Accuracy assessment of a new Monte Carlo based burnup computer code

Annals of Nuclear Energy 45 (2012) 29–36

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Accuracy assessment of a new Monte Carlo based burnup computer code B. El Bakkari a,b,⇑, T. ElBardouni b, B. Nacir a, C. ElYounoussi a,b, Y. Boulaich a,b, O. Meroun b, M. Zoubair b, E. Chakir c a

Unité Conduite Réacteur, Centre d’Etudes Nucléaires de la Maâmora CNESTEN/CENM B.P.1382 R.P.10001 – Rabat, Morocco ERSN-LMR, Department of Physics, Faculty of Sciences, Tetuan 93002, Morocco c Dept. of Physics, Faculty of Sciences Kenitra, Morocco b

a r t i c l e

i n f o

Article history: Received 6 November 2011 Received in revised form 14 February 2012 Accepted 17 February 2012 Available online 22 March 2012 Keywords: Burnup BUCAL1 VVER-1000 LEU MCNP NJOY99

a b s t r a c t This study aims to test for the suitability and accuracy of a new home-made Monte Carlo burnup code, called BUCAL1, by investigating and predicting the neutronic behavior of a ‘‘VVER-1000 LEU Assembly Computational Benchmark’’, at lattice level. BUCAL1 uses MCNP tally information directly in the computation; this approach allows performing straightforward and accurate calculation without having to use the calculated group fluxes to perform transmutation analysis in a separate code. ENDF/B-VII evaluated nuclear data library was used in these calculations. Processing of the data library is performed using recent updates of NJOY99 system. Code to code comparisons with the reported Nuclear OECD/NEA results are presented and analyzed. Ó 2012 Elsevier Ltd. All rights reserved.

1. Introduction Burnup calculations aim at following the time development of material compositions and neutronics during reactor operations. Such calculations are needed all the way, from the preliminary analysis of new concepts to decommissioning, for a safe and economic operation throughout reactor lifetime. Accurate prediction of reactor main neutronics parameters requires occurate simulation of particle transport process by solving the Boltzmann transport equation. The Monte Carlo method (Spanier and Gelbard, 1969) is one of the most suitable analysis methods because of its accurate modeling of physical phenomena. In the last couple of decades, its application has been expanded to burnup calculations (Jafarikia et al., 2010) and its practicability has been shown. Most of these calculations are based on existing standard multipurpose continuous energy Monte Carlo codes, such as RACER, MVP and MCNP (X-5 Monte Carlo Team, 2003). The computational issues to perform accurate Monte Carlo calculations are however continuously reduced due to improvements made in the basic Monte Carlo algorithms, due to the development of variance reduction techniques and due to developments in computer architecture (more powerful processors, the so-called brute force approach through parallel ⇑ Corresponding author at: Unité Conduite Réacteur, Centre d’Etudes Nucléaires de la Maâmora CNESTEN/CENM B.P.1382 R.P.10001 – Rabat, Morocco. Tel.: +212 668782702; fax: +212 537803326. E-mail address: [email protected] (B. El Bakkari). 0306-4549/$ - see front matter Ó 2012 Elsevier Ltd. All rights reserved. doi:10.1016/j.anucene.2012.02.011

processors and networked systems, . . .). This evolution of computer architecture is going to continue in the future. This paper is dedicated to test for the accuracy and suitability of a new home-made burnup code named BUCAL1, by investigating and predicting the neutronic behavior of a VVER-1000 LEU Assembly Computational Benchmark using UO2 and UO2GdO3 nuclear fuel types. This study is considered as continuation of earlier efforts (Bakkari et al., 2009a, 2009b) made for the qualification of BUCAL1 burnup code in which several nuclear fuels were treated under different irradiation conditions, such as: UO2, MOX and UO2–ThO2. In the present work, MCNP calculations were done using the ENDF/B-VII evaluated nuclear data library. Processing of the data library is performed using the recent updates of NJOY99 system. The Benchmark specification used for these calculations is given in Section 2. The nuclear data processing and qualification of ENDF/ B-VII library as well as the theoretical model and methodology employed in BUCAL1 burnup code are described in Section 3. The calculational results and comparisons with reported OECD/NEA results are presented and discussed in Section 4.

