USE OF LATTICE CODE DRAGON IN REACTOR CALUCLATIONS

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1 USE OF LATTICE CODE DRAGON IN REACTOR CALUCLATIONS ABSTRACT Dušan Ćalić ZEL-EN razvojni center Hočevarjev trg 1 Slovenia-SI8270, Krško, Slovenia dusan.calic@zel-en.si Andrej Trkov, Marjan Kromar J. Stefan Institute, Jamova 39, SI-1000 Ljubljana, Slovenia andrej.trkov@ijs.si, marjan.kromar@ijs.si, The computer code Dragon is a free deterministic code developed by various organizations. It is a property of École Polytechnique de Montréal. Dragon contains a collection of various models which can describe the neutron transport in a given geometry of a unit cell, reactor fuel assembly or in a reactor core. To obtain the final solution it is necessary to link together different modules at each step and any compromise at any level can lead to poor final results. For a nuclear engineer it is crucial to maintain the accuracy when reducing computational time. In the past the advanced self shielding models which were incorporated in the Dragon code Version4 were analysed. The conclusion obtained in that analysis was that the computational time of the burnup calculations was too long to be used for routine calculations. With the additional research and analysis presented in this paper satisfactory results were obtained that maintain the accuracy and reduce the computational time. In this paper these results will be presented. Results are compared to the reference results obtained by the Monte Carlo code SERPENT. 1 INTRODUCTION In order to model neutron transport in the nuclear reactor the deterministic or probabilistic approaches are used. However, exact computer simulations of such physically complex systems with complicated geometry, it is impossible to do it directly even with the use of advanced computers. Therefore different levels of modeling and calculations are applied, using various approximations. In this paper the focus will be on a lattice cell calculation using deterministic and probabilistic codes. Usually lattice cell calculations take a lot of computational time. In principle more accurate method requires more computational time. However it will be shown that with the use of a DRAGON [1] code a calculation scheme can be achieved which is fast and accurate. 2 DRAGON CODE In this paper all analyses were performed using lattice code DRAGON Version4. The computer code DRAGON is a result of the efforts made at École Polytechnique de Montréal to rationalize and unify different models and algorithms used to solve the neutron transport equation into a single code. DRAGON is therefore a lattice cell code which is divided into many calculation modules linked together using the GAN generalized driver [1] as shown on Figure

2 088.2 Figure 1: Data flow for lattice calculation [3] These modules perform the following tasks: LIB: module used to generate or modify a DRAGON microlib Modules used to analyze different geometries and to generate a tracking file for different deterministic evaluations. Among many modules two were selected suitable for the analysed geometry: o SYBILT: tracking module based on interface current method o EXCELT: tracking module used to generate the collision probability matrices Modules for resonance self-shielding calculations: o SHI: using the generalized Stamm ler method o USS: using a subgroup method ASM: module used to generate multigroup collision probability matrices FLU: module used to compute the neutron flux by solving transport equation EVO: module to perform in-core and out-core depletion of every material selected from the isotopic cross section library EDI: module supplies the main editing options by calculating reaction rates, average and condensed cross sections It was demonstrated [2] that the DRAGON code using Draglib libraries offers the accuracy of the results needed. However the CPU time of the calculations was unacceptably long. So in this paper the additional calculation option were explored. The analysis was performed to compare the results of depletion calculations performed with DRAGON using two different transport methods. These results were then compared to results of the calculations obtained with a reference Monte Carlo code SERPENT [4]. The comparison was performed on the multiplication factor and nuclide densities of some important nuclides.

