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Pre-conceptual study of small modular PbBi-cooled nitride fuel reactor core characteristics
Nuclear Engineering and Design 285 (2015) 23–30
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Nuclear Engineering and Design journal homepage: www.elsevier.com/locate/nucengdes
Pre-conceptual study of small modular PbBi-cooled nitride fuel reactor core characteristics Xianbao Yuan a,b , Liangzhi Cao a,∗ , Hongchun Wu a a b
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
Article history: Received 27 July 2014 Received in revised form 27 November 2014 Accepted 13 December 2014
a b s t r a c t In this paper a pre-conceptual neutronics study on a small modular Pb-Bi cooled reactor with nitride fuel (SMoPN) is presented. The SMoPN is designed to meet the requirements for nuclear energy expansion in the next decades, by using the plutonium and thorium nitride fuel to increase the efficiency and performance of fuel. Based on the existing experiences of nuclear reactor, the primary design parameters 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. © 2014 Elsevier B.V. All rights reserved.
1. Introduction Nuclear energy is considered to be the most effective solution to the current worldwide energy crisis, environmental pollution and economic sustainable development issues (Kessides, 2012). Throughout the history of nuclear power development, the direction of nuclear energy development has mainly been focused on the traditional pressurized water reactors (PWRs) and enlarging the power capacity of a single reactor for the economical and technical reasons. However, it faces enormous challenges to enlarge the power capacity of a single reactor continuously. Firstly, the improvement of economic benefits by increasing the power of single reactor exhibits limitation due to the vast upfront
∗ Corresponding author. E-mail address: [email protected] (L. Cao). http://dx.doi.org/10.1016/j.nucengdes.2014.12.013 0029-5493/© 2014 Elsevier B.V. All rights reserved.
investment, a large number of redundant equipments and slow repayment. Secondly, a single reactor with too large capacity may do harm to the grid. The grid has the danger to break if the power is too large for a single reactor. Thirdly, the reactor is too large to control, consequently brings the safety issues. Thereafter the small modular reactor (SMR) (Smith, 2010; Vujic´ et al., 2012) comes back to the sight of people and projects a ray of sunlight on the development of nuclear power. The SMR characterized by lower nominal power less than or equal to 300 MWe (IAEA-TECDOC-1451, 2005) and modularized construction, is recognized world-widely as one of the most important options for the future nuclear energy development. 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 remote areas, deserted coal plants; island and countries (or areas)
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that do not have the mature electricity grid systems and cannot deploy large size nuclear reactors. These flexibilities allow for SMRs to match energy requirements in light of the practical situation. At the same time, SMRs can be fabricated as an integrated modular in the factory, which can provide a unified standard to nuclear plant construction, shorten the approval process and construction duration, and can be installed underground totally. Therefore, SMRs have higher capability to decrease the risk of nuclear proliferation with more flexible ways to finance and more attraction to investors. In fact, the studies and utilizations of SMR can be traced back to the 1950s, mainly focusing on the warship and submarine in limited countries and regions, such as Russia, American and Japan. It has comprehensively thrived from the end of last century for the requirements of fast improvement of nuclear energy. At present, there are about 40 types of SMRs in the world, but most of them are still in the pre-conceptual design stage and mainly focus on the PWR and fast neutron reactors with metallic coolant. The mPower (Halfinger et al., 2012), IRIS (Franceschini et al., 2008; Shirvan et al., 2012), NuScale (Reyes and Lorenzini, 2010; Reyes and Young, 2011) and SMART (Chang et al., 2000; Yoon et al., 2012) are the representatives of integral PWR (IPWR), which are well developed and have the chances with near-term deployment. However, in the Generation IV International Forum documents, the liquid metal-cooled fast reactor is considered as the newest generation nuclear system that can be used for both electricity production and transuranium elements (TRU) incineration in the closed nuclear fuel cycle. It was mainly classified into three kinds of reactors according to the coolant: sodium, lead and lead-bismuth fast reactor, such as Super-Safe, Small & Simple (4S) (Ishii et al., 2011), Encapsulated Nuclear Heat-Source (ENHS) (Brown et al., 2001; Greenspan, 2002; Greenspan et al., 2008) and SVBR-100 (Zrodnikov et al., 2008). The 4S is being developed by Toshiba and the central research institute of electric power industry in Japan, with three decades lifetime, which is a 135 MWt cooled by liquid sodium with U–Pu–Zr (11.5% Pu) metallic fuel. The ENHS is a liquid-lead-cooled reactor of 50 MWe being developed by the University of California. It has 15–20 years life with U–Pu–Zr (11% Pu) metallic fuel or uranium–zirconium (13% uranium) and sits in 17 m deep silo. The SVBR-100 was designed by AKME-engineering with 280 MWth cooled by lead–bismuth. It is an integral design, with 12 steam generators and two main circulation pumps sitting in the lead–bismuth pool at 340–490 ◦ C. However, the uranium fuel is the main fuel adopted in those design schemes. A few design schemes selected the plutonium as fuel, and very few designs considering the fertile thorium (Toshinsky et al., 2013). In most of these schemes the oxide fuel (or metallic fuel) is used, and the advanced fuel type (nitride fuel) is only used in a few of design schemes (Smirnov, 2012). Several designs such as 4S use sodium as coolant, cannot avoid the potential dangers, for example: sodium-water reaction and coolant boiling because the sodium has the active chemical characteristic and the low boiling point. In the light of those challenges of small modular fast reactors, an innovative concept SMoPN is proposed, which is designed to meet the requirements of nuclear power fast development by enlarging the space of fuel utilization and increasing the efficiency of fuel utilization with plutonium extracted from PWR’s spent fuel and thorium. In addition, it has higher conversion ratio from 232 Th to 233 U because the PuN and ThN are used as the fissile fuel and fertile material, respectively. The 233 U reprocessed from the spent fuel discharged from SMoPN after 20 effective full power years operation, has two utilization ways: first it can be used as the fuel of SMoPN and form the U–Th closed fuel cycle in the further fuel cycle; second, it can be used as the fissile fuel for PWR. The liquid Pb-Bi is adopted as coolant and reflector material, and the whole reactor core is sunk into the coolant. These improve the neutron
