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Nuclear Fuel Chain Waste Activity Calculator - HELP

(last updated 5 Nov 2021)



This calculator computes activities and radioactive decay of the wastes arising from nuclear fuel production and power plant operation. For the usage of UO2 fuel, it covers uranium mine waste rock, uranium mill tailings, depleted uranium, and spent fuel. In addition, the activities of spent fuel can also be calculated for MOX fuel usage.

For a time given in the Output Parameters table, the resulting activities of the nuclides contained are calculated, plus those of any decay products growing in.

The calculator performs a complete decay analysis for the nuclides contained in its database and all their decay products, according to [Bateman 1910]; minor nuclides are listed at the end. No other nuclear reactions are considered.

The results are presented in numerical form in the Results table for the end time specified, and optionally, in an Output Chart showing the total activities vs. time for each of the four waste types. Note the logarithmic scales of the chart.
If the chart is enabled, computing time may increase considerably on old machines.
The contents of the numerical result field can be marked and copied to the clipboard for further use.

See special instructions for offline use of this calculator.

More detailed output charts showing the decay of each nuclide or each decay series involved can be obtained with the Universal Decay Calculator and the Uranium Decay Calculator.

The calculator uses the following assumptions:

The spent fuel is conditioned and disposed of in a final repository.

The material balance used for the activity calculations is presented in the Material Balance table. Upon entry of one value into any of the table's input fields, all other fields are calculated accordingly. So, it is possible to calculate the activities per tonne of uranium mined, or per tonne spent fuel, or per Gigawatt-year (GWae - this is the typical annual production of a 1300MW reactor) of electricity produced in the power plant, for example. (For more detailed material balance calculations, see the Nuclear Fuel Material Balance Calculator).

The parameters used for the calculation can be set in the Process Parameters tables. These parameters show reasonable initial values which can be modified as needed.


Output Parameters

Time Period
Enter numbers for Start and End time.
The numerical results displayed in the Results field are for the specified End time, while the chart covers the whole time period between Start and End time. For End time = 0, the numerical result shows all initial activities.

Chart Options
Select options. With charts enabled, computing time may reach several minutes on old machines.


Process Parameters

Ore Deposit: Waste/Ore Ratio
At conventional uranium mines, overburden and waste rock has to be removed to get access to the uranium ore. The waste-to-ore ratio can range between 1 and 5 for underground mines and between 1 and 60 for open pit mines.

Ore Deposit: Waste Rock Grade [wt-% U]
Weight-percent of uranium contained in the waste rock removed to get access to the uranium ore.

Ore Deposit: Ore Grade [wt-% U]
Weight-percent of uranium contained in the ore removed from the ore body for processing in the mill. Other units used are wt-% U3O8, among others (see also Unit Conversion). Ore grades being processed at present cover a wide range of 0.026% U (Rössing, Namibia) to 1.1% U (Key Lake, Canada). New uranium mining projects under development even have ore grades of up to 12.7% U (McArthur River Project, Canada).

Mill: Extraction Losses [%]
Not all of the uranium contained in the ore can be recovered in the milling process. The extraction losses are depending on the grade of the ore processed. Upon entry of an Ore Grade value, the calculator presents an estimated value for the Mill Extraction Losses. If you want to use another value for the losses, you can overwrite it.

Conversion: Losses [%]
Production losses during the conversion process.

Enrichment: Tails Assay [wt-% U-235]
Weight-percent of the isotope uranium-235 in the uranium contained in the waste stream (depleted uranium hexafluoride) of the enrichment plant. Typical values range between 0.25% and 0.30%. The tails assay can be selected according to economic feasibilty.
> See graphs: Cost balance of uranium enrichment · Optimal tails assay
(Note: feed cost includes uranium price plus conversion cost)
> See also: Uranium Enrichment Cost Optimizer
> View Current Uranium Prices

Fuel Fabrication: Losses [%]
Production losses during the fuel fabrication process.

Power Plant: Fuel · Type · Burnup · Initial Enrichment
Select plant and fuel type from drop-down list
(BWR = Boiling Water Reactor, PWR = Pressurized Water Reactor)

Power Plant: Efficiency [%]
Efficiency of converting thermal energy into net electricity, ranges between 32% and 34.5%.


Calculation Details

The formulae used by the calculator for the enrichment process can be found in Wikipedia .



[Bateman 1910] Harry Bateman: Solution of a system of differential equations occurring in the theory of radioactive transformations , in: Proceedings of the Cambridge Philosophical Society, Mathematical and physical sciences. Cambridge [etc.] Cambridge Philosophical Society. v. 15 (1908-10): Pages 423-427

ORNL is the source of the decay data used in this calculator.

The activity inventory data for the spent fuel is taken from:
Y. Ando and H. Takano, "Estimation of LWR Spent Fuel Composition", JAERI-Research 99-004, (1999). (in Japanese)


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