2. Benchmark specification The NEA Nuclear Science Committee has an Expert Group that deals with the status and trends of reactor physics, fuel performance, and fuel cycle issues related to the disposition of weapons-grade plutonium. This Group has been established to

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B. El Bakkari et al. / Annals of Nuclear Energy 45 (2012) 29–36

Fig. 1a. MCNP model of the VVER-1000 LEU Benchmark Assembly.

computer code certification process and to verification of calculation methods. The VVER-1000 LEU Assembly Computational Benchmark is one such Benchmarking activity performed by Expert’s Group. The VVER-1000 assembly (NEA, 2002) is hexagonal in design and consist of one central tube, 312 fuel pin locations (12 of which are U/Gd rods), and 18 guide tubes. The hexagonal lattice pitch of the assembly is 23.6 cm. The pins are cylindrical and cladded with Zr–Nb alloy. Fuel pin pitch is 1.275 cm. Cladding inside and outside diameters are 0.772 cm and 0.910 cm, respectively. The Benchmark Assembly is shown in Fig. 1a and consists of fuel rods with 3.7 wt.% enrichment. The 12 U/Gd pins have a 235U enrichment of 3.6 wt.% and a Gd2O3 content of 4.0 wt.%. Material composition of fuel pins, cladding and moderator is given in Table 1.

3. Computational methodology 3.1. Neutron data library processing Fig. 1b. Cell numeration in the 1/6 of the Benchmark Assembly to presenting the fission rate distribution.

facilitate the sharing information and experience in the physics and fuel behavior and to provide NEA member countries up-todate information about these issues, which can contribute to the

In this research, the more recent evaluated neutron data based on ENDF/B-VII (Chadwick et al., 2006) was used as the data source. The process to construct continuous cross section data libraries from the data source files is typically performed by the NJOY system code (MacFarlane, 2002) with its recent update file ‘‘up304’’.

31

B. El Bakkari et al. / Annals of Nuclear Energy 45 (2012) 29–36 Table 1 Material composition of the VVER-1000 Benchmark Assembly. Material name

Comment

Isotopic content (at./b-cm)

UO2

LEU fuel of 3.7 wt/o enrichment

235

U 8.6264E-4 U 2.2169E-2 235 U 7.2875E-4 238 U 1.9268E-2 16 O 4.1854E-2 152 Gd 2.5159E-6 154 Gd 2.7303E-5 Zr 4.259E-2 Nb 4.225E-4 H 6.717E-2 16 O 3.358E-2

16

O 4.6063E-2

238

U/GD

LEU fuel of 3.6 w/o of

235

U containing 4 w/o of Gd2O3

Cladding

Zirconium alloy

Moderator

Light water with 0.6 g/kg of boron, Tm = 575 K, d = 0.7235 g/cc

The procedure to process point-wise cross sections by each module of NJOY is shown in Fig. 2. The principal advantage of NJOY is its most general-purpose applicability and comprehensive capability to process data in the recent ENDF format. It takes the basic data from the nuclear data library and converts them into forms needed for applications. Resonance cross-sections are constructed using a method of choosing the energy grid that incorporates control over the number of grid points generated for some materials. Summation cross sections are reconstructed from their parts. The resulting point wise cross-sections are written onto a ‘‘Point-ENDF’’ (PENDF) file for future use. BROADR module reads a PENDF file and Doppler-broadens the data. After broadening and thinning, the summation cross-sections are again reconstructed from their parts. The results are written onto a new PENDF file for future use. HEATR module computes energy-balance heating and damage energy using reaction kinematics or applying conservation of energy. The ENDF photon production files can be used during this step, when available. GASPR module goes through all of the reactions given in an ENDF-format evaluation, determines which charged particles would be produced by the reaction and adds up the particle yield times the reaction cross section to produce the desired gas production cross sections. THERMR produces point-wise cross-section in the thermal range. Energy-to-energy incoherent inelastic scattering matrices can be computed for free-gas scattering or for bound atoms scattering using a precomputed scattering law in ENDF file. PURR is used to prepare unresolved-region probability tables. Finally ACER module prepares cross-sections and scattering laws in ACE format (a compact ENDF format) for the MCNP computer code.

