Physical study of an ultra-long-life small modular fast reactor loaded with U-Pu-Zr fuel

Annals of Nuclear Energy 142 (2020) 107390

Contents lists available at ScienceDirect

Annals of Nuclear Energy journal homepage: www.elsevier.com/locate/anucene

Physical study of an ultra-long-life small modular fast reactor loaded with U-Pu-Zr fuel Yucui Gao a,b, Liangzhi Cao a,d,⇑, Yongwei Yang b,c,⇑, Zelong Zhao b,c, Shengcheng Zhou a, Sheng Wang a a

School of Nuclear Science and Technology, Xi’an Jiaotong University, Xi’an, Shaanxi 710049, China Institute of Modern Physics, Chinese Academy of Sciences, Lanzhou 730000, China c School of Nuclear Science and Technology, University of Chinese Academy of Sciences, Beijing 100049, China d College of Mechanical and Power Engineering, China Three Gorges University, Yi Chang 443002, China b

a r t i c l e

i n f o

Article history: Received 5 May 2019 Received in revised form 6 December 2019 Accepted 16 February 2020

Keywords: Small modular fast reactor Neutronic analysis U-Pu-Zr fuel LBE coolant Small burnup reactivity swing

a b s t r a c t The physical characteristics of a small modular fast reactor loaded with U-Pu-Zr fuel were studied in this paper. The reactor can be operated for more than 20 years without refueling. The small burnup reactivity swing was achieved thanks to the good balance between the fuel breeding characteristics and decay of 241 Pu with a half-life of 14.239 years, which avoids increasing the initial excess reactivity of the core. Nuclide effect analyses in this paper show that the decay of 241Pu plays a non-negligible role in burnup reactivity swing for the ultra-long-life low power reactors loaded with U-Pu-Zr fuel. The reactor neutronic parameters such as burnup behavior, displacement per atom (DPA) of the fuel rod cladding, spent fuel composition, and reactivity feedback coefficients were analyzed. The operating modes of the reactor were also analyzed. Ó 2020 Elsevier Ltd. All rights reserved.

1. Introduction Recently, researches on Small Modular Fast Reactors (SMFRs) have been widely conducted in Russia, United States of America, China, Japan and other countries in the Generation IV Forum (Wang et al., 2015; Xiao, 2015; Wallenius, et al., 2018; Ueda et al., 2005; Georgy and Vladimir, 2012; Greenspan, 2003). Among them, Russia has relatively mature technology of lead based alloy cooled reactors, in which the Lead-Bismuth-Eutectic (LBE) cooled fast reactors have already been constructed for submarines. The typical Russian SMFRs are SVBR-100 fueled with UO2 with an average enrichment of 16.3%, BREST-300 fueled with U-Pu-N (Georgy and Vladimir, 2012; Xiao, 2015), both of them use LBE as the coolant. In Japan, the Super-Safe, Small, and Simple (4S) sodium cooled reactor loaded with the metal fuel with 24% enriched Pu was proposed. The ‘‘4S” reactor has the novel conceptual design of an annular reflector. Core reactivity could be controlled through the axial movement of the reflector and thus reduce the use of control system (Ueda et al., 2005). Thereafter, several conceptual designs using the concept of the annular reflector were carried out. The ⇑ Corresponding authors at: School of Nuclear Science and Technology, Xi’an Jiaotong University, Xi’an, Shaanxi 710049, China (L. Cao). Institute of Modern Physics, Chinese Academy of Sciences, Lanzhou 730000, China (Y. Yang). E-mail addresses: [email protected] (L. Cao), [email protected] (Y. Yang). https://doi.org/10.1016/j.anucene.2020.107390 0306-4549/Ó 2020 Elsevier Ltd. All rights reserved.

most typical one is Encapsulated Nuclear Heat Source (ENHS) reactor concept proposed in 1998 by Dave Wade at Argonne National Laboratory (ANL) and by Ehud Greenspan at University of California at Berkeley (UCB), which is one of the Secure, Transportable, Autonomous, Reactor (STAR) system concepts (Greenspan, 2003; Greenspan et al., 2008). Mauricio G performed a preliminary design of a Small Fast Sodium Reactor (SFSR) proposal based on the ‘‘4S” reactor project and Small Secure Transportable Reactor (SSTAR) in 2018 (Mauricio et al., 2018). Wallenius J in KTH completed the detailed physical and thermal–hydraulic design of SEALER which has a small volume using high enrichment of 235U (Wallenius et al., 2018; Wallenius and Bortot, 2018). Most of these designs adopted high enrichment of fissile nuclides to achieve the long life of the core, while the design of ENHS used the relatively low enrichment of fissile nuclides. E. Greenspan pointed out that the good breeding performance of a reactor can be achieved through the appropriate design of fuel, coolant, fuel pin grid geometry and so on (Greenspan et al., 2008). Also, Donny Hartanto at KAIST achieved the small burnup reactivity swing during an ultra-long time through selecting a combination of a Zr zoning and a concave or pan-shaped core, the core was loaded with low-enriched U-Zr fuel (Hartanto et al., 2016). However, as for the nuclide effect on burnup behavior of a reactor especially for the effect of the decay of 241Pu with a halflife of 14.239 years, there are few researches. In this paper, the nuclide effect analyses on the burnup behavior were conducted.

