Application of the Spectral-Shift Effect in the Small Lead-Based Reactor SLBR-50

In the design of a nuclear reactor, improving fuel utilization and extending burnup are two of the most important goals. A concept design of spectral-shift control rods is presented to extend cycle length and fuel utilization. First, a small lead-based reactor, SLBR-50, is preliminarily designed, and the design rationality is proved. Next, the concept design of spectral-shift control rods is presented and analyzed. Finally, numerical results of the small reactor design show that the burnup depth is extended by 73.3% and the fuel utilization rate for 235U and 238U is improved by 66.6 and 68.4%. All results are calculated using a Monte-Carlo code RMC. These results show advantages of the concept design for the spectral-shift control rod.


INTRODUCTION
Improving fuel utilization, extending burnup depth, and improving the nuclear plant economy are several important reactor design targets (Zhang et al., 2020a;Zhang et al., 2020b). It is still an open question when it comes to extending burnup depth with certain fuel weights. The spectral-shift effect is one of the solutions for the problem.
The spectral-shift effect was studied and the spectral-shift control concept was first proposed in 1961 in the Babcock and Wilcox company report (Mars and Gans, 1961). After that, the spectral-shift effect was studied in the pressurized water reactor design (Ronen and Galperin, 1980;Ronen and Fahima, 1984;Martin, 1988) and extended to the boiling water reactor design (Yokomizo et al., 1993). In the 21st century, the spectral-shift effect research was applied in the new-type advanced reactor. In the ABWR-II core design, spectral-shift rods were adopted and analyzed (Anegawa et al., 2001;Moriwaki et al., 2004). Results show that the average discharge burnup was improved by 5% and uranium weight was saved by 6∼7%. Recently, the spectral-shift control design was applied in other advanced reactors, such as SmAHTR (Greene, 2010;Ilas et al., 2014;Kotlyar et al., 2017;Mehta and Kotlyar, 2019), small modular reactors (Lindley and Parks, 2016), and molten salt reactors (Betzler et al., 2018). SmAHTR is a small advanced high-temperature graphite-moderator reactor designed by Oak-Ridge. The cycle length can be extended by up to 20% or coated particle (TRISO) fuel can be reduced by 15% while maintaining the cycle length with the spectral-shift effect (Kotlyar et al., 2017;Mehta and Kotlyar, 2019). In these new-type advanced reactor analyses, a reactor design with spectral-shift effect shows good improvements of the fuel utilization rate and cycle length extension. However, few research studies have been carried out on spectral-shift lead-based reactors (LBRs) or the spectral-shift for extending cycle length and the fuel utilization rate.
In this study, a 50-MWt small lead-based fast reactor, SLBR-50, is conceptually designed at the Nuclear Power Institute of China (NPIC) for research. Besides, detailed parameters of the SLBR-50 are introduced. Based on the SLBR-50, the concept design of control rods with the spectral-shift effect are proposed and analyzed, including the spectral-shift effect analyses and reactor performance improvement.
A continuous-energy Monte-Carlo reactor physics code, RMC (She et al., 2013;Wang et al., 2015;Liu et al., 2017), is adopted for the small reactor design. RMC has been developed by the Department of Engineering Physics, Tsinghua University, from 2010 as a tool for a reactor core analysis platform. It has several functions, such as complicated geometry modeling, criticality calculation, burnup calculation, and critical position searching calculation. Until now, RMC has already been used for reactor design and validation. In this study, all geometry modeling and calculation results are provided using RMC.

