Pre-Conceptual Study of Small Modular Pbbi-Cooled Nitride Fuel Reactor Core Characteristics

Nuclear Engineering and Design 285 (2015) 23–30

Contents lists available at ScienceDirect

Nuclear Engineering and Design

jou rnal homepage: www.elsevier.com/locate/nucengdes

Pre-conceptual study of small modular PbBi-cooled nitride fuel reactor core characteristics

a,b a,∗ a

Xianbao Yuan , Liangzhi Cao , Hongchun Wu

School of Nuclear Science and Technology, Xi’an Jiaotong University, No. 28, Xianning West Road, Xi’an, Shanxi 710049, PR China

College of Mechanical & Power Engineering, China Three Gorges University, No. 8, Daxue Road, Yichang, Hubei 443002, PR China

h i g h l i g h t s

•

The nitride fuel, stainless steel cladding and Pb-Bi coolant have a perfect compatibility with each other, as well as with excellent neutronics characteristics.

•

High conversion ratios have been achieved by optimizing the designed parameters to ensure 20 EFPY without refueling and shufﬂing.

•

The burn-up swings slightly due to the perfect breeding capability.

•

All of the important reactivity coefﬁcients are negative to assure SMoPN holding passive safety.

•

The control system can provide the enough shutdown margins in any operational conditions.

a r t i c l e i n f o a b s t r a c t

Article history: In this paper a pre-conceptual neutronics study on a small modular Pb-Bi cooled reactor with nitride fuel

Received 27 July 2014

(SMoPN) is presented. The SMoPN is designed to meet the requirements for nuclear energy expansion

Received in revised form

in the next decades, by using the plutonium and thorium nitride fuel to increase the efﬁciency and

27 November 2014

performance of fuel. Based on the existing experiences of nuclear reactor, the primary design parameters

Accepted 13 December 2014

were provided to match the design goals by the whole core three-dimensional calculation. The nitride fuel,

stainless steel cladding and Pb-Bi coolant have a perfect compatibility with each other, as well as with

excellent neutronics characteristics. High conversion ratios have been achieved to ensure 20 effective

full power years (EFPYs) without refueling and shufﬂing. During the core lifetime, the burn-up swings

slightly due to the perfect breeding capability. All of the important reactivity coefﬁcients are negative to

assure the SMoPN holding passive safety. The control system can provide enough shutdown margins in

both normal and abnormal operational conditions. Therefore, the SMoPN concept satisﬁes completely

the advanced design idea and the requirements of advanced nuclear reactor system.

1. Introduction investment, a large number of redundant equipments and slow

repayment. Secondly, a single reactor with too large capacity may

Nuclear energy is considered to be the most effective solution do harm to the grid. The grid has the danger to break if the power

to the current worldwide energy crisis, environmental pollu- is too large for a single reactor. Thirdly, the reactor is too large to

tion and economic sustainable development issues (Kessides, control, consequently brings the safety issues. Thereafter the small

2012). Throughout the history of nuclear power development, modular reactor (SMR) (Smith, 2010; Vujic´ et al., 2012) comes

the direction of nuclear energy development has mainly been back to the sight of people and projects a ray of sunlight on the

focused on the traditional pressurized water reactors (PWRs) and development of nuclear power.

enlarging the power capacity of a single reactor for the economical The SMR characterized by lower nominal power less than

and technical reasons. However, it faces enormous challenges or equal to 300 MWe (IAEA-TECDOC-1451, 2005) and modular-

to enlarge the power capacity of a single reactor continuously. ized construction, is recognized world-widely as one of the most

Firstly, the improvement of economic beneﬁts by increasing the important options for the future nuclear energy development.

power of single reactor exhibits limitation due to the vast upfront This is mainly because SMRs have some unique advantages. SMRs

can be used as energy source with multipurpose applications,

such as power generation, desalination, district heating, hydrogen

∗ production and industrial processes. They can be deployed in

Corresponding author.

E-mail address: [email protected] (L. Cao). remote areas, deserted coal plants; island and countries (or areas)

http://dx.doi.org/10.1016/j.nucengdes.2014.12.013

24 X. Yuan et al. / Nuclear Engineering and Design 285 (2015) 23–30

that do not have the mature electricity grid systems and cannot economic efﬁciency, increase the conversion ratio and avoid the

deploy large size nuclear reactors. These ﬂexibilities allow for SMRs potential dangers.

to match energy requirements in light of the practical situation. This paper is organized as follows. In Section 2, the design crite-

At the same time, SMRs can be fabricated as an integrated modu- ria of fuel, coolant and cladding selection, the design parameters

lar in the factory, which can provide a uniﬁed standard to nuclear and the core detailed conﬁguration are introduced. The neutronics

plant construction, shorten the approval process and construction performance including the effective multiplication factor, burn-up,

duration, and can be installed underground totally. Therefore, SMRs conversion ratio and the value of control system, was discussed by

have higher capability to decrease the risk of nuclear prolifera- assembly and core calculation with transport and diffusion calcu-

tion with more ﬂexible ways to ﬁnance and more attraction to lation codes in Section 3, respectively. The conclusions are drawn

investors. out in Section 4.

