Current Developments of the VVER Core Analysis Code KARATE-440

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1 Current Developments of the VVER Core Analysis Code KARATE-440 György Hegyi Hungarian Academy of Sciences Centre for Energy Research, Budapest, Hungary Reactor Analysis Department Konkoly Thege Miklós út H-1121, Budapest, Hungary András Keresztúri, Csaba Maráczy, István Panka, Emese Temesvári Hungarian Academy of Sciences Centre for Energy Research, Budapest, Hungary Reactor Analysis Department Konkoly Thege Miklós út H-1121, Budapest, Hungary {andras.kereszturi; csaba.maraczy; istvan.panka, ABSTRACT This paper represents the recent updating of core analysis code KARATE-440 for the purpose of Russian type PWR design. The fuel modifications and the upgraded regimes requiring more accurate calculations have necessitated the further development and validation of the code system. On the other hand even the calculations have reached a high quality level; it is very important to take into account the uncertainties of the calculations, especially the uncertainties of the input parameters related to the applied models which cannot be eliminated. A realistic estimation of these uncertainties is necessary for judging the reliability of the simulation results. Taking into account of these goals, the following improvements were implemented into the KARATE-440 code system: 1) a more detailed parametrization of the few group constants, 2) capabilities to handle the uncertainties of the basic nuclear data and the technological parameters. The updated code has been verified by some standard calculations. 1 INTRODUCTION Recently, the deterministic code systems have been well developed and used in the nuclear industry widely [1-2]. Due to the new challenges (more heterogeneous and higher enriched fuel assembly, the extension of operating cycle length and the safety requirements) the updating of nodal code for steady state and transient core analysis is carried on continuously to enhance the exactness and validity. The accuracy of the core- and rod-level calculations is highly influenced by the quality of the parameterized few group constants applied in these models. In the case of uranium dioxide fuel and light water moderator, the precision of few group constants can be significantly improved by the following-up of the isotopic concentration of Pu239 in the higher levels of computation. In case of the secondgeneration PWR, during the higher burn-up the importance of the number of higher mass Pu isotopes increases. Moreover the usage of MOX fuel is possible in these improved thirdgeneration reactors, which strengthens the consideration of the higher mass number of Pu 315.1

2 315.2 isotopes in the few group constant parameters [3]. A review of group constants is also required in the simulation of the long term shutdown cases, as the everyday practice shows that some fuel assemblies can be loaded into core after some time duration in spent fuel pool. It is connected with reload strategy which prefers low leakage core while the higher enriched fresh fuel is used [4]. On the other hand the calculations, as well as the experiments have their own uncertainties. It is very difficult to quantify the uncertainty for deterministic calculation. Often it is roughly approximated by comparing calculations and experimental data and stating that the observed difference is equivalent to the uncertainty of calculations. Even if this approach is known to be incorrect and we cannot mix the uncertainty or error and the bias in such complicated cases like the core physics calculations it is very difficult to quantify the uncertainty correctly. Meanwhile it is indispensable to give estimation, what precision can we reach with our codes and what margins must be set to avoid exceeding given (safety) limits. Fortunately, the possibilities of the computational burden increases so recently we can easily use the Monte Carlo method to analyse the uncertainties in applications where it was formerly impossible, due to the large number of calculations involved. In case of core physics problems the uncertainty analysis are based on the data library as most of the input variables bearing the uncertainty are present on the level of the lattice code and the related model. The important safety-related conclusions are made based on the output of 3D core calculations. That is why a calculation route easy to fit the available computer architecture was developed, which allows the propagation of the uncertainties through the whole chain of the calculations. In this stage the propagation of geometrical and material uncertainties as well as the uncertainties coming from the microscopic cross sections is taken into account. [5-6]. The present contribution gives a summary of the above mentioned code development. In Section 2, the modification of the KARATE code system is described. Section 3 gives a short description of the overall uncertainty evaluation scheme. In Section 4 some preliminary results are presented. 2 IMPROVEMENT OF THE KARATE MODELS The KARATE-440 code system version 5 applicable for the calculation of VVER-440 reactors is based on the ENDF/B-VI nuclear data library [1-2]. The main goal of the calculation is core reload design, however, certain problems amenable to a static code can be analysed by KARATE-440. Accordingly, stationary neutron physics and thermal hydraulics models have been implemented. These models are capable of following burnup and slow Xenon transient processes but do not allow for calculating faster transients demanded in a safety analysis. The intra assembly power distribution is also determined. The code system has been successfully used for many years [7-8]. The calculation is grouped into levels which are connected to the higher one through parametrized data libraries. Its computational levels are the following: 1. level: 70 group, 2D transport calculation for an assembly, or an assembly with surroundings. Generate few group constants for higher levels, MULTICELL module calculate the composition for 176 isotopes. 2. level: 4-group, 2D fine mesh reflector albedo calculations for the further levels, with detailed reflector geometry. 3. level: 2-group, 2D fine-mesh diffusion calculations for one assembly and its surroundings (SADR module).