DESIGN OF SLBR-50
Design of SLBR-50 The SLBR-50 is conceptually designed for research. Several basic parameters of the reactor are shown in Table 1. Thermal power of the SLBR-50 is 50 MW. The hot-condition average temperature is 700 K. As for materials, 19.95% enrichment UO 2 is applied as the fuel. The uranium total weight is 3835.3 kg in the SLBR-50. B 4 C is chosen as the control rod absorber material. In each pin cell, stainless steel is conducted as the clad material. Outside of the active core, BeO is applied as the reflector and stainless steel is conducted as the barrel. Heavy metal lead is adopted as the coolant in the lead-based reactor SLBR-50. Other parameters will be introduced in geometry modeling.   The geometry modeling of the SLBR-50 is divided into the pin cell, the lattice, and the whole core. The basic pin cell geometry is shown in Figure 1. The radius of the fuel region is 4.0 mm. The thickness of the air gap between the fuel and the clad is 0.1 mm, which is hard to show in the figure. The 0.6-mm-thick clad lies outside of the pin cell.
The hexagonal assembly geometry of the fuel, reflector, and control rod lattice are shown in Figure 2. The basic geometry is totally the same for these assemblies. 61 rods are arranged in regular matrix form. The thickness of the stainless steel assembly box is 2 mm. The assembly inner and outer distances are 88.0 and 92.0 mm separately. The assembly center distance is 93.5 mm.
The radial cut of SLBR-50 whole-core modeling is shown in Figure 3, and axial cuts of all rods out (ARO) and all rods in (ARI) cases are shown in Figure 4. The whole core consists of 144 fuel assemblies, 48 reflector assemblies, 18 control rod assemblies, and center guide tube assembly. Control rod assemblies are divided into three groups, including compensation, safety, and power adjustment. Besides, reflector assemblies are located outside of the active core. The barrel is explicitly modeled and the diameter of the barrel is 82 cm. In the axial cut, the height of the active core is 95 cm. On the top and the bottom of the active core, a 20-cm-high coolant reflector is arranged.  Nuclear Design Results of SLBR-50 Nuclear design calculations for the power distribution and control rod worth were conducted using the Monte-Carlo code RMC. In the calculation, the ENDF-VII.0 library was adopted. 10 layers were divided in the axial direction of the active core. To obtain the detailed power distribution results, a relatively refined calculation condition was applied in the calculation. 8 billion active particles were used (800 generations consisting of 10 million neutrons per generation, of which 300 generations were skipped). Normalized radial assembly power and axial power distribution results of the ARO case are shown in Figures 5, 6. In the radial assembly power result, the maximum assembly power is 1.46, which lies in the center of the reactor. In the axial power distribution, the maximum power is 1.268.
In the control rod worth calculation, 60 million active particles are used (600 generations consisting of 100 thousand neutrons per generation, of which 200 generations are skipped). The control rod worth results are shown in Table 2. Three sets of control rods are calculated. Integral rod worth (IRW) results are 6,915, 4,114, and 16,022 pcm for compensation, power adjustment, and safety control rod sets separately. Both differential rod worth (DRW) and integral rod worth (IRW) results show the shutdown depth is adequate for reactor control.
Rationality of the primary design for the SLBR-50 is confirmed by these nuclear design results. Apparently, parameters in the reactor design need to be researched to improve the reactor characteristic. In this study, the spectral-shift effect is researched and analyzed based on the SLBR-50.

THE CONCEPT DESIGN OF SPECTRAL-SHIFT CONTROL RODS
The basis of the spectral-shift effect is the difference of the fission absorption capacity in different energy ranges. 235 U and 239 Pu are dominant fission nuclides. As is shown in Figure 7, fission cross-sections of 235 U and 239 Pu show a similar pattern; the cross-section in the thermal energy region is larger than that in the fast energy region. Besides, 238 U can absorb fast neutrons and convert to 239 Pu. In this way, fuel breeding happens in the fast-spectrum reactor. Based on the fuel nuclides analysis of the different energy ranges, it can be concluded that the spectral-shift effect can balance the fuel breeding in the fast energy range and fission absorption in the thermal energy range. As a result, the fuel utilization rate will increase by the spectral-shift effect.
In this study, a concept design of a control rod with the spectral-shift effect is analyzed to realize the spectral-shift effect in the small lead-based reactor SLBR-50. The concept design of spectral-shift control rods is shown in Figure 8. Three sections are divided axially, including the control rod absorber, coolant, and moderator from the top to the bottom. Compared to the traditional control rod, the spectral-shift rod adds coolant and moderator sections. In the beginning of the spectral-shift scheme, the absorber section is inserted into the core active region. Spectral-shift control rods are withdrawn in the burnup procedure. With all absorbers withdrawn outside of the active core and the coolant section raised into the core, the fast-spectral operation procedure is finished. In the fast-spectrum operation, the reactor is operated in the fast spectrum to realize fuel proliferation. After that, spectral-shift rods continue withdrawing and moderators are moving to the core. In the spectrum-shift operation, neutrons will be moderated and the energy spectrum is softened. In this way, fuel utilization can be improved with the spectral-shift effect. The control rod moving procedure is shown in Figure 9. In the SLBR-50, YH 2 is applied as the moderator material.

