Decay Heat Simulator: Post-Shutdown Fission Product Decay

simulator intermediate ~10 min
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Decay heat at 1h ≈ 45 MW — 1.5% of operating power persists one hour after shutdown

A 3000 MWth reactor after 500 days of operation produces approximately 190 MW of decay heat at 1 second (6.3%), dropping to 45 MW at 1 hour (1.5%), and 25 MW at 1 day (0.83%). This heat must be continuously removed to prevent fuel damage.

Formula

P_decay/P₀ = 0.066 · [Math.pow(t, -0.2) - Math.pow(t + T_op, -0.2)]
Q_integrated = ∫ P_decay dt from 0 to t_display
P_decay(1s) ≈ 0.062 · P₀ (approximate for long-operated reactor)

The Heat That Won't Stop

When a nuclear reactor shuts down, the fission chain reaction halts within seconds as control rods absorb neutrons. But the fuel remains intensely radioactive — hundreds of different fission product isotopes are decaying simultaneously, releasing beta particles, gamma rays, and heat. This decay heat starts at about 6% of full power and drops following an inverse power law, but even 1% of a 3,000 MW reactor is 30 MW — enough to melt fuel if cooling is lost.

The Fukushima Lesson

The 2011 Fukushima Daiichi accident demonstrated the consequences of failing to remove decay heat. All three operating reactors shut down successfully during the earthquake. But when the tsunami destroyed backup generators, coolant pumps stopped. Within hours, decay heat boiled away the water covering the fuel. Without cooling, fuel temperatures exceeded 2,000°C, zirconium cladding reacted with steam to produce hydrogen, and three cores partially melted. Decay heat — not the chain reaction — caused the disaster.

Time Scales of Decay

Decay heat spans an enormous range of time scales. In the first seconds, short-lived isotopes like I-137 (half-life 24 seconds) dominate. Within hours, intermediate isotopes like I-131 (8 days) and Ba-140 (12.7 days) take over. After months, long-lived Cs-137 (30 years) and Sr-90 (29 years) sustain a low but persistent heat output that requires spent fuel cooling for years in storage pools before transfer to dry casks.

The ANS Standard Model

This simulation implements the ANS 5.1 standard approximation for decay heat following shutdown. Adjust reactor power, operating history, and time window to visualize the decay heat curve. Notice how longer operating history increases the long-lived fission product inventory, sustaining higher decay heat at late times. The integrated energy curve shows the total thermal energy that must be removed — a critical parameter for emergency cooling system design.

FAQ

What is decay heat in a nuclear reactor?

Decay heat is thermal energy produced by the radioactive decay of fission products after the chain reaction has stopped. At shutdown, decay heat is about 6–7% of full operating power, dropping to 1.5% after one hour and 0.4% after one day. It continues for years, which is why spent fuel must be actively or passively cooled in storage pools.

Why was decay heat important at Fukushima?

After the Fukushima earthquake triggered automatic shutdown on March 11, 2011, the fission chain reaction stopped within seconds. But decay heat continued at tens of megawatts. When the tsunami destroyed backup diesel generators, cooling pumps lost power. Without cooling, decay heat boiled away coolant water, exposing fuel, causing zirconium-steam reactions that produced hydrogen, and ultimately leading to three core meltdowns.

How long does decay heat last?

Decay heat never truly stops — it decreases asymptotically. After 1 second it is ~6% of operating power; after 1 day, ~0.5%; after 1 year, ~0.01%. Spent fuel pools must cool assemblies for 3–5 years before they can be transferred to dry cask storage. Some fission products (Cs-137, Sr-90) continue producing heat for centuries.

How is decay heat calculated?

The ANS 5.1 standard provides a conservative estimate: P_decay/P₀ ≈ 0.066 × [t^(-0.2) - (t + T_op)^(-0.2)], where t is time after shutdown and T_op is operating time. More accurate calculations use summation methods with hundreds of individual fission product decay chains.

Sources

Embed

<iframe src="https://homo-deus.com/lab/nuclear-engineering/decay-heat/embed" width="100%" height="400" frameborder="0"></iframe>
View source on GitHub