3 level: 2-group, nodal calculations for the core (in a sixty degree symmetrical part: GLOBUSKA module or for the full core: GLOBUS36). There is consistent, bi-directional connection between levels via parameterization. Core calculations are made with the GLOBUSKA nodal code using the homogenized few group cross sections(xs) of assemblies. The result of the core calculations gives input (flux boundary conditions) for the inhomogeneous type fine mesh diffusion calculations. The assembly and its vicinity are simulated with the SADR code. The MULTICELL transport code is used for fuel assembly calculations. Till now, the burnup, the thermo-hydraulic feedbacks and the concentrations of the isotopes U235, U238, Np239, Pu239, I135, Xe135 Pm149 and Sm149 were calculated. The resulting two-group cross-sections are parametrised before using them in the global calculation as in the case of the assembly calculations. For determination of fuel pin cell few-group cross sections the same transport procedure is applied. Here some extra calculations have to be introduced where the assemblies are surrounded by environments causing spectral perturbations. In this case, besides the parameters of the assembly library, the ratio of epithermal to thermal flux (SI) is introduced as an extra parameter. In KARATE, the reflector parts and the control assembly regions are excluded from the diffusion type calculations, and represented by albedo matrices which are deduced from a set of specific calculations with different inhomogeneous boundary conditions. The elements of the albedo matrices [α g,g ] are the reflection probabilities for neutrons entering the excluded region in group g' and returning to the fuel assemblies in group g. According to the results of the methodological investigations, the albedo matrix elements can be considered as a function of the soluble boric acid concentration [CB] and the moderator density, in any cases. For the reflector of the core, the albedo matrices depend on the position of the edge, too. In case of control assembly there is some further material dependent parameter: for region containing boron steel the albedo depends of its boron concentration, for region containing hafnium it depends on their concentration. In this special case the Hf174, Hf176, Hf177, Hf178, Hf179 and Hf180 isotopes are treated during the burnup calculations. To make the KARATE code system more realistic the quality of the few group constants had to be improved. The parametrization of XS was modified as its dependence on the isotopes of Pu was taken into account. As the fuel is burning out, its content of U235 and U238 are decreasing and an increase can be observed for other actinides (Np239, Pu239, Pu240, Pu241, Pu242 and Am241). The fission products were tracked in the calculation. The reactivity of a partially spent fuel assembly (FA) is changing with time which depends on measure of burn-up, the fuel enrichment and time of placement in spent fuel pool. The reason is that concentrations of some actinides and fission products are changing in time. Some isotope s changes (at least Xe135 and Sm149) must be considered in any case, but the others not so necessarily..in case of longer time they should be taken into account which makes necessity to follow changes of concentrations of sufficiently big amount of isotopes. The XS simulation in shut down state and the cooling procedure need modification in the parametrization, too. The Sm poisoning is taken into account in more detailed way (produced from decay of Nd149 through different fission fragments: Pm147, Pm148, Pm148m). The new method of the preparation of the cross-section library was tested in the following manner. MULTICELL spectral calculation was performed for a given assembly, including 4 cycle and 3 years cooling, during which the criticality (keff=1) was achieved by the iteration of buckling. The simulation was repeated by the PARACELL diffusion code

