Determination of the Computational Bias in Criticality Safety Validation of VVER-440/V213

Transcription

1 Determination of the Computational Bias in Criticality Safety Validation of VVER-440/V213 ABSTRACT Branislav Vrban 1 B&J NUCLEAR ltd. Alžbetin Dvor Miloslavov, Slovakia branislav.vrban@bjnuclear.eu Jakub Lűley 1, Štefan Čerba 1, Filip Osuský 2 2 Institute of Nuclear and Physical Engineering Slovak University of Technology in Bratislava, Ilkovičova , Bratislava, Slovakia jakub.luley@bjnuclear.eu, stefan.cerba@bjnuclear.eu, filip.osusky@stuba.sk The key issue in any criticality safety problem is to estimate and to predict the deviation of calculation from reality. If the calculated value is not equal to its true value bias occurs. In criticality calculations the computational bias is the difference between the computed and the actual value of keff. The fundamental assumption is that the computational bias is mostly caused by errors in the cross-section data. In addition the use of random variables in the calculation introduces a non-random bias in the computed result as well. The American National Standards are utilized to predict and bound the computational bias of criticality calculations. These standards require the validation of the analytical methods and data used in nuclear criticality safety calculations to quantify the computational bias and its uncertainty. This paper presents a method for determining the computation bias and bias uncertainty for VVER-440/V213 reactor. For this analysis a SCALE KENO 3D core model was developed by B&J NUCLEAR ltd. company. This model is based on technical data and operational history of NPP Jaslovské Bohunice provided by the Slovenské elektrárne a.s. Several calculation steps are used to address bias estimation method including sensitivity analysis, uncertainty analyses and cross section adjustment method. In addition the neutronic similarity of VVER-440/V213 core to several hundred critical benchmark experiments is evaluated by the use of three integral indices. The database of the benchmark experiment is based on the selection and processing procedure VALID provided by the Oak Ridge National Laboratory and specified in the IHECSBE. The results of all analyses performed are given and discussed in the paper. 1 INTRODUCTION The computational bias of criticality safety calculations, defined as difference between the computed and the actual values of keff, must be established through the validation of the applied methods to critical experiments. To meet the needs, one may utilize American National Standard ANSI/ANS [1] which allows the use of calculations in the determination of subcritical limits for the design of fissionable nuclear systems. The aforementioned validation procedure should be performed with experimental data sufficiently similar to the system under consideration. The area of applicability of the experiments chosen 322.1

2 322.2 for validation can be determined via comparison of relevant parameters between two systems by the use of similarity assessment method. This method is based on sensitivity and uncertainty analysis, including global integral indices ck, E and G. A computational bias can be found as a function of these parameters and statistical analysis with extrapolation to target system can be used to determine an upper subcritical limit (USL). Alternatively the computational biases may be predicted by the nuclear data adjustment tool TSURFER, which is based on a GLLS approach [2]. The approaches of bias estimation mentioned above are applied to SCALE [3] criticality calculations of VVER-440/213 reactor and real operational conditions. VVER reactors are a special design of Pressurized Water Reactors with a hexagonal geometry of fuel assemblies, Zirconium-Niobium alloy as fuel rod claddings material and with the steam generators with a tube sheet in the form of two cylindrical heads. VVER reactors are the most frequently built reactor types in the world. The first units with predecessors of VVER-440 type reactors were erected at the Novovoronesh NPP site in 1972 and 1973 [1]. The second step in the development of VVER-440 type reactors was the V-230 design which was mainly constructed in the period from 1973 to The third step in VVER-440 development was the V-213 reactor design referred as the second generation of the standard VVER-440 reactors equipped by many upgrades and enhancements. Slovakia has four nuclear reactors generating half of its electricity and two more under construction. In 1972, construction of the Bohunice V1 plant commenced, with two VVER-440 V-230 reactors. The first was