validation of the new code package apollo2.8 for ...

International Conference on Mathematics and Computational Methods Applied to Nuclear Science & Engineering (M&C 2013), Sun Valley, Idaho, USA, May 5-9, 2013, on CD-ROM, American Nuclear Society, LaGrange Park, IL (2013)

VALIDATION OF THE NEW CODE PACKAGE APOLLO2.8 FOR ACCURATE PWR NEUTRONICS CALCULATIONS A. Santamarina, D. Bernard, P. Blaise, P. Leconte, J-M. Palau, B. Roque, C. Vaglio, J-F. Vidal Commissariat à l’Energie Atomique et aux Energies Alternatives CEA, DEN, DER, SPRC, Cadarache F-13108 Saint-Paul-Lez-Durance, France. [email protected] ABSTRACT This paper summarizes the Qualification work performed to demonstrate the accuracy of the new APOLLO2.8/SHEM-MOC package based on JEFF3.1.1 nuclear data file for the prediction of PWR neutronics parameters. This experimental validation is based on PWR mock-up critical experiments performed in the EOLE/MINERVE zero-power reactors and on P.I.Es on spent fuel assemblies from the French PWRs. The Calculation-Experiment comparison for the main design parameters is presented : reactivity of UOX and MOX lattices, depletion calculation and fuel inventory, reactivity loss with burnup, pin-by-pin power maps, Doppler coefficient, Moderator Temperature Coefficient, Void coefficient, UO2-Gd2O3 poisoning worth, Efficiency of Ag-In-Cd and B4C control rods, Reflector Saving for both standard 2-cm baffle and GEN3 advanced thick SS reflector. From this qualification process, calculation biases and associated uncertainties are derived. This code package APOLLO2.8 is already implemented in the ARCADIA new AREVA calculation chain for core physics and is currently under implementation in the future neutronics package of the French utility Electricité de France. Key Words: APOLLO2, JEFF3.1.1, PWR, EOLE, V&V

1. INTRODUCTION The previous industrial version (e.g version 5 [1]) of the APOLLO2 code, used in PWR and fuel cycle calculations, is mainly based on the Collision Probability method and the Sn method [2]. APOLLO2.5 uses the CEA93 nuclear data library, processed from the European File JEF2.2 in the XMAS-172 group structure. This APOLLO2.5 package was fully validated against TRIPOLI4 Monte Carlo calculations, and extensively qualified against integral experiments for every relevant PWR design parameters [3]. However, target accuracies become smaller and smaller for LWR calculations. Therefore, a new version APOLLO2.8, based on the Method Of Characteristics [4], was developed to allow outstanding Light Water Reactor (LWR) calculations in 2D-exact heterogeneous geometry [5]. Moreover, calculation of fast and resonant reaction rates was improved, on the one hand by the determination of the optimized SHEM281 group mesh [6] which avoids resonance self-shielding approximation below 23eV, and on the other hand by a new space-dependent method which accounts for resonance overlapping effect [7]. In order to increase the LWR prediction capability, a new library based on the JEFF3.1.1 file [8], is used. This data file involves the feedback from Critical Experiments and LWR Post Irradiation Experiments. The APOLLO2.8 Reference calculation scheme SHEM-MOC was developed. The optimization allowed the determination of the accurate Optimized scheme REL2005. The Validation of these recommended schemes was performed against MC TRIPOLI4, both in BWR [5] and PWR [9] numerical benchmarks. After the description of the V&V process and the Reference calculation Scheme, this paper summarizes the Qualification work performed to demonstrate the accuracy of the APOLLO2.8 package for the PWR neutronics parameters prediction. This experimental validation is mainly based on PWR mock-up critical experiments performed in the EOLE reactor, and on P.I.Es and BOC measurements in French PWRs.

Alain Santamarina et al.

2. V&V PROCESS In order to supply a reliable code product to designers and users (CEA, AREVA and EDF), the rigorous VVQ-UQ method, e. g. Verification/Validation/Qualification/UQ, must be implemented. a) The first step of the VVQ-UQ process verifies that the numerical resolution of neutronics models and programming of each module are correct. This Verification is also based on the ‘Test Machine’ which avoids non-regression in the new APOLLO2.8 version. b) The second step corresponds to the Validation, which quantifies the accuracy of the neutronics models used in APOLLO2 to simplify the Boltzmann equation. The APOLLO2.8 Validation is carried out both for Functionalities (Pij, resonance self-shielding, fine flux, depletion, accurate SPH homogenization, Sn, MOC) and Reference Calculation scheme. This Validation is based on the comparison of APOLLO2.8 deterministic multigroup calculation against continuous-energy Monte Carlo TRIPOLI4 [10] reference calculation. Both calculations use the same nuclear data library (JEFF3.1.1). The APOLLO2-TRIPOLI4 comparison is performed on numerical benchmarks, representative of PWR and BWR geometries. The Validation for APOLLO2 Functionalities is automated through the MACH2 Machine [2]. The Validation process involves also the “calibration” of the Reference Scheme SHEM-MOC and Optimized Scheme REL2005: the deterministic modeling bias is determined for each PWR design parameter. c) The Qualification is the third step, corresponding to the comparison of the results of the global package (code + reference calculation scheme + nuclear data library), e. g. APOLLO2.8/SHEM-MOC/JEFF3.1.1, against experimental results from integral measurements. d) The Uncertainty Quantification (UQ) is finally carried out: the scaling factor of the APOLLO2.8 product for each design parameter, as well as the associated uncertainty, is obtained by transposition from the Experiments to the PWR Application [11]. For example when using a unique experiment i, the translation of the (C-E)/E bias from the Experiment to the Application is easily obtained, and the corresponding 1σ posterior uncertainty εA’ is given by: εA’ = εA (1 - rAE2 . wi )1/2 εA = (SA+ D SA)1/2 is the prior uncertainty due to nuclear data, S is the sensitivity vector of neutronics parameter to nuclear data, D is the covariance matrix, wi = [1+(δi/εEi)2]-1 is the weight of experiment i, where δi is the experimental uncertainty rAE = (SA+ D SE) / εA εE is the Representativity factor of Experiment and Application. Owing to the uncoupling of the small calculation bias (result of the Validation phase) from the calculation error due to nuclear data (derived from Calc/Exp comparison in the Qualification phase), our VVQ-UQ method allows the feedback to nuclear data evaluators and the improvement of the code [12]. 3. THE SHEM-MOC AND REL2005 CALCULATION SCHEMES The SHEM-MOC Reference Scheme for LWR assemblies performs a self-shielding calculation above 23 eV, followed by a heterogeneous exact-2D flux calculation: - Above the refined energy mesh (i.e E>23eV), a powerful space-dependent self-shielding, based on the French “Background Matrix” method, is implemented. The accurate Pij-UP1 Interface Current method (linear anisotropic interface fluxes) is used in the multicell pattern. Probability Tables are used for a more efficient quadrature in the Hom/Het equivalence. A new mixture resonant shielding treatment is used in the 33eV-200eV range to rigorously account for resonance mutual shielding of the major actinides. - Therefore, the exact-2D calculation is carried out on the SHEM 281-group using the Method Of Characteristics. The Silene GUI creates the MOC geometry, composed by segments, arcs or circles. The Optimized REL2005 is a two-step calculation scheme [5] [9]: a) in the first step, both self-shielded cross-sections (E > 23 eV) and the neutron energy spectrum are calculated in the 2D assembly geometry, using the Pij-UP1 Interface Current method. International Conference on Mathematics and Computational Methods Applied to Nuclear Science & Engineering (M&C 2013), Sun Valley, Idaho, USA, May 5-9, 2013

