nuclear data uncertainty propagation on power maps ...

PHYSOR 2014 – The Role of Reactor Physics Toward a Sustainable Future The Westin Miyako, Kyoto, Japan, September 28 – October 3, 2014, on CD-ROM (2014)

NUCLEAR DATA UNCERTAINTY PROPAGATION ON POWER MAPS IN LARGE LWR CORES A. Santamarina, P. Blaise, N. Dos Santos, C. Vaglio, C. De Saint-Jean Commissariat à l’Energie Atomique et aux Energies Alternatives CEA, DEN, DER, SPRC, Cadarache F-13108 Saint-Paul-Lez-Durance, France. Corresp. Author: [email protected]

ABSTRACT Nuclear data uncertainty propagation is more and more required in safety calculations of large NPP cores. In this study, nuclear data uncertainties have been propagated to LWR cores using accurate transport calculations. PWR benchmarks representative of the French NPP fleet were selected: one 900MWe (Fessenheim), one 1500MWe (CHOOZ), as two complementary GEN-III benchmarks belonging to the OECD/UAM benchmark, representative of large PWR UOX and –partially loaded - MOX cores surrounded by thick stainless steel reflector. Reactivity and assembly power map sensitivity coefficients to multigroup cross sections have been calculated using perturbation theory tools implemented in ERANOS2/SNATCH transport code. Different sources of nuclear data uncertainty were compared: covariance matrices from BOLNA, and French COMAC associated to JEFF3.1.1 evaluations, were used for uncertainty propagation. The total uncertainty on the multiplication factor keff is not sensitive to the size and the loading of the PWR cores; this uncertainty amounts to 560pcm (1σ) with COMAC, compared to 780 pcm with BOLNA covariances. The main component of keff uncertainty is ν U235, followed by 238U capture, σcU235 and σfU235. The uncertainty on the radial power map increases with the core size, due to higher Eigen Value Separation factor (EVS>20). For example, using COMAC covariances, the uncertainty in central assemblies increases from 1.5% for PWR-900MWe to 3.4% for large N4 and GEN-III PWRs. In the peripheral assemblies which can host the power peak, the uncertainty increases from 1.1% for 900MWe to 2% for large PWRs. Therefore, the potential power swing bias in JEFF3.1.1 core calculations varies from 2.6% for PWR-900MWe to 5-6% for N4 and large GEN-III PWRs. Using BOLNA covariance files, the uncertainty on the Pcentre/Pperiph power ratio amounts to 10% (5% with COMAC) for GEN-III PWR core, and up to 24% in the Gen-III MOX benchmark (12% with COMAC). Our powerful deterministic calculation scheme allowed the decomposition of the LWR parameter uncertainty in isotopic partial cross-section components. The main contributor to the power uncertainty is the 238U inelastic scattering: 3% and 5%, respectively for COMAC and BOLNA, in GEN-III central assemblies. However, 16O and 1H elastic scattering cross-sections should be also validated and improved in order to reduce their individual 1%-2% current contribution to the central power uncertainty. Key Words: sensitivity, uncertainty propagation, PWR large core, power map

1. INTRODUCTION A good understanding of the biases and uncertainties on reactor core calculations is essential for assessing safety features and design margins in current and future NPPs, as well as in experimental reactors such as MTRs. In recent years there has been an increasing demand from nuclear industry, safety and regulation for best estimate predictions to be provided with their confidence bounds.

Alain Santamarina et al.