4 315.4 using the old and new parameterized XS library and the values of the predetermined buckling. The deviation of the criticality calculated by PARACEL code from keff=1.0 characterizes the goodness of the new library. One can see in Figure 1 that the new parametrization reduce the deviation to its one fifth. Figure 1: Effective multiplication factor during the simulation of four theoretical cycles and 3 years cooling 3 UNCERTAINTY METHOD FOR THE CORE CALCULATIONS The uncertainty analysis is performed at different neutronic VVER-440 modelling stages using a Monte Carlo based approach, where the non deterministic treatment of a physical model that induces a stochastic nature on the code outputs is based on a sampling methodology. In this approach, the code input space defined by input parameters, boundary and initial conditions are treated as random variables. Thereafter, values of these inputs are selected according to a random sampling strategy and then propagated through the code in order to assess the output uncertainty in the corresponding calculations. The overall uncertainty evaluation scheme which we have developed and which is described below is shown in Figure 2. Our final goals are to quantify the uncertainties of our neutronic calculations at core level - originating from: the uncertainties of the basic nuclear data, the uncertainties of the technological parameters. The effect of depletion is considered at each level. The recent investigations have been made for a VVER-440 core. The applied statistical method is based on Monte Carlo sampling and it is a so called brute force method [11]. 3.1 Technological Uncertainties The technological uncertainties associated with uncertainties of geometrical and material characteristics of reactor structural elements are specified by their manufacturers. Some further assumptions were taken in order to find the uncertainty in fuel amount in the assemblies and in the fuel pins. E.g.: based on the assumption that all pellets in a fuel

5 315.5 assembly are coming from the "same fabrication batch", therefore they have "nearly" the same parameters. The type of distribution (uniform or normal), and its appropriate characteristic parameters for VVER fuel was collected in [9]. The parameters characterizing the second generation Russian fuel were selected to take them into account of the library preparations, such as: thickness of the shroud, lattice pitch of the fuel pins in the assembly, inner/outer diameter of clad, density & outer diameter of the pellet, distance among fuel pins and the wall of the assembly, distance between the assemblies, lattice pitch of fuel assembly, absolute difference in Gd content of the assembly, absolute difference in fuel enrichment, relative deviation in the length of the pins. Supposing the same sampled parameters for all the pins in a given assembly results some conservativism. One thousand Monte Carlo-type draws for all of the above parameters were raffled. These parameters were used in the preparation of the inputs of the multi-group spectral calculation. 3.2 Uncertainties of the Basic Nuclear Data As the MULTICELL is a 70 group, 2D transport code, first, the 44 group covariance matrices (44GROUPV6REC extracted from SCALE 5.1 code [10]) have to be converted into a 70 group scheme using linear interpolation. The next step is the preparation of a large number (1000) of perturbed (sampled) 70 group microscopic cross section libraries, which are inputs of MULTICELL calculations. 3.3 Overall Scheme of the Calculations The new version of the KARATE code system can be divided into two parts (see on Fig.2): the preparatory and a cycle calculations. The calculation scheme can be seen on the two consecutive parts of figure. The two sets are connected by the libraries, which are developed in the first part and used in the second one. The toolset for uncertainty evaluation comprises the following programs. The TECHBIZ (SORST) program organizes the input preparation. Its task is to prepare the set of (in this case 200) perturbed (sampled) 70 group microscopic cross section libraries (basic + fission products), which are inputs of MULTICELL calculation. Its routine SORST is responsible for the geometric and material input. Based on the MULTICELL results (fluxes and cross sections), the MULXS1MU program prepares homogenized cross section data for the assembly. It takes into account the irregularities coming from the shrouds of the assembly. The ENVIRMUL program organizes the input data for MULTICELL code in cases where the assembly and its surrounding are calculated.

6 315.6 Figure 2: Block diagram of the preparation part of the uncertainty calculation in the KARATE code system

7 315.7 The CORRFACT is a finite differential program used for evaluating the corrections of albedo matrices. The MULTICELL provides input for this procedure. At the end of the depletion calculation the PARAFA program finalizes the few group libraries to the core calculations. 4 VERIFICATION OF THE NEW VERSION OF THE KARATE-440 CODE The new code version was verified by a set of calculations. The simulation was based on an equilibrium cycle with 4.7 % enriched, 2 nd generation Russian fuel. The initial 3D burnup state was gained from the preliminary calculation. As some assemblies were 4 cycles in the core, four cycles were calculated by the new code version to get a reasonable good reference for comparison. The first calculations proof the good functioning of the developed programs comparing the results of old and new version and demonstrate the functioning of the procedure of library preparation. The depletion curve can be seen in Figure 3. Due to the modification of the code a ~0.05 g/kg difference can be observed in the critical boric acid concentration, which is the consequence of the detailed parametrization. The use of perturbed library causes a slightly higher critical boron concentration during the whole cycle. No change was observed in case of radial power peaking factor and burnup distribution calculated by the old and new code version. In Figure 4 one can see that the usage of perturbed library modifies the power and burnup distribution in very small quantities, but the maximum value of burnup can be found in the same position (Assembly number 59). Note that the investigations were performed for an arbitrary selected perturbed library, final conclusions regarding to the target uncertainties can be drawn only after a detailed statistical analysis using large number of perturbed libraries. Figure 3: Critical boron concentration as a function of burnup in the equilibrium cycle using the older (Ver. 5) and the newer (Ver. 6) GLOBUSKA code