economic efficiency, increase the conversion ratio and avoid the potential dangers. This paper is organized as follows. In Section 2, the design criteria of fuel, coolant and cladding selection, the design parameters and the core detailed configuration are introduced. The neutronics performance including the effective multiplication factor, burn-up, conversion ratio and the value of control system, was discussed by assembly and core calculation with transport and diffusion calculation codes in Section 3, respectively. The conclusions are drawn out in Section 4. 2. Core design 2.1. Design goals According to the NEA reports, the available fuel resources of is about 300,000 tons distributed in unbalance in the world. It is just only enough for 50 years in light of the current annual consumption. It is well known that a lot of depleted uranium is discharged in the mining process, the discharged PWR spent fuel has about 1% spent plutonium, and also there is plenty of thorium in nature. The fuel resource can be enlarged with several hundreds of times if the depleted uranium, spent fuel and thorium are utilized as fuel. Because the nitride fuel has high melting point, high density and excellent conductivity, the PuN (Kurosaki et al., 2000; Lyon et al., 1991; Kleykamp, 1999) and ThN (Adachi et al., 2005; Morss et al., 2007) are selected as the fuel in this design. The plutonium discharged from PWR after 33 GWd/t burn-up with 10 years of cooling (Ganda and Greenspan, 2009) and storage. The plutonium inventory for a single SMoPN unit is about 2845 kg, which is equivalent to the content of 300 tons spent fuel discharged from PWR, and the natural thorium (100% 232 Th) are selected as fuel to increase the efficiency of fuel utilization and enlarge the available space of fuel. As well known, the light water is the main coolant in the conventional nuclear reactor due to the plenty of practical experience. However, it is also a perfect moderating media and the neutron spectrum can be softened to decrease the breeding ability. The sodium has many merits as coolant, such as low melting point and outstanding capacity of heat transmission. But the sodium fire is a vital defect for sodium coolant. The Pb-Bi (Loewen et al., 2003) not only has low melting point, high boiling temperature, outstanding capacity of heat transmission and neutronic features, but also is chemical inert. The cladding is a critical factor to decide the safety of reactor, which is always the main aspect of nuclear reactor research and design. The Zr-4 is the traditional cladding materials in thermal reactors. It can only be permitted the highest temperature with 600 ◦ C to avoid the reaction between zirconium and water. However, the T91 ferritic-martensitic steel (FMS) (Weisenburger et al., 2008), an ASME codified structural materials, has been envisaged as a candidate for structures exposed to higher coolant temperature. Therefore, the spent plutonium and thorium, lead-bismuth and stainless steel T91 are selected as the fuel, coolant and cladding to meet the following design goals in this study, respectively. In this study, the following primary parameters for the SMoPN are selected: 235 U
• • • • • • •
Core thermal power: 300 MW. Core inlet/outlet temperature: 320/500 ◦ C. Number of fuel rods per assembly: 127. Fuel rod active length less than: 2.0 m. FA maximum discharge burn-up: 250 GWd/t. Number of fuel assemblies: 240. Number of control assemblies: 13.
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Fig. 1. Fuel rod and assembly design of the SMoPN.
For this study, the following design criteria are applied. • Negative coolant reactivity coefficient. • Core shutdown margin greater than or equal to 2% dk/k. • Maximum linear heat generation rate (MLHGR) at rated power less than or equal to 10 kW/m. • Maximum cladding surface temperature (MCST) at rated power less than or equal to 650 ◦ C. • Maximum temperature in the center of fuel rod less than or equal to 1000 ◦ C. • The average conversion ration greater than or equal to 0.97. Based on these selections and primary parameters, the fuel design and load pattern, the core arrangement, and the control assemblies design and position in the lifetime are optimized to satisfy all design criteria as well as to improve the economic benefits and safety of the SMoPN. 2.2. Fuel rod and assembly design The details of the fuel rod and assembly design are shown in Fig. 1. The fuel assembly of the SMoPN has a flat-to-flat diameter of 11.2 cm and contains 127 fuel rods. The smear density of the PuN and ThN fuel is 75%, and the fuel equivalent radius is 0.295 cm. The outer radius of the fuel rod is designed to be 0.415 cm, with a 0.75 mm cladding thickness. The pitch-to-diameter ratio is 1.2 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 eutectic 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.
is a closely packed array of tubes containing compacted born carbide pellets. It is grouped into two independent and diverse parts, viz. reactor control system (RCS) with seven control assemblies and reactor shutdown system (RSS) with six control assemblies, to avoid the accident of failure in part of control assemblies and increase the control performance. The RCS with seven control assemblies serves as reactor startup, regulation of reactor power and reactivity, and reactor shut-down. The RSS with six assemblies is only used to shutdown the reactor, and does not take part in the power and reactivity regulation in normal operation. The assembly bundles of the RSS are fully placed above the active core and the corresponding ducts are filled with the liquid Pb-Bi eutectic when the reactor operates in the normal conditions. The number of absorber assemblies is confirmed to match the requirements of regulation of power and reactor shutdown. Their positions are shown in Fig. 3. 2.4. Core arrangement In this design, the SMoPN contributes a 300 MWth nitride-fueled core, composed by hexagonal fuel assemblies with pins arranged on a hexagonal lattice. Fig. 3 shows a section of the core composed by 240 fuel assemblies surrounded by two rings of shielding assemblies, each of which consists of T91 stainless. The fuel assemblies of the core are arranged in four enrichments 14.04%, 15.18% 16.32% and 17.45% from inside to outside with PuN for flattening the power distribution and ensuring the core being at the critical during the
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.
