The journal of Nuclear Science and Technology - Volume 9, Number 2, June 2019

ISSN 1810-5408

Nuclear Science

and Technology

Volume 9, Number 2, June 2019

Published by

VIETNAM ATOMIC ENERGY SOCIETY

VIETNAM ATOMIC ENERGY INSTITUTE

NUCLEAR SCIENCE AND TECHNOLOGY

Volume 9, Number 2, June 2019

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)

....................................................................................................................................................................................................................

(VINATOM).

Pusblished by

Vietnam Atomic Energy Society, 59 Ly Thuong Kiet, Hanoi, Vietnam

Tel: 84-24-39420463 Fax: 84-24-39424133 Email: [email protected]

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....................................................................................................................................................................................................................

Contents

On Burnup Modelling Issues Associated with VVER–440 Fuels

Branislav Vrban, Štefan Čerba, Jakub Lüley, Filip Osuský,Mikuláš Vorobeľ,

Vladimír Nečas…………………………………………………………………………………………………...

01

Estimation of Tritium Production in VVER-440 Reactor Core During Normal

Operation

Štefan Čerba, Jakub Lüley, Branislav Vrban, Filip Osuský, Vladimír Nečas…………...... 10

Processing of the multigroup cross-sections for MCNP calculations

Jakub Lüley, Branislav Vrban, Štefan Čerba, Filip Osuský, Vladimír Nečas.................... 17

Conceptual design of a small-pressurized water reactor using the AP1000 fuel

assembly design

Van Khanh Hoang, Viet Phu Tran, Van Thin Dinh, Hoai Nam Tran………………………… 25

Low-energy experiments at the S3 spectrometer

S. Franchoo……………………………………………………………………………………………………….. 31

Dosimetric characteristics of 6 MV photons from TrueBeam STx medical linear

accelerator: simulation and experimental data

N. D. Ton, B. D. Linh, Q.T. Pham………………………………………………………………………… 37

Conceptual designing of a slow positron beam system using Simion simulation

program

Cao Thanh Long, Huynh Dong Phuong, Nguyen Trung Hieu, Tran Quoc Dung……….. 45

Nuclear Science and Technology, Vol.9, No. 2 (2019), pp. 01-09

On Burnup Modelling Issues Associated with VVER–440 Fuels

Branislav Vrban^1,2, Štefan Čerba¹, Jakub Lüley¹, Filip Osuský¹,

Mikuláš Vorobeľ¹and Vladimír Nečas¹

¹Slovak University of Technology in Bratislava, Faculty of Electrical Engineering and Information

Technology, Institute of Nuclear and Physical Engineering, Ilkovičova 3, 812 19 Bratislava, Slovakia, ²B&J

NUCLEAR Ltd., Alžbetin Dvor 145, 900 42 Miloslavov, Slovakia

Email branislav.vrban@stuba.sk

(Received 12 November 2019, accepted 19 November 2019)

Abstract: The paper investigates various computational modelling issues associated with VVER-440

fuel depletion, relevant to burnup credit. The SCALE system and the TRITON sequence are used for the

calculations. The effects of variations in depletion parameters and used calculation methods on the

isotopic vectors are investigated. The burnup behaviour of Gadolinium is quite important in actual core

analysis, but its behaviour is somewhat complicated, requiring special treatment in numerical modelling

and calculations. Therefore, a special part of the paper is devoted to the treatment of Gadolinium-bearing

fuels. Moreover, some discussions on power normalization are also included. To assess the acquired

modelling experience used to predict the VVER-440 spent fuel nuclide composition, the measured

compositions of Novovoronezh NPP irradiated fuel assembly are compared to data calculated by

TRITON sequence. The samples of fuel assembly with 3.6 wt. % U-235 enrichment underwent 4-cycle

campaign of totally 1109 effective full power days in the core and cooling period of 1-13 years.

Calculated concentrations are compared to measured values burdened with their experimental

uncertainties for totally 47 nuclides. The calculated results show overall a good agreement for all

nuclides, differences from measured are pointed out and discussed in the paper.

Keywords: burnup, VVER 440, modelling, SCALE.

consideration. Slovakia has four nuclear

reactors generating half of its electricity and

another two under construction. This paper

investigates and summarizes modelling issues

associated with VVER-440 fuel depletion

performed by the SCALE system [1]. The

effects of variations in the depletion parameters

and used calculation methods on the isotopic

vectors are investigated. The burnup behaviour

of Gadolinium, a burnable poison in nuclear

fuel, is quite important in actual core analysis;

therefore, a special part of the paper is devoted

to this issue. Finally, some discussions on

power normalization are also included. Other

publications relevant to burnup modelling

issues for PWR can be found in [2,3]. To

assess the ability of the SCALE system and the

associated nuclear data to predict the VVER-

440 spent fuel nuclide composition, the

I. INTRODUCTION

The prediction accuracy of burnup

calculations is a critical factor in the reactor

analysis sequence. The core properties depend

on the actual composition of the fuel; thus, the

characteristics of the reactor core undergo

changes during burnup. Moreover, the isotopic

composition of the spent fuel discharged from

the core is a key factor in both the operations

and the material control activities of the deep

geological repository. An accurate estimate of

the time-dependent radionuclide inventory in

this material is necessary to evaluate many

spent fuel issues, including neutron and

gamma-ray source terms for shielding analysis,

decay-heat source terms for temperature

distribution and radiological and chemical

toxicity

for

environmental

impact

ON BURNUP MODELLING ISSUES ASSOCIATED WITH VVER–440 FUELS

measured compositions of Novovoronezh NPP

triangular grid pattern. The assembly is

enclosed in a hexagonal wrapper with the

width across the flat equal to 145 mm (the 2^nd

generation FA). The FA and emergency reactor

control assemblies (ERC) are positioned in a

hexagonal grid with a spacing of 147 mm. The

fuel rods are in the bundle in a triangular grid

pattern with a pitch of 12.3 mm. The fuel rod

claddings are made of the E110 zirconium

alloy (Zr + 1% Nb), while the wrapper tubes of

FA and ERC are made of the E125 zirconium

alloy (Zr + 2.5% Nb). The modelled outside

diameter of fuel rod cladding is 9.1 mm and the

inside diameter is 7.75 mm. The cladding

houses a fuel column assembled of uranium

dioxide pellet. Generally, several types of

profiled fuel assemblies are used to maintain

power peaking factors under the design limits.

