Neutronics Analysis of SMART Reactor Fuel Cell and Fuel Assemblies with Two Absorber Materials: Gd2O3 – UO2 and Al2O3 – B4C Using SRAC Code and JENDL 3.3 and 4.0 Data Libraries

The SMART is a small modular nuclear reactor which has been developed by South Korea’s KAERI, utilizes 4.95% enriched uranium fuel and two types of absorber materials: Gd2O3 - UO2 and Al2O3 - B4C. This research focuses on the neutronic analysis of SMART at the fuel cell and fuel assembly levels using SRAC 2006 with JENDL 3.3 and 4.0 Nuclear Data Libraries. The study aims to compare the neutronic performance of the SMART fuel assembly using these two absorber materials. At the fuel level, three types of enrichment are considered: 2.82%, 3.25%, and 4.95%. Meanwhile, at the fuel assembly level, three types (A, B, and C) are investigated, based on the composition of fuel rods and absorber material rods. The results indicate that the SMART reactor with the KAERI design (enrichment of 4.95% and 3 types of fuel assemblies) can maintain critical conditions for 990 days (equivalent to 3 years) of operation for small modular reactor types. The two types of absorber materials are effective in absorbing excess positive reactivity from the fuel effectively. The use of absorbing materials greatly determines the neutronic characteristics and costs in the construction of nuclear reactors, It can be compared that using 2 absorbing materials can reduce the value of the effective multiplication factor and the infinitive neutron production in the core compared to using 1 absorbing material.


Introduction
The SMART (System-integrated Modular Advanced Reactor) reactor is a Small Modular Reactor (SMR) integral PWR type developed by KAERI with a capacity of 330 MW(t), and it is expected to incorporate more advanced technology than generation III+ reactors.In addition to generating electricity with a power output of 90 MW(e), this reactor is designed to efficiently utilize about 10% of the remaining heat for the desalination process, resulting in a production capacity of 40,000 tons/day of clean water.SMART reactors are particularly effective for supplying electricity to remote areas not connected to the main grid, such as small-scale industrial complexes.
In SMR, neutronic analysis and thermal-hydraulic analysis play a crucial role in the operation of the reactor [1].To date, there have been numerous studies related to SMR SMART, such as neutronic calculations for various types of fuel variations and calculation methods.Some of these studies include using MCNP to calculate SMART reactor cores [2], calculating the neutronics of SMR reactors with MOX fuel and UO2 enriched to less than 5% using MCNP [3], exploring calculations with Thorium fuel cycle [4], conducting neutronic calculations using a uranium-thorium mixed fuel with a seedblanket system [5] and performing neutronic calculations with two types of UO2 enrichment (2.82% and 4.88%) and Burnable Absorber (BA) Gd2O3 [6,7].
For the PWR reactor type, the level of enrichment is of utmost importance.Typically, PWR-type reactors use low-enriched uranium (LEU), while uranium with an enrichment above 20% is classified as high-enriched uranium (HEU) [8].The use of HEU as fuel for nuclear reactors is prohibited due to its potential to produce significant amounts of plutonium nuclides and its potential application in making nuclear weapons.As a result, for SMART's relatively small reactor core compared to conventional PWR reactors, the enrichment level in the fuel cell is the most critical factor that significantly determines the length of reactor operation in maintaining critical conditions.

SMART reactor characteristics
The SMART reactor design, developed by KAERI, consists of 57 Fuel Assemblies (FA) arranged in a core, as shown in Figure 3 It can be observed that there are 3 types of FA with varied arrangements, as depicted in Figure 2.
The FA is fabricated and arranged in the form of a 17 x 17 matrix with dimensions of 21.5 cm x 21.5 cm, containing 289 holes for fuel rods, material absorbers, instrument rods, and control rods.Broadly speaking, the FA design consists of a Top Nozzle, Bottom Nozzle, Spacer, fuel rod, and guide thimble tube [9], as illustrated in Figure 1.The specifications for the three types of FA can be seen in Table 1 and Figure 2  The basic information for the SMART reactor design, as shown in Table 2 The highlight of the SMART reactor design is related to the safety features, which consist of passive safety systems, such as the Passive Residual Heat Removal System, Emergency Core Cooling System, and the Reactor and Containment Overpressure Protections, along with multiple safety designs.In a series of simulations, it was shown that SMART's PRHRS (Passive Residual Heat Removal System) on the secondary side was tested to be highly effective at removing decay heat and maintaining the reactor in a stable condition for more than 20 days without the need for operator intervention or additional mitigation measures.This grace period can be extended indefinitely if the PRHRS condensate tank is accessible from outside the containment and is refilled periodically [10,11].
Furthermore, SMART's fuel management is designed to achieve a maximum cycle length of 990 days of effective full power (EFPD) within its operating life of 36 months (3 years).[11,12]

