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Design concept for a small pebble bed reactor with ROX fuel
Annals of Nuclear Energy 87 (2016) 471–478
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Design concept for a small pebble bed reactor with ROX fuel Hai Quan Ho, Toru Obara ⇑ Research Laboratory for Nuclear Reactors, Tokyo Institute of Technology, 2-12-1-N1-19, Ookayama, Meguro-ku, Tokyo 152-8550, Japan
a r t i c l e
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Article history: Received 15 July 2015 Received in revised form 8 October 2015 Accepted 9 October 2015
Keywords: Pebble bed reactor Rock-like oxide fuel High burnup Power peak reduction Temperature coefficient
a b s t r a c t The conceptual design of a small rock-like oxide fuel pebble bed reactor with once-though-then-out (OTTO) cycle is proposed here. TRISO-coated particles based on AGR-1 design were used to achieve a target burnup larger than 100 GWd/t-HM without any failure of spent fuel. In the first step, optimization of fuel composition was implemented by cell calculations. After that, whole core calculations were performed with and without movement of the fuel pebbles. With a heavy metal amount of 2 g per pebble and 20% uranium enrichment, the pebble bed reactor with OTTO cycle could achieve maximum burnup of about 145 GWd/t-HM and fissions per initial fissile atom (FIFA) of 75%. The results show that the core height can be reduced due to the fact that the impact of bottom core on burnup performance is insignificant. Also, the peak power density of the reactor exceeded the limit of that for the PBMR design. Therefore, subsequent optimizations of the core design were carried out by decreasing the core height and reactor power to reduce the construction cost as well as the peak power density. A reactor with 6-m core height and 120-MWth reactor power was ultimately determined as the optimal design for a pebble bed reactor with ROX fuel. This optimal design also has a negative temperature coefficient, and the peak power density was less than the limit of 10 W/cm3. Ó 2015 Elsevier Ltd. All rights reserved.
1. Introduction Nuclear energy has been expected to play an important role in the future energy supply; however, it has to meet today’s higher safety standards. The pebble bed reactor (PBR), a kind of hightemperature gas-cooled reactor (HTGR), is one of the most promising reactors in the generation IV initiative. This type of reactor is claimed to be have excellent passive safety features because of its graphite-moderated, helium-cooled and tristructural-isotropic (TRISO) fuel particles (Kadak, 2005). Rock-like oxide (ROX) fuel has been studied at the Japan Atomic Energy Agency (JAEA) as a new once-through type fuel concept. With both mineral and ceramic properties, it is desired to improve the performance of the fuel elements not only in normal operation, but also for geological disposal without further reprocessing (Akie et al., 1994; Kuramoto et al., 2003; Nitani et al., 2008). Previous studies have been performed to access the potential of using ROX fuel in HTGRs. A clean burn high temperature gas-cooled reactor (CBHTR) that uses PuO2-YSZ fuel and thereby recovers spent Pu fuel from light water reactors has been under development at JAEA (Minoru, 2013). Other research (Ho and Obara, 2015) showed that UO2-YSZ fuel can be used in small PBRs ⇑ Corresponding author. Tel./fax: +81 3 5734 2380. E-mail address: [email protected] (T. Obara). http://dx.doi.org/10.1016/j.anucene.2015.10.007 0306-4549/Ó 2015 Elsevier Ltd. All rights reserved.
with high-discharge burnup even if the fissile density is five times lower than that of conventional UO2 fuel. The UO2-YSZ fuel also presents an advantage in comparison with the UO2 fuel as it has higher stability in the geological disposal of spent fuel without significantly reducing burnup performance. However, the previous study only showed the possibility of using ROX fuel in oncethrough-then-out (OTTO) cycle pebble bed reactor; optimization for burnup performance was not performed. The purpose of this study was to introduce the design concept for a small PBR with ROX fuel and to optimize the ROX fuel composition so that the reactor can achieve as high a burnup as possible without any failure of the spent fuel in the OTTO cycle. The power peak was set to less than the limit of the reference PBMR design to ensure that the reactor can be cooled by natural circulation and still survive in accident scenarios. In addition, an analysis of temperature coefficients was carried out to show the negative reactivity coefficient of the PBR with the UO2-YSZ fuel. 2. Optimization of fuel composition by cell calculations 2.1. Fuel design To satisfy the high burnup in a once-though fuel cycle, the PBR with ROX fuel should utilize the fuel designs that have been successful in high burnup irradiation tests. It was found that the
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AGR-1 (Maki, 2009) could achieve a high burnup without any observable failures up to approximately 200 GWd/t-HM. Therefore, this study used the AGR-1 fuel design for the calculations. The main parameters of the fuel pebbles and AGR-1 TRISO particles are presented in Table 1. This study utilized low-enriched uranium with a maximum 20% concentration of 235U. A single-phase UO2-YSZ fuel, consisting of 81.75 mol% YSZ (78.6 mol% ZrO2 + 21.4 mol% YO1.5) and 18.25 mol% UO2, was used as the fuel in the kernel, as in the previous study (Ho and Obara, 2015). 2.2. Methodology In the first step, cell calculations were implemented to estimate the optimal fuel composition that could be applied for further analyses in a PBR with the same fuel design as mentioned above. Random parking (RP) with a packing fraction of approximately 61% was chosen to distribute the fuel pebbles in the cell geometry. The cell geometry was surrounded by a reflective boundary condition. In order to determine the optimal fuel composition, the amount of heavy metal in each pebble (HM loading) and the enrichment of uranium were changed. The HM loading can be adjusted by changing the number of TRISO particles in the graphite matrix of the fuel pebble: the more TRISO particles, the greater the HM loading, with 4.5 g being the maximum HM loading for the ROX fuel, corresponding to a TRISO-coated fuel particle (CFP) volume-packing fraction of 40%. Criticality analyses were performed using a continuous-energy Monte Carlo code, namely MVP-BURN (Okumura et al., 2006), and the JENDL-4.0 nuclear data library (Shibata et al., 2011).
