Computational burnup analysis of the TRIGA Mark II research reactor fuel

Progress in Nuclear Energy 130 (2020) 103536

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Computational burnup analysis of the TRIGA Mark II research reactor fuel
ˇ ˇc a, Luka Snoj a, b, *
Anˇze Pungerˇciˇc a, b, Duˇsan Cali
a
b

Reactor Physics Department, Joˇzef Stefan Institute, Jamova cesta 39, 1000, Ljubljana, Slovenia
Faculty of Mathematics and Physics, University of Ljubljana, Jadranska ulica 19, 1000, Ljubljana, Slovenia

A R T I C L E I N F O

A B S T R A C T

Keywords:
TRIGA research reactor and Fuel Burnup
Operational history analysis
Serpent-2
TRIGLAV
Excess reactivity measurements

In this study, analysis of the complete operational history of the “Joˇzef Stefan” Institute (JSI) TRIGA reactor was
performed. Reactor power changes, core configurations and weekly excess reactivity measurements were ana­
lysed to obtain the needed data for fuel burnup calculations. More than 50 years of reactor operation was
simulated using deterministic code TRIGLAV and stochastic code Serpent-2. The calculated core reactivities are
in good agreement compared with the excess reactivity measurements. Code-to-code comparison is presented.

Clear agreement is observed when comparing changes in core excess reactivity, and discrepancies are observed in
the comparison of individual fuel element burnup and its isotopic composition. The Serpent-2 results are in better
agreement with the measurements compared to the TRIGLAV code; nevertheless, a conclusion can be made that
the TRIGLAV code is viable for TRIGA fuel management and burnup analysis. A three-dimensional (3D) burnup
study was conducted, where individual fuel elements were further divided into multiple angular and axial
depletion zones. Notable burnup effects were observed, and an explanation using surrounding water distance is
presented.

1. Introduction
Determination of fuel element burnup in research reactors is an
important activity, as it is related to fuel utilisation and management,
characterisation of radiation fields in the reactor, reactor safety pa­
rameters and safety analyses, as well as spent fuel management. The
“Joˇzef Stefan” Institute (JSI) has been operating a TRIGA Mark II reactor
(Douglas et al., 2003) since 1966. Over this time, multiple burnup cal­
culations and measurements have been performed (Ravnik et al., 1999;
ˇ
Zagar
and Ravnik, 2000; Perˇsiˇc et al., 2000; Jeraj et al., 2002). Mea­
surements were performed using the fuel element reactivity worth
method (Ravnik et al., 1987). Burnup calculations for the JSI TRIGA
reactor were performed using only part of the operational history with
simplified operational data; this was done because the operational his­
tory analysis was not available. Burnup was calculated with determin­
istic codes, such as the in-house developed TRIGLAV code (Jeraj et al.,
2002; Perˇsiˇc et al., 2017). TRIGLAV is a two-dimensional (2D) diffusion
code used for calculation of fuel element burnup, excess reactivity and
power peaking factors (Snoj and Ravnik, 2008). As the TRIGA core is
highly heterogeneous and asymmetric, three-dimensional (3D) Monte
Carlo codes are superior to diffusion codes for burnup calculations.

Hence, we decided to repeat the analysis (reactivity worth of important

isotopes) using modern tools, which enable 3D Monte Carlo burnup
calculations using detailed operational data. Our goal was to improve
the TRIGA burnup analysis using modern burnup codes and validate the
results with multiple excess reactivity measurements. The JSI TRIGA
reactor had well-recorded individual reactor operation from 1966 to the
present. We decided to obtain the operational data and simulate the
complete history using reactor physics and burn-up code Serpent-2
(Leppă
anen et al., 2015; Maria, 2016). Only a few TRIGA reactors have
this much information available regarding its operation (Chiesa et al.,
2016; Idris Lyric et al., 2013; Khan et al., 2010; El Bakkari et al., 2013).
In addition, two experiments (i.e. criticality and fission rate profile)
performed at the JSI TRIGA reactor have been published in the ICSBEP
and IRPhEP handbooks (Jeraj and Ravnik, 2010). Several other exper­
iments that can be used for validation of computer codes and models
have been performed at the JSI TRIGA reactor (Raduloviˇc et al., 2014;
ˇ
Goriˇcanec et al., 2015; Stancar
et al., 2018; Ambrozic et al., 2020).
Our primary goal was to record and digitalise the complete opera­
tional history, different core configurations and individual reactor op­
erations for the purpose of experimental validation of computer codes
and models. As for the need for burnup experiments, we also decided to
analyse weekly excess reactivity measurements. The analysed opera­
tional history is presented in the first part of the paper.

* Corresponding author. Reactor Physics Department, Joˇzef Stefan Institute, Jamova cesta 39, 1000, Ljubljana, Slovenia.
E-mail addresses: (A. Pungerˇciˇc), (L. Snoj).

/>Received 22 June 2020; Received in revised form 29 September 2020; Accepted 9 October 2020
Available online 23 October 2020
0149-1970/© 2020 The Authors.
Published by Elsevier Ltd.
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A. Pungerˇciˇc et al.

Progress in Nuclear Energy 130 (2020) 103536

Due to the significant amount of fuel shuffling throughout the history
and diverse reactor operation, we developed an automated script called
STRIGA (Pungerˇciˇc et al., 2019). This script creates a Serpent 2 input of
the TRIGA research reactor (Calic et al., 2016) based on the loading
scheme, fuel element composition and burnup parameters, and it pre­

pares necessary inputs for Monte Carlo burnup calculations. This
methodology, together with that employed in the TRIGLAV code, is
presented in the second part of this paper. The last part focuses on the
burnup calculations, comparison between both codes, and most impor­
tantly, the validation performed using the excess reactivity
measurements.

Fig. 1. Schematic view of the “Joˇzef Stefan” Institute (JSI) TRIGA fuel elements
with its dimensions. Two different types of fuel elements based on cladding are
presented: Stainless steel SS-304 (top) and aluminium AL (bottom).

samarium disk above and below. In addition, the fuel elements are
divided into three groups. The first two groups have 8.5 wt. % or 12 wt.
% of 19.9 % low enriched uranium (LEU) in the U–Zr–H mixture, while
the third one is 8.5 wt % of 70 % high enriched uranium (HEU) in the
U–Zr–H–Er. The latter is a so-called FLIP fuel element, and it contains
erbium as a burnable absorber. In this study the fresh fuel element
composition was determined by considering recorded masses of 235 U
and 238 U. However, in 1999, all fuel elements except SS 12 wt % were
shipped back to the United States, meaning that burnup calculation is
the only way to determine their burnup and isotopic composition.
During the reconstruction of the JSI TRIGA reactor in 1991, the
control rods were replaced, and also another different one (transient)
was introduced. Since then four control rods have been in use: P =
transient, S = safety, R = regulating and C = shim. The latter three
feature a fueled follower SS 12% type fuel, which is thinner and has
rfollower = 1.66687 cm instead of rSS12 = 1.82245 cm, while for the
transient control rod, only air is left in its place when extracted. The
older control rods did not feature a fueled follower and were used in
different core position. Aluminium tube was left in their place when

extracted. In addition, the absorber for regulating control rod was
thinner, where rreg = 1.1 cm instead of rshim,safe = 1.6 cm. A schematic
view of the control rods before and after the reconstruction in 1991 is
presented in Fig. 2.

2. JSI TRIGA operational history analysis
The first part of our detailed burnup analysis is the JSI TRIGA Mark II
operational history analysis, which consists of several important parts
that are presented in detail in this section. These are as follows:
• Reactor description: description of the JSI TRIGA Mark II reactor.
• Reactor power changes: analysis of individual reactor operations to
accurately calculate released energy.
• Fuel shuffling: analysis of all of 240 core configurations used in the
complete operational history.
• Measurements of excess reactivity: analysis of weekly measure­
ments used for validating burnup calculations.
• Measurements uncertainty: evaluation of uncertainties in the
reactor operation parameters.

2.1. Reactor description
Analysis of reactor operation for the purpose of detailed burnup
determination was performed on a 250 kW TRIGA Mark II research
reactor at the “Joˇzef Stefan” Institute. Only a brief description of the
reactor is given here, comprising information that is important to un­
derstand the presented work; a more detailed description can be found
in descriptions of JSI TRIGA benchmark experiments (Raduloviˇc et al.,
ˇ
2014; Stancar
et al., 2018; Mele et al., 1994; Jeraj et al., 1997; Jeraj and
Ravnik, 2010; Ravnik and Jeraj, 2003).