A Gd₂O₃absorber is integrated with a mass

content of 3.35% into number of FAs to aid

fuel profiling. The profiling diagrams with

various initial enrichments and locations of

fuel bundles used in self-developed 2D SCALE

models are shown in Fig. 1.

irradiated fuel assembly are compared to data

calculated by the TRITON sequence in the last

part of the paper. The work done follows the

simplified specification of the computational

benchmark based on the #2670 ISTC project

[4] providing VVER-440 data for 8 samples

cut outs of 4 fuel pins of the fuel assembly

(FA) No. D26135 with the average reached

burnup 38.5 MWd/kgU. The #2670 ISTC

project has was carried out between years 2003

and 2005. Measurements of samples cut out of

were performed in RIAR Dimitrovgrad,

Russia, the final project report is publicly

accessible [6]. The FA irradiation was done

during the 15 - 18 core loads in the fourth

power unit of Novovoronezh NPP.

II. METHODS AND TECHNIQUES

A. VVER-440 geometry model description

All the current VVER-440 fuel

assemblies used in Slovakia are hexagonal and

the fuel rods are placed in the assembly in a

a) ERC fuel part - 3.84 _wt% U-235

b) FA - 4.25 _wt% U-235 c) FA & ERC fuel part - 4.87 _wt% U-235

Fig. 1. Profiling diagram for fuel rod bundles used in computational model

2

BRANISLAV VRBAN et al.

modelled with temperature of 933 K and the

B. Calculation methodology

temperature of structural materials and water

coolant is 555 K. The fuel pellet density is

10.55 g/cc and the density of zirconium alloys

equals 6.55 g/cc. Very fine depletion steps

(<0.5 MWd/kgHM) are used before

Gadolinium peak reactivity to track the fast

poison concertation changes. After peak

reactivity, longer steps are used but are kept

smaller than 1 MWd/kgHM.

An accurate treatment of neutron

transport and depletion in VVER-440 fuel

assemblies characterized by heterogeneous and

complex design requires the use of advanced

computational tools. The depletion module

TRITON [5], included in SCALE 6.1.3 code

system developed by ORNL, was used to

perform depletion simulations for two-

dimensional FA and ERC models. The

TRITON depletion module is coupling the 2D

transport code NEWT with the point depletion

and decay code ORIGEN-S. The TRITON

lattice physics modelling approach for PWR

C. Sensitivity and parametric evaluations

The effects of various relevant depletion

parameters on the models k_eff(due to the

reflective boundary conditions identical to k_inf)

and isotopic changes were investigated,

however just the most interesting cases are

presented. Variations of a single parameter are

studied in each case; the remaining parameters

are based on parameters used in BMA model.

fuel

is

extensively

described

in

SCALE/TRITON primer [6]. For the sake of

brevity, just the most important options used in

our best modelling approach (BMA) and based

on SCALE/TRITON primer and our

experience for burnup calculations are shown

here. The developed models are 2D assembly

models with reflective boundary conditions on

all sides, which represent infinite radial arrays

of infinite length fuel assemblies. An

unstructured coarse-mesh finite-difference

acceleration approach (CMFD) is used with

“partial-current” acceleration scheme. All

results of sensitivity and parametric

evaluations were calculated with the standard

SCALE V7-238 multigroup neutron library

based on ENDF/B-VII.0 evaluated data [7].

The V7-56 multigroup neutron library based on

ENDF/B-VII.1 [8] evaluated data was used in

the case of simplified benchmark calculation.

Fuel pins with burnable absorbers were

depleted by constant flux option instead of

constant power approach. The average specific

power of each model is derived from the

average reactor power of NPP Bohunice unit 4

during cycle 30 and equals to 33.05421

kW_th/kgHM. The average concentration of

boron acid (H₃BO₃) is obtained using the same

approach and reaches cb=2.56 g/kg. The fuel is

 Several VVER fuel types and enrichments

of U-235 are investigated in the paper.

 Since the real-life operating history of each

FA or ECS varies significantly, it is

necessary to determine an operating history

that is bounding in terms of its effect on

reactivity, or to define a simple operating

history with quantified margin that will

bound the effect of operational variations.

One of the most important parameters

varying is the boron acid concentration. The

four concentrations are investigated cb={1;

2.56; 4; 5} g/kg.

 The Gadolinium-bearing (Gd) pins should

be treated with special approach including

constant flux option and consideration of

spatial depletion. The influence of both

approaches to integral multiplication

parameter and to isotopic are studied.

 Calculations were performed to assess the

effect of assumed specific power, with

3

ON BURNUP MODELLING ISSUES ASSOCIATED WITH VVER–440 FUELS

varying the specific power from the half of

BMA power to the doubled value.

dissolution of the cut-out specimen including

control over fuel dissolution completeness,

radiochemical extraction of U, Pu, Np, Am,

Cm, Nd, Cs and Ce from fuel solution,

nuclide composition measurements of the

extracted elements, measurement of uranium,

 The moderator (also coolant) temperature

varies significantly within the fuel axial

profile, therefore it is necessary to assess its

influence on the fuel multiplication factor

and nuclide concentrations. The three water

moderator with boric acid temperatures are

plutonium,

neptunium,

americium,

neodymium, cerium and caesium mass

fractions using isotopic dilution and

measurements of Np-237, Cm and Ce-144

contents. All the results are burdened with

nuclide specific error range for a confidence

probability of Р=0.95. These errors are

considered in the results section of this

paper. The radiochemical examinations of

specific groups of nuclides were done in

different and are precisely taken into account

in the calculation model.

investigated

={541.05

K;

0.7803 g/cc, 555 K, 0.7604 g/cc; 570.45 K,

0.7258 g/cc}. It should be noted that the

moderator/coolant density was calculated

with assumption of the design pressure of

12.26 MPa.

D. The simplified benchmark

The calculation presented in the paper

is based on data published for samples No.

