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Evaluation of Kinetic Parameters RSG-GAS Reactor
Equilibrium Silicide Core Using Continuous-EnergyMonte Carlo Serpent 2 CodeSurian Pinem, Liem Peng Hong, Wahid Luthfi, Tukiran Surbakti & DonnyHartanto
To cite this article: Surian Pinem, Liem Peng Hong, Wahid Luthfi, Tukiran Surbakti & DonnyHartanto (22 Jan 2024): Evaluation of Kinetic Parameters RSG-GAS Reactor Equilibrium SilicideCore Using Continuous-Energy Monte Carlo Serpent 2 Code, Nuclear Science and Engineering,
DOI: 10.1080/00295639.2023.2284433
To link to this article: https://doi.org/10.1080/00295639.2023.2284433

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NUCLEAR SCIENCE AND ENGINEERING© 2024 American Nuclear Society
DOI: https://doi.org/10.1080/00295639.2023.2284433

Evaluation of Kinetic Parameters RSG-GAS Reactor Equilibrium
Silicide Core Using Continuous-Energy Monte Carlo Serpent2 CodeSurian Pinem, a* Liem Peng Hong, b,c Wahid Luthfi, a Tukiran Surbakti,aand Donny HartantodaNational Research and Innovation Agency (BRIN), Research Organization for Nuclear Energy, Research Center
for Nuclear Reactor Technology, 80th Building of KST B.J. Habibie (PUSPIPTEK) Serpong, South Tangerang,
Banten 15310, IndonesiabTokyo City University, Graduate School of Engineering, Cooperative Major in Nuclear Energy, 1-28-1,
Tamazutsumi, Setagaya, Tokyo, Japanc
Nippon Advanced Information Service, (NAIS Co., Inc.), Scientific Computational Division, 416 Muramatsu,
Tokaimura, Ibaraki, Japand
Oak Ridge National Laboratory, One Bethel Valley Road, Oak Ridge, Tennessee 37830
Received September 4, 2023
Accepted for Publication November 9, 2023

Abstract — The purpose of this study is to determine the kinetic parameters of the RSG-GAS
equilibrium core. The calculated kinetic parameters are the effective delayed neutron fraction βeff,
the neutron generation time Ʌ, and the prompt neutron lifetime ℓ since they are related to the safetyof nuclear operations. The kinetic parameters were calculated using the Serpent 2 code with the
ENDF/B-VII.1 and ENDF/B-VIII.0 nuclear data libraries. Calculations were performed using var­ious adjoint-weighted methods such as Meulekamp’s method, Nauchi’s method, the Iterated Fission
Probability method, and the Perturbation Technique. The calculated results of the six-group delayed
neutron fraction by the Meulekamp and the IFP methods showed no significant difference. Choosing
the IFP method as the reference, the maximum difference for βeff (694 pcm) is 0.73%, and the
maximum difference for Ʌ and ℓ is 1.89%. The calculated kinetic parameters with ENDF/B-VII.1 and
ENDF/B-VIII.0 are quite close, with a maximum difference of 0.9%. The sensitivity analysis results
indicate several nuclides and reaction types that dominantly affect the βeff and Λ. The results of the
kinetic parameter calculations can be used for the safety analysis of the RSG-GAS equilibrium core.
Keywords — Kinetic parameters, RSG-GAS, equilibrium core, Serpent 2, ENDF/B-VII.1, ENDF/B-VIII.0.
Note — Some figures may be in color only in the electronic version.

I. INTRODUCTION
The RSG-GAS reactor is an open pool–type multi­
purpose research reactor with a nominal thermal power of
30 MW. The reactor uses light water as a coolant andmoderator and also beryllium as a reflector. The fuel usedin the RSG-GAS reactor was Material Testing Reactor(MTR)–type oxide fuel (U3O8-Al) initially, which was*E-mail: suri001@brin.go.id

later converted to silicide fuel (U3Si2-Al) with the same
dimension, uranium density, and enriched uranium. The
reactor achieved its first criticality in 1987,[1] and in
1999, the core conversion program from oxide fuel(U3O8-Al) to silicide fuel (U3Si2-Al) was carried out toimprove reactor performance. Silicide fuel (U3Si2-Al) canbe used with higher-density uranium loading to extend
the operating cycle of the reactor.[2] The new equilibrium

1

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PINEM et al. · KINETIC PARAMETER RSG-GAS REACTOR EQUILIBRIUM SILICIDE CORE

