炉物理の研究 第 68 – 69 合併号 （2019 年 3 月）

第 47 回炉物理夏期セミナー

若手研究会 実施報告書
学生・若手 WG 担当幹事
東北大学
（株）東芝

相澤 直人
木村

礼

日時：8 月 27 日（木）19:30～21:30 （夏期セミナー2 日目）
内容：若手研究者の研究発表
若手研究者として、3 名の学生から自身の研究に関する発表があった。若手研究会においても、初の試みとして夏期セミナーの講義と同様に、研究発表および質疑応答のいずれも全て英語にて開催された。研究発表では、15 分の発表の後、15 分の質疑応答の時間を設けたが、英語にもかかわらず予定時間を上回るほどの活発な議論が交わされた。質疑応答では日本人・海外からの参加者問わず多くの学生が積極的に議論に参加しており，多くの学生が英語での議論を経験出来た大変有意義な研究会となった。
本研究会のプログラムについては以下の通りである。
19:30 ～ 19:35
開会の挨拶 （学生・若手小委員会担当幹事）
19:35 ～ 21:30
研究発表■ 研究発表者と発表タイトル「Development of New Statistical Geometry Model using Delta Tracking
Method」
名古屋大学

修士課程 2 年 小出 嵩大(※本発表は 9 月に開催の RPHA15＠韓国・済州島にて発表の内容を含む)「Concept of coated particle fuel LWR with long and high burnup」
東京都市大学 修士課程 1 年 鈴木 高也(※本発表は 9 月に開催の GLOBAL 2015＠フランス・パリにて発表の内容を含む)「Impact on burnup performance of coated particle fuel design in pebble bed
reactor with ROX fuel」
東京工業大学 博士課程 2 年 Ho Hai Quan1

炉物理の研究 第 68 – 69 合併号 （2019 年 3 月）

Development of New Statistical Geometry Model using the Delta-tracking Method
Takahiro Koide
Nagoya University, Furo-cho, Chikusa-ku Nagoya, Japan, 464-8603

section can be set arbitrary. Total cross sections including
delta scattering are set to be spatially constant throughout
the geometry as follows:

1. Introduction
In the case of neutron transport calculations for typicalreactors such as light water reactors or fast breeder
reactors, the spatial positions of nuclear fuels are usuallyknown. However, in the case of coated fuel particles in
the fuel compact used in very high temperature reactor(VHTR), we should treat a more complicated geometry
where fuel particles are randomly distributed in thesystem. In order to calculate such stochastic geometry
using the Monte Carlo method, the statistical geometry
model (STGM) has been developed and implemented in
the existing Monte Carlo codes [1,2].
In the accident of Fukushima Daiichi Nuclear Power
Station, the meltdown of core results in the formation of
corium, thus we should expect variety of fuel debris forms
in various moderating conditions. Consequently, there arelarge uncertainties, e.g., the distribution of fuel debris in
the system. As one of the possibilities, fuel debris could
be randomly distributed in water. It is difficult torigorously analyze neutronics characteristics for suchrandom geometry, while these random geometry can beeffectively treated by the STGM. However, in using
STGM, there are some implicit limitations such as fuelparticle radius. The applicability and validity of STGM
has not been sufficiently discussed. In the present study,
we propose a new STGM algorithm using the deltatracking method to cope the limitation of the traditional
STGM model.

∗
∗ (𝑟
Σ𝑡,𝑔
= Σ𝑡,𝑔 (𝑟⃗) + Σ𝑠,𝑔
⃗)

(1)

∗
Σ𝑡,𝑔
is a total cross section involving delta scattering inenergy group 𝑔 , Σ𝑡,𝑔 (𝑟⃗) is a total cross section in∗ (𝑟position 𝑟⃗ and energy group 𝑔 , Σ𝑠,𝑔⃗) is a delta
scattering cross section in position 𝑟⃗⃗⃗and energy group 𝑔.
∗
Σ𝑡,𝑔
is usually set to the maximum value of total crosssection throughout the system in the given energy group.
∗
By using Σ𝑡,𝑔
, total cross section becomes a constantvalue throughout the system and thus the system can beconsidered as a homogenized single area such as Fig. 1
from the viewpoint of flight analysis. Consequently, flightanalysis can be faster. With the delta-tracking method,flight analysis algorithm of random walk is simplified asfollows:

1. Determine the neutron source.
∗
2. Sample the neutron flight length using Σ𝑡,𝑔.
3. Determine the material at reaction point.

2. Delta-Tracking Method

Fig. 1. Determination of collision point utilizing thedelta-tracking method.

During the random walk of neutron, it is necessary toanalysis the neutron collision points. Generally, analysis
of collision points is carried out as follows:

3. Proposal of New Calculation Model for STGM
On the current STGM model, delta scattering is not used
for neutron flight analysis. In the current STGM method,
outgoing point of a neutron from a fuel particle isdetermined at first, then the distance to the nearest fuelparticle is sampled by the nearest neighbor distribution(NND), which is the probability distribution of distance
between fuel particles. In a fuel particle, ordinary flightanalysis is carried out. The advantage of this model is asfollows; positions of all of fuel particles are not necessaryin advance and collision estimations with these fuelparticles are not necessary during flight analysis [1].
On the other hand, all regions are virtually“homogenized” thus outgoing point of a neutron from afuel particle is not explicitly determined. In suchalgorithm, direct application of the current STGM method
is difficult since the outgoing point of a neutron is notknown, thus the nearest neighbor distribution cannot be
used. Furthermore, overlapping of fuel particles, which is
not physically allowed, is implicitly assumed in the

1. Search the intersection point of neutron flight path andboundary of nearest neighbor area.
2. Calculate the neutron flight length.
3. Move the neutron to the next boundary area, if the flight
length goes over the intersection point of boundaryarea.
4. The intersection point is assumed as the new emitting
point, and then iterate the procedures from 1 to 3.
However, longer calculation time is necessary for flightanalysis as the complexity of geometries become
increases, such as random distribution of fuel particles inthree dimensional geometry.
So, in order to increase computational efficiency offlight analysis, we introduced the delta-tracking method[3,4]. Delta scattering is a non-physical scattering
reaction by which energy and flight direction of neutron
do not change. Magnitude of the delta scattering cross2炉物理の研究 第 68 – 69 合併号 （2019 年 3 月）
 𝑓𝑝2 (𝑟): neutron source point is in moderator.

estimation of NND. Consequently, calculation accuracy
becomes worse as the fuel particle radius becomes large,
as shown in Fig. 2[5]. In this section, we propose a new
STGM algorithm using the delta-tracking method.