The JSI TRIGA reached first criticality on 31st May 1966. Since then,
300 different fuel elements have been in use. Information regarding all
different types of fuel element is presented in Table 1. In general, two
types of fuel elements were used as follows: stainless steel (SS) with a
zirconium rod in the middle and aluminium (AL) without the middle
rod. These setups are presented in Fig. 1. The SS fuel element features a
molybdenum disk below the fuel region, while the AL fuel element has a

2.2. Reactor operation from 1966 to 2019
One of the most important parameters in burnup determination is the
energy released during reactor operation. Therefore, each operation
written in the reactor logbooks was analysed. In total, 50 logbooks or
approximately 20 000 pages were analysed (depicted in Fig. 3). Our goal
was to digitalise all the needed parameters for future burnup calcula­
tions. The energy released can be calculated from the reactor power
level, date and time of both reactor start-up and shut-down or power
change. A part of this information in a computer readable format is
presented in Table 2.
Using reactor operation data, the annual released energy in the
reactor core is obtained (depicted in Fig. 4). It can be seen that, after
1991, the energy released was reduced since the TRIGA reactor was no
longer used for isotope production. In recent years, the annual average
reactor power decreased, mostly due to the higher number of reactor
operations at lower power for detector testing, benchmark experiments
and similar activities (Goriˇcanec et al., 2015; Raduloviˇc et al., 2014;
ˇ
ˇ
Henry et al., 2015; Filliatre et al., 2015; Stancar
and Snoj, 2017; Stancar

Table 1
Material composition of four types of fuel elements that were in use in the JSI
ˇ
TRIGA Mark II research reactor (Zagar
and Ravnik, 2000). For each fuel element
type, its years of utilisation are depicted.
Fuel element name

AL 8.5 %

SS 8.5 %

SS 12 %

FLIP

U–ZrH
SS-304
12

U–ZrH–Er
SS-304
8.5

277
19.9 (LEU)

192
70 (HEU)

a

Fresh fuel element material composition
Fuel type
U–ZrH
U–ZrH
Cladding
Al
SS-304
Uranium content [wt.
8.5
8.5
%]
Uranium mass [g]
185
190
Uranium enrichment
19.9 (LEU)
19.9 (LEU)
[wt. %]
235
37
38
U [g]
Burnable absorber
Absorber content [wt.
%]
Years of usage

55

134

/
/

/
/

/
/

Er
1.5

1966–1983

1970–1996

1991–2018

1973–1991

Fig. 2. Schematic representation of control rods used before (bottom) and after
(top) the reconstruction of the reactor in 1991. Two different types of old
control rods were in use, differing in the absorber radius. Thicker (rabs =
1.6 cm) rod types were used for Shim (position C-03) and Safety (C-11) control
rods, while a thinner (rabs = 1.1 cm) rod type was used for the Regulating
control rod (E− 13).

a

Composition of individual fresh fuel elements can vary but no more than 1 %
from the depicted values.
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A. Pungerˇciˇc et al.

Progress in Nuclear Energy 130 (2020) 103536

Fig. 3. Photograph of all logbooks written in the history of the JSI TRIGA Mark II research reactor operation (left). Example of logbook input, where reactor startup
on 150 W, reactor power change to 250 kW and measurements of excess reactivity are depicted.
Table 2
Example of the JSI TRIGA reactor operation logbook digitalisation from first criticality in 1966 until 2019. For each operation core configuration, individual com­
mentary and reactor power, together with the starting and ending date-time [year-month-day hour:minute] is written. The table is regularly updated.
Operation No. [#]

Start-up [y-m-d h:m]

Preactor [kW]

End [y-m-d h:m]

Δt [h]

Erel. [MWh]

Etot [MWh]

Commentary

Core conf. No.

1
2
3
⋮

1966-5-31 14:15
1966-6-6 8:40
1966-6-6 13:50

0.005
0.02
14
⋮

1966-5-31 14:25
1966-6-6 9:50
1966-6-6 14:05

0.17
1.17
0.25

0
0
0.0035

0
0
0.0035
⋮

First criticality

1
1
1
⋮

27165

2019-2-5 13:15

0.15

2019-2-5 13:20

0.08

0.00

24007.04

2019-2-5 13:20

250

2019-2-5 15:22

2.03

0.51

24007.55

ρexcess measure.

240

27166

240

pulse duration ( ̃ 10 ms (Vavtar et al., 2020)); therefore it was not
considered in the burnup calculations.
2.3. Core configurations
Another important part of burnup calculation is the fuel shuffling
history. Throughout the history, the fuel element position in the core has
been changed several times. To acquire the positions, all core configu­
rations (in total 240) were analysed and digitalised so their loading
patterns could be used in the burnup calculations or for other activities.
An example of two recent core configuration changes is presented in
Fig. 5.
During the analysis of the reactor logbooks and the fuel shuffling, it
was found that some fuel elements of the SS 8.5 wt. % type were already
previously used in another TRIGA reactor in Frankfurt am Main, Ger­
many. The problem was that the burnup of those fuel elements is un­

known. Therefore, additional analysis, as presented in 4.1.1, was
performed to understand and evaluate the effect of not knowing the
burnup of these fuel elements. Another important discovery was that,
after the reconstruction in 1991 new fresh fuel elements of the SS 12 wt.
% type, which are still in use today, were mixed together with the old,

Fig. 4. Analysis of the JSI TRIGA Mark II reactor operation by each year from
its start in 1966 to the end of 2018. Annual released energy and average reactor
power are depicted for each year. Average reactor power was calculated as
∑
Pi ti
Pavg = top , where i presents individual operation and top represents total time
reactor was operational in 1 year.

et al., 2018). In addition the pulse mode operation started after the
reconstruction was analysed (Pungerˇciˇc and Snoj, 2018); however, the
energy released during the individual pulse is negligible due to the short

Fig. 5. Examples of three different core configurations of the JSI TRIGA reactor. Each fuel element is labelled with a four-digit identification number. All three core
configurations were established in 2018.
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A. Pungerˇciˇc et al.

Progress in Nuclear Energy 130 (2020) 103536

Fig. 6. Measurements of excess reactivity performed at the JSI TRIGA reactor in the complete operational history (left) and selected period of 9 months (right),
where changes due to core shuffling and burnup are visible. Four core configuration changes were employed in this period. Energy released during operation on core
configurations 30 and 32 is depicted.

The last part of the operational history analysis was to record all the
excess reactivity measurements. Excess reactivity has been determined
regularly every Monday since the start of the operation in 1966. Usually,
the JSI TRIGA reactor does not operate during the weekend, which
means that measurements are without xenon contribution. Changes in
excess reactivity are directly connected to fuel burnup or fuel shuffling,
as presented in Fig. 6. As these changes can be used to validate burnup
calculations, we have decided to analyse all 2000 measurements per­
formed in the complete operational history.

reduce the error. Recently, this uncertainty was reduced to 2 %–5 %
ˇ
with an improved thermal power calibration method (Stancar
and Snoj,
2017). Other negligible uncertainty related to released energy is also in
the reactor startup or power change as only time on power is written;
therefore, the energy released during the transient is not considered.
Uncertainties in excess reactivity measurements are more difficult to
evaluate since they depend on the changes in the reactor core. For the
comparison of absolute reactivity measurements, the 1σ uncertainty can
be up to 500 pcm due to the control rod-worth measurements (Trkov
et al., 1987; Merljak et al., 2018), reactor physical parameters (Filliatre
et al., 2015; Snoj et al., 2010; Henry et al., 2015) and power redistri­
bution due to control rod insertion (Goriˇcanec et al., 2015). In the
analysis of relative changes in excess reactivity, the assumed uncertainty
is much smaller as the same control rod-worth measurements are being
used, and the changes in reactor physical parameters and flux redistri­
bution are negligible if the core configuration is the same.

2.5. Major sources of measurement uncertainty

3. Methods of burnup calculations

A major source of uncertainty in the fuel burnup determination re­
lates to uncertainty in reactor power measurements. In small research
reactors, the power is normally calibrated with respect to a single
neutron detector. Its response is proportional to the flux at its position.
Local flux is proportional to the total flux (power) of the reactor only if
its radial and axial distributions do not change. However, this is not the
case in the research reactors where operational reactivity changes
(burnup, power defect, xenon effect) are compensated for by moving the
control rods. Redistribution effects on neutron flux distribution due to
control rod insertion/withdrawal detected by a single detector may be in
the order of 20 % yielding the same error in reactor power readings
ˇ
(Goriˇcanec et al., 2015; Zerovnik
et al., 2014, 2015). Using two or more
detectors strategically located at different locations around the core can

Until now, all burnup calculations for the JSI TRIGA Mark II, as
presented in (Jeraj et al., 2002), have been performed either by using the
TRIGLAV (Perˇsiˇc et al., 2017) fuel management deterministic code or
other unit-cell based burnup calculations. Usually the isotopic compo­
sition was obtained with a standalone burnup code (e.g. WIMS-D
(Kulikowska, 1996)) and then used in Monte Carlo code, MCNP. For
the experiments with burned core configurations, higher discrepancies
between the reactivity measurements and those calculated were
ˇ
observed (Zagar

and Ravnik, 2000). For this purpose, we have decided
(in addition of using the TRIGLAV code) to simulate the complete
operational history using the Monte Carlo neutron transport and burnup
ănen et al., 2015), which is known for its burnup
code Serpent-2 (Leppa
capability (Maria, 2016). Nuclear data libraries for both codes are based
on the ENDF/B-VII.1 (Chadwick et al., 2011) nuclear data. Comparison
of continuous (Serpent) and 69-group cross-section (WIMS-D) energy
dependence for total neutron incident on 235 U is presented in Fig. 7.

coupling the operational history before and after the reconstruction.
This makes the burnup analysis more complex, as the complete history
from 1966 must be considered. All the fuel shufflings are presented in
JSI TRIGA fuel shuffling animation (Reference to the online animation).
2.4. Measurements of excess reactivity

3.1. The TRIGLAV code
The TRIGLAV fuel management and burnup code was developed at
the Reactor Physics Department of the “Jozef Stefan” Institute. A general
description of the code is given in (Perˇsiˇc et al., 2017), and a detailed
description of the burnup calculation is provided in (Ravnik et al.,
1999). The code is based on a four-group diffusion equation for r − ϕ
geometry, solved by the finite difference method. The TRIGLAV pro­
gram package consists of a four group 2D diffusion module and the
WIMSD-5B code (Kulikowska, 1996), which is linked automatically to
the diffusion module to calculate unit-cell-averaged effective group
constants. All 91 positions in the reactor core are treated separately in
the unit-cell approximation. The TRIGLAV geometry model, presented
in Fig. 8, represents the full TRIGA cylindrical core and graphite

Fig. 7. Energy dependence for total 235 U microscopic cross-section. Continuous
(Serpent-2) and 69-group (WIMS) cross-sections are presented. The latter is
acquired from the WIMS Library Update Project (Coordinated Research), and it
is based on the ENDF/B-VIII.1 nuclear data library (Chadwick et al., 2011).
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Progress in Nuclear Energy 130 (2020) 103536

Fig. 8. TRIGA Mark II reactor geometry in the TRIGLAV model with homogeneous unit-cells (left). TRIGLAV code methodology schematic flow-chart (right).