grid connected in 1978, the second two years later. The V2 units commenced operation in 1984 and The Slovak NPP Mochovce with VVER-440/V213 units 1 and 2 were put in operation in the summer of 1998 and the end of year 1999 due to the construction delay caused by political changes in the early 1990s. As a result of continuous upgrades implemented in NPP Bohunice V2 the reactors power level was increased from original thermal power level of 1375 MWth to current MWth in In order to extend the fuel residence time in active core accompanied by the improvement of fuel cycle efficiency the new second generation fuel with an average enrichment of 4.87 wt % 235 U and Gadolinium burnable absorbers (3.35 wt % Gd2O3) was incorporated in fuel loading patterns of NPP Bohunice and Mochovce unit in the last years. Two another units 3&4 of VVER- 440/213 are currently under construction in Mochovce locality and are planned to be put in operation in 2017 and 2018 respectively. 2 VVER-440 GEOMETRY MODEL DESRIPTION Detailed and precise KENO 3D model of the VVER-440/V213 reactor has been developed for criticality and shielding calculations. The whole-core 3D model shown in Fig. 1-a consists of the reactor in-vessel components such as fuel assemblies (including fuel rods, upper spacer grid, intermediate spacer grids, supporting grid, mixing grid, central tube and fuel endings), emergency reactor control assemblies (ERC - absorber and fuel part), core basket, barrel and the reactor pressure vessel. The boundaries of the created VVER-440 whole-core model are given by the outer surface of the dry shielding, the level of hot-leg piping and the basement of filtration mechanism. All the VVER-440 fuel assemblies (FAs) are hexagonal and the fuel rods are placed in the assembly in a triangular grid pattern. The fuel rod bundle of the assembly is enclosed in a hexagonal wrapper with the width across the flats equal to 145 mm (the 2 nd gen. FA). The FA and emergency reactor control assemblies are positioned in a hexagonal grid with a spacing of 147 mm. The fuel rods are located in the bundle in a triangular grid pattern with a pitch of 12.3 mm. The fuel rod claddings are made of the E110 zirconium alloy, while the wrapper tubes of FA and ERC are made of the E125 zirconium alloy.

3 322.3 a) 3D model geometry b) 30 th fuel loading pattern of NPP EBO unit 4 Figure 1: KENO 3D model of the VVER-440/V213 and fuel loading pattern The outside diameter of fuel rod cladding is 9.1 mm, the inside diameter is 7.75 mm. The cladding houses a fuel column assembled of UO2 pellets. The rods are filled with helium and the fuel pellet density is g/cm 3. Several types of profiled fuel assemblies are used to maintain power peaking factors under the design limits. A Gd2O3 absorber is integrated with a mass content of 3.35% into FAs to aid fuel profiling. The fuel loading pattern in the representative sixth of NPP Bohunice unit 4 during cycle 30 is shown in the Fig. 1-b. The profiling diagrams with various initial enrichments can be found elsewhere [4]. The FA with the average enrichment of 4.25 wt % 235 U exists in two modifications differing in rod claddings outer diameters. The fuel rod cladding outer diameter of the first modification is equal to 9.07 mm and the second modification diameter is identical to other FAs. In addition, another type of fuel rod bundle with the uniform enrichment of 1.6 wt % 235 U is used as a fuel part of central ERC. 3 CALCULATION METHODOLOGY 3.1 Burnup calculation An accurate treatment of neutron transport and depletion in modern fuel assemblies characterized by heterogeneous, complex designs, such as the VVER assembly configuration, requires the use of advanced computational tools capable of simulating multi-dimensional geometries. The depletion module TRITON [5], which is part of the SCALE system, was used to perform depletion simulations for 2D FA and ERC models. The isotopic compositions of the FAs and ERCs following burnup values shown in Fig. 1-b were calculated by SCALE system - TRITON depletion sequence and NEWT flux solver. Our modelling approach is based on parametric study of burnup modelling issues associated with VVER-440 fuel and on best modelling approach (BMA) extensively described in [4]. In this work the effects of variations in the depletion parameters, operation history, assembly type, Gadolinium presence, used energy group structure and time steps are investigated and graphically illustrated. For the sake of brevity, just the most important options used in burnup calculations are listed here. The developed models for the criticality calculations are 2D assembly models with reflective boundary conditions on all sides which represent infinite radial arrays of infinite length fuel assemblies. An unstructured coarse-mesh finite-difference acceleration approach (CMFD) is used with partial-current acceleration scheme. The 25 fine-mesh cells are used in the