Methodology
The neutronic calculations in this study are limited to cell-level calculations, considering various enrichment variations and FA levels.At the cell level, variations of UO2 enrichment will be carried out, starting from the lowest existing references, namely 2.82%, 3.25%, and 4.95%.These enrichment variations have been studied in previous research on SMART reactors, such as 2.82% enrichment [7,13], 3.25% [14][15][16]and 4.95% [17].Meanwhile, at the assembly level, a uniform variation of Uranium enrichment was used, namely 4.95%, based on the FA composition of the reactor manufacturer's standards from the KAERI design.This choice ensures that the research framework remains aligned with existing studies, facilitating comparisons with previous research.Neutronic calculations and analysis in this study used the SRAC program developed by JAERI (Japan Atomic Energy Research Institute).SRAC is a complete deterministic neutronic computing program designed to run under the Linux OS environment.It is equipped with various modules tailored for specific purposes.For the nuclide data library, JENDL 3.3 and 4.0 were utilized [18].The neutronic analysis aims to determine the behavior, population, distribution, and flux of neutrons expressed in parameters such as burnup, reactivity, multiplication factor, and other neutronic parameters.The multiplication factor describes the stability of the chain fission reaction in the reactor core, and conditions are categorized into three states: supercritical (k>1), critical (k=1), and subcritical (k<1).The multiplication factor k can be infinite (k-inf) and finite (k-eff), depending on the determination of the buckling geometry.If the core is considered to have no limit, then the buckling geometry is considered zero, resulting in the multiplication factor referred to as k-inf.The larger the buckling geometry (the smaller the core size), the more different the values of k-inf and k-eff will be.
In this study, the geometry used at the fuel cell level is IGT 4, while for the fuel assembly level, the geometry used is IGT 9, as shown in Figure 4. Particularly for the IGT 9 geometry, there is a rule that input is only allowed for 1/8 of the fuel assemblies.The input given to this 1/8th part will represent one set of fuel because SRAC will mirror the other 7/8th part.[19].Referring to the k-eff value (see Table 3), the first subcritical condition occurs after 450 days of operation for 2.82% fuel enrichment, 540 days of operation for 3.25% enrichment, and 900 days of operation for 4.95% enrichment.Meanwhile, from the k-inf value (Table 4), it was observed that the first subcritical period was longer than the previous k-eff period.At 2.82% fuel cell enrichment and 3.25% enrichment, the first subcritical period occurred at 630 days of operation, while at 4.95% enrichment, it occurred at 990 days of operation.the higher the concentration of U-235, the longer the fuel can maintain the chain reaction.And the longer the fuel is in the reactor, the higher the burnup rate.As for the Gd2O3-UO2 rods, which had a U-235 enrichment of 1.8 w/o, they reached their optimum value of k-eff and k-inf at 360 days of operation.Previously, they experienced an increasing trend at the beginning of operation, but after reaching the optimum value at 360 days, the Gd2O3-UO2 rods' k-eff and k-inf values decreased until the end of 990 EFFD, where the values reached 0.8 for both k-eff and k-inf.