Fig. 9. Schematic representation of the STRIGA methodology in which TRIGA reactor parameters are used to create Serpent-2 input for steady-state or burnup
calculations. Each of the four important inputs is described in the schematic.

reflector. On the reflector outer boundary, the zero flux boundary con­
dition is imposed. The unit-cell-averaged cross-sections were calculated
using 69-group WIMS library based on the ENDF/B-VII.1 nuclear data
library.
Fuel element burnup (BUel ) within the TRIGLAV code is calculated
using the WIMSD-5B code from which the fuel isotopic configuration is
obtained, as seen in Fig. 8. Unit-cell homogenised cross-sections at the
defined burnup are extracted and collapsed into neutron flux weighted
four-group constants that are used in 2D diffusion approximation. With
diffusion solution, a core power distribution is obtained and the fuel
element burnup increment can be calculated by knowing energy

released data for the defined cycle. Using the described procedure,
complete operational history can be simulated where different core

configurations and reactor operations can be considered. In the current
TRIGLAV methodology, the isotopic composition of individual fuel el­
ements is not transferred from cycle to cycle as only the burnup incre­
ment for individual fuel elements on each cycle is calculated. Such
procedure means that the mentioned BUel carries the information
regarding the complete operational history (power and loading pattern
changes).

Fig. 10. Graphical representation of the TRIGA Mark II reactor diverse power operation treatment in the simulation of the complete operational history.
5


A. Pungerˇciˇc et al.

Fig. 11. Differences in calculated nU−
250 kW was used as a reference.

Progress in Nuclear Energy 130 (2020) 103536

235

(left) and nPu−

239

as a function of fuel element burnup for different reactor powers defined in the burnup simulation. Pmax =

3.2. STRIGA tool

between the Serpent-2 and the TRIGLAV code. Criticality benchmark

core 132 (Jeraj et al., 1997; Mele et al., 1994) was selected.
• Burnup on fuel unit-cell: Burnup simulation on fuel element unitcell (fuel pin surrounded with water) to study the physics of fuel
composition changes through burnup.

The STRIGA tool is a simple data manipulation script, written in
standard FORTRAN-77 programming language that reads the TRIGLAV
inputs and creates inputs for 3D Monte Carlo calculations. Core
configuration inputs in TRIGLAV were already prepared for the com­
plete operational history. Detailed description of the STRIGA tool is
ˇ ˇc et al., 2017); only a brief
presented in (Pungerˇciˇc et al., 2019; Cali
description is presented in this paper. The STRIGA tool is based on the
validated steady-state Serpent-2 model (Calic et al., 2016), that is based
on the criticality benchmark (Mele et al., 1994) and MCNP models used
ˇ
in (Raduloviˇc et al., 2014; Stancar
et al., 2018; Goriˇcanec et al., 2015).
Steady-state SERPENT-2 calculations are completely consistent with the
MCNP ones, indicating that the geometry and material composition
employed in the model are well defined for reactor cores with fresh fuel
(Calic et al., 2016).
STRIGA requires two kinds of input data. The first represents reactor
component dimension and its material composition, while the second
represents the reactor operation data, as depicted in Fig. 9. To simulate
the complete history from 1966 to 2019, additional types of fuel ele­
ments and control rod positions have been added to the existing STRIGA
ˇ ˇc et al., 2017). Another advantage of the STRIGA tool is that it
script (Cali
reads the TRIGLAV core configuration input file, which is created using
ˇ

the graphical user interface (GUI) Triglav-W (Zagar
et al., 2006).
Through this interface, one can specify the reactor operation (power and
time) and select the core loading patter via an user-friendly fuel shuf­
fling interface. All fuel and non-fuel elements can be moved from one
location to another by a simple click and point procedure. In addition,
cool-down of the reactor core was added into the STRIGA tool, enabling
detailed calculations of diverse reactor operations.
For a given fuel cycle calculations using burned fuel the most
important information is the fuel isotopic composition that is taken from
the previous cycle. Within the STRIGA tool, the user can select which
isotopes are tracked within the burnup calculation. In the analysis, 269
isotopes were tracked. After each burnup calculation the fuel isotopic
library is created or updated. Such principle enables the extraction of
individual fuel element isotopic composition at different times in the
reactor operational history.

4.1. Simulation of complete operational history
The complete operational history consists of more than 25 000
reactor power changes and more than 240 core configurations. To
simulate each individual operation, high computer power and memory
would be needed, especially for calculations with Monte Carlo code
Serpent-2. Therefore, additional simplification was used to divide the
complete operational history into individual long operations on same
loading pattern or core configuration, as presented in Fig. 10. It has been
approximated that the reactor operated on maximum power Pmax =
∫t
250 kW for a period in which the energy released
Preactor (t)dt was the
0

same. At the end of the operation, fuel cooldown was approximated as
the sum of the total time the reactor was not operational. This principle
was used to create 240 different inputs for both Serpent-2 and the
TRIGLAV code. In this way, individual fuel element burnup was tracked
from its first insertion in the reactor core until today.
The approximation that the reactor operated on maximum power
Pmax = 250 kW was tested by repeating burnup simulation on a hypo­
thetical core configuration using the Serpent-2 code. Calculations were
repeated for 100 kW and 1 kW reactor powers. To keep fuel burnup the
same at different reactor powers, the irradiation time was increased
accordingly. The differences at the point of maximum TRIGA fuel
burnup were less than 0.1 % and 1 % for differences in the calculated
nU− 235 and nPu− 239 , respectively. We also repeated the simulation for
Preactor = 100 W and found similar discrepancy for nU− 235 and higher 10
% discrepancy for nPu− 239 . Reason behind higher relative differences in
nPu− 239 is that the amount of 239 P in TRIGA fuel elements is low, due to
the smaller content of 238 U compared with traditional light-water re­
actors. Relative differences in nU− 235 and nPu− 239 are presented in
Fig. 11. Despite higher relative differences observed, this effect is
negligible when comparing final absolute values in material composi­
tion. Similar conclusion can be made for fuel and moderator tempera­
ture. We have investigated the effects of Tfuel and Twater by repeating the
calculations with Tfuel = 600 K and Twater = 350 K. It has to be noted
that Twater represents the temperature of the water surrounding the fuel
and it is only one of the contributions to the neutron moderation in a
TRIGA reactor. The density of the water surrounding the fuel was
changed from 0.9975 cmg 3 to 0.9737 cmg 3 . Information for the analysed
cases are presented in Table 3. The other contribution is in the fuel itself
on hydrogen in the U–Zr–H fuel mixture. Regarding the effects of fuel

temperature, the differences at the point of maximum TRIGA fuel
burnup were less than 0.05 % and 10% for differences in the calculated

4. Burned fuel material composition calculations
Fuel element burnup analysis for the TRIGA Mark II reactor is per­
formed on three different cases, which are as follows.
• Complete operational history: Analysed data regarding the energy
released and fuel shuffling was used to create a burnup simulation of
the actual reactor operation performed from 1966 to 2019.
• Burnup on benchmark core No. 132: Burnup simulation on
selected core configurations was performed to study the differences

6


A. Pungerˇciˇc et al.

Progress in Nuclear Energy 130 (2020) 103536

Fig. 12. Differences in calculated nU− 235 (left) and nPu− 239 as a function of fuel element burnup for higher fuel temperature Tfuel = 600 K and core water temperature
Twater = 350 K. Tfuel = Twater = 300 K was used as a reference and for all burnup calculations presented in this paper. Both calculations were performed on maximum
steady state power Pmax = 250 kW.

nU− 235 and nPu− 239 , respectively. Resuls are presented in Fig. 12. The
noticeable effect on plutonium production is constant at 10 %. This is
due to the Doppler broadening of (n, γ) reaction resonances on 238 U.
There were no noticeable effects of surrounding water temperature on
nPu− 239 and for nPu− 239 the differences were below 0.1 %. A conclusion
can be made that for absolute determination of 239 Pu, fuel temperature
has to be taken into account, however for our analysis, mainly consisting

of comparing relative change due to burnup, negligible discrepancy is
introduced. However further more detailed analysis with detailed
thermodynamical model should be performed to fully analyse the tem­
perature effect on burnup.
Analysing the effect of different reactor powers and fuel tempera­
tures on depletion of 235 U and production of 239 P showed that there is
negligible effect on core excess reactivity due to long-lived isotopes if
approximation presented in Fig. 10 is taken into account. In addition we
observed that 239 P production depends slightly more on different reactor
power than fuel temperature, especially in smaller burnup below
MWd
1 kg(HM)
. However the amount of 239 P produced in TRIGA fuel is low and