silicide core was proposed and designed by Liem et al.[3]while the transition core strategies from oxide to silicide
were investigated and established by Liem andSembiring.[4]Kinetic parameters are essential for the safety ofreactor operation because they relate to the calculationof reactivity values and transient analysis of the reactor
core.[5–8] The kinetic parameters also depend on the coreburnup, so it is necessary to calculate the RSG-GAS
equilibrium core kinetic parameter. Some of the kinetic
parameters used so far in RSG-GAS were provided by thevendor, Interatom, and that was for the oxide fuel of
RSG-GAS. The kinetic parameters of RSG-GAS’s firstworking core were evaluated[9]; however, after the core
conversion to silicide fuel, the kinetic parameters were
not evaluated, and the present work tries to provide them.
It is expected that the calculated kinetic parameters of
RSG-GAS are also needed during the future validation
experiments.
The silicide equilibrium core configuration chosen inthis calculation comprises the 88th and 89th cores since
the burnup distributions were measured for the 88th core
and the calculation results are in good agreement with themeasured results.[10,11] The calculation of burnup frac­tion, excess reactivity, and control rod worth was also
carried out, and the results are also close to the experi­mental results.[12,13] In these calculations, beryllium
impurity after operating until the 88th core was also
considered.
Serpent 2 is a general-purpose, three-dimensional,
and continuous-energy particle code based on the Monte
Carlo transport method.[14] This code has the advantage
of solving problems of complex reactor core geometries
using a continuous-energy nuclear data library. Serpent 2
also was developed with capabilities to calculate pointkinetics parameters such as delayed neutron fractions andneutron generation time. Various methods of calculating
adjoint-weighted point-kinetics parameters are implemen­ted on Serpent 2 such as the Iterated Fission Probability(IFP) method; the Perturbation Technique; and methods
by Meulekamp, Nauchi, and Kameyama.[15] This paper
will evaluate kinetic parameters using the Serpent 2 codewith Meulekamp’s method, Nauchi’s method, the IFP
method, and the Perturbation Technique.
Calculations were carried out using the nuclear datalibraries ENDF/B-VII.1 and ENDF/B-VIII.0.[16,17] The
use of several methods and new cross-sectional datalibraries is essential to obtain accurate results. The calcu­
lated kinetic parameters are delayed neutron fraction,either its effective delayed neutron fraction βeff or sixgroup delayed neutron fraction βi followed by its

corresponding delayed neutron precursor decay constantλi, the average neutron lifetime ℓ, and the neutron gen­eration time Ʌ. The effective delayed neutron fraction βeff
is also calculated in one operating cycle of RSG-GAS,
the 88th core, to determine its changes during burnup.

II. RSG-GAS EQUILIBRIUM SILICIDE CORE
The equilibrium core of the RSG-GAS reactor con­sists of 40 standard fuel elements (FEs) and 8 control
elements (CEs) and is surrounded by beryllium asa reflector. The RSG-GAS FE is composed of 21 U3Si2Al fuel plates with 19.75 wt% enrichment and uranium
density of 2.96 g/cm3 U with 250 g of nominal 235U massin each FE. The RSG-GAS equilibrium core data areshown in Table I. Each fuel plate was mounted on support
parts of the fuel assembly, so light water (H2O) could
pass between each plate as a neutron moderator andcoolant. The cross-sectional dimensions of one FE are
8.1 cm long and 7.71 cm wide, with the left and right fuelsupport having a length of 8.05 cm and a width of
0.45 cm, as depicted in Fig. 1. The CE has the samecross-sectional size as the FE. However, the three outerplates on each side are replaced by two pairs of control
guide plates, into which the absorber blades are inserted.
So, the number of CEs is only 15 fuel plates, as depicted
in Fig. 2. The absorber on the CE is made of Ag-In-Cd
with a weight ratio of 80%-15%-5%.
The reactor core has a central irradiation position thatoccupies 2×2 grid positions and an irradiation position thatoccupies another four different places. In addition, there
are five rabbit system facilities; one is pneumatic, and therest are hydraulic. Beryllium reflector elements occupy theremaining 37 grid positions, with seven beryllium reflector
elements having 50-mm-diameter holes used as irradiation
facilities and filled with beryllium when not in use. The
equilibrium core of the RSG-GAS reactor with all irradia­
tion facilities within the core is shown in Fig. 3.

III. METHODOLOGY
III.A. Kinetic Parameters
Solving reactor dynamics problems using point kinetics
needs kinetic parameters such as effective delayed neutron
fraction βeff, neutron generation time Ʌ, and prompt neutron
lifetime ℓ. A delayed neutron fraction is used to show
a fraction of delayed neutrons to the whole neutron popula­tion being produced in a nuclear reactor. The prompt neutron
lifetime is the average age of a neutron from being born from
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3

TABLE I
Reactor Main Design Data of RSG GAS (Silicide Core)*
GeneralReactor type
Fuel element type
Cooling system
Moderator and coolant
Reflector
Nominal power [MW(thermal)]

Pool typeLow enriched uranium silicide MTR
Forced convection downflow
H2 O
Be and H2O
30Core characteristics

Number of FEs
Number of CEs
Number of fork-type absorbers (pairs)
Nominal cycle length (effective full power day)Average burnup at BOC (percent loss of 235U)
Average burnup at EOC (percent loss of 235U)
Average discharge burnup at EOC (percent loss of 235U)

40
8
8
25
23.3
31.3
53.7

Fuel/CEs
Fuel/CE dimension (mm)
Fuel plate thickness (mm)
Coolant channel width (mm)Number of plates per FE
Number of plates per CE
Fuel plate clad material
Fuel plate clad thickness (mm)
Fuel meat dimension (mm)
Fuel meat material235
U enrichment (wt%)
Uranium density in meat (g/cm3)
235
U loading per FE (g)235
U loading per CE (g)Absorber meat material
Absorber thickness (mm)Absorber clad material
Absorber clad thickness

77.1 × 81 × 600
1.3
2.55
21
15
AlMg2
0.38
0.54 × 62.75 × 600
U3Si2Al
19.75
2.96
250
178.6
Ag-In-Cd
3.38
SUS-3210.85*Ref.[1].

