Acta Polytechnica CTU Proceedings

https://doi.org/10.14311/APP.2022.37.0024
Acta Polytechnica CTU Proceedings 37:24–30, 2022 © 2022 The Author(s). Licensed under a CC-BY 4.0 licence

Published by the Czech Technical University in Prague

MODELLING OF FISSION GAS RELEASE IN UO2 DOPED FUEL
USING TRANSURANUS CODE

Jheffry Gonzaleza, b, c, ∗, Martin Ševečeka

a Czech Technical University in Prague, Faculty of Nuclear Sciences and Physical Engineering, Jugoslávských
partyzánů 1580/3, 160 00 Prague 6 – Dejvice, Czech Republic

b Royal Institute of Technology, Division of Nuclear Engineering, Kungliga Tekniska Högskolan, 100 44
Stockholm, Sweden

c Grenoble INP – Phelma, School of engineering in Physics, Applied Physics, Electronics & Materials Science, 3
Parvis Louis Néel, 38016 Grenoble Cedex 1, France

∗ corresponding author: jheffrygonzalez@gmail.com

Abstract. The expected benefits from Cr-doped fuel are improved retention of fission gases within
the pellets due to its large grain size. To demonstrate this, several experiments have been carried out
by Halden reactor and Studsvik. These experiments are now being used to benchmark several fuel
performance codes among them transuranus code. All this as part of a Coordinate Research Project
(CRP) by IAEA named Testing and Simulation for Advanced Technology and Accident Tolerant Fuels
(ATF-TS). This work is introducing a novel fission gas diffusivity model for doped fuel in transuranus
code. It is observed the benefits of introducing this new model when comparing to the standard model
already existing in transuranus. Nevertheless, more work needs to be carried out to fully understand
all the phenomena involved in adding dopant in UO2 due to change of thermo mechanical properties.

Keywords: Doped fuel, transuranus, ATF, fission gas release, diffusivity.

1. Introduction
The study of fission gas release, FGR, is an impor-
tant area within the fuel rod performance analysis
that needs to be covered because these gaseous fis-
sion products in the UO2 fuel pellet are detrimental
to the thermo-mechanical properties of the fuel [1].
Fission gas release depends on several mechanisms
that occur within the fuel pellet, more specifically
within the grain (see Figure 1). Few of these mecha-
nisms are, for instance, thermal contributions: grain
boundary diffusion, bubble migration, trapping and
resolution; and there are also athermal contributions:
recoil, knock-out and sputtering.

Figure 1. Basic mechanisms of fission gas release [2].

Because in this work we are dealing with doped

fuel, it is vital to understand how the properties and
characteristics of this fuel will impact on the FGR
mechanisms. Although there are other properties that
might need to be investigated this work focuses on the
selection of a suitable gas diffusivity model for doped
fuel.

The selected diffusivity model will be implemented
in transuranus code. The new implementation done
in the source code will be validated against experimen-
tal results performed carried out at the Halden reactor
(IFA 716 experiment) and the Studsvik Cladding In-
tegrity Program (SCIP-II). This work is also part of a
Coordinate Research Project (CRP) by IAEA1 named
Testing and Simulation for Advanced Technology and
Accident Tolerant Fuels (ATF-TS) and the results
will be also compared with other members that are
simulating this novel fuel in other fuel performance
codes.

In Section 2, the methodological details of this work
are explained, a brief explanation of the experiments
to compare to and considerations taken when per-
forming the simulations. Section 3 shows the results
obtained and their comparison against the tests. Fi-
nally, in Section 4, it will be shown all the conclusions
and also recommendations for future improvements
of the modelling of this fuel in transuranus.

2. Methods
The methodology used for the development of this
work is as follows i) study the models related to fis-

1https://www.iaea.org/projects/crp/t12032

https://doi.org/10.14311/APP.2022.37.0024
https://creativecommons.org/licenses/by/4.0/
https://www.cvut.cz/en
https://www.iaea.org/projects/crp/t12032

vol. 37/2022 Modelling of Fission gas release

sion gas release in transuranus (i.e. fission gas
diffusivity, thermal conductivity, etc.); ii) select the
gas diffusivity model from transuranus or introduce
a new model; iii) verify that the new implemented
model works as expected; iv) identify all the fuel prop-
erties and reactor conditions required in the input file
to run the simulation (type of fuel and cladding, flux,
linear power, temperature of the coolant, grain size,
etc); v) data collection of the experimental analysis
performed by Halden and Studsvik; vi) validate the
implemented model by benchmarking the results ob-
tain from transuranus with the experimental data.
FGR is strictly dependent on temperature; there-