2

Y. Gao et al. / Annals of Nuclear Energy 142 (2020) 107390

As a starting point, the preliminary conceptual physical design of a SMFR core was conducted. The reactor was elementarily oriented to the remote area electricity supply. The reactor should have the characteristics of no proliferation risk, economy and convenience. A relative stable operation and an ultra-long life will be beneficial to these characteristics. The SMFR core with power of 50 MWt which could be operated for 20 years without refueling was achieved. The power of 50 MWt (20MWe considering for 40% thermal efficiency) could realize the power supply with a population of about 25 000. The primary characteristic of the reactor is the smallest burnup reactivity swing during a long lifetime. The ultra-long life and small burnup reactivity swing was achieved through a good balance between the consumption and production of fissile nuclides rather than using high-enriched fissile material. U-Pu-Zr was selected as the fuel referred to the ENHS design. Based on this selection, analyses on the burnup reactivity swing for the ultralong-life reactor are discussed in detail in Sections 4.1 and 4.2. For the U-Pu-Zr fueled reactors, the disappearance of fissile nuclides mainly results from two points: decay of 241Pu and the consumption because of fission. The production of fissile nuclides is a result of the breeding of fissionable nuclides. So, the burnup process depends on the competitive relationships of the above three. The latter two have a direct relationship with the power level and the loading of U and Pu, while 241Pu decays with a half-life of 14.239 years which is irrelevant to the power. Hence, the influence extent of the decay of 241Pu in the combined effect of the three has relation to the operating power level and the loading of U, Pu and 241Pu, it is not realistic to adjust the content of 241 Pu considering for the nuclear proliferation. The main idea of this paper is that the decay of 241Pu plays a non-negligible role in burnup reactivity swing for reactors with power of tens of megawatts, due to the decay of 241Pu, the core operating power and Pu content will have a larger impact on burnup reactivity swing. There will be the case that the core burnup reactivity swing will be greater under the lower power operating. Detailed discussions on these results are presented in Section 4.2.

2. Core design objectives and computational method The preliminary SMFR core design objectives are determined as follows: 1) The output thermal power is about 50 MWt, corresponding to the electrical power about 20 MWe (~40% thermal efficiency) for the remote area power supply with a population of about 25,000. 2) In order to ensure the availability of the SMFR, once-through refueling scheme is adopted. So, the cycle length should be as long as possible. Considering the material constraint, the cycle length is set to 20 years without refueling. 3) Negative reactivity coefficients should be achieved during the whole life to ensure the safety of the core. For the core neutronic calculations, the open source Monte Carlo code OpenMC was used for the neutron transport and calculation of reactivity coefficients (Romano and Forget, 2013). The burnup process during the reactor’s life was calculated by the IMPC-Burnup Code (Liu et al., 2019). IMPC-Burnup is a code system that couples different codes for specific calculations. Such as FLUKA for proton transport calculation, OpenMC for neutron transport calculation, ORIGEN2 for burnup calculation in which the effective one-group cross sections for the nuclides are prepared according to the neutron spectra calculated by OpenMC. The code had been verified by the OECD-NEA pin cell problem and IAEA-ADS benchmark by comparison with experimental values and calculated results

