The journal of Nuclear Science and Technology - Volume 8, Number 4, December 2018
ISSN 1810-5408
Nuclear Science
and Technology
Volume 8, Number 4, December 2018
Published by
VIETNAM ATOMIC ENERGY SOCIETY
VIETNAM ATOMIC ENERGY INSTITUTE
NUCLEAR SCIENCE AND TECHNOLOGY
Volume 8, Number 4, December 2018
Editorial Board
Editor-in-chief
Tran Huu Phat (VINATOM)
Executive Editors
Vuong Huu Tan (VARANS)
Tran Chi Thanh (VINATOM)
Cao Đình Thanh (VINATOM)
Hoang Anh Tuan (VAEA)
Editors
Nguyen Kien Cuong (VINATOM)
Nguyen Nhi Dien (VINATOM)
Nguyen Thi Kim Dung (VINATOM)
Ho Manh Dung (VINATOM)
Nguyen Nam Giang (VINATOM)
Trinh Van Giap (VINATOM)
Le Ngoc Ha (108 Military Central Hospital)
Phan Son Hai (VINATOM)
Le Hong Khiem (IOP)
Dao Tien Khoa (VINATOM)
Tran Hoai Nam (Duy Tan University)
Dang Duc Nhan (VINATOM)
Nguyen Hao Quang (VINATOM)
Nguyen Mong Sinh (VINATOM)
Tran Duc Thiep (IOP)
Dang Quang Thieu (VINATOM)
Le Ba Thuan (VINATOM)
Le Huy Ham (VAAS)
Nguyen Quoc Hien (VINATOM)
Le Van Hong (VINATOM)
Nguyen Trung Tinh (VARANS)
Tran Ngoc Toan (VINATOM)
Duong Thanh Tung (VARANS)
Nguyen Nu Hoai Vi (VARANS)
Nguyen Tuan Khai (VINATOM)
Pham Dinh Khang (VINATOM)
Science Secretary
Hoang Sy Than (VINATOM)
....................................................................................................................................................................................................................
Copyright: ©2008 by the Vietnam Atomic Energy Society (VAES), Vietnam Atomic Energy Institute
(VINATOM).
Pusblished by
Vietnam Atomic Energy Society, 59 Ly Thuong Kiet, Hanoi, Vietnam
Vietnam Atomic Energy Institute, 59 Ly Thuong Kiet, Hanoi, Vietnam
....................................................................................................................................................................................................................
Contents
Reactivity induced transient analysis when the occurrence of leakage in the dry
irradiation channels of the Dalat Nuclear Research Reactor
Dau Duc Tu, Nguyen Minh Tuan, Le Vinh Vinh, Huynh Ton Nghiem, Nguyen Kien
Cuong, Tran Quoc Duong, Bui Phuong Nam
01
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, Pham Nhu
Viet Ha
10
20
26
Particle identification for neutron rich nuclei 63,65Cr from knockout reactions
N. D. Ton, L. X. Chung1, A. Corsi, A. Gillibert, P. D. Khue, B. D. Linh, A. Obertelli
Development of neutron survey meter using prescila neutron probe
Luong Thi Hong, Nguyen Tien Phong, Pham Thi Bich, Nguyen Duc Huyen
87
Study on the removal of interferences for the determination of Sr/86Sr isotopic
ratio in petroleum drill-hole water samples using isotope dilution – inductively
coupled plasma mass spectrometry (ID – ICP-MS)
Nguyen Thi Kim Dung, Thai Thi Thu Thuy
34
Nuclear Science and Technology, Vol.8, No. 4 (2018), pp. 01-09
Reactivity induced transient analysis when the occurrence
of leakage in the dry irradiation channels
of the Dalat Nuclear Research Reactor
Dau Duc Tu, Nguyen Minh Tuan, Le Vinh Vinh, Huynh Ton Nghiem,
Nguyen Kien Cuong, Tran Quoc Duong, Bui Phuong Nam
Reactor Center, Dalat Nuclear Research Institute, VINATOM
01 Nguyen Tu Luc Str., Dalat, Lamdong, Vietnam.
(Received 06 December 2018, accepted 28 December 2018)
Abstract: The leakage from the reactor pool back into the dry irradiation channels due to corrosion or
mechanics based reason is a postulated event that could occur under operating conditions of the Dalat
nuclear research reactor (DNRR), especially the channel 7-1 which has been installed more than 30
years. When it occurs, the air space in these channels will be occupied by the water, subsequently a
water column will appear in fuel region. The appearance of water column considerably enhances
medium of neutron moderation for its surrounding fuel assemblies. As a result, a positive reactivity is
inserted in the core and this event is classified as an insertion of excess reactivity. This event needs to
be addressed by analysis and assessment from safety point of view and the results of analysis are also
important for updating the reactor operating procedures. This paper presents assumptions, computer
models and the results of analysis for such event in the DNRR by using MCNP5 code (code for
neutronics analysis) and EUREKA-2/RR code (code for transient analysis). The calculation results
include value of reactivity insertion, change in power of reactor, as well as surface temperature of the
hottest fuel assembly. This research contributes to updating the reactor operating procedure.