Fig. 14. Relative difference in calculated fuel burnup between Serpent and
TRIGLAV as a function of burnup for all 300 fuel elements used in JSI TRIGA

such effects could be neglected in some cases. However effect on core
excess reactivity is present due to short-lived isotopes such as xenon and
samarium. Effect of such isotopes is analysed in Sec. 6.1. From this a
conclusion can be made that if xenon and samarium are of interest,

operation. Relative difference is defined as

detailed operational history for the last couple of days or weeks should
be taken into account.
Burnup of all 300 fuel elements accumulated in different periods of
the reactor operation history from 1966 to 2019 was calculated with
both the TRIGLAV and the Serpent-2 code. Complete operational history
simulation with TRIGLAV takes approximately 1 h on one standard PC

core, while Serpent simulation takes approximately three weeks on 56
cores (Intel Xeon Processor 25M Cache, 2.80 GHz). Accuracy of the
calculated burnup depends mainly on the experimental power calibra­
ˇ
tion accuracy (Stancar
and Snoj, 2017) and the precision of the opera­
tional records. As discussed in section 2.5, the 1σ uncertainty in reactor
power level is 10 %–15 %. However, we assumed only 5 % uncertainty
in final burnup as the uncertainty for longer operations averages out.
The final fuel burnup for randomly selected 16 fuel elements, 4 of each
type, (each fuel element is represented with a four-digit fuel identifi­
cation number) is presented in Fig. 13. It should be noted that these fuel
elements were not part of the same core configuration, but they were
used in different parts of the operational history.
First, we can observe that FLIP fuel elements have higher burnup (up
MWd 1
to 70 kg(HM)
), while the burnup for LEU fuel elements is around

Fig. 13. Final fuel burnup for 16 out of 300 fuel elements used in the history of
the JSI TRIGA reactor operation and calculated by simulating the complete
operational history. For each fuel type, 4 elements were chosen, which are
represented with a four-digit identification number, with exception of fuel
followers for regulation (REGU) and safety (SAFE) control rods.

Table 3
Material information defined in the Serpent-2 model of the JSI TRIGA reactor for
the analysis of fuel and water temperature effects on the fuel element burnup.
Analysed cases

Tfuel [K]

Reference calculation
Fuel temperature test
Water temperature test

300
600
300

ρfuel

[ g ]
cm3

6.04498E+00
6.04498E+00
6.04498E+00

Twater [K]
300
300
350

ρwater

(BUSerpent − BUTRIGLAV )
.
BUSerpent

[ g ]
cm3

9.97245E-01
9.97245E-01
9.73742E-01

1
Standard unit for burnup is energy released in MWd per mass of heavy
materials (HM) in kg. Heavy materials are nuclei with more than 92 protons.

7


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Progress in Nuclear Energy 130 (2020) 103536

Fig. 15. Individual fuel element burnup calculated by considering the complete operational history. Out of 240 core configurations, three were chosen (from left to
right: 80, 130, 240), schematically presented at the top. For each configuration fuel burnup calculated with Serpent at the end of the cycle is presented together with
relative differences between both codes used, defined as

30

MWd
kg(HM),

(BUSerpent − BUTRIGLAV )
.
BUSerpent

most important from the standpoint of the current reactor operation, is
within the ±7.5 % range. We can conclude that the difference between
both codes for most of the fuel elements is satisfactory, within 5 %,
accounting for all the differences between the two codes. Code-to-code
comparison for all 300 fuel elements is presented in Fig. 14.
To compare the differences between fuel elements of the same type,
core configurations and their position in the reactor core becomes
important. For this purpose, the following three core configurations
were chosen to further analyse the calculated burnup and the differences
between TRIGLAV and Serpent-2:

due to the higher local power of the FLIP fuel. The difference

in calc. burnup between TRIGLAV and Serpent is due to the higher
thermal neutron flux (Snoj and Ravnik, 2008) in the FLIP fuel elements.
Furthermore, the discrepancies between the codes are analysed.
Comparing the absolute differences, we can observe higher discrep­
ancies for FLIP-type fuel elements and the control rod fueled followers,
depicted as REGU for regulating and SAFE for safety control rod. For
FLIP-type fuel elements, the discrepancies can be explained similarly to
the difference in calculated burnup. Higher localised neutron flux results
in higher neutron flux gradients, which are not handled well by the 2D
diffusion approximation employed in the TRIGLAV code. Nevertheless,
the differences in fuel burnup are within 10 %. For fueled followers, the
relative difference is up to 15 % and this is because in the TRIGLAV code
we assume that the fueled follower is the same as a normal SS 12 % fuel
element, while in reality, it is smaller; this is considered in the Serpent-2
model, as previously presented in Fig. 2.
For all 300 fuel elements, relative difference in calculated final

burnup with both codes was evaluated. The highest discrepancies were
observed for control rod fuel followers and for the fuel element type SS
8.5 % with unknown initial burnup (obtained from TRIGA in Frankfurt
am Main, Germany). The difference for the SS 12 % type of fuel, which is

• Core No. 80: due to mixture of three different types of fuel elements
(SS, AL 8.5% and FLIP).
• Core No. 130: as it is the last core that was in operation before the
reconstruction in 1991 (maximum burnup in some fuel elements).
• Core No. 240: as being in operation when the study was performed
(February 2019).
Fuel element burnup calculated with Serpent-2 and the relative dif­
ference in comparison with the TRIGLAV code was analysed. For core
MWd
MWd
no. 80, burnup was between 10 kg(HM)
and 30 kg(HM)
for all types of fuel
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Progress in Nuclear Energy 130 (2020) 103536

Fig. 16. Final 239 Pu (top) and 137 Cs (bottom) number densities for 16 fuel elements calculated by simulating complete operational history. It should be noted that
aluminium fuel element No. 288 has only a quarter of fuel material compared with other AL 8.5 % elements.

elements. For core no. 130, three clear sets of fuel elements are visible:
MWd

The first is FLIP, with the highest burnup up to 70 kg(HM)
; the second is SS

(Jeraj et al., 2002), only selected isotopes were chosen. In Fig. 16, the
calculated number densities for two important isotopes in burnup
analysis 239 P and 137 Cs, are presented. The former is the product of
neutron absorption in 238 U, and as expected, the calculated amount is
lowest in the HEU FLIP fuel elements. The latter is the product of nuclear
fission; therefore, similar behaviour compared with fuel burnup can be
observed. For fuel element with ID no. 288, the lowest number densities
for both isotopes can be observed. The reason is that, in this experiment,
this fuel element contained only a quarter of the fuel compared with the
others. Higher discrepancies are observed between the two codes with
increased burnup. For 235 U, 137 Cs and 239 Pu analysis of the calculated
number density differences between both codes was performed for core
No. 240. The results are presented in Fig. 17. For 235 U and 137 Cs, similar
behaviour to fuel burnup can be observed, with the highest discrep­
ancies observed for control rod fuel followers. The radial neutron flux
distribution, calculated with both codes is highly visible when analysing
239
Pu as for the inner rings (B, C and D) higher number density up to 10
% is calculated with Serpent-2 and lower up to 15 % for outer rings (E
and F) compared with the TRIGLAV code.
The calculated differences for most fuel elements were within 5 %,

MWd
MWd
8.5 % with burnups between 10 kg(HM)
and 20 kg(HM)
; and the last is SS 8.5

%, which were brought from the Frankfurt TRIGA reactor and had
MWd
recorded burnups below 10 kg(HM)
. The effect of burnup is clearly visible

for core no. 240, where burnups in the middle part of the core are higher,
MWd
MWd
, compared with those on the periphery (up to 15 kg(HM)
).
at up to 20 kg(HM)

Fuel element burnup results are presented in top part of Fig. 15, while in
the bottom part, relative differences between Serpent-2 and TRIGLAV
for the same core configurations are presented. A slight shift of calcu­
lated burnup can be observed when analysing differences between both
codes for the complete core, as the burnup calculated with TRIGLAV is
higher compared with Serpent-2 on the right side of the core, which can
be seen in Fig. 15. This difference may occur due to the control rodinduced neutron flux redistribution (Goriˇcanec et al., 2015) or the
treatment of burnup in TRIGLAV. To understand the mentioned shift,
further analysis on just one core configuration was performed; this is
presented in section 4.2.
In addition to burnup, isotopic composition of individual fuel ele­
ments was analysed. Based on an analysis of isotopic effect on reactivity

Fig. 17. Comparison of calculated isotopic composition between Serpent and TRIGLAV for last core configuration established in 2019. Relative difference is defined
as

NSerpent − NTRIGLAV

.
NSerpent

Three isotopes are presented; from left to right, these are:

235

U,

239

9

Pu and

137

Cs.


A. Pungerˇciˇc et al.

Progress in Nuclear Energy 130 (2020) 103536

while higher discrepancies were due to difference in control rod treat­
ment in both codes. The difference in methodology for calculating
neutron flux distribution for both codes comes into effect when
comparing distribution of different isotopes, especially 239 Pu. These
differences are investigated further in the next chapters. We can
conclude that the difference in the calculated burnup between both

codes is relatively low. Hence, both methodologies could be used for
TRIGA fuel elements’ burnup calculations. However, the user should be
aware that these differences increase for individual isotope density
comparison.
Fig. 18. Relative change in burnup (y-axis) of initially fresh fuel elements (blue
dots) due to uncertainty in initial burnup of already irradiated fuel elements,
expressed as a relative change from the reference value (x-axis). (For inter­
pretation of the references to colour in this figure legend, the reader is referred
to the Web version of this article.)