Figure 6 k-inf fuel cells with various levels of enrichment
Next, we will examine the neutronic parameters at the fuel cell level at the end of the 990-day cycle of operation using JENDL 4.0, as shown in Table 5. Regarding the U05-% value (U-235 depletion fraction) for each fuel cell enrichment until the end of the 990 EFPD period, it can be seen that 4.95% enrichment has the lowest U05-% value.This is because the enrichment level impacts the ability of fuel cells to function during reactor operations.The smaller the enrichment value, the faster the fuel cell will experience shrinkage (depletion) and will no longer be usable.This is because the U-235 fissile material gets converted into other nuclides or spent fuel and cannot efficiently sustain fission reactions, eventually causing the reactor to reach a subcritical state.
Next, we compare the UO5-% between the lowest fuel enrichment of 2.82% and the Gd2O3 -UO2 rod, which contains U-235 fissile material at 1.8 w/o.As seen in Table 5, the presence of Gd2O3 relatively reduces the value of UO5-% in Gd2O3 -UO2 stems compared to 2.82% pure fuel, up to the end of the 990 EFPD period.The Gd2O3 -UO2 rods were still able to carry out fission reactions better than the 2.82% enrichment fuel cells, as indicated by the relatively lower UO5-% Gd2O3 -UO2 values (84.8%) than 2.82% enrichment fuel (89.3 %).However, the Gd2O3 -UO2 rods never reached the critical condition, as shown in Figure 5 and Figure 6, due to the physical characteristics of Gd2O3, which has a high neutron absorption cross-section.Nonetheless, Gd2O3 provides better efficiency than boron or other absorber materials at the beginning of the combustion cycle.Several studies have demonstrated that the use of gadolinium extends the fuel cycle, improves combustion, and optimizes the distribution of power density in the reactor core.
Next based on Figure 5 and Figure 6, it can be observed that the 4.95% enrichment experienced the first subcritical condition at 990 days of operation (k-inf of 0.99).It is also known that the SMART reactor has an EFPD (Effective Full Power Days) period of 990 days.Therefore, it can be concluded that KAERI designed the SMART reactor with an enrichment of 4.95% to enable it to operate for 3 years.This decision is driven by the relatively small size of the SMART reactor core compared to conventional PWR cores, leading to a higher probability of neutrons escaping from the reactor (the buckling geometry value of SMART reactors is relatively larger than conventional PWRs).In order to achieve the critical conditions and a relatively longer operating life of the reactor, the buckling material value must also be relatively greater.One way to increase the buckling value of the material is by increasing the enrichment of the fuel up to 4.95% compared to the enrichment of conventional PWR fuel cells (around ±3.25%).This is one of the considerations in the neutronic aspect to address the problem of neutron leakage for reactors that have relatively small core sizes or other types of SMR reactors.

