The amount of decay heat being generated in a fuel assembly at any time after shutdown can be exactly calculated by the determination of the number of fission products present at the time of shutdown. This is a fairly detailed process and is dependent upon power history. The concentrations, decay energies, and half-lives of fission products are known for a given type of fuel. By starting from a known value, based on power history at shutdown, the decay heat generation rate can be calculated for any time after shutdown. An exact solution must consider the fact that hundreds of different radionuclides are present in the core, each with its concentration and decay half-life. For this purpose, the SCALE/TRITON code can be used for depletion calculations. The SCALE/ORIGEN-ARP code can be used to calculate decay heat rates at specific initial fuel composition and discharge burnup levels.
See also: Brian J. Ade, Ian C. Gauld. Decay Heat Calculations for PWR and BWR Assemblies Fueled with Uranium and Plutonium Mixed Oxide Fuel Using Scale, ORNL/TM-2011/290, OAK RIDGE NATIONAL LABORATORY, 2011.
It is also possible to make a rough approximation by using a single half-life that represents the overall decay of the core over a certain period. An equation that uses this approximation is the Wigner-Way formula:
where
- Pd(t) = thermal power generation due to beta and gamma rays,
- P0 = thermal power before the shutdown,
- t0 = time, in seconds, of thermal power level before the shutdown,
- t = time, in seconds, elapsed since the shutdown.