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Fig. 4. Calculation model for 1/6 core. Fig. 3. Core arrangement of the SMoPN.
entire time of normal operation. Here, fuel enrichment is defined as the mass fraction of PuN in the mixed fuel PuN and ThN. A relatively low PuN content (14.04 wt% PuN) has been used for the inner three rings with 36 fuel assemblies in order to limit the power peaking factor at the beginning of the life and increase the internal conversion. Two rings of 42 fuel assemblies with slightly higher PuN fraction (15.18 wt% PuN) compose the second zone. 78 fuel assemblies with 16.32 wt% PuN are used in the third zone. 84 fuel assemblies with 17.45 wt% PuN are put in the outer two rings of the active core. In this core arrangement, the SMoPN is assured to be in the criticality in 20 EFPYs and has 200 pcm reactivity margin at the end of life. 3. Core neutronics analysis 3.1. Calculation method and tools In this study, the neutronics analysis was performed using the in-house transport code PIJ and a diffusion code CITATION. The PIJ code based on collision probability techniques, which covers 16 lattice geometries, is used to perform the two-dimensional assembly transport calculation for lattice physics study, after onedimensional ultra-fine group pin cell calculation to obtain the effective self-shielding resonance cross-sections, and generate the macroscopic cross sections and diffusion coefficients for subsequent core calculations. The calculation for each assembly type was performed with 40 burn-up steps using nominal parameters, with the hexagonal geometry for fuel assembly and annular assembly geometry for control assemblies. The super cell model is used for preparation of macro cross-sections of control assembly. And the calculations for different temperatures of fuel, cladding, coolant, with/without coolant between fuel pins were performed when calculated the reactivity coefficients. All neutronics calculations use 107-energy group structures in conjunction with JENDL-3.3 nuclear data library. The 107-energy group cross-section structures are collapsed to 16 (eight thermal and eight fast) energy groups at the end of the assembly calculations. Here, the thermal spectrum is separated with eight groups for more precise calculation. In these calculations, the materials, such as different enrichment fuels, the cladding materials and coolant are considered heterogeneously in a 1/6 symmetrical geometry. After the fuel assembly burn-up calculation, the 3-dimensional triangular (XT –YT –Z) core burn-up calculations are carried out with macroscopic cross-sections obtained by the above calculations in a 1/6 symmetric core geometry. The fuel assemblies are separated into
3, 3 and 39 meshes in X, Y and Z directions (see Fig. 4), respectively, and the power is obtained for each mesh. Using the result of neutronic analysis, a multi-channel thermalhydraulic code (TH code) is used for the thermal-hydraulic calculation. In the TH code, each channel is approximated as a fuel rod surrounded by coolant, because each fuel assembly in the SMoPN is isolated by its wrapper, every fuel assembly can be simulated as an independent channel, neglecting the inter wrapper flow and heat transfer. So, the scoping research of coolant flow in each channel can be executed by the inlet temperature, the outlet temperature and the total thermal power of this channel. Typically, the fuel assembly is composed of triangular rod bundles, and thus the Ushakov correlation (Ushakov et al., 1977) is used to analyze the heat convection between the heavy liquid metal coolant and the cladding in the TH code. It is applied to the three-dimensional power distribution obtained by the core burn-up calculation. In the TH code, the active core is divided into 10 axial meshes. In each of the 10 axial planes, the fuel pellet, gas gap, cladding and coolant are depicted by one dimensional model. In the calculation, the heat transfer and conduction in each the 10 axial planes are calculated from the bottom to the top of the active core. The heat generation distribution in the fuel pellet is assumed to be uniform and the nitride fuel heat transfer coefficient from the fuel to gap is assumed to constant 34 which is the synthesis of ThN (Adachi et al., 2005; Morss et al., 2007) and PuN (Kurosaki et al., 2000; Lyon et al., 1991; Kleykamp, 1999) by Bruggeman Model (Kim and Hofman, 2003), due to the limited experiment and data about ThN and PuN. SOBOLEV correlation (Sobolev, 2007) is used for evaluating the density, specific heat and thermal conductivity of Pb-Bi coolant. The heat transfer and conduction calculation are repeated until the inlet/outlet temperature, the surface temperature of clad, the centerline temperature of rod and coolant flow are converged. 3.2. Results and analysis Fig. 5 shows the effective multiplication factor (KEFF) variation with the burn-up. The initial KEFF is about 1.0131 and then goes down to the 1.0022 because of the decrease of fissile materials plutonium and the thorium breeding is very slow at the beginning. Although the conversion ratio from 232 Th to 233 U is above unity at the beginning of half year (as shown in Figs. 6 and 7), the fission neutron number of 233 U fission is lower than that comes from 239 Pu fission at the fast neutron spectrum, it could be the contributory cause of the KEFF decreasing. The KEFF arrives to 1.022 after 4 EFPYs mainly due to the accumulation of the 233 U. Subsequently, the KEFF decreases gradually and less-than unity after 20 EFPYs. The fertile material content reduction is the reason of decreasing
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Table 1 Reactivity coefficients for different variables.
Fig. 5. KEFF variations with the burn-up in 20 EFPY.
Fig. 6. Conversion ratio for each assembly in one-sixth core. 1.06 1.04
Conversion ratio
1.02 1.00 0.98 0.96 0.94 0.92 0.90 0
5
10
15
EFPY Fig. 7. Evolution of conversion ratio with the burn-up for 20 EFPYs.
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Reactivity coefficients
Results
Fuel temperature (pcm/K) Coolant temperature (pcm/K) Void (pcm) Axial expansion of rod (pcm/1%) Radial expansion of rod (pcm/1%)
−0.536 −0.21 −4673.57 −81.0 −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 whole life-time, due to the depleting of 239 Pu and the accumulating of 233 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 theory 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 important 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% broadening of the radial size of the fuel assemblies, respectively. From the above analysis, all reactivity coefficients which are important factors affecting the reactor safety are negative and assure that the SMoPN possess passive safety. 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 average conversion ratio with the burn-up. The conversion ratios for the assemblies with plutonium enrichments 14.04%, 15.18% 16.32% are larger than unity at the beginning of life and that of the inner assemblies is the highest. Although the conversion ratio of the two outer rings of assemblies is less than 1, the averaged conversion ratio for all fuel assemblies is larger than 1. The more outer assembly, the lower value due to the fact that the neutron flux and the fraction of fertile materials (mainly 232 Th) in the inner assemblies is higher than outer assemblies, as well as the blanket in the innermost assemblies. The conversion decreases with burn-up, and lower than unity after 5 EFPYs, which is resulted by the fertile material consumed gradually as burn-up. The average internal conversion ratio is about 0.97, which is higher than that of most current small modular fast reactor design and satisfies self-sustainable. The discharged burn-up is the capital factor to determine the cladding integrity in practice, which is about 150 GWd/tHM for fast reactor due to the limitation of material (Dubberley et al., 2003). However, some special fast reactors with special cladding material
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Fig. 8. Discharged burn-up for each assembly in one-sixth core (GWd/t).
