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# Recycled Nuclear Fuel Cost Calculator - HELP

(last updated 15 Feb 2016)

Contents:

## Introduction

This calculator performs calculations of the nominal cost of nuclear fuel produced from
• enrichment of natural uranium (Unat),
• re-enrichment of depleted uranium (Udep),
• enrichment of uranium recycled from spent fuel by reprocessing (Urep),
• plutonium recycled from spent fuel by reprocessing for use in mixed-oxide fuel (MOX), and
• low-enriched uranium blended down from highly enriched uranium (HEU).
It uses the following assumptions:
• The fuel is used in light water reactors, such as pressurized water reactors (PWR) or boiling water reactors (BWR).
• The complete fuel for the plant is alternatively supplied from one of the five sources. The amount of energy produced in the reactor is the same in each case.
• Depleted uranium is first re-enriched to natural assay, and then enriched further to fuel grade.
• Recycled uranium is enriched to its initial enrichment equivalent, which is higher than the initial enrichment to compensate for the presence of U-236, a neutron absorber. (For unrestricted selection of enrichment assays, see JOL's Friendly Enrichment Calculator.)
• The MOX fuel is a mixture of plutonium (with a given concentration of fissile plutonium, i.e. Pu-239 and Pu-241) and natural or depleted uranium. (For details of the MOX fuel production process, see the MOX Fuel Calculator)
• HEU fuel is blended down with a blendstock of natural uranium, depleted uranium, or slightly enriched uranium. In the latter case, the cost for the enrichment of the blendstock is included. The blending is performed with the chemical form of uranium hexafluoride (UF6). In the case of the presence of U-236 in the HEU feed, the U-235 assay of the blended material is raised to compensate for the neutron absorbing effect of U-236. (For details of the downblending process, see the Uranium Downblending Calculator)
• The calculator does not cover any transporation cost between the various steps of the fuel chain.

The material balance used for the cost calculations is presented in the Material Balance table. Upon entry of one value into any of the tables's input fields, all other fields are calculated accordingly. So, it is possible to calculate the fuel cost per tonne of uranium purchased, 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. (For more detailed material balance calculations, see the Nuclear Fuel Material Balance Calculator).

The results of the cost calculations are presented in the Cost Summary table. You can also enter a value into any of the Cost Summary table fields, instead of entering one into the material balance table. This facilitates cost comparison.
The Cost Summary information is also presented in chart form.

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

See special instructions for offline use of this calculator.

## Cost Parameters

All prices are in US-Dollars.
Source Material Cost:
• Unat - Natural Uranium [\$ per lb U3O8]
> View Current Uranium Prices
• Udep - Depleted Uranium [\$ per kg U]; entry of negative numbers is possible.
• Urep - Recycled Uranium [\$ per kg U] (these are hypothetical cost); entry of negative numbers is possible.
• MOX:
- plutonium cost [\$ per kg Pu] (these are hypothetical cost); entry of negative numbers (avoided disposal or management cost) is possible.
- uranium cost [\$ per kg U] (in case of depleted uranium, these are hypothetical cost); entry of negative numbers (e.g. avoided disposal cost for depleted uranium) is possible
• HEU:
- HEU cost [\$ per kg U] (these are hypothetical cost); entry of negative numbers (avoided disposal or management cost) is possible.
- Raw Blendstock uranium cost [\$ per kg U] (in case of depleted uranium, these are hypothetical cost); entry of negative numbers (e.g. avoided disposal cost for depleted uranium) is possible

Conversion Cost:
• Unat - Natural Uranium [\$ per kg U]
> View Current Uranium Prices
• Udep - Depleted Uranium [\$ per kg U]
Only used, when Udep supplied as U3O8.
• Urep - Recycled Uranium [\$ per kg U]
The conversion cost depends on the chemical form in which the recycled uranium is supplied. For U as UHN, for example, it is higher than for U as UO3.
• HEU [\$ per kg U]
This is the conversion cost for the HEU component.
Note: The cost for the conversion of the Raw Blendstock uranium is taken from the Unat column.

Re-Enrichment Cost:
(for re-enrichment up to natural-equivalent assay)
• Udep - Depleted uranium [\$ per SWU]

Enrichment Cost:
• Unat - Natural uranium [\$ per SWU]
> View Current Uranium Prices
• Udep - Re-enriched depleted uranium [\$ per SWU]
(for enrichment above natural assay; the enrichment cost for natural uranium is used)
• Urep - Recycled Uranium [\$ per SWU]
The cost is somewhat higher than for natural uranium.
• HEU:
Note: The cost for any enrichment of the Raw Blendstock uranium is taken from the Unat column.

Fuel Fabrication Cost:
• Unat - Enriched Natural Uranium [\$ per kg U]
The costs for fabrication of fuel from natural uranium, designed for burnups of 43 GWd/t U, are ranging between 200 and 400 \$ per kg U.
• Udep - Re-Enriched Depleted Uranium [\$ per kg U]
(the fuel fab. cost for enriched natural uranium is used)
• Urep - Enriched Recycled Uranium [\$ per kg U]
The cost is somewhat higher than for natural uranium.
• MOX [\$ per kg HM]
The cost is approx. four times that for natural uranium.
• HEU [\$ per kg U]
The cost includes the blending cost.