Keywords: Dalat nuclear research reactor (DNRR), MCNP5, EUREKA-2/RR, reactivity
insertion, transient analysis.
wet channel), 12 beryllium rods and a neutron
trap [1]. The fuel assemblies are VVR-M2
I. INTRODUCTION
A. General information
tubular
fuel
assemblies
designed
fuel
The Dalat reactor, which is a swimming
pool type reactor and uses light water as
moderator and coolant, has 500 kW thermal
power and put into operation in March, 1984. It
was reconstructed and upgraded from the USA
made 250 kW TRIGA reactor. A number of
structures from the original TRIGA reactor such
as the aluminum tank with the surrounding
concrete shield, four beam-ports, thermal
column and the graphite reflector were
remained.
and manufactured in Russia.
Each
assembly consists of three coaxial annular
tubes as well as a header and a tail. The
outermost fuel element has a hexagonal shape
of 32 mm in width across parallel sides and the
other two inner ones have a circular shape of
22 mm and 11 mm in outer diameter,
respectively. The beryllium rods of the reactor
have a hexagonal shape of 32 mm in width
across its parallel sides [1].
B. Description of dry irradiation channels
The reactor core is currently loaded 92
low enriched fuel (LEU) assemblies (19.75%),
3 irradiation channels (2 dry channels and 1
In the reactor core, there are two dry
irradiation channels located in cells 7-1 and 13-
©2018 Vietnam Atomic Energy Society and Vietnam Atomic Energy Institute
REACTIVITY INDUCED TRANSIENT ANALYSIS WHEN THE OCCURRENCE OF
…
2 and designed for neutron activation analysis
(NAA). Their characteristics are described in
Table I. They are vertical channels and made
of watertight aluminum tubes. Samples for
NAA are packaged in small plastic bags and
then placed in a high purity polyethylene
irradiation capsule (so-called rabbit). Finally,
the capsules are sent to and returned from the
channels by a pneumatic transfer system
(PTS). At these two channels, samples are
irradiated for a short time from 5 seconds to 5
minutes to analyze elements by measuring
emission ray gamma spectrum of the short-
lived radionuclides. The PTS of channel 7-1 is
a remote-control system located nearby the
reactor building. The PTS of channel 13-2 is
mainly used for fast analysis of elements. Its
terminal station and measuring equipments are
located in the reactor building [2]. These
channels enter the reactor from the top surface
of the reactor pool, pass through the pool,
penetrate into cells 7-1 and 13-2 of the reactor
core and terminate 25 cm from the bottom of
the reactor core as shown in Figures 1 and 2.
Table I. Characteristics of the dry vertical irradiation channels
Characteristics
Thermal neutron flux, n/cm2/s
Channel 7-1
Channel 13-2
(3.8 ÷ 4.4)1012
(3.8 ÷ 4.2)1012
Epithermal neutron flux, n/cm2/s
Fast neutron flux, n/cm2/s
Loading capacity, gram
(4.0 ÷ 4.5)1011
(3.0 ÷ 5.0)1012
(3.7 ÷ 4.1)1011
(3.0 ÷ 6.0)1012
20
45
20
10
4
5
Irradiation time (min.), sec
Irradiation time (max.), min.
Sample moving speed, m/s
30
20
Fig. 1. Technical drawing of pneumatic transfer channel 13-2 [2]
2
DAU DUC TU et al.
Fig. 2. The layout of pneumatic transfer systems (PTS) [2]
the DNRR operating procedures after 35 years
of operation.
C. The leakage and assumptions for the
transient analysis
Under normal operating conditions, the
The main assumption selected for
transient analysis is a small break occurring at
one of two dry irradiation channels (channel 7-
1 or 13-2) with diameter of 2 mm (Ø = 2 mm)
when the reactor is operating at the nominal
power (500 kW). This assumption was made in
order to simulate the above mentioned leakage.
The other physics parameters needed for the
transient analysis are given in Table II.
MCNP5 Monte Carlo code and ENDF/B-VII.0
nuclear data library were used to analyze
reactivity insertion and EUREKA-2/RR code
was used to study the transient of core power
and fuel surface temperature. In fact, the
possibility of simultaneous leakage at the 2 dry
channels is extremely low; therefore it was not
included in this investigation.
leakage from the reactor pool back into the
pneumatic irradiation channels due to
corrosion or mechanics based reasons is a
postulated event that could occur at the DNRR.