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b) in the second step, the exact-2D MOC calculation is carried out, using collapsed cross sections from the first step, in an optimized 26-group mesh. Moreover, the 281g/26g energy condensation is carried out through an equivalence procedure which preserves the reference reaction rates. Concerning the spatial discretization of PWR cells (Fig. 1) : - SHEM-MOC scheme recommends a refined mesh (REF), both inside fuel and moderator. The calculation is based on fine tracking values (∆r=0.04 cm, Nφ=24, Bickley polar quadrature Nψ=3), and a P3 modelling of the anisotropic scattering. - REL2005 recommends a simplified mesh (no sectors are used in the fuel, and a windmill mesh accounts for moderator thermal flux variations). Tracking options are less stringent.

Fig. 1. APOLLO2.8 spatial mesh for PWR 17x17 assembly: ‘WINDMILL’ (REL2005) and ‘REF’ (SHEM-MOC) The Validation of APOLLO2.8 Schemes on PWR cluster benchmarks, through a comparison to TRIPOLI4 calculations, allowed the following conclusions : 1/ SHEM-MOC Reference scheme is as accurate as continuous-energy calculation : bias less than 100 pcm on Keff and 0.3% on pin power, 2/ REL2005 Optimized scheme gives quite equivalent results to SHEM-MOC scheme : the disagreement with SHEM-MOC is less than 50pcm on Keff and 0.2% on pin power. These satisfactory results were confirmed by AREVA studies [13] : APOLLO2.8 was benchmarked against MCNP on a wide range of 14x14 to 18x18 PWR assembly types with UOX and MOX fuel. The APOLLO2/MCNP biases on pin fission rate (rms) are 0.17±0.07%. 4. QUALIFICATION OF PWR NEUTRONICS PARAMETERS 4.1 Reactivity of LWR lattices The lattice reactivity versus moderation ratio is mainly checked through Material Buckling Bm2 deduced from radial and axial flux measurements in critical experiments. The satisfactory C-E comparison observed in Table I is confirmed by regular core experiments where a complementary information is obtained: Keff is accurately measured through the critical soluble boron concentration, as shown in Table II for EPICURE-UH1.2 [14] and MISTRAL1 [15] in EOLE, which are PWR mockups (UO2 3.7%w/o235U and zirc4 clad ∅8.4x9.5mm). International Conference on Mathematics and Computational Methods Applied to Nuclear Science & Engineering (M&C 2013), Sun Valley, Idaho, USA, May 5-9, 2013

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Table I. Material Buckling Analysis of LWR-UOX lattices Pitch (cm)

VH2O/VUO2

q**

CB (ppm)

KeffAP2–1

Uncert (1σ σ)*

CRISTO3

0.96

0.45

0.37

750

+599 pcm

700 pcm

ZPR HiC-clad SS

1.24

0.96

0.50

0

-8 pcm

500 pcm

EPICURE UH1.2

1.26

1.25

0.51

569

+345 pcm

350 pcm

CAMELEON

1.26

1.80

0.57

610

+729 pcm

400 pcm

MISTRAL1

1.32

1.75

0.53

294

-188 pcm

400 pcm

CRISTO2-

1.58

3.56

0.76

832

-87 pcm

400 pcm

CRISTO2 ‘large’

1.71

4.40

0.79

672

+122 pcm

400 pcm

CRISTO1

1.86

5.46

0.89

750

+154 pcm

400 pcm

Experiment

* experimental uncertainty including buckling measurement uncertainty and technological uncertainties ** slowing-down density at thermal cut-off E = 4 eV

Table II. Calculation/Experiment comparison on the Keff of PWR-UOX regular cores Pitch (cm)

VH2O/VUO2

KeffAP2–KeffExp

Exp Unc. (1σ σ)

EPICURE UH1.2

1.26

1.25

+330 pcm

200 pcm

CAMELEON [16]

