# Uranium Separative Work Unit Calculator

## Description of Separative Work

The Separative Work Unit or SWU is a measure of the work expended during an enrichment process. The aim of an enrichment process is to increase the concentration of one or more isotopes in a multi-isotope element. For uranium, a typical enrichment process consists of a number of centrifuges arranged in the form of a cascade (a number of separating centrifuges arranged in parallel and in series).

A cascade has three streams of material:

1) The Feed material at a specific concentration of the desired isotope. If the feed is natural uranium, the desired isotope is U-235 and the feed concentration is 0.007

2) The Waste (or stripped) material at a specified concentration of the desired isotope. The waste concentration will always be smaller than that of the feed. For most typical enrichments, the waste concentration will be in the range of 0.002-0.0003 of U-235.

3) The Product (or enriched) material with a desired concentration of the desired isotope, which is always higher than that of the feed material. Nuclear reactors usually require U-235 concentrations of about 5% (that is, 0.05) or so. Nuclear weapons require material of concentration of about 90%.

The equation defining Separative Work is:

SWU = P·V(Np) + W·V(Nw) – F·V(Nf)

Where P is the product amount, Np is the product concentration, W is the waste amount, Nw is the waste concentration, F is the feed amount, Nf is the feed concentration, and V(x) is a value function that takes the form:

V(x)=(2x-1)ln(x/(1-x)) where x is a given concentration.

The value function V(x) is dimensionless, so the units of SWU is contingent on the units of P, W, and F. The value of a SWU can, therefore, be in terms of any amount of material. If P, W, and F are in units of kilograms, then the SWU will be a kg-SWU. Typically, a SWU is expressed in terms of kilograms or metric tonnes. The performance of a centrifuge can be expressed in terms of rate of enrichment, that is, SWUs per year or month. Individual centrifuges might be described in terms of kg-SWUs per year and entire cascades described in terms of Ton-SWUs per year. A SWU per unit time is referred to, not as separative work, but as separative power.

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