### RERTR Publications:

Foreign Research Reactor Spent Nuclear Fuel

#### ANL/RERTR/TM-26

##### APPENDIX D

EXAMPLE CALCULATION: NUCLEAR MASS INVENTORY,

PHOTON DOSE RATE AND THERMAL DECAY HEAT

In this example, a 280 g^{235}U MTR-type fuel assembly has been irradiated
at an average fuel assembly power ()
of 25 kW over an elapsed time ()
of 3584 days. The irradiation history of this fuel assembly is such that it
can __not__ be described simply, using a constant power ()
and a continuous irradiation time ().
It is assumed, however, that

where the sum of () traces
the fuel assembly irradiation history over all irradiation segments when the
fuel assembly power was constant and the irradiation time was continuous. The
elapsed time is the calendar time from the first through the last irradiation
segment. Assuming 1.25 g^{235}U burned per MWd, this fuel assembly has
112 g^{235}U burned and 40% ^{235}U burnup. The fission product
decay time () or cooling time
for this fuel assembly is assumed to be 3 years.

__Nuclear Mass Inventory
__

If the fuel assembly enrichment is 93%, then 300 g^{235}U, 40% ^{235}U
burnup data of Table 2 can be prorated to 280 g^{235}U. For enrichments
of 45 or 19.75%, similar prorated data from Table 3 or 4, respectively, should
be used. Table D1 summarize the spent fuel mass inventory of 280 g^{235}U
fuel assemblies which have 40% ^{235}U burnup.

**Table D1. Mass Inventory of Spent HEU, MEU and LEU Fuel Assemblies
**

Isotope | HEU-93% | MEU-45% | LEU-19.75% |

U-234 | 0 | 0 | 0 |

U-235 | 168 | 168 | 168 |

U-236 | 18 | 18 | 19 |

U-238 | 21 | 337 | 1125 |

U | 206 | 523 | 1311 |

Np-237 | 0.4 | 0.4 | 0.4 |

Np | 0.4 | 0.4 | 0.4 |

Pu-238 | 0.0 | 0.0 | 0.0 |

Pu-239 | 0.4 | 3.2 | 7.0 |

Pu-240 | 0.1 | 0.6 | 1.1 |

Pu-241 | 0.0 | 0.2 | 0.4 |

Pu-242 | 0.0 | 0.0 | 0.0 |

Pu | 0.5 | 3.9 | 8.6 |

Am-241 | 0.0 | 0.0 | 0.0 |

Am | 0.0 | 0.0 | 0.0 |

These 280 g^{235}U spent fuel inventory masses could also have been
estimated using linear interpolation of the 200 and 300 g^{235}U, 40%
^{235}U burnup data tabulated in Tables 2, 3 and 4. Note, inventory
masses for non-tabulated fuel assembly burnup should also use linear interpolation
of tabulated data (e.g. 45% ^{235}U burnup, interpolate between 40 and
50% tabulated data).

__Photon Dose Rate
__

The photon dose rate of this fuel assembly is calculated from data presented
in Table 8. The assembly power density is 0.089 MW/kg^{235}U (25 kW
/ 280 g^{235}U), the ^{235}U burnup is 40%, and the decay time
is 3 years. With these data, Table 8 estimates that the photon dose rate is
1.02 rem/h per g^{235}U burned. With 112 g^{235}U burned, the
dose rate is 114 rem/h at 1 meter from the fuel assembly.

For fuel with 40% burnup and with 112 g^{235}U burned, Fig. 1 estimates
that this fuel assembly will be self-protecting (dose rate greater than 100
rem/h) for about 4 years.

The photon dose rate for non-tabulated assembly power densities, ^{235}U
burnup and/or decay times can be estimated using linear interpolation of the
data in Table 8. Linear interpolation to determine the photon dose rate would
be necessary, for example, for a fuel assembly with the following parameters:
3.5 year decay time, 50% ^{235}U burnup and 0.134 MW/kg^{235}U
assembly power density. A simple table which interpolates each parameter separately
is a useful aid. Table D2 is constructed to determine the photon dose rate for
these non-tabulated fuel assembly parameters.

**Table D2. Fuel Assembly Parameter Linear Interpolation
**

Decay Time, y | Burnup, % ^{235}U |
Assembly Power Density, MW/kg^{235}U |
Photon Dose Rate, rem/h per g^{235}U burned |

3 | 50 | 0.179 | 1.31 |

3 | 50 | 0.089 | 1.07 |

3 | 50 | 0.134 | 1.19 |

4 | 50 | 0.179 | 1.10 |

4 | 50 | 0.089 | 0.931 |

4 | 50 | 0.134 | 1.0155 |

3.5 | 50 | 0.134 | 1.10 |

The bottom line, estimated photon dose rate is 1.10 rem/h per g^{235}U
burned.

__Thermal Decay Heat
__

**ORIGEN Calculation
**

The thermal decay heat calculated with the ORIGEN code for this example is
about 4.2 Watts.

**Integrated Emission Rate Equation
**

The thermal decay heat of this fuel assembly using the conservative heat load
equation based upon Eq. -1

Watts

is about 10.6 W. This result is based upon an average fuel assembly power
() of 25,000 Watts, a cooling
or decay time () of 1095 days
(3 y) and an elapsed time ()
of 3584 days.

**El-Wakil Equation
**

The thermal decay heat with these same data and the heat load equation based
upon Eq. -2

Watts

is about 5.1 W.

**Untermyer and Weills Equation
**

Similarly, using the heat load equation based upon Eq. -3 with a decay time
of 9.46·10^{7} seconds (1095 d) and an elapsed time of 3.10·10^{8}
seconds (3584 d)

Watts

is about 3.8 W.