1.26

1.80

+250 pcm

240 pcm

MISTRAL1

1.32

1.75

+220 pcm

180 pcm

Experiment

The reactivity of MOX fueled cores is also well predicted by APOLLO2.8/JEFF3.1.1 for moderation ratios ranging from VH2O/VFuel = 0.51 (ERASME experiments corresponding to HCPWRs) up to 2.1 overmoderated PWR-MOX lattices. Table III summarizes the C/E comparison for MOX lattices using standard PWR fuel pins (UO2-PuO2 7%Pu, zircaloy4 clad ∅8.36x9.50mm). The overestimation by 650 pcm of MISTRAL3 lattice reactivity is confirmed by the Keff calculation (+580 pcm) of the 100%MOX corresponding core; MISTRAL3 reactivity overestimation is mainly due to the huge 10-years Pu ageing. Table III. Material Buckling Analysis of PWR-MOX lattices Pitch (cm)

VH2O/VUO2

Pu ageing

KeffAP2–1

Exp Unc.(1σ σ)

MH1.2

1.26 cm

1.3

4y

+57 pcm

350 pcm

MISTRAL2

1.32 cm

1.7

8y

+374 pcm

350 pcm

MISTRAL3

1.39 cm

2.1

10 y

+653 pcm

350 pcm

Experiment

4.2 Assembly depletion and fuel inventory Qualification of fuel depletion calculation is mainly based on Post-Irradiation Experiments (PIE) carried out on spent 17x17 assemblies from various French PWRs. Bugey3 and Fess2 assemblies allowed the qualification of 3.1% U235-enriched UOX fuel up to 60 Gwd/t, meanwhile P.I.E after 2, 3, 4 and 5 cycles in Gravelines3 enabled the extension of the qualification up to EU235 = 4.5% and Bu = 62 Gwd/t [17]. The APOLLO2.8 product qualification was extended up to 85Gwd/t with the ALIX program (chemical analyses in fuel rods irradiated 5, 6 and 7 cycles) [18]. International Conference on Mathematics and Computational Methods Applied to Nuclear Science & Engineering (M&C 2013), Sun Valley, Idaho, USA, May 5-9, 2013

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Table IV. (C-E)/E biases (%) on isotopic ratios in ALIX-Gravelines5 assembly Isotopic measure 234 U/238U 235 U/238U 236 U/238U 237 Np/238U 238 Pu/238U 239 Pu/238U 240 Pu/238U 241 Pu/238U 242 Pu/238U 241 Am/238U 242m Am/238U 243 Am/238U 244 Cm/238U 245 Cm/238U 143 Nd/238U 145 Nd/238U 148 Nd/238U BU (MWd/t)

5 cycles E06 1.4 ± 2 5.7 ± 6.1 -0.8 ± 1.1 1.0 ± 2.7 -4.7 ± 4.1 4.2 ± 1.6 4.8 ± 1.3 -0.1 ± 1.7 -2.7 ± 3.9 0.6 ± 5 4.0 ± 7 -0.7 ± 5.5 -8.7 ± 9.9 -7.1 ± 11 1.4 ± 1.1 -0.6 ± 1.5 0.2 ± 2.1 64630

6 cycles E04 N05 2.9 ± 2.4 2.3 ± 2.4 11.4 ± 7.0 7.9 ± 7.0 0.0 ± 1.2 -0.1 ± 1.2 4.6 ± 2.4 4.1 ± 2.4 -4.6 ± 3.3 -4.1 ± 3.3 3.3 ± 1.8 0.5 ± 1.8 6.1 ± 0.9 6.0 ± 0.9 1.1 ± 2.0 -1.3 ± 2.0 -1.5 ± 2.8 -0.1 ± 2.8 5.9 ± 5 2.3 ± 5 14 ± 7 18 ± 7 0.2 ± 3.9 2.2 ± 3.9 -9.7 ± 6.4 -7.9 ± 6.4 -9.5 ± 8 -9.6 ± 8 3.0 ± 1.1 2.1 ± 1.1 -0.3 ± 1.2 -0.4 ± 1.2 0.6 ± 1.7 0.5 ± 1.7 73170 75010

7 cycles D13 2.2 ± 2.4 10.3 ± 7.0 0.2 ± 1.2 -2.4 ± 2.4 -4.2 ± 3.3 -0.8 ± 1.8 5.7 ± 0.9 -1.5 ± 2.0 -0.3 ± 2.8 0.44 ± 5 5.6 ± 7 0.9 ± 3.9 -8.2 ± 6.4 -11.7 ± 8 2.5 ± 1.1 -0.4 ± 1.2 0.2 ± 1.7 85060

Table IV summarises the C/E comparison on actinides for the rod cuts at assembly mid-height in 4 fuel pins. At these high burnups, 239Pu is still predicted within 4% target-accuracy. 236U-237Np-238Pu and 242Pu243 Am-244Cm build-ups are now accurately calculated, thanks to the improved resonance integrals for 235U and 241Pu respectively in JEFF3.1.1 evaluations [19]. 4.3 Reactivity loss with burnup – Cycle length The fuel reactivity versus burnup was obtained through sample oscillations of PWR rod cuts. The reactivity worth of these spent fuel samples were measured at the centre of the PWR-type Minerve lattice. The reactivity worth analysis of ALIX high-burnup fuels (Table V) shows that fuels irradiated 5 and 6 cycles (64 up to 75 GWd/t) are very consistent: (C-E)/E~1.6%. This calculation trend remains lower than the 2.3% uncertainty (1σ) mainly due to the reactivity worth calibration through boron samples [20]. These results are in very close agreement with complementary qualification in the 20-70 GWd/t range obtained from various PWR assemblies : Bugey-3, Fessenheim-2, Gravelines-2, Cruas-2 [21]. Table V. APOLLO2/JEFF3.1.1 calculation of the reactivity loss with burn-up Sample