Biases are induced by modelling assumptions (geometry simplification, spatial discretization) and deterministic calculation options (resonance self-shielding formalism, flux solver, etc.). Those biases are usually determined, almost straightforward, by comparison between deterministic calculations and reference Monte Carlo calculations, within the Validation phase of the VVQ&UQ (Verification, Validation, Qualification & Uncertainty Quantification) process of deterministic codes and calculation schemes deployment [1]. Global uncertainties on core parameters are assessed with the propagation of both technological and nuclear data uncertainties. Technological uncertainties have to be managed by the reactor designer with the knowledge of the design margins and their respects for core geometry, material balance, and the assessing of working parameters. Nuclear data uncertainties gather the uncertainties associated with microscopic measurements (counting rate, detector efficiency, etc.) and nuclear physics model uncertainties used to fit the previous measurements. In an ideal world, they should be provided under the form of covariance matrices by nuclear physicists during the process of producing nuclear data evaluations for international evaluated nuclear data files. In practice, this is not always the case and covariances are often issued from “expert” judgment. However these data are very important for uncertainty propagation and are currently the subject of a large effort in the international community [2]. At CEA, the CONRAD code enables to produce covariance matrices from marginalization technique [3]. To obtain reliable covariances associated with JEFF3.1.1 evaluations [4], a nuclear data re-estimation of the major isotopes was performed thanks to selected targeted integral experiments [5]. This work led to the emission of a new set of covariance matrices linked to JEFF3.1.1 : the COMAC file (COvariance MAtrices Cadarache) [6]. In this covariance file, a particular attention was paid to the re-evaluation of important isotopes 235U [7], 56Fe [8], 238U and 239Pu [9], meanwhile other evaluations are mainly based on ENDF/B-VII covariance file. For almost 30 years, nuclear data uncertainty propagation and nuclear data statistical adjustment in fast reactor applications have been widely used to produce “adjusted” sets of multigroup cross sections and to assess the uncertainty on neutronics design parameters. As a consequence, these methods are naturally implemented in calculation tools dedicated to GEN-IV neutron calculations, such as the ERANOS2 code [10]. Recent publications have already presented results of nuclear data propagation for GEN-IV reactors [11]. However, results concerning the nuclear data propagation on GEN-II and GEN-III reactor parameters are scarce. In order to fill the gap, an "indepth" discussion on “Uncertainty Analysis in Modeling” was organized at the 2005 OECD/NEA meeting, which led to a proposal for launching an Expert Group on "Uncertainty Analysis in Modeling" and endorsing the organization of a workshop with the aim of defining future actions and a program of work in the field of LWRs [12,13]. First results obtained on GEN-III UOX and MOX benchmarks [14] pointed out the high level of the uncertainty in calculated radial power map, and identified the cross sections that give large uncertainty components (predominance of 238U inelastic scattering, scattering of 56Fe, 1H and 16O). This paper will present the nuclear data uncertainties propagation to core parameters (reactivity, assembly power), for several GEN-II and GEN-III full core benchmarks. The accurate calculation route implemented for determining integral parameters and their sensitivity coefficients to partial cross sections is based on the ECCO [15] and SNATCH [16] transport tools in ERANOS2. This code package, mainly dedicated to fast GEN-IV reactors, has been used since the different perturbation theories (Standard, Generalized and Equivalent generalized formulas dedicated respectively to perturbations of keff, reaction rate ratio and reactivity worth) are available in SNATCH 3D transport calculations. This deterministic approach will allow the determination of the isotopic partial cross-section contributions to the radial power map uncertainty. PHYSOR 2014 – The Role of Reactor Physics Toward a Sustainable Future 2 / 13 Kyoto, Japan, September 28 – October 3, 2014

Nuclear Data Uncertainty Propagation on Power Maps in Large LWR Cores

The paper is split into 4 sections. The PWR benchmarks are described in section 2. Codes, calculation schemes, and covariance data are described in section 3. Sensitivity/Uncertainty results on core Reactivity and radial Power map are detailed respectively in section 4 and section 5. 2. GEN-II AND GEN-III BENCHMARKS Several benchmarks have been selected for the purpose of uncertainty propagation. In order to complete the UAM-LWR benchmarking, 2 actual PWR radial descriptions have been added to the study. They are described here below : •

•

The first core corresponds to Fessenheim 1rst loading, CPY 900MWe PWR type of the French NPP fleet. It is composed of 157 fuel assemblies with different UOX contents (2.1%, 2.6%, 3.1%). The movable burnable poisons are of PYREX type (boron silicate). The core is surrounded by a stainless steel radial baffle 2.2 cm thick. Hot and cold legs, as well as the neutron shielding and internal and external vessels are also reproduced. The second core corresponds to Chooz-B1 1rst loading that belongs to the French N4-type (1500MWe). This core, larger than the previous one, is composed of 205 fuel assemblies with three different enrichments (1.8%, 2.4%, 3.1%). Burnable poisons inside guide-tubes are also PYREX. The core is surrounded by baffle and water identical to CPY.

