79 urn:lsid:arphahub.com:pub:D015427E-53F6-553C-9279-2E51CD684756 Nuclear Energy and Technology NUCET 2452-3038 National Research Nuclear University MEPhI (Moscow Engineering Physics Institute) 10.3897/nucet.8.78447 78447 Research Article Reactor physics Neutronics and burnup analysis of VVER-1000 LEU and MOX assembly computational benchmark using OpenMC Code Hossain Md. Imtiaj 1 Akter Yasmin 1 Fardin Mehraz Zaman 1 Mollah Abdus Sattar 1 mosattar54@gmail.com Department of Nuclear Science & Engineering, Military Institute of Science and Technology, Dhaka, Bangladesh Military Institute of Science and Technology Dhaka Bangladesh

Corresponding author: Abdus Sattar Mollah (mosattar54@gmail.com)

Academic editor: Georgy Tikhomirov

 2022 14 03 2022 8 1 1 11 04D251DA-99A6-56DD-9C37-0C7B032A99ED 25 11 2021 22 02 2022 Md. Imtiaj Hossain, Yasmin Akter, Mehraz Zaman Fardin, Abdus Sattar Mollah This is an open access article distributed under the terms of the Creative Commons Attribution License (CC BY 4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.

A handful of computational benchmarks that incorporate VVER-1000 assemblies having low enriched uranium (LEU) and the mixed oxide (MOX) fuel have been put forward by many experts across the world from the Nuclear Energy Agency. To study & scrutinize the characteristics of one of the VVER-1000 LEU & MOX assembly benchmarks in different states were considered. In this work, the VVER-1000 LEU and MOX Assembly computational-benchmark exercises are performed using the OpenMC software. The work was intended to test the preciseness of the OpenMC Monte Carlo code using nuclear data library ENDF/B-VII.1, against a handful of previously obtained solutions with other computer codes. The kinf value obtained was compared with the SERPENT and MCNP result, which presented a very good similarity with very few deviations. The kinf variation with respect to burnup upto 40 MWd/kgHM was obtained for State-5 by using OpenMC code for both the LEU and MOX fuel assembly. The depletion curves of isotope concentrations against burnup upto 40 MWd/kg/HM were also generated for both the LEU and MOX fuel assembly. The OpenMC results are comparable with those of benchmark mean values. The neutron energy vs flux spectrum was also generated by using OpenMC code. Based on the OpenMC results such as kinf, burnup, isotope concentrations and neutron energy spectrum, it is concluded that the OPenMC code with ENDF/B-VII.1 nuclear data library was successfully implemented. It is planned to use OpenMC code for calculation of neutronics and burnup of the VVER-1200 reactor to be commissioned in Bangladesh by 2023/2024.

 VVER-1000 OpenMC multiplication factor burnup isotope concentrations Light Enriched Uranium (LEU) Assembly Mixed Oxide (MOX) fuel Assembly Benchmark Introduction