4 322.4 global NEWT grid per coarse-mesh cell. The 40 x 40 global unit coarse-mesh and 4 x 4 individual mesh for each unit is used in the all prepared models. All models were calculated with the standard SCALE V7-238 multigroup neutron library based on ENDF/B-VII.0 evaluated data [6]. Fuel pins with burnable absorbers were depleted by constant flux option instead of constant power approach. To allow more realistic depletion in outer edge of fuel pin driven by the high thermal flux in the moderator, the Gadolinium bearing pin is divided into the five regions so that they are equal-area rings. The average specific power of each model is derived from the average reactor power of NPP Bohunice unit 4 during cycle 30 and equals kwth/kghm. The average concentration of boron acid (H3BO3) is obtained using the same approach and reaches cb=2.56 g/kg. The fuel is modelled with temperature of 933 K and the temperature of structural materials and water coolant is 555 K. Very fine depletion steps (<0.5 MWd/kgHM) are used before Gadolinium peak reactivity to tract the fast poison concertation changes. After peak reactivity longer steps are used but are kept smaller than 1 MWd/kgHM. The isotopic vectors calculated for the each FA and ERC and associated burnup value are used in the following criticality calculation. 3.2 Criticality calculation The core material composition was based on the representative sixth described in model definition. Following burnup calculation of 59 isotopic vectors of fuel material were defined and homogeneously distributed in the individual FA s and ERC s definitions. All of these FAs and ERCs were placed to the model of core based on the real loading pattern shown in the Fig. 1-b. The used temperature specification was the same as in burnup calculation; 933 K for fuel, 555 K for incore structural materials and coolant, 541 K respectively 571 K for coolant and structural materials depending on the inlet or outlet coolant site of model. The boric acid concentration (0.09 g/kg) and the position of sixth group of ERCs (232 cm) correspond to the values of operational day for which the fuel depletion was determined. Criticality calculation was carried out with four cross section (XS) libraries; Continuous Energy, 27 group and 238 group ENDF/B-VII, and 44 group ENDF/B-V. In case of multigroup libraries the self-shielding calculation was necessary to perform, which means that 59 cells calculation using BONAMI/CENTRM/PMC codes were invoked within each multigoup criticality calculation. For 44 and 238 group libraries a default parameters were retained during cell calculation but for 27 group library the re-evaluation by CENTRM code was extended to area of U238 resonances due to course energy structure and library optimization for shielding transport applications [7]. To achieve acceptable statistical uncertainty of investigated parameters in peripheral regions of the core from 80 to 900 mill. neutron histories were calculated. The 44 group ENDF/B-V XS library is used for other analyses in paper if not stated otherwise. 3.3 Sensitivity analysis The sensitivity and uncertainty analysis of VVER-440/213 core was performed by the TSUNAMI-3D code using the SCALE 44-group ENDF/B-V library [3] recommended for LWR and mixed-oxide lattices. Forward and adjoint transport calculations were carried out with KENO6 and the sensitivity coefficients were computed by the SAMS module. For the neutron flux calculations square mesh was placed through the core with a uniform step of 2

5 322.5 cm in the inner core region. In outer part, the size of the mesh varies from 3 to 4 cm in order to achieve the best statistical uncertainty. In case of reactor internals and direct core vicinity the size of mesh was directly proportional to the distance from the core centre in a range from 6 to 50 cm. Based on Standard Perturbation Theory implemented in the TSUNAMI the sensitivity coefficients can be written in a simple form as follows: S k,σ = σ k k σ σ σ Φ ( 1 P k σ L σ )Φ 1 k Φ PΦ, (1) where S k,σ is the sensitivity coefficient of k eff with respect to σ, which represents nuclear data like cross sections, fission spectrum or nubar. Symbols L and P in Eq. (1) are net loss and production Boltzman operators; Φ and Φ are adjoint and forward fluxes respectively. All information necessary to determine the sensitivity coefficients by Eq. (1) can completely characterize the investigated system, therefore the sensitivity coefficients serve as the basis for evaluation of the keff uncertainty induced by cross section data, for the similarity assessment and for the application of cross section adjustment methods. For validation purposes the sensitivity coefficients for VVER-440/213 core were also calculated using SCALE 238 group ENDF/B-VII library. Afterwards the 238 group data were collapsed to 44 group structure for better visual comparison and evaluation of energy profiles. 