In fact, the studies and utilizations of SMR can be traced back

to the 1950s, mainly focusing on the warship and submarine in

2. Core design

limited countries and regions, such as Russia, American and Japan.

It has comprehensively thrived from the end of last century for the

2.1. Design goals

requirements of fast improvement of nuclear energy. At present,

there are about 40 types of SMRs in the world, but most of them

According to the NEA reports, the available fuel resources of

are still in the pre-conceptual design stage and mainly focus on

235

U is about 300,000 tons distributed in unbalance in the world.

the PWR and fast neutron reactors with metallic coolant. The

It is just only enough for 50 years in light of the current annual

mPower (Halﬁnger et al., 2012), IRIS (Franceschini et al., 2008;

consumption. It is well known that a lot of depleted uranium is dis-

Shirvan et al., 2012), NuScale (Reyes and Lorenzini, 2010; Reyes

charged in the mining process, the discharged PWR spent fuel has

and Young, 2011) and SMART (Chang et al., 2000; Yoon et al.,

about 1% spent plutonium, and also there is plenty of thorium in

2012) are the representatives of integral PWR (IPWR), which are

nature. The fuel resource can be enlarged with several hundreds

well developed and have the chances with near-term deployment.

of times if the depleted uranium, spent fuel and thorium are uti-

However, in the Generation IV International Forum documents,

lized as fuel. Because the nitride fuel has high melting point, high

the liquid metal-cooled fast reactor is considered as the newest

density and excellent conductivity, the PuN (Kurosaki et al., 2000;

generation nuclear system that can be used for both electricity

Lyon et al., 1991; Kleykamp, 1999) and ThN (Adachi et al., 2005;

production and transuranium elements (TRU) incineration in the

Morss et al., 2007) are selected as the fuel in this design. The pluto-

closed nuclear fuel cycle. It was mainly classiﬁed into three kinds of

nium discharged from PWR after 33 GWd/t burn-up with 10 years

reactors according to the coolant: sodium, lead and lead-bismuth

of cooling (Ganda and Greenspan, 2009) and storage. The pluto-

fast reactor, such as Super-Safe, Small & Simple (4S) (Ishii et al.,

nium inventory for a single SMoPN unit is about 2845 kg, which is

2011), Encapsulated Nuclear Heat-Source (ENHS) (Brown et al.,

equivalent to the content of 300 tons spent fuel discharged from

2001; Greenspan, 2002; Greenspan et al., 2008) and SVBR-100

232

PWR, and the natural thorium (100% Th) are selected as fuel to

(Zrodnikov et al., 2008). The 4S is being developed by Toshiba and

increase the efﬁciency of fuel utilization and enlarge the available

the central research institute of electric power industry in Japan,

space of fuel.

with three decades lifetime, which is a 135 MWt cooled by liq-

As well known, the light water is the main coolant in the con-

uid sodium with U–Pu–Zr (11.5% Pu) metallic fuel. The ENHS is a

ventional nuclear reactor due to the plenty of practical experience.

liquid-lead-cooled reactor of 50 MWe being developed by the Uni-

However, it is also a perfect moderating media and the neutron

versity of California. It has 15–20 years life with U–Pu–Zr (11% Pu)

spectrum can be softened to decrease the breeding ability. The

metallic fuel or uranium–zirconium (13% uranium) and sits in 17 m

sodium has many merits as coolant, such as low melting point and

deep silo. The SVBR-100 was designed by AKME-engineering with

outstanding capacity of heat transmission. But the sodium ﬁre is a

280 MWth cooled by lead–bismuth. It is an integral design, with

vital defect for sodium coolant. The Pb-Bi (Loewen et al., 2003) not

12 steam generators and two main circulation pumps sitting in the

◦ only has low melting point, high boiling temperature, outstanding

lead–bismuth pool at 340–490 C.

capacity of heat transmission and neutronic features, but also is

However, the uranium fuel is the main fuel adopted in those

chemical inert.

design schemes. A few design schemes selected the plutonium

The cladding is a critical factor to decide the safety of reactor,

as fuel, and very few designs considering the fertile thorium

which is always the main aspect of nuclear reactor research and

(Toshinsky et al., 2013). In most of these schemes the oxide fuel

design. The Zr-4 is the traditional cladding materials in thermal

(or metallic fuel) is used, and the advanced fuel type (nitride fuel)

reactors. It can only be permitted the highest temperature with

is only used in a few of design schemes (Smirnov, 2012). Several ◦

600 C to avoid the reaction between zirconium and water. How-

designs such as 4S use sodium as coolant, cannot avoid the potential

ever, the T91 ferritic-martensitic steel (FMS) (Weisenburger et al.,

dangers, for example: sodium-water reaction and coolant boiling

2008), an ASME codiﬁed structural materials, has been envisaged as

because the sodium has the active chemical characteristic and the

a candidate for structures exposed to higher coolant temperature.