21 and 182 taken from the fuel pin No. 6 of

the FA No. D26135. The axial position of

sample No. 21 with a length of ~ 10 mm cut

out from fuel was approx. 1 m above the

lower fuel pin plug. The sample No. 182 was

in the lower part of the core just approx. 10

cm above the fuel pin plug. Our results for

sample No. 149 from pin No. 54 can be

found in our previous work [9]. The data in

document [5] are not fully comprehensive,

therefore user effect may be present in our

approach. The spent fuel assembly was

operated from October 1987 up to July 1991

(1369 calendar days). There were 1109

effective full power days. A cooling period

(since the end of irradiation period to the

radiochemical analysis) made up approx. 12

years. Thus, the working assembly is typical

of the majority of fuel assemblies, which are

stored in NPP storage pools. The nuclide

composition of spent nuclear fuel specimens

was examined in the analytical and mass-

spectrometric analysis laboratories of the

RIAR [10]. The examination included

E. Results

The results of different fuel types and

the average enrichments of U-235 are shown

in Fig. 2. As it can be seen, for ERC with the

uniform enrichment of 1.6 wt% U-235 and

without integrated burnable absorbers, the

reactivity decreases monotonically with

burnup in a nearly linear fashion. In contrast,

for fuels with Gadolinium the reactivity

increases as fuel burnup proceeds, reaches a

maximum at the burnup where the absorber is

nearly depleted (between 6 to 8 MWd/kgHM),

and then decreases monotonically. The

reactivity peak is more noticeable in the

models with average enrichments of 3.84 and

4.25 wt% U-235 than in the 4.87 wt% U-235

case. This effect is caused by the different

ratio of fissile to absorbing Gd isotopes and

by their opposite influence on the criticality

parameters in each assembly type. Interesting

finding is that the highest peak value moves to

higher burnup for FAs with higher uranium

enrichment.

4

BRANISLAV VRBAN et al.

concentration changes causes significant

underestimation of the system reactivity in

early burnup stages. Later the reactivity of Gd

peak is systematically overestimated.

Fig. 2. Effect of assembly type

It is not shown, but we can conclude that

the reactivity trends of various boron acid

concentrations are parallel during the whole

burnup. The concentrations of important

isotopes gathered during depletion with

maximal and minimal investigated boron acid

concentrations are shown in Fig. 3.

Fig. 4. Effect of deplete-by-flux option

vs. spatial depletion

To find the cause, Gd isotopes depletion

is shown in Fig. 5. The Gd-155 and Gd-157

have much larger thermal cross sections than

U-235, thus their concentration changes

significantly influence the neutron balance of

the system. Gd-157 depletes more rapidly in

the case when spatial concentration changes

are not taken into account. This faster

concentration decrease is consequence of

higher effective absorption cross section

yielding to lower reactivity of the system.

Consequently, this concentration difference

causes higher reactivity amplitude of Gd peak

in later burnup steps.

Fig. 3. Effect of boron acid concentration

The agreement diverges mainly for Pu-

239 as a function of burnup. As mentioned

above, the Gd pins should be treated with

special approach including constant flux option

and consideration of spatial depletion. The

influence of both approaches to multiplication

parameter and to isotopic changes is shown in

Fig. 4 and Fig. 5. It is evident from Fig. 4 that

neglecting the depletion by constant flux

option does not lead to different results as

obtained by using BMA modelling approach.

On the other hand, ignoring of fast spatial Gd

To assess the effect of assumed specific

power, the fuel temperature was kept constant

in all calculation steps. Consistent with other

studies, the general trend is for reactivity to

decrease with increasing specific power. With

respect to reactivity the use of minimum

specific power seems to be conservative

modelling option. As shown in Fig. 6., the

concentrations of Pu-239 and Pu-241 decrease

with increasing specific power, which would

also tend to reduce reactivity.

5

ON BURNUP MODELLING ISSUES ASSOCIATED WITH VVER–440 FUELS

cross-section

for

thermal

neutrons.

Consequently, Pu-239 concentration is

sensitive to the level of system under-

moderation.

The results of the simplified benchmark

calculation for samples No. 21 and 182 of main

and minor actinides are mainly shown in Fig. 8

to Fig. 11. The calculated (denoted as C) and

experimentally determined (E) nuclide

concentrations are presented in the form of

C/E-1 ratio. As can be seen, the highest relative

deviation is in the case of U-235 and sample

No. 21, where the calculation overestimates the

average measurement value approximately by

20 %.

Fig. 5. Effect of spatial depletion

for burnable poisons.

We assume that almost all important

fission products decrease with decreasing

specific power which would tend to increase

reactivity.

Fig. 7. Effect of moderator temperature

Fig. 6. Effects of specific power.

The VVER-440 FAs are designed as

under-moderated, therefore one can expect

lower fuel multiplication properties with the

higher moderator temperature. The results

achieved confirm our expectations and are

fully in accordance with theory. The

concentrations of fissile actinide Pu-239, see

Fig. 7, are shown to rise with increasing

moderator temperature.

Fig. 8. Comparison of results – sample 21

The resonance absorption by U-238 is

enhanced by Doppler broadening with

increased fuel temperature. According to

almost no deviation of calculated and measured

values for U-238, we conclude that fuel

Isotope Pu-239 is formed from fertile U-

238 by absorption of a resonance and thermal

neutrons and then undergoing double decay

through U-239 and Np-239 isotopes. On the

other hand, Pu-239 has very high absorption

6

BRANISLAV VRBAN et al.

temperature was modelled in appropriate way.

As shown above, the concentration of Pu-239

is sensitive to the level of system under-

moderation due to its very high absorption

cross-section for thermal neutrons. The

comparison of results shows the good

agreement for Pu-239 nuclide and both

samples; therefore, we assume that fuel density

and system under-moderation was modelled

correctly.

Fig. 11. Comparison of results – sample 182.