## Process Parameters

Upon entry of any Process Parameters, the Assay Summary table is updated accordingly.
Source Material - Unat: Unat 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 feasibility.
> See graphs: Cost balance of uranium enrichment · Optimal tails assay
> See also: Uranium Enrichment Cost Optimizer

Source Material - Udep: Udep feed assay [wt-% U-235]
Weight-percent of the isotope uranium-235 in the depleted uranium used as feed for re-enrichment.

Source Material - Udep: Udep 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 re-enrichment plant. The tails assay must be lower than the assay of the depleted uranium feed used for re-enrichment.

Source Material - Udep: Udep supplied as U3O8 / UF6
in the case of depleted uranium being supplied as UF6, no conversion is required.

Source Material - Urep
The calculator assumes that the recycled uranium is re-enriched to initial enrichment equivalent after 5 year storage after unload from reactor, as selected under Power Plant below. (For unrestricted selection of enrichment assays, see JOL's Friendly Enrichment Calculator.)

Source Material - MOX: Puf equivalent of U-235 [g Puf per g U-235]
amount of fissile plutonium (Pu-239 and Pu-241) which produces the same energy in the reactor as 1 g of uranium-235.

Source Material - MOX: Puf concentration in total Pu [wt-%]
concentration of fissile plutonium (Pu-239 and Pu-241) in the plutonium used for MOX fuel.

Source Material - MOX: MOX U component assay [wt-% U235]
enter appropriate assay in case of use of depleted uranium, or leave initial value of 0.711 unchanged for natural uranium. In case of depleted uranium, it is assumed that it is from enrichment of natural uranium.

Source Material - HEU: HEU assay: [wt-% U-235] · [wt-% U-236]
Concentrations of U-235 and U-236 in weight-percent in the HEU material.

Source Material - HEU: Blendstock sample
Select origin of blendstock used for downblending of the HEU; the following blendstock parameters are initialized upon making a selection, but can be modified as needed.

Source Material - HEU: Final Blendstock (FB) assay [wt-% U-235]
Concentration of U-235 in weight-percent in the Final Blendstock material, after any enrichment. If an assay higher than the Raw Blendstock is entered, an enrichment step is assumed for the Blendstock. If an assay lower than the Raw Blendstock assay is entered, the latter is used instead for the calculation.

Source Material - HEU: Raw Blendstock (RB) assay [wt-% U-235]
Concentration of U-235 in weight-percent in the Raw Blendstock material, before any enrichment.

Source Material - HEU: Raw Blendstock (RB) tails assay [wt-% U-235]
Concentration of U-235 in weight-percent in the waste stream (depleted uranium hexafluoride) from enrichment of the Raw Blendstock material.

Source Material - HEU: Raw Blendstock (RB) supplied as U3O8 / UF6
in case of Raw Blendstock uranium being supplied as UF6, no conversion is required.

Source Material - HEU: Factor for U-236 effect [excess wt-% U-235 per wt-% U-236]
Excess concentration of U-235 needed to compensate for the effect of U-236 being present in the LEU product.
Typical values are in the 0.2 - 0.3 range, depending on reactor and fuel type.

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

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

Power Plant: Burnup and initial enrichment
The burnup is the thermal energy produced in the nuclear power plant from 1 t metric tonne of enriched uranium / heavy metal contained in the nuclear fuel. It ranges between 40 and 43.4 GWd/t for pressurized water reators (PWR), and 33 and 40 GWd/t for boiling water reactors (BWR). GWd stands for Gigawatt-days, 1 GWd = 24 million kilowatt-hours. The burnup has impacts on the isotope composition of the spent fuel, and thus also on the uranium isotope composition in uranium recycled from this spent fuel.
The initial enrichment figure is identical to the enrichment for fuel from enriched natural uranium. For fuel from recycled uranium, it describes the enrichment of natural uranium that would produce the same amount of energy. Actual enrichment figures for recycled uranium are higher to compensate for the presence of U-236, a neutron absorber. The composition of the uranium isotopes is determined according to the selection from the "burnup / initial enrichment" pick list, based on [Neghabian1991]. The actual figures for the current selection are shown in the Assay Summary table for reference. The figures are based on a 5 year storage time after reactor unload. For MOX fuel, the initial enrichment figure describes the enrichment of natural uranium that would produce the same amount of energy.

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

[NEA1994] The Economics of the Nuclear Fuel Cycle, OECD Nuclear Energy Agency, 1994
> Select chapters for download (PDF format)

[Neghabian1991] Verwendung von wiederaufgearbeitetem Uran und von abgereichertem Uran, von A.R. Neghabian, H.J. Becker, A. Baran, H.-W. Binzel, Der Bundesminister für Umwelt, Naturschutz und Reaktorsicherheit (Hg.), Schriftenreihe Reaktorsicherheit und Strahlenschutz, BMU-1992-332, November 1991, 186 S.

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