low boiling point. In the light of those challenges of small modular

Therefore, the spent plutonium and thorium, lead-bismuth and

fast reactors, an innovative concept SMoPN is proposed, which is

stainless steel T91 are selected as the fuel, coolant and cladding to

designed to meet the requirements of nuclear power fast develop-

meet the following design goals in this study, respectively.

ment by enlarging the space of fuel utilization and increasing the

In this study, the following primary parameters for the SMoPN

efﬁciency of fuel utilization with plutonium extracted from PWR’s

are selected:

spent fuel and thorium. In addition, it has higher conversion ratio

232 233

from Th to U because the PuN and ThN are used as the ﬁssile

233 •

fuel and fertile material, respectively. The U reprocessed from Core thermal power: 300 MW.

• ◦

the spent fuel discharged from SMoPN after 20 effective full power Core inlet/outlet temperature: 320/500 C.

•

years operation, has two utilization ways: ﬁrst it can be used as the Number of fuel rods per assembly: 127.

•

fuel of SMoPN and form the U–Th closed fuel cycle in the further fuel Fuel rod active length less than: 2.0 m.

•

cycle; second, it can be used as the ﬁssile fuel for PWR. The liquid FA maximum discharge burn-up: 250 GWd/t.

•

Pb-Bi is adopted as coolant and reﬂector material, and the whole Number of fuel assemblies: 240.

•

reactor core is sunk into the coolant. These improve the neutron Number of control assemblies: 13.

X. Yuan et al. / Nuclear Engineering and Design 285 (2015) 23–30 25

Fig. 1. Fuel rod and assembly design of the SMoPN.

For this study, the following design criteria are applied. is a closely packed array of tubes containing compacted born car-

bide pellets. It is grouped into two independent and diverse parts,

•

Negative coolant reactivity coefﬁcient. viz. reactor control system (RCS) with seven control assemblies

•

Core shutdown margin greater than or equal to 2% dk/k. and reactor shutdown system (RSS) with six control assemblies,

•

Maximum linear heat generation rate (MLHGR) at rated power to avoid the accident of failure in part of control assemblies and

less than or equal to 10 kW/m. increase the control performance. The RCS with seven control

•

Maximum cladding surface temperature (MCST) at rated power assemblies serves as reactor startup, regulation of reactor power

◦

less than or equal to 650 C. and reactivity, and reactor shut-down. The RSS with six assemblies

•

Maximum temperature in the center of fuel rod less than or equal is only used to shutdown the reactor, and does not take part in the

◦

to 1000 C. power and reactivity regulation in normal operation. The assembly

•

The average conversion ration greater than or equal to 0.97. bundles of the RSS are fully placed above the active core and the cor-

responding ducts are ﬁlled with the liquid Pb-Bi eutectic when the

Based on these selections and primary parameters, the fuel reactor operates in the normal conditions. The number of absorber

design and load pattern, the core arrangement, and the control assemblies is conﬁrmed to match the requirements of regulation of

assemblies design and position in the lifetime are optimized to sat- power and reactor shutdown. Their positions are shown in Fig. 3.

isfy all design criteria as well as to improve the economic beneﬁts

and safety of the SMoPN. 2.4. Core arrangement

2.2. Fuel rod and assembly design In this design, the SMoPN contributes a 300 MWth nitride-fueled

core, composed by hexagonal fuel assemblies with pins arranged

The details of the fuel rod and assembly design are shown in on a hexagonal lattice. Fig. 3 shows a section of the core composed

Fig. 1. The fuel assembly of the SMoPN has a ﬂat-to-ﬂat diameter by 240 fuel assemblies surrounded by two rings of shielding assem-

of 11.2 cm and contains 127 fuel rods. The smear density of the blies, each of which consists of T91 stainless. The fuel assemblies

PuN and ThN fuel is 75%, and the fuel equivalent radius is 0.295 cm. of the core are arranged in four enrichments 14.04%, 15.18% 16.32%

The outer radius of the fuel rod is designed to be 0.415 cm, with and 17.45% from inside to outside with PuN for ﬂattening the power

a 0.75 mm cladding thickness. The pitch-to-diameter ratio is 1.2 distribution and ensuring the core being at the critical during the

to get better breeding ratio. The assembly duct thickness is 0.30 cm

and the fuel assembly gap thickness is 0.1 cm. There is a Pb-Bi eutec-

tic plenum above the fuel region, and a Pb-Bi reﬂector is placed

below the fuel region. The radius is about 2.6 m with 1.957 m active

core in diameter and the height of the active core is 1.95 m. There is

one ring shield assembly with stainless steel in the outset core. And

the gap between the active core and the shield assembly is ﬁlled

with liquid Pb-Bi which has a perfect neutronic feature to serve

as the reﬂector. To get the negative void coefﬁcient and improve

the conversion ratio, there is a 30 cm length blanket (ThN) in the

middle of the pins located at the three innermost rings assembly.