4.1.1. Uncertainty propagation of initial fuel element burnup
In 1980, already irradiated fuel elements were obtained from the
Frankfurt TRIGA reactor. As the initial burnup of these fuel elements was
not accurately known, additional uncertainty was introduced in the final
burnup calculations. The effect of this uncertainty was studied, and the
results are presented in this section. The STRIGA tool was used to study
the propagation throughout different core configurations.
In 1991, soon after the reconstruction, these irradiated fuel elements
of type SS 8.5 % were used in mixed-core configurations from core No.
138 to core No. 146 (reference to the online animation) with the fresh SS
12%. Their effect is studied by analysing the burnup of the fresh fuel that
is present in the mixed cores. In total, fuel was mixed in multiple
MWd
different cores, which were studied in our case. We have chosen 20 kg(HM)

as a reference value of the unknown fuel burnup. This burnup was later
changed from − 100 % to +30 % and effects on accumulated burnup on
the fresh fuel elements were analysed. The effect on final burnup after
core No. 146 due to the mentioned burnup changes in a mixed core
configuration with fresh fuel is less than 6 %. This effect is reduced for

further operation and it is practically negligible for fuel burnups at core
No. 240. The effect on core No. 146 is presented in Fig. 18.
4.2. Burnup on benchmark core no. 132
The complete operational history includes a large number of
different parameters that could impact the calculated burnup, such as
fuel shuffling or mixing of different types of fuel elements. To analyse
the burnup in higher detail and compare the two methodologies used we
decided to perform burnup calculations on the benchmark core config­
uration with fresh fuel no. 132 (Jeraj et al., 1997; Mele et al., 1994). The
core schematic is presented in Fig. 19. An average core burnup of 50
MWd
kg(HM) was assumed and simulated by both Serpent-2 and TRIGLAV. This

Fig. 19. Schematic representation of core configuration No. 132, used as a
fresh fuel criticality benchmark and available in the ICSBEP handbook (Jeraj
et al., 1997; Mele et al., 1994).

outermost ring. This difference is almost negligible at lower burnups of
MWd
and becomes evident at larger burnups where the difference
10 kg(HM)
between fuel element in ring A and E is 20

approximately represents the energy released in the complete opera­
tional history, which is an overestimation for only one type of fuel
MWd
element, while the core burnup of 20 kg(HM)
represents the energy

MWd

kg(HM).

Similar behaviour can

be observed when analysing the production of isotope 239 Pu.
Differences in fuel burnup and consequently individual isotopes
between both codes were analysed. Serpent results were taken as a
reference value. Highest discrepancies, similar to operational history
analysis, are observed for control rod fueled followers and the central

released after the reconstruction in 1991 and can be used as a realistic
example.
The validation of the computational model with fresh fuel was
already performed (Calic et al., 2016) and taken as an initial condition in
this analysis. Excess reactivity as a function of core burnup was studied.
MWd
Both codes predict a similar change of ≈ − 6000 pcm at 20 kg(HM)
and ≈

− 13000 pcm at 50

MWd
kg(HM).

Both codes are in good agreement as the

discrepancy gradually increases to a difference of only 784 ± 20 pcm at
MWd
50 kg(HM)
. Higher discrepancies are observed for the first couple of steps

because of the xenon equilibrium treatment employed in the TRIGLAV
code. Comparison of reactivity changes with both codes is presented in
Fig. 20.
The individual fuel element burnup and its isotopic composition was
studied. The results are presented for three different core burnups,
MWd
MWd
MWd
which are as follows: 10 kg(HM)
, 20 kg(HM)
and 50 kg(HM)
. Serpentcalculated burnup parameters and discrepancies in comparison with
the TRIGLAV code are presented in Figs. 21 and 22. As expected, the fuel
burnup is higher in the inner rings and becomes lower towards the

Fig. 20. Excess reactivity (top) and difference between Serpent and TRIGLAV
criticality calculation (bottom) as a function of TRIGA core No. 132 burnup.
10


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Progress in Nuclear Energy 130 (2020) 103536

Fig. 21. Distribution of calculated fuel burnup and isotopic composition at three different average core burnups (from left to right). From top to bottom, three
parameters are presented: individual fuel burnup calculated by Serpent-2, the absolute difference compared with the TRIGLAV code and the number density of 239 Pu
calculated by Serpent. Control rods are denoted by letters: P = transient, S = safety, C = shim, R = regulating.

fuel element. In addition to fuel burnup, differences in the calculated

MWd
number densities were analysed at an average core burnup of 20 kg(HM)
.
The results are presented in Fig. 22. For

235

discrepancies is comparable to burnup calculations, at between −
3 %and 1 %. Similar distribution but higher discrepancies can be
observed for 137 Cs, while the distribution for 239 Pu is more uniform, as
the TRIGLAV code calculates higher number density (up to 20 %) in

U, the distribution of

Fig. 22. Distribution of calculated differences in number density between Serpent and TRIGLAV for three different isotopes (left to right): 235 U, 239 Pu, 137 Cs. Relative
difference is defined as

NSerpent − NTRIGLAV
.
NSerpent

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Progress in Nuclear Energy 130 (2020) 103536

Fig. 23. Changes of excess reactivity due to unit-cell burnup for four different types of TRIGA fuel. Serpent-2 results are compared with WIMSD-5B.

inner rings and lower (up to 30 %) in the outermost ring. As the pro­
duction of 239 Pu is a secondary order process the treatment of water
surrounding the fuel elements becomes important. As can be observed,
the TRIGLAV code underestimates number density in the outermost ring
surrounded by water, especially for the two elements on the border of E
ring.
Another observation can be made concerning spatial distribution.
Core configuration no. 132 is not symmetrical and the centre is shifted to
the left as presented in the core schematic in Fig. 19. Analysing the
differences between the two codes, we can observe a similar shift. This is
due to the assumption performed in the first step of the TRIGLAV burnup
calculations, where neutron flux or power distribution is assumed. The
assumption is that the distribution is symetrical and centred on the
middle of the core (A1 position). Concerning changes in core reactivity,
it can be concluded that the differences between both codes are negli­
gible. The differences in methodology become evident when comparing
the burnup of individual fuel element: For the same average burnup, the
comparison showed differences in individual rings of the reactor core,
which were most visible in the middle three rings. Such differences were
magnified when analysing isotopic composition. We observed that the
fuel element surrounding becomes important in the analysis of 239 Pu

content. It can be concluded that the TRIGLAV code is satisfactory for
core excess reactivity analysis; in contrast, isotope composition, higher
discrepancies were observed.
4.3. Burnup on fuel unit-cell
For each type of fuel element, the unit-cell was assumed as a fuel pin
surrounded with water and with reflective boundary conditions. The
same unit cell geometry is used in the TRIGLAV code, where homoge­
nised cross sections are generated at the unit-cell level with WIMSD-5B

(Kulikowska, 1996), where annular geometry with surrounding water
radius rwater = 2.31317 cm is defined. This is an average water amount in
the JSI TRIGA reactor defined in the TRIGLAV code (Persic et al., 2017).
ănen et al., 2015) code square geometry has to be
In the Serpent-2 (Leppa
defined if reflective boundary conditions are to be used. For this purpose
we defined a square geometry with half-width of 2.05 cm so that water
area of the Serpent-2 unit-cell matches the one in the WIMSD-5B code.
Serpent-2 and WIMSD-5B were used to calculate changes in unit-cell
MWd
reactivity and isotopic composition for burnups up to 30 kg(HM)
. The
MW
assumed power density for all fuel elements was 30 kg(HM)
. The results of

reactivity changes, together with dimensions of individual fuel pins, are
presented in Fig. 23.
The changes in reactivity at the unit-cell level show similar behav­
iour compared with full core calculations. There is a visible difference
between SS 8.5 % and AL 8.5 %, meaning that the inner zirconium pin
has a notable effect on burnup changes. All three LEU fuel elements
show similar behaviour, with a slight difference of faster reactivity
decrease for SS 8.5%. Noticeable differences can be observed for HEU
MWd
FLIP fuel with burnable absorbers; after average burnups of 5 kg(HM)
,

reactivity increases linearly with burnup, signifying positive reactivity
feedback on core burnup. It should be noted that all the changes pre­

sented here vary in relation to the specific power of each fuel pin, and
that FLIP fuel elements were always used in mixed core configurations,
resulting in a negative reactivity feedback on core burnup.
A comparison in changes of excess reactivity due to burnup between
WIMSD-5B and Serpent-2 was also performed, where good agreement
(between − 200 and + 200 pcm) for all fuel types was observed. In
addition, we investigated which isotopes made the highest contribution
to the discrepancies. We found that the effect was proportional to the
influence of a single isotope on reactivity changes, meaning, isotopes
235
U and 239 Pu made the highest contribution to the discrepancy. From
this, we can conclude that burnup on the unit-cell calculation performed
with WIMSD-5B in the TRIGLAV code is not the source of observed
discrepancies when comparing full core burnup calculations with both

Fig. 24. Calculated axial distribution of 239 Pu (top) and 235 U (middle) number
MWd
densities calculated with Serpent-2 for a burnup of 50 kg(HM)
. A hypothetical
core configuration with divided fuel elements on 100 depletion zones was
employed. Results for all four different types of fuel elements with its sche­
matics are presented. In addition, thermal neutron flux (bottom) in the fuel and
graphite region is depicted.