Evaluated Data

155

Gd 1.8541E-4 Gd 2.5602E-4 157 Gd 1.9480E-4 158 Gd 3.0715E-4 160 Gd 2.6706E-4 Hf 6.597E-6 156

10

B 4.794E-6 B 1.942E-5

11

All the cross-sections are represented on a union grid for linear interpolation by taking advantage of the representation used in RECONR and BROADR modules. The S(a, b) thermal scattering cross sections of bound nuclei were taken directly from the standard MCNP5 (release 1.40) cross section library respecting the irradiation conditions of the Benchmark Assembly. These thermal scattering data are essential to accurately model the neutron interactions at energies below 4 eV. 3.2. Validation of ENDF/B-VII data library The qualification of the processed nuclear data library ENDF/BVII was realized through the analysis of the integral parameters of Godiva, Flattop-25 and Bigten Benchmarks from the International Handbook of Evaluated Criticality Safety Benchmark Experiments – ICSBE Handbook (NEA, 2007). The calculated integral parameters were compared to experimental ones and summarized in Table 2. For each of the Benchmarks the measured as well as calculated values of integral parameters and the associated standard deviation are given. Table 2 shows that, calculated and experimental values agree well for the majority of integral parameters. However, big differences are also found, especially, for rc55Mn/rf235U and rc59Co/rf235U in Godiva and rc58Fe/rf235U in Bigten which may probably due to a bad estimation of the resonance region of the neutron capture cross sections of 55Mn, 59Co and 58Fe isotopes in the energy domain up to 10 keV as shown in Figs. 3–5. Godiva and Bigten systems have enough flux in this region (see Fig. 6) to make the capture cross sections of these isotopes relatively important for the estimation of these integral parameters. 3.3. Overview of BUCAL1 burnup code

ACE- Format Library

RECONR

ACER

BROADR

PENDF

HEATR

PURR

GASPR

THERMR

Fig. 2. Flow diagram of NJOY99 processing system for ACE format library construction.

BUCAL1 (Bakkari et al., 2009a, 2009b) is a FORTRAN computer code designed to aid in analysis, prediction, and optimization of fuel burnup performance in nuclear reactors. The code was developed to incorporate the neutron absorption reaction tally information generated directly by MCNP5 code in the calculation of fissioned or neutron-transmuted isotopes for multi-fueled regions. This allows us to benefit of the full capabilities provided by MCNP and to incorporate them into burnup calculations in the aim to perform more accurate and robust treatment of the problem. Neutron transmutation, fission, and radioactive decay are included in the modeling of the production and removal terms for each isotope of interest. For a fueled region, neutron transmutation, fuel depletion, fission-product poisoning, actinide generation, burnable poison loading and depletion effects are included in the calculation. The code uses the fourth order Rung Kutta method with the predictor–corrector approach for the resolution of the depletion equation for more than 900 isotopes.

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B. El Bakkari et al. / Annals of Nuclear Energy 45 (2012) 29–36 Table 2 Integral parameters calculated for Godiva, Flattop-25 and Bigten using MCNP and ENDF/B-VII neutron data library. Benchmark

Integral parameters

Godiva HEU-MET-FAST-001

Experiments (NEA, 2007)

keff

rf238U/rf235U rf233U/rf235U rf237Np/rf235U rf239Pu/rf235U rc55Mn/rf235U rc59Co/rf235U rc93Nb/rf235U rc197Au/rf235U Flattop-25 HEU-MET-FAST-028

keff

rf233U/rf235U rf238U/rf235U rf237Np/rf235U rf239Pu/rf235U Bigten IEU-MET-FAST-007

keff

4

10

3

10

2

10

1

10

0

10

-1

10

-2

10

-3

10

-4

10

-5

10

-4

10

-3

10

-2

10

-1

10

0

10

1

10

2

10

3

10

4

10

5

10

6

10

7

Incident neutron energy (MeV) Fig. 3.