Hot Full Power conditions at the beginning of the core life are used for technological description: fuel and coolant temperature, critical boron concentration. The 2D representation used in the SNATCH SN solver is reproduced on Fig. 1.

Figure 1. PWR 900MWe benchmark (left) and 1500 MWe benchmark (right)

For remainder, the GEN-III fresh UOX and MOX cores benchmark is given in Fig. 2. As for the GEN-II cores, operating conditions correspond to Hot Full Power conditions at the beginning of the core life. The UOX core is composed of 241 17×17 GEN-III PWR assemblies of 4 different types, corresponding to a foreseen realistic loading pattern: - UOX 4.2% 235U assembly (without UO2-Gd2O3 rods), - UOX 4.2% 235U assembly with 12 UO2-Gd2O3 (2.2% 235U) rods, - UOX 3.2% 235U assembly with 20 UO2-Gd2O3 (1.9% 235U) rods, - UOX 2.1% 235U assembly (without UO2-Gd2O3 rods). PHYSOR 2014 – The Role of Reactor Physics Toward a Sustainable Future 3 / 13 Kyoto, Japan, September 28 – October 3, 2014

Alain Santamarina et al.

The GEN-III MOX is loaded by 2 types of UOx assemblies (UOX 3.2% 235U assembly with 20 UO2-Gd2O3 rods and UOX 2.1% 235U assembly without Gd rods). The external ring of the core is loaded exclusively with MOX assemblies (zoned with 3.7%, 6.5%, 9.8%Pu content from peripheral MOX pins to central MOX pins). A radial Stainless Steel reflector, representative of a GEN-III heavy reflector of about 22 cm thickness, modelled by homogeneous SS assemblies, surrounds these cores. Borated water (critical boron concentration of 1300 ppm) completes the geometry.

Figure 2. GEN-III 1700MWe benchmark; UOX (left) and MOX (right)

3. CALCULATION TOOLS AND DATA 3.1 Transport and perturbation calculation The accurate calculation of the various core parameters and their associated sensitivity coefficients to nuclear data is based on an ECCO/SNATCH transport calculation using JEFF3.1.1 multigroup cross sections libraries. The calculation scheme relies on 4 different successive steps. • A space-dependent self-shielding calculation is carried out for cross sections in the standard fine ECCO 1968-group structure with a discretization of the fuel pins in 4 rings to accurately treat the 238U resonant absorption; UP0-ROTH×4 interface current method is used as flux solver for the subgroup self-shielding method. • A flux assembly calculation is performed based on the UP0-ROTH×4 interface current method using the 1968-group self-shielded cross-sections in ECCO. The flux obtained from the assembly calculation is used to calculate homogenized cross sections over the whole assembly and collapsed on the JEF 15-energy group structure (Table I). • A one fourth of the symmetrical 2D (X-Y) fresh core is then modelled using homogeneous assemblies with the SNATCH solver. A S4-P1 flux calculation, based on a discrete ordinate method to treat the angular variable is performed. The spatial discretization of the advection-reaction operator is made with a Discontinuous Galerkin method [17] (with uniform second-order polynomial basis). The core spatial mesh is based on a uniform 4-element discretization of the assemblies. • First order perturbation theories are implemented in SNATCH, and are used for the determination of the sensitivity coefficients of the neutronics parameters to nuclear data. Standard Perturbation Theory (SPT) is used for keff uncertainties to nuclear data, as Generalized Perturbation Theory (GPT) is used for power distribution uncertainty. 4 / 13

PHYSOR 2014 – The Role of Reactor Physics Toward a Sustainable Future Kyoto, Japan, September 28 – October 3, 2014