Fig. 3. Radial distribution function of packing fraction.
3.1.2 New STGM Algorithm
Fig. 2. Interference effect between two fuel spheres:
overlapping of fuel particles is implicitly assumed

The random walk algorithm of neutron using the new
STGM algorithm is as follows (Fig.4):

3.1 Random walk algorithm
1. Determine a material of the starting point. The starting
point on the first batch is decided by the average
packing fraction.
2. Sample a flight distance of neutron.
3. Determine a material at the collision point by a flight
distance and the radial distribution function of packing
fraction. The radial distribution functions are preparedin prior of a STGM calculation.
4. Determine a reaction of neutron by the cross section ofdetermined material. If a fission reaction occurs, thisposition is set as a new neutron source position.

In the delta-tracking method, the materials at neutron
generation collision points are necessary for flightanalysis. In the common delta-tracking calculation, theseinformation is easily known since material spatial
distribution is known. However, in the STGM we cansample the material of initial neutron source by using the
average packing fraction but not know the explicit
material distribution in advance. In order to resolve thisissues, the following approaches are used.
3.1.1 Material Assignment at Collision Position
In the average sense, packing fraction can be assumed
spatially uniform throughout the calculation system.
When the packing fraction is assumed to be spatially
uniform, material assignment at collision position is easy,i.e., material (fuel particle or moderator) can bestatistically assigned according the packing fraction.
However, in reality, the packing fraction has spatial
distribution especially the neighbor region of a fuelparticle. When many fuel particles with finite radius are
randomly distributed, these fuel particles may havephysical contact and it causes local fluctuation of thepacking fraction near a fuel particle. Thus in theapplication of STGM this fluctuation should be taken into
account.
In order to appropriately treat the fluctuation of thepacking fraction, we introduce a radial distributionfunction of the packing fraction 𝑓𝑝 (𝑟). 𝑓𝑝 (𝑟) is defined asa volume ratio of fuel to total (fuel + moderator) at
distance 𝑟. Thus, by using a uniform random number 𝜉 from 0 to 1, it is able to decide material at the collision
point as follows:

Fig. 4 Neutron random walk in the improved model.
The physical contact of fuel particles that causes
fluctuation of the packing fraction is already taken into
account in 𝑓𝑝 (𝑟) . Also, 𝑓𝑝 (𝑟) is calculated in systems
with random arrangement of fuel particles. Thus,
improvement of calculation accuracy and efficiency canbe expected compared to the current STGM model.
4. Radial Distribution Function of Packing Fraction
In the present improved STGM model, two radial
distribution functions are necessary. In this section, theseradial distribution functions are calculated by numericalintegration by the Monte Carlo method.
Specifically, an in-house code to calculate an average
packing fraction 𝑓𝑝 (𝑟) within a distance of 𝑟 isdeveloped and used. When the Monte Carlo integration is
performed from 𝑟 to 𝑟 + Δ𝑟, then the packing fractionin this range is expressed as follows: 𝜉 > 𝑓𝑝 (𝑟)：material at collision point is moderator, 𝜉 < 𝑓𝑝 (𝑟)：material at collision point is fuel.

𝑓𝑝 (𝑟 +In the present improved model, two different radial
distribution functions are necessary depending on the typeof neutron generation point as shown in Fig. 3.

Δ𝑟1) = ∑ 𝑛𝑖 .
2
𝑁
i

(2)

𝑛𝑖 and 𝑁 means numbers of samplings at i-th fuelparticle within the integral range and all samplings within
the integral range, respectively.

 𝑓𝑝1 (𝑟): neutron source point is in a fuel particle.

3炉物理の研究 第 68 – 69 合併号 （2019 年 3 月）
The radial distribution functions of packing fraction
for the simple cubic lattice (SCL) and 3D randomarrangement (RAND) are calculated using the above
method. Table I shows calculation condition and Fig. 5
shows calculation procedure. The origin is uniformly
sampled. In the case of RAND, fuel particle arrangement
is also changed for different initial random seed. As an
example, Fig. 6 shows the calculation example of theradial distribution function 𝑓𝑝1 (𝑟) in the case of average
packing fraction is 0.3.

given by the Monte Carlo integration. Table II shows
macroscopic cross sections used in this calculation.
Table II. Macroscopic cross section [cm-1]
FuelModerator

0.1
0.1
Σ𝑎
0.1
0.0
𝜈Σ𝑓
0.1
0.1
Σ𝑡
0.0
0.0
Σ𝑠
Figures 7(a) and 7(b) show the calculation result (relative
difference from the reference value) of k-infinity for SCL
and the RAND. The reference value is calculated at thesystem where fuel particles are explicitly arranged at 3dimensional space. In the case of RAND, 1,000
configuration with difference arrangements of fuelparticles are prepared, and the mean value of k-infinity
calculated from 1,000 configurations is used as thereference value. Number of configurations (1,000) is
chosen to sufficiently reduce statistical error for the
average value of k-infinity.
The relative difference of k-infinity is calculated asfollows:

Table I. Calculation condition to estimate radial
distribution of packing fraction
1000
𝑁
0.01
Δ𝑟 [cm]Number of iteration
1000
Fuel particle radius[cm]1.0

Fig. 5 Calculation procedure of 𝑓𝑝 (𝑟).