12


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Progress in Nuclear Energy 130 (2020) 103536

Fig. 25. Changes of core excess reactivity as a function of TRIGA core burnup calculated with Serpent-2 using one and 15 axial depletion zones (left). In addition,
manual division and automatic division using the STRIGA tool is compared. The reactivity rate of change with burnup is presented, and linear coefficients are
calculated (right).

Fig. 26. Differences of final fuel element burnup due to C-shim and R-regulating control rod insertion. All rods out case is taken as a reference for three cases of
insertion; from left to right 25 % in, 50 % in and 75 % in.

codes.

was subdivided into sections, while the others were left undivided due to
the computational limit. Four different cases were studied based on the
type (AL 8.5 %, SS 8.5 %, FLIP, SS 12 %) of the divided fuel element.
Schematic of the core is presented on the right side of Fig. 27. It was
assumed that transient (P) and safety (S) control rods were completely
extracted, while regulation (R) and shim (C) were half-inserted. This is
important only in cases where multiple axial depletion zones are
considered (Goriˇcanec et al., 2015).

5. TRIGA fuel burnup spatial effects
All the calculations performed with Serpent were conducted using a
single depletion zone for the fuel element, without axial, radial or
angular division. As the division of fuel elements into multiple depletion
zones is computationally intensive, it was decided to perform the anal­
ysis of burnup spatial effects on a hypothetical core configuration con­
sisting of fuel elements divided into multiple axial and annular depletion
zones. The core example had only fuel elements of type SS 12 wt. %,
which were filled into rings from B to E. In each ring, one fuel element

n235 (burned)

Fig. 28. Angular distribution of fuel burnup in units of n235U (fresh) for the fuel
U
element inserted in the core periphery, as depicted in Fig. 27. The colour scale
represents the difference in burnup in each depletion zone compared with the
average fuel burnup. (For interpretation of the references to colour in this figure
legend, the reader is referred to the Web version of this article.)

Fig. 27. Computational model of the hypothetical core configuration used in
the Serpent-2 code to study the angular distribution of isotopes in burned
TRIGA fuel. Four depletion zones where the 640-group neutron spectrum was
calculated are depicted.
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Fig. 29. Definition of angular distribution for angular burnup comparison with surrounding water thickness presented in 30.

Fig. 30. Burnup in units of depleted 235 U and amount of water as a function of fuel element angle. Calculations for four fuel elements one in each ring (B,C,D,E) are
depicted. Diffusion constant for water DH2O ≈ 1 cm is depicted. Graphite reflector and control rod are depicted with shaded area.

5.1. Axial distribution

(average core burnup of 50

MWd
kg(HM))

shows that, as expected, the burnup

of all three fuel elements was highest in the middle of the fuel element,
where the thermal neutron flux is higher. In addition, an increase of
burnup on the edges of the fuel meat is observed due to the increase of
thermal neutron flux in the graphite region of the fuel element. This is
not observed for fuel element type AL 8.5 % which has samarium ab­
sorbers on both sides that neglect this effect. Another observation is that
the isotope 239 Pu distribution is inverse compared to 235 U, which was an
expected result.
The highest differences can be observed comparing LEU (AL, SS 8.5
% and SS 12 %) and HEU (FLIP) elements. Due to the higher enrichment,

For all types of fuel elements, it can be observed (in Fig. 24) that the
distribution was not symmetrical; rather, it was slightly shifted down
due to the partially inserted control rods. Comparing different types of
fuel elements, higher differences can be observed. Axial distribution for
fresh fuel of neutron thermal flux and isotopic distribution of 235 U and
239
Pu were analysed, and the results—together with differences in fuel
dimensions—are presented in Fig. 24. The calculated statistical uncer­
tainty in thermal neutron flux in each of the 100 axial zones was less
than 2 %. Analysis of 235 U number density at the maximum burnup

14


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Progress in Nuclear Energy 130 (2020) 103536

the past would have to be analysed and individual simulation cycle
further divided.
5.3. Angular distribution
Angular spatial burnup effects were studied by dividing the fuel
element by angle into 20 equal (18 ◦ ) depletion zones to evaluate the
effect of fuel surrounding on angular burnup distribution. One fuel
element in the core periphery (depicted in Fig. 27) was chosen for this
analysis. Angular distribution for fuel type SS 12 % was studied at two
different burnups. The results are presented in Fig. 28. It can be observed
that the burnup is higher on the side of the fuel element facing towards
empty outermost ring filled with water. The differences in highest and
lowest burnup zones are almost negligible (up to 3%) for realistic
MWd
average core burnup of 20 kg(HM)
and become evident (up to 7 %) at

Fig. 31. Neutron lethargy spectrum with 640 energy group structure, defined
Φ
as Ψg = ( g ), for four depletion zones, depicted in Fig. 27, in fresh fuel
log

Eupper
Elower

element type SS 12 %.

a lower percentage of the initial number density of 235 U can be observed
for FLIP fuel elements. As previously mentioned, the AL and SS 8.5 %

fuel elements differ in their cladding material. The analysis showed no
differences in isotope distributions, and it can be concluded that the type
of cladding does not have noticeable effect on the burnup of TRIGA fuel
elements.
The analysis shows that using 15 axial depletion zones is adequate to
describe the axial effects. We compared the excess reactivity changes
with the original (without axial distribution) results. The difference for
fuel burnup of the JSI TRIGA reactor is 400 pcm, meaning that our
original results underestimate the reactivity decay. The comparison is
presented in Fig. 25. We can estimate that the complete simulation time
using 15 axial depletion zones would increase to three months while
preserving the accuracy of the simulations. Adding 20 angular and 5
radial divisions would increase the simulations to several years. This
evaluation was conducted for 1 node with 56 cores (Intel Xeon Processor
25M Cache, 2.80 GHz).

higher burnups of 50

MWd
kg(HM).

As the TRIGA core has an annular configuration that is not periodic,
the amount of water surrounding each fuel element depends on the fuel
element location. Moreover, the amount of water around fuel element
also varies significantly with the angle as depicted in Fig. 29. To analyse
this effect, the neutron spectrum was studied in four different regions, as
presented in Fig. 27, where region 3 is the one facing the water region. It
was observed that the thermal peak in region 3 was higher compared
with the other regions which directly resulted in higher burnups. The
640-group neutron spectrum results are presented in Fig. 31. We used a

simplse ray-tracing algorithm, described in appendix A, to determine the
amount of water around fuel elements. We chose four fuel elements,
each representing individual ring of the JSI TRIGA reactor (B (inner), C,
D, E (periphery), as presented in Fig. 29. The amount of water variation
was compared with fuel burnup where clear agreement in the shape of
the variation was observed, expect for regions with nearby control rods
and graphite reflector. In the region of the fuel element facing towards
the control rod, lower burnup is observed. The results are presented in
Fig. 30. From this, we can conclude that there is a direct connection
between the amount of water and fuel burnup, which can be determined
with simple and fast ray-tracing algorithms; the longer burnup simula­
tions with angular division would not be needed in some cases.
From the axial and angular distribution analysis, we can conclude
that the axial effects are more important in the TRIGA reactors, as the
differences between the highest and lowest burnup part of the fuel are
MWd
more than 25 % for realistic (20 kg(HM)
) and even more than 50 % for

5.2. Effect of control rod insertion on fuel burnup
Another assumption in our simulation of complete operational his­
tory was that control rods were extracted from the core. This was done
for the purpose of comparing excess reactivity measurements with cal­
culations and because control rod position changes with reactor opera­
tion and fuel shuffling. When the reactor is in operation, safety (S) and
transient (P) are extracted, while regulating (R) and shim (C) control
rods are inserted between 25 % and 50 %. To test this assumption, we
have simulated full JSI TRIGA burnup on the last core in operation today
and checked the differences in calculated fuel element burnups. Three
cases were assumed, where R-regulating and C-shim control rods were

inserted at 25 %, 50 % and 75 %. The results show (Fig. 26) a decrease in
burnup on fuel elements surrounding the control rods and increase on
the rest. This decrease is below 5 % for the first case (25 % inserted) and
below 15 % for the second (50 % inserted). The results are presented in
Fig. 26. From this analysis, we can conclude that, for more detailed
burnup calculation, control rod positions should be taken into consid­
eration. However, this is extremely difficult to incorporate into complete
operational history simulation, since all of the control rods positions in

overestimated (50

MWd
kg(HM))

burnups. It should be noted that this effect

could further increase if control rod position is taken into consideration,
especially for fuel elements in their close proximity. For future burnup
calculations, where control rod position will be considered, axial divi­
sion of depletion zones is necessary. The same cannot be stated for
angular effects, as even for the extreme cases with highest burnups of
MWd
50 kg(HM)
and highly heterogeneous fuel element position, the differ­
ences between the highest and lowest burnups were less than 7 %. The
axial effect could be considered by using the recorded control rod po­
sitions in the detailed model created by the STRIGA tool. Considering
operational history, axial position of the fuel elements is well defined;
however, their angular position and rotations were not recorded, and
therefore, they cannot be determined. This can be treated as an uncer­

tainty. It can be concluded that, in the future, even their angular position
should be reported when fresh fuel elements are inserted.
6. Validation of burnup calculations
The last part of the burnup analysis presented in this paper consists of
validating burnup calculations with parameters obtained from the
operational history analysis. For this purpose, weekly measurements of
excess reactivity were analysed and used for comparison with Serpent-2
and TRIGLAV calculations of the complete operational history.