from different studies. It also can be used for the burnup calculation of an ADS sub-critical core. Furthermore, MCNPX was used to calculate core parameters such as displacement per atom (DPA) of the fuel rod cladding and linear power density (Pelowitz, 2011). 3. Core scheme for physical study 3.1. Fuel assemblies Fast reactors are usually loaded with oxide fuel, nitride fuel, carbide fuel, or metal fuel. Among these fuels, the metal fuel has good heat conduction properties and reactors loaded with metal fuel have hardened neutron spectrum. Also, from the initial uraniumfissium (U-Fs) fuel to the subsequent U-Pu-Zr ternary fuel, metal fuel had been tested in the irradiation experiment on EBR-II (The Experimental Breeder Reactor-II). Given these reasons, in this paper, U-Pu-Zr ternary fuel was selected in the proposed core scheme (Walter et al., 1975; Riyas and Mohanakrishnan, 2008; Walters, 1999). Based on the irradiation experiments on EBR-II, the burnup of U-Pu-Zr metal fuel reaches up to 19.1% when the fuel density is 75% of nominal density of 15.85 g/cm3 and the ratio of the volume of gas plenum to the volume of fuel reaches to 0.6. The explanation given by L.C. Walters is that, when the volume of gas plenum increases, the release of fission gas will not increase the pressure in the fuel pin cladding, also, the fission pores in the fuel crystal combine gradually and then release to the chamber with the reduced fuel density, i.e. 75% of the nominal density, thus minimizing the swelling rate of U-Pu-Zr metal fuel (Hartanto et al., 2016; Waltar et al., 2012). For the U-Pu-Zr fuel, the content of Zr should not exceed 10%. Due to the low delayed neutron fraction of 239Pu, the Pu content should not exceed 20%. Since the ENHS reactor used the U-Pu10 wt%Zr fuel, therefore, in this paper, U-Pu-10 wt%Zr was adopted referred to the design of ENHS (Greenspan, 2003; Walters, 1999). Considering for the breeding performance of the reactor, large inventory of fissionable nuclides is needed. Therefore, for the uranium in U-Pu-10 wt%Zr, the preliminary option is depleted uranium referred to the ENHS reactor. Plutonium in the spent fuel of a typical PWR with 50 GWd/tHM after 10 years of cooling was used. The isotopic composition of Plutonium is given in Table 1 (Greenspan, 2003). For the U-Pu-10 wt%Zr ternary fuel, Pu content should be determined in order to get the small burnup reactivity swing and ultralong-life of the reactor, which needs scanning calculations and analyses. One of the main objectives of the ultra-long-life reactor is the smallest burnup reactivity swing, which means that the amount of consumption and production of fissile nuclides should reach a balance i.e. conversion ratio equals to a unit. In general, the conversion ratio of a reactor is defined as the ratio of the production rate of fissile nuclides to the consumption rate of fissile nuclides. In fast spectrum reactors, the fission rate of 238U is significantly high. The cross section data of different nuclides in ENDF/B-VIII are shown in

Table 1 Plutonium Composition in a typical PWR spent fuel. Plutonium Isotopes

Content (w/o)

238

3.18 56.35 26.6 8.02 5.83

Pu 239 Pu 240 Pu 241 Pu 242 Pu

3

Y. Gao et al. / Annals of Nuclear Energy 142 (2020) 107390 Table 3 Material parameters of the fuel assembly.

Fuel Cladding Reflector Balancer gas

Fig. 1. Cross section data of

238

U and

Material

Density g/cm3

U-Pu-Zr10% 15-15Ti 316L depleted uranium helium

11.88 7.92 7.98 18.7 0.0001347

239

Pu in ENDF/B-VIII.

Fig. 1. If the neutron energy higher than the value of 1 MeV, the fission cross section of 238U is nearly 10% of the capture cross section of 238U and nearly 1% of the fission cross section of 239Pu. When UPu-Zr ternary fuel was used, especially for the case of lower content of Pu and higher content of 238U such as U-10 wt%Pu-10 wt %Zr, the fission rate of 238U will be close to the fission rate of 239 Pu, thus we should just proceed the qualitative analysis using the general definition of conversion ratio (Liu and Xian, 2008). Geometry parameters of fuel assembly are shown in Table 2. Material parameters of fuel assembly are shown in Table 3. The fuel assembly configuration is shown in Fig. 2: LBE was selected as the coolant because of its many merits such as inertness, low melting point (123.5 °C), high boiling point (~1670 °C). Meanwhile, because of the high corrosion of LBE, the upper limit of LBE velocity is 2 m/s, so the coolant velocity of the core should be calculated after the geometry of the reactor core was determined. The most alarming problem of LBE is 210Po. 210 Po is generated mainly through the (n, c) reaction of 209Bi and beta decay of 210Bi. While according to studies of Lanfang Mao, the vast majority of 210Po will be contained in LBE, only a small amount of 210Po will migrate into the cover gas of the reactor. Lanfang Mao pointed out that the 210Po contamination will not lead to problems during normal operations namely no abnormal leakage of LBE or cover gas (Mao et al., 2014). Due to the high density of LBE, a depleted uranium slug was used as the balance weight at the bottom of the fuel pin. Due to the neutron economy and high corrosion of LBE, a smaller P/D value of about 1.1 was used for fuel assembly. 15-15Ti whose irradiation dose can reach up to 175 DPA was selected for the cladding material (Xie and Zhang, 2007). Comparing with the ordinary fast reactors whose pin diameters are mainly from 6 to 9 mm, larger pin diameter was selected mainly in consideration of satisfying the critical requirements