Δ𝑘∞ =

1.0
RAND

fp1(r)

0.8(3)𝑘𝑐𝑎𝑙𝑐 means a value of k-infinity calculated by STGM
(the previous or the improved model), 𝑘𝑟𝑒𝑓 means thereference value of k-infinity.

SCL

0.6

𝑘𝑐𝑎𝑙𝑐 − 𝑘𝑟𝑒𝑓
× 100 [%]
𝑘𝑟𝑒𝑓

0.4

1.6
1.2

Dk-infinity[%]

0.2
0.0
0

2
4
6
8
Distance from neutron source[cm]10Fig. 6 Distribution function of packing fraction 𝑓𝑝1 (𝑟).

0.8
0.4
0.0

-0.4

Previous Model
New Model
New Model (considering fission source)-0.8

In the case of SCL, Fig. 6 indicates a periodic structure
which is caused by regular and periodic arrangement offuel particle. These functions converge to the average
packing fraction when the sampled flight length is longer
than approximately 3cm.

-1.2

0.1

0.2
Packing Fraction[-]0.3

Fig. 7(a). Relative difference of k-infinity (SCL)
1.2
0.8

Dk-infinity[%]

5. Calculation of k-infinity using the conventional
and proposed STGM models
In this section, we calculate k-infinity of a system inwhich fuel particles are randomly distributed in water.
The conventional and the present STGM models are used.
Calculation conditions are as follows: a number ofneutron per batch is 10000, the active number of batches
is 1000, number of energy group is 1, and the average
packing fraction is 0.1, 0.2, or 0.3, the periodic boundary
condition is applied for all boundaries. Verification
calculation is carried out in the SCL and RAND. The
radial distribution function of packing fraction is used

0.4

0.0
-0.4
-0.8

Previous Model
New Model
New Model (considering fission source)

-1.2
-1.6
0.1

0.2
Packing Fraction[-]0.3

Fig. 7(b). Relative difference of k-infinity (RAND)As shown in Fig. 7(a), calculation accuracy of proposed
STGM model for SCL is better than that of previous
STGM model. However, as shown in Fig. 7(b),4炉物理の研究 第 68 – 69 合併号 （2019 年 3 月）
calculation accuracy of the proposed STGM model is not
significantly improved in RAND.
In the case of RAND, a packing fraction might show
spatial fluctuation. Therefore, in the actual Monte Carlocalculation, the fission source distribution may show
spatial dependence. For example, location where fuelparticles are clouded, higher fission density would beobserved. However, in the estimation of packing fraction
distribution, this effect is not taken into account.
In order to consider the fission source distribution
effect, we calculate the radial distribution function
directly from a process of neutron random walk with
explicit treatment of random distribution of fuel particles.
The distribution function of 𝑓𝑝1 (𝑟) considering the above
effect is calculated with the following calculation
conditions: the average packing fraction is 0.3, number ofneutrons per batch is 10000, the active number of batches
is 1000, and macroscopic cross section is Table II.
Estimation result is shown in Fig. 8.
By using 𝑓𝑝1 (𝑟) considering fission source
distribution effect, calculation result of proposed STGM
model becomes as a blue broken line. Consequently, it isclarified that calculation accuracy improves byconsidering fission source distribution. This result
suggests that the calculation accuracy and efficiency of
proposed STGM will be improved, if the fission source
distribution effect can quantitatively estimate before
Monte Carlo calculation.
As the result, it is clarified that the improve model canaccurately estimate k-infinity of the fuel particle
distribution system than the previous STGM model.

As a future work, further verifications of the proposed
STGM model and consideration of computing time will
be carried out.
References
Murata I, Takahashi A, et al. “New Sampling Method
in Continuous Energy Monte Carlo Calculation for
Pebble Bed Reactors,” J. Nucl. Sci. Technol., 34(8),734 (1997).
2. Nagaya Y, Okumura K, et al. “MVP/GMVP II:
General Purpose Monte Carlo Codes for Neutron andPhoton Transport Calculations based on Continuous
Energy and Multigroup Methods,” JAERI 1348, Japan
Atomic Energy Research Institute (2005).
3. Ishii K, Maruyama H, “Parallelized Monte Carlo
Nuclear Analysis Code VMONT,” JAERI-Conf 2000018, Japan Atomic Energy Research Institute (2000).
4. Jaakko L, “Performance of Woodcock delta-tracking
in lattice physics applications using the Serpent Monte
Carlo reactor physics burnup calculation code,” Ann.
Nucl. Energy, 37, pp715-722, (2010).
5. Koide T, Endo T, Yamamoto A, et al. "Impact of
Nearest Neighbor Distribution of Fuel Particle on
Neutronics Characteristics in Statistical Geometry
Model," Proc. PHYSOR2014, Kyoto, Japan, Sep. 28Oct. 2, 2014, (2014). [CD-ROM].
1.

0.38
On the Fly
MC Integration_0.3

fp1(r)

0.34
0.30
0.26
0.22
1

2
3
4
Flight Distance from Neutron Source[cm]5Fig. 8. 𝑓𝑝1 (𝑟) in consideration of a spatial distribution offission source.
6. Conclusions
In this study, we developed an improved statisticalgeometry model with the delta-tracking method. In theprevious STGM model, flight analysis of neutron iscarried out using the nearest neighbor distribution. In thepresent study, we simplify the calculation algorithm using
the radial distribution function of a packing fraction.
K-infinity obtained by the present improve andprevious STGM models are compared with reference
value. The calculation results indicate that prediction
accuracy of the improved model is higher than that of theprevious model.

