Xenon-135 Reactor Restart Recovery Time Calculator

Introduction: Why Xenon-135 Delays Reactor Restart

Xenon-135 is the transient fission product that most often turns a simple shutdown into a long restart wait. This calculator treats the reactor as a single mixed region and estimates how the xenon inventory behaves after power is reduced or the plant is scrammed.

At steady power, the chain from iodine-135 to xenon-135 sits close to balance because xenon is being created and burned away at the same time. Once the neutron flux falls, that balance breaks: iodine already in the core keeps decaying into xenon, while the reduced flux no longer removes xenon as quickly.

Use the page to explore the size of the xenon pit for different outage lengths. It is a quick educational model, so the value is in comparing scenarios and understanding trends rather than in predicting plant-specific operating limits.

Formula: How the I‑135 / Xe‑135 Model Estimates Xenon Recovery

This calculator uses the classic two-nuclide I‑135 / Xe‑135 model, where the half-life inputs are converted into decay constants and then used to follow xenon through the outage and the restart period.

Here, T_1/2 is the half-life in hours and λ is the decay constant in 1/hour. The defaults (about 6.6 h for I‑135 and 9.2 h for Xe‑135) are the textbook values used by the page.

Behavior During Shutdown

In the shutdown phase of the xenon recovery calculator, the core is assumed to have been at steady power long enough for iodine-135 and xenon-135 to reach equilibrium.

The iodine inventory decays approximately as:

I(t) = I0 · e−λI t

where I₀ is the iodine level at shutdown. Xenon then evolves according to the differential equation:

dX/dt = λI · I(t) − λX · X(t)

Solving this with equilibrium initial conditions gives the xenon concentration during the outage:

X(t) = Xe · e−λX t + [λI / (λX − λI)] · Xe · (e−λI t − e−λX t)

This expression reproduces familiar xenon behavior: xenon first increases, as iodine continues to decay into xenon, and then slowly decreases as xenon itself decays when the shutdown is long enough.

Behavior After Restart

When the reactor is restarted in this simplified model, power is assumed to jump immediately back to its pre-shutdown level, so xenon moves back toward equilibrium with the Xe-135 decay constant.

If X₀ is the xenon concentration at the moment of restart (after a shutdown of duration t_sd), then:

X(t) = X0 · e−λX t + Xe · (1 − e−λX t)

The calculator solves for the additional time t after restart for which the xenon level is within a target band (for example within ±5% of equilibrium):

|X(t) − Xe| / Xe ≤ 0.05

How to Use the Xenon Recovery Calculator

• Shutdown Duration (hours): The outage length between shutdown and the moment you want to check for restart. Longer outages change how much iodine has had time to feed xenon during the transient.
• Xe‑135 Half-life (hours): The half-life used for xenon‑135 in the model. The default (~9.2 h) matches the common textbook value on this page.
• I‑135 Half-life (hours): The half-life used for iodine‑135. The default (~6.6 h) is the companion value for the precursor chain.

The calculator compares the modeled xenon level with the pre-shutdown equilibrium. If the restart value stays above the page's 5% upper band, it reports a positive recovery delay; if it is already at or below that threshold, the delay reads as zero.

Worked Example: A 12-Hour Xenon Pit

Suppose the reactor has been operating steadily, then remains shut down for 12 hours with the default half-lives. The calculator first converts those half-lives into decay constants and evaluates the xenon remaining at restart.

Using the page's formula, the restart concentration comes out to about 0.83× equilibrium. That means the modeled xenon level is still below the pre-shutdown benchmark, so the calculator shows 0.0 additional recovery hours rather than a positive wait.

This is a useful example because it shows that restart delay and restart concentration are related but not identical. A short outage can still leave the xenon inventory in a non-equilibrium state, so it is worth checking both the ratio at restart and the time-to-recovery output.

Interpreting Xenon Recovery Results

The main output is a snapshot of how the modeled xenon inventory compares with equilibrium at the restart point. A larger value at restart usually means a deeper xenon pit and a longer period before the core can be expected to drift back toward the modeled target band.

• Xe at restart: The xenon concentration relative to the pre-shutdown equilibrium. Values above 1.00 mean the model still predicts more xenon than the steady-state baseline.
• Recovery time: The extra time after restart for xenon to fall back to the page's upper 5% band when the restart concentration begins above equilibrium.
• Risk beyond 24 hours: A smooth comparison score based on the calculated recovery time. It is useful for ranking scenarios, not for making an operational probability claim.

If the restart concentration is below equilibrium, remember that this page's recovery expression only solves the upper side of the band. In that case the calculator can show zero additional hours even though the xenon state is still different from the exact equilibrium point.

Xenon Recovery Model Comparison Table

Assumptions and Limitations of the Xenon Recovery Model

This xenon-poisoning calculator is intentionally simple, so the numbers should be read as a compact teaching model rather than a plant-analysis result. The main assumptions are:

• Two-nuclide approximation: Only I‑135 and Xe‑135 are tracked. Other poison pathways and fission-product chains are left out.
• Lumped, zero-dimensional core: The reactor is treated as one mixed region, so local xenon swings and spatial oscillations are not represented.
• Equilibrium before shutdown: The model assumes the reactor had already settled at steady power before the outage began.
• Instantaneous power change: Shutdown and restart are modeled as step changes in flux rather than gradual ramps.
• Constant cross-sections: Temperature, moderator density, burnup, and other changes that alter reaction rates are ignored.
• No feedbacks or control action: The page does not simulate control rods, boron, void feedback, or other plant-specific responses.

Because of those simplifications, the calculator is best used to understand trends: longer outages, different half-lives, and the relative size of the xenon peak. It should not be treated as a restart approval tool or as a substitute for core-following software.

Safety and Appropriate Use

Important: This xenon recovery calculator is for education and conceptual checking only. It does not include plant-specific procedures, margins, or operating restrictions, and must not be used for real reactor restart decisions, licensing work, or safety compliance. Always follow approved plant procedures, technical specifications, and regulatory guidance.

For detailed operational planning or safety analysis, rely on validated core simulation tools and the responsible reactor engineering and safety teams.