1 Introduction

The use of nuclear power as a source of electricity is an important contributor to the global energy mix [1]. Pressurized Water Reactors (PWRs) are a common type of nuclear power plant that uses the energy released during nuclear fission to generate electricity. However, the design and operation of PWRs are complex, with several factors influencing the performance and efficiency of these systems [2]. These factors include fuel enrichment, reactivity, and the management of spent fuel [3]. By carefully considering these factors and implementing strategies such as the use of burnable absorbers, it is possible to improve the performance and efficiency of PWRs while also ensuring their safe and reliable operation [4].

Conventional Pressurized Water Reactors (PWRs) were originally designed to operate for up to 12 months at the end of the fuel cycle (EOC). However, recent developments have resulted in an extension of the fuel cycle length, with most PWRs now designed to operate at an 18-month cycle length [5]. This extension of the reactor fuel cycle length has the benefit of reducing the frequency of fuel refueling over the power plant's operating lifespan (40 to 60 years) [2]. On the other hand, longer fuel cycles also require a higher enrichment of fuel to achieve the desired cycle length [6]. Improvements in fuel assembly design have allowed for better utilization of fuel, resulting in improved performance of the reactor core and an extension of its lifetime [7]. There are several advantages to extending the cycle operation length of a Pressurized Water Reactor, including enhanced fuel utilization, increased energy production per cycle, and reduced amounts of spent fuel [8].

In general, nuclear reactor physicists and core designers aim for a longer reactor fuel cycle, up to 24 months for PWRs. However, excess reactivity at the beginning of the cycle (BOC) requires a higher amount of soluble boron at the EOC. One strategy to minimize the concentration of soluble boron in the PWR reactor core during the fuel cycle is the use of a burnable absorber. Higher fuel enrichment is also important in the design of such a PWR core and requires a large quantity of Burnable Poison (BP) [9] to reduce excess reactivity during the fuel cycle and maintain the fuel and moderator coefficients and power peaking factors within safe limits [10]. The current PWR fuel design includes various types of burnable absorbers (discrete and integral) that maintain reactor performance during the 18-month fuel cycle length [11]. For example, a thin layer of Integral Fuel Burnable Absorber (IFBA) or a smaller number of Gadolinia rods may be used to control reactivity during the fuel cycle due to their high absorption cross section for thermal neutrons.

Over the past four decades, nuclear reactor fuel has undergone significant research and development and has been improved to the point where it can be safely and reliably irradiated in conventional power reactors up to 65 GWd/tU [12]. During this time, there have been several improvements to PWR design and reactor fuel material compositions [13]. However, most commercial PWRs continue to use zircaloy alloy as the cladding material for uranium oxide fuel [14]. In the event of a severe accident, such as a large loss of coolant, the fuel temperature will increase and hydrogen will be generated inside the pressure vessel due to the reaction between water and zircaloy, potentially causing significant damage to the power plant [15].

This research aims to perform preliminary soluble-boron-free neutronics calculations for the APR-1400 two-dimensional core to extend the fuel cycle length from the current 18 months to 24 months. Burnable absorbers such as IFBA will be used to control excess reactivity throughout the fuel cycle. The neutronics analysis will be performed on proposed homogeneous and heterogeneous cores to study the behavior of the reactor multiplication factor, fuel and moderator coefficients, flux spectrum, and radial power distributions for the APR-1400 reactor core using both IFBA and ATF materials [16].

2 Reactor Description and Computation Tool

2.1 Reactor Core Configuration

The APR-1400 is a four-loop reactor developed by the South Korea Electric Power Company (KEPCO). The reference reactor core was designed with 241 fuel assemblies, 93 control element assemblies, and 61 in-core instrument assemblies, with an active height of 3.810 m and a cylinder shape with a diameter of 3.647 m. The APR-1400 fuel assemblies were designed as a 16 × 16 lattice with 236 fuel rod positions and 20 lattice positions for other purposes, such as instruments and guide tubes. The reactor fuel assemblies allow for different configurations with various lattice position enrichments to optimize the power distribution across the APR-1400 core [17].

Two types of fuel assemblies were adopted in the original APR-1400 core design. The first type is labeled as X0, S0, and Q0, with fuel enrichment of 1.68 w/o for X0, 3.14 w/o for S0, and 3.14/3.64 for Q0. The second type contains 12 or 16 gadolinium rods within the lattice array and is labeled as S1, S2, Q1, Q2, and Q3. Figure 1 presents the APR-1400 reactor core layout [18].

Fig. 1
figure 1

Full reactor core layout configuration

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The number of gadolinium rods depends on the type of assembly and the position within the core. The gadolinium fuel assembly has been used to reduce excess reactivity in the APR-1400 reactor core design. In general, there are two types of commercial gadolinium rods in conventional light water reactors: low wt% and high wt% gadolinium. Nowadays, high wt% is widely used instead of low wt% because it can reduce thermal conductivity and contributes to long-lasting reactivity suppression [19, 20].

2.2 Calculation Tool

In this paper, the APR-1400 reactor fuel assemblies and core models were built using the continuous-energy Monte Carlo Serpent 2.31 code [21]. The neutronic parameters for the fuel assemblies and different configurations for the two-dimensional APR-1400 reactor core were calculated. These parameters include the multiplication factor, reactivity difference, neutron spectrum (thermal, epithermal, and fast spectrums), fuel burnup limit, linear pin power distribution, and radial power profile. The neutronics calculations were based on the ENDF/B‐VII.0 [22] data library and enhanced data libraries for 233U and 239Pu [23,24,25]. Based on these considerations, the number of cycles was fixed to 250, while 50 cycles were skipped, and the neutron population per cycle was set to 106 for the two-dimensional full core.

2.3 Reactivity Control

2.3.1 IFBA Coating

To suppress excess reactivity that arises from changes in fuel enrichment during the fuel life cycle, we applied a thin layer of integral fuel burnable absorber (IFBA) coating on the surface of the fuel pellets. Over the past 30 years, IFBA fuel rods have been widely used in the Westinghouse fuel design and are currently deployed in over 40 nuclear power plants worldwide, with a total of more than four million IFBA fuel rods in operation [26]. These fuel rods are available in various configurations, such as 14 × 14, 15 × 15, 16 × 16, and 17 × 17. The specifications for the APR-1400 core and fuel assemblies are given in Tables 1 and 2, respectively. In this study, the IFBA coating thickness on the outer surface of the fuel pellets ranged between 0.5 and 0.6 μm.

Table 1 APR-1400 homogeneous/heterogeneous core parameters
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Table 2 APR-1400 16 × 16 fuel assembly specifications
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2.3.2 Selection of ATF Cladding Material

It is widely recognized that the current designs of PWR fuel are vulnerable to accident conditions, particularly severe accidents. In response to this vulnerability, alternative reactor fuel designs have been developed with the aim of improving their resilience to cladding failure and reducing the risk of hydrogen generation during severe accidents. These new fuel designs should be compatible with existing reactor systems and be considered for use in future PWR designs. To this end, several advanced fuel-cladding materials have been studied and analyzed, including Cr, SiC, FeCrAl [16,17,18,19], metallic fuels, UN pellets, and Cr-doped UO2 pellets [27]. The selection of an advanced fuel cladding material depends on various factors, including its thermomechanical properties (such as thermal conductivity, oxidation resistance, melting point, heat capacity, and steam interaction) and its physical properties (such as the thermal neutron absorption cross section). In this study, we found that changes in fuel enrichment in both the heterogeneous and homogeneous core layouts led to excess reactivity during the fuel life cycle. To control this excess reactivity, advanced fuel cladding materials with a high absorption cross section, such as FeCrAl, AMPT, 310SS, and 304SS, could be used to replace the reference Zircaloy cladding in the APR-1400 reactor core [16,17,18,19]. Table 3 lists the material properties of different candidate advanced fuel cladding materials.

Table 3 The density and absorption cross section of alternative cladding materials
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3 Results

3.1 IFBA Coating

In order to investigate the effects of fuel enrichment and the use of an IFBA coating on the behavior of the APR-1400 reactor core, neutronics analyses were performed using the Serpent 2.31 Monte Carlo code. The fuel enrichment levels studied were 3.0%, 3.5%, 4.0%, 4.5%, and 4.95% for the homogeneous reactor core and (3.6%, 4.0%, 4.5%, and 5.0%) and (3.4%, 3.8%, 4.5%, and 5.0%) for the heterogeneous reactor core, as listed in Table 1. The IFBA coating, which contains boron as a strong thermal neutron absorber, was applied as a thin layer on the outer surface of the fuel pellets to control excess reactivity and reduce any residual reactivity penalty. The fuel rod with the IFBA coating is shown in Fig. 2. The neutronics analyses were conducted on both the homogeneous and heterogeneous reactor core designs to compare the effects of fuel enrichment and the use of the IFBA coating on the behavior of the APR-1400 reactor core.

Fig. 2
figure 2

Unit cell geometry of the fuel pellet coated with an IFBA coating

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The results of the two-dimensional APR-1400 reactor core are presented in Figs. 3, 4 and 5. Figure 3 shows the variation in keff between the reference case without any burnable absorber (BA) and for BAs with coating thicknesses of 0.5 µm and 0.6 µm. Compared with the reference case, the IFBA coatings with different thicknesses have a significant impact on keff at the beginning of cycle (BOC) toward the middle of fuel cycle (MOC). This happens because the higher absorption cross section of boron holds down the fuel reactivity until it is completely depleted around the MOC.

Fig. 3
figure 3

The APR-1400 homogeneous core with fuel enrichment of 3.0%

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Fig. 4
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The APR-1400 homogeneous core with various fuel enrichments

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Fig. 5
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Keff values for APR-1400 heterogeneous core with various fuel enrichments levels

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The initial values for keff are 1.34288 ± 0.00076, 1.04366 ± 0.00075, and 1.01853 ± 0.00076 for IFBA cladding thicknesses of 0.0 μm, 0.6 μm, and 0.5 μm, respectively, as shown in Figs. 3 and 4. The increase in fuel enrichment will lead to extending the cycle length for the homogeneous APR-1400 reactor core, and the IFBA-fuel pellet coating has a major impact on suppressing the reactivity. Furthermore, the fuel cycle length was extended from 540 effective full-power days (EFPDs) for the original design of the APR-1400 core [16] to 720 EFPDs for 3.0% enrichment and ~850 EFPDs, ~950 EFPDs, ~1100 EFPDs, and ~1200 EFPDs for the 3.5%, 4.0%, 4.5%, and 4.95% homogeneous fuel enrichment levels, respectively, as shown in Fig. 4.

Figure 5 presents the EFPD-dependent effective multiplication factor with and without an IFBA for both types of heterogeneous fuels. It can be observed that the excess reactivity is managed during the fuel life cycle. For the fuel enrichment configurations of (3.6%, 4.0%, 4.5%, and 5.0 %) and (3.4%, 3.8%, 4.5%, and 5.0%), the IFBA coating thicknesses were about 0.8 μm and 0.7 μm, respectively.

The reactivity differences at the BOC for the (3.6%, 4.0%, 4.5%, and 5.0%) and (3.4%, 3.8%, 4.5%, and 5.0%) heterogeneous core configurations with and without IFBA were 19499.0 pcm and 18056.0 pcm, respectively. The heterogeneous core configuration is more realistic than the homogeneous one because the homogeneous core configuration with one type of fuel enrichment is close to the ideal case. For this reason, all the calculations of the effective multiplication factor will be performed for the heterogeneous core configuration with a soluble-boron-free core.

Figure 6 shows the neutron spectrum for both types of heterogeneous core configurations. The IFBA-coated fuel pellets with thicknesses of 0.7 μm and 0.8 μm exhibited a high thermal neutron absorption cross section, as expected. More precisely, the thicker the IFBA coating, the harder the neutron spectrum in the thermal energy range due to the thermal neutrons being captured by the boron present in the IFBA coating layer.