The precursor of Np-237, which

precedes formation of U-232 and thus limits

fuel reprocessing by Tl-208 gamma radiation,

is the U-236, of which the calculated

concentration lies near to the measurement

error boundary.

Fig. 9. Comparison of results – sample 182.

It is worth mentioning, that overall

results of sample No. 182 are systematically

closer to the measured values. The reason of

this behaviour is not clear to us and should be

investigated further.

Fig. 12. Comparison of results – sample 21.

The minor actinides concentrations are

underestimated varying on the nuclide to

nuclide basics. The Am-241 concentration is

slightly underestimated (approx. -4 to -10%).

This deviation should be taken into account in

follow-on criticality and decay heat

calculations.

Fig. 10. Comparison of results – sample 21.

Contrary, the final concentration of Pu-

241 is slightly underestimated by approx. 5 to

10 %. This underestimation can influence the

multiplication properties of final spent fuel

configuration. In case of the neutron absorbing

materials the concentration of Pu-238 is

significantly

overestimated,

what

is

Fig. 13. Comparison of results – sample 182.

compensated by underestimating of Np-237.

7

ON BURNUP MODELLING ISSUES ASSOCIATED WITH VVER–440 FUELS

The Fig. 10 to Fig. 15 mainly show

results for fission products, for which most

calculation results lies slightly under or in the

error range of measurements.

VVER-440 reactors. The influence of

calculation approaches and parameters have

been summarized, however much more

effort is needed, and further calculations are

planned. It was demonstrated that special

care should be given to Gadolinium bearing

pins. Surprisingly the constant by flux

depletion option does not play a significant

role in the concentration calculations. The

influence of operational history to final

reactivity was proven and briefly analysed.

The

concentration

of

boron

acid

significantly influences Pu-239 production

as a function of burnup. It was found out

that with respect to reactivity the use of

minimum specific power seems to be

conservative modelling option. The relevant

effect was found in the case of variations of

Fig. 14. Comparison of results – sample 214

The higher discrepancies can be found

for Cs-134 (-30 %), Sm-148 (-19 %) and Ag-

109 (80 %) nuclides. The results of Cs-137 as

the primary source of penetrating gamma

radiation from spent fuel until 300 years of

discharge are satisfactory and lie under the

measurement errors.

moderator/coolant

temperature.

This

observation just supports the fact that axial

depletion should be carefully considered

where mainly the moderator temperature

plays a vital role. In fact, all investigated

parameters have little effect on fission-

product worth. The most sensitive isotope in

all investigated cases was Pu-239 isotope.

To assess the currently developed Best

Modelling Approach the comparison between

the calculation results and experimental data

from Novovoronezh NPP was provided.

Results obtained indicate that the U-235

Fig. 15. Comparison of results – sample 182

calculation

overestimates

the

average

III. CONCLUSIONS

measurement value approximately by 20 %.

The minor actinides concentrations were in

general underestimated, where in case of Am-

241 the underestimation reached approximately

-10%. For the investigated fission products, the

good agreement was achieved, where most

calculation results fell into the error range of

measurements. The higher discrepancies were

identified in the case of Cs-134 (-30 %)

nuclide.

The analysis of spent nuclear fuel

properties and nuclide compositions is a

very important stage for the nuclear fuel

cycle as well as for neutron-physical

calculations of VVER-type reactor cores

and their future improvement. This paper

described the main results of analyses

performed to achieve a better understanding

of the modelling issues associated with

8

BRANISLAV VRBAN et al.

[4]. L. Markova, F. Havluj, “Simplified

This work was based on simplified

benchmark definition and is affected by user

experience and chosen modelling approach.

The influence of the used cross-section library

is questionable and will be further investigated.

In the case of simplified benchmark, the higher

number of energy groups can bring better

results mainly for the main and minor

actinides, however, used 52 group library is

already optimized for pressurized water

reactors. Therefore, other approaches and

nuclear data libraries should be studied to

support the “best practices” used for VVER-

440 burnup credit calculations.

Benchmark Specification based on #2670

ISTC VVER PIE”, Proc. The 12th Meeting of

AER Working Group E, Modra, Slovakia,

April 16-18, 2007.

[5]. M. D. DeHart, “High-Fidelity Lattice Physics

Capabilities of the SCALE Code System Using

TRITON”, The American Nuclear Society and

the European Nuclear Society 2007 Int. Conf.

on Making the Renaissance Real, Washington,

D.C., Trans. Am. Nucl. Soc. 97, 598-600,

2007.

[6]. B. J. Ade, “A primer for Light Water Reactor

Lattice

Physics

Calculations”,

ORNL,

U.S.NRC, NUREG/CR-7041, 2012.

ACKNOWLEDGEMENT

[7]. M.B. Chadwick, et al., ″ENDF/B-VII.0: Next

Generation Evaluated Nuclear Data Library

for Nuclear Science and Technology″,

Nuclear Data Sheets, vol. 107, pp. 2931-

3060, 2006.

This study has been partially financially

supported by the Slovak Research Development

Agency No. APVV-16-0288 and by the Scientific

Grant Agency of the Ministry of Education of

Slovak Republic No. VEGA 1/0863/17.

[8]. M. B. Chadwick, M. Herman, P. Obložinský et

al, “ENDF/B-VII.1 Nuclear Data for Science

and Technology: Cross Sections, Covariances,

Fission Product Yields and Decay Data”,

Nuclear Data Sheets, vol. 112, no. 12, pp.

2887-2996, 2011.

REFERENCE

[1]. ORNL,

SCALE,

“A

Comprehensive

Modelling and Simulation Suite for Nuclear

Safety Analysis and Design”, Version 6.1,

ORNL/TM-2005/39, 2011.

[9]. B. Vrban, et. al., “The VVER-440 Burnup

Credit Computational Benchmark Used for the

SCALE System Qualification”, In APCOM

2018: 24th International conference on applied

physics of condensed matter, Slovak Republic.

AIP Publishing, 2018.

[2]. M.D. DeHart, ″Sensitivity and Parametric

Evaluations of Significant Aspects of Burnup

Credit for PWR Spent Fuel Packages″,

ORNL/TM-12973, Lockheed Martin Energy

Res. Corp., Oak Ridge Nat. Laboratory, 1996.