The main purpose of nuclear reactor theory is calculation of distribution of neutrons in the reactor core. From knowledge of it, we can determine the rate of fission reaction occurring in a nuclear reactor and hence reactor power and operating point (sub critical, critical or supercritical) hence, stability of fission chain reaction can be inferred. Generally, neutronic analysis is performed based on ‘‘Deterministic” and ‘‘Stochastic” methods. In deterministic methods the transport equation is solved as a differential equation. In stochastic methods such as Monte Carlo, discrete particle histories are tracked and averaged in a random walk directed by interaction probabilities. In Bangladesh, two Russian design VVER-1200 (2400 MWth) type nuclear reactors are under construction and to be commissioned by 2023/2024. A program has been undertaken at the Department of Nuclear Science and Engineering of Military Institute of Science and Technology, Dhaka, Bangladesh to introduce some Monte Carlo computer codes such as MCNPX (Louis and Amin 2016), SERPENT (Mercatali et al. 2021), SuperMC (Wu et al. 2015), and OpenMC (Romano et al. 2015) Romano and Forget 2013) for neutronics calculations of different types of nuclear reactors. As a part of this program, the OpenMC code has been adopted to perform neutronics analysis of benchmark problems for two types of fuel assembly (LEU and MOX) that are typically of the advanced Russian designs. Benchmarks are specified problems used to test nuclear data libraries & validate computer codes (Alhassan et al. 2014). These act as a learning tool for engineers that enable them to perform neutronic calculations for various types of nuclear reactors. To ease the sharing of prevailing information & intelligence about the forthcoming designs of VVER-1000 LEU & MOX fuel, a VVER-1000 LEU & MOX fuel assembly computational benchmark was put forward by a group of professionals at OECD/NEA (OECD NEA 2002). The benchmark was analyzed using six codes obtained from five institutions, of which two were developed using continuous energy Monte Carlo method, i.e. MCNP-4B & MCU & for the rest, the collision probability method was used. The average values obtained from these codes are denominated as “Benchmark Mean” which is mentioned below in the result section. Additionally, the same problem was analyzed using various codes & data libraries over the past several years. Some of them are EXCEL (Thilagam 2009), APOLLO2 & TRIPOLI4 (Petrov 2013), MCNPX (Louis and Amin 2016), VISWAM (Khan et al. 2016) & GETERA (Abuqudaira and Stogov 2018). Having been launched in December 2012, OpenMC is a fairly new Monte Carloparticle transport code (Romano and Forget 2013) which gives the user an advantage of obtaining results based on the average result of three different methods namely track length, collision probability & absorption. One can also use the results obtained from any individual method instead of the average one. In this study, ENDF/B-VII.1 was used. ENDF/B-VII.1 is an evaluated nuclear data library that contains all necessary cross-section data to perform a neutronic analysis. This library has nuclear data for 423 nuclides (ENDF/B-VII.1 2012). The work is intended to perform neutronic, burnup and isotope concentrations analysis of the VVER-1000 computational benchmark using OpenMC code.

 Benchmark description

The benchmark model has two fuel assemblies (LEU & MOX) of the VVER-1000 reactor. Each of the assemblies consists of 331 elementary cells of four types for LEU assembly & six types for MOX assembly inside a hexagonal lattice. Twelve Gd2O3 pins are located inside each assembly as a burnable absorber at completely different positions. The layout of both the assembly types obtained using OpenMC is shown in Figs 1 and 2. The assembly has a uniform enrichment of 3.7% in 235U except in Gd, bearing pins that contain 3.6% wt. of 235U and 4% wt. of Gd2O3. The assembly lattice pitch & the hexagonal cell pitch are respectively 23.6 cm & 1.275 cm. All three types of unit cells along with their dimensions for each assembly are given in Figs 1 and 2. The cladding and structural materials are of a Zircaloy. Both material & geometry specifications used in the assemblies are taken from the benchmark report (OECD NEA 2002).

10.3897/nucet.8.78447.figure1 4622D55A-4D5C-5E73-ACA8-5B2201321E53

LEU fuel assembly.

https://binary.pensoft.net/fig/658398 10.3897/nucet.8.78447.figure2 894351D5-8B0B-5E72-AFAD-9B88BE205545

MOX fuel assembly.

https://binary.pensoft.net/fig/658399 Geometry description

The cell type geometry specifications are given in Table 1. The fuel and non-fuel cells are shown in Fig. 3.

