Corresponding author: Evgeny V. Semenov (

Academic editor: Yury Kazansky

The paper is devoted to the definition of an analytical expression for estimating the burnup depth of nuclear fuel depending on its enrichment level, the periodicity of refueling, thermal stressthermal stress and the duration of the time period between refueling (reactor campaign) in a wide range of changes in key parameters for different types of thermal neutron reactors. The analytical expressions obtained in the work for the burnup depth are compared with numerous neutron physics calculations and experimental data from different authors for uranium fuel enrichment up to 9%. Calculations of the fuel share of the cost of electricity of nuclear power plants with PWR type reactors were performed and its sensitivity to changes in burnup depth and enrichment of fuel, the refueling periodicity, as well as to market prices for natural uranium, conversion, enrichment, fabrication of fuel assemblies and SNF handling were determined.

An important energy and economic characteristic of nuclear fuel is the so-called fuel _{2} two-oxide fuel) due to using other fuel matrix and cladding materials (

To identify analytical possibilities for selecting economically feasible parameters of the fuel cycle of NPPs with an extended reactor campaign, we consider three approaches to the evaluation of nuclear fuel burnup.

_{FA}) =

where _{FA} is the mass of uranium in each _{CORE}/_{CORE} is the number of _{CORE}, where _{CORE} = _{CORE}×_{FA} is the mass of fuel in the reactor core, is referred to as specific thermal stressthermal stress of fuel (about 40 kW/kgU for UO_{2}), and relation _{FA}/

Number of replaceable FAs (_{FA} = 470 kgU), number of FAs in core (_{CORE} = 163), and maximum theoretical ICUF (

Normally,

By excluding

_{∞} −

_{f}_{f}_{f}_{f}

_{f}_{5})(_{5}/_{F})(_{f}_{f}_{f}_{f}_{f}_{5})

In the obtained expression (4), _{F} = _{FA} is the mass of the fuel extracted during refueling; _{5} is the mass of uranium-235 in the fresh fuel loaded into the reactor instead of the spent fuel during reactor campaign; _{5} /_{F} is the fresh fuel enrichment; _{f}_{f}

Using enrichment in %, as generally accepted, expression (4) can be written as

_{f}_{5} (5)

As can be seen, nuclear fuel burnup is directly proportional to the product of only two variable parameters: initial enrichment (_{f}_{5}. By comparing expressions (5) and (2), we obtain an important relation

(∆_{f}_{5})(_{f}_{f}

By definition, the right-hand part in the above expression does not depend on the refueling multiplicity. Therefore, the left-hand part is not expected to depend as well on

Dependence of the product of the relative mass of fission products (burnt-up nuclides, Δ_{f} /_{5}) by the function of refueling ratio, (_{CORE}

∆_{f}_{5} = 1.53

As it follows from Fig.

Finally, it follows from expression (7) with typical values of _{f}_{5}=1.1–1.3, that is the mass of fissionable nuclides (mass of fission products) burnt exceeds by 10 to 30% the initial mass of uranium-235 in fresh fuel due to the generated plutonium burnup which is confirmed by experimental data

Influence of uranium fuel enrichment and burnup on the mass of fission products in the PWR reactor SNF with one fourth of the reactor core refueled. _{f}_{5} values using formula (4) and of the (∆_{f}_{5})(

Average uranium-235 enrichment of replaced fuel |
Average burnup of replaced fuel |
Relative mass of fission products in replaced fuel, ∆_{f}_{T} |
Ratio of fission product mass in SNF to U-235 mass in fresh fuel ∆_{f} |
Parameter (∆_{f}_{5})( |
---|---|---|---|---|

3.8 | 44.9 | 47 | 1.23 | 1.54 |

4.5 | 54.3 | 57 | 1.27 | 1.59 |

5.4 | 64.1 | 67 | 1.24 | 1.55 |

6.5 | 73.8 | 78 | 1.2 | 1.50 |

7.5 | 84.0 | 89 | 1.19 | 1.49 |

8.5 | 93.7 | 99 | 1.16 | 1.45 |

Substituting the obtained relation (7) into expression (5), taking into account (1) and (2), leads to the sought-after analytical relationship of fuel burnup with fuel enrichment, refueling ratio, thermal stress and reactor campaign in the following form

Burnup calculations using formulas (8) and (9) describe satisfactorily the grid diagrams contained in _{2} fuel), that is, in a broad range of the fuel cycle parameters: enrichment of 0.711 to 10% and refueling multiplicity of

Relationship between average burnup (

As it follows from expression (9) and Fig.

Average fuel burnup (

Therefore, analytical expressions (7)–(9), obtained for the first time in the paper, allow estimating analytically the dependence of nuclear fuel burnup on fuel enrichment, refueling multiplicity(or number of discharged FAs), reactor campaign(refueling interval) and fuel thermal stress, which is required for plotting grid diagrams as a convenient tool for selection of the fuel cycle parameters.

The fuel component, _{F}, (Rub/kW·h) in the NPP operating costs includes the

_{Т} = _{FA} + _{SNF}) = _{NFC}. (10)

Quantity _{NFC} = _{FA} + _{SNF} can be called as the cost of the nuclear fuel cycle (open or closed) in terms of 1 kg of uranium (or heavy metals) in fuel (Rub/kg h.m.), including the _{FA} = _{Х}_{FAB}, and the SNF handling cost, _{SNF}. Quantities _{Х}_{FAB} are the costs of enriched uranium and

where

The ratio of fuel costs to the electricity sold, _{F}/

_{F} = _{f}_{FA} + _{SNF})/_{FA} + _{SNF})/(24η

If burnup is measured in MW·day/kgU, then _{F} is expressed in Rub/MW·h.