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 burnup 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 gradually 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. 9. Relative power factor distributions for each assembly at the BOL.
Fig. 10. Relative power factor distributions for each assembly at the MOL.
Parameters
Primary
Full power to hot standby ($) Hot standby to refueling ($) Reactivity fault ($) Fuel cycle excess reactivity ($) Uncertainties ($) Maximum requirements ($)
2.52 0.95 1.73 4.5 0.93 10.27
Secondary 2.52 – 2.0 – – 4.5
Table 3 Information of control assemblies. Parameters
Primary
Secondary
Number of control assemblies Reactivity worth of control system ($) Worth of 1 stuck assembly ($) Reactivity worth available ($)
7 14.10 1.37 12.73
6 7.0 2.0 5.0
assemblies. The requirements of reactivity cover the insertion of positive reactivity by temperature defect, reactivity fault and fuel cycle excess reactivity. The temperature defects are induced by the reactor from full power to hot standby (the reactor power is zero but the coolant is at the inlet temperature for full power operation) and from the hot standby to refueling. The reactivity fault implies the ejection accident of the assembly with the maximum value. The total requirements of the reactivity are about 10.27$ and 4.5$ for primary (RCS) and secondary (RSS) bundles of control assemblies with 10% uncertainty, separately. The available reactivity worth of RCS with seven control assemblies, which considers the worth of one stuck assembly with the maximum value, is 12.73$, the shutdown margin is 2.46$. For RSS, there is about 0.5$ shutdown margin.
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Table 4 Design parameters for reference core of the SMoPN. Parameters
Values
Parameters
Values/materials
Thermal power (MWt) Inlet temperature (◦ C) Outlet temperature (◦ C) Number of fuel assembly Number of control assembly Number of reflector assembly Number of shielding assembly Flat to flat distance of FA (cm) Number of Pin in a FA P/D Fuel rod diameter (mm) Active fuel height (mm) Active core diameter (mm)
300 320 500 240 13 60 138 11.2 127 1.2 8.3 1950 1957
Cladding material Fuel material Coolant material Control absorber material Detailed size Heavy metal inventory in core (ton) Maximum linear power density (kW/m) Average discharge burn-up (GWd/t) Average conversion ratio Maximum centerline temperature (◦ C) Maximum cladding surface temperature (◦ C) Average flow velocity (m/s)
Stainless T91 PuN + ThN PbBi B4C Ref. Figs. 1–3 19.41 8.2 186.33 0.975 676 650 1.1
4. Conclusions
Fig. 11. Relative power factor distributions for each assembly at the EOL.
Hence, the two control systems are reliable to control the reactor in any operation considerations.
3.3. Summary of design Based on the above analysis, the core characteristics of the SMoPN in the lifetime 20 EFPYs are summarized in the following. • The core reactivity swing is near zero because the nitride thorium is used as the fertile material with conversion ratio 0.975. All of the reactivity coefficients are negative. • 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. • The maximum peak power factor is about 1.35 in radial direction and move gradually to center of core from outside with the burnup. • The control system can provide the enough reactivity to shutdown the reactor in any situation. All of the parameters and values of the SMoPN characteristics are listed in Table 4 and satisfy all design criteria and goals.
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 operation. The plutonium extracted from PWR and natural thorium are utilized as fuel of the SMoPN for advanced nuclear fuel cycle, which will increase the efficiency and space of fuel utilization. Especially, 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 innovative the SMoPN rod is set up at the center of the reactor core, hence burn-up swing is almost zero in the whole lifetime. Using liquid Pb-Bi, which had several decades of operation experience 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 the reflector material. Assuming that the coolant was lost totally, the leakage of neutron will be very high to induce the core going subcritical. The integrated modular structure of the SMoPN provides an opportunity to apply batch production of the standard reactor modules and the production-line methods for the core and construction. This will make it possible to reduce considerably the schedule period of the nuclear power plant construction. All of the important reactivity coefficients are negative to assure the SMoPN with passive safety. This innovative nuclear power technology based on the multi-purpose SMoPN with chemically inert Pb-Bi coolant, which may assure a high level of social acceptability of the nuclear plant. This will heighten the competitiveness of nuclear power plant at the investment market and promote nuclear power development. Acknowledgements This work was financially supported by the Program for Changjiang Scholars and Innovative Research Team in University (IRT1280), China Postdoctoral Science and Technology Fund (2013M532051) and Shanxi Province Postdoctoral Science and Technology Fund (20130018). Authors also appreciate helps from Yunlong Xiao, Baolin Liu, Chuanqi Zhao and Zhipeng Li of NECP laboratory of Xi’an Jiaotong University.
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Kurosaki, K., Yano, K., Yamada, K., et al., 2000. A molecular dynamics study on plutonium mononitride. J. Alloys Compd. 313, 242–247. Loewen, E.P., Tokuhiro, A.T., et al., 2003. Status of research and development of the lead-alloy-cooled fast reactor. J. Nucl. Sci. Technol. 40, 614–627. Lyon, W., Baker, R., Leggett, R., et al., 1991. Advancing Liquid Metal Reactor Technology with Nitride Fuels. Westinghouse Hanford Co., Richland, WA, United States. Morss, L.R., Edelstein, N.M., Fuger, J., et al., 2007. The Chemistry of the Actinide and Transactinide Elements, vol. 1–5. Springer, Dordrecht, Netherlands, pp. 1. Reyes, J.N., Lorenzini, P., 2010. NuScale power: a modular, scalable approach to commercial nuclear power. Nucl. News 53, 97. Reyes, J.N., Young, E., 2011. The NuScale Advanced Passive Safety Design. In: ASME 2011 Small Modular Reactors Symposium., pp. 193–198. Shirvan, K., Hejzlar, P., Kazimi, M.S., et al., 2012. The design of a compact integral medium size PWR. Nucl. Eng. Des. 243, 393–403. Smirnov, V.S., 2012. Lead-Cooled Fast Reactor BREST – Project Status and Prospects. In: International Workshop on Innovative Nuclear Reactors Cooled by Heavy Liquid metals Status and Perspectives, Pisa, April 17–20. Smith, R., 2010. Small reactors generate big hopes. Wall Street J., A1. Sobolev, V., 2007. Thermophysical properties of lead and lead-bismuth eutectic. J. Nucl. Mater. 362, 235–247. Toshinsky, G.I., Komlev, O.G., et al., 2013. Characteristics of Modular Fast Reactor SVBR-100 Using Thorium–Uranium (233) Fuel. In: International Conference on Fast Reactors and Related Fuel Cycles: Safe Technologies and Sustainable Scenarios (FR19), Paris, France, 4–7 March 2013. Ushakov, P.A., Zhukov, A.V., Matyukhin, N.M., 1977. Heat transfer to liquid metals in regular arrays of fuel elements. High Temp. 15, 868–873. ˇ ´ J., Bergmann, M., Skoda, Vujic, R., et al., 2012. Small modular reactors: simpler, safer, cheaper? Energy 45, 288–295. Weisenburger, A., Heinzel, A., Müller, G., et al., 2008. T91 cladding tubes with and without modified FeCrAlY coatings exposed in LBE at different flow, stress and temperature conditions. J. Nucl. Mater. 376, 274–281. Yoon, H.J., Ahn, Y., Lee, J.I., et al., 2012. Potential advantages of coupling supercritical CO2 Brayton cycle to water cooled small and medium size reactor. Nucl. Eng. Des. 245, 223–232. Zrodnikov, A., Toshinsky, G., Komlev, O., et al., 2008. Innovative nuclear technology based on modular multi-purpose lead-bismuth cooled fast reactors. Prog. Nucl. Energy 50, 170–178.
