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# Nuclear Fuel Material Balance Calculator - HELP

(last updated 12 Dec 2009)

Contents:

## Introduction

This calculator performs calculations of the material balance of the nuclear fuel chain. It uses the following assumptions: the uranium is mined in an open pit or underground mine, and it is enriched for use in light water reactors, such as pressurized water reactors (PWR) or boiling water reactors (BWR).

The material balance is presented in a flow chart. Upon entry of one value into any of the flow chart's input fields, all other fields are calculated accordingly. So, it is possible to calculate the balance per tonne of uranium mined, as well as per Gigawatt-year (GWae - this is the typical annual production of a 1300MW reactor) of electricity produced in the power plant, for example.

The parameters used for the calculation can be set in the Process Parameters table. These parameters show reasonable initial values which can be modified as needed. There are no other hidden parameters used in the calculation.

An enlarged version of this calculator is the Nuclear Fuel Energy and CO2 Balance Calculator, it also allows for calculation of an energy consumption and CO2 emission balance.
For the material balance of recycled nuclear fuel (from reprocessed uranium, or plutonium - MOX), or fuel from downblended highly enriched uranium (HEU), use the Recycled Nuclear Fuel Cost Calculator

> See also the Nuclear Fuel Supply Calculator, the Nuclear Fuel Cost Calculator and the Nuclear Fuel Population Health Risk Calculator.

## 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. Detailed data for waste/ore ratios of uranium mines in the U.S. can be found in [EPA 2006].

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 % U3O8, among others (see also Unit Conversion). Ore grades being processed at present cover a wide range of 0.026% U (Rössing, Namibia) over 1.1% U (Key Lake, Canada) up to 12.7% U (McArthur River, 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.

Mill: Solids in tailings effluent [wt-%]
Weight-percent of solids contained in the tailings effluent stream of the mill.
For wet disposal, typical values are in the 20 to 50% range. For its model mill, U.S. NRC assumes 50% solids by weight in the tailings slurry sent to the tailings retention system [NUREG-0706]. For thickened paste disposal, values are in the 50 to 75% range.

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

Conversion: Solid waste per t U [t]
Amount of solid waste arising from refining and conversion, per tonne U produced.

Conversion: Liquid waste per t U [m3]
Amount of liquid waste arising from refining and conversion, per tonne U produced. Ranges between 3 and 10 m3 per t U.

Enrichment: Product Assay [wt-% U-235]
Weight-percent of the fissile isotope uranium-235 in the uranium contained in the product stream (enriched uranium hexafluoride) of the enrichment plant. Values for use in pressurized water reactors (PWR) range between 3.6% and 4.1%, and for use in boiling water reactors (BWR) between 3.0% and 3.2%. (Note: Natural uranium contains 0.711 wt-% of uranium-235)

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)
> View Current Uranium Prices

Enrichment: Specific Electricity Consumption [kWh/SWU]
For gaseous diffusion enrichment plants, the specific electricity consumption is in the range of 2300 to 2500 kWh/SWU, while it is less than 50 kWh/SWU for modern centrifuge enrichment plants. SWU is the acronym for Separative Work Unit.

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

Fuel Fabrication: Solid waste per t U [m3]
Amount of solid waste arising from fuel fabrication, per tonne U produced.

Fuel Fabrication: Liquid waste per t U [m3]
Amount of liquid waste arising from fuel fabrication, per tonne U produced.

Power Plant: Fuel Burnup [GWd/t U]
Thermal energy produced in the nuclear power plant from 1 metric tonne of enriched uranium contained in the nuclear fuel. It ranges between 40 and 43.4 GWd/t U for pressurized water reators (PWR), and 33 and 40 GWd/t U for boiling water reactors (BWR). GWd stands for Gigawatt-days, 1 GWd = 24 million kilowatt-hours.

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 under Separative Work Unit (SWU) in the "Enriched uranium" article of Wikipedia.

## Bibliography

[EPA 2006] Technologically Enhanced Naturally Occurring Radioactive Materials From Uranium Mining, Volume 1: Mining and Reclamation Background , U.S. Environmental Protection Agency, EPA 402-R-05-007, 182 pp., January 2006, Revised June 2007

[NUREG-0706] Final Generic Environmental Impact Statement on Uranium Milling, Project M-25, U.S. Nuclear Regulatory Commission, Washington, DC, September 1980, 3 volumes, NUREG-0706

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