[10].L. J. Jardine, “Radiochemical Assays of

Irradiated VVER-440 Fuel for Use in Spent

Fuel Burnup Credit Activities”, Lawrence

Livermore National Laboratory, UCRL-

TR212202, April 2005.

[3]. M.D. DeHart, ″Parametric Analysis of PWR

Spent Fuel Depletion Parameters for Long

Term Disposal Criticality Safety″, ORNL/TM-

1999/99, Lockheed Martin Energy Res. Corp.,

Oak Ridge National Laboratory, 1999.

9

Nuclear Science and Technology, Vol.9, No. 2 (2019), pp. 10-16

Estimation of Tritium Production in VVER-440 Reactor

Core During Normal Operation

Štefan Čerba^1,2, Jakub Lüley¹, Branislav Vrban¹, Filip Osuský¹, Vladimír Nečas¹

¹Slovak University of Technology in Bratislava, Faculty of Electrical Engineering and Information

Technology, Institute of Nuclear and Physical Engineering, Ilkovičova 3, 812 19 Bratislava, Slovakia

²B&J NUCLEAR Ltd., Alžbetin Dvor 145, 900 42 Miloslavov, Slovakia

Email: [email protected], [email protected], [email protected], branislav.vrban@stuba.sk,

[email protected], [email protected]k

(Received 12 November 2019, accepted 19 November 2019)

Abstract: Slovakia as one of the world leading countries in the share of nuclear power in electricity

production and currently operates 2 nuclear power plants, each with 2 VVER-440 units. In addition to

these reactors there are 2 VVER-440 units under construction and 2 units in decommissioning. The

VVER-440 technology features thermal neutron spectrum, low enriched uranium dioxide fuel and

light-water coolant, diluted boric acid and 37 emergency reactivity control assemblies with boron steel

absorber. Due to the presence of ¹⁰B in the coolant/moderator which has high thermal neutron capture

cross-section, the absorption of neutron on these atoms may lead to tritium production. Tritium

strongly contributes to the level of radioactivity of the primary coolant, therefore the NPP staff must

have appropriate knowledge of its production during operation. This paper focuses on the estimation

of the tritium production for a specific scenario of the operation of the 3^rdunit of Mochovce NPP. For

simulations the SCALE6 system is used with the detailed calculation model developed at the B&J

NUCLEAR ltd. company. The calculations presented in the paper are performed using self-shielded

multi-group cross-section libraries, taking into account the operation conditions of Mochovce unit 3

NPP in the first fuel campaign.

Keywords: Tritium production, VVER-440, activity, criticality, SCALE system, Mochovce NPP.

has high isotopic exchange rate, high

residence time in the environment, long half-

life (12.3 years) and can easily leak into the

environment in a form of water. In addition,

the limits for radioactive releases allow the

dilution of tritium (12 GBq per year), in order

to decrease its volumetric activity, in waste

waters exiting the nuclear power plant. If

tritium is not separated effectively from

biosphere, it will become a part of the global

cycle. Once it is absorbed through food or

water, it will steadily exist in human body for

long time and induce internal radiation

damage [1].

I. INTRODUCTION

The light-water coolant as passes

through the reactor core, to remove the

generated heat from fuel assemblies, gets

activated by capturing moderated neutrons.

During normal operation numerous neutron

induced reactions take place, generating a

variety of radioactive nuclides, such as ¹⁶N,

¹⁷N, ¹⁴C or ³H. Due to the relatively long half-

life of the majority of these activation

products, their concentration in the primary

coolant directly influences the radiation

exposure

of

personnel

performing

maintenance activities. Among all radioactive

nuclides produced during reactor operation

tritium (³H) is one of the most important. It

VVER reactors are the most frequently

built reactor types in the world. The first units

ŠTEFAN ČERBA et al.

with predecessors of VVER-440 type reactors

experience of the research team with

evaluating neutron physical characteristics of

VVER-440 units for the Nuclear Regulatory

Authority of Slovak Republic for more than 3

years [5].

were erected at the Novovoronesh NPP site in

1972 and 1973 [2]. The second step in the

development of VVER-440 type reactors was

the V-230 design which was mainly

constructed in the period from 1973 to 1982.

The third step in VVER-440 development was

the V-213 reactor design. Slovakia has four

nuclear reactors of this type generating half of

its electricity and two more under construction.

In 1972, construction of the Jaslovské

Bohunice V1 plant commenced, with two

VVER-440 V-230 reactors. The first was grid

connected in 1978, the second two years later.

The V2 units commenced operation in 1984

and 1985. The Slovak NPP Mochovce with

VVER-440 V-213 units 1 and 2 were put in

operation in the summer of 1998 and the end of

year 1999 due to the construction delay caused

by political changes in the early 1990s. Two

another units 3&4 of VVER-440 V-213 are

currently under construction in Mochovce and

are planned to be put in operation in 2020 [3].

Since the operation of the Jaslovské Bohunice

V2 NPP and the first two units of Mochovce

NPP started decades ago, estimation of the

tritium inventory through calculation would be

a very challenging issue. However, the

construction of the 3^rdunit of Mochovce NPP

provides unique opportunity to develop a new

methodology to numerically estimate the

production rate of tritium in its primary coolant

and to compare the result with real experiment,

once the reactor is put into operation.

II. OVERVIEW OF THE CALCULATION

METHODOLOGY

A. The VVER-440 reactor core

The detailed and precise 3D model of

the VVER-440 V-213 reactor has been

developed for criticality and shielding

calculations in the KENO-VI code of the

SCALE6 system. The whole-core 3D model is

shown in Fig. 1 . It consists of the reactor in-

vessel components, such as fuel assemblies

(including fuel rods, upper spacer grid,

intermediate spacer grids, supporting grid,

mixing grid, central tube and fuel endings),

emergency reactor control assemblies (ERC -

absorber and fuel part), core basket, barrel and

the reactor pressure vessel. The boundaries of

the created VVER-440 whole-core model are

given by the outer surface of the dry shielding,

the level of hot-leg piping and the basement of

filtration mechanism [3].