Table 2 Geometry parameters of fuel assembly. Parameters

Value

Active core height/cm Ratio of Plenum/Fuel Length of the balancer/cm Reflector length/cm Fuel pin pitch Pitch of assembly Fuel rod numbers

140 0.6 10 20 1.9 16 61

Fig. 2. Fuel assembly configuration.

under the three constraints regarding to this scheme, these are: the low density of the fuel (75% of the nominal density), using of depleted uranium and the upper limit of the plutonium content (20%). The selection of larger diameter was mainly referred from the design of SEALER (Mauricio et al., 2018). For the purpose of power flattening, the core arrangement is such that the fuel pins in different zones have different fuel pin diameters and same composition of fuel, which referred from the work of Shengcheng Zhou (Zhou et al., 2018). The diameters of different fuel pins in different zones are shown in Table 4: 3.2. Core scheme LBE was adopted as the reflector. Donny Hartanto’s study showed that better neutronic performance will be achieved using

Table 4 Fuel rod diameters in different zones. Zones

Parameters

Value/cm

Zone-I

Fuel Radius Cladding Outer Radius Fuel Radius Cladding Outer Radius Fuel Radius Cladding Outer Radius

0.74 0.77 0.76 0.79 0.78 0.81

Zone-II Zone-III

4

Y. Gao et al. / Annals of Nuclear Energy 142 (2020) 107390

LBE as reflector compared with the traditional steel reflector (Hartanto and Kim, 2015). Borated stainless steel was used as shielding layer. The preliminary reactor core is shown in Fig. 3. Eight flow channels are reserved for the shutdown system. The reactor core includes two independent shutdown systems. The first control system is composed of six control rod assemblies. The reactivity worth requirements of the first control system is at least 4612 pcm. The second control system is composed of two safety rod assemblies. The reactivity worth requirements of the second control system is at least 2023 pcm. If the B4C with 10B enrichment of 92% is used, both of the two systems will meet the reactivity worth requirements and have a margin under the requirement of stuck rod criterion. The detailed design of the shutdown system will be conducted in future work. The geometry parameters and material parameters of the core are shown in Tables 5 and 6 respectively: The coolant velocity can be achieved through the equation:

Table 5 Core geometry parameters. Parameters

Value

Fuel assemblies number in Zone-I Fuel assemblies number in Zone-II Fuel assemblies number in Zone-III Core Radius/cm Core Length/cm Reflector assemblies number Shielding assemblies number

7 28 48 130 290 36 42

Table 6 Core material parameters.

Reflector Shielding Coolant

Material

Density g/cm3

LBE Borated stainless steel LBE

10.3 7.98 10.3

cQ DT ¼ P where c is the specific heat of LBE, which could be calculated through the equation,c ¼ 159  2:72  102  T þ 7:12  106  T 2 , Q is coolant flow, DTis the temperature difference between inlet and outlet, P is the power of the reactor. Temperature of inlet and outlet are preliminary set as 573.15 K and 673.15 K. The power of the reactor is 50 MW. Then the coolant velocity was 0.487 m/s by calculation, the value meets the limit of the LBE velocity of 2 m/s. 4. Analysis of the nuclide effect on burnup reactivity swing

to case 1, case 2, case 3 and case 4 respectively. The results in Fig. 4 show that, for 11% case and 12% case, keff have a decrease. The 12% case decreases faster than the 11% case. The 9% case increases considerably. The 10% case decreases initially and then increases, which decreases slower than the 11% case and increases slower than the 9% case. Therefore, as shown in Fig. 4, the plutonium content of 10% is more appropriate to the small burnup reactivity swing. 241

4.1. Analysis on the Pu content

4.2. Analyses on the effect of decay of

The scanning calculations and analyses on Pu content were done based on the preliminary determination of core geometry and material parameters other than fuel. The scanning scheme may lead to different initial keff (effective multiplication factor), however, the calculation provides the most appropriate Pu content which plays a decisive role in the approximately zero burnup reactivity swing and finally can be adopted for the ultra-long-life reactor core. Four different cases were considered and they were classified according to the plutonium content in the fuel. The values of the plutonium content i.e. 9%, 10%, 11%, 12% are correspond

Significant differences in burnup processes were observed for different operating power levels of the same reactor, as shown in Fig. 5. From Fig. 5, we could see two special points, one is that the lower power of the reactor, the larger burnup reactivity swing, the other one is that the breeding performance of the reactor may have a change if the power changes. To explain these results, the mass of uranium and plutonium for the reactor operating at 50 MW and 10 MW were analyzed at the same burnup respectively. The burnup of 50 MW-reactor after 603 days is close to the burnup of 10 MW-reactor after 3103 days,

Fig. 3. Radial reactor core map.