fore, choosing a good thermal conductivity model for
this type of fuel is essential. There is no thermal
conductivity model available for doped fuel; however,
according to Arborelius et al. there is only a small
change in thermal conductivity of fresh fuel due to
doping and this small difference is expected to be neg-
ligible after the burnup increase [3].Although it would
make sense to use standard undoped UO2 thermal con-
ductivity during simulations the reality is that in this
work the correlation used is the one proposed by Ohira
et al. for for high burnup UO2 pellets [4]. The reason-
ing for this is explained in Section 2.4. transuranus
uses a mechanistic model for fission gas behaviour and
release from doctoral thesis of [5]. For the intragranu-
lar diffusion coefficient, transuranus has different
models; nevertheless, the model that is most widely
accepted for fission gas diffusivity is from [6] which
will be named as a standard during this article.

2.1. Selection and modelling of FG
diffusivity

Turnbull model for the single gas atom diffusion coef-
ficient can be seen from Equations 1 to 4.

Def f = D1 + D2 + D3 (1)

D1 = 7.6 × 10−10e−
3500

T (2)

D2 = 3.22 × 10−16
√

Re−
13800

T (3)

D3 = 3.22 × 10−16R, (4)

where Deff is the effective diffusion coefficient, D1 is
the intrinsic high-temperature component, D2 is the
irradiation enhanced thermal component, D3 is the
athermal term and R is the rating in W/gU.

Because Che et al. showed a good agreement with
Halden FGR experiments when using an empirically
tuned enhanced gas diffusion, Cooper et al. decided to
investigate in deep the influence of dopant on fission
gas diffusivity. In that work, Cooper et al. proposed a
diffusion coefficient for uranium doped fuel [7]. Equa-
tion 5 shows enhancement of the diffusivity, using the

undoped UO2 diffusivity model in Equation 1 as a
baseline.

Ddoped = exp
(

H1
kb

[
1
T
−

1
T1

])
D

undoped
1 +

exp
(

H2
kb

[
1
T
−

1
T2

])
D

undoped
2 +

D
undoped
3 ,

(5)

where kb is the Boltzmann constant. H1, H2, T1 and
T2 are parameters derived for the multiscale analytical
enhanced diffusivity model (see Table 1). Dundoped1 ,
D

undoped
2 , and D

undoped
3 are calculated with Equa-

tions 2 to 4. Because there are a number of uncertain-
ties when obtaining these parameters Cooper et al.
examined two cases namely case A and case B. The
first case has minimal alterations migration energy
and sink strength given by the oxygen potential. In
contrast, case B overestimates this migration energy
and sink strength based on the experience from [8].

Parameter Case A Case B

T1 = T2 [K] 1773 1773
∆H1 [eV] 0.3198 0.3282
∆H2 [eV] -0.3345 -0.6998

Table 1. Parameters for the enhanced diffusivity
model derived for Cr-doped fuel [7].

Now, it is important to understand the distinc-
tion (if any) between the models before implementing
the proposed FG diffusivity for the doped fuel in
transuranus. Hence, by plotting the FG diffusion,
it is clearly depicted the difference between them (see
Figure 2). For the model of the FG diffusivity of doped
fuel, the two cases proposed by [7] are considered and
they are shown case A and case B.

Figure 2. Gas diffusivity in undoped UO2 fuel using
Turnbull et al. model, and gas diffusivity in Cr-doped
UO2 fuel applying Cooper et al. model.

From Figure 2, it is observed that from 700 to
1600 K there is a major difference between case A
of Cooper model and the standard diffusion model,
whereas for the case B the range is wider from 500 to

Jheffry Gonzalez, Martin Ševeček Acta Polytechnica CTU Proceedings

1600 K. The ratio between the doped fuel model and
the standard model can be as high as 3.4 and 17.5 for
case A and B respectively, at around 1000 K. This
ratio difference is significant; however, if we consider
the range of temperature from 500 to 2000 K the mean
ratio will be for case A a factor of 1.63 and for case B
a factor 4.66.