Burn-Up

(C-E)/E ± 1σ σ

E06 5-cycle N05 6-cycle E04 6-cycle D13 7-cycle

64.4 GWd/t 70.2 GWd/t 72.9 GWd/t 83.5 GWd/t

1.7% ± 2.3% 1.7% ± 2.3% 1.4% ± 2.3% 3.6% ± 2.3%

4.4 Pin-by-pin power map The experimental radial power map is obtained in EOLE experiments by integral gamma-spectrometry measurements directly on the fuel rods. The total uncertainty (statistical counting and technological uncertainty mainly linked to slight fuel rod bowing) amounts to ±0.8% (1σ). International Conference on Mathematics and Computational Methods Applied to Nuclear Science & Engineering (M&C 2013), Sun Valley, Idaho, USA, May 5-9, 2013

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UH1.4

UMZONE Water reflector

MOX 8.7% w/o

Zircaloy guide-tubes

MOX 7.0% w/o

Stainless steel guide-tubes for safety absorbers

MOX 4.3% w/o

Pilot rod

particular peak gamma scanning measurements for determination of MOX/UO2 power ratio





UO2 3.7% w/o

Fig. 2. EPICURE UH1.4 and UMZONE configurations The more representative experiments for the APOLLO2.8 qualification of pin-by-pin power map are the EPICURE-UH1.4 (UOX 17x17) and UMZONE (PWR mixed-loading mock-up) that are built with the actual PWR fuel pins (Fig. 2). C/E comparison is shown in Fig. 3 for UH1.4 core. The mean bias amongst pins bearing the power peak (‘Face’ located in front of guide-tubes) is: (C-E)/E = -0.05% (0.5% spread). 0 21

1

2

3

4

5

-0.5 0.1

0.0 -0.4 -0.2 -0.5 0.0 -0.6 0.6 0.9 0.5 0.3

6

7

8

9

10

11

12

13

14

15

-0.9

20 19 18

-0.8 -0.7

17

-0.7

16

-0.7

15

-0.5

14 13 12 11 10 9 8 7

-0.9 -0.3

6 5 4

-0.1 0.3

3 2 1

-0.3 -0.9

-1.0 -0.2 -1.2 -1.1 -0.7 -0.2 0.4 -0.2 0.7

-0.3 0.2 1.2 0.4 0.0 0.2 0.2 0.1 0.6

-0.7 0.0 0.3 0.3 0.3 0.6

-0.6 0.3 -0.9 -0.3 -0.4 0.0 0.4

0.6 0.0 0.0 0.3 -0.1 0.6

0.4 0.1 0.2 0.3 -0.4

0.4 0.2 0.2

0.7 0.7

0

Average µ Spread σ max(+) max(-)

All

Face

Angle

Asympt

Refl

-0.04

-0.05

-0.02

0.07

-0.75

0.54

0.52

0.56

0.51

0.20

1.18

0.95

0.73

1.18

-0.53

-1.16

-1.11

-1.16

-1.04

-0.93

Fig. 3. (C-E)/E in % on radial power map in UH1.4 ¼ core (PWR 17x17 mockup) C/E comparison for the mixed-loading core UMZONE is shown in Fig. 4 [22]. The average bias for UO2 pins is : (C-E)/E = -0.1% (rms=0.6%), meanwhile C/E amounts to +0.8%, +1.0%, +1.6% respectively in MOX 4.3%Pu peripheral row, MOX 7.0%Pu, MOX 8.7%Pu central zone. International Conference on Mathematics and Computational Methods Applied to Nuclear Science & Engineering (M&C 2013), Sun Valley, Idaho, USA, May 5-9, 2013

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17 16 15 14 13 1 2 (C-E)/E (%) 3 4 5 6 7 8 9 10 UO2 11 12 13 14 -0.5 15 16 -2.2 17 -1.4 18 19 20 21 22 23

12

11

10

9

8

7

6

5 4 3 Core Center

MOX

1.1 1.8 0.6 1.8 1.0 1.2 1.4 1.2 0.8 0.0 0.3 -0.4 0.2 -0.5 0.3 0.7 -0.2 0.6 0.3 -1.0 0.4 0.5 0.6 -0.1 0.2 0.2 0.2 0.4

0.6 0.7 1.3 0.8 0.2 -0.4 0.1 0.5 0.3 0.0 0.4 0.6

1.7 1.6 0.8 0.5 0.2 0.1

2

1

->

1.5 1.6 1.5 2.0 1.5 1.3 0.9 -0.3 -0.5

2.1 2.3 2.3 1.9 2.4 1.1 0.9 -0.1

1.8 0.9 1.4 1.2 -0.5 1.0

0.3 -0.3 -0.1 0.1 0.4 -0.2 -0.3 -1.4 -1.3 -0.8 -0.2 -0.7 -0.5 -0.8

Fig. 4. (C-E)/E in % on radial power map in UMZONE ¼ core (PWR mixed loading) 4.5 Fuel Reactivity Temperature Coefficient (Doppler) The experimental validation of Doppler reactivity worth in UOX and MOX fuels was achieved through sample oscillations in MINERVE reactor from 20°C up to 800°C. The test samples are constituted by pellet of UO2 or UO2-PuO2 in a stainless steel cladding. The enrichment of UO2 samples ranges from 0.2% to 5%. Three different Pu isotopic compositions have been used for the fabrication of mixed oxide samples corresponding approximately to 12, 20 and 37% 240Pu. The ratio of fissile plutonium over the total amount of heavy elements is 2%, 3.2% or 5% according to the various samples. The experimental uncertainty involves the measurement uncertainty (pilot rod signal), the sample temperature uncertainty, the uncertainties linked to sample actinide concentrations and the systematic uncertainty due to reactivity worth calibration. In agreement with APOLLO2.8 recommendation, the Crystal Lattice model for Doppler broadening was used to perform interpretation calculation, with an effective temperature Teff preserving 238U resonance integral in the actual UO2 crystal (using 2-phonon modes) [23]. The Calculation-Experiment comparison, summarized in Table VI, points out a slight trend to Fuel Temperature Coefficient underestimation for both UOX and MOX fuel : (C-E)/E = -3.2% ± 3.0% (1σ) for UOX (C-E)/E = -4.6% ± 3.0% (1σ) for MOX. Table VI. C/E-1 (in %) on Doppler worth in MINERVE oscillation experiment Oscillation samples