Pu

5

Y. Gao et al. / Annals of Nuclear Energy 142 (2020) 107390 Table 7 Fissile and fissionable isotope analyses for reactors in different power. Nuclides

Mass for 50 MW reactor/kg

Mass for 10 MW reactor/kg

Difference/kg

234

0.627 30.267 0.217 0.003 12479.115 0.001 48.268 893.998 416.425 114.411 91.266

3.142 30.409 0.520 0.001 12479.766 0.000 45.925 894.635 416.111 82.480 91.221

2.515 0.142 0.303 0.003 0.651 0.001 2.343 0.637 0.313 31.931 0.045

U U U 237 U 238 U 239 U 238 Pu 239 Pu 240 Pu 241 Pu 242 Pu 235 236

Table 8 Nuclides mass fraction for cases in Fig. 5, Fig. 6(a) and (b). Nuclides

Mass fraction in Fig. 5

Mass fraction in Fig. 6(a)

Mass fraction in Fig. 6(b)

235

0.002 0.798 0.003 0.056 0.027 0.008 0.006

0.002 0.798 0.003 0.064 0.027 0 0.006

0.002 0.798 0 0.100 0 0 0

Fig. 4. Burnup process for different Pu content. U U 238 Pu 239 Pu 240 Pu 241 Pu 242 Pu 238

Fig. 5. Burnup process in different power levels with days.

which is 2.14216 GWd/tHM and 2.20945 GWd/tHM respectively. The results are shown in Table 7. From Table 7, it can be observed that there is an obvious difference between the mass of 241Pu in the reactor operated at 50 MW and 10 MW. The half-life of 241Pu is 14.239 years. The initial inventory of 241Pu is 125.790 kg. In addition to other effects such as fission and breeding, the amount of 241Pu left after decay in 603 days will be 116.180 kg, the amount of 241Pu left after decay in 3103 days will be 83.567 kg. So for the 50 MW case and 10 MW case in Fig. 5, at the same burnup, the difference in 241Pu amount left just because of decay is about 32.613 kg. The difference is close to the number of 31.931 kg in Table 7 which encompasses other aspects such as fission and breeding. This means that the decay of 241Pu is the main reason for the difference in 241Pu amount that is shown in Table 7. In order to verify this interpretation further, the burnup calculations without 241Pu content for the reactor operated at 10 MW and 50 MW were conducted. The amount of 241Pu in the original

Plutonium composition showed in Table 1 was substituted by 239 Pu, and the amount of the 235U, 238U, 238Pu, 240Pu and 242Pu remained unchanged. The nuclides’ mass fraction is shown in Table 8. The results are shown in Fig. 6(a). Meanwhile, the burnup calculations were carried out in which the reactor has only uranium and 239Pu. The amount of the 238Pu, 240Pu, 241Pu and 242Pu in the original Plutonium composition showed in Table 1 were substituted by 239Pu, and the amount of the 235U and 238U remained unchanged. The nuclides’ mass fraction is shown in Table 8. The results of the burnup processes of the reactors operated at 50 MW and 10 MW are shown in Fig. 6(b): Comparing Fig. 6(a) with Fig. 6(b), because of the substitution of 238 Pu, 240Pu, and 242Pu by 239Pu, the initial keff in Fig. 6(b) is larger than that in Fig. 6(a), the breeding performance in Fig. 6(b) is inferior to that in Fig. 6(a) due to the lower mass ratio of fissionable nuclides to fissile nuclides. Comparing Fig. 6(a) with 50 MW and 10 MW case in Fig. 5, because of the substitution of 241Pu by 239 Pu, since the fission cross section of 241Pu is a little larger than 239 Pu, and the number of neutrons per fission of 241Pu is larger than 239 Pu, so the initial keff in Fig. 6(a) is smaller than that in Fig. 5. As for breeding performance, the breeding performance in Fig. 6(a) is much more superior to that in Fig. 5 due to the eliminated effect of decay of 241Pu, in other words, in Fig. 5, the decay of 241Pu plays a leading role in the disappearance of fissile nuclides. In both Fig. 6 (a) and Fig. 6(b), the comparison between case-1 and case-2 is conforming to the general experience that the higher power, the larger burnup reactivity swing due to the rapid consumption or production of fissile nuclides. So the above results verify the view suggested earlier further that the decay of 241Pu has a significant effect on the burnup process of the ultra-long-life low power reactor loaded with U-Pu-Zr. The ratio of the decay amount of 241Pu to the total consumption amount of 241Pu with different power levels were calculated, the results are shown in Fig. 7. Initially, the differences among the values with different power levels are quite large. As time goes on, the differences decrease gradually. It can be observed from Fig. 5,

6

Y. Gao et al. / Annals of Nuclear Energy 142 (2020) 107390

Fig. 6. (a). Burnup process for 50 MW and 10 MW reactors without

Fig. 7. Ratio of decay disappearance to total disappearance of power levels.

