# Discharge Reactivity of the Nuclear Fuel Cycle

Was Energy Ant was not technical enough for you? Well, have I got a post for you…

The EIA, as mentioned before, houses monolithic databases on energy generation and consumption in this country. One of them goes by the affectionate name Form RW-859 , or the Nuclear Fuel Data Survey.

Essentially, this database is a record of every fuel assembly to ever come out of a commercial nuclear reactor in the US. It contains information such as where the fuel is being stored, if the fuel form failed, the mass of the assembly, and when the reactor was operating.  (Unfortunately, my version of the survey contains data only up until 2002, so I am missing eight years of history.)

However, good ol’ RW-895 also contains some interesting neutronic data, such as the inital U-235 enrichment [w/o, weight percent] of each assembly as well as the burnup [MWd/kg].  In some sense, the enrichment is a measure of how much energy you *expect* to get out of the fuel and the burnup is a measure of how much energy you *did* get out of the fuel.

Using the above two pieces of information and my burnup-criticality model, Bright, I calculated the isotopic composition and multiplication factor of every fuel assembly at discharge (the time when the fuel is permanently removed from the reactor).  This data was then stored in a couple of different databases: one for immediately after discharge and one for time ‘now’ in which the fuel was allowed to cool down since it was removed.

If you really want, you can take a peak at my databases and the code that generated them. (As you may have guessed by the directory names here, this was done for a collaborator to try and apply machine learning algorithms to used fuel assemblies.)

Before I rant too much further, I should define the reactivity of a fuel assembly.  If ‘k’ is the multiplication factor, then the reactivity ‘rho’ is:

$\huge&space;\rho&space;=&space;\frac{k-1}{k}$Thus, reactivities greater than one mean that the fuel still has some ‘juice’ in it, while values less than one mean that the fuel has to rely on the sweet juice of other fuel elements.

If you are anything like me, you may idly wonder what the mass-weighted reactivity of the whole of the nuclear fuel cycle over the past 40 years has been.  This would give you, Oh Intuitive Reader, some idea of how efficient our system is at actually generating the energy it says it is going to.  Look. No. Further.

The mass-weighted average discharge reactivity is: -0.1083

Great! The above number is negative.  If it was positive, this would be like throwing out batteries after only using them part way.

But how can this number be negative? Zero charge seems like it would be the lowest you could go…” I hear your cries.  This is where the battery analogy falls apart.  The answer lies in the secret of batch-averaging, which deserves its own post.

But really, isn’t the distribution of these reactivities useful to know too?  I can’t deny you, Friendly Reader: