Comparison of the neutronic properties of the (Th-²³³U)O₂, (Th-²³³U)C, and (Th-²³³U)N fuels in small long-life PWR cores with 300, 400, and 500 MW_th of power

The geometry of the fuel cell used in the analyzed PWR is square, as shown in Fig. 1, with a pitch diameter of 1.4 cm, a cladding thickness of 0.057 cm, and a 60% fuel volume fraction. The fuel used is Th-²³³U, with the types of dioxide, carbide, and nitride. Two types of cladding are used in this study, namely zircaloy-4 and ZIRLO (Zr low oxygen). Both are cladding zirconium-based alloys commonly used in PWR, with almost the same composition, but ZIRLO exhibits superior mechanical properties and enhanced corrosion resistance compared to zircaloy-4 [25]. The height and diameter of the PWR under analysis are 240.8 cm and 224.0 cm, respectively, and it has three different power levels: 300 MW_th, 400 MW_th, and 500 MW_th. These power levels have power densities of 31.63 W/cc, 42.17 W/cc, and 52.72 W/cc, respectively. When compared to the average core power density of the conventional PWR AP1000 (109.7 W/cc) [26], each of these power levels represents approximately 28.83%, 38.44%, and 48.06% of the AP1000’s power density. This reactor’s design uses lower power levels to enable extended reactor operation.

Fig. 1.

The reflector is made of stainless steel and water, and it has a 22.4 cm thickness. The reactor core has three fuel regions (F1, F2, and F3) with a 1%²³³U content difference between each fuel region. F1 is the fuel region with the least fissile material, F2 is the fuel region with the medium fissile material, and F3 is the fuel region with the most fissile material [27]. The analyzed PWR design parameters are shown in Table 1. For the reactor core calculations in this study, a two-dimensional R–Z geometry is used, divided into three radial and axial fuel regions with different ²³³U enrichments, as shown in Fig. 2. In the radial direction, F1 and F2 each have a radius of 39.2 cm, while F3 has a radius of 33.6 cm. In the axial direction, F1 has a radius of 42 cm, while F2 and F3 each have a radius of 39.2 cm.

Fig. 2.

Calculations are performed using the Standard Reactor Analysis Code (SRAC). The fuel cell level calculations are performed using the PIJ module based on the collision probability method (CPM). Subsequently, the macroscopic cross-section values of the fuel are obtained at each burnup step. These values are then used to solve the multigroup diffusion equations using CITATION for the PWR core level. The SRAC system facilitates neutron calculations for different thermal reactors by generating accurate microscopic and macroscopic cross-sections. It supports core and static cell calculations, including burnup analysis, and provides essential parameters for reactor design and experimental analysis [27]. As a nuclear data library, we utilize JENDL 4.0.

Thermal neutrons support the fission reaction taking place in the PWR core. There are 107 neutron energy group structures in the SRAC module, with 74 fast neutron energy groups, 48 thermal neutron energy groups, and 15 overlapping groups [28]. In this calculation, the neutron group is condensed into eight neutron energy groups, which consist of a fast neutron energy group and seven thermal neutron energy groups, as shown in Table 2.

In Fig. 2, the fuel configuration (F1, F2, and F3) used in the core consists of five variations of ²³³U enrichment configurations, i.e., 3–4–5%, 4–5–6%, 5–6–7%, 6–7–8%, and 7–8–9%. In each fuel cell, ²³¹Pa is added as a burnable poison (BP). ²³¹Pa is not only able to reduce excess reactivity but can also increase fuel burnup [29]. For each fuel configuration, ²³¹Pa is randomly added between 0.20% and 7.45% with a minimum increment of 0.05%. Neutronic calculations aim to see which fuel configuration has an optimum criticality level or effective multiplication factor (k_eff) with excess reactivity not exceeding 1.00% dk/k for a minimum burnup period of up to 20 years. Other neutronic aspects also considered are power density distribution, PPF, fuel temperature (Doppler) coefficient, and burnup level for the three fuel types.

Neutronic calculations were carried out for the three types of dioxide, carbide, and nitride fuels, for two types of cladding, zircaloy-4 and ZIRLO, and for power levels of 300 MW_th, 400 MW_th, and 500 MW_th, with variations in the addition of ²³¹Pa as BP randomly between 0.20% and 7.45% with a minimum difference of 0.05%. Figure 3 shows the results of the k_eff calculation for the (Th-²³³U)O₂ fuel configuration.

Fig. 3.

Figure 3 shows that for the (Th-²³³U)O₂ fuel type, no fuel configuration reaches a critical condition throughout the reactor operation cycle with excess reactivity <1.00% dk/k. Both for the zircaloy-4 and the ZIRLO cladding types, the best performance is achieved with an enrichment configuration of 5–6– 7%²³³U at power levels of 300 MW_th and 400 MW_th, with excess reactivity slightly exceeding 1.00% dk/k.

For fuel (Th-²³³U)C, the optimal fuel performance is achieved with an enrichment configuration of 4–5– 6%²³³U for both cladding types at a 300 MW_th power level. As shown in Fig. 4 for the zircaloy-4 cladding type, the fuel configuration 4–5–6%²³³U reaches a critical condition with excess reactivity <1.00% dk/k until the 20th year. For fuel (Th-²³³U)C with 4–5–6%²³³U with a ZIRLO cladding type, critical conditions with excess reactivity close to 1.00% dk/k throughout the cycle up to the 20th year are possible.

Fig. 4.

Figure 5 shows that for (Th-²³³U)N fuel with an enrichment configuration of 6–7–8%²³³U for both cladding types at power levels of 300 MW_th and 400 MW_th, it can achieve a critical condition throughout the reactor operation cycle with excess reactivity <1.00% dk/k. Furthermore, the fuel configuration of 7–8–9% ²³³U for zircaloy-4 cladding type at a power level of 300 MW_th also maintains excess reactivity <1.00% dk/k throughout the reactor operation cycle. However, the fuel configuration of 7–8–9% ²³³U for the ZIRLO cladding type at a power level of 300 MW_th has the maximum excess reactivity value slightly exceeding 1.00% dk/k.

Fig. 5.

The excess reactivity for the three fuel types with the best criticality levels for various configurations of ²³³U enrichment is shown in Table 3. These values are displayed at the beginning of cycle (BOC) and the end of cycle (EOC) conditions. The maximum value of excess reactivity throughout the reactor operation cycle is also presented.

Based on the conducted neutronic calculations, it was observed that reaching a critical condition of up to 20 years is a challenge for (Th-²³³U)O₂ and (Th-²³³U)C fuels with a ²³³U enrichment configuration of 3–4–5%. Reducing the percentage of BP in this configuration causes higher excess reactivity at BOC. However, the k_eff value decreases sharply as the reactor operating time increases due to the depletion of fissile material. This condition is also observed in the (Th-²³³U)N fuel with ²³³U enrichment configurations of 3–4–5% and 4–5–6% in the reactor core.

Comparing the three fuel types, it is evident that the (Th-²³³U)N fuel exhibits the best performance regarding reactor criticality. In the (Th-²³³U)N fuel, two fuel configurations within the reactor core consistently maintain critical conditions throughout the operating cycle, with excess reactivity <1.00% dk/k. However, due to its higher density, achieving critical conditions throughout the operating cycle requires more fissile material for the (Th-²³³U)N fuel than the other two fuel types. Additionally, the neutronic calculations indicate that ZIRLO cladding yields a slightly higher k_eff value than the zircaloy-4 cladding type.

The power density distribution pattern for the three types of fuel with the best criticality is shown in Figs. 6–8, each for the power distribution pattern in the radial direction and the power distribution pattern in the axial direction obtained based on the calculation results using the SRAC code with the CITATION module. From Figs. 6–8, it can be seen that for both zirkaloy-4 and ZIRLO claddings, the power density distribution pattern for the three types of fuel has the same shape, both in the radial and axial directions.

Fig. 6.

Fig. 7.

Fig. 8.

In Figs. 6a, 7a, and 8a, a similar pattern of power density distribution is observed for the three fuel types. The radial power density distribution is nearly identical for the BOC and middle of cycle (MOC) near the center of the reactor core. However, beyond a distance of 81.44 cm from the core’s center, the power density at the MOC tends to resemble the density at the EOC. The peak power density in the radial direction occurs near the core for BOC, MOC, and EOC. In the radial direction, it can be seen that the power density distribution for (Th-²³³U)C and (Th-²³³U)N fuels is more uniform compared to (Th-²³³U)O₂ fuel during BOC and MOC.

In the axial direction, as shown in Figs. 6b, 7b, and 8b, the distribution patterns for the three fuel types also exhibit similarities. In the axial direction, it can be observed that all three fuels have significant variations in power density near the axial center up to a distance of approximately 81.20 cm during BOC, MOC, and EOC.

The differences in power density distribution under BOC, MOC, and EOC for the three fuel types are more significantly pronounced in the axial direction, suspected to be due to the more substantial disparity in neutron flux along the axial direction. On average, the power density at EOC is greater than at MOC and BOC due to the maximum fuel burnup condition at EOC. In the power density distribution, three peaks of power density delineate the boundaries between fuel regions F1 and F2, F2 and F3, and F3 and the reflector. The peaks of power density that emerge between the boundaries of fuel regions occur because there is a change in the density of the fuel material at these fuel region boundaries. At the boundaries between fuel regions F1 and F2, as well as F2 and F3, there are variations in material density due to an increase in the enrichment of ²³³U, which naturally leads to an increase in the number of fission reactions, thus resulting in the appearance of power density peaks at these fuel region boundaries. Meanwhile, the power density peak occurring between the boundary of fuel region F3 and the reflector is caused by neutron reflection in this area. This reflection results in an increase in the number of thermal neutrons at this boundary, inevitably causing an increase in the number of fission reactions and generating a power density peak.

It can be seen that the difference in power density distribution under BOC, MOC, and EOC conditions is only significant up to a distance of 81.20 cm from the center of the reactor core, which marks the boundary between the fuel regions F2 and F3. This condition is caused in the F3 fuel region with the highest enrichment level of ²³³U; there is a greater decrease in the k_eff value as the reactor operating time increases when compared to the other two fuel regions causing a greater decrease in power density at the time of MOC and EOC for this fuel region.

The peak power density of the three fuel types shown in Figs. 6–8 is indicated in Table 4. These peaks are displayed under BOC, MOC, and EOC conditions. It can be seen that the peak power density in both the radial and axial directions has the same value.

The PPF is the maximum local power density ratio to the average power density [30]. PPF is an important parameter that must be known to avoid fuel rod melting and violation of safety limits [31]. A smaller PPF will lead to more uniform fuel depletion and more even coolant distribution in the radial and axial directions, which can result in the reactor core using fuel more efficiently [32]. Table 5 shows the PPF value for the fuel with the best criticality level. The PPF values for the three fuel types do not significantly differ. The PPF value in the radial direction tends to be greater than the PPF value in the axial direction. During BOC, the PPF value in the radial direction for fuel (Th-²³³U)N tends to be greater than the PPF value for the other two types of fuel, while in the axial direction, the PPF value when BOC for fuel (Th-²³³U)C tends to be more significant. At MOC, the PPF value of (Th-²³³U)O₂ fuel tends to be greater than the PPF value of the other two fuel types in the radial and axial directions. During EOC, the PPF value of (Th-²³³U)O₂ fuel also tends to be greater than the PPF value of the other two fuel types, both in the radial and axial directions. From these results, it can be seen that fuel (Th-²³³U)O₂ has a relatively higher PPF value when compared to the other two fuel types, while fuels (Th-²³³U)C and (Th-²³³U)N tend to have PPF values as relatively the same. Generally, PPF values for all fuel types are still within safe limits for PWR-type reactors, with values below two.

The fuel temperature (Doppler) coefficient is the reactivity change per degree change in the average core fuel temperature. Reactors are typically constructed with a negative Doppler coefficient to assist control so that if a power excursion occurs, the negative reactivity will be fed back into the system [33]. We calculated the Doppler coefficient by increasing the fuel temperature by 100°C in the fuel cell calculation using the PIJ module in the SRAC code, then compared the reactivity obtained from the neutronic calculation using the CITATION module on the reactor core with the reactivity before the temperature increase. The Doppler coefficient for the three fuel types with the best performance level at each power level and type of cladding used is shown in Figs. 9–11. The calculation results show that the Doppler coefficient values for the three fuel types have the same pattern, with the most negative values occurring at the beginning of the reactor operating time and then less negative until the end. The less negative value of the Doppler coefficient is due to the reduced reactivity value as the reactor operating time increases.

Figure 9 shows the change in the Doppler coefficient value with increasing reactor operating time for fuel (Th-²³³U)O₂ with the best criticality level. The Doppler coefficient is relatively the same for fuels using zircaloy-4 and ZIRLO cladding. The average value of the Doppler coefficient of fuel (Th-²³³U)O₂ with the best criticality level is –2.94 pcm/°C at 300 MW_th power level, –2.77 pcm/°C at 400 MW_th power level, and –2.57 pcm/°C at a power level of 500 MW_th.

Fig. 9.

Figure 10 illustrates the variation of the Doppler coefficient value over reactor operating time for the fuel (Th-²³³U)C, which exhibits the best criticality level. Similar to (Th-²³³U)O₂ fuel, the Doppler coefficient value remains relatively consistent for both zircaloy-4 and ZIRLO cladding. The average Doppler coefficient for (Th-²³³U)C fuel is –3.15 pcm/°C at a power level of 300 MW_th, –3.00 pcm/°C at 400 MW_th, and –2.77 pcm/°C at 500 MW_th.

Fig. 10.

Figure 11 shows the change in the Doppler coefficient value with increasing reactor operating time for fuel (Th-²³³U)N at the best criticality level. In contrast to the other two fuel types, the Doppler coefficient is relatively the same for using zircaloy-4 and ZIRLO cladding for all power levels. However, there are several shifts at several points in the cycle time of reactor operation. At the BOC, the Doppler coefficient for (Th-²³³U)N fuel is less negative than the other two types of fuels, but at the EOC, this fuel exhibits a more negative Doppler coefficient than the other two fuels. The average Doppler coefficient of fuel (Th-²³³U)N is –3.32 pcm/°C at 300 MW_th power level, –3.17 pcm/°C at 400 MW_th power level, and –2.95 pcm/°C at 500 power level MW_th.

Fig. 11.

The calculations show that the Doppler coefficient tends to be less negative as the reactor power increases. The three fuel types have negative Doppler coefficient values from the beginning to the end of the reactor operating time. This negative Doppler coefficient value is important for the reactor to preserve its inherent safety characteristics during fast changes in the reactor core power [34]. On average, it can be seen that the most negative Doppler coefficient is found in fuel (Th-²³³U)N, followed by fuel (Th-²³³U)C and (Th-²³³U)O₂.

Figures 12–14 show the burnup levels for the three fuel types at power levels 300 MW_th, 400 MW_th, and 500 MW_th. From the calculations, the concentration of fissile material ²³³U, ²³¹Pa as burnable poison (BP), and the type of cladding used had no significant effect on changes in burnup level. As shown in Figs. 12–14, the burnup level will increase as the reactor power increases. We can see that the highest burnup level for each power level is found in fuel (Th-²³³U)O₂, followed by (Th-²³³U)C, and the lowest burnup level is found in fuel type (Th-²³³U)N. For all power levels, it can be seen that the gradient of increase in burnup level for type fuels (Th-²³³U)C and (Th-²³³U)N is not much different, but the gradient of the rise in burnup level for fuel type (Th-²³³U)O₂ is more significant when compared to the other two types of fuel. The high burnup level for fuel type (Th-²³³U)O₂ is because the fuel has a lower density when compared to the other two types of fuel. The higher the burnup level, the more the fuel efficiency improves and becomes more profitable. However, the high burnup level also demands more attention to technical issues. These include the increased accumulation of gaseous fission products within the fuel pin, which significantly increases the internal pressure and additional demands on the fuel cladding, which must withstand the reactor environment for extended periods [35, 36].

Fig. 12.

Fig. 13.

Fig. 14.