Fig. 6
figure 6

The neutron flux spectrums at the BOC for the APR-1400 heterogeneous core

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The APR-1400 reactor reactivity coefficients were evaluated to observe the reactor’s behavior across the fuel cycle and to verify the influence of the applied IFBA coating layers with different thicknesses. The coefficients were evaluated under normal conditions for the APR-1400 reactor. The temperature coefficients that were calculated were the moderator temperature coefficient (MTC) and the fuel temperature coefficient (FTC), as the change in fuel reactivity has a direct impact on these coefficients. The rate of change in the moderator or fuel per degree change in their temperatures is defined as follows:

$${\alpha }_{F,M}=\frac{d\rho }{d{T}_{F,M}}$$
(1)

where ρ is the reactivity in pcm and T is the temperature in K. During the fuel life cycle, positive values of the temperature coefficients (FTC and MTC) could raise safety concerns for the operating reactor.

In general, the FTC and MTC are mainly dependent on the evolution of 240Pu, which has a strong thermal neutron resonance absorption, and 238U during the life cycle. Figure 7 shows the FTC and MTC for both types of heterogeneous APR-1400 reactor cores during the fuel life cycle. As shown, both the FTC and MTC are more negative at the BOC and almost reach zero toward the EOC.

Fig. 7
figure 7

Temperature coefficients (FTC and MTC) for APR-1400 heterogeneous core throughout the fuel cycle

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The change in fuel temperature was about 300 K (from 900 to 1200 K), and the fuel density variation was ignored. Additionally, the moderator temperature changed from 600 to 630 K, and the moderator density changed accordingly in relation to the new temperature.

Figure 8 shows the radial power distribution for heterogeneous core configurations with and without an IFBA coating. The presence of the IFBA at the BOC for both types of heterogeneous cores did not have a significant impact on the radial power distribution. At the MOC and EOC, the IFBA was completely depleted, and the power distributions were almost identical, and more uniform compared to those at the BOC.

Fig. 8
figure 8

Presents the radial power distribution for heterogeneous core

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3.2 Alternative Cladding Material with IFBA Coating

The proposed alternative cladding materials with high absorption cross sections for thermal neutrons are listed in Table 3. The values of the multiplication factor during the fuel life cycle are shown in Fig. 9. As shown, utilizing FeCrAl, AMPT, 310SS, and 304SS as alternative cladding materials for both types of heterogeneous cores failed to extend the fuel cycle from 18 to 24 months. However, the SiC cladding showed closer results to the reference cladding material. The significant drop in reactivity during the fuel life cycle for FeCrAl, AMPT, 310SS, and 304SS occurred because of the high values of their thermal neutron absorption cross sections.

Fig. 9
figure 9

Keff values for the (3.6, 4.0, 4.5, 5.0%) and (3.4, 3.8, 4.5, 5.0%) heterogeneous cores with different cladding materials

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In order to suppress the excess reactivity associated with applying SiC as a cladding material (Brown et al., 2015), an additional coating layer of IFBA was applied to the outer surface of the fuel pellets. To manage the excess reactivity, the proposed IFBA coating thicknesses were about 0.6 µm and 0.8 μm for the (3.4%, 3.8%, 4.5%, and 5.0%) and (3.6%, 4.0%, 4.5%, and 5.0%) cores, respectively. Figure 10 shows the suppression of the initial core reactivity toward the EOC. The increment of the fuel enrichment across the APR-1400 reactor core required the adoption of a new cladding material with a higher absorption cross section to control the reactivity in the soluble-boron-free APR-1400 core. Furthermore, the thermomechanical properties of the selected ATF cladding materials—such as the melting point, thermal conductivity, and corrosion resistance necessary for extending the fuel cycle from 18 to 24 months were calculated [28].

