This is another one of those background information posts deriving the mass balances for uranium enrichment.

Let us consider the following enrichment  scenario:

We have mass F of unenriched uranium entering on the left. It has N_f of U-235 (0.72% for natural uranium). After enrichment mass P of product enriched to N_p of U-235 and mass W of waste with N_w of U-235.

First of all the total mass balance is

  [1]

We can now do the mass balance for U-235. The amount of U-235 in any stream is simply the total mass of the stream times the enrichment. We can therefore write the U-235 mass balance as:

 [2]

We can now substitute for W in equation [2] using equation [1] giving

Multiplying out the brackets we get:

Rearranging:

or

To get an idea of what this means let us consider the perfect enrichment process where we can completely separate the isotopes – i.e. N_w = 0.

We can see that in this example if we have the feed concentration of uranium fixed (i.e. N_f) then if we want to double the enrichment of the produce (i.e. N_p) we have to use twice as much feed.

Let us have a look at a graph of a more realistic example:

The amount of feed required and depleted uranium produce for one unit of enriched uranium produced.