Cycle Length Results
The burnup depth and critical rod position results for the small reactor design are shown in Table 3. Three sets of control rods are withdrawn in the order of safety rods, power adjustment rods, and compensation rods. The initial rod position is −95 cm, where the control rod absorbers are totally inserted. The fast-spectrum operation is from the beginning of life to 1500 EFPD. In  1500 EFPD, all control rod absorbers are withdrawn and the spectrum-shift operation begins. The spectral-shift effect can extend the cycle length from 1500 EFPD to 2600 EFPD, which has a 73.3% improvement for the cycle length with the same fuel weight. Besides, the spectral-shift design has the same shutdown margin as the fast-spectrum design.

Energy Spectrum Results
The kernel of the spectral-shift effect is the energy spectrum shift. Therefore, the energy spectrums are analyzed in typical burnup steps, shown in Figure 10. Energy sections are divided by an order of magnitude, from 1.0e-9 to 10 MeV. Each line shows the energy spectrum along all energy sections for the certain burnup. The energy spectrum analyses need to match with the spectralshift rod withdrawal procedure. Besides, the thermal-spectrum result is provided in the beginning of life with all moderator rods inserted. The thermal-spectrum result can be shown as a reference in the spectrum-shift analysis. In the fast-spectrum operation from 0 EFPD to 1500 EFPD, energy spectrums are similar. Control absorber insertion has little influence on the energy spectrum. In the spectral-shift operation from 1500 EFPD to 2600 EFPD, moderators are inserted, and the spectrum-shift phenomenon can be observed in the energy spectrum analyses. The energy spectrum distribution of 2600 EFPD is similar to the thermal spectrum. It can be concluded that the spectrum-shift control rod design takes advantage of the spectrum-shift effect sufficiently in the SLBR-50.

Fuel Utilization Rate Results
Nuclide density variation is an important result for the spectralshift effect. In the nuclide density analysis, only the spectral-shift scheme is conducted because that is the only scheme influenced by the spectral-shift effect. Considering the breeding of 238 U to 239 Pu, the fission reaction of 235 U, 238 U, and 239 Pu is the dominant nuclear reaction in the burnup. 235 U, 238 U, and 239 Pu are analyzed as the typical nuclides. The nuclide densities for these three nuclides are listed in Table 4, and the utilization rate variations in the burnup are shown in Figure 11.
As is shown in the table, the nuclide density of 235 U and 238 U is decreasing both in the fast-spectrum operation and the spectrumshift operation, and the nuclide density of 239 Pu is increasing. The phenomenon is caused by the relatively hard energy spectrum. In the burnup procedure, even though the spectrum-shift effect makes the energy spectrum softer than the original fast spectrum, the spectrum-shift effect is unable to change the harder energy spectrum in the SLBR-50. Therefore, the breeding of 239 Pu is stronger than the fission absorption in the burnup procedure. All in all, the spectral-shift improves the fuel utilization of 235 U and 238 U from 11.5 to 19.1% and from 2.06 to 3.47%.