Fig. 32. Effect of individual isotope on TRIGA reactor core reactivity as a
function of its average burnup. Operation at the maximum steady state Pmax =
250 kW was simulated using the Serpent Monte Carlo code. Statistical uncer­
tainty of a single calculations is σstat (ΔρExcess ) = 12 pcm.
15


A. Pungerˇciˇc et al.

Progress in Nuclear Energy 130 (2020) 103536

Fig. 33. Excess reactivity at the beginning of each cycle or core configuration for the JSI TRIGA reactor (top graph). Measurements and results of complete
operational history simulation using Serpent and TRIGLAV code are presented. Excess reactivity for benchmark core configuration No. 132 (not included in the
graph) is in within the 1σ agreement with both codes. The bottom graph depicts the difference between calculated and measured excess reactivity at each core
configuration together with 1σ and 2σ of the measurements.

Fig. 34. TRIGA core excess reactivity as a function of average core burnup for three different core configurations (from left to right: 69, 129, 216–232). For each
core, measurements are compared with Serpent-2 and TRIGLAV burnup simulations. It should be noted that the presented graphs represent only 3 out of 46 analysed
cycle excess reactivity changes. Core configurations 216–232 represent multiple identical loading patterns between which changes were made that do not affect the
fuel burnup.

6.1. Effect of isotopes on core reactivity

reactivity changes due to burnup, we have analysed the effect of indi­
vidual isotopes on core reactivity of the JSI TRIGA Mark II reactor.
Similar analysis (Jeraj et al., 2002) was already performed in the past for
a TRIGA SS 12 % fuel unit-cell using the WIMS (Kulikowska, 1996) code.

In the process of fuel burnup number density of more than 1400
different isotopes is constantly changing. For the purpose of analysing
16


A. Pungerˇciˇc et al.

Progress in Nuclear Energy 130 (2020) 103536

Fig. 35. Top graph shows the burnup reactivity coefficient, defined in Eq. (2), for 46 different core configurations. Each measurement is compared with the Serpent-2
and TRIGLAV burnup calculations. Bottom graph presents the relative difference between measurements and calculations. One sigma uncertainty, defined as σdiff =
√̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅
σ2calculations + σ2measurements , is depicted.

In that study, 40 different isotopes were studied at three different fuel
burnups, at: 3 %, 10 % and 20 % of the initial 235 U burned. Analysis was
repeated for the 14 isotopes that have the highest effect on reactivity
according to the cited analysis using the Serpent-2 neutron transport and
burnup code. Excess reactivity of the benchmark core configuration No.
132 (presented in Fig. 19) was calculated at different burnups, each time
excluding the analysed isotope. The effect of individual isotope i on the
core was determined as Eqn 1

where ρall presents core reactivity with all the isotopes and ρall− 1
excluding the one. The calculated results were compared with the results
presented in (Jeraj et al., 2002). Results from both analyses are included
in Table 4 and show extremely good agreement for most isotopes. The
results agree with our analysis of complete operational history, where
the highest discrepancies were observed for 239 Pu. It can also be
observed that the difference between both codes is increasing with
burnup. However, very good agreement can be observed for 149 Sm and
135
Xe, especially for higher burnups. We can conclude that the repeated

(1)

Δρi = ρall − ρall− i ,

Table 4
Effect of individual isotopes on core reactivity. Results were obtained by Monte Carlo simulations on benchmark core No. 132. Obtained results were compared to
WIMS unit-cell calculations, presented in (Jeraj et al., 2002). Calculations were performed with normalisation to maximum reactor power Pmax = 250 kW. Units of
(ninitial − nburned )
burnup are defined as BU [%] =
, where n presents 235 U number density.
ninitial
Effect on core excess reactivity [pcm]
Fuel el. burnup 3 %

Fuel el. burnup 10 %

Fuel el. burnup 20 %

Isotope

WIMS

Serpent

Δ

WIMS

Serpent

Δ

WIMS

Serpent

Δ

135

Xe

− 850

− 930

80

− 899

− 925

26

− 973

− 958

− 15

149

Sm

− 620

− 710

90

− 638

− 690

52

− 645

− 657

12

151

Sm

− 101

− 117

16

− 222

− 218

− 4

− 284

289

5

239

Pu

ỵ295

ỵ106

189

ỵ357

ỵ432

Ă75

ỵ840

ỵ984

Ă144

143

Nd

51

54

3

178

188

10

384

444

60

240

Pu

5

10

5

57

− 51

− 6

− 216

− 260

44

236

U

− 25

− 44

19

− 84

− 109

25

− 168

− 195

27

147

Pm

− 24

− 45

21

− 65

− 61

− 4

− 102

− 114

12

103

Rh

− 20

− 36

16

− 82

− 84

2

− 179

− 181

2

131

Xe

− 16

− 26

10

− 56

− 49

− 7

− 118

− 146

28

133

Cs

− 14

− 27

13

− 50

− 68

18

− 105

− 122

17

− 11

− 26

15

− 38

− 33

5

− 79

− 98

19

99

Tc

145

Nd

− 7

− 19

12

− 26

− 26

0

− 55

− 70

15

155

Eu

− 6

− 15

9

− 14

− 14

0

− 20

− 27

7

Δ = ΔρWIMS − ΔρSerpent . Serpent statistical uncertainty: 1σ Serpent = 5 pcm.
17

A. Pungerˇciˇc et al.

Progress in Nuclear Energy 130 (2020) 103536

calculated by TRIGLAV shows similar behaviour. In comparison with the
Serpent-2 code, higher discrepancies can be seen for the core configu­
rations before core No. 85. One of the possible reasons for those dis­
crepancies can relate to the fuel elements, type AL 8.5 %, which were
used in those mixed core configurations, as they represent the only
variable that changes in comparison after core No. 85. Another possible
explanation is that the leakage term in TRIGLAV is described with
buckling parameter, defined so that the calculated reactivity of bench­
mark core No. 130 matches the measured one. Since different mixed
core configurations were used before the reconstruction buckling
parameter was different, and therefore, the absolute comparison is
biased. As the source of the discrepancy is still unknown, it should be
further analysed in the future. Due to the simplicity of the diffusion
approximation within the TRIGLAV code, we can conclude that the re­
sults are in good agreement compared with the Monte Carlo results. We
can conclude that the TRIGLAV code can be used for simple predictions
of excess reactivity changes in TRIGA reactors.

Table 5
Statistical analysis of differences between the measured and calculated linear
burnup reactivity coefficient. The total number of coefficients is 46, which
represents 46 different core configurations and 2000 measurements of excess
reactivity in total.
Analysis of 46 differences
between calculations and

measurements

Average Median Within 1σ

Serpent
TRIGLAV

− 1.8 %
19.3 %

Within 2σ

− 1.0 % 24 (52.2 %) 40 (86.9 %)
22.9 % 14 (30.4 %) 28 (60.9 %)

analysis, using a different methodology and model, produces similar
results to those obtained before.
At lower burnups, the highest contribution to core reactivity is due to
isotopes 135 Xe (constant ≈ 900 pcm) and 149 Sm (constant ≈ 700 pcm),
while at higher burnups, the contribution from 143 Nd, 240 Pu, 236 U, 103 Rh
and 239 Pu becomes important.
Additional SERPENT-2 analysis was performed with various burn­
ups. The results are presented in Fig. 32 and show that at burnup of
MWd
20 kg(HM)
, which represents total burnup after the reconstruction in

6.3. Analysis of relative changes due to burnup
So far, only the measurements at the beginning of reactor operation
on each of the 240 cycles were used. We decided to further analyse the

relative changes of excess reactivity only due to fuel burnup on indi­
vidual core configurations. For this analysis, we have chosen the core
configurations where the burnup increment is substantial and where the
measurements were performed regularly without having a poisoned
reactor. In total, 46 core configurations were chosen resulting in 2000
measurements used for the analysis. 26 core configurations were used
before the reconstruction in 1991 and consisted mostly of mixtures be­
tween Al, SS 8.5 % and FLIP-type fuel elements. The rest were after the
reconstruction and had SS 12 % type fuel elements, except for the
already mentioned mixed core configurations 138–146. Fuel composi­
tion at the beginning of each cycle was taken from the operational his­
tory analysis. Results for three core configurations with their schematics
are presented in Fig. 34.
Results obtained from the burnup calculations were compared using
the measured linear coefficient of reactivity change, defined as
]
[
ΔρExcess
pcm kg(HM)
.
(2)
Burnup reactivity coefficient =
MWd
ΔBurnup

1991, the effect of 239 Pu is ≈ 500 pcm and increases up to ≈ 1700 pcm
when energy released in complete operational history is simulated on
one core.
This subsection together with Sec. 4.1 provides a clear overview of
the reactivity effects in the TRIGA Mark II reactor and our treatment of

its diverse operation in the burnup calculations. We showed that reac­
tivity effect of long-lived or stable isotopes (235 U239 Pu, 143 Nd) does not
change if different operating power is taken into account, however it is
known that reactivity effect 135 Xe, 149 Sm and 151 Sm highly depend on
the operating power due to the different saturation level. From this a
conclusion can be made that our methodology presented in Sec. 4.1 is
sufficient for the study of relative changes in excess reactivity, due to
uranium depletion and plutonium production, presented in the next
sections, however for absolute values of core excess reactivity detailed
operational history should be taken into consideration to accurately
predict the effect of xenon and samarium.
6.2. Comparison with measurements

