User:David MacQuigg/Sandbox/Separative Work Units

Calculation

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

SWUs are a function of the concentrations of the feedstock, the enriched output, and the depleted tailings.

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:

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

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

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