Nuclear Data Uncertainty Propagation on Power Maps in Large LWR Cores

F  The Boltzmann balance equation for a system without external source is denoted:  A − Φ = 0 k  where A is the removal operator and F the production operator. If now a small system perturbation close to this unperturbed state is considered, the reactivity perturbation can be estimated to the first order using the SPT as: δF   < Φ + ,  δA − Φ > δk k   = δρ = − (1) 2 + k < Φ , FΦ > with k : unperturbed effective multiplication factor Φ : unperturbed direct flux Φ + : unperturbed adjoint flux The perturbation of a normalized reaction rate R =< Σ i , Φ > such as an assembly power normalized to the total core power, can be estimated with the GPT by: δF  δR < δΣ i , Φ >  = − < Ψ + ,  δA − (2) Φ > R k  < Σi , Φ >  Σi F+ + )Ψ = with Ψ + being the importance function, solution of ( A + − . k < Σi , Φ >

3.2 Covariance data The covariance matrices used to propagate nuclear data uncertainties come from BOLNA [2], issued from cooperation between BNL-ORNL-LANL-NRG-ANL labs, and specific work from CEA through the COMAC file build to obtain consistent uncertainties associated with JEFF3.1.1 evaluations. Both matrices have been processed in the 15-group format (Table I). Table I. 15-group structure used for sensitivity and uncertainty calculations Group

Upper energy

1

19.64 MeV

2 3 4 5 6 7

6.06 MeV 2.23 MeV 1.35 MeV 498 keV 183 keV 67.4 keV

8 9 10 11 12 13 14 15

Characteristics (n,xn) reactions second and third chance fission Fast domain 1st resonance of O-16 Unresolved Resonances domain for U-238

Unresolved Resonances domain for heavy nuclei Resonances of light nuclei (Na-23, Fe-56) 9.12 keV Resolved Resonances domain Resolved Resonances domain 2.03 keV 1st resonance of Fe-56 454 eV Resolved Resonances domain 22.6 eV 1st resonances of U-238 4 eV 1st resonances of Pu-240, Pu-242 0.53 eV 1st resonances of U-235, Pu-239, Pu-241 0.1 eV – 10-5 eV Purely Thermal Domain 24.8 keV

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Alain Santamarina et al.

4. UNCERTAINTY PROPAGATION ON CORE REACTIVITY We first assessed the impact of the covariance data choice on PWR core reactivity uncertainty. Table II presents the propagated uncertainty due to major contributors using BOLNA and COMAC covariances. Large differences are observed on the total uncertainty: BOLNA gives a 780pcm (1σ) uncertainty on the keff calculation of PWR-UOX cores, as COMAC gives a reduced 560pcm uncertainty. This disagreement is mainly due to 235U covariances, particularly the uncertainty component linked to multiplicity νU235 which amounts to 600pcm with BOLNA instead of 310 pcm with COMAC covariance. The uncertainty component given by COMAC is lower because JEFF3.1.1-based calculations are more reliable, due to the 235U JEFF3.1.1 evaluation that had benefit from integral measurement feedbacks [4,7]. Table II. Propagated uncertainty and main contributors to the core keff

keff

Total Uncert. Contributor n°1

Contributor n°2

Contributor n°3

Contributor n°4

Contributor n°5

238

U (n,n’)

900 MWe

N4

GEN-III UOX

GEN-III MOX

1.01967

1.00128

1,01101

1,00966

COMAC

BOLNA

COMAC

BOLNA

COMAC

BOLNA

563 pcm

788 pcm

564 pcm

789 pcm

565 pcm

773

ν(

235

U)

ν(

235

U)

ν(

235

U)

ν(

235

U)

ν(

235

U)

ν(

235

U)

312 pcm

602 pcm

311 pcm

602 pcm

316 pcm

595 pcm

238

238

238

238

238

238

U (n,γ)

U (n,γ)

U (n,γ)

U (n,γ)

U (n,γ)