When it occurs, the air space in these channels
will be occupied by the water, subsequently a
water column will appear in fuel region. The
appearance of water column considerably
enhances medium of neutron moderation for its
surrounding fuel assemblies. As a result, a
positive reactivity is inserted in the core that
leads to an unwanted increase in fission rate,
reactor power and fuel temperature. The value
and speed of reactivity insertion mainly depend
on the leakage rate, volume and location of the
channels, power level and coolant temperature,
etc. This event is classified as an event of
insertion of excess reactivity. The events of
insertion of excess reactivity that has the most
potential consequences as a shim rod (SR) or
the automatic regulating rod (AR) of the
reactor can be withdrawn with the maximum
speed of 3.4 mm/s and 20 mm/s, respectively,
has been analyzed and described in the safety
analysis report (SAR) for the DNRR [2].
However, the event presented here has not
been analyzed in detail so far and the result of
this analysis is important to develop and update
II. CALCULATION MODELS
In the investigation, the reactor core and
its components such as fuel assemblies, control
rods, beryllium blocks, graphite reflector, beam
ports, thermal column, etc. were modeled
almost as exactly as they are. Figures 3 and 4
show in detail MCNP5 model for the core
configuration with 92 fuel assemblies of low
enriched fuel (LEU) and the irradiation
channels of the DNRR [3].
3
REACTIVITY INDUCED TRANSIENT ANALYSIS WHEN THE OCCURRENCE OF…
Table II. Summary of the reactor and safety parameters needed for the transient analysis
Parameters
Values
Power, kW
500
Coolant inlet temperature, oC
Reactor kinetics parameters
- Prompt neutron life, s
- Delayed neutron fraction (1$)
Temperature reactivity coefficients
- Moderator, (ΔK/K); (293 - 400oK)
- Fuel, (ΔK/K)/oC;
32
8.92510-5
7.55110-3
- 1.26410-2
(293 - 400oK)
(400 - 500oK)
(500 - 600oK)
- 1.8610-3
- 1.9210-3
- 1.5610-3
- Void, ΔK/K % of void
(0 - 5%)
-0.2432
-0.2731
-0.3097
(5 - 10%)
(10 - 20%)
Reactivity control
- Shutdown worth, % (2 safety rods)
4.98
3.4
- Maximum withdrawal speed of one shim rod,
mm/s
and of the regulating rod, mm/s
Reactor protection characteristics
- Response time to overpower scram, s
- Response time to fast period scram, s
Start-up range
20
0.16
9.1
6.7
Working range
- Drop time of control rods, s
0.67
Channel No.2
Channel No.3
Channel No.4
Channel No.1
Fig. 3. Cross-sectional and vertical views of the reactor modeled by MCNP5
4
DAU DUC TU et al.
Core center
Channel No.7-1
Channel No.13-2
Channel position
Fig. 4. Core configuration with 92 LEU fuel assemblies and the irradiation channels modeled by MCNP5
The EUREKA-2/RR model for the
DNRR is shown in Figure 5. The reactor core
contains 92 fuel assemblies and they were
divided into 5 distinct channels. Each fuel
channel can consist of one or more fuel
assemblies, in which fuel channel No. 1 was
chosen as the hottest channel containing the
hottest fuel assembly with maximum FR (radial
power factor). The number of fuel assembly in
each channel and FR factors taken from
MCNP5 calculations are given in Table III.
The axial power distribution was also taken
from MCNP5 calculations.
In the present model, each fuel channel
was divided more into 10 heat slabs along with
10 nodes as shown in Figure 5. The model uses
a total of 54 nodes, 50 heat slabs and 59
junctions. The junction No. 59 is declared as a
fill junction to simulate the primary coolant
flow (50 m3/h) passing through the reactor core
and by pass volume as shown in Figure 5.
Table III. The number of fuel assemblies in each channel and radial power factors
Fuel channel No.
The number of fuel assemblies
Radial power factor (FR)
1
2
3
4
5
1
1.421
1.256
0.932
0.887
0.985
17
18
28
28
With the scenario of leaking the
irradiation channel in reactor core, the
equation (1) was used to calculate the water
column height (h) depending on the time (t)
and the parameters L, S1, S2.
