APPENDIX D
EXAMPLE CALCULATION: NUCLEAR MASS INVENTORY,
PHOTON DOSE RATE AND THERMAL DECAY HEAT

In this example, a 280 g²³⁵U 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 g²³⁵U burned per MWd, this fuel assembly has 112 g²³⁵U burned and 40% ²³⁵U 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 g²³⁵U, 40% ²³⁵U burnup data of Table 2 can be prorated to 280 g²³⁵U. 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 g²³⁵U fuel assemblies which have 40% ²³⁵U 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 g²³⁵U spent fuel inventory masses could also have been estimated using linear interpolation of the 200 and 300 g²³⁵U, 40% ²³⁵U 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% ²³⁵U 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/kg²³⁵U (25 kW / 280 g²³⁵U), the ²³⁵U 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 g²³⁵U burned. With 112 g²³⁵U burned, the dose rate is 114 rem/h at 1 meter from the fuel assembly.

For fuel with 40% burnup and with 112 g²³⁵U 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, ²³⁵U 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% ²³⁵U burnup and 0.134 MW/kg²³⁵U 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, % 235U	Assembly Power Density, MW/kg235U	Photon Dose Rate, rem/h per g235U 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 g²³⁵U 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 9.46·10⁷ seconds (1095 d) and an elapsed time of 3.10·10⁸ seconds (3584 d)

           Watts

is about 3.8 W.