COMAC

BOLNA

489 pcm

668

U (n,γ)

ν(235U)

241 pcm

455 pcm

238

U (n,γ)

ν(235U)

238

U(n,γ)

261 pcm

292 pcm

264 pcm

296 pcm

258 pcm

289 pcm

240 pcm

273 pcm

235

16

235

16

235

16

238

16

U (n,f)

O (n,α)

U (n,f)

O (n,α)

U (n,f)

O (n,α)

U (n,f)

249 pcm

265 pcm

250 pcm

257 pcm

252 pcm

255 pcm

232 pcm

238

235

238

235

238

235

235

U (n,f)

U (n,γ)

U (n,f)

U (n,γ)

U (n,f)

221 pcm

156 pcm

225 pcm

155 pcm

225 pcm

235

235

235

235

235

U (n,γ)

U (n,f)

U (n,γ)

U (n,f)

U (n,γ)

U (n,γ)

156 pcm 238

U(n,n’)

U (n,f)

196 pcm 239

Pu (n,f)

O (n,α)

263 pcm 238

U(n,n’)

160 pcm 235

U (n,γ)

134 pcm

140 pcm

134 pcm

140 pcm

141 pcm

141 pcm

159 pcm

117 pcm

102pcm

134 pcm

100pcm

120 pcm

107 pcm

141 pcm

118 pcm

160 pcm

Contribution from both 238U(n,γ) and 235U(n,γ) are consistent between evaluations. The other contributors are different: for BOLNA, 235U(n,f) uncertainty is characterized by a low 140pcm component (compared to 260pcm using COMAC), on the contrary 16O(n,α) uncertainty seems pessimistic with 260pcm component as much as the 238U(n,γ) contribution. Table II points out that uncertainty in mixed-loading core is slightly lower than in UOX cores. Indeed the k∞ uncertainty of MOX assembly is higher than the one of UOX assemblies (700 pcm for MOX to be compared to 500pcm for UOX, using COMAC), however the keff uncertainty of a mixed-loading UOX/MOX core is lower due to uncorrelation between the uncertainties of 235U and 239Pu nuclear data. 6 / 13

PHYSOR 2014 – The Role of Reactor Physics Toward a Sustainable Future Kyoto, Japan, September 28 – October 3, 2014

Nuclear Data Uncertainty Propagation on Power Maps in Large LWR Cores

5. UNCERTAINTY PROPAGATION ON RADIAL POWER MAP Figures 3 to 6 present the normalized power distributions and associated uncertainties (with BOLNA) in the GEN-II and GEN-III cores. The ERANOS2 deterministic transport calculation was validated against reference TRIPOLI4 [18] Monte Carlo calculation: assembly power values are consistent within 3%. The propagation of the selected BOLNA and COMAC nuclear data uncertainties to an assembly power was performed for every assembly locations. Figs. 3 to 6 show that radial power maps are not similar. For the 900MWe, the power distribution presents a higher level at the centre and drops at the periphery. For the large N4 and GEN-III cores characterized by a smaller neutron leakage, the trend is inverted: the power is displaced from the centre to the periphery. Figure 7 compares the power profiles on the x-axis.

Figure 3. 900MWe Radial power map (left) and associated uncertainty with BOLNA (right)

Figure 4. 1500MWe Radial power map (left) and associated uncertainty with BOLNA (right)

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Alain Santamarina et al.

Figure 5. Gen-III UOX Radial power map (left) and associated uncertainty with BOLNA (right)

Figure 6. Gen-III MOX Radial power map (left) and associated uncertainty with BOLNA (right)

Figure 7. Radial power distribution on the main x-axis for the 4 benchmarks

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PHYSOR 2014 – The Role of Reactor Physics Toward a Sustainable Future Kyoto, Japan, September 28 – October 3, 2014

