The performance of the spectral shift control (SSC) method is evaluated and compared to the conventional poison method in the VVER-1000 fuel assembly design. The SSC method can be implemented by gradually adjusting the ratio of heavy water to light water moderator (D₂O/H₂O) during the fuel cycle. In this study, the efficiency of using the SSC design with or without a thermal absorber (gadolinium) is investigated. We apply the SSC with both 12 burnable absorber rods containing 4.0 wt.% Gd₂O₃ (Case 1) and without Gd₂O₃ (Case 2). The neutronic calculations indicate that the discharge burnup is enhanced by 60% and the conversion ratio (CR) is increased by 64.4% at the beginning of the cycle (BOC) compared to the benchmark data. The breeding of Pu²³⁹ and Pu²⁴¹ is extended to 33.7% and 29.5%, respectively, for the SSC design case (2), and better utilization of U-235 and U-238 has been achieved compared to BM.

Chemical spectral shift regulation, Neutronics, fuel cycle, VVER, SERPENT-2

During the last decades, there have been numerous efforts to extend the operational cycle of pressurized water reactors (PWRs) from months to years (Burns et al. 2020; Choi et al. 2023; Lindsay et al. 2023). However, these methods typically necessitated enrichment levels greater than 5% and an average discharge burnup level above 62 GWd/MTU. The increase in the enrichment led to an additional excess reactivity produced during the early stages of fuel life, which can be controlled by:

1. Using soluble boron in the cooling system, although effective, can lead to a much lower moderator temperature coefficient and boron-induced reactivity accidents, especially when used in large quantities.
2. Using control rods, while effective, can lead to an axial peak if inserted too deeply into the core.
3. Using burnable absorbers such as gadolinium, while effective, can lead to diminished neutron economy that can be used in increasing the conversion ratio (CR) of nuclear fuel (Elzayat et al. 2022; Lindsay et al. 2023).
4. Applying the spectral shift control (SSC) method, as demonstrated by the Vulcain experiment in the BR-3 nuclear plant at Mol, Belgium, and successfully operated in this nuclear plant between 1966 and 1968 (Sider and Matzie 1980), resulted in improved resource utilization and a higher CR.

In the concept of the SSC, the neutron spectrum shifts from intermediate at the beginning of the cycle (BOC) to thermal at the end of the cycle (EOC). With a resonance spectrum during the early stage of operation, neutrons can be captured in fertile materials such as U²³⁸, increasing the converted fissile plutonium (Kotlyar et al. 2017). This allows for the initial U²³⁵ enrichment to remain higher to sustain the neutron chain reaction at the EOC, enabling more power to be generated with the same enrichment (Yokornizo et al. 1993). Consequently, better fuel utilization, extending the operation of a single fuel loading to achieve a longer fuel cycle and lower initial U²³⁵ inventory than conventional light water reactors (LWRs) (Matzie and Sider 1979).

The SSC methods can be categorized into two groups:

1. The chemical method, achieved by varying the (D₂O/H₂O) ratio, initially aimed to enable an ultra-long fuel cycle for the Mixed Moderator PWR (MPWR) (Tochihara et al. 1998), and later extended to studies on VVER 1000 reactors with low-enriched uranium fuel (LEU).
2. The mechanical method, achieved by varying the moderator-to-fuel volume ratio (v _m / v _f) by inserting and withdrawing spectral shift rods.