10.3897/nucet.8.78447.figure3 00945333-9BA9-5B73-BCC3-5D0983E71278

Fuel & non-fuel cells.

https://binary.pensoft.net/fig/658400

Cell type geometry specification

Type of the Cell Cell Radius (in cm)
Fuel Fuel pellet radius = 0.386
Cladding outer radius = 0.4582
Guide tube cell Cladding inner radius = 0.545
Cladding outer radius = 0.6323
Central tube cell Cladding inner radius = 0.48
Cladding outer radius = 0.5626
Methodology

The models were represented in the OpenMC using python (python 3.7) code in Jupyter notebook. Initially, one of each of the different types of rods was created. To obtain the assemblies, they were placed in a hexagonal lattice with a lattice cell pitch of 1.275 cm and an assembly pitch of 23.6 cm. Modeling was done utilizing Boolean operations to define different zones within the cells. The hexagonal lattice and two different planes in the z-axis with reflecting boundary conditions bounded the geometry, which is equivalent to the geometry being infinite in the z-axis. For thermal scattering at low energies, S(α,β) table was used. The benchmark demands a solution for a variety of states, encompassing both hot and cold conditions, as shown in Table 2. Assumptions taken during the OpenMC process are:

Reactor States for both of the assembly

State State name Fuel temperature in K Non-fuel temperature in K Boron concentration (ppm) 149Sm 135Xe Moderator in fuel & central/guide tube Moderator density in g/cm3
State 1 Operating poisoned state 1027 575 600 Eq. MOD1 0.7235
State 2 Operating non-poisoned state 1027 575 600 0 MOD1 0.7235
State 3 Hot state 575 575 600 0 MOD1 0.7235
State 4 Hot state without boric acid 575 575 0 0 MOD2 0.7235
State 5 Cold state 300 300 0 0 MOD3 1.0033

Pin-by-pin Model

Reflective boundary condition in all directions (x, y & z)

Finite boundary at z-axis with reflective boundary conditions.

Cross-section data library: ENDF/B-VII.1

1000 batches with 100 inactive batches & 11000 particles in each batch.

In OpenMC code, there are three ways to calculate k-eigenvalue, including track-length estimator, collision estimator, and absorption estimator, respectively. They are expressed in the following equations:

k track-length = Σ all flights w j d j v Σ f W

k Collision = Σ all collisions w j v Σ f Σ t W

k track-length = Σ all absorption w j v Σ f Σ a W

where W is the total weight starting each generation (or batch), wj is the pre-collision weight of the particle as it enters event j, dj​ is the length of the jth trajectory, and υΣf and Σa are macroscopic neutron production cross section and absorption cross section.

The OpenMC Monte Carlo code was used to calculate the average kinf based on the combined collision estimator, track length estimator, & absorption estimator (Wu et al. 2015).

 Results and discussion Infinite multiplication factor

The infinite multiplication factor was calculated in eigenvalue mode of the OpenMC (Version 0.12.2) monte carlo code. To obtain accurate results based on the initial guess value for the fission source distribution, analysis of the iteration method source convergence is necessary. A study into convergence of Monte Carlo criticality analysis has proved that the Shannon entropy of the fission source distribution, Hsrc, is an effective parameter for identifying the convergence of the fission source distribution (Brown 2006). The OpenMC monte carlo code includes new tools for determination and plotting of Shannon entropy of the fission source distribution to assess problem convergence. To ensure that the result converges, the Shannon entropy was measured at zero burnups, and an approximation of the inactive batches was determined. The Shannon entropy versus generation curve as shown in Fig. 4, aids in determining the number of inactive batches. The number of inactive batches is taken to be 100, before which the entropy curve starts showing constant behavior.

10.3897/nucet.8.78447.figure4 51CDF54F-AB6B-514E-B5F5-D28EB9886122

Shannon entropy vs generation.

https://binary.pensoft.net/fig/658401

The OpenMC results of the present study were compared to the results of SERPENT code as well as the MCNP results (Mercatali et al. 2015). The kinf values obtained by using OpenMC code are given in Tables 3 and 4 at zero burnup for both LEU and MOX fuel assembly, respectively. Tables 3 and 4 reveal that OpenMC and other codes (such as SERPENT and MCNP) have a high degree of similarity in terms of nature and value.