Fig. 1. Change of k1 in cell calculations for different enrichment in the case of 3-g HM loading.
2.3. Results The change of the infinite multiplication factor (k1) as a function of operation time in the case of 3-g HM loading with different uranium enrichments is shown in Fig. 1. It can be seen that higher uranium enrichment made k1 decrease to unity more slowly, and as a result the operation time could be longer. Figs. 2 and 3 illustrate the burnup and FIFA, respectively, as a function of HM loading and uranium enrichment when the k1 became unity in cell calculations. According to Fig. 2, the burnup decreased with decreasing uranium enrichment at the same amount of HM loading. The case of 3-g HM loading with 20% uranium enrichment gave the highest burnup of about 135 GWd/t-HM when k1 equaled one. As can be seen in Fig. 3, the FIFA was almost the same at the same amount of HM loading even if the enrichment of uranium was changed from 12% to 20%. However, the FIFA was reduced from about 75% to 65% when the amount HM loading increased from 1.5 to 4.5 g. This is because the moderator-tofuel-volume ratio decreased when the amount of HM loading increased from 1.5 to 4.5 g. Decreasing the moderator-to-fuelvolume ratio made the neutron spectrum shift to being harder. Table 1 Fuel designs. Properties
Unit
Value
Fuel pebble Pebble radius Thickness of fuel-free zone Density of carbon matrix
cm cm g/cm3
3.0 0.5 1.74
lm
350 6.55 C/C/SiC/C 100/40/35/40 1.10/1.85/3.20/1.85
Coated particles Kernel diameter Kernel density Coating materials Layer thicknesses Layer densities
g/cm3 – lm g/cm3
Fig. 2. Burnup in cell calculations for different enrichments and HM-loading schemes.
This made the fuel burnup less effective by increasing the amount of HM loading. The results at critical state showed that 20% of enriched uranium and about 2.5–3 g of HM loading was the optimal fuel composition in cell calculations, at which the burnup and FIFA could reach their highest values. Therefore, this composition will be used as a reference design for subsequent analyses in this study. 3. Optimization of fuel composition in a small PBR without movement of fuel pebbles In the actual reactor, the neutron leakage is very complicated due to the existence of the graphite reflector. Chapter 2 performed the burnup calculation of the fuel with the reflective boundary condition. It is difficult to determine the buckling properly without taking into account the neutron leakage. Therefore, this chapter carried out the burnup performance by whole core calculations with graphite reflector to estimate more properly neutron leakage effects. In the analysis, it is assumed that there was no movement of fuel pebbles in the core during operation.
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Fig. 3. FIFA in cell calculations for different enrichments and HM-loading schemes.
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Fig. 4. Burnup in PBR without movement of fuel balls.
3.1. Reactor design In this chapter, the PBR geometry in a previous paper (Ho and Obara, 2015) was chosen and modeled. The 300-MWth core, 10 m in height and 3 m in diameter, was surrounded by a 1-m-thick graphite reflector with a 1-m-high void on top. The main parameters of PBR design are given in Table 2. The fuel pebbles were poured into the active core and stood stationary during operation. 3.2. Methodology The optimization procedure was similar to the cell calculations, in which the HM loading and the enrichment of uranium were changed to determine the maximum burnup and the FIFA. As suggested from the cell calculations, the HM loading and uranium enrichment in this analysis were changed in a smaller range, 2–4 g for HM loading and 16–20% for fuel enrichment. Criticality analyses were also performed using MVP-BURN code with a JENDL-4.0 nuclear data library. In the initial condition, the effective multiplication factor (keff) was more than unity and gradually decreased by burnup. The burnup and FIFA values when the reactor reached critical condition (keff = 1) were estimated. 3.3. Results Figs. 4 and 5 show the burnup and FIFA values by the whole core calculations without movement of the fuel pebbles as a function of HM loading and fuel enrichment, respectively. As in the previous cell calculations, the burnup and FIFA were decreased when the uranium enrichment decreased at the same amount of HM loading. Based on these figures, it is possible to achieve a high burnup and FIFA value of about 100 GWd/t-HM and 45%,
Table 2 Design parameters of reactor. Properties
Unit
Value
Thermal power Average power density Graphite reflector density Coolant Core temperature Number of fuel balls Packing fraction of pebble balls
MWth W/cm3 g/cm3 – K – –
300 4.24 1.74 Helium 1000 380,000 0.61
Fig. 5. FIFA in PBR without movement of fuel balls.
respectively, when the HM loading was about 3–3.5 g with 20% uranium enrichment. It can be seen that there was a small difference from the results by cell calculations. By the whole core calculation we could obtain a better composition to maximize the burnup and FIFA value. 4. Optimization of fuel composition in a small PBR with movement of fuel pebbles by adopting the OTTO cycle The analyses for whole core geometry were performed assuming the movement of fuel pebbles; the fuel pebbles were assumed to move from the top to the bottom of the core in the OTTO fuel cycle. The reactor core was based on the PBR geometry described in chapter 3 and utilized the fuel design described in chapter 2. 4.1. Methodology A Monte Carlo-based pebble bed reactor (MCPBR) code (Setiadipura and Obara, 2014) was used to calculate the burnup of the fuel pebbles when they moved uniformly through the core with constant velocity. In the MCPBR code, a burnup calculation
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Table 3 Burnup performance for 3-g HM loading in a fuel ball. Case
1
2
3
4
5
6
Uranium enrichment [%] Residence time of fuel balls [days]
20 762
20 648
20 496
17 496
17 476
16 476
keff Discharge burnup [GWd/t-HM] FIMA [%] FIFA [%] Peak pebble power [KW]
0.928 200 20.7 103.6 8.1
0.996 170 17.7 88.4 6.1
1.092 130 13.4 66.8 3.9
1.014 130 13.5 79.5 4.7
1.025 125 13.0 76.7 4.3
0.996 125 13.0 81.3 4.6
based on a continuous-energy Monte Carlo MVP-BURN code was coupled with an additional utility code to be able to simulate the OTTO cycle of PBRs. The JENDL-4.0 nuclear data library was used for the analysis. In previous study (Terry et al., 2002), the impact on fuel burnup was investigated by considering two velocity profiles of the pebbles. There were a uniform profile and a parabolic profile. The multi-pass scheme was used for refuelling, in which the pebbles were reintroduced repeatedly into the same radial position (channeling recirculation) and therefore the results can be preliminarily applied for the OTTO cycle. The results showed that although the maximum burnup for parabolic velocity profile was larger than that for uniform velocity profile; the average burnup was almost the same for both the velocity profiles. As a result, the radial fuel speed can give a small impact from the viewpoint of average burnup of the discharged fuel. The main interest of this study is to investigate the average burnup of the fuel. Therefore, the flow speed through the core is assumed to be radially uniform in the study. In the previous optimizations, only HM loading and uranium enrichment were changed. In this case, however, the procedure became more complicated since the burnup performance can be changed by simultaneous adjustment of three parameters, including HM loading, uranium enrichment and fuel pebble velocity. Hence, to simplify the optimization procedure, the first step was carried out with a constant 3-g HM loading in the fuel pebble, changing only the uranium enrichment and pebble velocity. From chapter 2 and 3 it was found that a maximum of 20% uranium enrichment is expected to provide high burnup as well as high FIFA. Therefore, the optimization started with the maximum uranium enrichment of 20% and then decreased the enrichment stepwise. The calculated conditions of several cases for the PBR with 3-g HM loading in a pebble, at different pebble velocities (corresponding to discharge burnup) and uranium enrichments, are shown in Table 3. In cases 1, 2 and 3, a maximum 20% of uranium enrichment was used to determine the maximum discharge burnup, in which the reactor could become critical at equilibrium conditions. The remaining analyses (cases 4, 5 and 6) with lower enrichment of uranium were then performed to find the highest FIFA value. After determining the optimal fuel composition for the PBR with 3-g HM loading in a pebble, the same procedures were implemented for different amounts of HM loading, from 1.5 to 4.5 g. In this study, the reactor power was set at 300 MWth. At the initial condition, the active core was filled by fresh fuel pebbles. The calculation was started from the initial condition until the neutron flux and nuclide density reached equilibrium, where the keff, discharge burnup and FIFA were estimated.
Table 3. The reactor could not reach criticality when the discharge burnup was larger than 130 GWd/t-HM, even if the enrichment of uranium was set to a maximum of 20%. Case 4 was implemented with the same discharge burnup of 130 GWd/t-HM, but with lower uranium enrichment than in case 3. From Table 3, a lower enrichment of uranium, with the same discharge burnup, gave a higher FIFA value as well as a higher peak pebble power (maximum power of a pebble in the core). For example, the FIFA value and peak pebble power (in cases 3 and 4) increased from 66.8% to 79.5% and 3.9 to 4.7 KW, respectively, if the fuel enrichment decreased from 20% to 17%. Because, to produce the same discharge burnup at the same power, the reactors in cases 3 and 4 had to have almost the same number of fission reactions. The fuel enrichment in case 4 was lower than that in case 3; this required the FIFA in case 4 to be higher than that in case 3 to produce the same number of fission reactions. It also can be seen that case 4, with 17% of fuel enrichment, yielded the highest burnup of 130 GWd/t-HM and the highest FIFA of 79.5%. However, case 4 could not be accepted due to the fact that the peak pebble power should be less than the limit of 4.5 kW to maintain the integrity of the fuel pebbles during operation (Bende, 1999). Only case 3 and 5 could be satisfied with the peak pebble power limit. Therefore, when considering both the discharge burnup and FIFA factors between cases 3 and 5, case 5 was considered the optimal fuel composition for 3-g HM loading, with a discharge burnup of 125 GWd/t-HM and a FIFA of 76.7%. Fig. 6 shows a comparison of the axial power density in the center core for various fuel compositions in the case of 3-g HM loading. It can be seen that, as is generally true for OTTO cycle pebble bed reactors, the peak power density appears at the top region, while it becomes very small at the bottom of the core.
4.2. Results The analysis results in the case of 3-g HM loading with different uranium enrichments and different residence times are shown in
Fig. 6. Axial power density profile at center of the OTTO PBRs for the same 3-g HM loading scheme.
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Fig. 7. Power density distribution (a) and thermal neutron flux (b) in the OTTO PBR with 3-g HM loading and 17% uranium enrichment.