Nuclear Data Uncertainty Propagation on Power Maps in Large LWR Cores

Concerning the uncertainty on the calculated power maps, all figures exhibit the same trend, e.g. a maximum value in the center and at the periphery, with a clear ring of mid-assemblies where the uncertainty is close to zero. This is due to the flux radial swing generated by any perturbation, particularly by nuclear data modifications. The radial swing increases with the size of the core due to the high Eigen Value Separation factor (EVS>20). Table III summarizes the radial power maps, as well as propagated uncertainties (1σ) from both BOLNA and COMAC evaluations. The central and peripheral positions, as well as the “pivot” position, are colored. Table III points out that the uncertainty in the power peak calculation increases with the PWR size : the uncertainty on the central assembly power increases from 4.5% in the 900MWe core up to 8%-10% in the N4 and GEN-III large cores, using BOLNA evaluations. Therefore the potential swing bias increases from 8% in the 900MWe core up to 16% in the N4-1500MWe core. Table III also exhibits a larger uncertainty in the GEN-III MOX benchmark, 15% (1σ) in the central assembly, specific of this mixed-loading pattern : MOX assemblies are not in a checkerboard but are loaded at the core periphery, thus Pu nuclear data modifications are located only on the peripheral row that infers strong flux tilt. Table III shows strong discrepancies between COMAC and BOLNA covariances, the former giving 2 to 3 times lower uncertainties. Table III. Power map on the main x-axis and associated uncertainties in %: in blue COMAC, in red BOLNA Core

assemb.1 assemb.2 assemb.3

assemb.4

assemb.5 assemb.6

assemb.7 assemb.8

assemb.9

900 MWe

1.08 1.5 4.5

1.05 1.5 4.3

1.14 1.2 3.4

1.09 0.8 2.3

1.18 0.2 0.5

1.21 0.4 1.4

1.04 1.1 3.2

0.81 1.5 4.2

N4 1500MWe

0.80 3.4 9.8

0.86 3.3 9.4

0.87 2.9 8.2

0.90 2.4 6.8

0.88 1.6 4.6

1.04 0.6 1.7

1.01 0.6 1.8

1.09 1.8 5.2

1.05 2.5 6.8

GEN-3 UOX

0.81 3.2 7.8

0.74 3.2 7.8

0.73 3 7.4

0.73 2.5 6.3

0.81 1.8 4.6

0.86 1.1 2.7

0.97 0.3 0.7

1.05 0.6 1.5

1.08 1.2 2.3

GEN-3 MOX

0.90 7.5 14.8

0.82 7.3 14.4

0.81 6.6 13.1

0.79 5.4 10.7

0.88 3.8 7.6

0.93 1.9 3.7

1.07 0.3 0.7

1.15 2.6 5.3

1.18 4.7 9.2

Deterministic S/U analysis is a powerful method because it supplies the isotopic partial cross-section contributions to the uncertainty. Table IV reproduces the detail of sensitivity coefficients and propagated uncertainties (on the x-axis) for major contributors in the case of N4 core. The results are almost identical for the other UOX cores. The main uncertainty component is given by the 238U inelastic scattering, with 5.3% contribution to the power uncertainty in the central assembly (compared to 2.8% using COMAC covariances). In the case of BOLNA file, a major contribution is also given by the 16O elastic scattering : this 8.1% component to the power uncertainty in the central assembly seems unrealistic because the integrated sensitivity to this nuclear data is limited to 0.62. On the contrary, the 16O(n,n) uncertainty component by 1% in COMAC is more reliable. Therefore, the strong COMAC/BOLNA disagreement on the power uncertainty is mainly linked to the 16O(n,n) contribution. PHYSOR 2014 – The Role of Reactor Physics Toward a Sustainable Future Kyoto, Japan, September 28 – October 3, 2014

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Table IV. Main contributors to the assembly power uncertainty (in %, at 1σ) for the N4 core assemb n°