241

241

Pu; (b). for 50 MW and 10 MW reactors only with uranium and

239

Pu.

Pu in different

Fig. 7, Fig. 8(a) and (b) that for the 10 MW case, the consumption of fissile nuclides due to fission and breeding of fissionable nuclides are relatively low, the decay of 241Pu accounts for a large proportion in the disappearance of fissile nuclides, which leads to a large decrease in keff at the beginning. For 100 MW, 40 MW and 50 MW cases, the consumption and production of fissile nuclides reach a balance, so the burnup reactivity swing is small. While for 100 MW case, there is a larger increase in the breeding of fissionable nuclides and relatively lower influence of decay of 241Pu, keff has a slow increase at the beginning. For the 40 MW and 50 MW cases, keff has a slow decrease at the beginning and then a slow increase, this is because of the lower breeding of fissionable nuclides and higher influence of decay of 241Pu compared with the 100 MW case. Based on the above analyses, for the SMFRs loaded with U-PuZr, especially having power of about dozens of MW, due to the decay of 241Pu, the core operating power has a large impact on the small burnup reactivity swing. There will be the case that the core burnup reactivity swing will be larger under the lower power operation.

Fig. 8. (a). Amount of different power levels.

241

Pu in different power levels (b). Amount of

239

Pu in

5. Core performance 5.1. Burnup and DPA The reactor could be operated with 50 MWt for 20 years without refueling. The burnup of the reactor after 20 years is 26.7 GWd/tHM, which is lower than the design limit of 120 GWd/tHM for the fast reactors. The DPA for the fuel rod cladding is 113.04 after 20 years which is lower than the threshold value of 175. The DPA is achieved through the equation:

Z DPA ¼ ð

rDX ðEÞ  uðEÞ  dEÞ  t

In the equation above, rDX is the displacement cross section of the cladding material 15-15Ti, uðEÞ is the neutron flux, t is the irradiation time of the material. DPA distribution could be achieved through the convolution of neutron flux with displacement cross section. The neutron flux distribution was achieved through mesh

7

Y. Gao et al. / Annals of Nuclear Energy 142 (2020) 107390

tally, the convolution could be achieved through the combined use of FM card, DE card, DF card and mesh tally in MCNPX (Yu et al., 2011). 5.2. Preliminary operating modes analyses

Table 9 Mass of U and Pu for the 50 MW reactors at BOL and EOL. Nuclides

Mass in BOL/kg

Mass in EOL/kg

Difference/kg

234

0.000 30.975 0.000 0.000 12516.620 0.000 49.877 883.821 417.208 125.790 91.441

6.359 23.698 2.335 0.004 12068.536 0.001 38.822 985.646 410.254 45.167 88.630

6.359 7.277 2.335 0.004 448.084 0.001 11.054 101.825 6.954 80.623 2.811

U U U 237 U 238 U 239 U 238 Pu 239 Pu 240 Pu 241 Pu 242 Pu 235 236

According to our analyses in chapter 4.2, due to the decay of Pu, the reactor power levels will have a large impact on burnup reactivity swing. There will be cases that the core burnup reactivity swing will be larger under the lower power operation. So the lower power operating mode will be different from the general Uranium based reactors. For the general Uranium based reactors, if just starting from the physical view, the reactor could realize any lower power operating modes. While for the reactor loaded with U-Pu-Zr fuel in this paper, due to the decay of 241Pu, there are limitations for the long time lower power operation. Several extreme examples were analyzed. As shown in Fig. 5, the reactor could be operated for 20 years under the full power operation or 25 years under the lower power operation at the power of 40 MW. If the power lowered to 30 MW, after about 8.7 years, the reactor must return to the full power operation, otherwise, the core excess reactivity will under 500 pcm. While after the reactor is operated at the full power for 13.1 years, the core excess reactivity is 883 pcm. Then at this time, if the reactor power lowered to 30 MW or 40 MW, the core excess reactivity of both cases will not under 500pcm in a long lower power operating time. The results are shown in Fig. 9.

241

5.3. Transuranium nuclides analysis The mass of the uranium and transuranic nuclides at BOL and EOL are shown in Tables 9 and 10. For the fissile and fissionable nuclides, the mass difference of 238U, 239Pu and 241Pu between BOL and EOL are larger than that of other nuclides. 238U is reduced by 448.084 kg which is mainly due to the (n, c) reactions. The build-up of 239Pu is 101.825 kg which is the result of the consumption and production. The consumption of 241Pu is 80.623 kg in which 77.746 kg of 241Pu is reduced because of its decay in 7303 days. The mass of the Np, Am and Cm nuclides for EOL are shown in Table 10. Mass of 241Am has the biggest build-up which is mainly due to the decay of 241Pu and neutron capture of 242Pu (Wallenius and Bortot, 2018). 5.4. Other parameters The maximum linear power density is 77.2 W/cm. Reactivity coefficients at BOL and EOL are shown in Table 11. The coefficients of reactivity are favorable with the negative values.

