The DRAGON program is used for the transport-burnup calculation. DRAGON (Marleau et al., 2016) is a deterministic reactor lattice calculation program developed by Montreal University of Technology, Canada. Many numerical method modules can be used to solve 1D/2D/3D neutron transport problems, such as interface flow method, collision probability method, discrete ordinate method, characteristic method, and spherical harmonic function method. The DRAGON can handle fuel assemblies with different geometric structures (e.g., tube bundles, plates, hexagons) and different reactor types (e.g., light water reactor, heavy water reactor), so it has a strong geometric applicability and flexibility (Guangwen and Shengyi, 2010). The feasibility of DRAGON for plate assembly calculation has been verified (Haitao et al., 2005; Ma et al., 2015; Zhao, 2017; Yu et al., 2020). DRAGON can also perform accurate calculations for nuclides with complex burnup chains (Canbakan and Hébert, 2015; Xia et al., 2021).

There are many modules available inside the DRAGON, so in this article, the subgroup method module is chosen for resonance self-shielding calculations, the Sanchez module is chosen to handle the double non-uniformity problem, and the MOC module is chosen to handle the transport calculations. The cross section library is selected from the 172-groups WIMSD.

The Schematic of plate fuel assembly is shown in Figure 1. The assembly consists of 13 fuel plates, two support plates, and water gaps (H₂O), where UO₂ particles, which is dispersed in the ⁴Zr matrix, is selected as the fuel, and ⁴Zr alloy is used as the material for the cladding, support plates, and matrix. The thicknesses of fuel core, fuel cladding, water gap between two fuel plates, the support plate, and fuel plate height are 3.0, 0.4, 2.3, 3.0, and 1,185.0 mm, respectively. Dispersion fuel has the advantages of reasonable irradiation stability, excellent thermal conductivity, good corrosion resistance, long service life, and high burnup, thus it is widely used in long-life PWR. The enrichment of UO₂ in this study is 60%. The loading arrangement of BPs is as follows: the BPs are uniformly mixed with the fuel to facilitate dispersion loading, and a symmetrical arrangement of fuel plates containing BPs is considered. To ensure the accuracy of the design, the calibration results are shown in Table 1.

The components of non-proliferative BP materials are naturally abundant, and the main materials are B₄C, Dy₂O₃, Er₂O₃, Eu₂O₃, Gd₂O₃, and Sm₂O₃.

Some actinide nuclides can be converted into fissile nuclides after absorbing neutron. When these nuclides are used as BPs, they can inhibit excessive reactivity by absorbing neutron at the beginning of lifetime, and they can also use the converted fissile nuclides to prolong the life of the assembly and enhance the reactivity. Finally, it leads to a gentle variation in the residual reactivity. The actinide nuclides selected in this study are ²³¹Pa, ²⁴¹Am, ²³⁷NP, ²³⁸Pu, and ²⁴⁰Pu.

Polycarboborane-siloxane-ethynyl (PACS) has good corrosion resistance and stability, thus it is an effective BP [21]. Figure 2 shows the chemical structure of PACS. In this study, two advanced polymeric BPs: PACS-J and PACS-L (Allen et al., 2003), are selected, and their compositions are shown in Table 2.

The candidate BPs burnup curves are shown in Figure 3. As seen in Figure 3A, only ²³¹Pa of the actinide BPs extends the life of the assembly at k_inf = 1.0 in the case of high fuel enrichment, and all other actinide BPs showed reactive penalties of different magnitudes.

Figure 3B shows that at k_inf = 1.0, the two advanced polymer BPs extend the life of the assembly at end of lifetime due to their own properties. At an initial k_inf = 1.20, assemblies containing both advanced polymer BPs showed a large reactive release in the middle and late life cycle and difficulties in reactivity control. The rate of reactive release of BPs was reduced by increasing the BPs content in a single plate (increasing the BPs self-shielding effect) to slow down the rate of BPs consumption. The fuel burnup curve of PACS-L does not meet the requirements for safe reactor operation because the reactivity fluctuates widely throughout the assembly lifetime and the reactivity is more difficult to control. The reactivity fluctuation of the burnup curve of the assembly containing PACS-J did not exceed 0.2 throughout the lifetime at the initial k_inf = 1.04, but the reactivity showed a large release in the middle and late stages of the lifetime, which prolonged the assembly lifetime but made the reactivity control difficult.

As seen in Figure 3C, the assembly containing the B₄C had no reactivity penalty at end of lifetime, but the assemblies containing the other BPs all caused a reactivity penalty. The nuclides have a small absorption cross section in BPs with different natural ratios, and the nuclides produced by offspring have different absorption cross sections and half-lives. This can lead to reactivity penalty if k_inf = 1.0. For highly enrichment assemblies, the use of natural ratios of non-proliferative BPs is not optimal.

Therefore, in this study, the natural proportion of non-proliferative BPs (Er₂O₃, Eu₂O₃, Gd₂O₃, and Sm₂O₃) corresponding to enriched isotope oxides (¹⁶⁷Er₂O₃, ¹⁵¹Eu₂O₃, ¹⁵⁷Gd₂O₃, and ¹⁴⁹Sm₂O₃) are selected, and all the separated isotopes are enriched at 100%.As seen in Figure 3D, at high fuel enrichment, the enriched isotope is consumed more quickly as BPs, causing less reactivity penalty at end of lifetime and greater burnup of the assembly than what can be achieved with naturally proportioned BPs. The use of enriched isotopes as BPs reduces the production of daughter nuclides in the burnup chain, resulting in a reduction of some daughter nuclides with absorption cross sections, reducing the reactivity penalty at end of lifetime and improving fuel utilization.