The blanket segment is only ThN in addition to the outside pin

claddings.

2.3. Control assembly design

The control assembly consists of an absorber bundle (seven

absorber pins, seven inner supplants and seven outer supplants)

contained within a wrapper (shown in Fig. 2). The absorber bundle Fig. 2. Control assembly design of the SMoPN.

26 X. Yuan et al. / Nuclear Engineering and Design 285 (2015) 23–30

Fig. 4. Calculation model for 1/6 core.

Fig. 3. Core arrangement of the SMoPN.

3, 3 and 39 meshes in X, Y and Z directions (see Fig. 4), respectively,

and the power is obtained for each mesh.

entire time of normal operation. Here, fuel enrichment is deﬁned Using the result of neutronic analysis, a multi-channel thermal-

as the mass fraction of PuN in the mixed fuel PuN and ThN. A rela- hydraulic code (TH code) is used for the thermal-hydraulic

tively low PuN content (14.04 wt% PuN) has been used for the inner calculation. In the TH code, each channel is approximated as a

three rings with 36 fuel assemblies in order to limit the power fuel rod surrounded by coolant, because each fuel assembly in the

peaking factor at the beginning of the life and increase the inter- SMoPN is isolated by its wrapper, every fuel assembly can be sim-

nal conversion. Two rings of 42 fuel assemblies with slightly higher ulated as an independent channel, neglecting the inter wrapper

PuN fraction (15.18 wt% PuN) compose the second zone. 78 fuel ﬂow and heat transfer. So, the scoping research of coolant ﬂow in

assemblies with 16.32 wt% PuN are used in the third zone. 84 fuel each channel can be executed by the inlet temperature, the outlet

assemblies with 17.45 wt% PuN are put in the outer two rings of the temperature and the total thermal power of this channel. Typically,

active core. In this core arrangement, the SMoPN is assured to be the fuel assembly is composed of triangular rod bundles, and thus

in the criticality in 20 EFPYs and has 200 pcm reactivity margin at the Ushakov correlation (Ushakov et al., 1977) is used to analyze

the end of life. the heat convection between the heavy liquid metal coolant and

the cladding in the TH code. It is applied to the three-dimensional

3. Core neutronics analysis power distribution obtained by the core burn-up calculation. In

the TH code, the active core is divided into 10 axial meshes. In

3.1. Calculation method and tools each of the 10 axial planes, the fuel pellet, gas gap, cladding and

coolant are depicted by one dimensional model. In the calculation,

In this study, the neutronics analysis was performed using the the heat transfer and conduction in each the 10 axial planes are

in-house transport code PIJ and a diffusion code CITATION. The calculated from the bottom to the top of the active core. The heat

PIJ code based on collision probability techniques, which covers generation distribution in the fuel pellet is assumed to be uniform

16 lattice geometries, is used to perform the two-dimensional and the nitride fuel heat transfer coefﬁcient from the fuel to gap

assembly transport calculation for lattice physics study, after one- is assumed to constant 34 which is the synthesis of ThN (Adachi

dimensional ultra-ﬁne group pin cell calculation to obtain the et al., 2005; Morss et al., 2007) and PuN (Kurosaki et al., 2000;

effective self-shielding resonance cross-sections, and generate the Lyon et al., 1991; Kleykamp, 1999) by Bruggeman Model (Kim and

macroscopic cross sections and diffusion coefﬁcients for subse- Hofman, 2003), due to the limited experiment and data about ThN

quent core calculations. The calculation for each assembly type was and PuN. SOBOLEV correlation (Sobolev, 2007) is used for evalu-

performed with 40 burn-up steps using nominal parameters, with ating the density, speciﬁc heat and thermal conductivity of Pb-Bi

the hexagonal geometry for fuel assembly and annular assembly coolant. The heat transfer and conduction calculation are repeated

geometry for control assemblies. The super cell model is used for until the inlet/outlet temperature, the surface temperature of clad,

preparation of macro cross-sections of control assembly. And the the centerline temperature of rod and coolant ﬂow are converged.

calculations for different temperatures of fuel, cladding, coolant,

with/without coolant between fuel pins were performed when 3.2. Results and analysis

calculated the reactivity coefﬁcients. All neutronics calculations

use 107-energy group structures in conjunction with JENDL-3.3 Fig. 5 shows the effective multiplication factor (KEFF) variation

nuclear data library. The 107-energy group cross-section struc- with the burn-up. The initial KEFF is about 1.0131 and then goes

tures are collapsed to 16 (eight thermal and eight fast) energy down to the 1.0022 because of the decrease of ﬁssile materials plu-

groups at the end of the assembly calculations. Here, the ther- tonium and the thorium breeding is very slow at the beginning.

