Separative work units

The work ${\displaystyle W_{\mathrm {SWU} }}$ necessary to separate a mass ${\displaystyle F}$ of feed of assay ${\displaystyle x_{f}}$ into a mass ${\displaystyle P}$ of product assay ${\displaystyle x_{p}}$, and tails of mass ${\displaystyle T}$ and assay ${\displaystyle x_{t}}$ is given by the expression

${\displaystyle W_{\mathrm {SWU} }=P\cdot V\left(x_{p}\right)+T\cdot V(x_{t})-F\cdot V(x_{f})}$

where ${\displaystyle V\left(x\right)}$ is the value function, defined as

${\displaystyle V(x)=(2x-1)\ln \left({\frac {x}{1-x}}\right)}$

and satisfies

${\displaystyle V''(x)={\frac {1}{(x(1-x))^{2}}}.}$

The feed to product ratio is given by the expression

${\displaystyle {\frac {F}{P}}={\frac {x_{p}-x_{t}}{x_{f}-x_{t}}}}$

whereas the tails to product ratio is given by the expression

${\displaystyle {\frac {T}{P}}={\frac {x_{p}-x_{f}}{x_{f}-x_{t}}}}$

For example, beginning with 102 kilograms (225 lb) of natural uranium (NU), it takes about 62 SWU to produce 10 kilograms (22 lb) of Low-enriched uranium (LEU) in ²³⁵U content to 4.5%, at a tails assay of 0.3%.

The number of separative work units provided by an enrichment facility is directly related to the amount of energy that the facility consumes. Modern gaseous diffusion plants typically require 2,400 to 2,500 kilowatt-hours (kW·h), or 8.6–9 gigajoules, (GJ) of electricity per SWU while gas centrifuge plants require just 50 to 60 kW·h (180–220 MJ) of electricity per SWU.

Example:

A large nuclear power station with a net electrical capacity of 1300 MW requires about 25 tonnes per year (25 t/a) of LEU with a ²³⁵U concentration of 3.75%. This quantity is produced from about 210 t of NU using about 120 kSWU. An enrichment plant with a capacity of 1000 kSWU/a is, therefore, able to enrich the uranium needed to fuel about eight large nuclear power stations.