Fig. 10
figure 10

Keff values for the (3.4, 3.8, 4.5, 5.0%) and (3.6, 4.0, 4.5, 5.0%) heterogeneous cores with 0.6 µm and 0.8 µm IFBA coated SiC cladding

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Figure 11 shows the FTC and MTC in the case of the SiC cladding material covered by IFBA coating for the APR-1400 heterogeneous cores throughout the fuel life cycle. The FTC and MTC are both significant reactivity feedback parameters [29, 30]. Both are measures of reactor stability during the fuel life cycle. The more negative the values of the two coefficients, the safer the reactor is during operation. The FTC values were more negative at the BOC and less negative toward the EOC. The MTC exhibited the same behavior, except that near the EOC, its value was slightly positive. This happened as a result of decreasing the concentration of boron in the IFBA during the life cycle, which completely burned around 600 EFPDs near the EOC. The change in fuel temperature was about 300 K (from 900 to 1200 K), and the fuel density variation was ignored. Additionally, the moderator temperature changed from 600 to 630 K, and the moderator density changed accordingly in relation to the new temperature.

Fig. 11
figure 11

Temperature coefficients (FTC and MTC) for the APR-1400 heterogeneous core with SiC as an alternative cladding material with IFBA coating

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Figure 12 presents the thermal neutron spectrum for the (3.4%, 3.8%, 4.5%, and 5.0%) and (3.6%, 4.0%, 4.5%, and 5.0%) cores at the BOC. As expected, the thickness of the IFBA coating plays a major role in softening the thermal energy peak due to the large absorption cross section for thermal neutrons. More thermal neutron absorbing materials allow less neutrons to reach the fuel. Therefore, thermal peaks are lower in all IFBA coating cases. Consequently, the thermal neutron spectral softening leads to more accumulation of fission products and actinides.

Fig. 12
figure 12

Thermal neutron flux spectrums at the BOC for the APR-1400 heterogeneous core with SiC as cladding material with 0.8 μm, and 0.6 μm IFBA coating

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Figure 13 shows the radial power distribution for (3.6, 4.0, 4.5, 5.0%), and (3.4, 3.8, 4.5, 5.0%) heterogeneous core configurations as SiC as cladding material with and without an IFBA coating. The core power distributions were illustrated at the BOC, MOC, and EOC, with different IFBA thickness about 0.6 μm, and 0.8 μm for (3.4, 3.8, 4.5, 5.0%), and (3.6, 4.0, 4.5, 5.0%) core configurations, respectively. As expected, the effect of applying a thin IFBA coating in the range of μm does not have a major impact on the core radial power distribution through the reactor fuel life cycle.

Fig. 13
figure 13

Presents the radial power distribution for SiC as alternative cladding material with different IFBA thickness

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4 Conclusion

In this study, both homogenous and heterogeneous neutronics analyses were performed for a soluble-free-boron APR-1400 reactor core, successfully extending the cycle length to 24 months and suppressing the excess reactivity by using an integral fuel burnable absorber (IFBA) as a thin coating layer on the outer surface of the fuel pellets. This increased fuel cycle length is highly desirable as it allows for a more efficient utilization of the available nuclear fuel and hence reduces the cost associated with frequent refueling. The key findings from this work are summarized as follows:

  • SiC shows promising results as an alternative cladding material, but its excess reactivity can be suppressed by adding an additional layer of IFBA coating to the outer surface of the fuel pellets. Replacing the reference cladding material with SiC cladding coated with a thin layer of IFBA does not have a major impact on the thermal neutron spectrum and radial power distribution in the reactor throughout the fuel life cycle.

  • The IFBA coating does not significantly affect the radial power distribution at the beginning of the fuel cycle, but it leads to more uniform power distribution at the middle and end of the cycle.

  • FTC and MTC, measures of reactor stability during the fuel life cycle, were analyzed and found to be more negative at the beginning of the cycle and approach zero toward the end. Therefore, the results of this study demonstrate the potential of IFBA coating and SiC cladding as effective measures to enhance the safety and efficiency of nuclear reactors.

  • The study also highlights the importance of considering the impact of fuel burnup and cladding materials on reactor stability and power distribution. Overall, this study contributes to the ongoing efforts to optimize the design and operation of nuclear reactors, with the ultimate goal of ensuring the safe and sustainable use of nuclear energy.

In future work, the APR-1400 equilibrium cycle analysis will be performed using the SIMULATE-3 reactor analysis code. The core loading pattern will be optimized using a genetic algorithm that is integrated with the SIMULATE-3 code. This optimization process is expected to improve the efficiency and stability of the extended fuel cycle in the APR-1400 reactor.