2.2. Implementation and verification
In this work both cases of Cooper model are consid-
ered. Therefore, it was necessary to have two new
versions of transuranus that includes case A and
B in which the only difference is the parameters in
Table 1. The implementation done in transuranus
was revised by transuranus developers to ensure
that the coding is up to their standards and minor
modifications of the code were proposed by them in
terms of clarity of the code.
As evidenced in Figure 2, the value of diffusion

coefficient of doped fuel is significantly larger over the
range of from 500 to 1600 K, this would mean that
if the size of the grain remains the same one would
expect a greater FGR when comparing to standard
UO2 fuel. Hence, for the verification of the modelling,
several tests were performed. In these tests the grain
size was kept the same but using the new model im-
plemented in TU. Table 2 shows the percentage of
fission gas release inside the fuel rod and the internal
rod pressure difference when using Turnbull model
and Cooper model in an another Halden case (IFA
429).

Test cases Parameter Model Value

IFA420cd FGR Turnbull 12.34 %
Cooper 23.17 %

Pressure Turnbull 6.45 MPa
Cooper 7.27 MPa

IFA420ch FGR Turnbull 17.79 %
Cooper 42.95 %

Pressure Turnbull 6.95 MPa
Cooper 11.18 MPa

Table 2. Model verification using IFA 429 case.

For both cases, there is a considerable increase in
FGR and pressure when using the diffusivity model
for doped fuel. This could confirm that the implemen-
tation was done correctly and that the benchmark of
the code with experimental data can be carried out.

2.3. Experimental data
The implemented model in transuranus is validated
with experimental data performed by Halden and
Studsvik. From the experimental data and fuel charac-
teristics all the input data required is gathered to run
the simulation. Some of the input data are unchanged

overtime while other data are constantly changing as it
is the case of the the power, fast flux and temperature
of coolant. For this variable data, an additional pro-
cessing is needed because transuranus have a maxi-
mum number of record for the Macro-step that can
be included in the input file. This limit is up to 5000,
however, the data steps provided is around 160000
for IFA 716 and 24000 for SCIP-II. Hence, a software
called Fuel Rod Analysis ToolBox (FRAtoolbox) is
used to merge the quantities of the large number of
data sets [9].

2.3.1. Halden experiment IFA 716
The main objective of the IFA 716 experiment is to in-
vestigate the effect of dopant concentration and grain
size on the FGR [10]. The experiment was carried
out between January 2011 and May 2015 for a total
operation time of 842 days divided in 15 operation
cycles. IFA 716 assembly consisted in six rods each
with different type of fuel.

Few of these characteristics for the IFA 716 case
(rod 1 and 2) are reported in Table 3; clearly, the main
differences between these two fuels are the Cr2O3 con-
tent and the fuel average grain diameter. Moreover,
there are some pellets that have a hollow section this
only applies for the pellets on the top where instrumen-
tation was inserted to obtain, for instance, the on-line
measurement of the fuel temperature center line. Fig-
ure 3 shows the average linear heat rate measured for
the rods 1 and 2 versus time [10]. Evidently, rod 1 has
a total operation time of 840 days while rod 2 only has
over 700 days. This difference is due to a malfunction
in rod 2 that caused this rod to be removed from the
reactor, in contrast, rod 1 (and the others) remained
until the end of the test. The average linear heat rate
(LHR) of both rods are roughly the same throughout
the experiment; therefore, the average LHR of rod 1
will be used during the simulation in transuranus.

Figure 3. IFA 716 average linear heat rate measured
during the test.

2.3.2. Studsvik experiment SCIP-II
The main objective of SCIP-II experiment is to inves-
tigate the effect of power ramps on doped fuel with

vol. 37/2022 Modelling of Fission gas release

IFA 716 Rod 1 IFA 716 Rod 2

Cladding material Zircaloy-4 Zircaloy-4
Fuel material UO2 + Cr2O3 UO2
Fill gas He He
Pellet outer diameter [mm] 9.12 9.13
Pellet inner diameter, hollow section [mm] 1.8 1.8
Cladding outer diameter [mm] 10.75 10.75
Cladding thickness [mm] 0.725 0.725
Active fuel length [mm] 399.5 399.4
Free volume [m3] 5.8 5.95
Fuel density [g/cm3] 10.50 10.55
Fill gas pressure [MPa] 1 1
Fuel Cr2O3 content [ppm] 1580 N/A
Fuel U-235 enrichment [wt %] 4.9 4.89
Fuel average grain diameter [µm] 71 11