3.4 Uncertainty and similarity analysis TSUNAMI-IP utility uses sensitivity data generated by TSUNAMI-3D sequence and cross section-covariance data stored in the 44GRPCOV library for estimation of the response uncertainty. The SCALE covariance library includes evaluated covariances obtained from ENDF/B-VII, ENDF/B-VI [8], and JENDL3.3 [9] for more than 50 materials. ORNL has a database of pre-calculated sensitivity profiles for several hundred critical benchmark experiments specified in the International Handbook of Evaluated Criticality Safety Benchmark Experiments (IHECSBE) [10]. These sensitivities may be input to TSUNAMI-IP utility, along with calculated sensitivity profile of application system. In our approach 543 benchmark experiments and cases with various energy group structures were used. Three global integral indices [3] are used in the analysis to assess the similarity of VVER 440/V213 neutronic core design (hereinafter application index a) and a single experiment (e) on a system-wide basis for all nuclides and reactions. Each integral index is normalized such that a value of 1.0 represents complete similarity between application core design and specific benchmark experiment and the value of 0.0 indicates no similarity. The uncertainty of the integral response R (for instance keff) on the target integral parameter by the use of XS sensitivity coefficients denoted by symbol S and XS covariance matrix M is evaluated by the well-known sandwich formula: R 2 S MS T, (2) R R where the impact of the individual reactions and energy groups can be evaluated separately. The diagonal elements of the resulting matrix, defined as the solution of Eq. (2), represent the relative variance values for each of the system under consideration. The off-diagonal elements are the relative covariances between given experiments. These covariances transformed to correlation coefficients (ck) describe the level of similarity in the predicted response biases between various systems in the frame of XS induced uncertainties. The E parameter given by Eq. (3) assesses similarity between two systems based on the magnitude and shape of all sensitivity profiles.

6 322.6 T E S S S S a e a e. (3) The G index assesses the similarity of two systems based on normalized differences in the energy dependent sensitivity data for fission, capture and scatter. A physical interpretation of the G index is the ratio of the sum of the sensitivity coefficients of the application that are covered by the experiment to the sum of the sensitivity coefficients of a given application. The G index is defined as follows: G a, n e ', n a, n 1 S S S x, j x, j x, j, (4) n x j n x j where the symbol n stands for the number of application system nuclides, x represents the reaction and j the summation which is performed over all energy groups. The nuclidereaction specific partial integral index based on the same coverage criteria as G is denoted g. Undercoverage or noncoverage can be penalized with a penalty defined as p g = Z MZ T, (5) where Z is a vector of all groupwise sensitivity differences Z j for all nuclides defined as Z j = S a j S e j if S a j > S e j otherwise Z j = Use of cross section adjustment method As stated in SCALE manual [3], the TSURFER code uses the generalized linear leastsquares method (GLLS) to consolidate a prior set of measured integral responses (such as keff) and corresponding calculated values obtained using the SCALE nuclear analysis code system. The initial estimates for the computed and measured responses are improved by adjusting the experimental values and the nuclear data used in the transport calculations - taking into account their correlated uncertainties so that the most self-consistent set of data is obtained. By the application of cross section adjustment method, TSURFER provides an estimate for the computational bias and application uncertainty. 