Contents lists available at ScienceDirect
Nuclear Engineering and Design journal homepage: www.elsevier.com/locate/nucengdes
Pre-conceptual study of small modular PbBi-cooled nitride fuel reactor core characteristics Xianbao Yuan a,b , Liangzhi Cao a,∗ , Hongchun Wu a a b
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
Article history: Received 27 July 2014 Received in revised form 27 November 2014 Accepted 13 December 2014
a b s t r a c t In this paper a pre-conceptual neutronics study on a small modular Pb-Bi cooled reactor with nitride fuel (SMoPN) is presented. The SMoPN is designed to meet the requirements for nuclear energy expansion in the next decades, by using the plutonium and thorium nitride fuel to increase the efficiency and performance of fuel. Based on the existing experiences of nuclear reactor, the primary design parameters 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. © 2014 Elsevier B.V. All rights reserved.
1. Introduction Nuclear energy is considered to be the most effective solution to the current worldwide energy crisis, environmental pollution and economic sustainable development issues (Kessides, 2012). Throughout the history of nuclear power development, the direction of nuclear energy development has mainly been focused on the traditional pressurized water reactors (PWRs) and enlarging the power capacity of a single reactor for the economical and technical reasons. However, it faces enormous challenges to enlarge the power capacity of a single reactor continuously. Firstly, the improvement of economic benefits by increasing the power of single reactor exhibits limitation due to the vast upfront
∗ Corresponding author. E-mail address: [email protected] (L. Cao). http://dx.doi.org/10.1016/j.nucengdes.2014.12.013 0029-5493/© 2014 Elsevier B.V. All rights reserved.
investment, a large number of redundant equipments and slow repayment. Secondly, a single reactor with too large capacity may do harm to the grid. The grid has the danger to break if the power is too large for a single reactor. Thirdly, the reactor is too large to control, consequently brings the safety issues. Thereafter the small modular reactor (SMR) (Smith, 2010; Vujic´ et al., 2012) comes back to the sight of people and projects a ray of sunlight on the development of nuclear power. The SMR characterized by lower nominal power less than or equal to 300 MWe (IAEA-TECDOC-1451, 2005) and modularized construction, is recognized world-widely as one of the most important options for the future nuclear energy development. 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 remote areas, deserted coal plants; island and countries (or areas)
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that do not have the mature electricity grid systems and cannot deploy large size nuclear reactors. These flexibilities allow for SMRs to match energy requirements in light of the practical situation. At the same time, SMRs can be fabricated as an integrated modular in the factory, which can provide a unified standard to nuclear plant construction, shorten the approval process and construction duration, and can be installed underground totally. Therefore, SMRs have higher capability to decrease the risk of nuclear proliferation with more flexible ways to finance and more attraction to investors. In fact, the studies and utilizations of SMR can be traced back to the 1950s, mainly focusing on the warship and submarine in limited countries and regions, such as Russia, American and Japan. It has comprehensively thrived from the end of last century for the requirements of fast improvement of nuclear energy. At present, there are about 40 types of SMRs in the world, but most of them are still in the pre-conceptual design stage and mainly focus on the PWR and fast neutron reactors with metallic coolant. The mPower (Halfinger et al., 2012), IRIS (Franceschini et al., 2008; Shirvan et al., 2012), NuScale (Reyes and Lorenzini, 2010; Reyes and Young, 2011) and SMART (Chang et al., 2000; Yoon et al., 2012) are the representatives of integral PWR (IPWR), which are well developed and have the chances with near-term deployment. However, in the Generation IV International Forum documents, the liquid metal-cooled fast reactor is considered as the newest generation nuclear system that can be used for both electricity production and transuranium elements (TRU) incineration in the closed nuclear fuel cycle. It was mainly classified into three kinds of reactors according to the coolant: sodium, lead and lead-bismuth fast reactor, such as Super-Safe, Small & Simple (4S) (Ishii et al., 2011), Encapsulated Nuclear Heat-Source (ENHS) (Brown et al., 2001; Greenspan, 2002; Greenspan et al., 2008) and SVBR-100 (Zrodnikov et al., 2008). The 4S is being developed by Toshiba and the central research institute of electric power industry in Japan, with three decades lifetime, which is a 135 MWt cooled by liquid sodium with U–Pu–Zr (11.5% Pu) metallic fuel. The ENHS is a liquid-lead-cooled reactor of 50 MWe being developed by the University of California. It has 15–20 years life with U–Pu–Zr (11% Pu) metallic fuel or uranium–zirconium (13% uranium) and sits in 17 m deep silo. The SVBR-100 was designed by AKME-engineering with 280 MWth cooled by lead–bismuth. It is an integral design, with 12 steam generators and two main circulation pumps sitting in the lead–bismuth pool at 340–490 ◦ C. However, the uranium fuel is the main fuel adopted in those design schemes. A few design schemes selected the plutonium as fuel, and very few designs considering the fertile thorium (Toshinsky et al., 2013). In most of these schemes the oxide fuel (or metallic fuel) is used, and the advanced fuel type (nitride fuel) is only used in a few of design schemes (Smirnov, 2012). Several designs such as 4S use sodium as coolant, cannot avoid the potential dangers, for example: sodium-water reaction and coolant boiling because the sodium has the active chemical characteristic and the low boiling point. In the light of those challenges of small modular fast reactors, an innovative concept SMoPN is proposed, which is designed to meet the requirements of nuclear power fast development by enlarging the space of fuel utilization and increasing the efficiency of fuel utilization with plutonium extracted from PWR’s spent fuel and thorium. In addition, it has higher conversion ratio from 232 Th to 233 U because the PuN and ThN are used as the fissile fuel and fertile material, respectively. The 233 U reprocessed from the spent fuel discharged from SMoPN after 20 effective full power years operation, has two utilization ways: first it can be used as the fuel of SMoPN and form the U–Th closed fuel cycle in the further fuel cycle; second, it can be used as the fissile fuel for PWR. The liquid Pb-Bi is adopted as coolant and reflector material, and the whole reactor core is sunk into the coolant. These improve the neutron