5炉物理の研究 第 68 – 69 合併号 （2019 年 3 月）

Concept of coated particle fuel LWR with long and high burnup
Takaya SUZUKI
Cooperative Major in Nuclear Energy, Tokyo City University
1. INTRODUCTION
Considering growing nuclear power demand of theworld countries, there is a need to enhance the safety of
the current light water reactors (LWRs). Safety of nuclear
power generation premises a prevention of radioactivity
release to the environment. The coated particle fuel LWR(CPF-LWR) employs coated particle fuel for improving
the safety. Use of the CPF provides an additional barrier
especially for leakage of volatile fission products in theevent of cladding failure. Fuel particles are embedded in
SiC matrix that forms fuel pellets. Those pellets are
cladded by usual zircaloy (Figure 1). The fuel structure in
the cladding entirely different from current pellet fuel.
However design parameters of fuel assembly are totallycompatible with conventional LWR fuel, so that no
modification is necessary to current LWR core design.
The CPF had been originally developed for the use
in high temperature gas cooled reactor because it showed
excellent retention capability for fission products inside
the coating layers at below 1,600°C.
The SiC matrix provides one more barrier between
fuel particles and claddings to the dispersion of fission
products. Also it maintains relatively low fuel operating
temperatures due to the high thermal conductivity of SiC.
Use of the CPF is expected to reduce the risk ofradioactivity release, however, the core life is remarkably
shortened due to much less initial fissile inventory. The
inventory of CPF-LWR using CPF is less than 10% of thepresent pellet-type fuel with packing fraction (PF)=0.3
which is similar value as high temperature test reactor’s(HTTR’s) fuel design. To overcome the problem, the fuelcomposition, the packing fraction of CPF in SiC matrix,
and diameter of kernel were optimized through parametricstudies.
2. MODELS AND METHOLOGIESThe burnup characteristics of CPF-LWR wereanalyzed by a unit cell of fuel pin of conventional ABWR.
The calculation code used is MVP-BURN which is aburn-up calculation module of MVP which is general
purpose monte carlo codes for neutron and photontransport calculations based on continuous energy andmultigroup methods. Reference parameters for ABWR
are summarized in Table 1. The design of the TRISO-type
coated particle fuels in Table 1 is the same as that used in
HTTR developed by Japan Atomic Energy Agency. For
improving burnup characteristics of CPF-LWR, 20%
Helium gas

SiC
Pyro-carbon
Coated particle fuel(High density)

SiC

Fuel kernel
Cladding

Pyro-carbon(Low density)

Figure 1 Concept of SiC-coated particle fuel and afuel rod.
Table 1 Design parameters.
Parameter
Total power(MWt)Liner power(Wt/cm)
Coolant temperature(°C）
Void fraction of coolant (%)
Coated particle fuel type
Fuel temperature(°C)
Pellet radius(cm)Fuel pin radius(cm)Cladding material
Clad thickness(cm)Fuel pin pitch(cm)

Value
3,900
164
327
40
TRISO
627
0.96
1.12
Zircaloy
0.071
1.44

enriched UO2 (20%UO2), depleted uranium-PuO2 (UMOX) ThO2-PuO2 (T-MOX) and pure PuO2 were selected
as fuel of CPF-LWR. The plutonium enrichment in UMOX and T-MOX fuel was set as 30%, 70% and 100%.
These fuel materials are loaded in the kernel region of CPF.
The compositions of four types of fuels are shown in
Figure 2. The plutonium composition used in this analysis
corresponds to that which is recovered from spent fuel oflow-enriched uranium pressurized-water reactor fuel thathas released 33MWd/kg fission energy and has been
stored for 10 years prior to reprocessing as shown in
Table 2.
Two kinds of parametric surveys were conducted toevaluate the impacts of PF and kernel diameter on burnup
characteristics. The surveyed PF was ranging from 0.3 to
0.05 and kernel diameter was from 600μm to 340μm. And,heavy metal amounts are equivalent for all cases.
Regarding safety parameters, Doppler coefficient,moderator temperature coefficient and void coefficientwere evaluated. In this paper, the core life is defined as
duration where the k-infinity (k-inf.) maintains more thanunity. In a typical ABWR using 3.5% enriched UO2, the炉物理の研究 第 68 – 69 合併号 （2019 年 3 月）

cycle length until refueling is about 400 effective fullpower days (EFPD) and discharged burnup of three-batchcore is 38GWd/t. Evaluated core life and burnup for CPFLWR were compared to these reference values.

Figure 3 Core lives for various fuels(packing fraction = 0.3).
Figure 2 Composition of heavy metal in CPF-LWR fuel.
Table 2 Isotopic composition of plutonium.
Nuclidewt%

Pu-238
1.3

Pu-23960.3

Pu-24024.3

Pu-241
9.1

Pu-242
5.0

3. RESULTS
This chapter described the results for each evaluatedsubjects about burnup characteristics of CPF-LWR.
3.1. The effect of fuel composition
Figure 3 shows comparison of core life for examined
seven types of fuels with PF=0.3. The core life of CPFLWR using 3.5% enriched UO2 was only about one month.
The core life in case of 20% enriched UO2, however, wasextended to about 400 EFPD. Although the fissile
inventories of U-MOX (Pu: 30%) and T-MOX (Pu: 30%)
was only about half of that of 20%UO2, the core lives of
two types of MOX (Pu: 30%) fuels were extended to about
500 EFPD. Furthermore, the core lives of U-MOX (Pu:70%), T-MOX (Pu 70%) and pure PuO2 were 2-3 times
longer than that of the MOX (Pu: 30%).
3.2. The effect of heavy metal amount3.2.1. Heavy metal amount change by adjusting PF
Figure 4 shows variation of core life by adjusting PF foreach fuel composition. The core lives for all cases
shortened with decreasing PF. Core lives of 20% UO2 andtwo types of MOX (Pu: 30%) fuels with PF<0.3 didn’t
reach 400 EFPD. The pure PuO2 with PF=0.3 showed thelongest core life of 1,500 EFPD. In spite of the fact thatthe heavy metal amount in SiC pellets of CPF-LWR was
only one third of that of a conventional LWR pellets, thetwo types of MOX (Pu: 70%) and pure PuO2 particle fuelcould achieve similar or longer core lives.

