Science and Technology of Nuclear InstallationsVolume 2011 (2011), Article ID 659406, 4 pagesdoi:10.1155/2011/659406

Research Article

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

Diego Ferraro and Eduardo Villarino

Nuclear Engineering Department, INVAP S.E., Comandante Luis Piedrabuena 4950, San Carlos de Bariloche, Río Negro R8403CPV, Argentina

Received 30 August 2010; Accepted 26 November 2010

Academic Editor: Juan Ferreri

Copyright © 2011 Diego Ferraro and Eduardo Villarino. Diego Ferraro and . This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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 the VTT 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.

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.

The Serpent 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.

Fuel

Material
UO₂

Density
10 g/cm³

Temperature
600ºC

U-235 enrichment
3% wt

Diameter
1 cm

Gd-pin poison
Gd₂O₃

Poison percentage on Gd-Pin
3% wt

Average power density
20 W/g

Clad

Material
Zircaloy-2

Density
6.55 g/cm³

Temperature
300ºC

Inner diameter
1 cm

Outer diameter
1.2 cm

Moderator

Material
H₂O

Void
0%

Condition
Saturated at 286ºC and 70.06 bar

Lattice pitch
1.6 cm

The models developed in Condor (using Collision probabilities 2D) and Serpent (using Monte Carlo 2D) are shown on Figures 1(a) and 1(b), respectively.

(a)

(b)

Figure 1: Models developed for BWR cluster (a) Condor v 2.61 (b) Serpent v. 1.1.7.

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. Table 2 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.

Serpent
Condor + esin2001
Condor + EWLUP 172
Benchmark

k infinite
1.0016 ± 0.0007
0.9908
1.0062
1.0014 ± 0.011

In addition, results for burnup evolution for both models and those reported on the benchmark are shown on Figure 2.

Figure 2: Burnup results for both models.

As it can be seen from Table 2 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 for ²³⁵U, 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 Figures 3–5 good agreement is obtained in the evolution of the most relevant isotopes for both models.

In addition, the radial distribution for ¹⁵⁵Gd 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)
Benchmark
Benchmark Stdev
Serpent
Condor + esin2001
Condor + EWLUP 172

0.125
1.29E-04
3.4E-06
1.28E-04
1.28E-04
1.29E-04

0.302
1.20E-04
3.3E-06
1.18E-04
1.18E-04
1.19E-04

0.393
9.41E-05
3.8E-06
9.25E-05
9.00E-05
9.31E-05

0.467
4.95E-05
8.6E-06
4.71E-05
4.26E-05
4.60E-05

As it can be seen, the results for radial distribution of ¹⁵⁵Gd obtained are consistent between models and reported values.

Finally, the thermal flux profile in the horizontal direction () of the fuel assembly is compared for two burnups for two vertical positions (measured in cm where 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 ( 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 ( 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 the Serpent 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 the Serpent 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.

References

J. Leppänen, “PSG2 / Serpent—A Continuous-energy Monte Carlo Reactor Physics Burnup Calculation Code v1.1.7”.

C. Maeder and P. Wydler, International Comparison Calculations for a BWR Lattice with Adjacent Gadolinium Pins, EIR, Wurenlingen, Switzerland, 1984.

E. Villarino, “Condor Calculation Package,” in Proceedings of the PHYSOR 2002, Seoul, South Korea, October 2002.

“Improvements of the WIMS library from ENDF/B-IV – DIN/GN/00196”.

“WIMS-D library Update Project – IAEA”.