economic efficiency, increase the conversion ratio and avoid the potential dangers. This paper is organized as follows. In Section 2, the design criteria of fuel, coolant and cladding selection, the design parameters and the core detailed configuration are introduced. The neutronics performance including the effective multiplication factor, burn-up, conversion ratio and the value of control system, was discussed by assembly and core calculation with transport and diffusion calculation codes in Section 3, respectively. The conclusions are drawn out in Section 4. 2. Core design 2.1. Design goals According to the NEA reports, the available fuel resources of is about 300,000 tons distributed in unbalance in the world. It is just only enough for 50 years in light of the current annual consumption. It is well known that a lot of depleted uranium is discharged in the mining process, the discharged PWR spent fuel has about 1% spent plutonium, and also there is plenty of thorium in nature. The fuel resource can be enlarged with several hundreds of times if the depleted uranium, spent fuel and thorium are utilized as fuel. Because the nitride fuel has high melting point, high density and excellent conductivity, the PuN (Kurosaki et al., 2000; Lyon et al., 1991; Kleykamp, 1999) and ThN (Adachi et al., 2005; Morss et al., 2007) are selected as the fuel in this design. The plutonium discharged from PWR after 33 GWd/t burn-up with 10 years of cooling (Ganda and Greenspan, 2009) and storage. The plutonium inventory for a single SMoPN unit is about 2845 kg, which is equivalent to the content of 300 tons spent fuel discharged from PWR, and the natural thorium (100% 232 Th) are selected as fuel to increase the efficiency of fuel utilization and enlarge the available space of fuel. As well known, the light water is the main coolant in the conventional nuclear reactor due to the plenty of practical experience. However, it is also a perfect moderating media and the neutron spectrum can be softened to decrease the breeding ability. The sodium has many merits as coolant, such as low melting point and outstanding capacity of heat transmission. But the sodium fire is a vital defect for sodium coolant. The Pb-Bi (Loewen et al., 2003) not only has low melting point, high boiling temperature, outstanding capacity of heat transmission and neutronic features, but also is chemical inert. The cladding is a critical factor to decide the safety of reactor, which is always the main aspect of nuclear reactor research and design. The Zr-4 is the traditional cladding materials in thermal reactors. It can only be permitted the highest temperature with 600 ◦ C to avoid the reaction between zirconium and water. However, the T91 ferritic-martensitic steel (FMS) (Weisenburger et al., 2008), an ASME codified structural materials, has been envisaged as a candidate for structures exposed to higher coolant temperature. Therefore, the spent plutonium and thorium, lead-bismuth and stainless steel T91 are selected as the fuel, coolant and cladding to meet the following design goals in this study, respectively. In this study, the following primary parameters for the SMoPN are selected: 235 U
• • • • • • •
Core thermal power: 300 MW. Core inlet/outlet temperature: 320/500 ◦ C. Number of fuel rods per assembly: 127. Fuel rod active length less than: 2.0 m. FA maximum discharge burn-up: 250 GWd/t. Number of fuel assemblies: 240. Number of control assemblies: 13.
X. Yuan et al. / Nuclear Engineering and Design 285 (2015) 23–30
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Fig. 1. Fuel rod and assembly design of the SMoPN.
For this study, the following design criteria are applied. • Negative coolant reactivity coefficient. • Core shutdown margin greater than or equal to 2% dk/k. • Maximum linear heat generation rate (MLHGR) at rated power less than or equal to 10 kW/m. • Maximum cladding surface temperature (MCST) at rated power less than or equal to 650 ◦ C. • Maximum temperature in the center of fuel rod less than or equal to 1000 ◦ C. • The average conversion ration greater than or equal to 0.97. Based on these selections and primary parameters, the fuel design and load pattern, the core arrangement, and the control assemblies design and position in the lifetime are optimized to satisfy all design criteria as well as to improve the economic benefits and safety of the SMoPN. 2.2. Fuel rod and assembly design The details of the fuel rod and assembly design are shown in Fig. 1. The fuel assembly of the SMoPN has a flat-to-flat diameter of 11.2 cm and contains 127 fuel rods. The smear density of the PuN and ThN fuel is 75%, and the fuel equivalent radius is 0.295 cm. The outer radius of the fuel rod is designed to be 0.415 cm, with a 0.75 mm cladding thickness. The pitch-to-diameter ratio is 1.2 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 eutectic 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.
is a closely packed array of tubes containing compacted born carbide pellets. It is grouped into two independent and diverse parts, viz. reactor control system (RCS) with seven control assemblies and reactor shutdown system (RSS) with six control assemblies, to avoid the accident of failure in part of control assemblies and increase the control performance. The RCS with seven control assemblies serves as reactor startup, regulation of reactor power and reactivity, and reactor shut-down. The RSS with six assemblies is only used to shutdown the reactor, and does not take part in the power and reactivity regulation in normal operation. The assembly bundles of the RSS are fully placed above the active core and the corresponding ducts are filled with the liquid Pb-Bi eutectic when the reactor operates in the normal conditions. The number of absorber assemblies is confirmed to match the requirements of regulation of power and reactor shutdown. Their positions are shown in Fig. 3. 2.4. Core arrangement In this design, the SMoPN contributes a 300 MWth nitride-fueled core, composed by hexagonal fuel assemblies with pins arranged on a hexagonal lattice. Fig. 3 shows a section of the core composed by 240 fuel assemblies surrounded by two rings of shielding assemblies, each of which consists of T91 stainless. The fuel assemblies of the core are arranged in four enrichments 14.04%, 15.18% 16.32% and 17.45% from inside to outside with PuN for flattening the power distribution and ensuring the core being at the critical during the
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.