3.6 Determination of Upper Subcritical Limit (USL) Based on the criteria for subricitality listed in [1], a USL may be determined based on the analysis of a number of critical systems. Basically two methods of USL estimation are available. The first method called Confidence Band with Administrative Margin applies a statistical calculation of the bias and its uncertainty plus and administrative margin to a linear fit of critical experiment benchmark data. Here calculational bias β is defined is given as k c -1, where k c is the mean value of keff resulting from the calculation of benchmark criticality experiments. The USL Method 1 is defined as USL 1 (x) = 1 Δk m W + β, (6) where Δk m is administrative limit, W is the confidence band which accounts for uncertainties in the experiments, the calculational approach and XS data and β stands for the bias uncertainty. Usually adjustments are applied to prevent taking credit for a positive bias by assuming k c (x) = 1 everywhere that k c (x) > 1. In the second method referred as a lower tolerance band approach, statistical techniques are applied in order to determine a combined lower confidence band plus subcritical margin. The USL Method 2 is defined as

7 322.7 where s P is the pooled standard deviation for the set of criticality calculations and term C α P. s P provides a band for which there is a probability P with a confidence α that an additional calculation of keff for critical system will lie within the band. The recommended purpose of Method 2 is to apply it in parallel with Method 1 to verify that the chosen administrative margin is conservative relative to a purely statistical basic. More details of USL calculation methods can be found in [12]. A computer program USLSTATS available in SCALE package is used to evaluate USLs based on Methods 1 and 2. 4 RESULTS 4.1 Criticality calculation First verification of the prepared material and geometrical model was aimed to comparison of integral parameter keff. Calculated results based on different energy structure and evaluated data were subjected to comparison with real operational criticality of NPP Bohunice V2. All calculated values are presented in Tab. 1. Lowest computational bias was achieved by calculation with CE library. Best result using multigroup approach was calculated with 27 group library which can be explained by applied re-evaluation during cell calculation compared to finer group structures. Positive finding, from the point of computational time, was also almost identical keff calculated with 44 and 238 group library. Each multigroup calculation is able to determine local parameters like fission source distribution, whole core neutron flux and quantities connected to reaction rates like spatial power distribution. Energy structure Table 1: Comparison of keff for different energy structures. CE 27 group 44 group 238 group keff ± ± ± ± Sensitivity, uncertainty and similarity analysis As it was mentioned above, the TSUNAMI sequence computes the contributors to the application response uncertainty due to the XS covariance data. No. USL 2 (x) = 1 (C α P. s P ) + β(x), (7) Table 2: Uncertainty contribution in keff of VVER-440/213 core Covariance Matrix Nuclide- Reaction Nuclide- Reaction Contributions to Uncertainty in keff (% Δk/k) Due to the Matrix No. Nuclide- Reaction Covariance Matrix Nuclide- Reaction Contributions to Uncertainty in keff (% Δk/k) Due to the Matrix Pu nubar 239 Pu nubar 3.99E U nubar 238 U nubar 9.39E U n,gamma 238 U n,gamma 3.26E U n,gamma 235 U n,gamma 8.23E Pu fission 239 Pu fission 1.43E Pu n,gamma 240 Pu n,gamma 6.99E Pu fission 239 Pu n,gamma 1.32E Pu chi 239 Pu chi 6.81E U n,n' 238 U n,n' 1.31E U fission 235 U fission 5.39E Pu n,gamma 239 Pu n,gamma 1.26E U fission 235 U n,gamma 5.37E U nubar 235 U nubar 1.22E U chi 235 U chi 4.66E Xe n,gamma 135 Xe n,gamma 1.04E Nd n,gamma 143 Nd n,gamma 4.26E-02

8 322.8 The relative standard deviation of VVER-440/213 keff due to XS covariance data is 0.64%. Tab. 2 lists the top 16 covariance matrices that contribute to the keff uncertainty. These contributors represent more than 98.15% of the total uncertainty induced by XS data. The top contributor to keff uncertainty is the 239 Pu nubar reaction, see Fig. 2. This is due to high values of burnup reached in the core and, as can be seen in Fig. 1-a, also due to the very high sensitivities below 1 ev threshold. In case of 239 Pu fission large positive sensitivities exist bellow 1 ev and 100 kev thresholds. The uncertainty associated to the XS data in the energy range bellow 100 kev is quite large and reaches almost 2.5%. The contribution of 239 Pu n, gamma reaction to the total keff uncertainty is mainly driven by large XS uncertainty above 1 kev. Despite the low sensitivities in this