Neutronic analysis at FA level with various fuel types and compositions.
Based on Figure 7 and Figure 8, it can be observed that the three types of FA initially experienced a supercritical condition, as indicated by k values above 1.However, after operating for 990 days, the three FAs reached a subcritical condition, as evidenced by their keff values being less than 1 as seen in Table 6.Based on k-eff (Figure 7 and Table 6) The k-eff values obtained in descending order are as follows: FA type C > type B > type A. The composition of the fuel assembly significantly affects the economic number and reactivity of the neutrons in the assembly.The greater the amount of fuel, the higher the reactivity of the assembly.Therefore, the presence of a BA in the FA aims to balance the heat flux within the fuel assemblies and absorb the excess positive reactivity of the fuel with the negative reactivity of the neutron-absorbing material.
Next, let's examine the neutronic parameter values of the fuel assemblies after 990 days of operation (EFPD).Based on Table 8, the value of the depletion fraction of U-235 (UO5-%) in each FA is influenced by the composition of the fuel and the absorber material.The depletion fraction of U-235 (UO5-%) in type B is the smallest among the other two types.This is because the ratio of the number of rods containing fissile material (U-235) to absorber material is relatively the smallest among the other two FAs.
The ratios of the amount of absorber material (Gd2O3 and B4C) to rods containing fissile material (UO2 fuel rods and Gd2O3 -UO2 rods) for each FA are as follows: FA A was 0.169 (40/236), FA B was 0.098 (24/244), and FA C was 0.116 (28/240).Additionally, the type of absorber material greatly affects the production of neutrons due to its relation to the absorption cross-section.Based on the material characteristics, the Gadolinium absorption cross-section (σa = 46000 barns) is larger than the Boron absorption cross-section (σa = 755 barns) [21,22].Therefore, if more Gd2O3 is used as an absorber material compared to B4C, it will significantly affect the decrease in resulting neutron production.
Furthermore, the results of the neutronics at the FA level obtained in this study will be compared with existing research.The first comparison is for the same type of FA arrangement as in this study.There are two studies used as references: Lee's research [23] using the code CASMO-3/MASTER and Ramdhani's study [17] using the SRAC2006 code.Look on Figure 9, all three FAs in the initial operating conditions experienced a supercritical condition, characterized by a k-inf value > 1.00.Moreover, type C FA exhibited the largest relative multiplication factor among the other two FAs.Additionally, all three types of FAs were able to maintain supercritical conditions for a relatively long time, as seen from the kinf value dropping below 1 (subcritical condition) after a period of 1100 days.Next, a comparison of the k-eff and k-inf values obtained from Ramdhani's research will be conducted [17] to examine the k-eff and k-inf values at the beginning of reactor operation using JENDL 3.3 and 4.0.
Table 9 The k-eff value of each FA at the beginning of the operation uses the JENDL 3.3 and JENDL 4.0 nuclide data libraries.[24] which uses the JENDL 3.3 data library %difference is a relative percentage comparison between the reference k-eff value and the k-eff value obtained in this study using the JENDL 3.3 and JENDL 4.0 nuclide library data Based on Table 9 and Table 10, it can be observed that all three FAs at the start of operation are in supercritical conditions.When compared with Ramdhani's research [17] , the largest difference obtained is <2.5% (k-inf for FA type B using JENDL 4.0).Furthermore, by comparing the results obtained using JENDL 3.3 and JENDL 4.0, it can be seen that the neutronic results using JENDL 4.0 are relatively higher than those using JENDL 3.3.This difference is due to data updates and an increased number of nuclides (JENDL 3.3 had 337 nuclides, while JENDL 4.0 has 406 nuclides, including 69 new inputs) and apart from that, there are several corrections such as cross sections at the thermal neutron energy with the experimental results reported recently [25].
Next, the conversion ratio (CR) and breeding ratio (BR) values of the three FAs are reviewed.The BR values are found to be low, and CR < 1.The breeding ratio (BR) represents the ratio between the fissile material produced and the fissile material that is removed.Since the SMART reactor uses UO2 a b d enriched oxide fuel, it is technically not a breeder reactor.Nevertheless, the choice of oxide fuel has advantages, including high burnup capability and a high melting point.In addition, several studies have been conducted using different FA fuels and compositions compared to the KAERI designs.The aim is to assess the neutronics of the FAs and consider economic and cost aspects in building the reactor.As seen on Figure 10, there are 4 studies: (1) Kamalpour [6] which used two types of enrichment (4.88% and 2.82%) and Gd2O3 as absorber material, with the neutronic code MCNPX 2.6 (2) Jang [26] which employed 4.95% fuel enrichment and two absorber materials: WABA (Al2O3/B4C) and IBA (Gd2O3).The reactor height was similar to the SMART reactor (200 cm), but the output power was 180 MWt.(3) Akbari-Jaehouni [27] which used (Th/U)O2 fuel with two enrichments (4.88% and 2.82%) and IFBA absorber material (Gd2O3-UO2).(4) Nailatussaadah [13] which used two types of fuel enrichment (4.88% and 2.82%) and one Gd2O3-UO2 absorber material.From Figure 10, it can be observed that the multiplication factor, which represents the production of neutrons at the FA level, is influenced by the type and amount of absorber material arranged in the FA.Besides that, on Figure 10, there are FAs that reach the first subcritical state for more than 3 years, with some even approaching 5 years of operation before becoming subcritical.When compared to the composition of FAs in this study, the multiplication factors for FA types A, B, and C in this study were relatively smaller than those reported in the various studies described previously.This difference is due to the presence of two types of absorber materials: BA rods Gd2O3 -UO2 and shim rods (Al2O3 -B4C).These two absorber materials cause the multiplication factor value to be lower than those that only have one type of absorber material or do not have any absorber material.The presence of burnable absorbers and shim rods in the FAs serves to control the positive reactivity of the fuel.BA materials, which are consumed as the UO2 fuel depletes, undergo transmutation into materials with low absorption crosssections.This is in contrast to their initial state with a high absorption cross-section.The advantage of BAs lies in their ability to compensate for depletion and also their role in controlling control rods.For example, the number of control rod mechanisms required can be reduced, leading to less rapid changes in local power density due to the prolonged depletion process.Additionally, BA placement can be optimized to avoid power peaking and improve power distribution, especially when there is a significant difference in reactor criticality between fresh and used fuel sets.However, incomplete combustion of BA can leave a small amount of poison at the end of each fuel cycle, which then requires compensation by adding a slightly greater amount of fuel.
In addition to designing a superior and safe FA, attention must also be paid to the mechanism, thermal-hydraulic aspects, and physical characteristics of the constituent materials.It is crucial to ensure that the materials used in designing the reactor can support the reactor's long life and operate at the intended power capacity without issues.By doing so, the reactor can avoid unwanted events such as small / medium / large break loss of coolant accident.

