Separative Work Units (SWUs)

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

Fig.1 Logarithmic function used in calculating Separative Work Units.

The work Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle W_\mathrm{SWU}} necessary to separate a mass Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle F} of feed of assay $x_{f}$ into a mass Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle P} of product assay Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle x_{p}} , and tails of mass Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle T} and assay Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle 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 Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle V\left(x\right)} is the value function, defined as:

Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle V(x) = (2x - 1) \ln \left(\frac{x}{1 - x}\right)}

and satisfies

Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle 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

Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \frac{T}{P} = \frac{x_{p} - x_{f}}{x_{f} - x_{t}}}

Examples

For example, beginning with 102 kg of natural uranium (NU), it takes about 62 SWU to produce 10 kg of Low Enriched Uranium (LEU) with ²³⁵U content at 4.5%, and 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 kW hours of electricity per SWU, while gas centrifuge plants require just 50 kWh per SWU.

Examples:
A large nuclear power station with a net electrical capacity of 1300 MW requires about 25 tonnes per year of LEU with a ²³⁵U concentration of 3.75%. This quantity is produced from about 210 tonnes 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.

For more examples see Uranium Enrichment / Separative Work Units These examples are relevant to the question - Will worldwide distribution of MEU (Moderately Enriched Uranium, 20% U-235, or HALEU to use official industry jargon) will this massive production and shipment of fissile material be an easy target for the Bad Guys?

Note for Wannabe Bomb Makers:
Enriching uranium is very difficult. To get above 90% (weapons grade) it takes a lot of "work" by the centrifuges. The work increases asymptotically as you approach 100% (see Figure 1). It is also difficult starting with natural uranium (0.7%). Centrifuges work best with a 50/50 mixture of isotopes. If you can steal some 20% from a nearby power plant with a "new generation" reactor, it will be a bit easier than starting with 5%, which is the best you can find in an "old generation" power plant.