Case 1 produced the highest peak power density because of its highest discharge burnup while the optimal case 5 gave about 23 W/cm3 in peak power density. Fig. 7a shows the power density distribution in the optimal reactor (case 5) in case of 3 g HM loading per pebble. The peak power density appeared at the top region, because fresh fuel pebbles were deposited onto the top of the core and the spent fuel pebbles were discharged from the bottom of the core during operation. Fig. 7b shows the thermal neutron flux (E < 1.86 eV) distribution in the core. The variations were similar to the power density profile, since the reaction rate was mainly attributed to the thermal flux. It can be seen that the power density peaks (corresponding to thermal flux peaks) at the top of the core appeared adjacent to inner core and side reflector regions. The reflection of thermal neutron flux at side reflector is the reason for the increase of power density in this region. The radial thermal flux gradually became flat when the fuel pebbles moving to bottom core, because the bottom region contained the pebbles with a very low fissile content. After finishing optimization of the fuel composition for the PBR with 3-g HM loading in a pebble, the same procedures were implemented while changing the HM loading from 1.5 to 4.5 g. The optimization results for these other HM-loading schemes are summarized in Table 4. In case of 1.5-g HM loading with 19% uranium enrichment, the reactor could achieve a discharge burnup of 120 GWd/t-HM with a FIFA of about 66%. The reactor with 4.5-g HM loading per pebble, in fact, could give a higher burnup value than 110 GWd/t-HM as shown in Table 4. However, the peak pebble power exceeded the limit of 4.5 KW if the discharge burnup was larger than 110 GWd/t-HM. Table 4 also shows that most of the cases had almost the same FIFA value, with 2-g HM loading giving the highest discharge burnup value, approximately Table 4 Burnup performance for different HM-loading schemes per fuel ball. HM loading [g] Uranium enrichment [%] Residence time of fuel balls [days]
1.5 19 229
2 20 369
3 17 476
3.5 16 534
4.5 15 629
keff Max. discharge burnup [GWd/t-HM] FIMA [%] FIFA [%] Peak pebble power [KW]
1.028 120 12.6 66.1 3.7
1.027 145 15.1 75.7 4.5
1.025 125 13.0 76.7 4.3
1.016 120 12.5 77.9 4.4
1.010 110 11.5 76.5 4.4
Fig. 8. Axial power density profile at the center of the reactors for various fuel compositions.
145 GWd/t-HM. Therefore, from the viewpoint of discharge burnup and actinides transmutation, 2-g HM loading per pebble with 20% uranium enrichment was the optimal fuel composition for a PBR utilizing the UO2-ROX fuel. Fig. 8 illustrates the power density profile at the center of the optimal reactors for each HM-loading scheme per fuel pebble. The power density profiles were nearly identical for all reactors, with a peak power density of about 25 W/cm3. This value was far beyond the power peak limit for PBMR design of 10 W/cm3. Therefore, in the next section, optimization was performed to reduce this peak power density to below the limit. Thermal (E < 1.86 eV) and fast (E > 0.1 MeV) neutron flux profiles are shown in Fig. 9. The fast neutron flux in the axial direction does not vary between the alternative cases, while differences in the thermal neutron flux can easily be observed: the lower HM loading produced significantly larger thermal neutron flux at the top region of the active core. Because, the reactors with the same power produce equal number of fission reactions. A reactor with lower (higher) fissile density had higher (lower) thermal neutron flux to generate the same power level. As a result, the thermal
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Fig. 9. Axial neutron flux profile (average) in the reactors for various fuel compositions: (a) thermal neutron flux; (b) fast neutron flux.
Table 5 Burnup performance of reactors with different core heights. Core height [cm]
300
400
500
600
1000
Discharge burnup [GWd/t-HM] Residence time [days] keff FIMA [%] FIFA [%] Max. power density [W/cm3]
145 111 0.960 15.1 75.7 26.9
145 147 0.985 15.1 75.5 25.3
145 184 0.997 15.1 75.6 24.4
145 221 1.003 15.1 75.4 24.4
145 369 1.027 15.1 75.7 23.0
neutron flux was largest for 1.5-g HM loading, whereas it became smallest for 4.5-g HM loading. 5. Optimization of the core designs In previous sections, optimization of the fuel composition was performed. The results showed that the core height could be reduced since the impact of the bottom core on burnup performance proved insignificant. Also, the peak power density of the reactor exceeded the limit of that for PBMR design. Hence, in this section, further optimization of core designs will be carried out by changing the core height and reactor power to reduce the construction cost as well as the peak power density. 5.1. Optimization of core height As can be clearly seen from Figs. 8 and 9, the power density and neutron flux at the bottom of the core were very small. Therefore, the impact of the bottom core on burnup performance was insignificant; as a result, it was deduced that the core height could be reduced without changing the burnup performance at equilibrium state. The optimal core in Section 4.2, with 2-g HM loading and 20% uranium enrichment, was used to investigate the effect on burnup performance when changing the core height. The pebble velocity remained constant to achieve the same discharge burnup of 145 GWd/t-HM as before. Table 5 shows the burnup performance results when the core height changed from 3 m to 10 m. According to this table, the reactors could be critical if the core height was greater than 6 m whereas it became subcritical for reactors with a core height of 5 m or less. This phenomenon can be explained from the power density and thermal neutron flux distribution in Fig. 10. In the
cases of PBRs with 65 m core height, the power density and neutron flux were fairly significant at the bottom region. This means that in these cases, the neutron flux in both the top and bottom regions contributed to the criticality of the reactors. Hence, the neutron flux in the top region itself could not make the reactor critical without the bottom region. Conversely, in the case of reactors with core heights of 6 m or more, due to the very small neutron flux and power density at the bottom region, reducing the core height did not decrease the neutron flux greatly; therefore, the reactor could be critical without the bottom region. Table 5 also shows that the main reactor physical parameters were not changed even if the core height decreased from 10 m to 6 m. Reducing the core height also decreased the number of pebbles loaded into the core. For example, a PBR with 10-m core height required approximately 380,000 pebbles in comparison to 230,000 pebbles in the PBR with 6-m core height.