The VVER-440 fuel assemblies (FAs)

are of hexagonal shape and consist of 126

UO₂fuel pins, placed in the assembly in a

triangular grid pattern. The bundle of fuel

rods in the assembly is enclosed in a

hexagonal wrapper with 145 mm width across

the flat. The fuel assemblies and emergency

reactor control assemblies are positioned in a

hexagonal grid with a spacing of 147 mm.

The fuel rods are located in the bundle in a

triangular grid pattern with 12.3 mm pitch.

The fuel rod cladding is made from E110

zirconium alloy, while the wrapper tubes of

FA and ERC are made from E125 zirconium

alloy [3].

This paper presents the first step of a

complex joint long-term research activity

between the Slovak University of Technology

in Bratislava and the B&J NUCLEAR ltd.

research company. This activity is based on

the detailed 3D model of the VVER-440

reactor core developed in the state-of-the art

SCALE6 [4] calculation system and the

11

ESTIMATION OF TRITIUM PRODUCTION IN VVER-440 REACTOR CORE …

(EFPD) without requiring the positions of the

ERC assemblies to be adjusted. Compared to

the ERC assemblies the boric acid ensures

uniform distribution of absorber in the core,

however requires time consuming dilution, if

its concentration is to be decreased, and may

cause positive reactivity feedback, in case of

high concentration. The critical boron acid

concentration was calculated using the

ANDREA macro code [6]. This code, the

product of Nuclear Research Institute (NRI)

REZ, has been being developed since 2005.

Fig. 1. KENO 3D model of the VVER-440 V-213

The code is designed to support safety analyses

of VVER type reactors [7]. The results of

reactor core

critical boric acid concertation are shown in

Fig. 3 .

Fig. 2. Equivalent sixth of the fuel loading pattern

As it was mentioned in the introduction

part, the analysis presented in this paper was

carried out for the first fuel loading of

Mochovce unit 3, considering a simplified

approach. This approach assumes fresh fuel

g/kg. As a result of fuel burnup, the reactivity

composition without burnup through the cycle

and variable critical boron acid concentration

boric acid concentration that reaches 0 g/kg at

and coolant cycling. The fuel loading pattern

Fig. 3. Critical boric acid concentration through the

fuel cycle

As it can be seen, the critical boric acid

concentration of fresh fuel (0 EFPD) is 5.059

of the system decreases, so does the critical

266.95 EFPD. Usually, after the boric acid

concentration has reached zero, the operation

used in the present analysis is shown in Fig. 2 .

Due to the 60° symmetry of the core, only one

of the reactor continues by withdrawing the

sixth of the pattern is presented. The fuel

ERC assemblies from operation position (in

loading pattern is based on our previous work

our case 225 cm) to the upper edge of the core

and consists of FA and ERC assemblies with

2.4 % and 3.6% enrichment of ²³⁵U [2].

(250) and by decreasing the reactor power

(1741 MWth in our case), core inlet

temperature (268 ℃) and the pressure at the

B. Critical boric acid concentration

main steam collector, however these

operational regimes were not considered in our

analysis.

The critical boric acid concentration is a

concentration that ensures critical state of the

reactor for the given effective full power day

12

ŠTEFAN ČERBA et al.

density of the sought atoms at the given time

C. Dilution of boric acid

step. Since the functions of concentrations of

¹H, ²H and ¹⁰B, ¹¹B atoms are relatively

complex the fuel cycle (0 – 266.95 EFPD) has

been divided to 9 intervals while a simple

exponential fit was used for each interval.

By operating the reactor for certain

EFPDs the reactivity of the system decreases.

To ensure criticality, the reactivity bond by

boric acid is released by diluting its

concentration. The dilution is performed by

pumping out a certain amount of moderator

and replacing it with demineralized H₂O. As

the boric acid is diluted the concentration of

¹⁰B and ¹¹B atoms decreases, however the

concentrations of ¹⁶O, ¹H and ²H proportionally

D. Calculation of tritium inventory in

coolant

The calculation of tritium inventory in

the first fuel loading of Mochovce NPP unit 3

was performed in the KENO-VI module of the

SCALE 6.1.3 system, based on assumption

presented in the previous chapters. SCALE6 is

a comprehensive modelling and simulation

suite developed for nuclear safety analyses by

the Reactor and Nuclear Systems Division

(RNSD) of the Oak Ridge National Laboratory

(ORNL). The KENO-VI is a Monte Carlo

criticality solver designed to calculate the k_eff

and other quantities of three-dimensional

systems. The KENO-VI criticality calculations

were performed using 238g cross-section

libraries based on ENDF/B-VII.0 [8] evaluated

data and with cell treatment using the

CENTRM/PMC sequence.

2

increase. The concentrations of ¹⁰B and H

atoms in coolant are illustrated in Fig. 4 and

Fig. 5 .

Fig. 4. Concentration of ¹⁰B in coolant through the

fuel cycle

The analysis was split into several

calculation steps, while the steps represented

the reactor operation between 0-5, 5-15, 15-30,

30-60, 60-100, 100-140, 140-180, 180-220

and 220-266.95 EPFD. For each time bin a

stand-alone calculation was carried out with

the same reactor power, ERC position,

temperatures, fresh fuel composition and

variable coolant isotopic composition. The

( )

isotopic composition of isotope in

Fig. 5. Concentration of ¹H in coolant through the

coolant was calculated using Eq. (1) and the

dilution coefficients were derived from the

exponential functions Fig. 4 and Fig. 5 . The

neutron flux was estimated to be constant

within a given calculation step.

fuel cycle

In order to use these concentrations in

the estimation of ³H inventory, the

concentrations should be substituted by simple

functions that accurately represent the number

( )

(1)

13

ESTIMATION OF TRITIUM PRODUCTION IN VVER-440 REACTOR CORE …

To estimate the isotopic composition of

tritium, 3 production routes were considered:

( )

(6)

(7)

 Eq. (2) - (n,α) on and subsequently

(n,nα) on - 21 kbarn * 50 mbarn thermal XS

 Eq. (3) - (n,t2α) on – 0.4 barn thermal

XS

( )

²H component can be

( )

The

 Eq. (4) - (n,γ) on and subsequently (n,γ)

on – 28 barn * 40 mbarn thermal XS

( )

calculated by Eq. (8) and the

2

10

component of H and the concentrations of B

and ¹H can be calculated by Eq. (1).

