Reactor Operations · Calibrated to DOE-HDBK-1019

The Xenon-135 Transient Simulator

Watch iodine-135 decay into xenon-135, burn out under flux, and spike after a trip — the fission-product poison every operator has to out-wait. Set a power history and read the reactivity, the peak, and the dead time.

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Scenario

Power history

Power (%)Duration (h)

Each row holds the reactor at that power for that many hours, in order. The simulation runs the schedule, then coasts a further 80 h so any post-shutdown peak is visible.

Shutdown margin

If xenon's negative reactivity climbs past this margin, the reactor can't be made critical — that window is the xenon dead time (precluded startup), shaded red on the chart.

γI = 0.06282  ·  γXe,direct = 0.002566 · fission-fraction weighted, ENDF/B-VIII.1
Plant · calibration
power density 104.6 W/cm³  →  φ = 2.60×10¹³ n/cm²·s
Θ = σaφ/λXe = 3.19 · benchmark 3.19

Thermal power alone does not set the flux — power density does. Two plants at 1000 and 3000 MWth with the same power density run at essentially the same flux and the same xenon concentration. That is why core volume is asked for.

Xe worth pins the reactivity scale to your core; it does not affect the benchmark ratio. Defaults reproduce the NRC reference curves.

Xe-135 reactivity (pcm) dead time Reactor power
Hover the strip chart to read reactivity at any hour.
Equilibrium Xe @ end power
steady-state poison
Peak negative reactivity
after last power drop
Xenon dead time
startup precluded
Xenon-free after
|ρ| < 100 pcm

The model

dNI/dt = γI·Σf·φ − λI·NI
dNXe/dt = γXe·Σf·φ + λI·NIλXe·NXeσaXe·φ·NXe

Iodine-135 is fed by fission and only decays (it's a weak absorber, so its burnup is dropped). Xenon-135 is fed a little directly by fission and mostly by that iodine decay, then leaves two ways: it decays, and at power it burns out by absorbing a neutron (the σa·φ term). Trip the reactor and the burnout term vanishes instantly, but iodine keeps decaying into xenon for hours — so xenon overshoots to a peak near 8 hours before its own decay finally wins.

λI — iodine-135 decayT½ = 6.57 h2.930 × 10⁻⁵ s⁻¹
λXe — xenon-135 decayT½ = 9.10 h2.116 × 10⁻⁵ s⁻¹
γI — cumulative I-135 yield6.282 % ± 0.0880.062819
γXe — direct Xe-135 yield0.2566 % (cum. Xe − cum. I)0.002566
σaXe — Xe-135 absorption2.6 million barns2.6 × 10⁻¹⁸ cm²

Fission yields from ENDF/B-VIII.1 (U-235 thermal, 0.0253 eV, MF=8 MT=459 cumulative); the direct ¹³⁵Xe term is the difference of the cumulative Xe and I yields. Decay constants and σa from DOE-HDBK-1019/2-93 and the U.S. NRC Reactor Physics Review (HRTD, §2.1), cross-checked against Lamarsh & Baratta, Introduction to Nuclear Engineering. Benchmark curves digitised from NRC Figs 2.1-12 and 2.1-14. The reactivity scale is calibrated so equilibrium ¹³⁵Xe at 100% power equals the reference −2800 pcm; the same model then reproduces the post-trip peak and the equilibrium-versus-power curve without further tuning — see the validation table below.

Validation

Every figure below is recomputed live from the constants and flux currently set in the panel above — nothing here is hard-coded. Move the flux slider and the errors move with it. The model is calibrated at one point (equilibrium ¹³⁵Xe at 100% power); everything else is an output.

BenchmarkSourceReferenceThis modelError
Equilibrium ¹³⁵Xe @ 100%NRC HRTD §2.1, Xenon slide −2800 pcmanchor
Equilibrium ¹³⁵Xe @ 80% (÷ 100%)NRC Fig 2.1-14, pre-trip 0.9566
Equilibrium ¹³⁵Xe @ 50% (÷ 100%)NRC Fig 2.1-14, pre-trip 0.8117
Post-trip peak ÷ equilibrium
calibration-free — independent of the anchor, of Σf, and of the yields
NRC Fig 2.1-14, trip from 100% 1.7329

The shape of this model is governed by a single dimensionless group, Θ = σaφ / λXe — the ratio of xenon burnout rate to xenon decay rate. Θ is what has been benchmarked, not φ on its own: published σa values span 2.6–3.5 × 10⁶ b, so only the product σaφ is pinned down by the reference curves. Current Θ = , benchmark Θ = 3.19.

Model scope

Reactor type
Generic large PWR. Zero-dimensional (point) model — one core-average xenon concentration, spatially uniform flux.
Fuel
UO₂. Fission yields are U-235 thermal values from ENDF/B-VIII.1. A beginning-of-life core is therefore represented well; a high-burnup core with a significant Pu-239 fission fraction is not (Pu-239's direct ¹³⁵Xe yield is roughly four times that of U-235).
What “100% power” means here
A reference core-average thermal flux of φ = 2.6 × 10¹³ n/cm²·s, editable above. Power fraction enters the model only as a flux multiplier — there is no thermal-hydraulic model behind it.
How reactivity is calculated
Linearly in xenon concentration, ρ = −C·NXe, with the single constant C fixed by the equilibrium anchor. This is the standard first-order treatment and is accurate while xenon absorption stays small against total core absorption.
Are the concentrations physically correct?
As ratios, yes. As absolute values, no. Σf is not modelled, so the plotted I-135 and Xe-135 curves are normalised to the 100% equilibrium value and carry no atoms/cm³ scale. The reactivity trace is unaffected by this.
Known limitations — read before citing
  • No axial or radial xenon oscillations. Spatial xenon redistribution needs a nodal or 3-D method. Do not use this for axial offset control studies.
  • Local flux peaking is not represented. Xenon in a high-flux region of a real core behaves more severely than this core-average result.
  • Xe-135m is folded into the direct yield rather than tracked separately. Its 15.3-minute half-life makes this exact on the timescale of the peak, but not below roughly one hour.
  • No samarium-149, no burnup, no flux feedback. Power history is prescribed, not solved.
  • Peak timing is soft. The post-trip peak is broad — the reference curve stays within 1% of its maximum from about 6 to 9 hours — so quote a window, not a single hour.

Part of the NeutronRise reactor operations cluster: Point Kinetics Simulator · Decay Heat Calculator