3 MODEL OF THE BENCHMARK The calculations are performed on a pressurised water reactor (PWR) lattice constructed in a 3 3 pin-array configuration. The extra region of Zr, Inconel and water on the outside is added to preserve the fuel to the moderator ratio of the overall assembly as it is in the Krško nuclear power plant (NPP) core. The fuel region is further discretized into different regions using rings. This discretization is important to treat more realistically the radial behavior of the fuel due to the resonant absorption of U-238 (rim effect). Therefore the fuel was divided into four rings with the following volume ratios [5] (from the inside to the outside): 50%, 30%, 15% and 5% as shown on Figure 2. Figure 2: PWR lattice model used in calculations The fuel cell is composed of UO 2 with enrichment 4.75% of U-235 at a temperature 300 K. The moderator is light water without boron at a temperature 300 K and density g/cm 3. The calculations were performed using DRAGON formatted library based on the ENDFB-VII.0 evaluation with 172 and 281 energy groups. 4 TRACKING MODULES In the past the effect of self shielding models was studied with the use of DRAGON code for a similar geometry. It was then concluded that the use of the subgroup method gives the best results for the given geometry, regarding the calculation time and the accuracy of the results [2]. Therefore the self-shielding calculation was performed by the USS module using a subgroup approach with physical probability tables. For this analysis two different transport modules were used, SYBILT and EXCELT. Both modules are based on a collision probability tables however there are some differences how the modules perform the neutron tracking. 4.1 SYBILT tracking module This module is part of a collision probability technique based on an interface current method. In this case, a unit assembly is subdivided into cells and collision probability

4 088.4 matrices are computed for each uncoupled cell. The detailed flux can then be reconstructed from the knowledge of interface currents surrounding each cell. 4.2 EXCELT tracking module The EXCELT tracking module performs the tracking with the use of specular conditions. The suitable parameters that define the EXCELT tracking module have been selected at zero burnup conditions. Parameters like the number of angles and track density have a large impact on the neutron multiplication factor and computation time. Therefore, optimal parameters were selected based on the accuracy of the multiplication factor (that is based on convergence of the result for the multiplication factor) and calculation time. 5 CALCULATION COMPARISONS First a comparison between two tracking modules in the DRAGON code has been performed by calculating the multiplication factors during the burnup calculations. The comparison of the multiplication factors was performed taking the SERPENT calculations as the reference case. The results are presented in Figure 3. Slight dissipation of the results is caused by the statistical nature of the Monte Carlo method used in the SERPENT code. Figure 3: Relative difference in the multiplication factors between the two transport modules used and the reference SERPENT calculations It can be seen on Figure 3 that the DRAGON calculations with EXCELT tracking module have a good agreement at the beginning, but at the end of the cycle, the difference is larger, that is, total K eff between the BOC (beginning of the cycle) and EOC (end of the cycle) is 410 pcm. The deviation in the multiplication factor using SYBILT tracking module is even larger compared to the reference SERPENT results. It appears that the difference between the two tracking modules is quite constant with a maximum difference of 330 pcm. However the advantage of the SYBILT tracking modules is the calculation time. For this kind of burnup calculations the SYBILT was much faster with the calculation time around 3 minutes while when using EXCELT tracking module the calculation time was around 30 minutes.

5 088.5 One way to find the deviations between the two tracking modules is to examine the average number densities of isotopes for the four rings of the fuel region that effect the multiplication of the neutrons. Figure 4 shows the relative differences between the transport modules in DRAGON calculations for some important actinides and fission products at four different burnup steps: 10 GWd/tU, 20 GWd/tU, 30 GWd/tU and 40 GWd/tU. Figure 4: Comparison of number densities for important actinides and fission products between SYBILT and EXCELT transport modules at four different burnup steps The isotopes with the biggest difference are Am-241 and plutonium isotopes Pu-239 and Pu-241. The biggest differences are for the burnup step at the end of cycle (40 GWd/tU). The differences are always lower than 2%. Concerning the fission products, the biggest differences are in Eu-151 and Gd-155 isotopes.