Figure 5 shows variation of burnup by adjusting PF.
All fuel types and PFs examined here showed higher
burnup compared to conventional UO2 pellet. Amongthem, MOX fuels and pure PuO2 achieved 3-8 times
higher burnup than reference and showed distinctive
tendency that the burnup had a maximum value at around
PF=0.1-0.2.
This phenomenon can be explained by neutron
spectrum softening with decreasing PF. Correlation of PF
and neutron flux per unit lethargy for the case of purePuO2 is shown in Figure 6. It indicates that the thermal
neutron flux was increased with decreasing PF. As aconsequence of this trend, the initial reactivity was raisedfor smaller PF and contributed to the core life extension
and burnup enhancement.
Figure 7 shows instant conversion ratio for each fueltype at end of life (EOL). In this study, conversion ratio(CR) was defined as follows;𝐶𝑅∑𝑇ℎ232
𝛷 + ∑𝑈234
𝛷 + ∑𝑈238
𝛷 + ∑𝑃𝑢238
𝛷 + ∑𝑃𝑢240
𝛷
𝑐
𝑐
𝑐
𝑐
𝑐
=
𝑈233
𝑈235
𝑃𝑢239
∑𝑎 𝛷 + ∑𝑎 𝛷 + ∑𝑎
𝛷 + ∑𝑃𝑢241
𝛷
𝑎

(1)

where ∑𝑐 𝛷 in numerator and ∑𝑎 𝛷 in denominatorare generation rate and depletion rate of fissile nuclides,
respectively. The CR decreased with decreasing PF. This
is why burnup is lower for small PF.
Comparing these two contrary effects on burnup
mentioned above, namely reactivity increase by spectrum
softening and reduction of instant conversion ratio, theformer impact was more dominant.
By reducing PF from 0.1 to 0.05, neutron spectrum
is continued to be softened, however, the reactivity cannot
be maintained for longer burnup due to less fuel inventory.
This is why the burnup has maximum value at around
PF=0.1 then decreased in the region of PF<0.1.
3.2.2. Difference in the impact on burnup by adjusting
PF and kernel diameter
Figure 8 shows differences on core lives byadjusting PF and kernel diameters of CPF. This research
revealed that the differences between adjusting heavy

炉物理の研究 第 68 – 69 合併号 （2019 年 3 月）

metal amount of two variation method were small.

Figure 4 Variation of core life by adjusting PF for eachfuel composition.

Neutron flux per unit lethargy

Figure 5 Variation of burnup by adjusting PF for eachfuel composition.
Pure
PuO2

Neutron energy[eV]Figure 6 Correlation of the PF and the neutron flux per
unit lethargy in pure PuO2.

Figure 7 Instant conversion ratios for the each fueltypes.

Figure 8 Differences of core life of 20% enriched UO2
and pure PuO2 by changing PF and kernel diameter.
3.3. Changes of plutonium consumption rate at EOL
by burning of MOX fuels and pure PuO2
Figure 9 shows Changes of plutonium composition
and amount in MOX (Pu: 30%) between beginning of life(BOL) and EOL. In this analysis, PF was fixed at 0.3.The
values in Figure 9 are summarized in Table 3. T-MOX(Pu: 30%) had the best plutonium consumption rate of
50%. This rate was 10% higher than that of U-MOX (Pu:30%). Table 4, 5 show the results for plutonium
enrichment 70% and 100%, respectively. Increasing
plutonium enrichment of U-MOX and T-MOX, theconsumption rate of each fuel exhibited conflicting trends.
In U-MOX, the rate increased with increasing the content
of plutonium in SiC pellets, but decreased in T-MOX.
This analysis revealed that T-MOX fuel is more
beneficial than U-MOX in the effective consumption of
plutonium. The principal factor of the gap of plutonium
consumption between U-MOX and T-MOX is thedifferences in the composition rate of Pu-239 at EOL. The
rate of Pu-239 in U-MOX at EOL is larger than T-MOX
so that U-238 in U-MOX is converted to Pu-239 withburnup. As a result, the consumption rate of T-MOX waslarger than that of U-MOX.

炉物理の研究 第 68 – 69 合併号 （2019 年 3 月）

Pu-240[wt%]Pu-241[wt%]Pu-242[wt%]Plutonium amounts[kg/assembly]
Consumption rate of Plutonium [%]24.3 34.4
9.1 21.5
5.0
11.2
15.9 8.3
47.8

3.4. Reactivity coefficients
Doppler coefficient, moderator temperature
coefficient and void coefficient at PF=0.3 were evaluated.
In all of the calculations, reactivity coefficients (RC)are evaluated by taking the difference in k-inf. anddividing by the nominal k-inf., i.e.,
𝑘𝑖𝑛𝑓.,𝑝𝑒𝑟𝑡 −𝑘𝑖𝑛𝑓.,𝑛𝑜𝑚𝑘𝑖𝑛𝑓.,𝑛𝑜𝑚 𝑘𝑖𝑛𝑓.,𝑝𝑒𝑟𝑡

R𝐶 =
(2)

where kinf.,pert is the perturbed k-inf. (e.g., alteredtemperature of fuel, water conditions, or void fraction)and kinf., nom is the nominal k-inf..

Figure 9 Changes of plutonium composition and amountin MOX (Pu: 30%) between BOL and EOL.
Table 3 Changes of plutonium composition and amountin MOX (Pu: 30%) fuel.
NuclideU-MOX(Pu:30%)PF=0.3150(GWd/t)

BOL

Pu-238[wt%]Pu-239[wt%]Pu-240[wt%]Pu-241[wt%]Pu-242[wt%]Plutonium amounts[kg/assembly]
Consumption rate of Plutonium [%]

EOL

1.3
1.8
60.3 31.2
24.3 33.0
9.1
22.0
5.0
12.0
4.8
2.9
40.3

T-MOX
(Pu:30%)PF=0.3160(GWd/t)

BOL

EOL

1.3
2.1
60.3 22.7
24.3 35.9
9.1
24.5
5.0
14.8
4.8
2.4
50.0

3.4.1. Doppler coefficient
Doppler coefficient was investigated by increasing
the water coolant temperature by 20 ℃.
Figure 12 shows correlation of Doppler coefficientand plutonium enrichment in the two types of MOX fuels.
This analysis revealed that the coefficient of MOX fuelwas more negative than that of the conventional UO2pellet fuel.
This analysis revealed that Doppler coefficient was
degraded with increasing plutonium enrichment.