(

)

→

+

(2)

(3)

(4)

(

→

)

( )

(8)

(

)

→

In the above mentioned equations

(

)

(

)

→ →

represents the sum of the group-by-group flux

weighted collision rate of nuclide and

(

)

reaction , which can be defined by Eq.

Considering

the

abovementioned

̅̅̅̅̅̅̅

( )

(9), where is the volume integrated

average neutron flux, defined by Eq. (10).

reactions and the radioactive decay of tritium

with 12.3 y. half-life, the tritium balance

equation can be written as follows:

̅̅̅̅̅̅̅

( )

∑

(9)

( )

(10)

̅̅̅̅̅̅̅

( )

∫ ∑

(5)

( )

In

each

calculation

step

the

3

concentration of H was estimated using the

calculated neutron flux, weighted XS and

concentrations of nuclides in the coolant.

However, the concentrations of the coolant

changes also during a single calculation step,

thus this change has to be taken into account,

for instance by assuming constant neutron flux

and the time integral of number densities

through the time step. Since the coolant

circulates with 2.5 m/s velocity, it takes

approximately 1 s to go through the fuel core,

to get activated by thermal neutrons, and

additional 17 s to run through the rest of

primary circle (PC) and to come back to the

( )

where

,

( )

and are the time dependent

3

2

3

7

10

concentration of H, H, H, Li and B in the

unity of volume,

the ³H decay constant

,

and

are the microscopic cross-

sections of (n,α), (n,t2α) and (n,γ) reactions and

is the corresponding neutron flux. The time

dependent concentrations of Li and H can be

7

2

( )

defined by Eq. (6) and Eq. (7), where

2

represents the concentration of H as result of

( )

as result of

moderation dilution and

(n,γ) reaction on ¹H atoms.

3

core. The activation of H can be calculated in

14

ŠTEFAN ČERBA et al.

two ways, by taking into account the

F. Discussion

The number density and the activity of

circulation time ( = in-core time) and the total

volume of coolant in the primary circuit or by

neglecting circulation ( = in-core + out-of-

core time) and using only the volume of

moderator in the core.

³H is strongly influenced by the assumption of

coolant circulation. The difference in the total

³H activity is more than 40 %. Due to

decreasing boron concentration saturation of

3

the curve of H number density can be seen.

E. Results

10

Among all reactions 87.95 % occurred on B,

The results of the tritium concentration

are presented in Fig. 6 , where CASE 1

represents the conditions where only the in-

core time was taken into account and CASE 2

the conditions where the total-time (in + out)

was considered. The atom concentrations were

achieved by multiplying the result achieved by

solving Eq. (5) by the neutron source term

(4.523E19 n/s). The results of total and

volumetric tritium activities at the end of fuel

cycle (266.95 EFPD) are shown in Table I. The

volume of moderator for CASE 1 represents

the total volume in primary circuit and for

CASE 2 the volume in the core.

2

7

11.57 % on H and 0.48 % on Li. In CASE 1

3

the total volumetric activity of H reached 9.64

MBq/l and in CASE 2 5.69 MBq/l. Just for

better imagination, this activity is more than 28

000 or 56 000 times higher than the

3

international limit for H in drinking water [9].

According to document [10] published in 2018,

the total released activity of tritium per one

reactor unit is 2441.5 GBq. Compared to our

results this value is approximately 3 times

higher. However, considering the difference in

the critical boric acid concentrations,

enrichment, fuel cycle length and the rough

estimation of coolant circulations, the results

are acceptable.

Table I. Tritium activity at the end of fuel cycle

No

circulation

Coolant assumption

Circulation

III. CONCLUSION

Decay const. [s^-1]

Moderator V. [m³]

Total activity [Bq]

Vol. activity [Bq/l]

2.5638E-09

In this paper the results of the first

approach to estimate the tritium production rate

in the Slovak NPPs was presented using

SCALE6, the ANDREA diffusion solver and

several in-house c++ utilities. The estimation

of the tritium inventory was performed

assuming fresh fuel isotopic composition,

reference core parameters, and various critical

boric acid concentration, calculation by the

ANDREA code. Three nuclear reactions were

242.00

12.77

7.6107E11 4.4917E11

9.6403E06 5.6895E06

7

taken into account, ¹⁰B (n,α) followed by Li

1

2

(n,nα), ¹⁰B (n,t2α) and H (n,γ) followed by H

(n,γ). The change of the moderator isotopic

composition was assumed by using an

exponential fit through a calculation step. The

total tritium activity was assumed either by

considering the coolant circulation time with

Fig. 6. Concentration of ¹H in coolant through the

fuel cycle

15

ESTIMATION OF TRITIUM PRODUCTION IN VVER-440 REACTOR CORE …

Portorož, ISBN 978-961-6207-39-3 Slovenia,

September 5-8, 2016.

the total coolant volume (reference case) or by

neglecting circulation and using only the

volume of coolant in the model. In the

reference scenario the volumetric activity of

tritium at the end of fuel cycle reached 9.64

MBq/l. Among this activity 87.95 % was

[3]. F. Osuský, B. Vrban, Š. Čerba, J. Lüley, V.,

Nečas, ″Effective dose calculation in the

VVER-440 reactor maintenance area″, In 28th

Symposium of AER on VVER Reactor

Physics and Reactor Safety. Olomouc: Nuclear

Research Institute, 2018.

10

produced due to the B (n,t2α), and 11.57 %

2

by H (n,γ) reactions, thus in further steps it

[4]. ORNL,

SCALE,

“A

Comprehensive

will be justified to neglect the minor tritium

Modelling and Simulation Suite for Nuclear

Safety Analysis and Design”, Version 6.1,

ORNL/TM-2005/39, 2011.