55

Mn capture cross section.

Using BUCAL1 one can do standard burnup calculation, burnup calculation followed by a space of time of cooling, burnup calculation with shuffling of fueled regions and burnup calculation with reloading new fresh fuels. Continuation card in BUCAL1 allows users to restart calculations after unwanted stops. In the current version of BUCAL1, the two groups of nuclides under consideration are: (1) Actinides (ACT) that contain heavy metal nuclides with atomic number Z P 90 and their decay daughters. (2) Fission Products (FP) produced by fissions and their decay/ capture daughters. Specifically, the calculated reaction rates of fission products and actinides are shown in Table 3. Only the neutron capture cross sec-

(CE/E) % e4

1.000 (±1.0 ) 0.1643 (±1.8e3) 1.59 (±3.0e2) 0.8516 (±1.2e2) 1.4152 (±1.4e2) 0.0027 (±2.0e4) 0.038 (±3.0e3) 0.03 (±3.0e3) 0.1 (±2.0e3)

0.99974 0.16055 1.56931 0.84258 1.38755 0.00338 0.00549 0.03384 0.09362

(±1.9 ) (±3.2e5) (±3.1e4) (±1.7e4) (±2.8e4) (±6.8e7) (±1.1e6) (±6.8e6) (±1.9e5)

0.026 2.282 1.301 1.059 1.954 25.11 85.56 12.80 6.38

1.000 (±1.0e3) 1.608 (±3.0e3) 0.1492 (±1.6e3) 0.7804 (±1.0e2) 1.3847 (±1.2e2)

1.00284 1.56620 0.12765 0.70543 1.33321

(±2.0e4) (±3.1e4) (±2.6e5) (±1.4e4) (±2.7e4)

0.284 2.600 14.446 9.606 3.719

0.996 (±2.0e3) 0.03739 (±3.4e4) 0.3223 (±3.0e3) 1.1936 (±8.4e3) 1.58 (±3.0e2) 0.11 (±3.0e3) 1.011 (±1.4e2) 0.000078 (±2.0e6) 0.0013 (±3.0e5) 0.00215 (±9.0e5) 0.000036 (±1.0e6) 0.009 (±3.0e4) 0.0123 (±2.0e4) 0.0031 (±1.0e4) 0.0095 (±2.0e4) 0.0164 (±1.0e3) 0.167 (±3.0e3)

0.99453 (±1.6e4) 0.03364 (±6.7e6) 0.29768 (±6.0e5) 1.15210 (±2.3e4) 1.53954 (±3.1e4) 0.10837 (±2.2e5) 0.975104 (±2.0e4) 0.000079 (±1.6e8) 0.001372 (±2.7e7) 0.001873 (±3.7e7) 0.000031 (±6.2e9) 0.008308 (±1.7e6) 0.011088 (±2.2e6) 0.004867 (±9.7e7) 0.009034 (±1.8e6) 0.018385 (±3.7e6) 0.170243 (±3.4e5)

Cross section (barn)

Cross section (barn)

rf238U/rf235U rf237Np/rf235U rf239Pu/rf235U rf233U/rf235U rc238U/rf235U r(n,a) 10B/rf235U r(n,a)27Al/rf235U r(n,p)46Ti/rf235U r(n,p)47Ti/rf235 r(n,p)48Ti/rf235U r(n,p)54Fe/rf235U r(n,p)58Ni/rf235U rc58Fe/rf235U rc59Co/rf235U rc63Cu/rf235U rc197Au/rf235U

10

ENDF/B-VII

e3

10

4

10

3

10

2

10

1

10

0

10

-1

10

-2

10

-3

10

-4

10

-5

10

-4

10

-3

10

-2

10

-1

10

0

10

1

0.148 10.026 7.638 3.476 2.561 1.478 3.55 0.70 5.51 12.90 13.20 7.69 9.85 57.01 4.91 12.11 1.94

10

2

10

3

10

4

10

5

10

6

10

7

Incident neutron energy (MeV) Fig. 4.

