## Uranium Enrichment Formula

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:

Product Enrichment | Amount of Feed Required | Amount of Depleted Uranium Produced |
---|---|---|

1% | 1.54 | 0.54 |

2% | 3.46 | 2.46 |

3% | 5.38 | 4.38 |

4% | 7.31 | 6.31 |

5% | 9.23 | 8.23 |

6% | 11.15 | 10.15 |

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

This is an excellent explanation. It makes perfect sense even to someone who failed their O level maths. Thanks professor Pete.