Table 3. Fuel characteristics of IFA 716 rod 1 and 2 simulated in this work [11].

a based irradiation. This based irradiation was car-
ried out between September 2006 and August 2009
at the OKG2 reactor divided in 3 cycles. Similarly,
as the IFA 716 case, the fuel characteristics for the
SCIP-II case are reported in Table 4. Rods L707 and
L708 are fundamentally the same, there is no major
distinction between the two according to the given
data. What makes these rods different is the base ir-
radiation that they underwent before being subjected
to power ramps in a test reactor. Both rods have a
total operation time of 1095 days as based irradiation
with an average LHR of 14 and 13 kW/m for rod L707
and L708, respectively. This led to a mean BU of 28
MWd/kgU in the case of L707 and 26 MWd/kgU for
L708.
The ramp test for each rod was carried out differ-

ently for both, with rod L707 having a total time of
21.33 h while rod L708 with a total time of 14.32 h.
The ramp was hold for 12 h and around 1 minute
for rod L707 and L708, respectively. Figure 4 depicts
the average LHR during the ramp test for each rod.
In contrast to the Halden experiment, there is no
in-situ measurement of fuel center line temperature
or plenum pressure which will make the implemented
model harder to validate against this experiment. The
only measurement that is given comes from the post-
irradiation examination where the data for FGR is
obtained.

2.4. Additional considerations
The only criteria for selection thermal conductivity
model is how close the fuel center line temperature
(FCLT) obtained from transuranus is to the ex-
perimental data. transuranus has a set of thermal
conductivity models for different fuels including a cor-
relation for the standard UO2. When using the LWR
standard correlation (model already implemented in
transuranus) proposed by [12], it results in the
Figure 8 (top) where evidently there is not a good
agreement between this model and the experimental

Figure 4. SCIP II ramp test.

data. Therefore, exploring other thermal conductivity
models is necessary to continue to the validation of
the FGR. The model that best fit to the experimen-
tal results is surprisingly a correlation used for high
burnup UO2. Consequently, the correlation for high
burnup UO2 pellets found in transuranus is the
thermal conductivity model of choice for the study of
FGR in this work.

In addition to using a thermal conductivity for high
burnup UO2, it is considered that the gas diffusivity
model for doped fuel is the same independently of the
chromia concentration in the fuel because this diffu-
sivity model does not have a correlation as function
of the amount of chromia content.

3. Results
The parameters to benchmark are fuel center line
temperature, upper plenum pressure, and fission gas
release. However, no all data is available for all the
rods tested. For instance, for SCIP-II, the only data to
compare is the FGR obtained in the post-irradiation
examination.

Jheffry Gonzalez, Martin Ševeček Acta Polytechnica CTU Proceedings

SCIP-II Rod L707 SCIP-II Rod L708

Cladding material Zircaloy-4 Zircaloy-4
Fuel material UO2 + Cr2O3 UO2 + Cr2O3
Fill gas He He
Pellet outer diameter [mm] 8.67 8.67
Cladding outer diameter [mm] 10.05 10.05
Cladding thickness [mm] 0.605 0.605
Active fuel length [mm] 480 480
Fuel density [g/cm3] 10.50 10.55
Fill gas pressure [MPa] 1 1
Fuel U-235 enrichment [wt %] 3.0 3.0
Fuel average grain diameter [µm] 49 49

Table 4. Fuel characteristics of SCIP-II rod L707 and L708 simulated in this thesis.

3.1. Benchmark of Halden IFA 716
Because pressure transducer of rod 2 was damaged,
there is no benchmark of this for rod 2. On the other
hand for rod 1, the pressure of case A and B for rod 1
is the same during the first 300–350 days of operation
and for both cases transuranus predicted well the
pressure when compared to the experimental data.
However, after 350 days of operation transuranus
underestimates the pressure when using diffusivity
model case A while when using case B the pressure is
overestimated (see Figure 5).

Figure 5. Predicted vs. measured rod pressure for
rod 1, including the two cases for the diffusivity of
doped fuel.