1

2

3

4

5

6

7

8

9

0.80

0.86

0.87

0.90

0.88

1.04

1.01

1.09

1.05

BOLNA

9.8%

9.4%

8.2%

6.8%

4.6%

1.7%

1.8%

5.2%

6.8%

COMAC

3.4%

3.3%

2.9%

2.4%

1.6%

0.6%

0.6%

1.8%

2.5%

Sensitivity

-0.32

-0.30

-0.27

-0.22

-0.15

0.05

0.06

0.17

0.23

BOLNA

5.3%

5.1%

4.5%

3.7%

2.5%

0.9%

0.9%

2.8%

3.8%

COMAC

2.8%

2.7%

2.4%

2.0%

1.4%

0.5%

0.5%

1.5%

2.0%

Sensitivity

-0.62

-0.59

-0.52

-0.43

-0.29

-0.11

0.11

0.33

0.45

BOLNA

8.1%

7.7%

6.8%

5.6%

3.8%

1.4%

1.5%

4.3%

5.5%

COMAC

0.9%

0.9%

0.8%

0.6%

0.4%

0.2%

0.2%

0.5%

0.6%

Power Total uncertainty

238

16

U (n,n’)

O (n,n)

Fig.8 reproduces the 238U(n,n’) sensitivity variation as a function of the assembly position, and the core size. Each core exhibits the same general trend: a negative sensitivity in the core center, and a positive contribution at the periphery. The sensitivity in central assemblies increases from -0.18 for the PWR-900MWe to -0.32 for the N4 and GEN-III large cores. Since 238U(n,n’) uncertainties are strongly energy-correlated and amount to 10% in COMAC and 20% in BOLNA, the uncertainty component on central assembly power amounts to 2.8% and 5.3% respectively.

Figure 8. Integrated Sensitivity profile of power distribution to 238U(n,n’) for each NPP

Another significant uncertainty component, 1% on the central assembly power, is the hydrogen elastic scattering, due to its high sensitivity value shown in Figure 9. Indeed the radial power map of large LWRs is very sensitive to the migration area of fast neutrons (Fermi’s age), thus to scattering cross-section uncertainties (inelastic scattering of heavy isotope 238U, elastic scattering of light isotopes 1H and 16O). In the specific GEN-III case, characterized by a Stainless Steel neutron reflector, the supplementary uncertainty component linked to 56Fe cross-sections amounts to 1.7% (BOLNA) on the central assembly power. This 56Fe uncertainty component is limited to 1.2% using COMAC, which means that JEFF3.1.1-based calculations of the GEN-III power map is not jeopardized by the SS reflector, thanks to the dedicated PERLE experiment [19]. 10 / 13

PHYSOR 2014 – The Role of Reactor Physics Toward a Sustainable Future Kyoto, Japan, September 28 – October 3, 2014

Nuclear Data Uncertainty Propagation on Power Maps in Large LWR Cores

Figure 9: Sensitivity profiles of the GEN-III central assembly power to partial cross sections

Concerning the GEN-III MOX core, Table V details the contributors to the uncertainty on the mixed-loading power map. The contribution of scattering cross-sections (238U, 1H, 16O) decreases, meanwhile higher contributions arise from fissile isotopes nuclear data. The huge power sensitivity to the reactivity of fissile isotopes is illustrated in Fig.10 where sensitivity to 239 Pu(n,f) varies from -6 at core center to +4 in peripheral assemblies. Therefore, modifications of plutonium nuclear data will impact only the reactivity of MOX peripheral assemblies, meanwhile modifications of 235U nuclear data will impact only the reactivity of central assemblies. Thus, this heterogeneous mixed-loading pattern emphasizes the sensitivity of the radial power map to the respective k∞ value of UOX and MOX assemblies. Table V. Main contributors to the assembly power uncertainty (in %, at 1σ) for the GEN-III MOX core assemb n°

1

2

3

4

5

6

7

8

9

Power

0.90

0.82

0.81

0.79

0.88

0.93

1.07

1.15

1.18

BOLNA

14.8%

14.4%

13.1%

10.7%

7.6%

3.7%

0.7%

5.3%

9.2%

COMAC

7.5%

7.3%

6.6%

5.4%

3.8%

1.9%

0.3%

2.6%

4.7%

Uν

BOLNA

9.5%

9.2%

8.2%

6.7%

4.7%

2.3%

0.7%

3.4%

5.9%

241

Pu (n,f)