Table 4 Changes of plutonium composition and amountin MOX (Pu: 70%) fuel.

NuclideU-MOX(Pu:70%)PF=0.3
310(GWd/t)

BOL

Pu-238[wt%]Pu-239[wt%]Pu-240[wt%]Pu-241[wt%]Pu-242[wt%]Plutonium amounts[kg/assembly]
Consumption rate of Plutonium [%]

EOL

1.3
1.9
60.3 32.9
24.3 32.6
9.1
21.9
5.0
10.7
11.1
6.3
43.13

T-MOX
(Pu:70%)PF=0.3330(GWd/t)

BOL

EOL

1.3
2.4
60.3 28.0
24.3 34.0
9.1
23.4
5.0
12.2
11.1
5.7
48.89

Table 5 The changes of plutonium composition andamount in pure PuO2 fuel.
NuclidePu-238[wt%]Pu-239[wt%]Pure PuO2
PF=0.3428(GWd/t)

BOL

EOL

1.3
60.3

2.7
30.2

Figure 12 Doppler coefficient and plutonium
enrichment.
3.4.2. Moderator temperature coefficient and void
coefficient
Moderator temperature coefficient was evaluated byincreasing the temperature of the fuel by 20◦C, and void
coefficient was investigated by raising void fraction incoolant by 5%.
Figure 13 shows plutonium enrichment andmoderator temperature coefficient. Void coefficient isshown Figure 14. These coefficients showed that thevalues increased with increasing plutonium enrichment.
Through the investigation, it is found that CPF-LWR
using U-MOX or T-MOX was negative. However, thesecoefficients were less negative than conventional UO2pellet.

炉物理の研究 第 68 – 69 合併号 （2019 年 3 月）

CPF-LWR using coated particle MOX fuel ispossible to achieve higher burnup and similar core life
with conventional pellet type LWR. It also enables
effective consumption of plutonium.
However, burnup reactivity loss is slightly larger
than that of traditional LWR. To overcome this problem,
further optimization of fuel design or use of burnablepoison will be considered.
Conventional
ConventionalpelletpelletUO2
UO2

REFERENCE[1] M.S. Kazimi, K. R. Czerwinski, M.J. Driscoll, P.

Plutonium enrichment [%]Hejzlar and J.E. Meyer, “ON THE USE OF
THORIUM IN LIGHT WATER REACTORS”,
MIT-NFC-TR-016, April 1999

Plutonium enrichment [%]Figure 13 Moderator temperature coefficient andplutonium enrichment.

[2] I. TANIHIRA and Y. SNIMAZU, “Small PWR
Using Coated Particle Fuel of Thorium andPlutonium”; Journal of Nuclear Science andTechnology, Vol. 44, No. 8, p.1045–1051, 2007

[3] Rachel A. Shapiro and Matthew J. Vincenzi,“OPTIMIZATION OF FULLY CERAMIC
MICRO-ENCAPSULATEDFUELASSEMBLY
FOR PWR”, PHYSOR 2014, September 28 October 3, 2014, on CD-ROM (2014)[4] J. Carson Mark1 with an Appendix by Frank vonConventionalpelletUO2

Plutonium enrichment [%]Figure 14 Void coefficient and plutonium enrichment.
4. Conclusions
In this study, the burnup characteristics improvementof CPF-LWR was performed by adjusting fuelcomposition and design parameters of coated particle fuel.
As a result, it was found that CPF-LWR with properly
designed particle fuel using MOX fuel or pure PuO2 fuelshowed excellent burnup characteristics. The core life andburnup are extended by 1~4 times and 3~8 times,
respectively, than current LWR. Specifically, the fuelspecification which achieved the longest core life
(1,500EFPD) and the highest
burnup (420GWd/t) was pure PuO2 with PF=0.3. In thecase by replacing pure PuO2 with U-MOX (Pu: 30%) and
T-MOX (Pu: 30%), the core lives and burnups exceeded
those performances of current, in spite of half of fissile
amounts in SiC pellet. Moreover, a core using U-MOX or
T-MOX was possible to effectively consume plutonium.
Focusing on T-MOX (Pu: 30%) with PF=0.3, it showedthat the most superior consumption rate of 50% in thisanalysis. The value exceeded 10% than the rate of UMOX (Pu: 30%).
The reactivity coefficients were evaluated about
Doppler coefficient, moderator temperature coefficientand void coefficient at PF=0.3. The analysis revealed that
evaluated all coefficients are negative. CPF-LWR had
almost equivalent reactivity coefficient with theconventional LWR.