- L: Height from the center of the
reactor core to the surface of the reactor pool
surface
- h: Height of water column in the
irradiation channel (depending on the time
since the accident started)
2
S1 2g
2S2
- S1: The section of breaking
(1)
h L L
t
- S2: The section of irradiation channel
- g: The gravity acceleration
In which:
5
REACTIVITY INDUCED TRANSIENT ANALYSIS WHEN THE OCCURRENCE OF…
Fig. 5. Schematic diagram of the model prepared for EUREKA-2/RR analysis [4]
III. RESULTS AND DISCUSSION
library. The number of simulated events is 260
cycles and each of 106 particles. The calculation
The MCNP5 calculations for the DNRR
results of reactivity insertion depending on time
are shown in Table IV and Figures 6 and 7.
were performed with the critical calculation
(KCODE) and the ENDF/B-VII.0 nuclear data
Table IV. Time-dependent reactivity insertion for the channels 7-1 and 13-2 when air occupies by water
Time
Reactivity of channel 7-1
Reactivity of channel 13-2
(second)
(cents)
(cents)
1
2
3
4
5
1.62
5.07
7.09
8.52
9.63
0.02
0.05
0.04
0.06
0.05
0.35
1.96
2.90
3.57
4.09
0.03
0.05
0.09
0.09
0.08
6
DAU DUC TU et al.
6
7
8
9
10.54
11.31
11.97
12.55
0.07
0.07
0.06
0.04
4.51
4.87
5.18
5.46
0.06
0.05
0.06
0.08
The calculation results shown in
Figures 6 and 7 revealed that about 9.0
seconds after the leakage occurs, the
channels 7-1 and 13-2 will be flooded with
water to the corresponding height on the top
surface of the reactor core and the
maximum reactivity insertions are 12.55 and
5.46 cents, respectively. The reactivity
insertion at the channel 7-1 is greater than
the channel 13-2. This can be explained by
the fact that the channel 7-1 is located
closer to the center of the reactor core and
its volume is larger than the volume of the
channel 13-2.
Fig. 6. Reactivity insertion versus time when water occupies the air space in the channel 7-1
Fig. 7. Reactivity insertion versus time when water occupies the air space in the channel 13-2
For the next step, the calculation results
of reactivity depending on the time by MCNP5
were introduced into the transient calculations
using EUREKA-2/RR. The calculation results
of the transition of power and fuel surface
temperature for the reactor at the hottest
channel for the cases of channel 7-1 and 13-2
are shown in Figures 8 and 9, respectively.
7
REACTIVITY INDUCED TRANSIENT ANALYSIS WHEN THE OCCURRENCE OF…
The transient calculations (see Figure.
8) show that as soon as the event occurs, the
time to reach the power scram set point are 3
and 8 seconds (power scram point of the
reactor was set at 550 kW). From Figure 9, it
is seen that after 3.4 and 8.5 seconds, the fuel
surface temperature increases to reach to the
channels 7-1 and 13-2, respectively. These
temperature values are much lower than the
design limit imposed for the transient
conditions (the design limit of fuel surface
temperature is 400 oC). Therefore, this type of
transient does not cause safety concern for the
DNRR if the reactor protection system fulfills
its safety functions.
o
o
maximal values (90.8 C and 92.2 C) for the
Fig. 8. The change in reactor power
Fig. 9. The fuel surface temperature
dry irradiation channels 7-1 and 13-2. The
IV. CONCLUSIONS
results showed that approximately 9.0
seconds after starting the event, the
channels 7-1 and 13-2 will be flood with
water to the height corresponding to the top
of reactor core. The maximal values of
This report presented the investigation
of reactivity insertion and transient analysis
in power and fuel surface temperature for
the DNRR when the leakage occurs in the
8
DAU DUC TU et al.
reactivity insertion determined by MCNP5
for the channels 7-1 and 13-2 were
12.55 0.04 and 5.46 0.08 cents,
REFERENCE
[1]. Nuclear Research Institute, Regulations of
operation of Dalat nuclear reactor, March 2014.
respectively. The transient analysis by
[2]. Nuclear Research Institute, Safety analysis
report for the Dalat nuclear reactor, 2012.
EUREKA-2/RR showed that the fuel surface
o
temperature does not exceed 92.2 C that is
[3]. MCNP - A General Monte Carlo N-Particle
Transport Code, Version 5, April, 2003.
o
very low compared to design limit (400 C).
The results of this investigation are
considered to update the operating procedures
of the DNRR after 35 years of operation.
[4]. EUREKA-2/RR: A Computer Code for the
Reactivity Accident Analyses in Research
Reactors, Private Communication.
9
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
Tải về để xem bản đầy đủ
48 trang
13920
Free
Bạn đang xem 20 trang mẫu của tài liệu "The journal of Nuclear Science and Technology - Volume 8, Number 4, December 2018", để tải tài liệu gốc về máy hãy click vào nút Download ở trên
File đính kèm:
- the_journal_of_nuclear_science_and_technology_volume_8_numbe.pdf
