A Versatile Methodology for Reactor Pressure Vessel Aging Assessments

Figures & data

Fig. 1. Contribution of ²³⁵U, ²³⁸U, ²³⁹Pu, and ²⁴¹Pu to the total fission neutron emission rate as a function of time in the case of (a) UOX assemblies and (b) MOX assemblies.

TABLE I Data for Fission Neutron Spectrum Modeling

Nuclide	Incident Neutron Energy	Fission Spectrum Type	Spectrum Coefficient, a ($\mathrm{M}\mathrm{e}\mathrm{V}$)	Spectrum Coefficient, b ($\mathrm{M}\mathrm{e}{\mathrm{V}}^{-1}$)
^235U	Thermal	Watt	0.988	2.249
^238U	2.6 MeV	Watt	0.920	3.121
^239Pu	Thermal	Watt	0.966	2.842
^241Pu	Thermal	Maxwell	1.3597	—

Fig. 2. Radial cut of the MCNP6 reactor modeling with tallies indicated by black and white sections. (1) Fuel assemblies; (2) core baffle; (3) moderator bypass; (4) core barrel; (5) thermal neutron shield; (6) downcomer; (7) RPV; (8) capsules of the French surveillance program.

Fig. 3. Axial cut of the MCNP6 reactor modeling and axial segmentation of the considered tallies indicated by black and white sections. (1) Fuel assemblies; (2) core baffle; (3) moderator bypass; (4) core barrel; (5) thermal neutron shield; (6) downcomer; (7) RPV.

Fig. 4. Radial cut of the MCNP6 (a) UOX assembly and (b) MOX assembly modeling. For MOX assemblies, three different types of fuel pins are modeled with high (orange), medium (pink), and low (red) Pu content.

Fig. 5. Atomic displacement cross section of ⁵⁶Fe processed at 300 K from the JEFF-3.3 nuclear data library and comparison between the NRT-dpa model and the ARC-dpa model.

TABLE II Composition of RPV Steel*

Nuclide	Normalized Atomic Fraction	Nuclide	Normalized Atomic Fraction
^natC	9.2284E-03	^28Si	3.6399E-03
^50Cr	1.1591E-04	^29Si	1.8430E-04
^52Cr	2.2327E-03	^30Si	1.2234E-04
^53Cr	2.5314E-04	^55Mn	1.3619E-02
^54Cr	6.2886E-05	^31P	1.4314E-04
^58Ni	4.1908E-03	^32S	1.3141E-04
^60Ni	1.6015E-03	^33S	1.0372E-06
^61Ni	6.9335E-05	^34S	5.8221E-06
^62Ni	2.2028E-04	^36S	2.3510E-08
^64Ni	5.5836E-05	^63Cu	4.8282E-04
^92Mo	4.2747E-04	^65Cu	2.1490E-04
^94Mo	2.6861E-04	^59Co	2.8212E-04
^95Mo	4.5924E-04	^natVa	1.0879E-04
^96Mo	4.8235E-04	^54Fe	5.5666E-02
^97Mo	2.7728E-04	^56Fe	8.8106E-01
^98Mo	6.9608E-04	^57Fe	2.0635E-02
^100Mo	2.7728E-04	^58Fe	2.7833E-03

*16MND5 steel.³⁷

TABLE III Material Constants*

Material	$E_d$($\mathrm{e}\mathrm{V}$)	$b_{ARC-dpa}$	$c_{ARC-dpa}$
Fe	40	−0.568 $\pm$ 0.020	0.286 $\pm$ 0.005
Cu	33	−0.68 $\pm$ 0.050	0.16 $\pm$ 0.010
Ni	39	−1.01 $\pm$ 0.110	0.23 $\pm$ 0.010

*Reference 31.

Fig. 6. Relative fission neutron emission rate distribution differences (%) between the developed and the reference methodologies at (a) fuel assembly level and at (b) fuel pin level $\left(\frac{\mathrm{S}\mathrm{I}\mathrm{M}\mathrm{U}\mathrm{L}\mathrm{A}\mathrm{T}\mathrm{E}5-\mathrm{M}\mathrm{C}\mathrm{N}\mathrm{P}6}{\mathrm{M}\mathrm{C}\mathrm{N}\mathrm{P}6}\right)$.

Fig. 7. (a) Fast neutron flux and (b) ARC-dpa axially integrated azimuthal distributions and relative differences between using the SIMULATE5 and MCNP6 fission neutron source terms.

Fig. 8. (a) Fast neutron flux and (b) ARC-dpa axially integrated azimuthal distributions and relative differences between the use of beginning-of-cycle and end-of-cycle fuel compositions in the MCNP6 fixed source calculation.

Fig. 9. Relative differences (%) in the cycle-averaged dpa rate distribution on the RPV between the use of a detailed vessel material and the use of a simplified vessel material $\left(\frac{simplified-detailed}{detailed}\right)$.

TABLE IV Summary of Methodological Biases on RPV Aging Estimates

Methodology Step	Nature	Bias Range (%)
Fission neutron source term	Spatial description	$\pm$2
	Fission spectrum description	Within $\pm$1
Neutron transport	Moderator density	≤ [+10; +11]
	Fuel composition	Within $\pm$0.5
Displacements per atom evaluation	Use of only Fe, Cu, and Ni	[−0.9; −0.4]

Fig. 10. Number of irradiation cycles of each fuel assembly for the considered fuel loading (UOX assemblies are indicated in green, and MOX assemblies are indicated in purple). For symmetry reasons, only a quarter of the core is represented.

Fig. 11. Evolution along the cycle of (a) the azimuthal fast neutron flux distribution on the RPV (axially integrated) and (b) the axial distribution for azimuthal position 0 deg on the RPV.

Fig. 12. Relative differences (%) in the cycle-averaged ARC-dpa rate distribution on the RPV between integration methods 1 and 2 $\left(\frac{method2-method1}{method1}\right)$.

Fig. 13. Relative differences (%) in the cycle-averaged ARC-dpa distribution on the RPV between the temporal mesh a and the temporal mesh b $\left(\frac{b-a}{a}\right)$.

Fig. 14. Relative differences (%) in the cycle-averaged ARC-dpa distribution on the RPV between the temporal mesh a and the temporal mesh c $\left(\frac{c-a}{a}\right)$.

Fig. 15. Contributions of neutron energies to the cycle-averaged, axially integrated, ARC-dpa rate in the capsules and at several azimuthal locations in the RPV, for the reactor cycle described in Sec. III.A.

Fig. 16. Cycle-averaged $W_{\mathrm{A}\mathrm{R}\mathrm{C}-\mathrm{d}\mathrm{p}\mathrm{a}/{\varphi }_{E>1\mathrm{M}\mathrm{e}\mathrm{V}}}$ distribution on the vessel for the reactor cycle described in Sec. III.A.

B. VEILLARD-BARON and Y. MEYZAUD, “Structure des racteurs nuclaires - Aciers spciaux,” Techniques de l’ingnieur, bn3730 (1998).

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