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. Separative work is ''not'' energy. 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

Definition

The work

W_\mathrm

necessary to separate a mass

F

of feed of assay

x_

into a mass

P

of product assay

x_

, and tails of mass

T

and assay

x_

is given by the expression: :

W_\mathrm = P \cdot V\left(x_\right)+T \cdot V(x_)-F \cdot V(x_)

where

V\left(x\right)

is the

value function The value function of an optimization problem gives the value attained by the objective function at a solution, while only depending on the parameters of the problem. In a controlled dynamical system, the value function represents the optimal payo ...

, defined as: :

V(x) = (2x - 1)  \ln \left(\frac\right)

and satisfies :

V''(x)=\frac.

The feed to product ratio is given by the expression :

\frac = \frac

whereas the tails to product ratio is given by the expression :

\frac = \frac

Example

For example, beginning with of

natural uranium Natural uranium (NU or Unat) refers to uranium with the same isotopic ratio as found in nature. It contains 0.711% uranium-235, 99.284% uranium-238, and a trace of uranium-234 by weight (0.0055%). Approximately 2.2% of its radioactivity comes ...

(NU), it takes about 62 SWU to produce {{convert, 10, kg of

Low-enriched uranium Enriched uranium is a type of uranium in which the percent composition of uranium-235 (written 235U) has been increased through the process of isotope separation. Naturally occurring uranium is composed of three major isotopes: uranium-238 (238U ...

(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-hour A kilowatt-hour ( unit symbol: kW⋅h or kW h; commonly written as kWh) is a unit of energy: one kilowatt of power for one hour. In terms of SI derived units with special names, it equals 3.6 megajoules (MJ). Kilowatt-hours are a common bi ...

s (kW·h), or 8.6–9

gigajoule The joule ( , ; symbol: J) is the unit of energy in the International System of Units (SI). It is equal to the amount of work done when a force of 1 newton displaces a mass through a distance of 1 metre in the direction of the force applie ...

s, (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.

References

Nuclear fuels