Table 3 compares the infinite multiplication factor computed by OpenMC with ENDF/B-VII.1 nuclear data library with those of the literature values obtained from SERPENT code using ENDF/B-VII nuclear data library at zero burnup for LEU fuel assembly, and shows that OpenMC and SERPENT agree quite well in case of LEU fuel assembly. As demonstrated in Table 3, there is a little variation due to the use of different nuclear data libraries. The comparison of these two nuclear data libraries can help explain the causes. In the case of MOX fuel assembly (Table 4), the OpenMC results are comparable with those of the results obtained from SERPENT code. Using PREPRO code (Diop et al. 2007), a detailed comparison was done between the two libraries. In ENDF/B-VII.1, there were around 170 variations, with 120 of them differing by 1% or more of total cross-sections from the same isotope in ENDF/B-VII.0. Because these methods utilized various different data libraries such as ENDF/B-VI.0, JEFF2.2, JEFF 3.1, JENDL 3.2, ENDF/B-VII.0, etc., the result differs even more from those shown in benchmark problem & benchmark mean results. Another explanation is that neutron data for fuel material, non-fuel material, and the S(α, β) table was used for 579 K instead of 575 K for S2–S4 stats due to the unavailability of data at these two temperatures. Table 5 shows a comparison of different results achieved by different codes for the cold state (State-5) for LEU and MOX fuel assembly. The JEFF 3.3 nuclear data library was also used in the OpenMC code to calculate the kinf for the State-5 only (Table 5). The difference between the maximum and the minimum kinf value for the same state is roughly 680 pcm for LEU and about 1695 pcm for MOX fuel, according to the table. All of the values for the various codes were collected from various sources that are cited in the references. We can conclude from this comparison that the OpenMC results are acceptable.

kinf for Zero burnup (For LEU)

LEU SERPENT(SE) (ENDF/B-VII.0) OpenMC (OP) (ENDF/B-VII.1) MCNP (JEFF 2.2) ∆K (OP-SE)*105
State 1 1.13997 ±8.8E-05 1.13923 ± 2E-04 - -74
State 2 1.17587 ± 8.8E-05 1.17520± 2E-04 1.1800 ± 6E-05 -67
State 3 1.18996 ± 8.6E05 1.18849± 2E-04 1.1925 ± 6E-05 -147
State 4 1.24993 ± 8.7E05 1.24896± 2.5E-04 1.2531 ± 7E-05 -97
State 5 1.32305 ±7.7E05 1.32210± 2E-04 1.3235 ±6E-05 -95

kinf for at Zero burnup (for MOX fuel)

MOX SERPENT(SE) (ENDF/B-VII.0) OpenMC (OP) (ENDF/B-VII.1 MCNP (JEFF 2.2) ∆K (OP-SE)*105
State 1 1.17382 ± 8.4E-05 1.17131 ±1.8E-04 - -51
State 2 1.19762 ± 8.6E-05 1.19740 ±1.8E-04 1.1922 ± 7E-05 -22
State 3 1.21429 ± 8.4E-05 1.21378 ± 1.8E-04 1.2091 ± 6E-05 -51
State 4 1.24923 ±8.4E-05 1.24822 ± 1.8E-04 1.2430 ± 6E-05 -99
State 5 1.33013 ± 7.6E-05 1.33033 ± 1.8E-04 1.3256 ± 6E-05 20
10.3897/nucet.8.78447.figure5 9EC8E0FC-964A-5788-BDF6-0CCB9B58E84C

Variation of kinf vs burnup

https://binary.pensoft.net/fig/658402

Comparison of different results (State-5)

NAME (Data library) LEU MOX
SERPENT(JEFF3.1) 1.32088 1.32908
OpenMC(JEFF3.3) (Present study) 1.31670 1.3297
SCALE(ENDF/B-VII.0) 1.31770 1.32652
MCNP4B(JEFF2.2) 1.3235 1.3256
GETERA(BNAB-93) 1.3175 1.31213
Burnup effects

The variation of kinf with respect to burnup (MWd/kgHM) is shown in Fig. 5 for LEU and MOX fuel assembly, respectively for State-1. The time burup steps were considered upto 10 MWd/kgHM to model Gd depletion accurately. The S1 state was followed upto 40 MWd/kgHM using the power density 108 MW/m3 given in the benchmark problem. The benchmark values are also included in Fig. 5 for comparison purposes. At burnup of 8 MWd/kgHM the peak value of kinf is seen in Fig. 5 for LEU fuel assembly. In the case of MOX fuel assembly, the peak value of kinf is observed at burnup of ~10 MWd/kgHM. The OpenMC results for the both LEU and MOX fuel assembly are comparable with those of benchmark mean values.

 Reactivity effects

The reactivity effect was computed using the kinf values obtained from various reactor operational states at zero burnup for LEU and MOX fuel assembly is given in Tables 6 and 7. The OpenMC reactivity values are comparable with those of benchmark mean value including SERPENT value (Mercatali et al. 2015).

Reactivity effects (at zero burnup for LEU fuel)

Initial state final state Effect (Kinit.– Kfin) / (Kinit. * Kfin)*1000 (mk)
OpenMC Benchmark mean SERPENT (OP-SE)
State 1 State 2 effect on reactivity 135Xe &149Sm -26.30 -30.22 -26.78 -0.48
State 2 State 3 Fuel temperature (Doppler effect) -9.43 -09.86 -10.07 +0.64
State 3 State 4 Soluble boron effect -40.18 -40.23 -40.31 +0.13
State 4 State 5 Moderator temperature effect -44.00 -41.73 -44.21 +0.21

Reactivity effects (at zero Burnup for MOX fuel)

Initial state final state Effect (Kinit.– Kfin) / (Kinit. * Kfin)*1000 (mk)
OpenMC Benchmark mean SERPENT (OP-SE)
State 1 State 2 135Xe & 149Sm effect on reactivity -23.31 -24.15 -23.89 -0.58
State 2 State 3 Fuel temperature (Doppler) -11.04 -12.21 -11.39 +0.35
State 3 State 4 Soluble Boron -23.43 -23.19 -23.10 -0.33
State 4 State 5 Moderator Temperature -49.44 -47.95 -48.69 -0.75
Isotopic composition changes with burnup

Figs 6–22 exhibits the results of various radionuclide concentrations for LEU and MOX fuel assembly with respect to burnup for the operating poisoned condition (S1). Predictor Integrator, a first-order predictor algorithm, was employed for depletion analysis. The concentration of neutron poisons Xe-135 and Sm-149 must be in equilibrium for state-1, which is an operating poisoned state. The main difference between State-1 and State-2 is that the former requires the xenon concentration and neutron flux to remain in equilibrium, whereas the latter does not. The purpose of building this forced equilibrium before running the simulation is to account for the xenon oscillation that occurs during a depletion analysis which has a significant impact on the reactivity (Isotalo et al. 2013). Burnup calculation is carried out for this state only.

Isotopic composition changes of nuclides 235U, 236U, 238U, 239Pu, 240Pu, 241Pu, 242Pu, and 149Sm in cell-1 and cell-24 (as shown in Figs 2 and 3) of the LEU and MOX fuel assembly as a function of burnup is depicted in Figs 6–22. These changes were obtained from burnup calculation in State-1 which is compared with the Benchmark mean value. In addition, for both the LEU and MOX fuel assemblies, two additional isotopes, 155Gd and 157Gd, are compared in cell-24. Because of its large thermal fission cross-section of approx. 583 barns, U-235 is used as the primary fuel in an LEU fuel assembly. As the fission process progresses and burnup increases, the concentration of U-235 in LEU assembly falls. Because Pu is the major fuel in MOX assembly, 239PU shows similar behavior which can be seen from Fig. 8 below. In an LEU assembly, all U-235 atoms do not cause fission. Radiative capture yields U-236 in a small fraction of U-235, hence the concentration of U-236 rises with burnup. The same goes for the MOX assembly since it also contains U-235 along with Pu. Despite the fact that U-238 makes up the majority of the fuel element material in an LEU assembly, its overall fission cross-section is too low compared to that of U-235. However, due to its fast fission & thermal fission (very small amount) and radiative capture, the concentration of U-238 drops as burnup increases. By radiative capture of neutrons, the fertile atom U-238 generates U-239 in an LEU assembly. U-239 quickly emits a beta particle to transform into Np-239 and Np-239, in turn, releases a beta particle to transform into Pu-239, which is relatively stable. Thus, the concentration of Pu-239 increases with burnup in LEU assembly. And in MOX assembly, since the main fuel is Pu-239, as burnup increases the fuel gets used up and its concentration decreases. In an LEU assembly, initially, there’s no existence of Pu-240, but as the burnup increases, its concentration also builds due to the neutron capture of previously generated Pu-239. In MOX assembly, the concentration of Pu-240 rises by a large margin with the increase of burnup because the radiative capture of neutrons by U-238 produces Pu-240 after subsequent beta decays. By neutron capture, some Pu-240 nuclei may in turn form Pu-241. In both the LEU and MOX assemblies, the concentration of Pu-241 rises in a similar manner to that of Pu-240. But in LEU assembly, Pu-241 just takes a little longer to grow its concentration as Pu-239 does not exist in this assembly. Pu-242 comes into being when due to the neutron capture of Pu-241. Since neither of the two assemblies had an initial concentration of Pu-242, variation of Pu-242 concentration with burnup in both the LEU and MOX assemblies indicates a similar scenario. However, because of the presence of Pu-241 in the MOX core, the concentration of Pu-242 in MOX assembly rises earlier and is greater than that of LEU assembly. The thermal neutron absorption cross-sections of Gd-155 and Gd-157 are very large. As a result, in LEU assembly, they burn extremely quickly. However, due to the harder neutron spectrum in MOX assembly, Gd isotopes burn slowly. Gd-157 depletes faster in both assemblies than Gd-155, because of its larger absorption cross-section.

The isotopic concentrations for cell-1 are shown in Figs 6–13.

The isotopic concentrations for cell 24 are shown in Figs 14–23.

Assembly average concentration changes with burnup is shown in Figs 24–32.

10.3897/nucet.8.78447.figure6 D8E200A4-88CC-5DCB-BFC3-0CA6AD2E5371

Variation of 235U concentration vs burnup.

https://binary.pensoft.net/fig/658403 10.3897/nucet.8.78447.figure7 233CA843-9848-55DC-8C6B-C79423375F15

Variation of 236U concentration vs burnup.

https://binary.pensoft.net/fig/658404 10.3897/nucet.8.78447.figure8 5464F3ED-59D4-55F9-A469-5FD25E7B5DAF

Variation of 238U concentration vs burnup.

https://binary.pensoft.net/fig/658405 10.3897/nucet.8.78447.figure9 53D35988-59B8-5935-B79A-20A55A2F99D2

Variation of 239Pu concentration vs burnup.

https://binary.pensoft.net/fig/658406 10.3897/nucet.8.78447.figure10 42E70362-AA10-57AD-BEFE-7410789F29B3

Variation of 240Pu concentration vs burnup.

https://binary.pensoft.net/fig/658407 10.3897/nucet.8.78447.figure11 D719E75A-BE88-5A55-AF96-F82CBCD11F44

Variation of 241Pu concentration vs burnup.

https://binary.pensoft.net/fig/658408 10.3897/nucet.8.78447.figure12 A0EB4DE9-6A9E-55C1-AD77-A0513BBE31E4

Variation of 242Pu concentration vs burnup.

https://binary.pensoft.net/fig/658409 10.3897/nucet.8.78447.figure13 15F9DEB1-8CF2-51B3-BB41-E7555EF405AF

Variation of 149Sm concentration vs burnup.

https://binary.pensoft.net/fig/658410 10.3897/nucet.8.78447.figure14 83EF837F-26F0-5C3B-9CAA-5D5C989091E4

Variation of 235U concentration vs burnup.

https://binary.pensoft.net/fig/658411 10.3897/nucet.8.78447.figure15 45938EFA-DCC2-525C-B9A9-6AB5311BB714

Variation of 236U concentration vs burnup.

https://binary.pensoft.net/fig/658412 10.3897/nucet.8.78447.figure16 F6937C80-22F3-5A72-9A41-EE7E92A945DE

Variation of 238U concentration vs burnup.

https://binary.pensoft.net/fig/658413 10.3897/nucet.8.78447.figure17 19B8FE59-7FAF-57EE-84C2-178C40FA445E

Variation of 239Pu concentration vs burnup.

https://binary.pensoft.net/fig/658414 10.3897/nucet.8.78447.figure18 6CC91D17-E410-506F-9F19-D7CAA02149C3

Variation of 240Pu concentration vs burnup.

https://binary.pensoft.net/fig/658415 10.3897/nucet.8.78447.figure19 2BB8D8DA-0983-5455-A2FE-CF3CCA027B9F

Variation of 241Pu concentration vs burnup.

https://binary.pensoft.net/fig/658416 10.3897/nucet.8.78447.figure20 D056D3B6-DFAA-5EF6-9A7A-E89F3A8006EF

Variation of 242Pu concentration vs burnup.

https://binary.pensoft.net/fig/658417 10.3897/nucet.8.78447.figure21 D93EC11E-867C-527B-870E-8E48B06B431C

Variation of 149Sm concentration vs burnup.

https://binary.pensoft.net/fig/658418 10.3897/nucet.8.78447.figure22 F11CA2F5-8749-56D3-9B49-F3903A6773F9

Variation of 155Gd concentration vs burnup.

https://binary.pensoft.net/fig/658419 10.3897/nucet.8.78447.figure23 AB7D8A7B-CD18-5B8C-95DC-F9F2D5A5B77A

Variation of 157Gd concentration vs burnup.

https://binary.pensoft.net/fig/658420 10.3897/nucet.8.78447.figure24 DCE6629A-8F11-56B1-82EE-1033B698D9E8

Variation of 235U average concentration.

https://binary.pensoft.net/fig/658421 10.3897/nucet.8.78447.figure25 66421753-7776-5673-B827-AC38BF280A0D

Variation of 236U average concentration.

https://binary.pensoft.net/fig/658422 10.3897/nucet.8.78447.figure26 940AA80E-4BBA-5D49-98CF-F987768F4AA8

Variation of 238U average concentration.

https://binary.pensoft.net/fig/658423 10.3897/nucet.8.78447.figure27 785E2DF3-D708-53F4-B056-554E2EE73848

Variation of 239Pu average concentration.

https://binary.pensoft.net/fig/658424 10.3897/nucet.8.78447.figure28 89DA03F2-280D-5EBB-A6D9-8A1B6C5DCDE1

Variation of 240Pu average concentration.

https://binary.pensoft.net/fig/658425 10.3897/nucet.8.78447.figure29 4C6FA8EB-CC9C-55C6-9CCF-4FE6D6F2B4D3

Variation of 155Gd average concentration.

https://binary.pensoft.net/fig/658426 10.3897/nucet.8.78447.figure31 DA6321A7-C80B-5D08-8667-44DD2C0949A0

Variation of 242Pu average concentration.

https://binary.pensoft.net/fig/658427 10.3897/nucet.8.78447.figure30 01C33B15-BE23-5128-9257-D793AEEFBE30

Variation of 157Gd average concentration.

https://binary.pensoft.net/fig/658428 10.3897/nucet.8.78447.figure32 9C7EF177-38D5-5F66-AFCB-DBD84C8CB263

Variation of 241Pu average concentration.

https://binary.pensoft.net/fig/658429 10.3897/nucet.8.78447.figure33 7484F404-26EC-578D-8AE1-8054DF7DC380

Comparison of neutron flux spectrum at BOC, MOC and EOC for LEU fuel assembly.