BOLNA

4.8%

4.6%

4.2%

3.4%

2.4%

1.2%

0.1%

1.6%

3.2%

239

Pu (n,f)

BOLNA

4.0%

3.9%

3.5%

2.9%

2.0%

1.0%

0.1%

1.4%

2.6%

Sensitivity

-0.20

-0.20

-0.19

-0.16

-0.11

-0.06

0.01

0.07

0.10

BOLNA

3.3%

3.4%

3.3%

2.7%

1.9%

0.9%

0.1%

1.2%

1.8%

COMAC

1.8%

1.7%

1.7%

1.5%

1.0%

0.5%

0.1%

0.7%

1.0%

Sensitivity

-0.30

-0.30

-0.29

-0.24

-0.19

-0.09

0.01

0.12

0.17

BOLNA

5.0%

5.0%

4.8%

4.1%

2.9%

1.3%

0.3%

2.0%

2.5%

COMAC

0.5%

0.5%

0.5%

0.4%

0.3%

0.1%

0.03%

0.2%

0.3%

COMAC

0.6%

0.6%

0.6%

0.5%

0.3%

0.2%

0.0%

0.2%

0.3%

Total uncertainty 235

238

16

1

U (n,n’)

O (n,n)

H (n,n)

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Alain Santamarina et al.

Figure 10. Integrated Sensitivity of power map to 239Pu(n,f) for Gen-III MOX benchmark

6. CONCLUSIONS This study has presented the results of nuclear data uncertainty propagation on the main design parameters of GEN-II (900MWe, 1500MWe) and large GEN-III cores (UOX and partial MOX) from actual French PWR fleet. The multiplication factor and the radial power maps, as well as the corresponding sensitivity profiles to partial cross-sections obtained from SPT-GPT, were determined using accurate 15-group transport calculations. Two nuclear data covariance files were used for uncertainty propagation: on the one hand the international BOLNA file, and on the other hand the CEA COMAC file more representative of the uncertainties associated with JEFF3.1.1 evaluations. This deterministic calculation scheme allowed the decomposition of the LWR parameter uncertainty in isotopic partial cross-section components. The keff total uncertainty, not sensitive to the PWR core size, amounts to 560pcm (1σ) with COMAC, compared to 780 pcm with BOLNA covariances. The uncertainty on the radial power map increases with the PWR core size, due to higher Eigen Value Separation factor. Using COMAC covariances, the uncertainty in the central assemblies increases from 1.5% for PWR-900MWe to 3.4% for large N4 and GEN-III PWRs. In the peripheral assemblies the uncertainty increases from 1.1% for 900MWe to 2% for large PWRs. Therefore, the potential power swing bias in JEFF3.1.1 core calculations varies from 2.6% for PWR-900MWe to 5.4% for N4 and GEN-III PWRs. Using BOLNA covariance files, the uncertainty on the Pcentre/Pperiph power ratio amounts to 10% (5% with COMAC) for GEN-III core. The main contributor to the power uncertainty is the 238U inelastic scattering: 3% and 5%, respectively for COMAC and BOLNA, in GEN-III central assemblies. To meet the target-accuracy required by GEN-III design, 238U(n,n’) uncertainty has then to be reduced from current 15% standard deviation to 5% (1σ). This improvement can be achieved only through the use of targeted integral measurements with a strong sensitivity to 238U(n,n’); some work has already been performed that allowed 238U scattering data re-estimation [20]. Furthermore, 16O and 1H elastic scattering cross-sections should also be validated and improved in order to reduce their individual 1%-2% current contribution to the central power uncertainty. AKNOWLEDGEMENTS This work has been partially co-financed by CEA’s industrial partners Electricité de France and AREVA. The authors are indebted to Drs D. Bernard - P. Leconte - J-F. Vidal for the TRIPOLI4 calculation of the PWR cores to validate ERANOS2 deterministic transport calculations. 12 / 13

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Nuclear Data Uncertainty Propagation on Power Maps in Large LWR Cores

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