∆T = 20°C - 800°C

UO2 (0.2% enrichment)

-3.3% ± 3.9%

Metallic U (0.7% enrichment)

1.9% ± 5.5%

UO2 (0.7% enrichment)

-3.9% ± 3.9%

UO2 (3.0% enrichment)

-3.0% ± 3.4%

MOX (2.53% Pu)

-3.3% ± 3.7%

MOX (3.75% Pu)

0.1% ± 3.5%

MOX (4.73% Pu,)

-4.9% ± 3.6%

MOX (5.24% Pu)

-5.0% ± 4.1%

MOX (7.28%Pu)

-8.2% ± 3.6%

International Conference on Mathematics and Computational Methods Applied to Nuclear Science & Engineering (M&C 2013), Sun Valley, Idaho, USA, May 5-9, 2013

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4.6 Moderator Reactivity Temperature Coefficient CREOLE is the unique Reactivity Temperature Coefficient (RTC) experiment to be representative of the operating conditions of PWR power reactors. The experimental device in EOLE facility consists of a pressurized central test loop (200 Zr-clad fuel pins in the standard 1.26cm square pitch), a large vacuum gap separation zone and a peripheral driver core of variable sizes surrounded by a water reflector [24]. The CREOLE program was conceived to supply accurate differential RTC of standard UOX (clean and Boron poisoned) and MOX fuel type lattices throughout the whole PWR temperature range (from room temperature up to 300°C). In addition to the differential measurements, integral RTC was accurately measured by equivalence with soluble boron and driver core loading variations. Table VII presents the biases between JEFF3.1.1 calculations and RTC differential measurements in various temperature ranges for the UO2 non-borated lattice [25]. Table VII. RTC from Differential Measurements and ∆α = C-E bias (UO2 clean lattice) α and ∆α (in pcm/°C) Experiment TRIPOLI4 (C – E ) (exact geometry) APOLLO2-RZ (C – E)

20 – 111°C - 2.61 ± 0.12 + 0.01 ± 0.13 (0.04)* + 0.10 ± 0.12

111 – 186°C - 3.76 ± 0.14 + 0.12 ± 0.15 (0.05)* + 0.17 ± 0.14

186 – 242°C - 4.44 ± 0.16 + 0.08 ± 0.17 (0.07)* + 0.17 ± 0.16

242 – 289°C - 5.33 ± 0.18 + 0.00 ± 0.20 (0.08)* + 0.20 ± 0.18

* Monte Carlo statistical uncertainty

Table VIII summarizes the comparison of the calculations and experimental values for the average RTC in the whole investigated temperature range (20°C up to 300°C) for the three experimental configurations. Results correspond to a synthesis of three kinds of independent measurements: differential measurement, integral measurement by equivalence both with soluble-boron worth and with driver core fuel pins worth. Table VIII. Summary of C - E biases on the average RTC (in pcm/°C). UO2 (pure water) - 3.78 ± 0.03 + 0.01 - 0.07 (0.02)*

RTCExp ± Unc.(1σ σ) APOLLO2 (C – E ) TRIPOLI4 (C – E)

UO2 (CB=1166 ppm) - 0.22 ± 0.02 + 0.03 - 0.004 (0.01)*

UO2-PuO2 - 2.85 ± 0.03 + 0.20 + 0.16 (0.02)*

* Monte Carlo statistical uncertainty

These results show a good agreement between the deterministic and Monte Carlo methods. RTC and C/E biases correspond to the CREOLE core, characterized by a 10% relative reactivity worth of the experimental loop, and consequently should be multiplied by a factor of 10 to be compared with PWRs. Thus, discrepancies between calculation and experiment on the RTC for clean and boron-poisoned UO2 PWR lattices are less than 1 pcm/°C, which corresponds to the target accuracy in LWR design calculation. 2 ∆α uncertainty margins 1.5

∆α(C−E) in pcm/oC

1

0.5

0

−0.5

−1

−1.5

−2

0

10

20

30

40 50 Temperature in oC

60

70

80

Fig. 6. Temperature dependence of the C-E bias on RTC in MISTRAL1 UOX core International Conference on Mathematics and Computational Methods Applied to Nuclear Science & Engineering (M&C 2013), Sun Valley, Idaho, USA, May 5-9, 2013

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CREOLE satisfactory results are confirmed by the APOLLO2.8 analysis of RTC differential measures in the 10°C-80°C range, in MISTRAL1-UOX (Fig. 6) and MISTRAL-MOX cores [26].

4.7 Void coefficient Void coefficient in MOX lattices limit the Pu load of MOX assemblies for Pu recycling in LWRs. The APOLLO2.8 prediction of void effects is qualified through MISTRAL3 experiments. The Reference core corresponds to a “homogeneous” 100% MOX 7%Pu PWR-type fuel pins. The critical core contains 1388 pins in a 1.39 cm square pitch (VH2O/VMOX = 2.1). Local Void was investigated : 40%-void, 60%-void, 100%-void were implemented in the 7x7 central cells. Partial 40% and 60% void were simulated by an Al over cladding of the 7x7 central fuel pins, and 100%-void was simulated by an Al block, drilled by 7x7 holes to introduce the MOX pins. Void worth is measured by equivalence with soluble boron poisoning. The Calculation-Experiment comparison on the void reactivity worth is summarized in Table IX [27]. The APOLLO2 void worth is slightly overestimated for 40% void, but satisfactory for high void fractions. Table IX. Calculation/Experiment bias on void worth in MISTRAL3 100%MOX MISTRAL3 Configuration