a fission reaction until it finally induces fissions with fuel,undergoes a capture reaction, or escapes from the reactor
core. On the other hand, the neutron generation time (neutron
lifetime) is the average age of a neutron in the reactor corefrom being produced until it finally reacts with the reactor
components or leaves the reactor core.
Delayed neutrons differ from prompt neutrons being
produced by fission reactions in the way that delayed
neutrons are produced by radionuclide-producing neutrons
during their decay process. These radionuclides or isotopes
are called the delayed neutron precursor, and their half-life
has a delayed effect on the neutron being produced.
Delayed neutrons in a nuclear reactor are created from
NUCLEAR SCIENCE AND ENGINEERING · VOLUME 00 · XXXX 2024

fission products emitting neutrons through radioactive
decay, which leads to delayed neutron intensity thatchanges through time. Some fission products like 87Br
with a half-life of 55.65 s decay into 86Kr (2.52%), and137
I with a half-life of 24.13 s decays into 136Xe (7.14%).
Both mentioned isotopes decay by (β−,n) reaction, emitting
a neutron, and both are considered as delayed neutron
precursors. Isotopes that are in a highly excited state also
allow them to eject a neutron during their decay. The
delayed neutron fractions of 235U and 239Pu are 650 and
210 pcm, respectively.[18] Since the delayed neutron pre­cursor half-life will affect the delayed neutron intensity as
a function of time, in general, there are six groups of

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PINEM et al. · KINETIC PARAMETER RSG-GAS REACTOR EQUILIBRIUM SILICIDE CORE

Fig. 1. RSG GAS standard FE (in units of millime[1]ters).

delayed neutrons. Although delayed neutrons make up
only around 1% of the neutron population in the reactor
core, they are important for controlling a nuclear reactor.

III.A.1. Meulekamp-Spriggs (k-Ratio)
In general, the effective delayed neutron fraction βeff
or the ratio of the delayed neutron to the total neutron
generated on each fission could be written as

Fig. 2. RSG GAS control FE with absorber blades
inserted (in units of millimeters).[1]But, there are various approximations regarding how tocompute these parameters. Meulekamp used the ratio offission induced by delayed neutrons to all fission
induced by delayed and prompt neutrons to compute
βeff.[19] This led to some modifications to the βeff
equation:

where
ϕð~
r; Ω; EÞ = neutron fluxr; Ω0 ; E0 Þ = adjoint neutron fluxϕþ ð~r; E0 Þ = macroscopic cross section for fission reaction probabilityΣf ð~χ ðE0 Þ = fission neutron energy spectrumνðE0 Þ = total number of fission neutron emissions on each fission
χd ðE0 Þ = delayed neutron energy spectrum
νd ðE0 Þ = number of delayed neutron emissions on each fission.
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5

Fig. 3. Equilibrium core of the RSG-GAS reactor.[1]This equation could be simplified using the operator
h f ; gi to perform an integration over all spatial, angular,
and energy variables. By some simplification, this inte­
gration could be written into

Spriggs rewrote the βeff equation, so it focused only on
counting the delayed neutron fraction; hence, the k-ratiois then introduced as follows[20]:0By this equation, β0 is defined as another delayed neutron
fraction by counting the delayed neutron produced by
precursors from nuclear data at each fission history, andkd came from the delayed neutron energy spectrum. On
the other hand, the counting delayed neutrons are also
proportional to the counting fission induced by thedelayed neutrons. This counting process could lead tothe very definition of IFP or the number of fissions
produced by neutrons that are limited in a critical system.
This happens because in a critical system, the neu­tron will induce a prompt neutron from fission, somefission products that are precursors for the delayed neu­tron will decay, and all these neutrons will induce
another fission after interacting with the critical system
until they reach the limit because it is a critical system.
NUCLEAR SCIENCE AND ENGINEERING · VOLUME 00 · XXXX 2024

If the system is supercritical, the number of neutrons
and fissions will increase on each generation, and thecounting process will be hard to follow. Meulekamp
implements this approximation by counting fissions
induced by delayed neutrons on a generation of theneutron that is used as the seed for the next generation,then called the next fission probability, so it is notnecessary to trace all fissions induced by all secondary
neutrons on the system.

III.A.2. Chiba (Modified k-Ratio)
In 2009, Chiba proposed some modifications to theimplementation of the k-ratio since the Meulekamp approx­
imation is not fully applicable to the various systems
mentioned.[21] By assuming that νp ðE0 Þ is a number ofprompt neutron emissions on each fission, νp ¼ ν νd .
With the small amount of delayed neutron fractions and theneutron spectrum that is almost equal to the prompt neutronenergy spectrum, the total produced neutrons that are basi­cally formulated into χν ¼ χ p νp þ χ d νd then could beapproximated with χν ffi χp νp . But, since βeff focused ona delayed neutron, Eq. (3) could be modified with the pre­viously mentioned approximation, χd νd ¼ χν χ p νp , so that

6

PINEM et al. · KINETIC PARAMETER RSG-GAS REACTOR EQUILIBRIUM SILICIDE COREhχ ν ip pwhere hχνileads to a k-ratio of prompt neutron generation ateach fission to a total neutron generation. Since kp is so close
to k because the prompt neutrons are constituting almost 99%of the total neutron population, using this equation could leadto higher sensitivity in the calculation of variables k and kp .
From the basic neutron transport equation,