The chemical method was initially introduced by Mars and Gans in 1961, involving the utilization of a mixture of light and heavy water (Mars and Gans 1961). At the BOC, the D₂O concentration was altered from 79% to 60% mole, gradually decreasing to 2% mole at the EOC. The fluctuation in heavy water concentration regulates the reactivity of the core and enhances the power density, ultimately resulting in an extended cycle life. Several studies and experiments have been conducted to identify the most appropriate changes that could enable the SSC design to achieve its extra benefits. In spectral shift control reactors, introduced in (Alcala 1984), the neutronic and thermal-hydraulic behavior were optimized for low-enriched uranium graphite cells cooled with water to determine the optimal cell design for implementing the SSC system. The D₂O/H₂O ratio concentration utilized in the coolant system flows through tubes arranged within the graphite blocks. In LR-0 reactor model (Nagy et al. 2014), the neutron absorption profile for employing thermal poison in control rods was investigated. It was found that epithermal neutron poisons or using double-layer control rods (with epithermal neutron poison in the outer layer and thermal neutron poison in the inner layer) might be more suitable for a mixed D₂O/H₂O moderator reactor. According to a study on the utilization of the SSC method in single-batch small modular reactors (SMRs), it was found that a combination of a slightly wetter lattice and chemical method can result in a significant enhancement in natural uranium utilization, reaching up to 49%, compared to conventional LWRs (Lindley and Parks 2016).

The mechanical method varies depending on the type of reactor. In PWRs, achieving high burnup and CR can be accomplished by using fertile rods (Okumura et al. 1988). In boiling water reactors (BWRs), the mechanical method of SSC can be achieved by changing the water column in spectral shift rods, causing a change in the void fraction (Yokornizo et al. 1993). In TRU-fueled very high-temperature reactors (VHTRs), the moderator-to-fuel volume ratio changes by varying the number of TRISO particles per unit volume (Tsvetkov et al. 2008). A study on utilizing a movable graphite structure in the Small Advanced High-Temperature Reactor (SmAHTR), where graphite serves as a moderator material, could extend the operational cycle (Kotlyar et al. 2017). In a liquid-fueled molten salt reactor (MSR), zirconium hydride rod assemblies can be utilized as a moderator in the reactor, allowing the moderator-to-fuel ratio to vary throughout the reactor’s lifetime (Betzler et al. 2018). The concept of spectral shift rods (SSRs) is analyzed in a small lead-based reactor, where SSRs are divided axially into three sections including moderator, coolant, and control rod absorber from the bottom to the top. During the burnup procedure, the SSRs are gradually withdrawn from the active core to induce a change in the neutron spectrum shift (Zhao et al. 2021).

The main objective of the current paper is to assess the neutronic characteristics of the VVER-1000 LEU fuel assembly (FA) employing chemical spectral shift regulation. This study investigates the impact of varying the ratio between heavy water and light water on the VVER-1000 FA described in the OECD computational benchmark (Kalugin and Gehin 2002). The VVER-1000 FA employs the poison control reactivity method by adding 600 ppm H₃BO₃ in the moderator system and incorporates 12 burnable absorber pins with 4.0 wt.% Gd₂O₃.

In the previous study (Elzayat et al. 2022), we applied the chemical SSC method through diluting D₂O/H₂O molecular ratio from 65% to 0% in the presence of gadolinium, and from 73% to 0% in the absence of gadolinium, with considering different decrements: 10%, 13%, 15%, and 19% in both cases. These sudden changes in the molecular ratio of D₂O/H₂O leads to a higher reactor response to the reactivity changes and diminish neutronic parameters values. Additionally, ¹³⁵Xe and ¹⁴⁹Sm did not reach equilibrium throughout the fuel cycle. Thus, in this study, the impact of the chemical method in both the presence and absence of gadolinium is examined by diluting the molecular ratio of D₂O/H₂O with equal decrements of 5% in all cases. This dilution process thermalizes the neutron spectrum and burns effectively fissile materials which bred at the BOC. Specifically, the molecular ratio of D₂O/H₂O is increased at the BOC, resulting in a hardened spectrum that facilitates the capture of neutrons in fertile material such as U²³⁸ rather than in poison control materials, thus enhancing the breeding of Pu fissile material along with suppressing the excess reactivity of the fresh fuel. Therefore, the SSC method has the potential to improve the CR value while achieving high discharge burnups, thereby prolonging the fuel cycle, compared to traditional poison control methods used in typical PWRs.

According to the Monte Carlo simulation, the following parameters were studied: the variation of infinite multiplication factor (k_∞), conversion ratio (CR) versus burnup, and the evolution of the isotopic composition of the fuel assembly (²³⁵U, ²³⁶U, ²³⁸U, ²³⁹Pu, ²⁴⁰Pu, ²⁴¹Pu, and ²⁴²Pu), the accumulation of fission product poisons (¹³⁵Xe and ¹⁴⁹Sm) and burnout of burnable absorbers (¹⁵⁵Gd and ¹⁵⁷Gd). The obtained results were compared and analyzed according to the corresponding benchmark mean values (BM) (Kalugin and Gehin 2002).

The influence of the chemical spectral shift control (SSC) method on the fuel utilization and the cycle length of the VVER-1000 FA has been demonstrated by determining the time evolution of the following parameters: k_∞, CR, U²³⁵, U²³⁸, Pu²³⁹, Pu²⁴⁰, Pu²⁴¹, Pu²⁴², Xe¹³⁵, Sm¹⁴⁹. The simulation was performed by Serpent-2 for two cases: case (1) (D₂O/H₂O + 4.0 wt.% Gd₂O₃) and case (2) (D₂O/H₂O).

The variation of the multiplication factor with burnup

Fig. 2 illustrates the variation of the infinite multiplication factor (k_∞) during burnup. As depicted in Fig. 2, the reactivity is highly sensitive to the D₂O/H₂O ratio, resulting in small variations in k_∞ during operation. Fig. 2 shows that in case (2), two important criteria have been achieved. Firstly, the reduction in D₂O quantity is lower than in the second case, which reduces the spectral shift design cost. Secondly, the suppression of k_∞ has occurred in case (1) more than in case (2) due to the thermal absorption cross section for gadolinium. This effect is more noticeable at the EOC where more thermal neutrons are produced. Additionally, from Fig. 2, there is a small fluctuation in the k_∞ during burnup due to the variation in D₂O/H₂O ratio that needs to be smoothly lowered and controlled to maintain a constant reactor power and temperature. Compared to the previous work (Elzayat et al. 2022), flattening the k_∞ curve can be achieved by decreasing the rate at which the ratio of D₂O/H₂O is decreased. Fig. 2 illustrates that the discharge burnup for both cases (1&2) of the SSC method reached about 40 MWd/KgHM compared to 25 MWd/KgHM in the benchmark model. Through comparing the discharge burnup for both cases with the benchmark mean values (blue line in Fig. 2), the fuel burnup has improved by 60% compared to the benchmark values.

Figure 2. 

Variation of infinite multiplication factor during burnup.

Time evolution of the average isotopic concentration

Fig. 3 shows the average number density of U²³⁵ in the fuel assembly as a function of burnup. As depicted in Fig. 3, the U²³⁵ concentration decreases at a slow rate in both cases of the SSC method, leading to a ≈31% increase in its unburned inventory at the EOC compared to the benchmark case. This decrease is due to the limitation of the thermal absorption cross section of U²³⁵ by the neutron spectrum hardening. Consequently, there is a necessity for increased U²³⁵ enrichment. However, the high production and effective burning of other fissile nuclides (Pu²³⁹ and Pu²⁴¹) counterbalance this drawback of the SSC design.

Figure 3. 

Average number density of U²³⁵ in the fuel assembly.

Fig. 4 illustrates the average number density of U²³⁸ in the fuel assembly vs. burnup. Fig. 4 shows a 0.62% decreasing in the U²³⁸ inventory at the EOC compared to the benchmark (BM) model and the consumption rate of U²³⁸ increases with the application of the SSC method, primarily due to the increase of its radiation capture cross-section as a function of the hardened neutron spectrum. This results in a significant accumulation of fissile plutonium isotopes such as Pu²³⁹ and Pu²⁴¹ breeding in the reactor.

Figure 4. 

Average number density of U²³⁸ in the fuel assembly.

Figs 5, 7 show that, for the SSC design, the buildup rates for Pu²³⁹ and Pu²⁴¹ isotopes increase by approximately 57% and 45%, respectively, compared to the BM at 25 MWd/HMkg. At the EOC, the maximum values of Pu²³⁹ and Pu²⁴¹ are 33.7% and 29.5%, respectively, for SSC design compared to the benchmark, as shown in Figs 5, 7. The total amount of Pu²³⁹ in the assembly increases during the initial burnup. Afterward, more thermal neutrons are produced, leading to the progressive burning of Pu²³⁹, as illustrated in Fig. 5.

Figure 5. 

Average number density of Pu²³⁹ in the fuel assembly.

As shown in Figs 6, 8, the production rate of non-fissile plutonium isotopes (Pu²⁴⁰ and Pu²⁴²) has achieved a maximum increase of about 25.7% and 3.3%, respectively, at EOC for SSC method compared to the benchmark.

Figure 6. 

Average number density of Pu²⁴⁰ in the fuel assembly.

Figure 7. 

Average number density of Pu²⁴¹ in the fuel assembly.

Figure 8. 

Average number density of Pu²⁴² in the fuel assembly.

According to Figs 9, 10, the inventory values of Xe¹³⁵ and Sm¹⁴⁹ have increased by 24.7% and 21.9%, respectively, in the SSC design compared to the benchmark. This increase is attributed to their low burnout rate through the hardened neutron spectrum, which can delay the restarting of the reactor after shutdown. Furthermore, equilibrium cannot be achieved due to the regular variation in the D₂O/H₂O ratio throughout the fuel cycle as shown in Figs 9, 10.

Figure 9. 

Average number density of Sm¹⁴⁹ in the fuel assembly.

Figure 10. 

Average number density of Xe¹³⁵ in the fuel assembly.

Figs 11, 12 depict the time evolution of the average concentration of Gd¹⁵⁵ and Gd¹⁵⁷ in the fuel assembly. As illustrated, gadolinium isotopes exhibit a slower burnout rate compared to the benchmark model. Gd¹⁵⁵ and Gd¹⁵⁷ act as thermal neutron absorbers, and their poison effect becomes apparent at the EOC where thermal neutrons are generated.

Figure 11. 

Average number density of Gd¹⁵⁵ in the fuel assembly.

Figure 12. 

Average number density of Gd¹⁵⁷ in the fuel assembly.

The variation of the conversion ratio with burnup

Fig. 13 demonstrates the variation of conversion ratio (CR) during burnup for both cases of the SSC method compared to the benchmark model. At the BOC, Fig. 13 shows that the conversion ratio for Case (2) is higher than for Case (1). The conversion ratio for both cases (i.e., 1&2) is higher than for the BM mean values by about 58% and 64.4%, respectively, due to the gadolinium poison effect. As the EOC approaches, CR values decrease, coinciding with the complete depletion of gadolinium isotopes. At this stage, both cases (1&2) exhibit similar moderation conditions, with 100% H₂O content. In the benchmark model, CR starts with a low value since the poison effect of (H₃BO₃ and Gd₂O₃) dominated at BOC. Towards the EOC, the CR increases as the soluble boron and gadolinium isotopes are entirely burnt out. At the BOC, the CR in the case (2) is higher than that of case (1) due to the gadolinium effect. The conversion ratio shows rapid and smaller fluctuations with every change in the D₂O/H₂O molecular ratio, similar to the infinite multiplication factor. These fluctuations can be further reduced by diluting the D₂O/H₂O ratio by 1% throughout the fuel cycle.

Figure 13. 

Variation of conversion ratio during burnup.

