# Power, Burnup, and Related Models

## Power

The power associated with an LWR fuel rod is typically given as rod averaged linear power (or linear heat rate) in units of W/m. This power varies in time and space. The axial variation in power is given as a scaling factor as a function of distance from the bottom of the rod.

### Radial Power Profile

For the calculation of the radial power profile in Bison, see BurnupFunction.

## Decay Heat

Heat generation due to the radioactive decay of fission products is computed using the `simplified method'' described in the 1979 ANS-5.1 Standard on Decay Heat Power in Light Water Reactors (ANS, 1979). This method assumes that the decay heat power from fissioning isotopes other than is identical to that of and that the fission rate is constant over the operating history at a maximum level corresponding to . This simplified method overestimates decay heat power, especially with respect to LWR cores that contain an appreciable amount of plutonium. For finite reactor operating time, the decay heat power is approximated as (1) where is the time following reactor shutdown (s), is the total operating time including intermediate periods at zero power (s), is the neutron capture factor, is the energy released per fission (MeV/fission), and is the decay heat power (MeV/fission) for thermal fission of for an infinite-time base irradiation (tabulated in Table 4 of ANS (1979)).`

As implemented in Bison, the decay and peak powers are prescribed as fission power densities at finite element material volumes. Spatial variation of the peak power is dictated by the axial and radial power profiles in the fuel, thus the decay power follows the same profiles.

## Burnup Calculation

Burnup is used to calculate fuel properties and the fuel densification and swelling rates. It is computed at each material or integration point based on the following equation from Olander (1976) (2) where is the volumetric fission rate, is time, and is the initial density of heavy metal atoms in the fuel, which can be computed as (3) where is the initial fuel density, is Avagrado's number, and is the molecular weight. A burnup increment is computed for each time increment and summed to give the total burnup. (4)

### Fission Rate

The fission rate is calculated from the local power density. (5) where is the fission rate (fission/m/s), is the power density (W/m), and is the energy released per fission (J/fission). is commonly taken to be 3.28451e-11 J/fission.

### Fast Neutron Flux and Fluence

Fast neutron flux may be specified by the user as a simulation input or calculated from the linear heat rate with the Fast Neutron Flux AuxKernel.

Fast neutron fluence is the time-integrated fast neutron flux; the incremental form of the equation is solved in Fast Neutron Fluence AuxKernel.

## References

- ANS.
American national standard for decay heat power in light water reactors.
Technical Report ANSI/ANS-5.1-1979, American Nuclear Society, 1979.[BibTeX]
- D. R. Olander.
*Fundamental aspects of nuclear reactor fuel elements*. Technical Information Center, Energy Research and Development Administration, 1976.[BibTeX]