Chiba has done some modifications to the k-ratio by con­sidering another fictitious state that uses parameter a asa scaling factor to adjust perturbation from the reference state,

where

where
L = loss term of the neutron transport that includes theabsorption reaction and leakage caused by the geometry,soF = production term for neutron transport,

III.A.3. Nauchi and Kameyamathat applied to its adjoint neutron flux and on a fictitious
condition without a delayed neutron,

where

Another approximation is by calculating adjoint neu­tron flux ϕþ properly so that it acts as a weighted function
to the delayed neutron fraction. Nauchi and Kameyama
estimated βeff by taking into account the number ofneutrons instead of fissions induced by neutrons, calledfission neutrons in the next generation.[22] This approachr; Ω0 ; E0 Þ, which has auses M ð~r; Ω0 ; E0 Þ instead of ϕþ ð~similar physical meaning as a function of the fission
neutron production, so Eq. (3) could be modified tokso the kp ratio could be processed by assuming ϕp � ϕ forsimplification (but could lead to some errors) into
Nauchi also developed a method to calculate neutron
generation time, which came from a modified generalequation for Λ:

where υ is the neutron velocity for corresponding neutron energy, direction, and position. In Monte Carlo, this neutron
velocity is important to identify the flight time of a neutron on each track (random walk) within the reactor component.
This value, which includes the estimated track length, is evaluated in each neutron collision and absorption. The
modification by Nauchi is made by changing the weighted factor of the adjoint neutron flux into M, which is producedby the accounting number of fission neutrons in the next generation:

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III.A.4. Iterated Fission Probability
In 2010, Nauchi and Kameyama also developed a newweighting factor to calculate IFP, which then became thename of their new method.[23] Iterated fission probability as
defined in Sec. III.A.1 carries the same physical meaning asadjoint neutron flux since the distribution of neutron flux
from counting yielded neutrons due to the fission reaction
will be proportional to the adjoint neutron flux, which leads
to fission probability induced by the neutron at the next
generation. This approach will be valid in a critical system
when the number of neutrons or fission power generated
will achieve a definite level and not increase or decrease
exponentially. In this method, IFP was calculated by the
number of fission reactions induced by neutrons that could
be evaluated from power generated and neutron flux, using
pointwise or multigroup cross-section data sets. By calcu­
lating IFP IFP ð~r; Ω0 ; E0 Þ, effective delayed neutron fraction
and neutron generation time could be calculated bya similar equation as before with small modification of
the weighting factor:

7

and adjoint equation

which could be formulated to the exact perturbation for­mula for reactivity increment,

where ΔF ¼ Fp F þ and ΔL ¼ Lp Lþ and by introdu­
cing υc as a uniform neutron poison as a perturbation,
where c is an amplitude constant for homogeneous poison1υ (υ = neutron speed). Then, the reactivity increment due
to perturbation could be formulated to

The derivative of this equation on c ! 0 will be equal to
the negative of the adjoint neutron generation time or, ingeneral, the neutron generation time equal to the negativevalue of the reactivity curve slope:

III.B. Core Modeling and Calculations
Kiedrowski et al. also developed a power iteration
method to calculate the adjoint-weighted tally by using
IFP in continuous-energy k-eigenvalue calculation.[24]These tallies are then used to calculate adjoint flux andpoint-kinetics parameters and to test various cases and tocompare those values to reference data.

III.A.5. Verboomen (Perturbation Technique)
Verboomen et al. are developing a perturbation techni­que to calculate neutron generation time properly fora thermal reactor and fast reactor so it could reduce thedifference up to 10%.[25] The Perturbation Technique isimplemented by adding a macroscopic capture cross sectionin each point of the reactor as a perturbation so the reactivity
change could be recorded. A perturbed model could be for­mulated by Eq. (20):NUCLEAR SCIENCE AND ENGINEERING · VOLUME 00 · XXXX 2024

The Serpent core model being used in this study isbased on the previous study on the 88th core of RSGGAS.[9,12] With a total of 48 fuel elements in the core, 5
FEs and 1 CE were fresh fuels. The burnup value for 22
burned FEs came from the burnup measurement, while theremaining 20 burned fuel’s burnup values (FE and CE)
came from the RSG-GAS report that was calculated using
the in-house fuel management code, BATAN-FUEL.
Depletion on the 88th core cycle of RSG-GAS was calcu­
lated with an average thermal power of 15 MW and gener­
ated 627.3375 MWd of thermal energy.
Core thermal power and generated thermal energy are
shown in Fig. 4, while control rod position during the 88th
core cycle operation is shown in Fig. 5. To achieve about 25
to 30 pcm of the standard deviation of keff, the depletioncalculation was carried out using 50 000 neutron histories
per cycle, with a total of 300 cycles, and 100 of them areinactive cycles.
Since all previously mentioned methods of calculating
point-kinetics parameters, such as the Meulekamp method,

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PINEM et al. · KINETIC PARAMETER RSG-GAS REACTOR EQUILIBRIUM SILICIDE CORE

Fig. 4. Core thermal power and energy generated of the 88th core cycle operation.

