Burnup calculation of the OECD VVER-1000 LEU benchmark assembly using MCNP6 and SRAC2006
Nuclear Science and Technology, Vol.8, No. 4 (2018), pp. 10-19
Burnup calculation of the OECD VVER-1000 LEU benchmark
assembly using MCNP6 and SRAC2006
Nguyen Huu Tiep*, Nguyen Thi Dung, Tran Viet Phu, Tran Vinh Thanh and Pham Nhu Viet Ha
Institute for Nuclear Science and Technology, Vietnam Atomic Energy Institute
179 Hoang Quoc Viet, Cau Giay, Hanoi, Vietnam
(Received 16 November 2018, accepted 28 November 2018)
Abstract: The present work aims to perform burnup calculation of the OECD VVER-1000 LEU (low
enriched uranium) computational benchmark assembly using the Monte Carlo code MCNP6 and the
deterministic code SRAC2006. The new depletion capability of MCNP6 was applied in the burnup
calculation of the VVER-1000 LEU benchmark assembly. The OTF (on-the-fly) methodology of
MCNP6, which involves high precision fitting of Doppler broadened cross sections over a wide
temperature range, was utilized to handle temperature variation for heavy isotopes. The collision
probability method based PIJ module of SRAC2006 was also used in this burnup calculation. The
reactivity of the fuel assembly, the isotopic concentrations and the shielding effect due to the presence
of the gadolinium isotopes were determined with burnup using MCNP6 and SRAC2006 in
comparison with the available published benchmark data. This study is therefore expected to reveal
the capabilities of MCNP6 and SRAC2006 in burnup calculation of VVER-1000 fuel assemblies.
Keywords: VVER-1000 LEU fuel assembly, fuel burnup, MCNP6, SRAC2006.
configurations. In this regard, the Experts
Group has carried out a benchmarking effort
called the OECD VVER-1000 LEU (low
enriched uranium) and MOX assembly
computational benchmark for verification of
the Russian calculation codes and methods in
support for the WG plutonium disposition
mission [1]. The benchmark consists of two
different hexagonal fuel assemblies: a uniform
LEU fuel assembly with 12 UGD (uranium-
gadolinium) rods and a profiled MOX fuel
assembly with 12 UGD rods. These two
assemblies are representative of the advanced
designs under active R&D in Russia for
VVER-1000 reactors and similar to the
designs that are expected to be used in the
plutonium disposition mission. Various
solutions of the benchmark are reported in the
I. INTRODUCTION
The United States and Russian
Federation, under a mutual agreement, have
been working towards the final disposition of
weapons-grade (WG) surplus plutonium in
each country as mixed-oxide (MOX) fuel in
existing commercial nuclear reactors. To
support this mission, the OECD/NEA
established an international Experts Group to
facilitate the sharing of existing information
and experience and to deal with the physics
and fuel behavior of MOX fuel as it relates to
the WG plutonium disposition. Recent work
in Russia, where WG MOX fuel will be used
in both fast reactor (BN-600) and light water
reactors (VVER-1000), has focused on the
certification of the calculation codes and the
design of MOX fuel assemblies and core
©2018 Vietnam Atomic Energy Society and Vietnam Atomic Energy Institute
NGUYEN HUU TIEP et al.
literature and they are based on different
methodology for MCNP, which involves
high precision fitting of Doppler broadened
cross sections over a wide temperature
range, will be utilized to handle temperature
variation for heavy isotopes [14]. In
addition, the collision probability method
based PIJ module of SRAC2006 will also be
utilized in the burnup calculation of the
VVER-1000 LEU assembly. The ENDF/B-
VII.0 nuclear data library will be used in the
MCNP6 and SRAC2006 calculations,
respectively. This study is therefore
expected to reveal the capabilities of
MCNP6 and SRAC2006 in burnup
calculation of VVER-1000 fuel assemblies.
calculation codes and nuclear data libraries
[1-7]. Most of these solutions have been
obtained by means of collision probability or
similar methodologies, while few of them are
based on Monte Carlo methods.
In
Vietnam,
the
reactor
fuel
management in general and fuel burnup
calculation in particular have been studied for
years, especially for the Dalat Nuclear
Research Reactor (DNRR) [8-10]. While a
huge experience with the fuel burnup
calculation of the DNRR has been
accumulated over 30 years, there are only few
publications related to fuel burnup calculation
for power reactors like VVER-1000. In 2016,
Hiep et al. [11] developed an MCNP5-
ORIGEN coupling scheme for burnup
calculation of VVER-1000 fuel assemblies.