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Fig. 4. Calculation model for 1/6 core. Fig. 3. Core arrangement of the SMoPN.
entire time of normal operation. Here, fuel enrichment is defined as the mass fraction of PuN in the mixed fuel PuN and ThN. A relatively low PuN content (14.04 wt% PuN) has been used for the inner three rings with 36 fuel assemblies in order to limit the power peaking factor at the beginning of the life and increase the internal conversion. Two rings of 42 fuel assemblies with slightly higher PuN fraction (15.18 wt% PuN) compose the second zone. 78 fuel assemblies with 16.32 wt% PuN are used in the third zone. 84 fuel assemblies with 17.45 wt% PuN are put in the outer two rings of the active core. In this core arrangement, the SMoPN is assured to be in the criticality in 20 EFPYs and has 200 pcm reactivity margin at the end of life. 3. Core neutronics analysis 3.1. Calculation method and tools In this study, the neutronics analysis was performed using the in-house transport code PIJ and a diffusion code CITATION. The PIJ code based on collision probability techniques, which covers 16 lattice geometries, is used to perform the two-dimensional assembly transport calculation for lattice physics study, after onedimensional ultra-fine group pin cell calculation to obtain the effective self-shielding resonance cross-sections, and generate the macroscopic cross sections and diffusion coefficients for subsequent core calculations. The calculation for each assembly type was performed with 40 burn-up steps using nominal parameters, with the hexagonal geometry for fuel assembly and annular assembly geometry for control assemblies. The super cell model is used for preparation of macro cross-sections of control assembly. And the calculations for different temperatures of fuel, cladding, coolant, with/without coolant between fuel pins were performed when calculated the reactivity coefficients. All neutronics calculations use 107-energy group structures in conjunction with JENDL-3.3 nuclear data library. The 107-energy group cross-section structures are collapsed to 16 (eight thermal and eight fast) energy groups at the end of the assembly calculations. Here, the thermal spectrum is separated with eight groups for more precise calculation. In these calculations, the materials, such as different enrichment fuels, the cladding materials and coolant are considered heterogeneously in a 1/6 symmetrical geometry. After the fuel assembly burn-up calculation, the 3-dimensional triangular (XT –YT –Z) core burn-up calculations are carried out with macroscopic cross-sections obtained by the above calculations in a 1/6 symmetric core geometry. The fuel assemblies are separated into
3, 3 and 39 meshes in X, Y and Z directions (see Fig. 4), respectively, and the power is obtained for each mesh. Using the result of neutronic analysis, a multi-channel thermalhydraulic code (TH code) is used for the thermal-hydraulic calculation. In the TH code, each channel is approximated as a fuel rod surrounded by coolant, because each fuel assembly in the SMoPN is isolated by its wrapper, every fuel assembly can be simulated as an independent channel, neglecting the inter wrapper flow and heat transfer. So, the scoping research of coolant flow in each channel can be executed by the inlet temperature, the outlet temperature and the total thermal power of this channel. Typically, the fuel assembly is composed of triangular rod bundles, and thus the Ushakov correlation (Ushakov et al., 1977) is used to analyze the heat convection between the heavy liquid metal coolant and the cladding in the TH code. It is applied to the three-dimensional power distribution obtained by the core burn-up calculation. In the TH code, the active core is divided into 10 axial meshes. In each of the 10 axial planes, the fuel pellet, gas gap, cladding and coolant are depicted by one dimensional model. In the calculation, the heat transfer and conduction in each the 10 axial planes are calculated from the bottom to the top of the active core. The heat generation distribution in the fuel pellet is assumed to be uniform and the nitride fuel heat transfer coefficient from the fuel to gap is assumed to constant 34 which is the synthesis of ThN (Adachi et al., 2005; Morss et al., 2007) and PuN (Kurosaki et al., 2000; Lyon et al., 1991; Kleykamp, 1999) by Bruggeman Model (Kim and Hofman, 2003), due to the limited experiment and data about ThN and PuN. SOBOLEV correlation (Sobolev, 2007) is used for evaluating the density, specific heat and thermal conductivity of Pb-Bi coolant. The heat transfer and conduction calculation are repeated until the inlet/outlet temperature, the surface temperature of clad, the centerline temperature of rod and coolant flow are converged. 3.2. Results and analysis Fig. 5 shows the effective multiplication factor (KEFF) variation with the burn-up. The initial KEFF is about 1.0131 and then goes down to the 1.0022 because of the decrease of fissile materials plutonium and the thorium breeding is very slow at the beginning. Although the conversion ratio from 232 Th to 233 U is above unity at the beginning of half year (as shown in Figs. 6 and 7), the fission neutron number of 233 U fission is lower than that comes from 239 Pu fission at the fast neutron spectrum, it could be the contributory cause of the KEFF decreasing. The KEFF arrives to 1.022 after 4 EFPYs mainly due to the accumulation of the 233 U. Subsequently, the KEFF decreases gradually and less-than unity after 20 EFPYs. The fertile material content reduction is the reason of decreasing
X. Yuan et al. / Nuclear Engineering and Design 285 (2015) 23–30
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Table 1 Reactivity coefficients for different variables.
Fig. 5. KEFF variations with the burn-up in 20 EFPY.
Fig. 6. Conversion ratio for each assembly in one-sixth core. 1.06 1.04
Conversion ratio
1.02 1.00 0.98 0.96 0.94 0.92 0.90 0
5
10
15
EFPY Fig. 7. Evolution of conversion ratio with the burn-up for 20 EFPYs.