energy range, this contribution is the sixth largest as it is shown in Tab. 1. a) b) Figure 2: Sensitivity and covariance profiles to 239 Pu nubar; fission and n,γ reactions The next presented profiles belong to 135 Xe and 143 Nd fission products. Here the most important contributor to keff uncertainty is reaction n, gamma, which is in 135 Xe case important also from the reactivity management point of view. We assume that bellow 1 ev their impact is driven by quite high sensitivities and above this threshold, by the very large uncertainties as shown in Fig.3 b. a) b) Figure 3: Sensitivity and covariance profiles to 135 Xe and 143 Nd n,γ reactions The similarity assessment procedure identified three groups of potential experiments, where the values of the ck coefficients got over 0.6. However, as it can be seen in Fig. 4, only cases of experiment MIX-COMP-THERM-002 reached ck values greater than 0.7.

9 322.9 Figure 4: Graphical results of similarity assessment procedure The E coefficients for these cases reach unsatisfactory values above 0.6, just one case got score above Nevertheless the big portion (around 40%) of VVER-440 sensitivities is uncovered (G) by above mentioned cases. More details with description of the first 20 experiments with the highest ck values can be found in Tab. 4. The values of g indices for nuclide reaction pairs, having a great impact on the neutron balance of the active core, are given in Tab. 3. The presented data highlight those nuclide reaction pairs which are not sufficiently covered by the MIX-COMP-THERM-002 experiment. Table 3: Results of nuclide-reaction specific partial integral index g ID 1 H scatter 1 H total 10 B total 16 O capture 235 U fission 238 U n,n' 238 U scatter 238 U capture 238 U total 239 Pu fission 239 Pu nubar As it is stated in [11], Eq. 5 does not provide a proper penalty for dissimilarities between two sensitivity profiles. However, our results are based on the approach which is already implemented in SCALE system. As it is recommended, just experiments that exhibit a certain degree of similarity to the application are used in the penalty assessment calculation. Data in Tab. 4 show that just 4 cases reach ck values higher than 0.7, therefore our penalty assessment based on the small amount of experiments cannot be considered as decisive. According to calculation the standard deviation in the keff of VVER-440/213 due to uncovered sensitivity coefficients reach 0.26%. Results prove that the most important contributor to additional penalty, bringing almost 55% of the total value, is 238 U n,n reaction. The rest portion mainly consists from contribution of fission products ( 135 Xe, 143 Nd and 103 Rh). 4.3 Use of cross section adjustment method Based on the similarity assessment results, 20 experiments listed in Tab. 4 were selected for inclusion in the adjustment procedure performed by the TSURFER code. In our analyses, all within-series experiments were assumed to have a correlation of 0.9, and following the data published in current version of DICE database [13], all experiments not in the same series were assumed to be uncorrelated. The achieved goodness of fit represented by χ 2 parameter reached acceptable value of 1.562E-01. According to calculation the new adjusted value of keff equals to with XS induced uncertainty of 0.45% what approximately gives the relative bias of -2.26%. We can conclude that GLLS calculation identified the small tendency of our calculation approach to overestimate the keff where the 238 U n,gamma and 238 U n,n nuclide reaction pairs were found to be the most important contributors to the calculated bias value. As it can be seen in Fig. 5-a), the case of capture reaction adjustments were applied almost in all reactions above 1 ev. We conclude that these XS adjustments mainly

10 influence the effective resonance integral of the system. The adjustments of inelastic reaction were applied mainly above 1 MeV, but almost constant relative change was applied almost in all other energies. Table 4: Uncertainty contribution in keff of VVER-440/213 core ID IHECSBE ID Case No. Fissile material Average Fission Group Energy Percent of fission below ev Percent of capture below ev Neutron gas temperature cladding ck E G 219 MIX-COMP-THERM MOX ev K Zircaloy MIX-COMP-THERM MOX ev K Zircaloy MIX-COMP-THERM MOX ev K Zircaloy MIX-COMP-THERM MOX ev K Zircaloy MIX-COMP-THERM MOX ev K Zircaloy MIX-COMP-THERM MOX ev K Zircaloy MIX-COMP-THERM MOX ev K Zircaloy MIX-COMP-THERM MOX ev K Zircaloy MIX-COMP-THERM MOX ev K Zircaloy MIX-COMP-THERM MOX ev K Zircaloy MIX-COMP-THERM MOX ev K Zircaloy MIX-COMP-THERM MOX ev K Zircaloy MIX-COMP-THERM MOX ev K Zircaloy MIX-COMP-THERM MOX ev K Zircaloy MIX-COMP-THERM MOX ev K Zircaloy MIX-COMP-THERM MOX ev K Zircaloy MIX-COMP-THERM MOX ev K Zircaloy MIX-SOL-THERM UO2(NO3) ev K MIX-SOL-THERM N3O9Pu ev K MIX-SOL-THERM UO2(NO3) ev K *In every case the light water is used as the moderator and reflector material. 