Decay Heat Calculator
Calculate decay heat with our free science calculator. Uses standard scientific formulas with unit conversions and explanations.
Reviewed by Manoj Kumar, Mathematics Educator
Formula
P(t)/P0 = 0.066 * [t^(-0.2) - (ts + t)^(-0.2)]
Where P(t) is the decay heat at time t after shutdown, P0 is the operating thermal power, t is the time after shutdown in seconds, and ts is the total operating time before shutdown in seconds. The constant 0.066 represents approximately 6.6% of operating power.
Worked Examples
Example 1: PWR Reactor One Day After Shutdown
Problem:A 3000 MWt pressurized water reactor has operated for 365 days. Calculate the decay heat 1 day (86,400 seconds) after shutdown.
Solution:P0 = 3000 MW = 3e9 W\nts = 365 * 86400 = 31,536,000 s\ntsd = 86,400 s\nP/P0 = 0.066 * (86400^-0.2 - (31536000+86400)^-0.2)\n= 0.066 * (0.09120 - 0.02776)\n= 0.066 * 0.06344 = 0.004187 = 0.419%\nDecay heat = 0.004187 * 3e9 = 12.56 MW
Result:Decay Heat: 12.56 MW (0.419% of operating power) after 1 day
Example 2: Spent Fuel Pool Heat Load
Problem:Calculate decay heat from a 1000 MWt reactor fuel bundle 30 days after shutdown, operated for 3 years (1095 days).
Solution:P0 = 1000 MW = 1e9 W\nts = 1095 * 86400 = 94,608,000 s\ntsd = 30 * 86400 = 2,592,000 s\nP/P0 = 0.066 * (2592000^-0.2 - (94608000+2592000)^-0.2)\n= 0.066 * (0.04542 - 0.02488)\n= 0.066 * 0.02054 = 0.001356 = 0.136%\nDecay heat = 0.001356 * 1e9 = 1.356 MW
Result:Decay Heat: 1.356 MW (0.136% of operating power) after 30 days
Frequently Asked Questions
What is decay heat and why is it important for nuclear reactor safety?
Decay heat is the thermal energy produced by the radioactive decay of fission products and actinides in nuclear fuel after the fission chain reaction has been stopped. Even after a reactor is shut down by inserting control rods and stopping the fission process, the accumulated fission products continue to emit beta particles, gamma rays, and alpha particles as they undergo radioactive decay, generating significant heat. Immediately after shutdown, decay heat is approximately 6 to 7 percent of the full operating power, which for a 3000 MW thermal reactor means about 200 MW of heat must still be removed. This is why nuclear reactors require robust and redundant cooling systems that function even during shutdown conditions.
How does the Way-Wigner formula estimate decay heat after reactor shutdown?
The Way-Wigner formula is an empirical approximation that estimates the fraction of operating power remaining as decay heat at time t after shutdown. The formula is P(t)/P0 equals 0.066 times the quantity t to the negative 0.2 power minus (ts plus t) to the negative 0.2 power, where ts is the operating time before shutdown and t is the time after shutdown. The factor 0.066 represents approximately 6.6 percent of operating power, and the negative 0.2 exponent captures the characteristic slow decay of fission product activity. This formula is remarkably simple yet provides reasonable estimates (within about 20 percent) for shutdown times from about one second to one hundred million seconds after a long period of reactor operation.
How does operating time before shutdown affect the decay heat level?
The operating time before shutdown significantly affects the initial decay heat level and its long-term evolution. Longer operating times allow more fission products to accumulate, including longer-lived isotopes that contribute to decay heat for extended periods. A reactor that has operated for one year produces more decay heat at any given time after shutdown than one operated for just one month, because the long-lived fission products (with half-lives of months to years) have had more time to build up. However, the effect of operating time diminishes for short-lived isotopes, which reach secular equilibrium relatively quickly. For operating times exceeding about two years, the decay heat profile becomes largely independent of operating duration for the first few days after shutdown.
What role did decay heat play in the Fukushima nuclear accident?
The Fukushima Daiichi accident in March 2011 was fundamentally a decay heat removal failure. When the earthquake struck, the three operating reactors automatically shut down their fission chain reactions successfully. However, the subsequent tsunami destroyed the backup diesel generators needed to power the emergency cooling systems. Without active cooling, the decay heat (still producing tens of megawatts of thermal power) caused the water in the reactor vessels to boil away, uncovering the fuel. The fuel temperature then rose to the point where zirconium cladding reacted with steam, producing hydrogen gas and causing explosions. This accident dramatically demonstrated that managing decay heat is equally important as controlling the chain reaction in nuclear safety.
References
Reviewed by Manoj Kumar, Mathematics Educator · Editorial policy