40%-VOID

60%-VOID

100%-VOID

Experimental Void Worth

-660 pcm

-1050 pcm

-1410 pcm

(C-E)/E ± 1σ σ* APOLLO2.8 – SHEM-MOC

+4.6% ± 1.4%

+0.4% ± 0.8%

+1.7% ± 0.5%

(C-E)/E ± 1σ σ* APOLLO2.8 – REL2005

+4.6% ± 1.4%

+0.5% ± 0.8%

+2.0% ± 0.5%

* measurement uncertainty combining residual reactivity and soluble boron concentration (overclad diameter unc. not included)

4.8 Kinetic parameters Integral measurements of the effective delayed neutron fraction (βeff) were performed in EOLE reactor using noise analysis technique coupled with the determination of the absolute total fission integral of the core. Both UOX (MISTRAL1 core) and MOX (MISTRAL2 core) LWR lattices were investigated [28]. For UOX cores, the use of the JEFF-3.1.1 delayed neutron data in a 8 time-groups structure allows the reduction of the C/E bias : from +2.8% ± 1.5% with APOLLO2.5/JEF2 down to +0.8 ± 1.5% with APOLLO2.8. Therefore, required industrial target accuracy of ± 2% is met. For MOX cores, C/E comparison was already satisfactory using JEF-2 delayed neutron data. However, JEFF-3.1.1 data still allows an improvement in C/E comparison : (C-E)/E=+0.2±1.6%. 4.9 UO2-Gd2O3 Lumped Burnable Poisons CAMELEON is the first PWR-mockup experiment in EOLE reactor (1982-1984) carried out to answer the global qualification of absorbers and burnable poisons in PWR configurations. Reactivity worth of AIC - B4C - Hf - Stainless Steel absorbers, Pyrex and Gd LBPs, were extensively measured. The worth measurements were performed by equivalence with soluble boron poisoning. The cylindrical core is composed of 1764 UO2 3.5% 235U enriched fuel pins (Al-clad), arranged in a standard 1.26 cm lattice pitch. The core is reflected by borated water. Fig.5 represents the radial cross section of the reference 17x17 25 guide-tubes configuration that serves as reference for the study of Gd poisoned configurations. The Gd-poisoned configurations are built with 2 different types of Gd pins. The so-called “type A” Gd pins contains 7% Gd2O3 on natural uranium oxide matrix, as “type B” Gd pin contains 3% Gd2O3 on 5% enriched UO2 matrix. Amongst the investigated Gd clusters, configurations 12D1 and 12D3 correspond to real PWR assemblies. APOLLO2.8 results (Table X) point out that the poisoning worth of 12-Gd clusters is predicted within experimental uncertainty [29]. International Conference on Mathematics and Computational Methods Applied to Nuclear Science & Engineering (M&C 2013), Sun Valley, Idaho, USA, May 5-9, 2013

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Fig. 5. CAMELEON Reference core (PWR 17x17 mock-up) Table X. (C-E)/E bias and experimental uncertainty on Gd-cluster reactivity worth Configuration/Gd-type ∆ρ(Gd): (C-E)/E± ±1σ σ

12D1/A

12D3/A

12D1/B

12D3/B

-0.2% ± 1.3%

0.1% ± 1.3%

-0.6% ± 1.5%

-0.3% ± 1.6%

The GEDEON1 experiment in the MELUSINE 8MW irradiation reactor at CEA-Grenoble was designed for the validation of Gd depletion calculation. The irradiated 13x13 PWR assembly enabled to burn simultaneously four UO2-Gd2O3 rods (5%Gd in 3.2% 235U enriched UO2) and to discharge them at increasing burn up steps. At each discharge burn up, a set of several pins (one Gd, one adjacent UO2 pin and a UO2 monitor pin) is removed from successive quadrants of the PWR assembly. For each fuel pin, 2 sample pellets are extracted at different axial positions and dissolved for chemical analysis. The APOLLO2.8 analysis is summarized in Fig. 6 [30]: depletion kinetics is accurately predicted for both absorbing isotopes 157Gd and 155Gd.

Fig. 6. C/E comparison on Gd(t) / Gd(0) depletion ratio for 155Gd and 157Gd (up to 12 GWd/t) 4.10 Efficiency of control rods Various absorber clusters, increasing from 9 and 17 to standard 24 absorbers, were introduced in the central 17x17 assembly of the CAMELEON Ref core (Fig. 5). Moreover, clusters of various LWR absorber types were compared : B4C, Hf and Ag-In-Cd. The reactivity worth of each absorber cluster was measured through the variation of the soluble boron critical concentration. International Conference on Mathematics and Computational Methods Applied to Nuclear Science & Engineering (M&C 2013), Sun Valley, Idaho, USA, May 5-9, 2013

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Validation of the new code package APOLLO2.8

Fig. 7. APOLLO2.8 MOC mesh and thermal flux in the CAMELEON-Ref configuration The APOLLO2.8 geometry of the various configurations is refined accordingly to SHEM-MOC scheme (Fig. 1) and to the flux variation in the reflector [31]. Thermal fluxes in the Ref core are shown in Fig. 7, pointing out the strong thermal flux (in red) located around the guide-tubes. In order to confirm the results obtained by the APOLLO2 deterministic calculation, full 3D exact representation were carried out by TRIPOLI4. The C/E comparison on absorber cluster worth is summarized in Table XI. B4C reference absorber seems over-predicted by 1.5%, AIC clusters are overestimated by 2% and advanced Hf clusters by 3%. Table XI. C/E on CAMELEON absorber cluster worth for APOLLO2.8 and TRIPOLI4 Absorber cluster