The coupling scheme was verified against the
II. CALCULATION METHODOLOGY
The VVER-1000 LEU benchmark
hexagonal assembly consists of 300 fuel pin
cells with 3.7 wt% 235U, 12 UGD (Uranium-
Gadolinium) pin cells with 3.6 wt% 235U and
4 wt% Gd2O3, 18 water filled guide tubes for
control rod insertion and one central water
filled instrumentation tube. The configuration
and main design parameters of the VVER-
1000 LEU fuel assembly are shown in Fig. 1
OECD
VVER-1000
LEU
benchmark
assembly [1]. However, the predictor-
corrector method has not yet been applied in
the scheme and this can result in potential
errors during the burnup calculation.
Additionally, only the cross sections for 24
actinides and 61 fission products were used in
this verification due to the unavailability of
many MCNP5 cross sections.
and Table
I,
respectively.
Detailed
information of material composition and
geometry of fuel pins, cladding, moderator,
UGD pins, central and guide tubes, etc. can be
easily found in Ref. [1]. The cell numeration
of the one-sixth of the fuel assembly for
simulating different isotopic compositions is
illustrated in Fig. 2.
The present work aims at performing
a comparative burnup analysis of the OECD
VVER-1000 LEU computational benchmark
assembly using the Monte Carlo code
MCNP6 [12] and the deterministic code
SRAC2006 [13]. The new depletion
capability of MCNP6 will be applied in the
burnup calculation for the VVER-1000 LEU
The burnup calculation for the VVER-
1000 LEU benchmark assembly under the
hot operating poisoned condition (the S1
state) will be performed using MCNP6 and
assembly.
The
On-The-Fly
(OTF)
11
BURNUP CALCULATION OF THE OECD VVER-1000 LEU BENCHMARK ASSEMBLY…
SRAC2006. Under this condition, the fuel
temperature is 1027 K and the moderator
temperature is 575 K with equilibrium 135Xe
and 149Sm concentrations and a power
density of 108 MWt/m3 up to a burnup 40
MWd/kgHM. In the MCNP6 and SRAC
calculations, the UGD rods are divided into 5
annuli of equal area as required in the
benchmark document [1] in order to account
for the shielding effect due to the gadolinium
isotopes. This allows the calculation of
nuclide concentrations as a function of the
radial position in the UGD rods.
However, the default nuclear data
in MCNP6 are given at certain
temperatures for heavy isotopes (293.6,
600, 900, 1200 and 2500K); while the
fuel temperature of 1027K is needed in
this calculation. There are various
methods to cope with such kind of
temperature dependence [14]. One of the
suitable methods for MCNP6 is the OTF
methodology for fitting of Doppler
broadened cross sections and this method
was applied in this study. The OTF data
for heavy isotopes in the VVER-1000
LEU
benchmark
assembly
that
In the MCNP6 simulation, the
statistical error of ~30 pcm was obtained as
the neutron history of 5x106 for parallel
depletion calculation was selected and the
burnup calculation was performed with 160
steps of 0.25 MWd/kgHM. MCNP6 includes
the new depletion capability that links steady
state flux calculations in MCNP6 and nuclide
depletion calculations in CINDER90. A
steady state flux calculation is run in MCNP6
to determine the system eigenvalue, group
fluxes, energy integrated reaction rates,
fission multiplicity, and recoverable energy
per fission. CINDER90 then uses these
values generated by MCNP6 to perform
depletion calculation to generate new number
densities for the next time step. MCNP6
takes the new number densities generated by
CINDER90 for the next steady state flux
calculation. This linked process is repeated
until the end of the final time step. It is noted
that CINDER90 contains transmutation data
information for over 3400 isotopes, 1325
fission products, yield set for 30 actinides.
correspond to the temperature range of
293.6 to 1200 K were created from the
ENDF/B-VII.0 library at the temperature
of 293.6 K.
The PIJ module with its cell burnup
routine of the SRAC2006 code system was
also utilized for the burnup calculation of
the VVER-1000 LEU benchmark assembly.
The PIJ module that is based on the
collision probability method was used for
lattice cell calculations. The cell burnup
routine used one-group collapsed flux
distribution and the collapsed microscopic
cross sections to solve the depletion
equation using the Bateman’s method. The
burnup calculation using the cell burnup
routine of the PIJ module was performed
with 40 steps of 0.25 MWd/kgHM followed
by 5 steps of 1.0 MWd/kgHM and 10 steps
of 2.5 MWd/kgHM. The 107 neutron energy
groups based on the ENDF/B-VII.0 library
were collapsed to four groups for use in the
SRAC2006 calculations.