Table 10 Mass of Np, Am, Cm for the 50 MW reactors in EOL. Nuclides 237

Np Np Am 242 Am 243 Am 239 241

Mass in EOL/kg

Nuclide

Mass in EOL/kg

3.451 0.172 68.577 0.001 3.222

242

0.270 0.003 0.189 0.005

Cm Cm Cm 245 Cm 243 244

Table 11 Reactivity coefficients of the proposed scheme.

Fuel temperature coefficient (pcm/K) Coolant temperature coefficient (pcm/K) Coolant void coefficient (pcm/%void)

BOL

EOL

0.421 0.154 55.250

0.306 0.155 12.882

6. Conclusions In the current study, the nuclide effect analysis on burnup reactivity swing for an ultra-long-life SMFR with low power was completed. As a starting point, a preliminary physical reactor core with the thermal power of about 50 MWt was achieved. The core achieved the design objectives. The core can operate for 20 years without refueling for the remote area power supply with a population of about 25,000. The ultra-long-life of the core was achieved through the small burnup reactivity swing. In this paper, two important factors which influence the burnup reactivity swing are stated. One is the composition of the U-Pu-Zr fuel which is generally known, the composition among the 235U, 238U, 238Pu, 239Pu, 240 Pu, 241Pu and 242Pu influences the balance between the consumption and production of fissile nuclides, namely the conversion ratio; and the other factor is the reactor operating power level that

Fig. 9. (a). Lower power operating case 1(30 MW to 50 MW); (b). Case 2(50 MW to 30 MW); (c). Case 3(50 MW to 40 MW).

8

Y. Gao et al. / Annals of Nuclear Energy 142 (2020) 107390

is the main idea of this paper in which the key point is the nuclide 241 Pu whose half-life is 14.239 years. The decay of 241Pu plays a non-negligible role in burnup reactivity swing. In many effect factors, there are competitive relationships among the decay of 241Pu, breeding of fissionable nuclides and fission of fissile nuclides. The latter two has the same variation to the power change, while 241 Pu decays according to the stable rate of half-life of 14.239 years which has no relationship with the operating power. Therefore, the influence extent of the decay of 241Pu has relation to the operating power. If the operating power is large, the disappearance of fissile nuclides due to fission and the proliferation of fissionable nuclides are large. Therefore, the decay of 241Pu accounts for a small proportion in the disappearance of fissile nuclides, and the influence extent of the decay of 241Pu is small. However, if the operating power is small, the disappearance of fissile nuclides due to fission and the proliferation of fissionable nuclides are small. At this time, the effect of the decay of 241Pu could not be ignored. So, for the ultra-long life lower power SMFR loaded with U-Pu-Zr, in consideration of the small burnup reactivity swing, the effect of decay of 241 Pu could not be ignored. Due to the decay of 241Pu, the core operating power will have a large impact on burnup reactivity swing and the reactor lower power operating modes will have some limitations. As for the core scheme, there is still a margin for the core optimization. Such as the reactivity control system which should has the advantage of simplicity and somewhat self-adaptability. Thus could contribute to the intrinsic safety of the core. The complete of the margin and safety analysis will be our future work.

CRediT authorship contribution statement Yucui Gao: Conceptualization, Methodology, Formal analysis, Investigation, Writing - original draft, Visualization. Liangzhi Cao: Conceptualization, Validation, Resources, Project administration, Supervision, Writing - review & editing, Validation. Yongwei Yang: Conceptualization, Validation, Resources, Writing - review & editing, Validation. Zelong Zhao: Software, Writing - review & editing. Shengcheng Zhou: Methodology, Writing - review & editing. Sheng Wang: Writing - review & editing.

Declaration of Competing Interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Acknowledgements This work is supported by the Strategic Priority Research Program of Chinese Academy of Sciences (Grant No. XDA21010202).