5.2. Power peak reduction Previous studies show that although the effects of a DLOFC accident are limited by the negative reactivity feedback and the capability of the reactor to transfer the decay heat from the core, fuel temperatures are considerably higher compared to normal operating conditions. With the peak power density larger than 10 W/cm3, the fuel temperature in a PBMR can exceed the temperature limit of 1600 °C in a depressurization accident (Boer et al., 2009; Tran and Kato, 2009; Tran et al., 2008). Therefore, in this study the maximum power density was set to less than 10 W/cm3, to keep the fuel temperature below the maximum permissible temperature of the reference PBMR design during normal operation and during a DLOFC transient. For the previous optimal reactor in Section 5.1, the peak power density was approximately 24.4 W/cm3, about 2.5 orders larger than limit. Hence, in order to reduce the peak power density, the reactor power was decreased from 300 to 120 MW as presented in Table 6. The pebble velocity was also decreased, which resulted in an extended residence time of the fuel, to maintain the discharge burnup target and uranium transmutation ratio. The maximum power density could be reduced to 9.6 W/cm3 when the reactor power was set to 120 MW. Fig. 11 presents the power density distribution and thermal neutron flux for ultimately optimal core. It can be seen that the final optimal core gave a high burnup of
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Fig. 10. Axial power density profile (a) and axial thermal neutron flux profile (b) in 300-MWth reactors with various core heights.
Table 6 Burnup performance of 6-m-core-height reactors with different powers.
Table 7 Temperature coefficients for optimal reactor design.
Reactor power [MWth]
300
200
150
120
Temperature [K]
Temperature coefficient [pcm/K]
Discharge burnup [GWd/t-HM] Residence time [days] keff FIMA [%] FIFA [%] Max. power density [W/cm3]
145 221 1.003 15.1 75.4 24.4
145 332 1.006 15.1 75.6 16.1
145 442 1.005 15.1 75.5 12.1
145 553 1.007 15.1 75.4 9.6
300–400 600–700 900–1000
16.5 6.6 5.2
145 GWd/t-HM along with keeping the peak power density smaller than limit of 10 W/cm3. 6. Temperature coefficient In general, a change in the temperature leads to a change in multiplication factor and thereby alters the reactivity of the system. This effect should be thoroughly considered as it has an important bearing on the operation of a reactor, and ultimately on the safety of the system. For thermal reactors in general and
PBRs in particular, the negative temperature coefficient is a required parameter to ensure stability during both normal operation and accident conditions. This analysis estimated the temperature coefficient for the ultimately optimal core in Section 5.2 with 6 m in core height and 120 MW in reactor power. The core composition at equilibrium state was used to calculate the keff by changing the core (fuel and moderator) and reflector temperature from 300 K to 1000 K. Table 7 demonstrates the negative temperature coefficient for the optimal reactor design. Furthermore, the temperature coefficient became more negative with a decreasing core temperature.
Fig. 11. Power density distribution (a) and thermal neutron flux (b) in ultimately optimal PBR with 120-MWth power.
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7. Discussion An analysis for cell calculation was performed to determine the optimal fuel composition. The highest 20% enrichment of uranium with 3-g HM loading in a pebble could give a discharge burnup of about 135 GWd/t-HM and FIFA of 75%. This means that even if the ROX fuel has low fissile density, the UO2-ROX fuel PBR can be expected to achieve high burnup when fuel with high uranium enrichment is used. By adopting OTTO fuel management for the fuel pebbles, the reactor could achieve higher burnup and FIFA values. For example, 2-g HM loading in a pebble and 20% of uranium enrichment gave a discharge burnup of 145 GWd/t-HM and a FIFA of 75% in the optimal case. However, the OTTO cycle made the power density shift to the top region of the core, and as a result, the peak power density became quite high, about 24.4 W/cm3. This value was far beyond the power peak limit for PBMR design of 10 W/cm3. The peak in the power profile can be reduced to 9.6 W/cm3 if the reactor power decreases from 300 MW to 120 MW. Therefore, if the power peak is to remain below 10 W/cm3, a further increase of the reactor power is unattractive for OTTO fuel management. In case of multi-pass fuel management, the reactor power can be increased, as the axial power density is flattened and the power peak is reduced compared to a PBR with OTTO fuel cycle. However, a PBR with a multi-pass cycle may not achieve as high a burnup as a PBR with an OTTO fuel cycle. From the viewpoint of economy issues, it was found that the reactor power as well as burnup performance do not change much, even if the core height decreases from 10 m to 6 m, even as the construction cost is considerably reduced. Decreasing the core height also significantly decreases the amount of fuel pebbles required for loading into the core. For example, a 10-m-tall PBR core required approximately 380,000 pebbles in comparison to 230,000 pebbles for 6-m core. In the multi-pass cycle, the power density profile is flatter, resulting in a higher power density at the bottom region; thus, reducing the core height becomes infeasible due to the effects on the burnup profile. Regarding the temperature coefficient, the ROX fuel reactor had a negative temperature coefficient, required for the passive safety feature of the pebble bed reactor. 8. Conclusion The purpose of this study was to introduce the design concept of a small PBR with ROX fuel and optimize the ROX fuel composition, so that the reactor can achieve as high a burnup as possible without any failure of the spent fuel in a once-though OTTO cycle.