4.4 Determination of Upper Subcritical Limit Due to having the small amount of experiments with acceptable level of similarity, the USLSTATS calculation was performed with all experiments previously used in similarity procedure. The keff values for these experiments were successfully retrieved from DICE database. No option to input unique experimental uncertainty for each experiment currently exists in SCALE environment, therefore uniform experimental uncertainty of 0.3 was used in calculation. Previously calculated uncertainty due to cross-section covariance data were automatically added for the all used experiments. In our calculation the W band was determined at a 95% confidence level. Neither administrative margin nor penalty was applied. The parameter P was set to 0.99 and α to The results of USL calculation are illustrated in Fig. 5-b). In this figure, the upper blue line represents a linear fit to a set of calculation based on critical experiments. The second green line represents the lower confidence band for a single additional calculation. This confidence band accounts for uncertainties in the experiments, the calculational approach and used nuclear data. The third line (short dashes) represents the USL1 preventing taking credit for a positive bias above the point where the blue line exceeds criticality. The USL2 function is shown by the yellow colour. It should be noted that due the small amount of similar experiments the data used in analysis did not pass the test for normality.

11 a) TSURFER relative cross section adjustments b) USLSTATS results Figure 5: Relative changes in cross sections and ULS results The calculated values of USL1 are and respectively, which suggests the relevancy of 5% administrative margin requested by Slovak Regulatory Authority for subriticality calculations. 5 CONCLUSION The detailed model of VVER-440/213 reactor was developed by B&J NUCLEAR ltd. for criticality and shielding analyses including reactor core, core basket, core barrel, pressure vessel with all internals in an appropriate level of accuracy. Applied simplifications result in the low computational bias of keff which did not exceed 0.8% in all computational cases. Special attention was given to the methodology applied to determination of fuel isotopic vectors modelled in one sixth symmetry core configuration what is one of the reasons of small calculation bias. Subsequently the defined model was introduced to sensitivity, uncertainty and similarity analysis. The relative standard deviation of keff induced by XS data was determined to 0.64%, which is comparable to bias identified in criticality calculations. The similarity assessment was not so successful. Only 20 benchmarks from more than 500 were identified with ck value greater than 0.6 and only 4 with ck value greater than 0.7. Low correlation is accompanied by not sufficient coverage of sensitivity profiles between selected benchmarks and target VVER-440/213 core. Significant portion of uncovered sensitivity profiles belong to fission products. The new adjusted of calculated keff value was found by use of GLLS method. The relative bias between original and adjusted response reached -2.26%. This result shows the small overestimation of used calculation methodology, adopted cross section data and applied simplifications. However, the identified overestimation is in principle consistent with previous results. It should be noted, that the results of TSURFER analyses rely on the availability of quality uncertainty and correlation data. The determination of Upper Subcriticality Limit pointed out the necessity of having the administrative margin about the level of 5% for subcriticality calculations. Moreover, the results of USL method 1 shown that if more benchmarks suitable for VVER-440 are available, the administrative margin can be lowered almost to the half of the original value. Even though our core belongs to PWR s family the ORNL pre-calculated sensitivity profiles and benchmarks in DICE database do not cover the Russian technology in a frame of similarity assessment and biasing methods. Especially the data for fission products will be welcomed. Finally more effort is needed to extend the DICE database by benchmarks based on experiments denoted to VVER reactors.