12
NGUYEN HUU TIEP et al.
Fig. 1. VVER-1000 LEU benchmark assembly configuration
Fig. 2. Cell numeration in the one-sixth of VVER-1000 LEU benchmark assembly
Table I. Main design parameters of VVER-1000 LEU benchmark assembly.
Parameter
Value
300
Number of UO2 fuel cells
Number of fuel cells with Gd
Number of guide tubes
Number of central tubes
Fuel cell inner radius, cm
Fuel cell outer radius, cm
12
18
1
0.3860
0.4582
13
BURNUP CALCULATION OF THE OECD VVER-1000 LEU BENCHMARK ASSEMBLY…
Central tube cell inner radius, cm
Central tube cell outer radius, cm
Pin pitch, cm
0.5450
0.6323
1.2750
23.6
Fuel assembly pitch, cm
235U enrichment, wt%
3.7
Gd2O3 density, g/cm3
7.4
increases with burnup at the beginning of
the cycle thanks to the use of Gd2O3 in the
UGD pins for excess reactivity control. As
the gadolinium isotopes burn out, the
reactivity starts to decrease with burnup in
a nearly linear manner due to the effect of
fissile material depletion and neutron
absorber accumulation. It was also seen
that the effect on reactivity of the
gadolinium burnable absorber and the time
at which the reactivity starts to decrease
can be well simulated by MCNP6 and
SRAC2006.
III. RESULTS AND DISCUSSION
A. Infinite multiplication factor versus
burnup
The infinite multiplication factor (k-
inf) of the VVER-1000 LEU benchmark
assembly as a function of burnup was
calculated using MCNP6 and SRAC2006. It
was found that the k-inf results obtained
with MCNP6 and SRAC2006 compare well
with the benchmark mean (BM) values as
shown in Fig. 3. The k-inf values calculated
with MCNP6 and SRAC2006 were slightly
different from the BM values at the first
burnup steps and such difference became
B. Concentration of isotopes versus burnup
significantly
bigger
after
about
5
The variation of the concentration
of the nuclides 235U, 236U, 238U, 239Pu,
240Pu, 241Pu, 242Pu, 135Xe, 149Sm, 155Gd,
157Gd in Cell 1 and Cell 24 (see Fig. 2) as
a function of burnup was calculated using
MCNP6 and SRAC2006 in comparison
with the BM values as shown in Figs. 4
and 5. It can be seen that the isotopic
concentrations calculated by MCNP6 and
SRAC2006 generally agree well with the
BM values. The maximum deviations of
the MCNP6 and SRAC2006 results with
the BM values for Cell 1 are -7.93% for
149Sm and 7.29% for 239Pu at the end of
MWd/kgHM. After the gadolinium burns
out, the k-inf value calculated by
SRAC2006 and the BM value tend to
approach to each other and their differences
with that calculated by MCNP6 become
roughly stable. The maximum differences in
the k-inf calculated with MCNP6 and
SRAC2006 with the BM values are 413 pcm
and 352 pcm, respectively; whereas those
for MCU, TVS-M, WIMS8A, HELIOS,
MULTICELL [1], and MCNP5-ORIGEN
[11] are 440, 400, 460, 260, 360, and 585
pcm, respectively.
the
burnup
(40
MWd/kgHM),
As can be seen in Fig. 3, the
respectively.
reactivity of the fuel assembly slightly
14
NGUYEN HUU TIEP et al.
Fig. 3. Variation of k-inf of VVER-1000 LEU benchmark assembly versus burnup
As can be seen in Fig. 5, the burnable
absorbers 155Gd and 157Gd deplete quickly at
the beginning burnup steps and such quick
depletion can be simulated by both MCNP6
and SRAC2006. In particular, 157Gd depletes
faster than 155Gd because of its larger thermal
neutron absorption cross section (Gd-155σa
60,801 barn and Gd-157σa 253,939 barn at
E=0.0253 eV). The maximum deviations of the
MCNP6 and SRAC2006 results with the BM
values are -53.1% and 65.14% for 157Gd at 7
MWd/kgHM, respectively. Those maximum
deviations are 24.13%, 14.98%, 25.62%,
3.06% and 61.67% for MCU, TVS-M,
WIMS8A, HELIOS and MULTICELL,
respectively. The discrepancies of 157Gd was
large at the first burnup values, because 157Gd
burns out quickly in the first burnup steps and
its concentration becomes very small, leading
to a large uncertainty in the calculation results.