References Georgy, T., Vladimir, P., 2012. Modular lead-bismuth fast reactors in nuclear power. Sustainability. 4, 2293–2316. Greenspan, E. et al., 2008. Innovations in the ENHS reactor design and fuel cycle. Prog. Nucl. Energy 50 (2–6), 129–139. https://doi.org/10.1016/j. pnucene.2007.10.022. Greenspan, E., et al. 2003. STAR: The Secure Transportable Autonomous Reactor System - Encapsulated Fission Heat Source. NERI Project No. 99-154. Department of Nuclear Engineering University of California Berkeley. Greenspan, E., et al., 2008. ‘‘Long-Life Cores with Small Burnup Reactivity Swing” , Proc. of the 2000 Int. Topical Mtg. On Advances in Reactor Physics and Mathematics and Computation into the Next Millennium, PHYSOR-2000, Pittsburgh, PA, May 7-11. Hartanto, D. et al., 2016b. Impacts of burnup-dependent swelling of metallic fuel on the performance of a compact breed-and-burn fast reactor. Nucl. Eng. Technol. 48 (2), 330–338. https://doi.org/10.1016/j.net.2015.12.009. Hartanto, D. et al., 2016a. An optimization study on the excess reactivity in a linear breed-and-burn fast reactor (B&BR). Ann. Nucl. Energy 94, 62–71. https://doi. org/10.1016/j.anucene.2016.02.017. Hartanto, D., Kim, Y., 2015. Alternative reflectors for a compact sodium-cooled breed-and-burn fast reactor. Ann. Nucl. Energy 76, 113–124. https://doi.org/ 10.1016/j.anucene.2014.09.048. Liu, Z.Q. et al., 2019. Development and validation of depletion code system IMPCBurnup for ADS. Nucl. Sci. Tech. 30 (3), 44. https://doi.org/10.1007/s41365-0190560-z. Liu, X.L., Xian, C.Y., 2008. Study on in-core physical design limit zone for lead bismuth eutectic cooled long-life cycle reactor. Nucl. Power Eng. 29 (4), 1–361. Mao, L.F. et al., 2014. Preliminary analysis of polonium-210 contamination for China LEAd-based Research Reactor. Prog. Nucl. Energy 70, 39–42. https://doi.org/ 10.1016/j.pnucene.2013.07.009. Mauricio, G. et al., 2018. Alternative proposal of a small fast sodium reactor concept. Nucl. Eng. Des. 337, 128–140. https://doi.org/10.1016/j.nucengdes.2018.06.024. Pelowitz., D., User’s Manual 2.7. 0. Los Alamos National Laboratory 2011.MCNPX Los Alamos. New Mexico. Riyas, A., Mohanakrishnan, P., 2008. Studies on physics parameters of metal (U–Pu– Zr) fuelled FBR cores. Ann. Nucl. Energy 35 (1), 87–92. https://doi.org/10.1016/j. anucene.2007.05.015. Romano, P.K., Forget, B., 2013. The OpenMC Monte Carlo particle transport code. Ann. Nucl. Energy 51, 274–281. https://doi.org/10.1016/j.anucene.2012.06.040. Ueda, N. et al., 2005. Sodium cooled small fast long-life reactor ‘‘4S”. Prog. Nucl. Energy 47 (1–4), 222–230. https://doi.org/10.1016/j.pnucene.2005.05.022. Wallenius, J. et al., 2018. Design of SEALER, a very small lead-cooled reactor for commercial power production in off-grid applications. Nucl. Eng. Des. 338, 23– 33. https://doi.org/10.1016/j.nucengdes.2018.07.031. Wallenius, J., Bortot, S., 2018. A small lead-cooled reactor with improved Amburning and non-proliferation characteristics. Ann. Nucl. Energy 122, 193–200. https://doi.org/10.1016/j.anucene.2018.08.043. Waltar, A.E. et al., 2012. Fast Spectrum Reactors. Springe, Spring Street, NewYork, NY 10013, USA. Walter, C. M., et al., 1975.U–Pu–Zr metal alloy: a potential fuel for LMFBR’s. ANL-7628. ARGONNE NATIONAL LABORATORY. Walters, L.C., 1999. Thirty years of fuels and materials information from EBR-II. J. Nucl. Mater. 270 (1–2), 39–48. https://doi.org/10.1016/S0022-3115(98)007600. Wang, M.H. et al., 2015. Preliminary conceptual design of a lead-bismuth cooled small reactor (CLEAR-SR). Int. J. Hydrogen Energy 40 (44), 15132–15136. https://doi.org/10.1016/j.ijhydene.2015.03.097. Xiao, H.C., 2015. Lead-cooled natural safe fast reactor BREST-the most potential reactor in the modern nuclear power system. Nucl. Sci. Eng. Xie, G.S., Zhang, R.X., 2007. Fuel Assemblies of Fast Reactors. Chemical Industrial Press, Beijing. Yu, Q.Z. et al., 2011. Calculation and analysis of DPA in the main components of CSNS target station. Acta Phys. Sin. 60 (5). Zhou, S.C. et al., 2018. Conceptual core design study of an innovative small transportable lead-bismuth cooled fast reactor (SPARK) for remote power supply. Int. J. Energy Res. 42, 3672–3687. https://doi.org/10.1002/er.4119.