232 233

mal spectrum is separated with eight groups for more precise Although the conversion ratio from Th to U is above unity

calculation. In these calculations, the materials, such as different at the beginning of half year (as shown in Figs. 6 and 7), the ﬁs-

233

enrichment fuels, the cladding materials and coolant are consid- sion neutron number of U ﬁssion is lower than that comes from

239

ered heterogeneously in a 1/6 symmetrical geometry. After the Pu ﬁssion at the fast neutron spectrum, it could be the contrib-

fuel assembly burn-up calculation, the 3-dimensional triangular utory cause of the KEFF decreasing. The KEFF arrives to 1.022 after

233

(XT–YT–Z) core burn-up calculations are carried out with macro- 4 EFPYs mainly due to the accumulation of the U. Subsequently,

scopic cross-sections obtained by the above calculations in a 1/6 the KEFF decreases gradually and less-than unity after 20 EFPYs.

symmetric core geometry. The fuel assemblies are separated into The fertile material content reduction is the reason of decreasing

X. Yuan et al. / Nuclear Engineering and Design 285 (2015) 23–30 27

Table 1

Reactivity coefﬁcients for different variables.

Reactivity coefﬁcients Results

Fuel temperature (pcm/K) −0.536

Coolant temperature (pcm/K) −0.21

−

Void (pcm) 4673.57

Axial expansion of rod (pcm/1%) −81.0

Radial expansion of rod (pcm/1%) −1.7

of fuel conversion ability. Within the whole lifetime, the KEFF is

slightly higher than 1, and the swing is near zero, which implies

that the reactor is easy to control.

Table 1 lists some of important reactivity coefﬁcients viz. fuel

Doppler coefﬁcient, void coefﬁcient, Pb-Bi coolant temperature

coefﬁcient, axial and radial expansion coefﬁcients. The delayed

neutron fraction is about 0.00302 with a small changing in the

239

whole life-time, due to the depleting of Pu and the accumulat-

233

Fig. 5. KEFF variations with the burn-up in 20 EFPY.

ing of U. The fuel Doppler coefﬁcient, one of the most important

parameters in dynamic analysis, was evaluated to be −0.536 pcm/K

for temperature changes in the fuel from 1200 K to 1600 K for a

ﬂooded core state using diffusion calculation. The Pb-Bi coolant

temperature coefﬁcient was obtained by the same diffusion the-

ory and way as the fuel Doppler coefﬁcients, to be −0.21 pcm/K for

the coolant temperature changing from 600 K to 900 K, with the

corresponding density variation. The Pb-Bi coolant density is about

−

31.5 pcm for the 1% coolant density change. The Pb-Bi coolant

void coefﬁcient was calculated in the state that the Pb-Bi coolant

was lost totally, which is −4673.57 pcm. The Pb-Bi was also used as

the reﬂector materials in the SMoPN, which is about two assembly

thickness. The reﬂective ability will fail when the Pb-Bi coolant in

the core leaks entirely. Naturally, the leakage of neutron should be

increased and the core fails to achieve criticality. It is a very impor-

tant feature for the SMoPN, which ensures the core safety with the

most severe leakage of coolant in the primary loop. The fuel pin will

prolong in the axial direction and the lattice will expand under the

irradiation and the temperature increased situation, especially, the

ﬁrst several years at the beginning of reactor startup. These surely

induce the reactivity swing and ﬁnally affect the safety. Therefore,

in this section, the reactivity coefﬁcients of axial prolongation and

radial expansion are also evaluated to be −81.0 pcm and −1.7 pcm

for the 1% pin prolonging in axial direction and the 1% broaden-

ing of the radial size of the fuel assemblies, respectively. From the

above analysis, all reactivity coefﬁcients which are important fac-

Fig. 6. Conversion ratio for each assembly in one-sixth core. tors affecting the reactor safety are negative and assure that the

SMoPN possess passive safety.

1.06

Figs. 6 and 7 present the conversion ratio for each fuel assembly

in the one-sixth core at the beginning of life and the evolution of

1.04

average conversion ratio with the burn-up. The conversion ratios

for the assemblies with plutonium enrichments 14.04%, 15.18%

1.02

16.32% are larger than unity at the beginning of life and that of

the inner assemblies is the highest. Although the conversion ratio 1.00

tio

of the two outer rings of assemblies is less than 1, the averaged ra

conversion ratio for all fuel assemblies is larger than 1. The more 0.98

ion

s outer assembly, the lower value due to the fact that the neutron

er 232

v 0.96 ﬂux and the fraction of fertile materials (mainly Th) in the inner

assemblies is higher than outer assemblies, as well as the blanket in

0.94 the innermost assemblies. The conversion decreases with burn-up,

and lower than unity after 5 EFPYs, which is resulted by the fer-

0.92 tile material consumed gradually as burn-up. The average internal

conversion ratio is about 0.97, which is higher than that of most cur-

0.90 rent small modular fast reactor design and satisﬁes self-sustainable.