59

Co capture cross section.

tion is considered for fission products since neutron absorption by fission products is primarily via (n, c) reaction. For actinides, four types of reactions are considered including capture, fission, (n, 2n) and (n, 3n) because they lead to the production of significant quantities of fission products and higher-mass actinides. Fig. 7 gives the simplified flow diagram of BUCAL1. 4. VVER-1000 LEU Benchmark analysis In the present Benchmark analysis, calculations are performed considering hot operating poisoned conditions (Tfuel = 1027 K, Tmoderator = 575 with 135Xe and 149Sm equilibrium concentrations),

33

10

4

10

3

10

2

10

1

10

0

10

-1

10

-2

10

-3

10

-4

10

Flux normalized to 1

Cross section (barn)

B. El Bakkari et al. / Annals of Nuclear Energy 45 (2012) 29–36

-5

10

-4

10

-3

10

-2

10

-1

10

0

10

1

10

2

10

3

10

4

10

5

10

6

10

7

10

-1

10

-2

10

-3

10

-4

10

-5

Godiva Bigten

10

-2

10

Incident neutron energy (MeV) Fig. 5.

Fe capture cross section.

4.1. k1 versus burnup The infinite multiplication factor (k1) of the VVER-1000 LEU Benchmark Assembly was computed with respect to burnup using BUCAL1 and compared to the k1 values obtained by the predefined burnup codes, results are presented in Fig. 8a. The differences between BUCAL1 calculated and BM k1 values are also shown separately in Fig. 8b. Fig. 8a shows that, the results obtained using BUCAL1 are in satisfactory agreement with the results estimated by the rest of burnup codes. As the burnup increases the reactivity increase initially till the gadolinium isotopes burn out, and then decreases with burnup in a roughly linear manner. This UOX assembly designs uses Gd2O3 in UO2 as burnable absorber to control part of the core reactivity at the beginning of cycle (Thilagam et al., 2009a, 2009b). The effect on reactivity of this strong absorber is well simulated by BUCAL1. The deviation from BM values shown in Fig. 8b is within ±300 from 0 to 15 MW d/kg HM then it increases as a function of burnup till it reaches 600 pcm at 40 MW d/kg HM. 4.2. Isotopic composition variation in pin cells with respect to burnup Figs. 9–17 display the isotopic composition variation of nuclides U, 236U, 238U, 239Pu, 240Pu, 241Pu, 242Pu, 155Gd and 157Gd, respectively in cell-1 and cell-24 of the VVER-1000 LEU Benchmark Assembly obtained using BUCAL1 and compared to the Benchmark

235

10

0

10

1

Energy (MeV)

58

a power density of 108 MW t/m3, up to a burnup of 40 MW d/ kg HM with sufficiently fine burnup steps to provide accurate results, particularly till the burn out of the Gd absorber. MCNP calculations were done with a nominal source size of 7e+6 neutrons and the estimated statistical errors (1r) were reduced to 30 pcm for k1 values and less than 8% for reaction rates. Neutronic calculations were done using 147 burnable isotopes (102 FP and 45 ACT). In order to reduce the MCNP running time, burnup calculations were done considering 6 pin-cells as follow: 2 pin-cells for the U/Gd in and outer rings and 4 pin-cells that were chosen to be representative for the rest of fuel elements, according to the power distribution of fuel elements in the core. Results of calculations were compared to the reported ones (NEA, 2002) obtained using several burnup codes such as: MCU, TVS-M, WIMS8A, HELIOS, Multicell and to the Benchmark Mean (BM) values.

-1

Fig. 6. Neutron flux for Godiva and Bigten.

Table 3 MCNP-tallied reactions used in BUCAL1.