Through the above calculations, this article conducted a selection study on different types of BPs. The results show that ²³¹Pa, B, ¹⁵⁷Gd, ¹⁶⁷Er, and PACS-J is more suitable than other BPs for long-life reactors. The reactive release of B₄C and ¹⁶⁷Er as BPs was smooth throughout the burnup cycle, with no significant fluctuations throughout the life cycle and little to no reactive penalty at end of lifetime. ¹⁵⁷Gd, when used as BPs, causes only a small reactivity penalty, but the reactivity is released more rapidly over the life span. When ²³¹Pa and PACS-J are used as BPs, the lifetime of the assembly is extended beyond that of non-BPs fuel assemblies due to ²³¹Pa own burnup chain and PACS-J own characteristics, resulting in improved fuel utilization. However, when PACS-J is used as a single BPs, there are difficulties in lifetime reactivity control.

From Calculation Rresults , it can be seen that ²³¹Pa, B, ¹⁵⁷Gd, ¹⁶⁷Er and PACS-J showed better results than other BPs. Therefore, this article performs neutronics characteristics analysis for ²³¹Pa, B, ¹⁵⁷Gd, ¹⁶⁷Er and PACS-J.

The analysis parameters of ²³¹Pa, B, ¹⁵⁷Gd, ¹⁶⁷Er and PACS-J are shown in Table 3. The neutron absorption cross sections for the different BPs are given in Table 3. Table 3 also contains the BPs content in a single plate, the number of plates in the assembly containing different BPs and the reactivity penalty at end of lifetime, which are the input parameters and results of the selection calculations performed in Calculation Rresults . In order to visualize the arrangement of fuel plates containing BPs in the assembly, Figure 4 shows the arrangement of fuel plates containing different BPs in the assembly.

The neutron absorption cross section of ¹⁵⁷Gd is the largest among the selected BPs. When ¹⁵⁷Gd is used as BPs, the initial residual reactivity can be suppressed by adding only 5.20% of ¹⁵⁷Gd₂O₃ at beginning of lifetime, but the large absorption cross section makes the BPs consume faster, and a large reactivity release occurs in the middle and late stages of the lifetime, producing reactivity fluctuations. There is a certain neutron absorption cross section for the daughter nuclides produced by the absorption of neutrons by ¹⁵⁷Gd, which causes a small reactivity penalty at end of lifetime.

The neutron absorption cross section of ¹⁰B is the largest of the two isotopes, and the burnup chain of B is very simple, absorbing neutrons and converting them directly to helium and lithium, which are essentially “transparent” to neutrons, with essentially no reactivity penalty at end of lifetime, but as a diffuse BPs the swelling of fuel elements due to helium release needs to be considered.

¹⁶⁷Er has a smaller neutron absorption cross section compared to ¹⁵⁷Gd, but has a certain neutron absorption cross section that burnup slower compared to ¹⁵⁷Gd, reducing the BPs content in a single plate and making ¹⁶⁷Er₂O₃ as completely consumed as possible at end of lifetime. The daughter nuclides produced by the absorption of neutrons by ¹⁶⁷Er have a certain neutron absorption cross section, which causes a small reactivity penalty at end of lifetime.

The neutron absorption cross section of ²³¹Pa is relatively small compared to ¹⁵⁷Gd and ¹⁶⁷Er, so the burnup rate is significantly slower and better control of reactivity can be achieved. The burnup chain of ²³¹Pa is different from the other nuclides (Kulikov et al., 2017). ²³¹Pa acts as the parent nucleus of this burnup chain, and fissionable ²³²U and ²³³U exist directly in the burnup chain. ²³²Pa is generated after the capture of neutrons by ²³¹Pa, and ²³²Pa has a half-life of only 1.3 days and decays to form ²³²U. The fission and capture cross sections of ²³²U are very similar, which allows ²³²U to both capture neutrons to produce the fissile nuclide ²³³U and to fission directly to supplement reactivity. The capture and fission cross section of ²³²U is shown in Figure 5. The special burnup chain of ²³¹Pa offers the possibility to achieve high burnup with ²³¹Pa assemblies.

PACS-J has a high hydrogen content and high boron content, and its high hydrogen content makes PACS-J have its own slowing effect as BPs, which can better slow down neutrons at end of lifetime, improve thermal neutron utilization, and promote the consumption of fission nuclide Pu. Therefore, PACS-J can extend the burnup and improve fuel utilization at end of lifetime when used as BPs.

From the above neutronics characteristics analysis, it is known that the main neutron absorber in PACS-J is ¹⁰B, and the absorption cross section of ¹⁰B is 3,838barn.Because the higher fuel enrichment makes the life time initial reactivity larger, when PACS-J is used as a single BP for reaction control, although increasing the content (70%) of BP in a single plate to increase the self-shielding effect, the assembly reactivity fluctuation is still the largest among the selected BPs. Therefore, in the case of high fuel enrichment, PACS-J can be considered in combination with BPs with small neutron absorption cross section (slow-burnup).