Fig. 4. Concentration of isotopes in Cell 1 as a function of burnup
15
BURNUP CALCULATION OF THE OECD VVER-1000 LEU BENCHMARK ASSEMBLY…
Fig. 5. Concentration of isotopes in Cell 24 as a function of burnup
section as mentioned above and thus it burns
most in the outer zone, where the thermal
neutron flux is highest. Consequently, the
concentration of 157Gd at the outer zone is
very small as compared to the inner zones,
leading to a large statistical error.
C. Radial isotopic concentration in UGD rod
To investigate the variation of the
isotopic composition in the radial direction
of the UGD rod, Cell 24 was divided in to 5
regions to account for the shielding effect
due to the gadolinium isotopes. The
concentrations of 235U, 239Pu at 40
MWd/kgHM and 155Gd và 157Gd at 2
MWd/kgHM were calculated using MCNP6
and SRAC2006 and compared with the BM
values as shown in Table II. It can be seen
that the 235U, 239Pu, and 155Gd concentrations
versus radius calculated by MCNP6 were in
good agreement with the BM values within
6.35%. However, the difference in the 157Gd
concentration calculated by MCNP6 and the
BM values was as high as -32.45% at the
outer zone. It is because that 157Gd has very
large thermal neutron absorption cross
The
235U,
155Gd
and
157Gd
concentrations calculated by SRAC2006
generally agreed well with the BM values.
However, the 239Pu concentration calculated
by SRAC2006 showed a big difference with
the BM value for the radial fuel zone 4 of -
24.36% as can be seen in Table II. The
reason might be mainly due to the using of
only four neutron energy groups for the
lattice cell calculations with the PIJ module
in which the spatial self-shielding effect of
238U or any other resonant nuclide could not
be properly taken into account.
Table II. Isotopic composition in Cell 24 vs radius, atoms/barn*cm
U-235 concentration vs radius in Cell 24 at 40 MWd/kgHM
Fuel zone number
Radius, cm
1
2
3
4
5
0.173
0.244
0.299
0.345
0.386
16
NGUYEN HUU TIEP et al.
BM
2.193E-04
2.135E-04
2.277E-04
-2.64
2.126E-04
2.094E-04
2.203E-04
-1.51
2.053E-04
1.998E-04
2.116E-04
-2.68
1.975E-04
1.942E-04
2.015E-04
-1.67
1.879E-04
1.818E-04
1.889E-04
-3.25
MCNP6
SRAC
Discrepancy, % (MCNP6-BM)/BM
Discrepancy, % (SRAC-BM)/BM
3.85
3.62
3.08
2.00
0.56
Pu-239 concentration vs radius in Cell 24 at 40 MWd/kgHM
Fuel zone number
1
2
3
4
5
Radius, cm
0.173
0.244
0.299
0.345
0.386
BM
1.083E-04
1.065E-04
9.847E-05
-1.66
1.107E-04
1.092E-04
9.778E-05
-1.36
1.159E-04
1.139E-04
9.699E-05
-1.73
1.273E-04
1.245E-04
9.629E-05
-2.20
1.978E-04
1.967E-04
2.083E-04
-0.56
MCNP6
SRAC
Discrepancy, % (MCNP6-BM)/BM
Discrepancy, % (SRAC-BM)/BM
-9.07
-11.67
-16.31
-24.36
5.29
Gd-155 concentration vs radius in Cell 24 at 2 MWd/kgHM
Fuel zone number
1
2
3
4
5
Radius, cm
0.173
0.244
0.299
0.345
0.386
BM
1.676E-04
1.676E-04
1.704E-04
0.00
1.636E-04
1.632E-04
1.665E-04
-0.24
1.551E-04
1.530E-04
1.580E-04
-1.35
1.333E-04
1.284E-04
1.366E-04
-3.68
8.407E-05
7.873E-05
8.536E-05
-6.35
MCNP6
SRAC
Discrepancy, % (MCNP6-BM)/BM
Discrepancy, % (SRAC-BM)/BM
1.67
1.80
1.86
2.44
1.54
Gd-157 concentration vs radius in Cell 24 at 2 MWd/kgHM
Fuel zone number
1
2
3
4
5
Radius, cm
0.173
0.244
0.299
0.345
0.386
BM
1.502E-04
1.489E-04
1.519E-04
-0.87
1.353E-04
1.328E-04
1.373E-04
-1.85
1.074E-04
1.003E-04
1.087E-04
-6.61
5.624E-05
4.674E-05
5.716E-05
-16.89
8.722E-06
5.892E-06
7.697E-06
-32.45
MCNP6
SRAC
Discrepancy, % (MCNP6-BM)/BM
Discrepancy, % (SRAC-BM)/BM
1.15
1.51
1.20
1.64
-11.75
