# Calculations for a BWR Lattice with Adjacent Gadolinium Pins Using the Monte Carlo Cell Code Serpent v.1.1.7

Authors: Diego Ferraro; Eduardo Villarino
Journal: Science and Technology of Nuclear Installations
 (2011)

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## Abstract

Monte Carlo neutron transport codes are usually used to perform criticality calculations and to solve shielding problems due to their capability to model complex systems without major approximations. However, these codes demand high computational resources. The improvement in computer capabilities leads to several new applications of Monte Carlo neutron transport codes. An interesting one is to use this method to perform cell-level fuel assembly calculations in order to obtain few group constants to be used on core calculations. In the present work theVTT recently developed Serpent v.1.1.7 cell-oriented neutronic calculation code is used to perform cell calculations of a theoretical BWR lattice benchmark with burnable poisons, and the main results are compared to reported ones and with calculations performed with Condor v.2.61, the INVAP's neutronic collision probability cell code.


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## Body

## 1. Introduction

The Monte Carlo method is traditionally used in neutronic calculations to solve criticality and shielding problems due to its capability to model complicated geometries and its quasicontinuous energy treatment. However its high computational requirements had restricted its applications to other areas in neutronic calculations. With the advance in computer performance the use of this method to perform cell calculations to obtain few group constants arises as a very promising future application. This application is even more interesting when few group constants are needed to core calculations involving high heterogeneous 3D devices, such as irradiations facilities.TheSerpent code [1] is a new Monte Carlo continuous-energy neutron transport code developed in the VTT Technical Research Centre of Finland oriented to pin cell calculations with the capability of burnup and few group constants generation. Nowadays this code is oriented to pintype assembly calculations, but it has the capability to model more general 3D geometries, which makes it an interesting option to obtain few group constants in complicated devices on a reactor core.In the present work a well-known BWR lattice benchmark calculation [2] is performed using Serpent code and nuclear data from ENDF/B-VI.8. The main results are compared with reported values and with calculations performed with the INVAP’s collision probability code Condor [3] using nuclear data from WIMS library (69 groups) [4] and WLUP library (172 groups) [5].


## 2. Models

The fuel element with adjacent poisoned pins with Gadolinium reported on the theoretical benchmark [2] was modeled in Serpent and Condor codes. This fuel element consists of a 4 × 4 pin assembly with two Gadolinium poisoned pins. The main characteristics are listed on Table 1.Table 1
Problem specification.
FuelMaterialUO2Density10 g/cm3Temperature600ºCU-235 enrichment3% wtDiameter1 cmGd-pin poisonGd2O3Poison percentage on Gd-Pin3% wtAverage power density20 W/gCladMaterialZircaloy-2Density6.55 g/cm3Temperature300ºCInner diameter1 cmOuter diameter1.2 cmModeratorMaterialH2OVoid0%ConditionSaturated at 286ºC and 70.06 barLattice pitch1.6 cmThe models developed inCondor (using Collision probabilities 2D) and Serpent (using Monte Carlo 2D) are shown on Figures 1(a) and 1(b), respectively.Models developed for BWR cluster (a)Condor v 2.61 (b) Serpent v. 1.1.7.
(a)(b)As it can be seen, the Gd pins were divided into four zones in both models. In addition all the pins were divided in four zones on Serpent model. Regarding burnup calculations, the Condor model evolves each zone individually, while the developed Serpent model only differs in the evolution for the two types of fuel pin. The Condor model was run using nuclear data from esin2001 [4] library (based on WIMS-69) and WLUP library [5] (172 groups). Serpent model was run using nuclear data from ENDF/B-VI.8 in ACE format. Both Condor and Serpent burnup calculations used the predictor-corrector method. Condor burnup calculations evolved the isotopes included on the burnup chain defined on each library used. In Serpent code the decay and fission data is obtained directly from the ENDF/B-VI.8 library, but inventory report was demanded for 70 isotopes.


## 3. Results Comparison

Results were obtained for both models. The running time (sequential, notparallel mode) involved on Serpent calculations reached 435 min on a 2 Ghz CPU, while the calculations performed on Condor code required 4 minutes for esin2001 library and 10 min for EWLUP 172 for the same CPU.Results regarding infinite multiplication factors, main isotope evolution, and flux profiles were compared. Table2 shows the results for the infinite multiplication factor for fresh/hot/clean condition. Serpent result includes the statistical convergence.Table 2
Results for Clean/Hot/Fresh condition.
SerpentCondor + esin2001Condor + EWLUP 172Benchmarkk infinite1.0016 ± 0.00070.99081.00621.0014 ± 0.011In addition, results for burnup  evolution for both models and those reported on the benchmark are shown on Figure2.Figure 2
Burnup results for both models.As it can be seen from Table2 and Figure 2 a good agreement exist between both codes and benchmark results. Furthermore, reactivity results obtained with Serpent have a better agreement with those obtained with Condor + EWLUP 172 due to the fact that nuclear data sets are similar.Another comparison regarding isotope burnup was performed. The evolution for235U, 239Pu, and 155Gd in the poisoned pin are shown on Figures 3, 4, and 5, respectively.Figure 3
235U burnup in the poisoned pin.Figure 4
239Pu in the poisoned pin.Figure 5
155Gd burnup in the poisoned pin.As it can be seen from Figures3–5 good agreement is obtained in the evolution of the most relevant isotopes for both models.In addition, the radial distribution for155Gd in the poisoned pin at 2000MWd/tonU has been calculated with both models for each radial zone. The results are shown on Table 3.Table 3
155Gd Radial distribution at 2000 MWd/tonU in the poisoned pin.
155Gd numerical density [at/cmb]Mean radius (cm)BenchmarkBenchmark StdevSerpentCondor+ esin2001Condor+ EWLUP 1720.1251.29E-043.4E-061.28E-041.28E-041.29E-040.3021.20E-043.3E-061.18E-041.18E-041.19E-040.3939.41E-053.8E-069.25E-059.00E-059.31E-050.4674.95E-058.6E-064.71E-054.26E-054.60E-05As it can be seen, the results for radial distribution of155Gd obtained are consistent between models and reported values.Finally, the thermal flux profile in the horizontal direction (x) of the fuel assembly is compared for two burnups for two vertical positions (measured in cm where x,y=0,0 is the centre of the fuel assembly of  Figure 1). The results are shown on Figures 6 and 7. These results are not reported on the benchmark.Figure 6
Thermal flux profiles on both models for two different vertical positions (x,y=0,0 is the centre of the fuel assembly of  Figure 1) for BU = 0 MWd/tonU.Figure 7
Thermal flux profiles on both models for two different vertical positions (x,y=0,0 is the centre of the fuel assembly of Figure 1) for BU = 4000 MWd/tonU.The results obtained for thermal flux profiles show a fairly good agreement between both codes, even when the fuel assembly is evolved to 4000 MWd/tonU. As far as the averaged zones do in which flux is obtained do not match exactly, slight differences are encountered.


## 4. Conclusions

The results obtained with theSerpent code for this simple benchmark show a fairly good agreement with reported values and with those calculated with INVAP’s cell code Condor.The main results regarding reactivity, isotope evolution, and flux profiles show a good agreement, which encourages the future test of the code in other problems, such as more complicated geometries. The next step would be the generation of few group constants to be used in core calculations.Furthermore, as far as theSerpent code is a cell-oriented code, the running time is accessible. Nevertheless the running time involved is much bigger than Condor (2D collision probability code).A future work will involve the test of Serpent code in MTR type fuel assemblies to obtain few-group constants generation and perform core calculations.



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*Source: 659406-2010-12-19.xml*