6 088.6 With the additional testing the accuracy of the SYBILT results could not be increased. With the increased number of parameters used in the SYBILT tracking module the final solution (multiplication factor) did not converge. Thus it was concluded that this tracking module is only good for quick estimates of the effect. Since the accuracy of the SYBILT results was not satisfactory, it was decided that in the next analyses only the EXCELT tracking module will be used. A possible way to increase the accuracy of the results using EXCELT module was to use the nuclear data library with additional energy groups. Until now the DRAGON formatted library (draglib) was used based on the ENDFB-VII.0 evaluations with 172 energy groups. Additionally the same evaluated library with 281 energy groups was tested. The results of DRAGON calculations using only the EXCELT tracking module with 172 and 281 energy groups are presented on Figure 5. The results of the SERPENT code were used as a reference. Figure 5: Relative difference in the multiplication factors between 281-group and 172- group libraries and the reference SERPENT calculations As shown in Figure 5 the burnup results are quite sensitive to the type of libraries used in the DRAGON code. The DRAGON code was compared with the reference SERPENT code where the library is based on the same evaluation data; ENDFB-VII.0 library was used. The results of the calculations performed with the 281-energy group library show a better agreement with the reference SERPENT results than the ones performed with the 172-group library. The maximum difference is less then 250 pcm. It is evident from the comparison of the DRAGON results using the 281 and 172-group libraries that the difference is rather small at the beginning of the cycle, but at the burnup step of 7 GWd/tU the difference becomes higher. Using the library with the increased number of energy groups does not increase the calculation time, but the accuracy of the results is increased with regard to the reference calculation with SEPRENT. The total K eff between BOC and EOC is 410 pcm in the case of the 172-group library and 160 pcm in the case of the 281-group library. DRAGON code with the 281-group library is a good trade off between the accuracy of the result and the CPU time. To analyze the differences between the results obtained with the SERPENT and DRAGON codes it was necessary to perform the sensitivity analysis for each of the 232 nuclides presented in the DRAGON library.

7 088.7 For each of the analysed isotopes the number densities in the DRAGON code was replaced with the number densities computed with the SERPENT code. This was evaluated for the four burnup steps. Comparison of the neutron multiplication factors is presented in Figure 6 for the burnup steps 10, 20, 30 and 40 GWd/tU. Only the results with K eff > 10 pcm are presented in Figure 6. Figure 6: Differences between the multiplication factors calculated with SERPENT and DRAGON code for the major isotopes and for the four burnup steps It is obvious from Figure 6 that the highest impact on K eff value comes from the U-235. This impact is around 230 pcm for the burnup step 30 GWd/tU which means that the DRAGON code underestimates the concentration of U-235 during the burnup. However the concentration of the Pu-241 is overestimated. The impact on the K eff value is around 80 pcm at the end of the cycle. The fission products that significantly stand out are Sm-149 and its precursor Pm-148m. Their impacts are around 70 pcm. 6 CONCLUSION Different analyses have been carried out to demonstrate that DRAGON code can use various methods to solve the neutron transport equation. It was interesting to see that an appropriate calculation scheme can give good results in a reasonably short time. However, it as it was presented in the past [2] this is not so obvious for the inexperienced user since the DRAGON code provides so many options which are easily used and combined; but some of them are not time efficient so that the calculation time is increased. Indeed some results are very sensitive to some input parameters and modelling options including the tracking of the geometry, self shielding options and the nuclear data library. At the end the final optimum scheme was chosen based on the accuracy and the CPU time. In this case this was the EXCELT tracking option using the USS SUBG self shielding option and using draglib 281-group library.

8 088.8 In the case of the burnup calculations the relative differences from the SERPENT results are very small at the beginning of the cycle, that is, about -30 pcm, but they are increased at the end of the cycle to become about -200 pcm (see Figure 5). It was demonstrated that DRAGON code is a good choice for deterministic neutron transport calculations. However the use of this code requires experience in using various input parameters and modelling options that are available in the code. REFERENCES [1] G. Marleau, A. Hébert, R. Roy, A user Guide for DRAGON Version4, Report IGE-294, Institut de génie nucléaire, École Polytechnique de Montréal [2] D. Ćalić, M. Kromar, A. Trkov, Use of Monte Carlo and deterministic codes for calculation of plutonium radial distribution in a fuel cell, Nuclear Energy for New Europe 2011, Bovec, Slovenia, 2011 [3] A. Hébert, Applied Reactor Physics, Presses Internationales Polytechnique, April 2010 [4] J. Leppänen, PSG2/Serpent a Continuous energy Monte Carlo Reactor Physics Burnup Calculational Code, VTT Technical Research Centre of Finland, March 2012 [5] A. Santamarina, C. Collignon, C. Garat, French Calculation Schemes for Light Watr Reactor Analysis, Proc of Int. Mtg. on the Physics of Fuel Cycles and Advanced Nuclear Systems PHYSPR 2004, Chicago, ANS