Figure 7 shows the result of the comparison of the
predicted FCLT versus the measured FCLT taken
from the test for rods 1 and 2. It can be observed that
for Rod 1 (see Figures 7a and 7b), there is a good
agreement between the experimental and simulation
when the burnup is low enough (< 17 MWd/KgUO2)
while at higher burnup there points that fall out of the
established uncertainty zone of ±9 % and yet close
to this zone. Around 100 % of agreement is found
if we accept this uncertainty. In case of Rod 2, in
Figure 7c at low burnup the predicted temperature
fall within the uncertainty opposite to what occurs
at higher burnup with several data points falling far
from this zone. This over-prediction of the temper-

ature, after approximately 400 days of operation, is
also observed in Cooper et al. work; however, the tem-
perature difference between predicted and measured
is larger [7].
Finally, for the fission gas release, the given data

did not contain the evolution of fission gas release
versus operation time; instead, what is available is the
fission gas release at different stages of the experiment.
Nevertheless, this is not true for rod 2, where no data
was collected at any point and the rod presented signs
of leakage at around 700 days of operation. Hence,
no puncture was performed to obtain the fission gas
release. Figure 6 shows the predicted fission gas release
for rod 1 for both diffusivity cases, the predicted fission
gas release for rod 2 and the measures taken by Halden
at four different times with their uncertainty for rod 1.
Despite having a good agreement between measured
and predicted for FCLT and pressure, the fission gas
release shows a wide difference between the measured
and simulation. This is more evident for rod 1 case
A where the prediction of FGR is 1.6 % while case
B gives a better results with 3.8 % at 625 days. The
measured value for the fission gas release at the same
time was 5.71 % ± 1.36 %. Surprisingly, the fission
gas release of rod 2 is lower than the rod 1 when using
diffusivity case B.

Figure 6. Predicted fission gas release for rod 1 and 2.

vol. 37/2022 Modelling of Fission gas release

(a) . Rod 1 UO2 doped fuel diffusivity case A (b) . Rod 1 UO2 doped fuel diffusivity case B

Figure 7. Predicted vs. measured fuel center line temperature for IFA-716 rods 1 and 2. For burnup lower than 17
MWd/KgUO2 (shown as ’5’) and burnup higher than 17 MWd/KgUO2 (shown as ’?’).

3.2. Benchmark of Studsvik SCIP-II
Unfortunately, there is no data to compare FCLT or
pressure as it was done with IFA-716. Table 5 shows
the fission gas release obtained during the post irradia-
tion examination and the fission gas release predicted
by transuranus using fission gas diffusivity case
B. For this experiment, the prediction overestimate
the experimental data. This is more evident for the
1 minute ramp (rod L708) where there is almost no
release according to PIE but the prediction is 2.5 %.

Rod L707 Rod L708

FGR / PIE 3.0 % 0.04 %
FGR / transuranus 5.8 % 2.5 %

Table 5. Fission gas release comparison at the end
of ramp

4. Conclusions
The fission gas diffusivity model was compared to
two different experiments, one for ramp test and the
other for long period operation. The results show that
there are still uncertainties in the prediction using
this model in transuranus. The Halden experiment,
however, was surrounded by some failures in sensors
during the experiment. As a result, it is unclear

whether these experimental results can be trusted.
Similarly, there was a lack of data to make a better
comparison against the SCIP-II experiment. It will be
important to continue the validation, perhaps against
other experiments, to draw a final conclusion on this
model with the transuranus code. Additionally,
defining the model exclusively for doped fuel can be
beneficial to improving the accuracy of the predictions.

Acknowledgements
This project is financed from the state budget by the Tech-
nology Agency of the Czech Republic and the Ministry of
Industry and Trade within the THETA Programme. A
support from the IAEA CRP ATF-TS T12032 is acknowl-
edged.

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Jheffry Gonzalez, Martin Ševeček Acta Polytechnica CTU Proceedings

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Acta Polytechnica CTU Proceedings 37:24–30, 2022
1 Introduction
2 Methods
2.1 Selection and modelling of FG diffusivity
2.2 Implementation and verification
2.3 Experimental data
2.3.1 Halden experiment IFA 716
2.3.2 Studsvik experiment SCIP-II

2.4 Additional considerations

3 Results
3.1 Benchmark of Halden IFA 716
3.2 Benchmark of Studsvik SCIP-II

4 Conclusions
Acknowledgements
References