Fig. 5. Control rod position of the 88th core cycle operation.

the Nauchi method, the IFP method, and the Perturbation
Technique, have been developed in Serpent,[15] the kinetic
parameter calculation was being carried out with all thesemethods. Kinetic parameters being calculated were thedelayed neutron fraction from the beginning of cycle (BOC)of the 88th core burned to the end of cycle (EOC) of the 88th
core and at BOC of the 89th core, while the neutron

generation time and prompt neutron lifetime were calculated
at the BOC of the 88th and 89th cores.
Both ENDF/B-VII.1 and ENDF/B-VIII.0 nuclear
data were used in our calculation. Sensitivity analysis
was carried out with previously implemented sensitivity
calculation capabilities of Serpent based on Generalized
Perturbation Theory to propagate nuclear data
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KINETIC PARAMETER RSG-GAS REACTOR EQUILIBRIUM SILICIDE CORE · PINEM et al.
uncertainties to adjoint-weighted quantities such as
delayed neutron fraction, its corresponding decay con­stant, and prompt neutron lifetime.[26,27] In general, thesensitivity coefficient derived from the sensitivity analy­
sis was defined as the change of the parameter of interest
due to a change of other parameters being considered(perturbed), such as microscopic cross sections thatwere variated in this calculation using different nuclear
data sets. For the sensitivity analysis, 252 groups ofneutrons for tallying were used with a total of 1200
cycles, 100 of them were inactive cycles, and 200 000
were neutron histories per cycle.

IV. RESULTS AND DISCUSSION
The effective delayed neutron fraction and neutron
generation time were calculated by different methods forcomparing the consistency of the results obtained. The
results of the six-group delayed neutron fraction βi anddelayed neutron decay constant λi are shown in Tables II
and III. The selected six-group delayed neutron

parameters were calculated using Meulekamp’s method
and the IFP method. Based on the calculation of the sixgroup delayed neutrons, there was no significant differ­ence between Meulekamp’s method and the IFP method,whether it uses ENDF/B-VII.1 and ENDF/B-VIII.0.
The calculated results of βeff, Λ dan ℓ using ENDF/
B-VII.1 and ENDF/B-VIII.0 at the BOC of the 88th core
are shown in Tables IV and V. Kinetic parameters thatwere calculated by a different method were compared to
the IFP method because this calculation gave good resultsof kinetic parameter calculation in another MTR-type
reactor.[7] Based on the calculation results in Table IV,
the βeff value from the Perturbation Technique, comparedwith the IFP method of 694.01 pcm, gave a maximum
difference of 0.77% lower than the IFP method. The
value of Λ and ℓ with the IFP method were 78.32 and79.90 s, respectively, and it also gave a maximum differ­ence of 1.85% with Nauchi’s method. There is no sig­
nificant difference in the value of βeff, Λ, and ℓ incomparison between ENDF/B-VII.1 and ENDF/B-VIII.0.
The calculated results of βeff, Λ dan ℓ using ENDF/
B-VII.1 and ENDF/B-VIII.0 on the BOC of the 89th core

TABLE II
Six-Group Delayed Neutron Parameters of 88th Core Using Meulekamp’s Method with ENDF/B-VII.1
Meulekamp’s Method

IFP Method

Group
i

βi
(pcm)

λi
(s−1)

βi
(pcm)

λi
(s−1)

1
2
3
4
5
6

24.14 ± 0.05
125.02 ± 0.12
119.25 ± 0.11
265.27 ± 0.16
110.42 ± 0.11
45.96 ± 0.07

0.013
0.033
0.121
0.303
0.851
2.856

23.74 ± 0.44
125.81 ± 0.04
121.28 ± 1.03
265.9 6 ± 1.49
110.70 ± 0.98
46.57 ± 0.64

0.013
0.033
0.121
0.303
0.851
2.856

TABLE III
Six-Group Delayed Neutron Parameters of 88th Core Using Meulekamp’s Method with ENDF/B-VIII.0
Meulekamp’s Method

IFP Method

Group
i

βi
(pcm)

λi
(s−1)

βi
(pcm)

λi
(s−1)

1
2
3
4
5
6

24.21 ± 0.05
125.38 ± 0.11
119.57 ± 0.11
265.73 ± 0.17
110.74 ± 0.11
46.12 ± 0.07

0.013
0.033
0.121
0.303
0.851
2.856

24.38 ± 0.46
126.03 ± 1.04
121.97 ± 1.02
267.43 ± 1.49
111.33 ± 0.98
46.19 ± 0.64

0.013
0.033
0.121
0.303
0.851
2.855

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PINEM et al. · KINETIC PARAMETER RSG-GAS REACTOR EQUILIBRIUM SILICIDE CORE
TABLE IV
Comparison of Kinetic Parameters Obtained by Different Methods at 88th Core Using ENDF/VII.1

Parameters

Meulekamp’s Method

Nauchi’s Method

Iterated Fission
Probability

Perturbation Technique

Delayed neutron
fraction, βeff (pcm)
Neutron generation
time, Λ (µs)
Prompt neutron
lifetime, ℓ (µs)

691.49 ± 0.26 (0.36%)

689.4 1 ± 0.29 (0.66%)

694.01 ± 2.41

694.47 ± 0.17 (−0.77%)—

79.77 ± 0.01 (−1.85%)

