# Calculation of Decay Heat – Wigner-Way formula

## Calculation of Decay Heat – Wigner-Way formula

The amount of decay heat being generated in a fuel assembly at any time after shutdown can be exactly calculated the determination of the amount of fission products present at the time of shutdown. This is a fairly detailed process and is dependent upon power history. For a given type of fuel, the concentrations, decay energies, and half-lives of fission products are known. 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 take into account the fact that there are hundreds of different radionuclides present in the core, each with its own concentration and decay half-life. For this purposes the SCALE/TRITON code can be used for depletion calculations and SCALE/ORIGEN-ARP code can be used for calculation of decay heat rates at specific initial fuel composition and discharge burnup level.

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 of time. 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 shutdown,
• t0 = time, in seconds, of thermal power level before shutdown,
• t = time, in seconds, elapsed since shutdown.

References:
Nuclear and Reactor Physics:
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