Separative work units

Separative work – the amount of separation done by an enrichment process – is a function of the concentrations of the feedstock, the enriched output, and the depleted tailings; and is expressed in units which are so calculated as to be proportional to the total input (energy / machine operation time) and to the mass processed.

The same amount of separative work will require different amounts of energy depending on the efficiency of the separation technology. Separative work is measured in Separative work units SWU, kg SW, or kg UTA (from the German Urantrennarbeit – literally uranium separation work)
 * 1 SWU = 1 kg SW = 1 kg UTA
 * 1 kSWU = 1 tSW = 1 t UTA
 * 1 MSWU = 1 ktSW = 1 kt UTA

Separative work unit is not a unit of energy, but serves as a measure of the enrichment services. In the early 2020s the cost of 1 SWU was approximately $100. The unit was introduced by Paul Dirac in 1941.

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


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

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


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

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

The feed to product ratio is given by the expression


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

whereas the tails to product ratio is given by the expression


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

Example
For example, beginning with 102 kg of natural uranium (NU), it takes about 62 SWU to produce 10 kg 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.