Coefficients were determined using linear regression across the
measurements and calculations. Fig. 35 presents the results for all 46
analysed core configurations. The measurements predict the reduction
of the coefficient for starting core configurations, which is due to the
gradual insertion of FLIP-type fuel elements that contain burnable
absorber erbium, which reduces the negative reactivity change due to
burnup. Similar observations can be made when comparing core con­
figurations before and after reconstruction, as the coefficients are higher
after core No. 138. (The first core conf. after reconstruction was No.
132). All the observed changes were well predicted by both the TRI­
GLAV and Serpent-2 codes, as clear change after the reconstruction was
observed.
For the comparison of individual coefficients, the relative difference
between calculations and measurements was analysed. The results are
presented in the bottom graph of Fig. 35. It can be observed that the
relative differences are smaller and mostly within 20 % after the
reconstruction and around 40 % before the reconstruction, which is due

to the improvement in quality of the measured data. It can be observed
that the coefficient calculated from the TRIGLAV results is almost
constantly smaller than the measurements, which again shows a sys­
tematic discrepancy.
For better understanding of differences further statistical analysis
was performed. The results are presented in Table 5. The average value
of relative differences between Serpent and the measurements is − 1.8 %
and the median is − 1.0 % which means that no systematic discrepancy

The main analysis, which encompasses both the acquisition of
operational data and the developed methodology of operational history
simulation, is the comparison of measurements of excess reactivity
performed at the beginning of each of the cycle with calculations per­
formed by TRIGLAV and Serpent-2. For the measurements, a 1σ uncer­
tainty of 500 pcm is assumed, as the same uncertainty was determined
for the benchmark core configuration. This uncertainty is under­
estimated for individual absolute measurements but overestimated for
relative changes on the same core configuration. Thus, we have focused
our results on the shape of the burnup curve rather than absolute results.
The comparison between simulations and measurements is presented in
Fig. 33, where clear agreement between Serpent and the measurements
is observed for the first 80 core configurations. Almost all values are
within the 1σ uncertainty. The differences after core No. 80 can be
explained according to the introduction of older fuel elements with
unknown burnup. After the reconstruction in 1991, a constant discrep­
ancy of 1000 pcm − 1500 pcm is observed, which is in agreement with
discrepancy for benchmark core No. 190, as discussed in the previous
chapter. Since the calculated absolute values using Serpent-2 are not in
perfect agreement with the reactivity measurements, the curve of the
calculated Serpent-2 results follow the curve of the measurements

throughout the operational history, and therefore, the conclusion is that
the simulation methodology presented in this paper is satisfactory.
Excess reactivity throughout the complete operational history
18


A. Pungerˇciˇc et al.

Progress in Nuclear Energy 130 (2020) 103536

can be observed as the distribution between positive and negative dif­
ference is equal. The systematic discrepancy is clearly visible for the
TRIGLAV results as the average value is +19.3 % and the median 22.9
%. That the average and the median match for both codes shows that the
data are statistically relevant. The agreement between Serpent and
measurements is good, as 52.2 % of the calculated coefficients are within
1σ, and 86.9 % are within 2σ of the measurements. For TRIGLAV, the
agreement is not as good because only 30.4 % of coefficients are within
1σ and 60.9 % within 2σ.
The comparison of excess reactivity measurements and calculations
shows that, with the Serpent code and the methodology of simulating
complete operational history we can predict the changes of excess
reactivity due to burnup relatively well. In this case limitations of the
TRIGLAV code can be observed as it very well predicts the changes in
coefficient due to different fuel elements but fails to accurately describe
each operation. It should be noted that the number of coefficients was 46
and with further TRIGA reactor operation more will be available and the
analysis will become even more statistically relevant. In the future,
further improvement to the methodology of the operational history
calculations can be performed and the coefficients used for further

validation.

addition the position of the control rods should be considered, which
could explain the presented discrepancies in comparing calculated and
measured excess reactivity. A similar conclusion can be made for
angular distribution; it was shown that, for realistic burnups, the effect is
negligible since the difference between maximum and minimum burnup
was below 7 %. However, it could be substantial for individual isotopes,
due to the spectrum change presented in the paper.
The main study presented in this paper is the analysis of core reac­
tivity with burned fuel elements. It was shown that the effects of reactor
poisons 135 Xe and 149 Sm on TRIGA core reactivity are − 930 pcm and −
690 pcm, respectively. The results were compared to similar findings
obtained with unit-cell analysis with WIMSD-5B (Jeraj et al., 2002) and
it can be observed that highest discrepancies are for 239 Pu. Nevertheless,
the results are in good agreement, and it can be concluded that the
physics of the fuel burnup changes can be sufficiently described with
using only unit-cell calculations. In addition, weekly measurements of
excess reactivity were used to validate the complete operational history
simulations, and it can be concluded that the agreement between both
absolute and relative excess reactivity data and Serpent-2 simulation is
good. The relative changes are also well described by the TRIGLAV code.
One of the main motivations for this work was to investigate the
discrepancies of measured and calculated keff for core No. 190. By
simulating the complete history, detailed fuel burnup information for
each core configuration was obtained and used in the validated MCNP
model. We were able to explain 4000 ± 100 pcm out of a 5500 ± 500
pcm discrepancy. Further analysis is needed to understand the
remainder. The overall conclusion to the presented work is that, by
having both full Monte Carlo burnup calculations and detailed opera­

tional history data, we were able to obtain accurate fuel burnup data
that can be used in the future for experimental campaign support,
reactor decommissioning, fuel management, and most importantly,
validation of new methodologies for calculating burnup (Roskoff and
Haghighat, 2018).

7. Discussion and conclusion
The JSI TRIGA research reactor offered a unique opportunity to
perform a detailed analysis of its fuel element burnup as the complete
operational history is well documented. With the performed operational
history analysis, data were obtained that enable simulation of the
complete operational history. As each individual operation was recor­
ded, in the future all of the 27 000 reactor power changes could be
simulated. In addition, excess reactivity measurements were recorded,
enabling the validation of burnup methodologies and the study of un­
certainty propagation through burnup and multiple sensitivity studies
(ParkDong et al., 2018; García-Herranz et al., 2008).
The final fuel element burnup and its isotopic composition were
calculated with both Monte Carlo Serpent and deterministic TRIGLAV
code. For most fuel elements the differences between both codes are
within 10%, which increases to 30% when comparing isotopes, such as
239
Pu and 137 Cs. Two methodologies were also compared on criticality
benchmark core No. 132. It can be concluded that the highest difference
is for fuel elements with higher amounts of surrounding water, meaning
that the unit cell employed in the TRIGLAV code could be improved in
the future. Nevertheless, it is shown that despite the simplicity of the
TRIGLAV code the obtained results show great promise in using the code
for TRIGA reactor fuel management and burnup analysis.
The analysis of spatial burnup effects showed that, in the future, axial

and angular depletion zone division should be implied as the differences
between maximum and minimum burnup in a fuel element could be
more than 25 %, resulting in high sensitivity of control rod insertion. In

Declaration of competing interest
The authors declare that they have no known competing financial
interests or personal relationships that could have appeared to influence
the work reported in this paper.
Acknowledgements
The authors acknowledge the project (Young researcher project Anˇze
Pungerˇciˇc, 52060) was financially supported by the Slovenian Research
Agency.
The authors acknowledge the financial support from the Slovenian
Research Agency (research core funding No. P2-0073).

Appendix A. Supplementary data
Supplementary data to this article can be found online at />A Ray-tracing algorithm for water thickness determination
In the analysis of fuel burnup spatial effects, it was determined that fuel surrounding is important from the standpoint of the fuel burnup and
isotope distribution. Water thickness around fuel elements was determined with a simple ray-tracing algorithm described here.
For a defined point in Cartesian coordinate system P a set of rays is defined, varying in direction D so that the whole 360∘ angle is covered. In a
TRIGA research reactor fuel elements, control rods and graphite reflector can all be defined with a circle at position C and radius R > 0. Considering a
⃒
⃒
parameterized ray X(t) = P + tD and a implicitly defined circle ⃒X − C|2 = R2 , a substitution of the ray equation into the circle equation can be made,
by defining Δ = P − C, to obtain quadratic equation in t Eqn 3:

⃒
⃒
⃒ 22
⃒ 2

⃒D| t + 2(D ⋅ Δ)t + ⃒Δ| − R2 = 0,
19

(3)


A. Pungerˇciˇc et al.

Progress in Nuclear Energy 130 (2020) 103536

where the formal roots of the equation are Eqn 4
√̅̅̅
− D⋅Δ ± δ
⃒ 2
t=
,
⃒D|

(4)

⃒
⃒
⃒
⃒
and the determinant is defined as δ = (D ⋅Δ) − ⃒D|2 (⃒Δ|2 − R2 ). If δ < 0, the line does not intersect the circle. If δ = 0, the line is tangent to the circle
(one point of intersection). If δ > 0, the line intersects the circle in two points, and the one closer is chosen in our case.
The algorithm calculates the distance between the source point of the ray and the closest intersection with the circle. This is done for all defined
rays and circles (core elements). Number of rays defines the angular resolution. A python script was created that reads the TRIGA reactor core
configuration and defines the needed fuel elements, control rods and graphite reflector. Two examples of the described ray-tracing algorithm for a
TRIGA reactor are presented in Fig. 36. In the last step the distance is averaged over multiple rays to obtain the water thickness at desired angles.

Fig. 36. Screenshot of the ray-tracing algorithm for determination of water thickness around fuel elements in a TRIGA reactor.

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