Cs-137 in Spent Fuel as it leaves the reactor

I am now going to get a rough idea of how much caesium 137 there is in spent nuclear fuel. One reason for choosing Cs-137 is that it is a major fission product, it has a reasonably long half-life (30.17 years), it has a low melting and boiling point and is readily absorbed by the human body.

I am going to assume that the Cs-137 does not decay to any appreciable amount while it is in the reactor. This is just to make this post a bit simpler and I have shown how to take this into account in this post if anyone is interested.

I have shown how to get a rough idea of how many fission events are necessary to produce a certain amount of energy and expressed this as fissions per tonne of Uranium in a Rough Model of a Nuclear Reactor.I have also given data on now many atoms of a particular isotope is produced per fission in Composition of Spent Fuel.

So mow we can simply multiply the two numbers – i.e. number of fissions per tonne of Uranium by the probability that a certain isotope (in this case Cs-137) will be produced.

For example  if there are 1.33×1026 fissions per tonne of uranium and 6% of them result in an atom of Cs-137 then we would expect 1.33×1026 x 0.06 = 7.97 x 1024 atoms of Cs-137 to be produced. We can then compare it with published data.

 

Number of fission product atoms per gram of uranium
Burnup GWDays/TU Measured1 Calculated – basic model Calculated – advanced model
0.00 0.00E+000 0.00E+000 0.00E+000
1.20 1.94E+017 2.04E+017 1.94E+017
4.70 7.63E+017 8.00E+017 7.60E+017
9.90 1.60E+018 1.69E+018 1.60E+018
15.10 2.43E+018 2.57E+018 2.44E+018
20.00 3.17E+018 3.41E+018 3.24E+018
25.60 4.05E+018 4.36E+018 4.14E+018
29.60 4.64E+018 5.04E+018 4.79E+018
34.70 5.40E+018 5.91E+018 5.61E+018
40.00 6.15E+018 6.81E+018 6.47E+018
46.80 7.14E+018 7.97E+018 7.57E+018

The basic model is where I have assumed that the Cs-137 does not undergo decay in the reactor whereas the more advanced model takes this decay into account.

Not bad for such a rough model. However, this is the amount of Cs-137 in the fuel as it leaves the reactor. Once out of the reactor it is no longer being produced but simply decays. I shall look at this in a later post.

1 Irradiated Fuel Measurements, J. Parker (http://www.fas.org/sgp/othergov/doe/lanl/lib-www/la-pubs/00326413.pdf)

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