17AIC

17Hf

17B4C

24AIC

24HF

∆ρcluster in pcm

-7300

-7280

-7570

-9190

-9070

APOLLO2.8

1.5% ± 0.5%

3.0% ± 0.5%

1.5% ± 0.5%

2.8% ± 0.4%

3.1% ± 0.4%

TRIPOLI-4

1.0% ± 0.5%

3.4% ± 0.5%

1.1% ± 0.5%

2.5% ± 0.4%

2.9% ± 0.4%

4.11 Reflector saving Table XII. C/E comparison for Keff and δrefl for various PWR reflectors Experiment/Reflector

MISTRAL/H2O FLUOLE/SS-2cm PERLE/SS-22cm

ρmeas residual reactivity (pcm)

109 ± 130*

165 ± 140*

154 ± 140*

TRIPOLI4 (C-E)/E in pcm

+190

-60

+121

SHEM-MOC (C-E)/E in pcm

+220

+4

+242

REL2005

+280

+155

+304

δrefl measurement (cm)

7.25 ± 0.14*

6.43 ± 0.15*

9.72 ± 0.25*

δrefl TRIPOLI4 (cm)

7.30

6.46

10.27

δrefl SHEM-MOC (cm)

7.32

6.42

10.36

δrefl REL2005

7.31

6.42

10.28

(C-E)/E in pcm

(cm)

* Experiment uncertainty (1σ) including lattice pitch and overclad diameter uncertainties

International Conference on Mathematics and Computational Methods Applied to Nuclear Science & Engineering (M&C 2013), Sun Valley, Idaho, USA, May 5-9, 2013

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APOLLO2.8 calculation of Reflector Saving for standard 2-cm PWR baffle was qualified in the FLUOLE mock-up experiment [32]. Furthermore, the advanced thick SS reflector implemented in GEN3 reactors was studied in the PERLE core [33]. In these experiments, the reflector saving δrefl was obtained from radial buckling measurements ; the flux attenuation versus SS penetration was measured by miniature fission chambers and metallic foils, using fast, intermediate and thermal response functions. Table XII summarizes TRIPOLI4 and APOLLO2.8 C/E comparison [34] for core critical Keff and δrefl measurements: the reactivity worth of heavy reflectors are well predicted (compared to H2O), and δrefl is calculated within 0.5cm accuracy for each PWR reflector. 5. CONCLUSIONS The Qualification work has demonstrated the accuracy of the new APOLLO2.8 product, based on JEFF3.1.1 nuclear data, for the prediction of PWR design parameters. The C/E comparison for the main parameters has demonstrated that target-accuracy is met : Keff of UOX and MOX cores slightly overestimated by 250 ± 200pcm (1σ), actinide concentrations predicted within 5% accuracy in spent fuel up to 85 GWd/t, reactivity loss with burnup within 3%, pin-by-pin power within 2%, Doppler coefficient within 5%, Moderator Temperature Coefficient within 1 pcm/K, Void coefficient within 3%, βeff within 2%, UO2-Gd2O3 poisoning worth within 2%, AIC and B4C control rod efficiency overestimated by 2% ± 1%, Reflector Saving for both standard 2-cm and advanced thick SS baffle within 5 mm. This APOLLO2.8 code is already implemented in the new LWR calculation chain ARCADIA of AREVA [35] and is under implementation in the future advanced package of the Electricité de France utility [36]. ACKNOWLEDGMENTS The authors acknowledge their industrial partners AREVA and EdF for their financial support to the V&V of the APOLLO2.8/JEFF3.1.1 code package. REFERENCES 1. S. Loubière, R. Sanchez, M. Coste, A. Hébert, Z. Stankovski, I. Zmijarevic, “APOLLO2 Twelve Years After,” Proc. Int. Conf. M&C99, Madrid (Spain), September 27-30, 1999. 2. A. Santamarina, C. Collignon, C. Garat, “French Calculation Schemes for Light Water Reactor Analysis,” Proc. Int. Conf. PHYSOR2004, Chicago (USA), April 25-29, 2004. 3. A. Santamarina, C. Chabert, A. Courcelle, O. Litaize, “Qualification of APOLLO2.5 for UOX and MOX Fuelled PWRs,” Proc. PHYSOR2002, Seoul (Korea), October 7-10, 2002. 4. R. Sanchez, “APOLLO2 Year 2010,” Nucl. Eng. & Technology, Vol 42 n°5, pp.474-499 (2010). 5. A. Santamarina, N. Hfaiedh, V. Marotte, S. Misu, A. Sargeni, C. Vaglio, I. Zmijarevic, “Advanced neutronics tools for BWR design calculations,” Nucl Eng & Design, 238 (2008). 6. N. Hfaiedh and A. Santamarina, “Determination of the Optimized SHEM Mesh for Neutron Transport Calculation,” Proc. Int. Conf. M&C2005, Avignon (France), Sept 12-15, 2005. 7. M. Coste, S. Mengelle, “New resonant mixture self-shielding,” PHYSOR2004, Chicago, April 25-29. 8. A. Santamarina et al., “The JEFF-3.1.1 Nuclear Data Library. Validation results from JEF-2.2 to JEFF-3.1.1,” JEFF Report 22, OECD/NEA Data Bank 2009. 9. J-F Vidal, O. Litaize, D. Bernard, A. Santamarina, C. Vaglio, “New Modelling of LWR Assemblies using APOLLO2 Code”, Proc. M&C2007, Monterey (USA), April 15-17, 2007. 10. J.-P. Both et al., “TRIPOLI4 – A three dimensional polycinetic particle transport Monte Carlo code”, Proc. of Int. Conf. SNA’2003, Paris (France), September 22-24 (2003). 11. A. Santamarina, D. Bernard, N. Dos Santos, C. Vaglio, L. Leal, “Re-estimation of Nuclear Data and JEFF3.1.1 Uncertainty Calc.,” Proc. PHYSOR2012, Knoxville, April 15-20, 2012. International Conference on Mathematics and Computational Methods Applied to Nuclear Science & Engineering (M&C 2013), Sun Valley, Idaho, USA, May 5-9, 2013