Actinides

Fission products

Reaction type

MCNP reaction identifier

(n, c) (n, f) (n, 2n) (n, 3n) (n, c)

102 6 16 17 102

Mean (BM) values as a function of burnup. Cell numeration in the fuel assembly to presenting fission rate distribution and isotopic composition is as shown in Fig. 1b. According to these figures, it is remarked that, for all the isotopes, the isotopic compositions produced by BUCAL1 agree well with the BM values. It seems also that the deviations from the BM values increase as a function of burnup. Actually, there is a strong incentive to investigate this increase of errors, which is expected to be due to the associated errors on neutron cross sections, half-lifes, branching ratios, burnup chains simplifications, numerical solution and also to the statistical error propagation as a function of burnup. Deviations from BM values at 40 MW d/kg HM are found to be 3.9%, 2.4%, 0.1%, 2.7%, 4.3%, 2.0% and 0.5% for cell-1 and 3.4%, 2.1%, 0.1%, 1.7%, 5.4%, 3.1% and 2.2% for cell-24 for 235 U, 236U, 238U, 239Pu, 240Pu, 241Pu and 242Pu, respectively. 235U drop faster in cell-1 rather than in cell-24 due to the higher neutron flux in UO2 pin cells results in building up of 236U by neutron capture. For 155Gd and 157Gd these deviations are found to be 1.1% and 1.7%, respectively. 157Gd depletes faster than 155Gd due to its higher absorption cross section 155ra = 62,000 barns and 157ra = 252,000 barns at 2200 m/s).

4.3. Pin-by-pin fission reaction rates Detailed pin-by-pin fission rate distributions estimated by MCNP code using the ENDF/B-VII nuclear data library for the Benchmark Assembly compared with the BM results provided in the Benchmark report (NEA, 2002) are shown in Fig. 18. Calculation results show, good agreement with the BM results for all the pin cells. The fission reaction rates fall down to 0.32 at the U/Gd pins (cells 24 and 35), which is expected. Deviations from the BM values are found to be within ±2%.

34

B. El Bakkari et al. / Annals of Nuclear Energy 45 (2012) 29–36

Fig. 7. Simplified follow diagram of BUCAL1.

800 1,15

BUCAL1 MCU TVS-M WIMS8A HELIOS MULTICELL

1,05

400 200 Δk (pcm)

k−inf

1,10

600

1,00 0,95

0 -200

BUCAL1

-400 -600

0,90

-800 0

10

20

30

40

Burnup (MWd/kgHM) Fig. 8a. Variation of k1 with burnup for VVER-1000 LEU Benchmark Assembly.

0

10

20

30

Burnup (MWd/kgHM) Fig. 8b. Differences from BM values.

40

35

9,0x10

-4

8,0x10

-4

7,0x10

-4

6,0x10

-4

5,0x10

-4

4,0x10

-4

3,0x10

-4

2,0x10

-4

1,0x10

-4

BM value/Cell1 Bucal1/Cell1 BM value/Cell24 BUCAL/Cell24

Atom density (at./b-c)

Atom density (at./b-cm)

B. El Bakkari et al. / Annals of Nuclear Energy 45 (2012) 29–36

1,6x10

-4

1,4x10

-4

1,2x10

-4

1,0x10

-4

8,0x10

-5

6,0x10

-5

4,0x10

-5

2,0x10

-5

BM value/Cell1 BUCAL1/Cell1 BM value/Cell24 BUCAL1/Cell24

0,0 0

10

20

30

40

0

Burnup (MWd/kgHM) 235

U isotopic composition as a function of burnup.

Fig. 12.

-4

7,0x10

-5

1,2x10 1,0x10

6,0x10

-5

-4

5,0x10

-5

8,0x10

-5

4,0x10

-5

6,0x10

-5

3,0x10

-5

2,0x10

-5

1,0x10

-5

4,0x10

-5

2,0x10

-5

BM value/Cell1 BUCAL1/Cell1 BM value/Cell24 BUCAL1/Cell24

0

239

10

20

30

BM value/Cell1 BUCAL1/Cell1 BM value/Cell24 BUCAL1/Cell24

0

40

2,2x10

-2

2,1x10

-2

2,1x10

-2

2,0x10

-2

2,0x10

-2

2,0x10

-2

1,9x10

-2

1,8x10

-2

236

Fig. 13.