12 ACKNOWLEDGMENTS The authors would like to thank Martin Gajdoš, head of Nuclear safety department at Slovenské elektrárne, a.s. for valuable comments and support. REFERENCES [1] ANS, Nuclear criticality safety in operations with fissionable materials outside reactors, American National Standards Institute, 2014, La Grande Park Illinois, USA. [2] B. L. Broadhead, B. T. Rearden, C. M. Hopper, J. J. Wagschal, C. V. Parks, "Sensitivity and Uncertainty Analysis Capabilities and Data in Scale", Nucl. Technol., 174, 236, [3] ORNL, SCALE, A Comperhensive Modeling and Simulation Suite for Nuclear Safety Analysis and Design, Version 6.1, ORNL/TM-2005/39, [4] B. Vrban, Š. Čerba, J. Lűley, J. Haščík, "Investigation of burnup modelling issues associated with VVER-440 fuel", Proc. The 9 th Int. Conf. on Sust. Develop. Thr.Nuc. Res. and Edu., Pitesti, Romania, May 18-20, RATEN ICN Pitesti, [5] D. DeHart, "High-Fidelity Lattice Physics Capabilities of the SCALE Code System Using TRITON", The ANS and the ENS 2007 Int. Conf. on Making the Renaissance Real, Washington, D.C., Trans. Am. Nucl. Soc. 97, pp , [6] M. B. Chadwick, et. al.: "ENDF/B-VII.0: Next Generation Evaluated Nuclear Data Library for Nuclear Science and Technology", Nuclear Data Sheets, Volume 107, , [7] D. Wiarda, et. al.: Development and Testing of ENDF/B-VI.8 and ENDF/B-VII.0 Coupled Neutron-Gamma Libraries for SCALE 6, ORNL/TM-2008/047, Oak Ridge National Laboratory, 2009 [8] P. F. Rose: "ENDF-201, ENDF/B-VI Summary Documentation", BNL-NCS-17541, 4 th Edition, [9] K. Shibata, et. al.: "Japanese Evaluated Nuclear Data Library Version 3 Revision-3: JENDL-3.3", J. Nucl. Sci. Technol. 39, [10] Nuclear Energy Agency, International Handbook of Evaluated Criticality Safety Benchmark Experiments, NEA/NSC/DOC(95)/03/1-VIII, Organisation for Economic Co-operation and Development, [11] J. A. Roberts, B. T. Rearden: "Determination and Application of Partial Biases in Criticality Safety Validation", Nuc. Sci. and Eng,, 173, 43-57, [12] J. J. Lichtenwaller, et. al.: Criticality Benchmark Guide for Light-Water-Reactor Fuel in Transportation and Storage Packages, NUREG/CR-6361, Oak Ridge National Laboratory, [13] A. Nouri, et al. DICE: "Database for the International Criticality Safety Benchmark Evaluation Program Handbook", Nuc. Sci. and Eng, 145, 2003.