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12. A. Santamarina, “From Integral Experiments to Nuclear Data Improvement,” Proc. Int. Conf. on Nuclear Data ND2007, Nice (France), April 23-26, 2007. 13. E. Martinolli et al., “APOLLO2-A – Areva’s New Generation Lattice Physics code: Methodology and Validation,” Proc. PHYSOR2010, Pittsburgh (USA), May 9-14, 2010. 14. J. Mondot et al., “The EPICURE Experiment,” Proc. Int. Conf. on Reactor Physics PHYSOR90, Vol. 121, pp.32-40, Marseille (France), April 6-11, 1990. 15. S. Cathalau, P. Blaise, A. Santamarina, O. Litaize, T. Yamamoto et al., “Full MOX recycling in ALWR: Lessons drawn through MISTRAL Program,” Proc PHYSOR2002, Seoul Oct 7-9 16. L. Martin, A. Santamarina, D. Doutriaux, “CAMELEON, a Benchmark Experiment for Absorbers and Poisons in PWR Assemblies,” Transactions ANS, vol46, pp755-756 (1984). 17. C. Chabert, A. Santamarina, C. Poinot, “Qualification of the APOLLO2 Code using PWR-UO2 Isotopics Assays” Proc. Conf. PHYSOR2000, Pittsburg (USA), May 7-11, 2000. 18. C. Vaglio, A. Santamarina , D. Bernard, R. Eschbach, “JEFF3.1.1 validation of the fuel inventory calculation for high burn-up PWR fuel,” Proc. ICAPP2011, Nice, May 2-5, 2011. 19. H. Derrien, A. Courcelle, L. Leal, A. Santamarina, “Re-evaluation and Validation of 241Pu Resonance Parameters in the Range Thermal to 20 eV,” Nucl. Sci. & Eng., 150, p109 (2005). 20. P. Leconte, C. Vaglio, R. Eschbach, M. Antony, A. Pepino, “Reactivity Loss Validation of HighBurnup PWR Fuels with Pile-Oscillation,” Proc. PHYSOR2012, Knoxville, April 2012. 21. D. Bernard, A. Santamarina, A. Sargeni, “Experimental Validation of the LWR Reactivity Loss with Burn up”, Proc. Conf. PHYSOR2006, Vancouver (Canada), Sept 10-14, 2006. 22. J-F. Vidal, P. Blaise, “Qualification of APOLLO2.8/JEFF-3.1.1 for calculation of plutonium recycling PWRs using EPICURE exp.,” Proc. PHYSOR2010, Pittsburgh, May 9-14, 2010. 23. A. Meister, A. Santamarina, “The Effective Temperature for Doppler Broadening of Neutron Resonances in UO2,” Proc. Int. Conf. PHYSOR-98, Long Island (USA), October 5-8, 1998. 24. A. Santamarina, L. Erradi “CREOLE PWR Reactivity Temperature Coefficient Experiment,” NEA/NSC/DOC : CREOLE-PWR-EXP-001 IRPhE Handbook, March 2008 Edition. 25. L. Erradi, A. Santamarina, “Analysis of CREOLE Experiment on the Reactivity Temperature Coefficient for PWR UO2 and MOX Lattices,” Proc M&C2009, Saratoga Springs, May 3-7. 26. L. Erradi, A. Santamarina, “Analysis of the MISTRAL Experiments on the Reactivity Temperature Coefficient for UOX and MOX,” Proc. PHYSOR2010, Pittsburgh, May 9-14. 27. C. Vaglio, A. Santamarina, O. Litaize, “Accurate calculation of void reactivity in MOX lattice,” Proc. Int. Conf PHYTRA, Marrakech (Marocco), March 14-16, 2007. 28. A. Santamarina, P. Blaise, L. Erradi, “Calculation of LWR Kinetic Parameter βeff. Validation on the MISTRAL Experiments,” Annals of Nuclear Energy, vol 48, (oct 2012). 29. P. Blaise, J-F. Vidal, A. Santamarina, “Validation of the REL2005 code on Gd-poisoned PWR assemblies through CAMELEON Exp,” Proc ICAPP’09, Tokyo, May 10-14, 2009. 30. P. Blaise, N. Dos santos, “Interpretation of GEDEON experiment in Melusine for validation of Gd depletion using APOLLO2.8,” Proc. PHYTRA2, Fez (Marocco), Sept 26-28, 2011. 31. P. Blaise, O. Litaize, A. Santamarina, J-F. Vidal, “Qualification of the APOLLO2.8 code on PWR Absorber Clusters through CAMELEON,” Proc. PHYSOR2010, Pittsburgh, May 9-14. 32. J-F. Vidal , R. Le Tellier, P. Blaise, O. Litaize, A. Santamarina, N. Thiollay, C. Vaglio, “The Analysis of the FLUOLE experiment”, Proc. PHYSOR2008, Interlaken, Sept 14-19, 2008. 33. A. Santamarina, C. Vaglio et al., “The PERLE experiment for the qualification of PWR heavy reflectors”, Proc. Int. Conf. PHYSOR2008, Interlaken (Switzerland), Sept 14-19, 2008. 34. C. Vaglio, A. Santamarina, P. Blaise, O. Litaize, G. Noguère, J.F. Vidal, “Interpretation of PERLE exp. for the validation of iron nuclear data”, Nucl. Sci. & Eng., Vol 166, p89 (2010). 35. D. Porsch, M. Leberig , S. Kuch, P. Magat, K. Segard, “Status of V & V of AREVA’s ARCADIA System for PWR Applications,” Proc. PHYSOR2012, Knoxville, April 15-20. 36. Courau, M. Cometto, E. Girardi, D. Couyras, N. Schwartz, “Elements of Validation of Pin-by-Pin Calculations with Future EDF Calc. Scheme”, ICAPP’08, Anaheim, June 8-12, 2008. International Conference on Mathematics and Computational Methods Applied to Nuclear Science & Engineering (M&C 2013), Sun Valley, Idaho, USA, May 5-9, 2013

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