Criticality and core burnup calculations were performed by MCPBR code using the JENDL-4.0 nuclear data library. Results of the optimal cases show that we could design a 120-MWth OTTO cycle small pebble bed reactor that could achieve a high discharge burnup of 145 GWd/t-HM and a FIFA value of 75%. In this case, the velocity of fuel pebbles is approximately 1.1 cm/day together with 2-g heavy metal loading per pebble and 20% uranium enrichment. The total power in a pebble and the maximum power density must be less than 4.5 kW and 10 W/cm3, respectively, to keep the fuel temperature below 1600 °C, the limit of the reference PBMR design during normal operation and during a DLOFC transient. Furthermore, the core height can be reduced without any effect on the burnup profile. Reducing the core height will improve economic efficiency, not only in construction but also in normal operation. References Akie, H., Muromura, T., Takano, H., Matsuura, S., 1994. A new fuel material for once-through weapons plutonium burning. Nucl. Technol. 107, 182–189. Bende, E.E., 1999. Plutonium burning in a pebble-bed type high temperature nuclear reactor (Ph.D. thesis). Delft University of Technology, Netherlands. Boer, B., Kloosterman, J.L., Lathouwers, D., Van der Hagen, T.H.J.J., 2009. In-core fuel management optimization of pebble-bed reactors. Ann. Nucl. Energy 36, 1049– 1058. Ho, H.Q., Obara, T., 2015. Burnup performance of OTTO cycle pebble bed reactors with ROX fuel. Ann. Nucl. Energy 83, 1–7. Kadak, A.C., 2005. A future for nuclear energy: pebble bed reactors. Int. J. Crit. Infrastruct. 1 (4), 330–345. Kuramoto, K., Nitani, N., Yamashita, T., 2003. Durability test on irradiated rock-like oxide fuels. J. Nucl. Mater. 319, 180–187. Maki, J.T., 2009. AGR-1 Irradiation Experiment Test Plan. INL/EXT-05-00593. Idaho National Laboratory Report. Minoru, G., 2013. Conceptual design study of high temperature gas-cooled reactor for plutonium incineration. In: IAEA Deep Burn Technical Meeting. Nitani, N., Kuramoto, K., Nakano, Y., Yamashita, T., Kimura, Y., Nihei, Y., Ogawa, T., 2008. Fuel performance evaluation of rock-like oxide fuels. J. Nucl. Mater. 376, 88–97. Okumura, K., Nagaya, Y., Takamasa, M., 2006. MVP-BURN: Burnup Calculation Code Using a Continuous Energy Monte Carlo Code MVP. Japan Atomic Energy Agency, Japan. Setiadipura, T., Obara, T., 2014. Development of Monte Carlo-based pebble bed reactor fuel management code. Ann. Nucl. Energy 71, 313–321. Shibata, K., Iwamoto, O., Nakagawa, T., Iwamoto, N., Ichihara, A., Kunieda, S., Chiba, S., Furutaka, K., Otuka, N., Ohsawa, T., Murata, T., Matsunobu, H., Zukeran, A., Kamada, S., Katakura, J., 2011. JENDL-4.0: a new library for Nuclear Science and Engineering. J. Nucl. Sci. Technol. 48, 1–30. Terry, W.K., Gougar, H.D., Ougouag, A.M., 2002. Direct deterministic method for neutronics analysis and computation of asymptotic burnup distribution in a recirculating pebble-bed reactor. Ann. Nucl. Energy 29, 1345–1364. Tran, H.N., Kato, Y., 2009. An optimal loading principle of burnable poisons for an OTTO refueling scheme in pebble bed HTGR cores. Nucl. Eng. Des. 239, 2357– 2364. Tran, H.N., Kato, Y., Muto, Y., 2008. Optimization of burnable poison loading for HTGR cores with OTTO refueling. Nucl. Sci. Eng. 158, 264–271.
Contents lists available at ScienceDirect
Annals of Nuclear Energy journal homepage: www.elsevier.com/locate/anucene
Design concept for a small pebble bed reactor with ROX fuel Hai Quan Ho, Toru Obara ⇑ Research Laboratory for Nuclear Reactors, Tokyo Institute of Technology, 2-12-1-N1-19, Ookayama, Meguro-ku, Tokyo 152-8550, Japan
a r t i c l e
i n f o
Article history: Received 15 July 2015 Received in revised form 8 October 2015 Accepted 9 October 2015
Keywords: Pebble bed reactor Rock-like oxide fuel High burnup Power peak reduction Temperature coefficient
a b s t r a c t The conceptual design of a small rock-like oxide fuel pebble bed reactor with once-though-then-out (OTTO) cycle is proposed here. TRISO-coated particles based on AGR-1 design were used to achieve a target burnup larger than 100 GWd/t-HM without any failure of spent fuel. In the first step, optimization of fuel composition was implemented by cell calculations. After that, whole core calculations were performed with and without movement of the fuel pebbles. With a heavy metal amount of 2 g per pebble and 20% uranium enrichment, the pebble bed reactor with OTTO cycle could achieve maximum burnup of about 145 GWd/t-HM and fissions per initial fissile atom (FIFA) of 75%. The results show that the core height can be reduced due to the fact that the impact of bottom core on burnup performance is insignificant. Also, the peak power density of the reactor exceeded the limit of that for the PBMR design. Therefore, subsequent optimizations of the core design were carried out by decreasing the core height and reactor power to reduce the construction cost as well as the peak power density. A reactor with 6-m core height and 120-MWth reactor power was ultimately determined as the optimal design for a pebble bed reactor with ROX fuel. This optimal design also has a negative temperature coefficient, and the peak power density was less than the limit of 10 W/cm3. Ó 2015 Elsevier Ltd. All rights reserved.