8 315.8 Figure 4: Radial power peaking factor (middle in the hexagons) and burnup distribution (down in the hexagons) calculated by GLOBUSKA (Ver. 6) in the end of the equilibrium cycle (425.0 effective day) using the unperturbed library (left) and the perturbed library (right) 5 CONCLUSION The appearance of new requirements (increasing enrichment, longer burnup period, simulating the reactivity of a partially spent fuel assembly) have made further development for the KARATE-440 code system which was elaborated for the core design of VVER-440 type reactors. Another important goal was to establish a methodology and tool set for analyses of uncertainties in our core calculations. The developed method makes it feasible to evaluate uncertainties in all neutron-physical characteristics, including boric acid concentration, power distribution, peaking factors or reactivity coefficients, thanks to the total Monte Carlo approach based on sampling the input data distributions and processing a large number of calculations. Till now, the verification of the new code version was completed. The workability of the new method was demonstrated. ACKNOWLEDGMENTS This work has been carried out in the frame of VKSZ_ Hungarian project supported by the National Research, Development and Innovation Fund. REFERENCES [1] Keresztúri A., Hegyi Gy., Korpás L., Maráczy Cs., Makai M., Telbisz M., General features and validation of the recent KARATE-440 code system, International Journal of Nuclear Energy Science and Technology 5 (3) 2010, pp [2] Cs. Hegedűs, Gy. Hegyi, G. Hordósy, A. Keresztúri, M. Makai, Cs. Maráczy, F. Telbisz, E. Temesvári, P. Vértes, The KARATE Program System, PHYSOR 2002, Seoul, Korea, October 7-10, 2002

9 315.9 [3] NEA/NSC/DOC(2002)10, A VVER-1000 LEU and MOX Assembly Computational Benchmark, Specification and Results, Nuclear Science ISBN [4] I.Ovdiienko, I.Bilodid, M.Ieremenko, V.Khalimonchuk, A.Kuchin, Effect of fuel burnup history on neutron-physical characteristics of VVER-1000 core,, Proceedings of the 23 rd Symposium of AER on VVER Reactor Physics and Reactor Safety, Štrbské Pleso, Slovakia, October 30 - November 4, 2013 [5] Ivanov, K., Avramova, M., Kamerow, S., Kodeli, I., Sartori, E., Ivanov, E., Cabellos, O., Benchmarks for uncertainty analysis in modelling (UAM) for the design, operation and safety analysis of LWRs Volume I: Specification and Support Data for the Neutronics Cases (Phase I), NEA/NSC/DOC (2013)7, OECD/NEA [6] I. Panka and A. Keresztúri (2013). Uncertainties of the neutronic calculations at core level determined by the KARATE code system and the KIKO3D code. Kerntechnik: Vol. 78, No. 4, pp , doi: / [7] V. Krýsl, P. Mikoláš, D. Sprinzl, J. Švarný, E Temesvári, I. Pós& L. Heraltová, Full- Core VVER-440 Calculation Benchmark,Kerntechnik Vol 79, No. 4,Aug. 2014, pp [8] I. Panka and A. Keresztúri (2015). Assessment of the uncertainties of MULTICELL calculations by the OECD NEA UAM PWR pin cell burnup benchmark. Kerntechnik: Vol. 80, No. 4, pp , doi: / [9] Panka I., Keresztúri A., Korpás L., Bóna G., Developing of the engineering factors of Fuel Assembly containing Gd with 4.7% average enrichment for the core monitoring system (VERONA), inner report, MTA-EK-RAL /01/M1 (in Hungarian) [10] Broadhead; B. L.: SCALE 5.1 Cross-Section Covariance Libraries, ORNL/TM- 2005/39, Version 5.1, Vol. I, Book 3, Sect. M19, November, 2006 [11] I. Panka, Gy. Hegyi, Cs. Maráczy, A. Keresztúri, Uncertainties of the KIKO3D- ATHLET calculations using the Kalinin-3 benchmark (Phase II) data, Proceedings of the 25 th Symposium of AER, Balatongyörök, Hungary, October 13 16, 2015