Conclusion
When designing a nuclear power plant, the core size and enrichment level are two integral factors that must be carefully considered.For small reactors, the geometric buckling value factor is higher than that of conventional PWR reactors.Thus, to design a small reactor with critical conditions and a relatively long lifespan, one approach is to increase the buckling factor by using higher enrichment than conventional PWR fuel (3.25%).KAERI designed the SMART reactor with an enrichment of 4.95%, considering that it experienced subcritical conditions (k-inf<1) after 990 days of operation.
At the Fuel Assembly level, the fuel composition of each type (A, B, and C) meets the criticality requirements and can operate while maintaining criticality for 990 days.Based on the k-eff factor, the SMART reactor FA types are ranked from highest to lowest value as follows: FA type C > type B > type A. The level of enrichment, fuel composition, and the amount of absorber material significantly influence the neutronic output from the SRAC calculation and the reactor's operational longevity.Additionally, comparing the neutronic results obtained using JENDL 3.3 and 4.0, it can be observed that the neutronic results using JENDL 4.0 are relatively larger than those from JENDL 3.3.This difference is attributed to data updates and an increased number of nuclides (JENDL 3.3 had 337 nuclides, while JENDL 4.0 has 406 nuclides, including 69 new inputs).

Figure 1 FA
Figure 1 FA Chart (number 1 = top nozzle, 2 = bottom nozzle, 3 = spacer, 4 = fuel rod and 5 = guide thimble tube) Figure 2 shows the configuration of FA types A, B, and C used in the SMART reactor core (Figure 3).Each fuel rod has the same enrichment of 4.95% U-235; however, each FA has a different number of BA rods.The composition of the burnable absorbers used in this study was Gd2O3-UO2 rods (4 w/o Gd2O3 -1.8 w/o U-235) and Shim rods Al2O3 -B4C (with a B-10 content of 0.0111 gr/cm).

Figure 2 FuelFigure 3
Figure 2 Fuel Assembly's (FA) for the SMART reactor core

Figure 5 and
Figure 5 and Figure 6 show the values of k-eff and k-inf at the fuel cell level, considering fissile material with various enrichment levels of 2.82%, 3.25%, and 4.95%, along with Gd2O3-UO2 rods (4 w/o Gd2O3 -1.8 w/o U-235).

Figure 5 k
Figure 5 k-eff fuel cells with various levels of fuel enrichment

Figure 7 k
Figure 7 k-eff various types of SMART FA reactors with JENDL 3.3 and 4.0 nuclide libraries

Figure 10 (
Figure 10 (a) k-eff is proportional to the operating time of the reactor for different types of IBA (Integral burnable absorbers).[6] (b) k-eff various FAs with the arrangement of variations of WABA (wet annular burnable absorber) and BA on length of operating time [26] (c) k-eff on FA with single (homogeneous) fuel rods [27] (d) k-inf for the FA arrangement with variations of IBA and 2 types of UO2 enrichment (2.82% and 4.88%) [13]

Table 1
FA specifications on SMART reactors

Table 3 k
-eff fuel cells with various levels of fuel enrichment at first operation, 990 days and first subcritical condition

Table 4 k
-inf fuel cells with various levels of fuel enrichment at first operation, 990 days and first subcritical condition

Table 5
Fuel cell neutronic parameters at the end of 990 days of operation

Table 6 k
-eff fuel cells with various levels of fuel enrichment Figure 8 k-inf various types of SMART FA reactors with nuclide libraries of general 3.3 and 4.0

Table 7 k
-inf fuel cells with various levels of fuel enrichment

Table 8
Neutronic parameters at the end of the 990-day SMART reactor operating cycle using JENDL 4.0

Table 10
The k-inf value for each FA at the beginning of the operation uses the JENDL 3.3 and JENDL 4.0 nuclide libraries.