1. Introduction Nuclear energy has been expected to play an important role in the future energy supply; however, it has to meet today’s higher safety standards. The pebble bed reactor (PBR), a kind of hightemperature gas-cooled reactor (HTGR), is one of the most promising reactors in the generation IV initiative. This type of reactor is claimed to be have excellent passive safety features because of its graphite-moderated, helium-cooled and tristructural-isotropic (TRISO) fuel particles (Kadak, 2005). Rock-like oxide (ROX) fuel has been studied at the Japan Atomic Energy Agency (JAEA) as a new once-through type fuel concept. With both mineral and ceramic properties, it is desired to improve the performance of the fuel elements not only in normal operation, but also for geological disposal without further reprocessing (Akie et al., 1994; Kuramoto et al., 2003; Nitani et al., 2008). Previous studies have been performed to access the potential of using ROX fuel in HTGRs. A clean burn high temperature gas-cooled reactor (CBHTR) that uses PuO2-YSZ fuel and thereby recovers spent Pu fuel from light water reactors has been under development at JAEA (Minoru, 2013). Other research (Ho and Obara, 2015) showed that UO2-YSZ fuel can be used in small PBRs ⇑ Corresponding author. Tel./fax: +81 3 5734 2380. E-mail address: [email protected] (T. Obara). http://dx.doi.org/10.1016/j.anucene.2015.10.007 0306-4549/Ó 2015 Elsevier Ltd. All rights reserved.
with high-discharge burnup even if the fissile density is five times lower than that of conventional UO2 fuel. The UO2-YSZ fuel also presents an advantage in comparison with the UO2 fuel as it has higher stability in the geological disposal of spent fuel without significantly reducing burnup performance. However, the previous study only showed the possibility of using ROX fuel in oncethrough-then-out (OTTO) cycle pebble bed reactor; optimization for burnup performance was not performed. The purpose of this study was to introduce the design concept for a small PBR with ROX fuel and to optimize the ROX fuel composition so that the reactor can achieve as high a burnup as possible without any failure of the spent fuel in the OTTO cycle. The power peak was set to less than the limit of the reference PBMR design to ensure that the reactor can be cooled by natural circulation and still survive in accident scenarios. In addition, an analysis of temperature coefficients was carried out to show the negative reactivity coefficient of the PBR with the UO2-YSZ fuel. 2. Optimization of fuel composition by cell calculations 2.1. Fuel design To satisfy the high burnup in a once-though fuel cycle, the PBR with ROX fuel should utilize the fuel designs that have been successful in high burnup irradiation tests. It was found that the
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AGR-1 (Maki, 2009) could achieve a high burnup without any observable failures up to approximately 200 GWd/t-HM. Therefore, this study used the AGR-1 fuel design for the calculations. The main parameters of the fuel pebbles and AGR-1 TRISO particles are presented in Table 1. This study utilized low-enriched uranium with a maximum 20% concentration of 235U. A single-phase UO2-YSZ fuel, consisting of 81.75 mol% YSZ (78.6 mol% ZrO2 + 21.4 mol% YO1.5) and 18.25 mol% UO2, was used as the fuel in the kernel, as in the previous study (Ho and Obara, 2015). 2.2. Methodology In the first step, cell calculations were implemented to estimate the optimal fuel composition that could be applied for further analyses in a PBR with the same fuel design as mentioned above. Random parking (RP) with a packing fraction of approximately 61% was chosen to distribute the fuel pebbles in the cell geometry. The cell geometry was surrounded by a reflective boundary condition. In order to determine the optimal fuel composition, the amount of heavy metal in each pebble (HM loading) and the enrichment of uranium were changed. The HM loading can be adjusted by changing the number of TRISO particles in the graphite matrix of the fuel pebble: the more TRISO particles, the greater the HM loading, with 4.5 g being the maximum HM loading for the ROX fuel, corresponding to a TRISO-coated fuel particle (CFP) volume-packing fraction of 40%. Criticality analyses were performed using a continuous-energy Monte Carlo code, namely MVP-BURN (Okumura et al., 2006), and the JENDL-4.0 nuclear data library (Shibata et al., 2011).
Fig. 1. Change of k1 in cell calculations for different enrichment in the case of 3-g HM loading.
2.3. Results The change of the infinite multiplication factor (k1) as a function of operation time in the case of 3-g HM loading with different uranium enrichments is shown in Fig. 1. It can be seen that higher uranium enrichment made k1 decrease to unity more slowly, and as a result the operation time could be longer. Figs. 2 and 3 illustrate the burnup and FIFA, respectively, as a function of HM loading and uranium enrichment when the k1 became unity in cell calculations. According to Fig. 2, the burnup decreased with decreasing uranium enrichment at the same amount of HM loading. The case of 3-g HM loading with 20% uranium enrichment gave the highest burnup of about 135 GWd/t-HM when k1 equaled one. As can be seen in Fig. 3, the FIFA was almost the same at the same amount of HM loading even if the enrichment of uranium was changed from 12% to 20%. However, the FIFA was reduced from about 75% to 65% when the amount HM loading increased from 1.5 to 4.5 g. This is because the moderator-tofuel-volume ratio decreased when the amount of HM loading increased from 1.5 to 4.5 g. Decreasing the moderator-to-fuelvolume ratio made the neutron spectrum shift to being harder. Table 1 Fuel designs. Properties
Unit
Value
Fuel pebble Pebble radius Thickness of fuel-free zone Density of carbon matrix
cm cm g/cm3
3.0 0.5 1.74
lm
350 6.55 C/C/SiC/C 100/40/35/40 1.10/1.85/3.20/1.85
Coated particles Kernel diameter Kernel density Coating materials Layer thicknesses Layer densities
g/cm3 – lm g/cm3
Fig. 2. Burnup in cell calculations for different enrichments and HM-loading schemes.
