Calculators / Reactor and fuel cycle
Xe-135 poisoning: equilibrium worth and the iodine pit
Xe-135 has the largest thermal absorption cross section of any fission product, 2.65 × 106 barns. At power it settles at an equilibrium worth; after a shutdown it first rises as I-135 keeps decaying into it, then burns away — the iodine pit.
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The model
dI/dt = γ_I·Σf·φ − λ_I·I dXe/dt = γ_Xe·Σf·φ + λ_I·I − λ_Xe·Xe − σ_Xe·φ·Xe ρ_Xe = −σ_Xe·Xe / (ν·Σf)
With γI = 0.0639, γXe = 0.00228, ν = 2.43, and half-lives of 6.58 h (I-135) and 9.14 h (Xe-135). At equilibrium ρXe does not depend on Σf.
Equilibrium worth and the pit after shutdown
| FLUX (n/cm²/s) | EQUILIBRIUM ρ | PEAK ρ AFTER SHUTDOWN | PEAK AT |
|---|---|---|---|
| 1.00 × 1012 | -304.3 pcm | -305.1 pcm | 0.769 h |
| 1.00 × 1013 | -1,517 pcm | -1,839 pcm | 5.57 h |
| 5.00 × 1013 | -2,350 pcm | -6,200 pcm | 9.31 h |
| 1.00 × 1014 | -2,523 pcm | -11,360 pcm | 10.1 h |
| 3.00 × 1014 | -2,653 pcm | -31,850 pcm | 10.8 h |
The equilibrium worth saturates at high flux toward -2,723 pcm, while the pit keeps deepening: the higher the flux before shutdown, the more iodine is waiting to decay.
Assumptions
- One-group, spatially uniform flux (point model); no xenon oscillations.
- Direct and iodine-chain yields for U-235 thermal fission; I-135 is not burned by neutrons.
Sources
- Lamarsh & Baratta Ch. 7; Duderstadt & Hamilton Ch. 15.
- Half-lives: IAEA NUBASE2020.
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.