7

producing reaction on Li. In the following

steps of this research activity several

improvements will have to be done. First of all,

it will be necessary to use a more complex

exponential fit of number densities for coolant

dilution. It will be required to better assume the

circulation time through the core and the

neutron flux that contributes to tritium

activation. In addition, fuel burnup will also

have to be taken into account. After having our

methodology improved, it will be implemented

in the complex calculation system to optimize

the fuel loading pattern of VVER-440 reactors

in Slovakia.

[5]. B. Vrban, Š. Čerba, J. Lüley, F. Osuský, V.,

Nečas, ″Criticality safety calculation of

VVER-440 core by SCALE system″, In 28th

Symposium of AER on VVER Reactor

Physics and Reactor Safety. Olomouc: Nuclear

Research Institute, 2018.

[6]. F. Havlůj, R. Vočka, J. Vysoudil, ″ANDREA

2: Improved version of code for reactor core

analysis″, In: Proceedings of the 22nd

International

conference

on

Nuclear

Engineering, Prague, Czech Republic, July 7-

11, 2014.

[7]. B. Vrban, Š. Čerba, J. Lüley, V. Nečas,

ACKNOWLEDGEMENT

“Current

Status

of the

WWER-440

Engineering Core Calculations at the Slovak

University of Technology in Bratislava”, Proc.

Power engineering 2018. Energy-Ecology-

Economy 2018, Tatranské Matliare, ISBN

978-80-89402-98-4 Slovakia, Jun 5-7, 2018.

This study has been partially financially

supported

by

the

Slovak

Research

Development Agency No. APVV-16-0288 and

by the Scientific Grant Agency of the Ministry

of Education of Slovak Republic No. VEGA

1/0863/17. Special thanks go also to B&J

NUCLEAR ltd.

[8]. M.B. Chadwick, et al., ″ENDF/B-VII.0: Next

Generation Evaluated Nuclear Data Library for

Nuclear Science and Technology″, Nuclear

Data Sheets, vol. 107, pp. 2931-3060, 2006.

REFERENCE

[9]. Canada´s Nuclear Regulator, “Standard

Guidelines for Tritium in Drinking Water”,

Part of the Tritium Studies Project, Minister of

Public Works and Government Services

Canada, ISBN 978-0-662-474997-5, January

2008.

[1]. ANS, “Nuclear criticality safety in operations

with fissionable materials outside reactors”,

American National Standards Institute, La

Grande Park Illinois, USA, 2014.

[2]. Vrban, Š. Čerba, J. Lüley, F. Osuský,

“Determination of the Computational Bias in

Criticality Safety Validation of VVER-

[10].P. Bryndziar, V. Balev., “Report on monitoring

releases and readioactivy arround the

Mochovce NPP” (in Slovak), Slovenské

elektrárne, a.s., Mochovce, May 2018.

440/V213”,

Proc.

25th

International

Conference Nuclear Energy for New Europe,

16

Nuclear Science and Technology, Vol.9, No. 2 (2019), pp. 17-24

Processing of the multigroup cross-sections

for MCNP calculations

Jakub Lüley^1,2, Branislav Vrban¹, Štefan Čerba¹,

Filip Osuský¹, Vladimír Nečas¹

¹Slovak University of Technology in Bratislava, Faculty of Electrical Engineering and Information

Technology, Institute of Nuclear and Physical Engineering, Ilkovičova 3, 812 19 Bratislava, Slovakia

²B&J NUCLEAR Ltd., Alžbetin Dvor 145, 900 42 Miloslavov, Slovakia

E-mail: [email protected], [email protected], [email protected], ,

[email protected], [email protected]k

(Received 13 November 2019, accepted 19 November 2019)

Abstract: Stochastic Monte Carlo (MC) neutron transport codes are widely used in various reactor

physics applications, traditionally related to criticality safety analyses, radiation shielding and

validation of deterministic transport codes. The main advantage of Monte Carlo codes lies in their

ability to model complex and detail geometries without the need of simplifications. Currently, one of

the most accurate and developed stochastic MC code for particle transport simulation is MCNP. To

achieve the best real world approximations, continuous-energy (CE) cross-section (XS) libraries are

often used. These CE libraries consider the rapid changes of XS in the resonance energy range;

however, computing-intensive simulations must be performed to utilize this feature. To broaden our

computation abilities for industrial application and partially to allow the comparison with

deterministic codes, the CE cross section library of the MCNP code is replaced by the multigroup

(MG) cross-section data. This paper is devoted to the cross-section processing scheme involving

modified versions of TRANSX and CRSRD codes. Following this approach, the same data may be

used in deterministic and stochastic codes. Moreover, using formerly developed and upgraded cross-

section processing scheme, new MG libraries may be tailored to the user specific applications. For

demonstration of the proposed cross-section processing scheme, the VVER-440 benchmark devoted to

fuel assembly and pip-by-pin power distribution was selected. The obtained results are compared with

continues energy MCNP calculation and multigroup KENO-VI calculation.

Keyword: MCNP, Multigroup calculation, VVER, criticality

flux, implicit sensitivity coefficients or adjoint

flux and to perform cell treatment, S/U

calculation can be still memory and time

expensive and special attention must be given to

the preparation of the covariance matrix. [1,2,3]

Alternatively, the multigroup option is still an

effective method for other applications and in

case of cross-section adjustment, it can also

extend the applicability of S/U calculation. The

main advantage of multigroup calculation is not

only in the reduction of the calculation time but

also offers to an engineer utilization of the

adjoint calculations in problems where the

forward transport calculation is not efficient. [4]

I. INTRODUCTION

A lot of effort has been spent on the

development of techniques to effectively

compute sensitivity coefficients and cross-

section induced uncertainties (S/U) by Monte-

Carlo codes and continues-energy libraries.

MCNP6 and SCALE6.2 have currently

implemented approaches to calculate the

adjoint weighted tallies, which allow both

codes to carry out S/U analyses related to

criticality safety calculations using CE

libraries. Although, it is no necessary for CE

libraries to calculate flux moments from mesh