To estimate the cost of manufacturing the FAs replaced with fuel mass

Φ(

where

_{FA} = _{F}_{R}

– Φ(_{D}_{FAB}, (15)

in which _{F}_{U3O8} +_{UF6} is the price of natural uranium hexafluoride; _{U3О8}, _{UF6}, _{D}_{R}_{F}_{R}_{D}_{FAB}) depends only on the separation waste dump depth (tails assay), _{0}, with which the _{0} depends only on the ratio of prices (_{F}_{D}_{R}_{F}_{D}_{R}_{0} = 0.228%; with (_{F}_{D}_{R}_{0} < 0.228%; and with (_{F}_{D}_{R}_{0} > 0.228%. According to data from JSC Atomenergoprom (_{0} = 0.16–0.19%. In 2011, the market prices for uranium and enrichment reached their historical peaks: _{U3О8} = 148 $/kg, _{R}_{U3О8} = 57 $/kg, _{R}

Historical dynamics of market prices for natural uranium and uranium conversion/enrichment services, and of estimated cost of enriched uranium (

Parameter | 2011 | 2018 | 2021 |
---|---|---|---|

Uranium oxide concentrate price, _{U3O8}, $/kgU |
148 | 65 | 91 |

_{UF6}conversion price, $/kgU |
11 | 10 | 19 |

Uranium hexafluoride price, _{F} |
159 | 75 | 110 |

Separation work price, _{R} |
149 | 36 | 55 |

Optimal tails assay, _{0}, % |
0.220 | 0.155 | 0.158 |

Enriched uranium cost, _{x} |
2772 | 1002 | 1496 |

The costs of fuel assembly fabrication and SNF management are to a lesser extent determined by market quotations, but may depend on the depth of fuel burnup (enrichment). Since according to data in _{FAB}, growing from 300 to 450 $/kgU, and the SNF handling cost, _{SNF}, growing from 840 to 1770 $/kgU, which is practically proportional to the burnup. Such regularity is explained by the growth in the

Influence of uranium fuel burnup on the NFC cost characteristics.

Burnup depth, |
45 | 55 | 65 | 75 | 85 | 95 | |

_{FAB}, $/kgU |
300 | 330 | 360 | 390 | 420 | 450 | |

SNF transportation cost, _{TR,} $/kgU |
230 | 280 | 330 | 380 | 430 | 480 | |

SNF encapsulation and disposal cost, _{DIS}, $/kgU |
610 | 745 | 880 | 1015 | 1150 | 1290 | |

SNF handling cost, _{SNF}=_{TR}+_{DIS}, $/kgU |
840 | 1025 | 1210 | 1395 | 1580 | 1770 | |

Fuel enrichment*, |
3.9 | 4.6 | 5.6 | 6.5 | 7.3 | 8.2 | |

Enriched uranium cost**, _{x} |
2011 | 2090 | 2545 | 3200 | 3800 | 4330 | 4940 |

2018 | 760 | 920 | 1150 | 1360 | 1540 | 1750 | |

_{FA}=_{x}_{FAB}, $/kgU |
2011 | 2390 | 2875 | 3560 | 4190 | 4750 | 5390 |

2018 | 1060 | 1250 | 1510 | 1750 | 1960 | 2200 | |

Fuel component of NPP electricity cost***, _{F} |
2011 | 8.8 | 8.7 | 9.0 | 9.1 | 9.1 | 9.2 |

2018 | 5.2 | 5.1 | 5.1 | 5.1 | 5.1 | 5.1 |

* Calculation based on formula (8) with _{D}

It is important to note that, according to the presented results, the market prices for natural uranium and separation work have major effect on the fuel component of the electricity cost as compared with effects from fuel burnup and, accordingly, fuel enrichment.

The paper presents newly obtained analytical expressions (8), (9) for estimating the burnup of nuclear fuel depending on fuel enrichment, refueling periodicity, reactor campaign and specific thermal stress of fuel in a wide range of these parameters (without taking into account the constraints from the physicochemical processes in conditions of high burnups) as applied to thermal reactors. It has been shown that nuclear fuel burnup is directly proportional to the multiplication of only two parameters: enrichment of the fuel loaded during refueling, and ratio of the burnt fuel mass (≈ fission product mass) to the mass of fissionable nuclides in the loaded fuel according to expression (4). The latter ratio (∆_{f}_{5}) depends practically only on the refueling multiplicity and changes in a range of 1.0 to 1.5. The obtained analytical expressions for the burnup estimation are convenient as applied to variable-based economic, thermal-physical, strength and other calculations for reactor fuel batches with different cycle durations (12 to 24 months) and fuel enrichments (up to 10%), including the accident tolerant fuel under development.

It has been shown that fuel burnup increases practically linearly with the enrichment growth in the considered range of 0.7 to 10% with the preset refueling multiplicity, as shown by expression (8), and decreases linearly with the reactor campaign(refueling interval) increase with the preset fuel enrichment according to (9).

It has also been shown that the fuel component of the PWR NPP electricity cost is not so particularly sensitive to the fuel burnup change but is much more sensitive to the volatility of market prices for natural uranium, conversion and separation work or to changes of enriched uranium cost.

^{235}U enrichments above 5%.

Russian text published: Izvestiya vuzov. Yadernaya Energetika (ISSN 0204-3327), 2023, n. 2, pp. 94–105.