This made the fuel burnup less effective by increasing the amount of HM loading. The results at critical state showed that 20% of enriched uranium and about 2.5–3 g of HM loading was the optimal fuel composition in cell calculations, at which the burnup and FIFA could reach their highest values. Therefore, this composition will be used as a reference design for subsequent analyses in this study. 3. Optimization of fuel composition in a small PBR without movement of fuel pebbles In the actual reactor, the neutron leakage is very complicated due to the existence of the graphite reflector. Chapter 2 performed the burnup calculation of the fuel with the reflective boundary condition. It is difficult to determine the buckling properly without taking into account the neutron leakage. Therefore, this chapter carried out the burnup performance by whole core calculations with graphite reflector to estimate more properly neutron leakage effects. In the analysis, it is assumed that there was no movement of fuel pebbles in the core during operation.
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Fig. 3. FIFA in cell calculations for different enrichments and HM-loading schemes.
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Fig. 4. Burnup in PBR without movement of fuel balls.
3.1. Reactor design In this chapter, the PBR geometry in a previous paper (Ho and Obara, 2015) was chosen and modeled. The 300-MWth core, 10 m in height and 3 m in diameter, was surrounded by a 1-m-thick graphite reflector with a 1-m-high void on top. The main parameters of PBR design are given in Table 2. The fuel pebbles were poured into the active core and stood stationary during operation. 3.2. Methodology The optimization procedure was similar to the cell calculations, in which the HM loading and the enrichment of uranium were changed to determine the maximum burnup and the FIFA. As suggested from the cell calculations, the HM loading and uranium enrichment in this analysis were changed in a smaller range, 2–4 g for HM loading and 16–20% for fuel enrichment. Criticality analyses were also performed using MVP-BURN code with a JENDL-4.0 nuclear data library. In the initial condition, the effective multiplication factor (keff) was more than unity and gradually decreased by burnup. The burnup and FIFA values when the reactor reached critical condition (keff = 1) were estimated. 3.3. Results Figs. 4 and 5 show the burnup and FIFA values by the whole core calculations without movement of the fuel pebbles as a function of HM loading and fuel enrichment, respectively. As in the previous cell calculations, the burnup and FIFA were decreased when the uranium enrichment decreased at the same amount of HM loading. Based on these figures, it is possible to achieve a high burnup and FIFA value of about 100 GWd/t-HM and 45%,
Table 2 Design parameters of reactor. Properties
Unit
Value
Thermal power Average power density Graphite reflector density Coolant Core temperature Number of fuel balls Packing fraction of pebble balls
MWth W/cm3 g/cm3 – K – –
300 4.24 1.74 Helium 1000 380,000 0.61
Fig. 5. FIFA in PBR without movement of fuel balls.
respectively, when the HM loading was about 3–3.5 g with 20% uranium enrichment. It can be seen that there was a small difference from the results by cell calculations. By the whole core calculation we could obtain a better composition to maximize the burnup and FIFA value. 4. Optimization of fuel composition in a small PBR with movement of fuel pebbles by adopting the OTTO cycle The analyses for whole core geometry were performed assuming the movement of fuel pebbles; the fuel pebbles were assumed to move from the top to the bottom of the core in the OTTO fuel cycle. The reactor core was based on the PBR geometry described in chapter 3 and utilized the fuel design described in chapter 2. 4.1. Methodology A Monte Carlo-based pebble bed reactor (MCPBR) code (Setiadipura and Obara, 2014) was used to calculate the burnup of the fuel pebbles when they moved uniformly through the core with constant velocity. In the MCPBR code, a burnup calculation
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Table 3 Burnup performance for 3-g HM loading in a fuel ball. Case
1
2
3
4
5
6
Uranium enrichment [%] Residence time of fuel balls [days]
20 762
20 648
20 496
17 496
17 476
16 476
keff Discharge burnup [GWd/t-HM] FIMA [%] FIFA [%] Peak pebble power [KW]
0.928 200 20.7 103.6 8.1
0.996 170 17.7 88.4 6.1
1.092 130 13.4 66.8 3.9
1.014 130 13.5 79.5 4.7
1.025 125 13.0 76.7 4.3
0.996 125 13.0 81.3 4.6
based on a continuous-energy Monte Carlo MVP-BURN code was coupled with an additional utility code to be able to simulate the OTTO cycle of PBRs. The JENDL-4.0 nuclear data library was used for the analysis. In previous study (Terry et al., 2002), the impact on fuel burnup was investigated by considering two velocity profiles of the pebbles. There were a uniform profile and a parabolic profile. The multi-pass scheme was used for refuelling, in which the pebbles were reintroduced repeatedly into the same radial position (channeling recirculation) and therefore the results can be preliminarily applied for the OTTO cycle. The results showed that although the maximum burnup for parabolic velocity profile was larger than that for uniform velocity profile; the average burnup was almost the same for both the velocity profiles. As a result, the radial fuel speed can give a small impact from the viewpoint of average burnup of the discharged fuel. The main interest of this study is to investigate the average burnup of the fuel. Therefore, the flow speed through the core is assumed to be radially uniform in the study. In the previous optimizations, only HM loading and uranium enrichment were changed. In this case, however, the procedure became more complicated since the burnup performance can be changed by simultaneous adjustment of three parameters, including HM loading, uranium enrichment and fuel pebble velocity. Hence, to simplify the optimization procedure, the first step was carried out with a constant 3-g HM loading in the fuel pebble, changing only the uranium enrichment and pebble velocity. From chapter 2 and 3 it was found that a maximum of 20% uranium enrichment is expected to provide high burnup as well as high FIFA. