Burnup Dependent Monte Carlo Neutron Physics Calculations of IAEA MTR Benchmark

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Burnup dependent Monte Carlo neutron physics calculations of IAEA

MTR benchmark

Khurrum Saleem Chaudri a , *, Sikander M. Mirza b

a Department of Nuclear Engineering, Pakistan Institute of Engineering and Applied Sciences (PIEAS), Nilore, Islamabad 45650, Pakistanb Department of Physics & Applied Mathematics, Pakistan Institute of Engineering and Applied Sciences (PIEAS), Nilore, Islamabad 45650, Pakistan

a r t i c l e i n f o

Article history:

Received 2 November 2014

Received in revised form

23 December 2014

Accepted 30 December 2014

Available online 22 January 2015

Keywords:

OpenMC code

Monte Carlo methods

MTR benchmark

Depletion studies

a b s t r a c t

In this work, OpenMC code has been used for reactor physics calculations of the IAEA 10 MW MTR

benchmark. To perform the burnup dependent studies i.e. Beginning of Life (BOL) and End of Life (EOL)

calculations are carried out using OpenMC. The isotopic number densities have been generated using

WIMS code and comparison of global core parameters has been performed. Along with the prevalent 9-

isotope vector methodology, a set of 16-isotopes, based on their relative importance, have been

employed in the whole core calculations and the corresponding computed values of integral parameters

been compared. Comparison of effective core multiplication factor is made with studies performed by

various organizations, employing different codes based on diffusion theory and Monte Carlo method-

ologies. The OpenMC predicted values of the multiplication factor and cell averaged thermal uxes in

centralux trap for HEU and LEU cores are found in good agreement with the corresponding published

data.

2015 Elsevier Ltd. All rights reserved.

1. Introduction

Recent times have seen emergence of open source nuclear

reactor physics computational tools as a norm. Various codes

including DRAGON (Marleau et al., 2006), OpenMC (Romano and

Forget, 2013), OpenMOC (Boyd et al., 2014), MocDown (Seifried

et al., 2014), PyNE (Scopatz et al., 2012) are examples of codes be-

ing developed as open source. Active participation of nuclear

community in such projects helps in verication &validation and

debugging of such codes, and helps these codes to rise to the level

of well-established codes.

Availability of advanced computational resources & tools has

rekindled interest in high delity simulations for design and safetyof nuclear reactors. Use of Monte Carlo based codes, Computational

Fluid Dynamics (CFD) approach and multi physics calculations are

few examples of such high delity simulation efforts in reactor

physics. International Atomic Energy Agency (IAEA) Coordinated

Research Project CRP-1496 is indicative of the combined efforts of

nuclear industry think-tank towards enhancement of the state-of-

art analysis using computational tools and their validation against

experimental data. The IAEA benchmark Material Test Reactor

(MTR) (Haack, 1992; Winkler and Zeis, 1980) was set for validating

and verication of tools and methodology needed to perform

necessary calculations to convert High Enriched Uranium (HEU)

reactors to Low Enriched Uranium (LEU) reactors, using computa-

tional tools including MTR-PC (MTR-PC, 2001). With the availability

of advanced computational resources and tools, such benchmarks

are being revisited by the nuclear community to re-assess their

results (Bousbia-Salah et al., 2008).

Monte Carlo simulations offer a powerful method of simulating

complex physical phenomenon including neutron transport in

multiplying media such as nuclear reactors. With detailed three

dimensional modeling of actual geometry, continuous energy crosssection representation is possible in various Monte Carlo based

codes including MCNP (MCNPX, 2003), Serpent (Leppanen, 2012),

OpenMC (Romano and Forget, 2013) etc. Typically large computa-

tional times required by various Monte Carlo based codes are

surpassed by their superior features including their ability to

perform calculations for complex heterogeneous geometries. These

codes have been used mostly for benchmarking the results ob-

tained from other deterministic codes based on diffusion and

transport theory. According to the Smith challenge (Smith, 2003),

in 2030 we would be able to calculate pin by pin power prole of a

full scale PWR with required accuracy (1% uncertainty) using a* Corresponding author. Tel.: 92 51 111174327; fax: 92 51 9248600.

E-mail address:[email protected](K.S. Chaudri).

Contents lists available atScienceDirect

Progress in Nuclear Energy

j o u r n a l h o m e p a g e : w w w . e l s e v i e r . c o m/ l o c a t e / p n u c e n e

http://dx.doi.org/10.1016/j.pnucene.2014.12.018

0149-1970/

2015 Elsevier Ltd. All rights reserved.

Progress in Nuclear Energy 81 (2015) 43e52
mailto:[email protected]://www.sciencedirect.com/science/journal/01491970http://www.elsevier.com/locate/pnucenehttp://dx.doi.org/10.1016/j.pnucene.2014.12.018http://dx.doi.org/10.1016/j.pnucene.2014.12.018http://dx.doi.org/10.1016/j.pnucene.2014.12.018http://dx.doi.org/10.1016/j.pnucene.2014.12.018http://dx.doi.org/10.1016/j.pnucene.2014.12.018http://dx.doi.org/10.1016/j.pnucene.2014.12.018http://www.elsevier.com/locate/pnucenehttp://www.sciencedirect.com/science/journal/01491970http://crossmark.crossref.org/dialog/?doi=10.1016/j.pnucene.2014.12.018&domain=pdfmailto:[email protected]


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desktop PC in one hour. Introduction of multi-core processors has

now revised this timeline to 2019 (Martin, 2007). Recent Monte

Carlo codes including MCNPX (Fensin et al., 2010) and Serpent

(Leppanen and Pusa, 2009) are equipped with capability to

perform burnup analysis. Clearly, this approach entails a corre-

sponding huge computational effort.

One method that can give accurate enough result for problems

involving burnup dependent number densities when using Monte

Carlo based codes is employing lattice codes like WIMS (Halsall

and Tauman, 1997) in conjunction with Monte Carlo codes. Such

lattice codes can generate burnup dependent number density

values for an equivalent unit cell representative of full geometry.

These burnup dependent number densities can then be used in

neutron physics codes performing full three-dimensional analysis

of core. This approach has been used and veried in several works.

One such example of generating burnup dependent number den-

sity in WIMS and then using them in detailed three dimensional

modeling with MCNP was veried against experimental data of

TRIGA reactor (Jeraj et al., 2002). This methodology used U-235, U-

236, U-238, Pu-239, Pu-240, Pu-241, Pu-242, Tc-99, Rh-103, Xe-

131, Cs-133, Xe-135, Nd-143, Pm-147, Sm-149 and Sm-151 (16

isotopes in total). Similar methodology, with varying number of

isotopes included in burned fuel, was used to perform MTRbenchmark static calculations with MCNP5 code (Bousbia-Salah

et al., 2008). This methodology used only U-235, U-236, U-238,

Pu-239, Pu-240, Pu-241, Pu-242, Xe-135 and Sm-149 (9 isotopes in

total) on basis of number densities provided in original IAEA

benchmark specication (Winkler and Zeis, 1980) for Monte Carlo

methodology based codes.

In present work both above stated methodologies, to obtain

burnup dependent number densities, have been employed and the

corresponding values of computed integral parameters have

compared for the IAEA 10 MW benchmark reactor (Winkler and

Zeis, 1980). The difference in values of reactivities obtained by us-

ing different number of isotopes used is quantied. The OpenMC

code has been used to perform three dimensional neutron physics

analysis while WIMSD-4 is used for generation of number densities

at various stages of fuel burnup. Various reactor physics parameters

including effective multiplication factor and spatial ux proles in

different energy groups have been calculated and compared.

2. Computational framework

IAEA 10 MW benchmark reactor, specication provided in Ap-

pendix-F of IAEA-TECDOC-233 (Winkler and Zeis, 1980) has been

used to perform the analysis presented in this study. Standard

values of the reactor design parameters have been used as quoted

in literature (Bousbia-Salah et al., 2008). Analyses are performedfor

HEU core i.e. 93% enriched fuel and LEU core i.e. 20% enriched fuel.

Three type of conguration with both HEU and LEU have beenstudied: (i) Fresh, (ii) Beginning of Life (BOL) and (iii) End of Life

(EOL).

In this work, tools used for the simulation include OpenMC

(Romano and Forget, 2013) and WIMSD-4 (Halsall and Tauman,

Fig. 1. Radial cross sectional view of the modeled core at core mid plane indicated in Fig. 2.

K.S. Chaudri, S.M. Mirza / Progress in Nuclear Energy 81 (2015) 43e5244


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Fig. 2. Axial cross sectional view of the benchmark core with AA marks indicating core mid plane.

Fig. 3. Standard Fuel Element (SFE) cross sectional view as modeled in OpenMC.


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1997). The OpenMC is modern structured code which can perform

Monte Carlo based calculations for nuclear reactors. OpenMC is

being developed as an open source code under the banner of

Computational Reactor Physics Group (CRPG) of Massachusetts

Institute of Technology (MIT). This code is written in Fortran 2008.

Like MCNP, OpenMC uses ACE format cross sections. Constructive

Solid Geometry (CSG) is used to model geometry in this code. For

the time being, rst and second order surfaces can be modeled in

OpenMC. Input of the code is provided in XML format. Code version

0.5.4 was used to perform the analysis presented in this work. 3-

dimensional geometry was modeled in OpenMC to perform the

presented calculations. ACE formatted ENDF/B-VII.1 cross sections,

prepared for 293.6 K, obtained from the National Nuclear Data

Center (NNDC) Brookhaven National Laboratory (BNL), were used

in the simulations presented in this work. OpenMC team has a plan

of implementing burnup capability in the code but for the time

being OpenMC cannot perform burnup calculations.

WIMSD-4 (Halsall and Tauman, 1997) is a well tried and tested

code for group constant generation and fuel burnup studies.

WIMSD performs one dimensional transport theory based calcu-

lations for the modeled geometry and then provides homogenized

or region-wise cross section as requested by the user. One dimen-

sional unit cell model based on Standard Fuel Element (SFE), sameas used in IAEA-TECDOC-233 Appendix-F, was used in the WIMSD

code to obtain burnup dependent number densities.

3. Computational methodology

The IAEA benchmark 10 MW MTR core was modeled with exact

specication as provided in the IAEA documentation (Winkler and

Zeis, 1980). Radial and axial cross sectional view of modeled core

are shown in Figs. 1 and 2 respectively. Figs. 3 and 4 show the

exploded view of Standard Fuel Element (SFE) and Control Fuel

Element (CFE). Various colors inFigs. 1e4represent different ma-

terials including fuel, aluminum, water etc.

The OpenMC based Monte Carlo simulation was carried out for

20,000 particles per cycle and total of 850 cycles were employed.

First 50 cycles from these 850 cycles were discarded and then score

accumulation was started. Keeping number of histories (particles

per cycle multiplied by no. of cycles) xed, better source conver-

gence is achieved if we use relatively large number of particles per

cycle (Brown, 2006; Macdonald, 2012). A ssion source uniformly

distributed in reactor was used as input. To assess the convergence

of source, Fig. 5 shows the results obtained for Shannon entropy

and effective multiplication factor against cycle number. Fig. 5

provides quantitative measure that results being presented in this

study are accurate.

To accumulate scores including uxes and ssion, OpenMC

provides a very handy feature of dening a mesh and then accu-

mulate the scores over that mesh. Various radial and axial meshes

were dened to get ux proles in respective directions. To get the

ux at central axial plane of core in xy-direction, a 100 100 mesh

has been dened. Flux inx-direction is obtained for 100 points forcentral radial plane. Axialux (z-direction) is obtained for30 points

at the central plane ofux trap. For ssion scores, a 6 5 mesh is

dened with one mesh covering one full fuel assembly.

Burnup dependent number densities, for use in the OpenMC

calculations, were generated by the WIMS code. Unit cell based on

SFE, used in IAEA-TECDOC-233 (Winkler and Zeis, 1980) and else-

where (Bousbia-Salah et al., 2008) was modeled in WIMS. This

Fig. 4. Control Fuel Element (CFE) cross sectional view simulated in OpenMC.



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methodology of using unit cell to generate burnup dependent

number densities has its roots in the methodology which is being

used in lattice cell calculation codes (usually transport theory

based) coupled with 3D whole core codes, based on diffusion or

transport theory. Such combinations of codes extensively used in

nuclear community are WIMS/CITATION, DRAGON/DONJON,

CASMO/SIMULATE etc. Lattice cell codes calculate the group aver-

aged cross-sections for few-group to be used in whole core calcu-

lations. Group constants for each different fuel assembly (different

enrichment, different control rodor burnable poison conguration)

are calculated separately based on equivalent unit cell made for

each fuel assembly. Calculations reported in Appendix F of IAEA-TECDOC-233 by different organizations have used this methodol-

ogy, i.e. lattice cell cross section generation in conjunction with 3D

calculations, extensively. Main approximations used in generating

burnup dependent number densities using WIMS are that unit cell

was based on Standard Fuel Element (SFE) and equal power dis-

tribution forall fuel assemblies, and hence fuel plates, is assumed to

provide input for POWERC card in WIMS code.

At this point, two different approaches were encountered in

reported literature. For Monte Carlo based code calculations, only 9

isotopes (U-235, U-236, U-238, Pu-239, Pu-240, Pu-241, Pu-242,

Xe-135 and Sm-49) are used in IAEA-TECDOC-233 (Winkler and

Zeis, 1980). Lately, Jeraj (Jeraj et al., 2002) has used WIMSD-5 in

combination with MCNP4B and validated his result against

experimental values to determine a set of 16 isotopes to getcomputational result close to experimental values. These 16 iso-

topes include above mentioned 9 isotopes plus Tc-99, Rh-103, Xe-

131, Cs-133, Nd-143, Pm-147 and Sm-151. In this study, both ap-

proaches (9 and 16 isotope burnup vector) are used so as toquantify the difference between the two mentioned approaches.

4. Results

Monte Carlo based static reactor physics calculations have been

performed for the IAEA benchmark MTR core. Table 1 contains

results of multiplication factor comparison calculated by using 9

and 16 isotopes burnup vector with the help of OpenMC code. For

comparison, the range of corresponding values reported in IAEA-

TECDOC-233, Appendix-F (Winkler and Zeis, 1980) are also

included. It is evident fromTable 1that results obtained by using

16-isotopes burned number densities from WIMS code are giving

better results as compared to 9-isotopes approach. Figs. 6 and 7

provide the comparison ofssion product inventory obtained forHEU and LEU cores. Both these gures clearly show that the

number densities of 7 isotopes included in addition to 9-isotope

approach are quite signicant. All the isotopes are present in

greater quantity as compared to Xe-135 in both HEU and LEU cores.

The rest of results presented in this work are calculated by using 16

isotopes burnup vector in OpenMC code. Slightly different number

densities of Xe-135 in HEU and LEU cores are obtained. This is due

to the fact that abscissae ofFigs. 6 and 7are showing percentage of

U-235 burnt which is achieved at different times (days of opera-

tion) for both HEU and LEU core so a direct comparison cannot be

made.

A study was conducted to see the difference in multiplication

factor while using different set of cross section libraries. ENDF/B-

VII.1 and JEFF-3.2 libraries (293 K) were used in this study, basedon their availability.Table 2summarizes the results obtained. It can

be seen that the difference in multiplication factor by using

Fig. 5. Convergence assessment by observing Shannon entropy and effective multi-plication factor against number of cycles.

Table 1

Comparison of multiplication factor results using 9-isotope and 16-isotope methodologies.

Core enrichment, stage keff Difference (pcm), (9e16 isotopes)

This work Reported (Winkler and Zeis, 1980)

9-Isotopes 16-Isotopes

93%, BOL 1.06094 0.00024 1.04190 0.00023 1.02333e1.04199 1904 47

93%, EOL 1.04305 0.00024 1.02006 0.00024 1.0090e1.05337 2299 48

20%, BOL 1.05916 0.00025 1.03750 0.00023 1.02127e1.05782 2166 48

20%, EOL 1.04452 0.00024 1.01925 0.00023 1.0120e1.05468 2527 47

Fig. 6. Fission fragment inventory for the case of HEU core.

K.S. Chaudri, S.M. Mirza / Progress in Nuclear Energy 81 (2015) 43e52 47


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different libraries is quite small, with maximum difference of

255 pcm. The results provided hereafter are calculated using ENDF/B-VII.1 library (293 K).

Table 3 compares the results of multiplication factorfor HEUand

LEU cores for fresh, BOL and EOL congurations with reported re-

sults. Name of the organization along with the code used to pro-

duce the reported value are provided in the table. It is evident that

results match well and lie within the spectrum of reported results.

The differences are due to different computational tools (using

different methodology) and different cross sections libraries used

to perform these simulations.

Table 4provides the comparison of thermal neutron ux aver-

aged over the whole water box i.e. 8.1 7.7 60 cm3. The com-

parison of calculated values in this work matches very well with

other organization values. Modeling of full details of heterogeneous

geometry in OpenMC code is providing slightly higher ux as

compared to diffusion theory based codes where homogenous

geometry is modeled.

Figs. 8e10 show thermal, epithermal and fast ux spatial pro-

les obtained for 93% fresh core. Consistent with the expected

behavior, thermal ux has a large peak in ux trap present at the

center of the core while fast ux shows a minimum in this region.

Sharpness of thermal ux peak in ux trap matches well with the

corresponding reported results presented in IAEA-TECDOC-233,Appendix-F.

Figs. 11e13show thermal, epithermal and fast ux radial prole

obtained for all 6 core compositions i.e. 93% and 20% Fresh, BOL,

EOL. Figs.14e16give the corresponding axial ux plots for thermal,

epithermal and fast ux respectively for the 6 studied core com-

positions. All 6 cases for thermal, epithermal and fast ux are

plotted on the same graph in order to provide a comparison ofux

magnitude obtained when altering core composition. The trend

obtained fromFigs. 11e16reveal the fact that 93% BOL and EOL

cores display maximum ux values among the six studied core

compositions. These values occur in sets of two i.e. 93% BOL& EOL,

20% BOL & EOL and nally 93% & 20% Fresh cores (in order of

maximum to minimum values ofux). The kinks in axial thermal

ux prole near the top and bottom of fuel are due to thermali-

zation of neutrons from axial reector.

Figs. 17 and 18 provide the comparison of power fractions (%)

produced in each assembly for HEU and LEU cores respectively.

Anticipated pattern of larger power fraction being produced near

Fig. 7. Inventory ofssion fragment present in the case of LEU core.

Table 2

Comparison of multiplication factor results using different cross section libraries with OpenMC code.

Cross section library HEU (93%) LEU (20%)

Fresh BOL EOL Fresh BOL EOL

ENDF/B-VII.1 1.19382 0.00025 1.04190 0.00023 1.02006 0.00024 1.15494 0.00025 1.03750 0.00023 1.01925 0.00023

JEFF-3.2 1.19229 0.00025 1.03935 0.00024 1.01823 0.00024 1.15296 0.00026 1.03539 0.00026 1.01709 0.00025

Absolute difference (pcm) 153 50 255 47 183 48 198 51 211 49 216 48

Table 3

Computed Eigen-values for the IAEA 10 MW MTR benchmark core.

