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JOL's Friendly Enrichment Calculator - HELP

(last updated 22 Nov 2009)

Contents:


Introduction

This calculator performs detailed calculations for the enrichment of natural and reprocessed uranium by gaseous diffusion. It determines the mass balance, the concentrations of minor isotopes in the product and tails streams, the additional enrichment required to compensate for the presence of the neutron-absorbing isotopes U-234 and/or U-236, the cost, and the optimum tails assay for minimum cost.
It uses the following assumptions: the uranium is supplied as fresh natural uranium, or as recycled uranium, and it is enriched for use in light water reactors, such as pressurized water reactors (PWR) or boiling water reactors (BWR).

This calculator is based on "JOL's Friendly Enrichment Program" and is provided here courtesy of J.O. Liljenzin .

The material balance used for the calculations is presented in the Material Balance table. Upon entry of one value into any of the tables' input fields, all other fields are calculated accordingly, once the "Calculate" button is clicked. So, it is possible to calculate the fuel cost per tonne of uranium purchased, per tonne of uranium fuel, or per Gigawatt-year of electricity produced in the power plant, for example.
Note: One Gigawatt-year electrical (GWae) this is the typical annual production of a 1300 MWe reactor.

The results of the cost calculations are presented in the Cost Summary table and the associated diagram. 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.

Detailed results of the calculation (including the concentrations of the minor isotopes, in particular) are presented in the Results window. Its contents can be marked and copied for further use.

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.

See special instructions for offline use of this calculator.

Check also the following alternatives to this calculator, if the concentrations of the minor isotopes are not required:

 

Cost Parameters

Cost figures are entered separately for Natural, Depleted, and Recycled Uranium. Negative and zero values are permissible, to account for avoided disposal cost, for example. The distinction between the uranium types is made depending on the isotopic composition: if any of the artificial isotopes U-232, U-233, or U-236 is present, Recycled Uranium is assumed; otherwise, the distinction between Depleted and Natural uranium is made based on the U-235 assay.

All prices are in US-Dollars.

Uranium Supply: Market Price [$ per lb U3O8] or [$ per kg U]
Select price from dropdown list, or enter value either in the "$ per lb U3O8" or in the "$ per kg U" field. Upon entry of a value into one of the input fields, the other one is filled in automatically.
For current figures, see also Current Uranium Prices

Conversion: Market Price [$ per kg U]
for current figures, see Current Uranium Prices

Enrichment: Market Price [$ per SWU]
for current figures, see Current Uranium Prices

Fuel Fabrication: Market Price [$ per kg U]
 

 

Process Parameters

Uranium Supply: Supply source, as UF6 / U3O8
Select sample source from drop-down list, and/or enter isotopic composition values individually.
In case supply as UF6 is selected, the conversion step is omitted in the calculation. The supply as UF6 / U3O8 choice is initialized by making a selection from the drop-down list, but can be changed as required.
The sample data for recycled uranium is taken from [Neghabian 1991].

Uranium Supply: Isotopic composition of supply [wt-%] or [at-%]
Isotopic composition of the uranium supply in weight-percent [wt-%] or atom-percent [at-%]. The isotopic composition is initialized according to the selection made from the drop-down list, but individual values can be entered instead.
The sample data for recycled uranium is taken from [Neghabian 1991].

Conversion: Losses [%]
Production losses during the conversion process from U3O8 to UF6.

Enrichment: Equivalent 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, assuming that no neutron-absorbing nuclides were present. Actual product assays must be slightly higher to assure the required reactivity of the fuel (see "Real product assay" in the Result window).
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%.

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. The calculator can be directed to

Enrichment: Reactivity penalty factor for U-234 / U-236
The neutron-absorbing effect of the isotopes U-234 and in particular U-236 (for recycled uranium) requires additional enrichment to assure the desired reactivity of the fuel. Penalty factors are used to describe the magnitude of the effect. For the isotopes U-234 and U-236, the calculator can be independently directed to

Enrichment: Cascade key weight
Arithmetic mean of the molecular weights of the major isotopes (M*, for details, see bibliography). For U-238 and U-235 as UF6, the value is   [(238+6•19)+(235+6•19)]/2 = (352+349)/2 = 350.5
When using this calculator on a feed with a quite high concentration of U-236, it is recommended to reduce the key-weight from the normal 350.5 to 350.0 - in extreme cases even to a value little lower than 350.

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

Power Plant: Fuel Burnup [GWd/t U]
Thermal energy produced in the nuclear power plant from 1 t 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 calculator performs uranium isotope enrichment calculations for gaseous diffusion using symmetric diffusers. For given feed concentrations of the isotopes U-232, U-233, U-234, U-235, U-236, and U-238, it computes the concentrations of these isotopes in the enriched uranium product and in the depleted uranium tails, based on the desired equivalent product assay and tails assay. The calculations are based on the method for constant key weight cascades described in [de la Garza 1961] and [de la Garza 1963].
If selected, the calculator takes penalty factors for U-234 and/or U-236 into account to determine the real product assay required to compensate for the neutron-absorbing effect of these isotopes. If automatic computation of a penalty factor is selected, then it is calculated according to [Hida 1986].

In addition, the calculator determines a mass balance per unit product for the enrichment process and the complete nuclear fuel production chain, taking conversion losses and fuel fabrication losses into account.
The mass balance per unit product is then used to establish a cost balance of the complete nuclear fuel production chain per unit fuel product, composed of the cost for uranium supply, conversion, enrichment, and fuel fabrication.
If selected, the calculator determines the optimum tails assay for the minimum total production cost.

The mass balance per unit product is used as the basis for the Material Balance table, where the mass balance can be scaled to any one material in the process. The Cost Summary table and diagram show the corresponding cost for the scaled mass balance.

 

Bibliography

 

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