Hippel2 and Edward Lyman, “Explosive Properties
of Reactor-Grade Plutonium”, Science and Global
Security, 17:170–185, 2009[5] Akito YAMAMOTO, Tadashi IKEHARA, Takuya
ITO and Estsuro SAJI, “Benchmark Problem Suit forreactor Physics Study of LWR Next Generation
Fuels”, Jounal of NUCLEAR SCIENCE andTECHNOLOGY, vol.39, NO.8, p.900-912, August2002

炉物理の研究 第 68 – 69 合併号 （2019 年 3 月）

Young Gen Workshop in
AESJ reactor physics summer seminar

IMPACT ON BURNUP PERFORMANCE OF COATED PARTICLE FUELDESIGN IN PEBBLE BED REACTOR WITH ROX FUEL
Hai Quan Ho*
Department of Nuclear Engineering, Tokyo Institute of technology
2-12-1-N1-19, Ookayama, Meguro, Tokyo 152-8550, Japan
Phone: +81-3-5734-2380, Fax: +81-3-5734-2380
Email: quan.h.aa@m.titech.ac.jp

Keywords: reactor design, high temperature gas cooled reactors, pebble bed reactor,
rock like fuel, coated particle fuel
ABSTRACT

oxide as fuel in PBRs can be expected to achieve high burnup
and improve chemical stabilities. In the once-through fuelconcept, the main challenge is to achieve as high a burnup as
possible without failure of the spent fuel. To satisfy the highdischarged burnup, the PBR with ROX fuel should utilize fueldesigns that were successful in high burnup irradiation tests.
Over the past few decades, fuel irradiation tests have been
conducted in many countries, including the United Kingdom,
Germany, the United States, Japan, and Russia. In experiments,
it was found that the AGR-1 [5] and Deep-Burn [6] could
achieve high burnup without any observable failures up to
approximately 200 GWd/t-HM and 740 GWd/t-HM,
respectively.
This study investigated the impact on burnup performance ofdifferent coated fuel particles (CFP), comparing the AGR-1
design and Deep-Burn design in a PBR with ROX fuel. The
MCPBR [7] code, which was specifically designed formodelling the OTTO cycle movement of PBRs, was used toperform the burnup analysis.

The pebble bed reactor (PBR), a kind of high-temperature
gas-cooled reactor (HTGR), is expected to be among the next
generation of nuclear reactors as it has excellent passive safety
features, as well as online refueling and high thermal efficiency.
Rock-like oxide (ROX) fuel has been studied at the Japan
Atomic Energy Agency (JAEA) as a new once-through type
fuel concept. Rock-like oxide used as fuel in a PBR can be
expected to achieve high burnup and improve chemical
stabilities. In the once-through fuel concept, the main challenge
is to achieve as high a burnup as possible without failure of the
spent fuel. The purpose of this study was to investigate theimpact on burnup performance of different coated fuel particle(CFP) designs in a PBR with ROX fuel. In the study, the AGR1 Coated Particle design and Deep-Burn Coated Particle design
were used to make the burnup performance comparison.
Criticality and core burnup calculations were performed by
MCPBR code using the JENDL-4.0 library.
Results at equilibrium showed that the two reactors utilizing
AGR-1 Coated Particle and Deep-Burn Coated Particle designs
could be critical with almost the same multiplication factor keff.
However, the power peaking factor and maximum power per
fuel ball in the AGR-1 coated particle design was lower thanthat of Deep-Burn coated particle design. The AGR-1 design
also showed an advantage in fissions per initial fissile atoms(FIFA); the AGR-1 coated particle design produced a higher
FIFA than the Deep-Burn coated particle design. These results
suggest that the difference in coated particle fuel design canhave an effect on the burnup performance in ROX fuel.

2. OUTLINE OF THE CORE
2.1 Fuel design

1. INTRODUCTION
A pebble bed reactor (PBR) with a once-through-then-out(OTTO) cycle demonstrates many advantages, such as
excellent passive safety features, continuous refueling, andhigh thermal efficiency [1]. Rock-like oxide (ROX) fuel has
been studied at the Japan Atomic Energy Agency (JAEA) as a
new once-through type fuel concept [2,3,4]. Using rock-like

1

炉物理の研究 第 68 – 69 合併号 （2019 年 3 月）
Table 1 shows the configuration of the fuel for the AGR-1 andDeep-Burn designs. Both fuel designs have the same fuelpebble geometry. The single-phase YSZ fuel, which consistedof 81.75 mol% YSZ (78.6 mol% ZrO2 + 21.4 mol% YO1.5) and18.25 mol% UO2, was used as fuel in the kernel. The kernel
diameter of AGR-1 CFP is 50 µm larger than the Deep-Burn
CFP, whereas the Deep Burn has a 50-µm thicker buffer layer
than AGR-1.
2.2 Reactor design
The schematic view of the reactor core was shown in the Fig.
1. The 300 MWt core, 10-m high and 3-m in diameter, wassurrounded by a 1-m-thick graphite reflector with a 1-m-highvoid on top. The pebble packing fraction was 0.61. The total
heavy metal loading in a fuel ball was 3 g with 20% of low
uranium enrichment. The OTTO cycle was considered for thefuel-loading scheme, in which the core region was separated
into 20 horizontal layers and 5 axial flow channels.
2.3 Calculation method
The MCPBR code was used with the JENDL-4.0 library to
calculate the burnup of the fuel spheres when they uniformly 2
moved through the core with constant velocity. In MCPBR, aburnup calculation based on a continuous-energy Monte Carlocode, namely MVP-BURN, is coupled with an additional utility
code to be able to simulate the OTTO cycle of PBR. The
treatment of the OTTO cycle was shown in the Fig. 2. The fuelballs in the upper regions progressively move to the next-lower
regions, while the top region is refilled by fresh fuel and theballs in the lowest region are directly discharged into the spent
fuel tank. The calculation procedure was stopped when reactor
core reached the equilibrium condition in which the discharged
fuel reached the target burnup of 120 GWd/t-HM. The
discharged burnup was set about 120 GWd/t-HM and 112
GWd/t-HM for the AGR-1 reactor and Deep Burn reactor,
respectively, to achieve the same keff at equilibrium condition.
Hence, the fuel pebble velocity in AGR-1 reactor was also
lower than that in Deep Burn reactor.
3. ANALYSIS RESULTS
3.1 Burnup performanceFig. 1. Reactor geometry
The summarized steady state is shown in Table 2. The
effective multiplication factors (presented in Fig. 3) were alittle higher for AGR-1 at the beginning of the cycle, butbecame identical at the equilibrium state. Because at the initialcondition, the total HM loading was the same for both thereactors and the AGR-1 reactor have higher thermal neutron
flux than the Deep-Burn reactor. Moreover, the higher thermal
neutron flux along with the lower pebble velocity leaded to炉物理の研究 第 68 – 69 合併号 （2019 年 3 月）
decrease the amount of U-235 in the AGR-1 reactor faster thandesign was smaller than that of the Deep-Burn design. This
meant that a larger amount of uranium was burned in the AGR1 reactor than in the Deep-Burn reactor before discharging.
3.2 Power density and neutron flux comparisonsFig. 5 shows the power density distribution in the axial andradial directions. In the axial direction, the peak power density
in the AGR-1 core was slightly lower than in the Deep-Burncore, resulting in a smaller power peaking factor in the AGR-1
reactor. Moreover, the AGR-1 design gave the lower maximumof total power in a fuel ball than the Deep-Burn design (2.38
kW vs. 3.03 kW). However, the power density in the bottom
became larger in the AGR-1 reactor due to the fact that the
average power density was the same for both the reactors. In
the radial direction, it can be seen that the radial power density
profile for the AGR-1 and Deep-Burn designs were almost
identical.
The thermal neutron flux (E < 1.86 eV) can be observed inFig. 6. The AGR-1 reactor showed a larger thermal neutron flux
than the Deep-Burn reactor due to the difference in kernel
diameter. The smaller kernel diameter in the Deep-Burn design
enhanced resonance absorption, leading to decreased thermal
neutron flux in the Deep-Burn core.