78.32 ± 0.05

79.15 ± 0.00 (−1.06%)—

81.14 ± 0.05 (−1.55%)

79.90 ± 0.1480.75 ± 0.00 (−1.06%)

TABLE V
Comparison of Kinetic Parameters Obtained by Different Methods at 88th Core Using ENDF/VIII.0

Parameters

Meulekamp’s Method

Nauchi’s Method

Iterated Fission
Probability

Perturbation Technique

Delayed neutron
fraction, βeff (pcm)
Neutron generation
time, Λ (µs)
Prompt neutron
lifetime, ℓ (µs)

691.75 ± 0.27 (0.65%)

691.32 ± 0.29 (0.71%)

696.25 ± 2.46

695.77 ± 0.19 (0.07%)—

79.19 ± 0.01 (−1.84%)

77.76 ± 0.05

78.55 ± 0.00 (0.07%)—

80.77 ± 0.01 (−1.84%)

79.31 ± 0.05

78.55 ± 0.00 (0.96%)

are shown in Tables VI and VII, respectively. The βeff
value with the IFP method was 691.34 pcm, and Nauchi’s
method gave the maximum difference of 0.41%. The
values of Λ dan ℓ with the IFP method were 78.73 and80.14 s, and the calculated results of each parameter
while using ENDF/B-VII.1 and ENDF/B-VIII.0 nuclear
data are in good agreement, with a maximum differenceof 1.87%. The kinetic parameter values of the 88th and89th cores also did not change significantly because thedominant fissile material in the reactor core did notchange that much at the beginning of each equilibrium
core, namely, 235U.

The delayed neutron fraction and the neutron genera­tion time varied with increasing fuel burnup in the reactor
core. Changes in kinetic parameters depend on the burnup
so it needs to be considered in the calculations. To deter­mine the effect of the fuel fraction on the βeff value,
depletion calculations were carried out throughout theoperation of the 88th core cycle. The calculation was
performed from the BOC value until the EOC of the88th core, and its results are shown in Fig. 6, with βeff
slightly decreasing as the 88th core cycle operated.
It is noticed that there was no significant change inthe βeff value during reactor operation since on average,

TABLE VI
Comparison of Kinetic Parameters Obtained by Different Methods at 89th Core Using ENDF/VII.1

Parameters

Meulekamp’s Method

Nauchi’s Method

Iterated Fission
Probability

Perturbation Technique

Delayed neutron
fraction, βeff (pcm)
Neutron generation
time, Λ (µs)
Prompt neutron
lifetime, ℓ (µs)

689.40 ± 0.27 (0.28%)

688.51 ± 0.30 (0.41%)

691.34 ± 2.41

693.23 ± 0.197 (−0.27%)—

80.12 ± 0.01 (−1.77%)

78.73 ± 0.05

79.51 ± 0.00 (−0.99%)—

81.55 ± 0.01 (−1.76%)

80.14 ± 0.05

80.93 ± 0.00 (−0.99%)

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TABLE VII
Comparison of Kinetic Parameters Obtained by Different Methods at 89th Core Using ENDF/VIII.0

Parameters

Meulekamp’s Method

Nauchi’s Method

Iterated Fission
Probability

Perturbation Technique

Delayed neutron
fraction, βeff (pcm)
Neutron generation
time, Λ (µs)
Prompt neutron
lifetime, ℓ (µs)

690.82 ± 0.27 (0.93%)

690.27 ± 0.30 (1.01%)

697.32 ± 2.46

694.76 ± 0.19 (0.37%)—

79.59 ± 0.01 (−1.87%)

78.13 ± 0.05

78.99 ± 0.00 (−1.10%)—

80.88 ± 0.01 (−1.86%)

79.40 ± 0.05

80.27 ± 0.00 (−1.10%)

Fig. 6. Total delayed neutron fraction as a function of reactor operation days of 88th core cycle.

each RSG-GAS fuel burnup was increased by around 7%
loss of 235U with a maximum fuel burnup of around 56%
loss of 235U. So, the increase in 239Pu isotopes that hada lower delayed neutron fraction (around 210 pcm) did
not affect the core effective delayed neutron fraction
dramatically at the end of the core cycle. Because of no
significant changes in the average fuel fraction and fissile
material during the RSG-GAS operating cycle, the βeff
value fluctuated within a range of 670 to 700 pcm, closeto 650 pcm as the βeff value of 235U.[18] Calculation using
ENDF/B-VII.1 also showed a slightly stronger fluctuat­ing βeff value than ENDF/B-VIII.0; however, the fluctua­tion was within or on the same order as the standard
deviation of the βeff.
NUCLEAR SCIENCE AND ENGINEERING · VOLUME 00 · XXXX 2024

Sensitivity analyses were performed for effective
delayed neutron fraction βeff and neutron generation
time Λ that were calculated with the ENDF/B-VII.1 and
ENDF/B-VIII.0 nuclear data libraries to identify domi­
nant nuclides and reaction types. The βeff sensitivity foreach isotope and each nuclear reaction was obtained andsorted according to their absolute values. Then, βeff sen­sitivity was further classified according to its tendency toincrease and decrease when perturbed parameters
increased, as shown in Tables VIII and IX, respectively.
Both tables show sensitivity with an absolute value ofmore than 1%, including its isotopes, as well as nuclear
reactions being perturbed. The top five contributors that
had a tendency to increase βeff were 235U (nu-delayed and12