0 5 10 15 20

The discharged burn-up is the capital factor to determine the

EFPY

cladding integrity in practice, which is about 150 GWd/tHM for fast

reactor due to the limitation of material (Dubberley et al., 2003).

Fig. 7. Evolution of conversion ratio with the burn-up for 20 EFPYs.

However, some special fast reactors with special cladding material

28 X. Yuan et al. / Nuclear Engineering and Design 285 (2015) 23–30

Fig. 8. Discharged burn-up for each assembly in one-sixth core (GWd/t).

Fig. 9. Relative power factor distributions for each assembly at the BOL.

the value can reach above 200 GWd/tHM (Douglas et al., 2007;

Kim et al., 2010) without any breach, Fig. 8 shows the discharged

burn-up for each assembly in one-sixth core. The value is higher

for inner assemblies than those of outers due to the higher neutron

ﬂux in the inner region. The highest value is 229.62 GWd/t, which

is beyond the common value, but it can be endured due to that its

maximum linear power is only 8.2 kW/m in the whole lifetime and

more advanced cladding and structure materials can be used for

the future deployment. Moreover, as the average discharge burn-

up is only 186.33 GWd/t, the maximum discharge burn-up could

be further decreased by optimizing the fuel enrichment zoning.

Figs. 9–11 illustrate the power peak factor distribution for each

assembly at BOL (Beginning of Life), MOL (Middle of Life) and EOL

(End of Life) in one-sixth core. The largest power peak factor locates

at 15.18% enrichment assemblies at the BOL, and then moves grad-

ually to the center of the core. This is the synergy between the

ﬁssile material enrichment and the neutron ﬂux to induce the

phenomena. Although the two outmost rings assemblies have the

highest PuN enrichment, due to the severe neutron leakage, the

power peak factor is always the smallest, lower than unity.

Tables 2 and 3 present the detailed analysis on the ability of

control system by comparison of the requirements of reactivity

and the value of control systems for the two bundles of control

Table 2

Reactivity worth requirements.

Fig. 10. Relative power factor distributions for each assembly at the MOL.

Parameters Primary Secondary

Full power to hot standby ($) 2.52 2.52

Hot standby to refueling ($) 0.95 – assemblies. The requirements of reactivity cover the insertion of

Reactivity fault ($) 1.73 2.0

positive reactivity by temperature defect, reactivity fault and fuel

Fuel cycle excess reactivity ($) 4.5 –

cycle excess reactivity. The temperature defects are induced by the

Uncertainties ($) 0.93 –

reactor from full power to hot standby (the reactor power is zero

Maximum requirements ($) 10.27 4.5

but the coolant is at the inlet temperature for full power operation)

and from the hot standby to refueling. The reactivity fault implies

Table 3

the ejection accident of the assembly with the maximum value. The

Information of control assemblies.

total requirements of the reactivity are about 10.27$ and 4.5$ for

Parameters Primary Secondary primary (RCS) and secondary (RSS) bundles of control assemblies

with 10% uncertainty, separately. The available reactivity worth of

Number of control assemblies 7 6

Reactivity worth of control system ($) 14.10 7.0 RCS with seven control assemblies, which considers the worth of

Worth of 1 stuck assembly ($) 1.37 2.0

one stuck assembly with the maximum value, is 12.73$, the shut-

Reactivity worth available ($) 12.73 5.0

down margin is 2.46$. For RSS, there is about 0.5$ shutdown margin.

X. Yuan et al. / Nuclear Engineering and Design 285 (2015) 23–30 29

Table 4

Design parameters for reference core of the SMoPN.

Parameters Values Parameters Values/materials

Thermal power (MWt) 300 Cladding material Stainless T91

◦

Inlet temperature ( C) 320 Fuel material PuN + ThN

◦

Outlet temperature ( C) 500 Coolant material PbBi

Number of fuel assembly 240 Control absorber material B4C

Number of control assembly 13 Detailed size Ref. Figs. 1–3

Number of reﬂector assembly 60 Heavy metal inventory in core (ton) 19.41

Number of shielding assembly 138 Maximum linear power density (kW/m) 8.2

Flat to ﬂat distance of FA (cm) 11.2 Average discharge burn-up (GWd/t) 186.33

Number of Pin in a FA 127 Average conversion ratio 0.975

◦

P/D 1.2 Maximum centerline temperature ( C) 676

◦

Fuel rod diameter (mm) 8.3 Maximum cladding surface temperature ( C) 650

Active fuel height (mm) 1950 Average ﬂow velocity (m/s) 1.1

Active core diameter (mm) 1957

4. Conclusions

The innovative SMoPN is designed to satisfy the requirement for

the advanced nuclear reactor, which not only improves the safety,

but also enhances the utilization of nuclear fuel and decreases

the costs of fuel reprocessing. The innovative SMoPN concept that

has a 20-year core lifetime without refueling and shufﬂing was

proposed. The thermal output is 300 MWth in the normal opera-

tion.

