12' active fuel height. You can confirm that these are good round numbers in [3] which is also an excellent overall reference.
Each rod thus has a volume of $\pi(\frac{1}{2}0.3225 in.)^2 \times 144 in. = 11.7 in^3 = 192 cm^3$. The density of UO2 is about 11.0 g/cm$^3$ and to use round numbers, $\frac{238}{(238+16+16)} = 88\%$ of that is going to be U. Multiply that all out and you get about 55 g of U-235 in one fuel rod.
A Westinghouse-style 17x17 assembly has 25 non-fuel locations (24 control rod guide tubes, 1 instrument tube again see [3]), so that gives us $157\times(17 \times 17 - 25) = 41448$ fuel rods, which gives us ~2300 kg of U-235 in the core.
Spent fuel pool, casks, etc.
After 36-54 months of operation (3x18 month cycles being pretty typical), fuel assemblies are discharged from the core into the plant's spent fuel pool. Although $\frac{2}{3}-\frac{3}{4}$ of the U-235 has been consumed by fission[4], a significant amount remains. Let's assume an average assembly is therefore left with about $\frac{1}{3} \times (17 \times 17 - 25) \times 55 gg = 5 kg$ of U-235.
After several years in the spent fuel pool, the fuel may be moved into casks holding several assemblies for further storage or transport. Depending on the country, the plant, etc. these may be held on-site pending the availability of a geological repository.
For a plant after 60 years of operation, that suggests up to ~2000 assemblies (assuming 18-month cycles with 1/3 of the core replaced at each reload) between the SFP and casks may be on site, which would be a further 10,000 kg of U-235.
Summary
So, our typical PWR unit might have on the order of 10-15,000 kg of U-235. A nuclear site may have 2 or more units (1 and 2 unit sites being predominate), so you'd have to multiply the above numbers depending on your definition of "one place" but to answer the question, our PWR has >>65 kg U-235.
References
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$\begingroup$ @PhilSweet that's embarrassing, thanks. I've corrected it. $\endgroup$– NickBJan 27 at 10:57
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