Calculators / Reactor and fuel cycle
SWU calculator: feed, tails and separative work
How much natural uranium and separative work a kilogram of enriched product needs. The mass balance is exact; the separative work follows the standard value function.
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The formulas
F/P = (x_p − x_w) / (x_f − x_w) feed per kg product W/P = (x_p − x_f) / (x_f − x_w) tails per kg product SWU = V(x_p) + W·V(x_w) − F·V(x_f) V(x) = (2x − 1) · ln(x / (1 − x))
Natural feed (0.711 %), 0.25 % tails
| PRODUCT | FEED kg/kg | TAILS kg/kg | SWU/kg |
|---|---|---|---|
| 3 % | 5.97 | 4.97 | 3.81 |
| 4.5 % | 9.22 | 8.22 | 6.87 |
| 5 % | 10.3 | 9.3 | 7.92 |
| 10 % | 21.1 | 20.1 | 18.9 |
| 19.75 % | 42.3 | 41.3 | 41 |
Worked example
One tonne of 4.5 % LEU needs 9.22 t of natural uranium and 6,870 SWU, and leaves 8.22 t of tails.
Tails assay trades feed against work
| TAILS | FEED kg/kg | SWU/kg |
|---|---|---|
| 0.2 % | 8.41 | 7.69 |
| 0.25 % | 9.22 | 6.87 |
| 0.3 % | 10.2 | 6.23 |
For 4.5 % product. The app also finds the tails assay that minimises total cost for a given feed-to-SWU price ratio.
Assumptions
- Ideal cascade, U-235 treated as the only light isotope (U-234 ignored).
- Assays are mass fractions of U-235.
Sources
- Lamarsh & Baratta, Introduction to Nuclear Engineering, §4 (isotope separation).
- Benedict, Pigford & Levi, Nuclear Chemical Engineering, Ch. 12.
Numbers on this page computed by the physics code of Nuclear Toolkit 1.4.1, the same code as the app. How it is checked.
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