PINEM et al. · KINETIC PARAMETER RSG-GAS REACTOR EQUILIBRIUM SILICIDE CORE
TABLE VIII
Sensitivities of βeff in Increasing Direction*
Sensitivity
Perturbation

ENDF/B-VII.1

ENDF/B-VIII.0

Deviation

Ratio

Nubar delayed
Total cross section
S(α,β) scattering cross section
Nubar total
Total cross section
Elastic scattering cross section
Capture cross section
Nubar delayed
Total cross section
Nubar delayed
Fission cross section

96.305%9.776%
9.140%
2.488%
2.274%
2.059%
1.760%
1.469%
1.447%
1.303%
1.059%

96.512%−15.950%−8.508%2.429%−0.902%−1.088%0.840%
1.410%−1.021%1.275%−0.076%0.207%−25.726%−17.648%−0.059%−3.176%−3.146%−0.920%−0.060%−2.468%−0.029%−1.136%1.002−1.632−0.931
0.976−0.397−0.5280.477
0.959−0.7060.978−0.072

Nuclide
235

U

1

H
1
H
235

U
O
16
O
1
H
239
Pu
235
U
238
U
235
U
16

ENDF/B-VIII.0 to ENDF/B-VII.1*Absolute value > 1.0%.

TABLE IX
Sensitivities of βeff in Decreasing Direction*
Sensitivity
Perturbation

ENDF/B-VII.1

ENDF/B-VIII.0

Deviation

Ratio

Nubar prompt
Nubar prompt
Nubar total
nxn cross section
Elastic scattering cross section
Nubar prompt
S(α,β) scattering cross section
Total cross section
Elastic scattering cross section−93.816%−4.200%−2.731%−1.553%−1.124%−1.099%−0.556%−0.481%−0.410%−94.082%−4.098%−2.688%−1.246%−8.282%−1.037%3.005%
1.907%−1.704%−0.266%0.102%
0.042%
0.307%−7.158%0.062%
3.561%
2.388%−1.294%

1.003
0.976
0.984
0.802
7.369
0.944
−5.401−3.966
4.156

Nuclide
235

U
Pu
239
Pu
9
Be
1
H
238
U
9
Be
9
Be
9
Be
239

ENDF/B-VIII.0 to ENDF/B-VII.1*Absolute value > 1.0%.

nu-total), 1H [s(α,β) scattering and total reaction], and16
O (elastic scattering and total reaction), while nudelayed from 235U dominated with higher than 96% sen­sitivity. On another hand, the top five contributors witha tendency to decrease the βeff value were 235U (nuprompt), 239Pu (nu-prompt and nu-total), 9Be [(n,n) reac­tion], and 1H (elastic scattering reaction) while nu-prompt
from 235U dominated with higher than 93% sensitivity.
The ENDF/B-VIII.0 to ENDF/B-VII.1 deviation
showed the relative difference of ENDF/B-VIII.0 bydirectly subtracting its value to ENDF/B-VII.1 to empha­
size the amount of difference of sensitivity between both
nuclear data, while the ratio was used to show that theirratio with a ratio close to unity meant the sensitivities ofboth nuclear data libraries were almost equal. Since nu-

delayed and nu-prompt of 235U were almost equal on
both nuclear data and dominated the βeff sensitivity,a small difference on this isotope will affect βeff signifi­
cantly in both libraries. But, for other isotopes like 1H,
their response on s(α,β) scattering and the total reaction
was opposed to ENDF/B-VIII.0 by more than −8% sen­sitive compared to ENDF/B-VII.1 on 9% sensitivity as
shown in Table VIII. The elastic scattering of 16O hadless sensitive and an opposed response to βeff on ENDF/
B-VIII.0 compared to ENDF/B-VII.1. The elastic scatter­ing of 1H also was 7% lower on ENDF/B-VIII.0 com­pared to ENDF/B-VII.1 as shown in Table IX, with the9
Be (n,n) reaction also having a small difference on thesensitivity of βeff from both nuclear data. But, in compar­
ison to nu-delayed and nu-prompt of 235U, their
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13

TABLE X
Sensitivities of Λ in the Increasing Direction*
Sensitivity
Perturbation

ENDF/B-VII.1

ENDF/B-VIII.0

Deviation

Ratio

Nubar prompt
S(α,β) scattering cross section
Elastic scattering cross section
Nubar total
nxn cross section

2.641%
2.605%
2.448%
1.975%
1.400%

2.602%
3.593%
2.633%
1.943%
1.382%−0.039%0.988%
0.185%−0.031%−0.019%

0.985
1.379
1.076
0.984
0.987

Nuclide
235

U
Be
9
Be
235
U
9
Be
9

ENDF/B-VIII.0 to ENDF/B-VII.1*Absolute value > 1.0%.