https://binary.pensoft.net/fig/658430 10.3897/nucet.8.78447.figure34 6E61297D-35DB-5954-A1D6-69B5861A8D60

Comparison of neutron flux spectrum at BOC, MOC and EOC for MOX fuel assembly.

https://binary.pensoft.net/fig/658431 10.3897/nucet.8.78447.figure35 C9023444-06FF-5FBC-B5B6-3E4DD5B6184F

A typical neutron energy spectrum of a Light Water Reactor used as a weighting function in a generation of ORIGEN library [Tanaka et al. 2015].

https://binary.pensoft.net/fig/658432 Neutron flux distribution

Figs 33 and 34 present the neutron energy spectrum with respect to fluxes at three burnup cycles i.e. Beginning of Cycle (BOC), Middle of Cycle (MOC) and End of Cycle (EOC) for State-1 of LEU and MOX fuel assembly, respectively. The typical neutron energy spectrum is comprised of three kinds of spectra; thermal Maxwellian spectrum in thermal energy range, 1/E spectrum in epi-thermal energy range and fission spectrum in fast energy range. The shape of the typical spectrum has been given as results from neutron transport phenomena which are supposed to be observed in the LWR. Emitting neutrons by nuclear fission and moderation by light water are being considered in the phenomena for generation of such neutron energy spectrum (Figs 33 and 34). The neutron energy flux spectrum for each energy group has been calculated by dividing the neutron flux by the width of every energy group, φ(cm−2.s−1.eV−1) = Φ(cm−2.s−1)/ΔE(eV) by using OpenMC code. As may be seen from the Figs 33 and 34, good agreements are noticed between the neutron energy flux spectrum for BOC, MOC and EOC with slight variation among them especially MOX fuel assembly. No such neutron energy spectrum is available in the benchmark report to compare with OpenMC results. For comparison purpose, a typical neutron energy spectrum of a Light Water Reactor (Tanaka et al. 2015) is shown in Fig. 35. The neutron energy spectrum (Figs 33a and 34a) of VVER-1000 for State-1 (LEU and MOX fuel assembly) is almost identical shape of light water reactor (Fig. 3). Hence, the OpenMC code was successfully used for obtaining a neutron energy spectrum.

 Conclusion

The kinf values were calculated for VVER-1000 LEU & MOX assemblies that are typically of the advanced Russian designs in different reactor operating states using OpenMC code with nuclear data library ENDF/B-VII.1. The kinf values were also calculated against fuel burnup upto 40 MWd/kgHM. In addition, the isotope composition was also calculated for burnup upto 40 MWd/kgHM as per benchmark requirements. The calculated results were compared with the benchmark mean values along with the literature data. The OpenMC results showed very good agreement with the benchmark mean values alongwith other literature values. The neutron energy spectrum was successfully generated by using OpenMC code for both LEU and MOX fuel assembly for State-1. It is concluded that the OpenMC code along with the nuclear data library ENDF/B-VII.1 was successfully implemented at the Department of Nuclear Science and Engineering Department, MIST. In Bangladesh, two Russian design VVER-1200 (2400 MWth) type nuclear reactors are under construction and to be commissioned by 2023/2024. Based on the experience achieved for implementation of OpenMC code in the field of neutronics and burnup calculations, it is planned to calculate kinf or to perform burnup calculations for VVER-1200 and other PWR and BWR by using OpenMC along with SuperMC.

 Authorship contribution statement

Md. Imtiaj Hossain: Methodology, Data collection, Formal analysis, Writing – original draft. Yasmin Akter: Resources, data analysis, writing. Mehraz Zaman Fardin: Resources, literature review, writing. A. S. Mollah: Supervision, Conceptualization, Results interpretation, Writing – review & editing.

 Acknowledgements

The authors really acknowledge the efforts of the Department of Nuclear Science and Engineering, Military Institute of Science and Technology, Dhaka, Bangladesh for their academic support. The authors thank the referees for their critical reading of the paper and for the improvements they suggested.

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