20
Reactivity coefficients
Results
Fuel temperature (pcm/K) Coolant temperature (pcm/K) Void (pcm) Axial expansion of rod (pcm/1%) Radial expansion of rod (pcm/1%)
−0.536 −0.21 −4673.57 −81.0 −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 whole life-time, due to the depleting of 239 Pu and the accumulating of 233 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 theory 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 important 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% broadening of the radial size of the fuel assemblies, respectively. From the above analysis, all reactivity coefficients which are important factors affecting the reactor safety are negative and assure that the SMoPN possess passive safety. 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 average conversion ratio with the burn-up. The conversion ratios for the assemblies with plutonium enrichments 14.04%, 15.18% 16.32% are larger than unity at the beginning of life and that of the inner assemblies is the highest. Although the conversion ratio of the two outer rings of assemblies is less than 1, the averaged conversion ratio for all fuel assemblies is larger than 1. The more outer assembly, the lower value due to the fact that the neutron flux and the fraction of fertile materials (mainly 232 Th) in the inner assemblies is higher than outer assemblies, as well as the blanket in the innermost assemblies. The conversion decreases with burn-up, and lower than unity after 5 EFPYs, which is resulted by the fertile material consumed gradually as burn-up. The average internal conversion ratio is about 0.97, which is higher than that of most current small modular fast reactor design and satisfies self-sustainable. The discharged burn-up is the capital factor to determine the cladding integrity in practice, which is about 150 GWd/tHM for fast reactor due to the limitation of material (Dubberley et al., 2003). However, some special fast reactors with special cladding material
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Fig. 8. Discharged burn-up for each assembly in one-sixth core (GWd/t).
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 burnup 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 gradually 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. 9. Relative power factor distributions for each assembly at the BOL.
Fig. 10. Relative power factor distributions for each assembly at the MOL.
Parameters
Primary
Full power to hot standby ($) Hot standby to refueling ($) Reactivity fault ($) Fuel cycle excess reactivity ($) Uncertainties ($) Maximum requirements ($)
2.52 0.95 1.73 4.5 0.93 10.27
Secondary 2.52 – 2.0 – – 4.5
Table 3 Information of control assemblies. Parameters
Primary
Secondary
Number of control assemblies Reactivity worth of control system ($) Worth of 1 stuck assembly ($) Reactivity worth available ($)
7 14.10 1.37 12.73
6 7.0 2.0 5.0
assemblies. The requirements of reactivity cover the insertion of positive reactivity by temperature defect, reactivity fault and fuel cycle excess reactivity. The temperature defects are induced by the reactor from full power to hot standby (the reactor power is zero but the coolant is at the inlet temperature for full power operation) and from the hot standby to refueling. The reactivity fault implies the ejection accident of the assembly with the maximum value. The total requirements of the reactivity are about 10.27$ and 4.5$ for primary (RCS) and secondary (RSS) bundles of control assemblies with 10% uncertainty, separately. The available reactivity worth of RCS with seven control assemblies, which considers the worth of one stuck assembly with the maximum value, is 12.73$, the shutdown margin is 2.46$. For RSS, there is about 0.5$ shutdown margin.
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Table 4 Design parameters for reference core of the SMoPN. Parameters
Values
Parameters
Values/materials
Thermal power (MWt) Inlet temperature (◦ C) Outlet temperature (◦ C) Number of fuel assembly Number of control assembly Number of reflector assembly Number of shielding assembly Flat to flat distance of FA (cm) Number of Pin in a FA P/D Fuel rod diameter (mm) Active fuel height (mm) Active core diameter (mm)
300 320 500 240 13 60 138 11.2 127 1.2 8.3 1950 1957
Cladding material Fuel material Coolant material Control absorber material Detailed size Heavy metal inventory in core (ton) Maximum linear power density (kW/m) Average discharge burn-up (GWd/t) Average conversion ratio Maximum centerline temperature (◦ C) Maximum cladding surface temperature (◦ C) Average flow velocity (m/s)
Stainless T91 PuN + ThN PbBi B4C Ref. Figs. 1–3 19.41 8.2 186.33 0.975 676 650 1.1
4. Conclusions
Fig. 11. Relative power factor distributions for each assembly at the EOL.
Hence, the two control systems are reliable to control the reactor in any operation considerations.
3.3. Summary of design Based on the above analysis, the core characteristics of the SMoPN in the lifetime 20 EFPYs are summarized in the following. • The core reactivity swing is near zero because the nitride thorium is used as the fertile material with conversion ratio 0.975. All of the reactivity coefficients are negative. • 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. • The maximum peak power factor is about 1.35 in radial direction and move gradually to center of core from outside with the burnup. • The control system can provide the enough reactivity to shutdown the reactor in any situation. All of the parameters and values of the SMoPN characteristics are listed in Table 4 and satisfy all design criteria and goals.
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 operation. The plutonium extracted from PWR and natural thorium are utilized as fuel of the SMoPN for advanced nuclear fuel cycle, which will increase the efficiency and space of fuel utilization. Especially, 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 innovative the SMoPN rod is set up at the center of the reactor core, hence burn-up swing is almost zero in the whole lifetime. Using liquid Pb-Bi, which had several decades of operation experience 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 the reflector material. Assuming that the coolant was lost totally, the leakage of neutron will be very high to induce the core going subcritical. The integrated modular structure of the SMoPN provides an opportunity to apply batch production of the standard reactor modules and the production-line methods for the core and construction. This will make it possible to reduce considerably the schedule period of the nuclear power plant construction. All of the important reactivity coefficients are negative to assure the SMoPN with passive safety. This innovative nuclear power technology based on the multi-purpose SMoPN with chemically inert Pb-Bi coolant, which may assure a high level of social acceptability of the nuclear plant. This will heighten the competitiveness of nuclear power plant at the investment market and promote nuclear power development. Acknowledgements This work was financially supported by the Program for Changjiang Scholars and Innovative Research Team in University (IRT1280), China Postdoctoral Science and Technology Fund (2013M532051) and Shanxi Province Postdoctoral Science and Technology Fund (20130018). Authors also appreciate helps from Yunlong Xiao, Baolin Liu, Chuanqi Zhao and Zhipeng Li of NECP laboratory of Xi’an Jiaotong University.
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