TABLE XI
Sensitivities of Λ in Decreasing Direction
Sensitivity
Perturbation

ENDF/B-VII.1

ENDF/B-VIII.0

Deviation

Ratio

Total cross section
Total cross section
Fission cross section
Capture cross section
Elastic scattering cross section
Capture cross section
S(α,β) scattering cross section
Capture cross section
Total cross section
Total cross section
Elastic scattering cross section
Total cross section
Fission cross section
Nubar total
Nubar prompt
Total cross section−57.211%−41.088%−35.147%−30.676%−19.312%−8.143%−7.223%−5.898%−3.091%−3.005%−2.921%−2.042%−1.814%−1.324%−1.311%−1.011%−53.404%−41.165%−35.005%−30.500%−16.622%−8.102%−6.283%−6.025%−1.877%−3.089%−3.008%−2.046%−1.805%−1.287%−1.275%−0.930%3.807%−0.077%0.142%
0.177%
2.690%
0.041%
0.940%−0.127%
1.214%−0.085%−0.087%−0.005%0.009%
0.037%
0.036%
0.082%

0.933
1.002
0.996
0.994
0.861
0.995
0.870
1.022
0.607
1.028
1.030
1.002
0.995
0.972
0.973
0.919

Nuclide
1

H

235

U
235
U
1
H
1
H
9
Be
1
H
235
U
9
Be
16
O
16
O
239
Pu
239
Pu
239
Pu
239
Pu
238
U

ENDF/B-VIII.0 to ENDF/B-VII.1*Absolute value > 1.0%.

contribution to the βeff value might be neglected since theuse of 1H, 16O as a moderator (H2O), and 9Be reflectors
was constant with their depletion being omitted duringcore depletion calculation.
The sensitivity of neutron generation time was alsoclassified according to its tendency to increase and to
decrease as shown in Tables X and XI. The top fivecontributors that tended to increase Λ are 235U (nuprompt and nu-total) and 9Be [s(α,β) scattering, elastic
scatting, and (n,n) reaction] with all five contributors
having below 4% sensitivity to increase Λ while theirvalue was increased. Meanwhile, the top five contributors
that tended to decrease Λ were 1H (total, capture, andelastic scattering reaction), 235U (total and fission reac­tion), and 9Be (capture reaction), with the total reaction of
NUCLEAR SCIENCE AND ENGINEERING · VOLUME 00 · XXXX 20241

H dominating the sensitivity of Λ by more than 53%.
Compared to the sensitivity of βeff, both nuclear data
showed a good agreement when calculating the sensitiv­
ity of Λ with ENDF/B-VIII.0, which had lower than 4%absolute deviation to ENDF/B-VII.1.

V. CONCLUSION
Several calculations to evaluate the kinetic para­
meters in the equilibrium core of the RSG-GAS reac­
tor with silicide fuel were carried out using theSerpent code with the ENDF/B-VII.1 and ENDF/
B-VIII.0 nuclear data libraries. In this study, the IFP
method was used as a reference for comparison with

14

PINEM et al. · KINETIC PARAMETER RSG-GAS REACTOR EQUILIBRIUM SILICIDE CORE

other methods. The values of delayed neutron fraction
βeff and prompt neutron lifetime ℓ obtained with the
IFP method using ENDF/B-VIII.0 were 696.25 pcm
and 79.31 µs, respectively, and there was no signifi­
cant difference when compared with other methods.
The sensitivity of βeff mainly originated from235
U (nu-delayed, nu-total, and nu-prompt), 1H [s(α,β) scattering, elastic scattering reaction, and total
239
reaction],Pu(nu-prompt
andnu-total),16
O (elastic scattering and total reaction), and 9Be[(n,n) reaction] while nu-delayed and nu-prompt
from 235U dominated with higher than 93% sensitiv­
ity. On the other hand, the sensitivity of neutron gen­eration time Λ mainly originated from 1H (total,
capture, and elastic scattering reaction), 9Be [capture
reaction, s(α,β) scattering, elastic scatting, and (n,n)
reaction], and 235U (nu-prompt, nu-total, total, andfission reaction), with the total reaction of1
H dominating sensitivity of Λ by more than 53%.
The calculated values of the kinetic parameter on the
BOC of the 88th and 89th cores did not show
a significant difference between ENDF/B-VII.1 andthe latest ENDF/B-VIII.0 nuclear data. The results ofcalculated kinetic parameters could be used for ana­lyzing the safety of the equilibrium core of the RSGGAS reactor either in steady-state or transientconditions.

Acknowledgments
Thanks are due the head of the Research Center for Nuclear
Reactor Technology (PRTRN) Research Organization for Nuclear
Energy (ORTN) National Research and Innovation Agency (BRIN)
for supporting this research through DIPA 2022. Also Thanks for the
support of Department of Mechanical and Nuclear Engineering of
the University of Sharjah, United Arab Emirates.

Disclosure Statement
No potential conflict of interest was reported by theauthor(s).

Funding
This research has been supported by BRIN Indonesia
through Rumah Progam Hasil Inovasi Teknologi Nuklir (RPHITN) - Program House for Nuclear Technology Innovation on
fiscal year 2022 number B-277/V/TN/4/2022 with its budget
came from DIPA-124.01.1.690503/2022.

ORCID
Surian Pinem http://orcid.org/0000-0001-6990-1059
Liem Peng Hong
http://orcid.org/0000-0002-02854507
Wahid Luthfi http://orcid.org/0000-0002-4499-3433
http://orcid.org/0000-0002-4081Tukiran Surbakti
774X
Donny Hartanto http://orcid.org/0000-0002-9554-1111

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