The plutonium extracted from PWR and natural thorium are uti-

lized as fuel of the SMoPN for advanced nuclear fuel cycle, which

will increase the efﬁciency and space of fuel utilization. Espe-

cially, the nitride fuel used in the SMoPN can help to increase

the conversion ratio up to 0.97, which ensures the core has

a long lifetime, 20 full effective power years (EFPYs) without

refueling and shufﬂing. The burn-up reactivity loss of the inno-

vative the SMoPN rod is set up at the center of the reactor

core, hence burn-up swing is almost zero in the whole life-

time.

Using liquid Pb-Bi, which had several decades of operation expe-

rience as coolant, not only improves natural circulation, but also

enhances the safety and improves the economy of neutron at the

same time. To avoid the severest accident of LOCF (Loss of Coolant

Flow), the core was sunk in the coolant which was also used as

Fig. 11. Relative power factor distributions for each assembly at the EOL.

the reﬂector material. Assuming that the coolant was lost totally,

the leakage of neutron will be very high to induce the core going

subcritical.

Hence, the two control systems are reliable to control the reactor The integrated modular structure of the SMoPN provides an

in any operation considerations. opportunity to apply batch production of the standard reac-

tor modules and the production-line methods for the core and

construction. This will make it possible to reduce considerably

3.3. Summary of design the schedule period of the nuclear power plant construc-

tion.

Based on the above analysis, the core characteristics of the All of the important reactivity coefﬁcients are negative to assure

SMoPN in the lifetime 20 EFPYs are summarized in the following. the SMoPN with passive safety. This innovative nuclear power tech-

nology based on the multi-purpose SMoPN with chemically inert

• Pb-Bi coolant, which may assure a high level of social acceptabil-

The core reactivity swing is near zero because the nitride thorium

ity of the nuclear plant. This will heighten the competitiveness of

is used as the fertile material with conversion ratio 0.975. All of

nuclear power plant at the investment market and promote nuclear

the reactivity coefﬁcients are negative.

• power development.

The maximum discharge burn-up is about 230 GWd/t less than

the design criteria and the maximum linear power is 8.2 kW/m.

• Acknowledgements

The maximum peak power factor is about 1.35 in radial direction

and move gradually to center of core from outside with the burn-

This work was ﬁnancially supported by the Program for

up.

• Changjiang Scholars and Innovative Research Team in Univer-

The control system can provide the enough reactivity to shut-

sity (IRT1280), China Postdoctoral Science and Technology Fund

down the reactor in any situation.

(2013M532051) and Shanxi Province Postdoctoral Science and

Technology Fund (20130018). Authors also appreciate helps from

All of the parameters and values of the SMoPN characteristics Yunlong Xiao, Baolin Liu, Chuanqi Zhao and Zhipeng Li of NECP

are listed in Table 4 and satisfy all design criteria and goals. laboratory of Xi’an Jiaotong University.

30 X. Yuan et al. / Nuclear Engineering and Design 285 (2015) 23–30

References Kurosaki, K., Yano, K., Yamada, K., et al., 2000. A molecular dynamics study on plu-

tonium mononitride. J. Alloys Compd. 313, 242–247.

Loewen, E.P., Tokuhiro, A.T., et al., 2003. Status of research and development of the

Adachi, J., Kurosaki, K., Uno, M., et al., 2005. A molecular dynamics study of thorium

lead-alloy-cooled fast reactor. J. Nucl. Sci. Technol. 40, 614–627.

nitride. J. Alloys Compd. 394, 312–316.

Lyon, W., Baker, R., Leggett, R., et al., 1991. Advancing Liquid Metal Reactor Tech-

Brown, N., Carelli, M., Conway, L., et al., 2001. The Encapsulated Nuclear Heat

nology with Nitride Fuels. Westinghouse Hanford Co., Richland, WA, United

Source for Proliferation Resistant Low-Waste Nuclear Energy. Lawrence Liver-

States.

more National Laboratory (LLNL), Livermore, CA, pp. 2001.

Morss, L.R., Edelstein, N.M., Fuger, J., et al., 2007. The Chemistry of the Actinide and

Chang, M.H., Sim, S.K., Lee, D.J., et al., 2000. SMART behavior under over-pressurizing

Transactinide Elements, vol. 1–5. Springer, Dordrecht, Netherlands, pp. 1.

accident conditions. Nucl. Eng. Des. 199, 187–196.

Reyes, J.N., Lorenzini, P., 2010. NuScale power: a modular, scalable approach to

Douglas, C., et al., 2007. Fuels for sodium-cooled fast reactors: US perspective. J. Nucl.

commercial nuclear power. Nucl. News 53, 97.

Mater. 371, 202–231.

Reyes, J.N., Young, E., 2011. The NuScale Advanced Passive Safety Design. In: ASME

Dubberley, et al., 2003. S-PRISM high burn-up metal-fuel core design. In:

2011 Small Modular Reactors Symposium., pp. 193–198.

Proceedings of ICAPP, Cordoba, Spain, Paper 3142.

Shirvan, K., Hejzlar, P., Kazimi, M.S., et al., 2012. The design of a compact integral

Franceschini, F., Petrovic,´ B., et al., 2008. Core physics analysis of 100% MOX core in

medium size PWR. Nucl. Eng. Des. 243, 393–403.

IRIS. Ann. Nucl. Energy 35, 1587–1597.

Smirnov, V.S., 2012. Lead-Cooled Fast Reactor BREST – Project Status and Prospects.

Ganda, F., Greenspan, E., 2009. Plutonium recycling in hydride fueled PWR cores.

In: International Workshop on Innovative Nuclear Reactors Cooled by Heavy

Nucl. Eng. Des. 239, 1489–1504.

Liquid metals Status and Perspectives, Pisa, April 17–20.

Greenspan, E., 2002. The encapsulated nuclear heat source reactor for low-

Smith, R., 2010. Small reactors generate big hopes. Wall Street J., A1.

waste proliferation resistant nuclear energy. Prog. Nucl. Energy 40,

431–439. Sobolev, V., 2007. Thermophysical properties of lead and lead-bismuth eutectic. J.

Nucl. Mater. 362, 235–247.

Greenspan, E., Hong, S.G., Lee, K.B., et al., 2008. Innovations in the ENHS reactor

Toshinsky, G.I., Komlev, O.G., et al., 2013. Characteristics of Modular Fast Reactor

design and fuel cycle. Prog. Nucl. Energy 50, 129–139.

TM SVBR-100 Using Thorium–Uranium (233) Fuel. In: International Conference on

Halﬁnger, J.A., Haggerty, M.D., et al., 2012. The B&W mPower scalable, practical

Fast Reactors and Related Fuel Cycles: Safe Technologies and Sustainable Sce-

nuclear reactor design. Nucl. Technol. 178, 164–169.

narios (FR19), Paris, France, 4–7 March 2013.

IAEA-TECDOC-1451, 2005. Innovative small and medium sized reactors: design fea-

Ushakov, P.A., Zhukov, A.V., Matyukhin, N.M., 1977. Heat transfer to liquid metals in

tures, safety approaches and R&D trends.

regular arrays of fuel elements. High Temp. 15, 868–873.

Ishii, K., Matsumiya, H., Handa, N., et al., 2011. Activities for 4S USNRC licensing.

Vujic,´ J., Bergmann, M., Skoda,ˇ R., et al., 2012. Small modular reactors: simpler, safer,

Prog. Nucl. Energy 53, 831–834.

cheaper? Energy 45, 288–295.

Kessides, N., 2012. The future of the nuclear industry reconsidered: risks, uncertain-

Weisenburger, A., Heinzel, A., Müller, G., et al., 2008. T91 cladding tubes with and

ties, and continued promise. Energy Policy 48, 185–208.

without modiﬁed FeCrAlY coatings exposed in LBE at different ﬂow, stress and

Kim, Y.S., Hofman, G.L., 2003. AAA Fuels Handbook. Department of Energy, United

States. temperature conditions. J. Nucl. Mater. 376, 274–281.

Yoon, H.J., Ahn, Y., Lee, J.I., et al., 2012. Potential advantages of coupling supercritical

Kim, T.K., et al., 2010. Feasibility study of ultra-long life fast reactor core concept. In:

CO2 Brayton cycle to water cooled small and medium size reactor. Nucl. Eng.

PHYSOR 2010 – Advances in Reactor Physics to Power the Nuclear Renaissance,

Des. 245, 223–232.

Pittsburgh, Pennsylvania, USA, May 9–14, 2010, on CD-ROM. American Nuclear

Zrodnikov, A., Toshinsky, G., Komlev, O., et al., 2008. Innovative nuclear technology

Society, LaGrange Park, IL.

based on modular multi-purpose lead-bismuth cooled fast reactors. Prog. Nucl.

Kleykamp, H., 1999. Selection of materials as diluents for burning of plutonium fuels

Energy 50, 170–178.

in nuclear reactors. J. Nucl. Mater. 275, 1–11.