collision probability method based PIJ
module of SRAC2006 was also utilized in
this benchmarking calculation. The reactivity
of the fuel assembly and the concentration of
isotopes versus burnup obtained with
MCNP6 and SRAC2006 generally show a
good agreement with the BM values. The
maximum difference in the k-inf calculated
by MCNP6 and SRAC2006 with the BM
values was 413 pcm and 352 pcm,
IV. CONCLUSIONS
A comparative burnup analysis of the
OECD VVER-1000 LEU benchmark
assembly was performed in this study using
the Monte Carlo code MCNP6 and the
deterministic code SRAC2006. The new
depletion capability of MCNP6 and the OTF
methodology for MCNP were applied in the
the MCNP6 calculations; whereas the
17
BURNUP CALCULATION OF THE OECD VVER-1000 LEU BENCHMARK ASSEMBLY…
[3]. N. Petrov, G. Todorova, N. P. Kolev, “APOLLO2
and TRIPOLI4 solutions of the OECD VVER-
1000 LEU and MOX assembly benchmark”,
Annals of Nuclear Energy 55 (2013) 93–107.
respectively; while at the end of burnup
(40 MWd/kgHM) the deviations in the
nuclide concentrations calculated by
MCNP6 and SRAC2006 with the BM
values were generally within -7.93%. It
was also found that the effect on the
reactivity of the gadolinium burnable
absorber and the depletion of the 155Gd
and 157Gd isotopes at the beginning of the
fuel cycle can be well simulated using
MCNP6 and SRAC2006.
[4]. M. Zheng, W. Tian, H. Wei, D. Zhang, Y. Wu,
S. Qiu, G. Su, “Development of a MCNP–
ORIGEN burn-up calculation code system and
its accuracy assessment”, Annals of Nuclear
Energy 63 (2014) 491–498.
[5]. L. Mercatali, A. Venturini, M. Daeubler, V. H.
Sanchez, “SCALE and SERPENT solutions of
the OECD VVER-1000 LEU and MOX
burnup computational benchmark”, Annals of
Nuclear Energy, 83 (2015) 328-341.
The isotopic composition variation of
nuclides 235U, 239Pu, 155Gd and 157Gd as a
function of radii of annular regions of the UGD
rod was also calculated with MCNP6 and
SRAC2006 and compared with the BM results.
They were found to be generally in good
agreement; however, the SRAC2006 results
showed a large discrepancy with the BM
values for the 239Pu concentration that might be
mainly due to the using of only four neutron
energy groups in the SRAC2006 calculations.
Consequently, it is highly recommended that
MCNP6 and SRAC2006 can be used for
burnup calculation of VVER-1000 fuel
assemblies. Further investigation of the burnup
calculation using MCNP6 and SRAC2006 at
the full core level and MOX core of the
VVER-1000 reactor is being planned.
[6]. H. K. Louis, E. Amin, “The Effect of burnup
on reactivity for VVER-1000 with MOXGD
and UGD fuel assemblies using MCNPX
code”, Journal of Nuclear and Particle Physics
2016, 6 (3) 61-71.
[7]. S. A. Khan, V. Jagannathan, U. Kannan, A.
Mathur, “Study of VVER-1000 OECD LEU
and MOX computational benchmark with
VISWAM code system”, Nuclear Energy and
Technology 2 (2016) 312-334.
[8]. L. B. Vien, L. V. Vinh, H. T. Nghiem, N. K.
Cuong, “Design analyses for full core
conversion of the Dalat nuclear research
reactor”, Nuclear Science and Technology, Vol.
4, No. 1, p.10-25, March 2014.
[9]. N. N. Dien, L. B. Vien, L. V. Vinh, H. T.
Nghiem, N. K. Cuong, “Full core conversion
and operational experience with LEU fuel of
the Dalat nuclear research reactor”, RERTR
2014 - 35th International Meeting on Reduced
Enrichment for Research and Test Reactors,
IAEA Vienna Interational Center, Vienna,
Austria, October 2014.
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