U isotopic composition as a function of burnup.

BM value/Cell1 BUCAL1/Cell1 BM value/Cell24 BUCAL1/Cell24

20

30

40

4,0x10

-5

3,5x10

-5

3,0x10

-5

2,5x10

-5

2,0x10

-5

1,5x10

-5

1,0x10

-5

5,0x10

-6

240

Pu isotopic composition as a function of burnup.

BM value/Cell1 BUCAL1/Cell1 BM value/Cell24 BUCAL1/Cell24

0,0 0

10

20

30

40

0

238

U isotopic composition as a function of burnup.

10

20

30

Burnup (MWd/kgHM)

Burnup (MWd/kgHM) Fig. 11.

10

Burnup (MWd/kgHM)

Atom density (at./b-cm)

Atom density (at./b-cm)

-2

40

Pu isotopic composition as a function of burnup.

Burnup (MWd/kgHM)

2,3x10

30

0,0

0,0

Fig. 10.

20

Burnup (MWd/kgHM)

Atom density (at./b-cm)

Atom density (at./b-cm)

Fig. 9.

10

Fig. 14.

241

Pu isotopic composition as a function of burnup.

40

B. El Bakkari et al. / Annals of Nuclear Energy 45 (2012) 29–36

1,6x10

-5

1,4x10

-5

1,2x10

-5

1,0x10

-5

8,0x10

-6

6,0x10

-6

4,0x10

-6

2,0x10

-6

1,2

BM value/Cell1 BUCAL1/Cell1 BM value/Cell24 BUCAL1/Cell24

1,0

Fission rates

Atom density (at./b-cm)

36

0,8

BM value MCNP/ENDFB-VII

0,6

0,4

0,0 0,2

0

10

20

30

0

40

Atom density (at./b-cm)

Fig. 15.

2,00x10

-4

1,75x10

-4

1,50x10

-4

1,25x10

-4

1,00x10

-4

7,50x10

-5

5,00x10

-5

2,50x10

-5

242

BM value/Cell24 BUCAL1/Cell24

0,00 10

20

30

40

Burnup (MWd/kgHM)

Atom density (at./b-cm)

Fig. 16.

2,25x10

-4

2,00x10

-4

1,75x10

-4

1,50x10

-4

1,25x10

-4

1,00x10

-4

7,50x10

-5

5,00x10

-5

2,50x10

-5

155

Gd isotopic composition as a function of burnup.

30

40

50

60

70

not use the calculated neutron flux as input to other computer codes to generate the nuclide inventory for the next time step. Instead, BUCAL1 directly uses the neutron absorption tally/reaction information generated by MCNP5 for each nuclide of interest to determine the new nuclide inventory. This allows the full capabilities of the MCNP code to be incorporated into the calculations and a more direct solution technique to be employed. The accuracy testing of BUCAL1 was done by code to code comparisons with several burnup codes from the NEA/OECD. Infinite multiplication factor (k1) and isotopic compositions of important isotopes were compared and analyzed for a VVER-1000 LEU Benchmark Assembly. Generally, the calculation results obtained by BUCAL1 show good agreement compared to the Benchmark Mean (BM) values and results reported at NEA document. At the end of burnup (40MW d/kg HM), the relative deviation from the BM value for the infinite multiplication factor (k1) using BUCAL1 is found to be 600 pcm and within ± 6% for the isotopic composition of important isotopes. The effect on reactivity of strong absorbers (155Gd and 157Gd) is well simulated by BUCAL1. References

BM value/Cell24 BUCAL1/Cell24

0,00 0

10

20

30

40

Burnup (MWd/kgHM) Fig. 17.

20

Fig. 18. Pin-by-pin fission rates distribution.

Pu isotopic composition as a function of burnup.

0

10

Pin Cell

Burnup (MWd/kgHM)

157

Gd isotopic composition as a function of burnup.

5. Conclusion New burnup code utility called BUCAL1 was developed. The code is different in comparison to other burnup codes as it does

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