Fig. 2. The OTTO cycle
the Deep-Burn reactor during operation. Therefore, the keff in
the AGR-1 reactor decrease more quickly than in the DeepBurn reactor and as a result, the keff became almost the same forboth the reactors in the equilibrium condition.
The FIMA for both designs were about 12% corresponding
to the discharged burnup of 120 GWd/t-HM. The FIFAdecreased from 62.5% to 58.6% by switching the fuel from theAGR-1 design to the Deep-Burn design. The uraniumtransmutation can be seen more clearly in the Fig. 4. The spent
fuel balls were discharged at the bottom of the core, where theamount of remaining U-235 and U-238 of the AGR-1 fuelFig. 3. The effective multiplication factor at equilibrium condition
3炉物理の研究 第 68 – 69 合併号 （2019 年 3 月）Top

Fig. 4. U-235 and U-238 density distribution at equilibrium condition

Fig. 5. The power density distribution at equilibrium condition:(a) axial position, (b) radial position

Fig. 6. The thermal neutron flux distribution at equilibrium condition:(a) axial position, (b) radial position
4. DISCUSSION
The effective multiplication factors keff were about 1.17 forboth the reactor utilizing the AGR-1 design and that using the
Deep-Burn design at the equilibrium condition. The maximum

power per fuel ball strongly affected the integrity of thedischarged fuel. In this study, the AGR-1 design showed anadvantage compared to the Deep-Burn design due to the factthat its 2.38 kW of peak pebble power was lower than the 3.03
kW of the Deep-Burn design.
4炉物理の研究 第 68 – 69 合併号 （2019 年 3 月）
From the viewpoint of actinides transmutation, with the samekeff at equilibrium state, the AGR-1 design displayed a slightly
larger FIFA than the Deep-Burn design 62.5% compared to58.6%, respectively. This can be explained by the the lower
4
pebble velocity together with thermal neutron flux distribution
in Fig. 4: the thermal neutron flux was higher in the AGR-1
core design than in the Deep-Burn core, resulting in more
fission reactions occurring in the core with the AGR-1 fueldesign.
Regarding the fuel fabrication economy, with the sameamount of heavy-metal loading, the amount of AGR-1 CFP ina ball was about 1.5 times smaller than that of the Deep-Burn
CFP. For example, 3-g heavy metal loading required
approximately 7×104 CFPs in a ball for the AGR-1 design incomparison to 11×104 CFPs for the Deep-Burn design.
5. CONCLUSIONSThe burnup performance of a PBR with ROX fuel wasinvestigated for both the AGR-1 and Deep-Burn coated fuelparticle designs. At equilibrium condition, the reactor with theAGR-1 fuel design showed better behavior than the Deep-Burnfuel design in term of the integrity of discharged fuel, as wellas the actinides transmutation. In addition, using the AGR-1
design can reduce the number of CFP fabricated in the fuelmatrix by about 1.5 times compared to the Deep-Burn design.
These results suggest that the AGR-1 coated fuel particle design
should be a candidate for ROX fuel PBRs in further analyses.
REFERENCE[1] Andrew C. Kadak, A future for nuclear energy: pebble
bed reactors, Int. J. of Critical Infrastructures, 2005 Vol.1, No.4,5
pp.330 – 345.
[2] H. Akie, T. Muromura, H. Takano, S. Matsuura, A new
fuel material for once-through weapons plutonium burning,
Nucl. Technol. 107 (1994) 182 – 189.
[3] N. Nitani, K. Kuramoto, Y. Nakano, T. Yamashita, Y.
Kimura, Y. Nihei, T. Ogawa, Fuel performance evaluation ofrock-like oxide fuels, Journal of Nuclear Materials 376 (2008)
88-97.
[4] K. Kuramoto, N. Nitani, T. Yamashita, Durability test on
irradiated rock-like oxide fuels, Journal of Nuclear Materials
319 (2003) 180 – 187.
[5] J.T. Maki, AGR-1 Irradiation Experiment Test Plan,
INL/EXT-05-00593, Rev. 3, October 20, 2009.
[6] C. Rodriguez, A. Baxter, D. McEachern, M. Fikani, andF.Venneri, Deep-Burn: making nuclear waste transmutation
practical, Nuclear Engineering and Design, vol. 222 (2003)
299 – 317.
[7] Topan Setiadipura, Toru Obara, Development of Monte
Carlo-Based pebble bed reactor fuel management code,
Annals of Nuclear Energy 71 (2014) 313-321.