Organization (code) HEU (93%) LEU (20%)


T hi s wor k ( OpenMC) 1 .19 382 0.00025 1.04190 0.00023 1.02006 0.00024 1.15494 0.00025 1.03750 0.00023 1.01925 0.00023

Bousbia et al., (MCNP5) 1.18962 0.00034 1.05768 0.00032 1.03959 0.00031 1.17238 0.00033 1.05617 0.00032 1.04111 0.00032

ANL (VIM) 1.189 0.0033 e* 1.045 0.0036 1.168 0.0033 e* 1.048 0.0034

ANL (DIF2D) 1.18343 1.02333 1.03366 1.16830 1.02127 1.03934

EIR (CODIFF) 1.19394 e* 1.07230 1.15937 e* 1.04981

OESGAE (EXTERMINATOR) 1.1966 1.0320 1.0090 1.1813 1.0320 1.0120

CEA (NEPTUNE) 1.202 1.04041 1.05337 1.187 1.0394 1.05468

JAERI (ADC) 1.18104 1.04199 1.02195 1.18339 1.05782 1.04122

CNEA (EXTERMINATOR) 1.20018 1.03620 1.01425 1.18150 1.03334 1.01300

e

*: Value not calculated.

Table 4

Computed average water box thermalux 1014 (n/cm2-s)for the IAEA 10MW MTR

benchmark core.

Organization (code) HEU (93%) LEU (20%)


This work (OpenMC) 1.87004 2.17595 2.23519 1.82359 1.93065 1.97141

Bousbia et al.,

(MCNP5)

e* e* e* e* e* e*

ANL (VIM) e* e* e* e* e* e*

ANL (DIF2D) e* 2.1345 2.1999 e* 1.9017 1.9498

EIR (CODIFF) e* 2.220 2.285 e* 2.025 2.068

OESGAE

(EXTERMINATOR)

e* e* e* e* e* e*

CEA (NEPTUNE) e* e* e* e* e* e*

JAERI (ADC) e* e* e* e* e* e*

CNEA

(EXTERMINATOR)

e* 1.9831 2.0507 e* 1.7220 1.7691

e*: Value not calculated.



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Fig. 8. Thermal ux prole (a) contour and (b) 3D surface plot for HEU fresh core at core mid-plane.

Fig. 9. Epithermal ux prole (a) contour and (b) 3D surface plot for HEU fresh core at core mid-plane.

Fig. 10. Fast

ux pro

le (a) contour and (b) 3D surface plot for HEU fresh core at core mid-plane.



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the center is followed. This pattern is predominant in fresh core. At

BOL, when more burnt fuel assemblies are near the middle and lessburnt assemblies are present near the periphery, much atter

prole is obtained as compared to fresh core.

Fig. 11. Radial thermal ux at core mid-plane for studied core compositions.

Fig. 12. Radial epithermal ux proles for studied cases at core mid-plane.

Fig. 13. Studied core composition radial fast

ux pro

le at core mid-plane.

Fig. 14. Axial thermal ux for the studied core compositions at core mid-plane.

Fig. 15. Axial epithermal ux at core mid-plane for the studied core composition.

Fig. 16. Axial fast

ux for the studied core compositions at core mid-plane.



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5. Conclusion

Burnup dependent steady state neutron physics calculations are

performed for the IAEA 10 MW MTR benchmark using Monte Carlo

based code OpenMC. To perform the burnup dependent neutron

physics calculations, burnt fuel number densities are generated

using WIMS code. Two different approaches (9 isotopes vs. 16

isotopes) adopted by different researchers were compared and 16

isotope approach was found better. The latter approach was then

used to perform analysis presented in this work. Multiplication

factor, ux (thermal, epithermal and fast) and power fraction pro-

duced in different fuel assemblies were calculated. The results were

found to be in very good agreement with those presented in liter-

ature. It can be concluded that 16 isotopes approach can be used to

Fig. 17. Power fractions (%) distributions in each fuel assembly for different HEU core congurations.

Fig. 18. Power fractions (%) distributions in each fuel assembly for different LEU core con

gurations.



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perform burnup dependent neutron physics calculations using

Monte Carlo based codes. With the availability of computational

resources and tools, such exercises can help validate both the

methodology adopted to perform the calculations and the rela-

tively newer tools used to perform these calculations.

Acknowledgements

Authors would sincerely like to thank Anis Bousbia-Salah for his

cooperation and helpful discussions during this work. Authors

would also like to thank the whole team of OpenMC in general and

Paul K. Romano in particular for their discussions, support and help

in using the code OpenMC.

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