We conducted a comparison between two dilution process models relative to the benchmark model (BM). Table 2 shows the variations of neutronic parameters and assembly average isotopic composition with two different dilution processes. Firstly, the molecular ratio of D₂O/H₂O was diluted by 10%, 13%, 15%, and 19% along the fuel cycle, as shown in Elzayat et al. (2022). Secondly, the molecular ratio of D₂O/H₂O was diluted by 5% throughout the burnup process. Through adjusting the D₂O/H₂O molecular ratio smoothly, an improvement occurs in the neutronic parameter as in k_∞ and CR which varies with small fluctuations with varying the D₂O/H₂O ratio, as listed in Table 2. Additionally, a better utilization occurs for burning U²³⁵ and U²³⁸ to bred more fissile material Pu isotopes. Comparing Figs 5, 7 with those in previous study for the same isotopes (Elzayat et al. 2022) shows that Pu²³⁹ and Pu²⁴¹ exhibit a higher buildup value for a 5% decrement along the fuel cycle, increasing by 9.5% and 15.5%, respectively, compared to larger decrements at 25 MWd/HMkg. This indicates that a smaller decrement produces harder neutrons, which breed more plutonium fissile isotopes that are effectively burned at the EOC. The buildup rate of Xe¹³⁵ and Sm¹⁴⁹ decreases when diluting by 5% compared to using a small number of large decrements as listed in Table 2. Table 2 demonstrates better utilization of neutrons throughout the dilution process by 5% along the fuel cycle, which can change the reactivity in a smoother manner.

Table 2.

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Comparison of neutronic parameters and assembly average isotopic composition for different dilution processes

Neutronic parameters		Previous work (Elzayat et al. 2022)	Current work
		The dilution process
		10%, 13%, 15%, and 19%	5%
k ∞		Shows rapid and large fluctuations (the maximum fluctuation in k∞ < 7%)	Shows rapid and small fluctuations (the maximum fluctuation in k∞ < 2.9%)
CR		Shows rapid and large fluctuations (the maximum fluctuation in CR < 14%)	Shows rapid and small fluctuations (the maximum fluctuation in CR < 6%)
Assembly average isotopic composition	U 235	The inventory increases by 32% compared with BM at EOC.	The inventory increases by 31% compared with BM at EOC.
	U 238	The inventory decreases by 0.45% compared with BM at EOC.	The inventory decreases by 0.62% compared with BM at EOC.
	Pu 239 and Pu241	The inventory increases by 39% and 28%, respectively, compared with BM at EOC.	The inventory increases by 33.7% and 29.5%, respectively, compared with BM at EOC.
	Pu 240 and Pu242	The inventory increases by 18% and 3%, respectively, compared with BM at EOC.	The inventory increases by 25.7% and 3.3%, respectively, compared with BM at EOC.
	Xe 135 and Sm149	The inventory increases by 51% and 66%, respectively, compared with BM at EOC.	The inventory increases by 24.7% and 21.9%, respectively, compared with BM at EOC.

Based on the preceding analysis, it is evident that the SSC design offers several advantages, including enhanced conversion ratio throughout the operational cycle, improved fuel utilization, and a prolonged reactor life cycle.

It was observed that for both cases of the SSC method, there is a 60% improvement in the fuel discharge burnup compared to the benchmark reference model. Moreover, the existence of gadolinium in the first case of the SSC method would result in a reduction of D₂O quantity by 12% at the BOC and by 100% at the EOC relative to the second case, without affecting the achieved discharge burnup. This, in turn, could potentially reduce the capital cost of implementing the SSC method.

Smoothly reducing the (D₂O/H₂O) ratio by 5% results in an enhancement in the variation of k_∞during burnup and in the conversion ratio values, besides better utilization of the fuel source to breed more fissile material. Furthermore, significant improvements can be achieved by decreasing it by 1% or lower throughout the process.

Comparing case (2) to case (1), several improvements are notable, including enhanced conversion ratio, increased breeding of plutonium isotopes, better utilization of U²³⁸, and reduced use of enriched U.

However, there are also drawbacks to consider. The equilibrium condition of Xe¹³⁵ and Sm¹⁴⁹ has not been achieved. It is important to highlight that in the SSC design, the significant contribution of Pu²³⁹ and Pu²⁴¹ to power generation will reduce the values of the main kinetic parameters. These continuous physical changes in the reactor parameters during the operating cycle emphasize the necessity of conducting a precise safety analysis for this type of reactivity control.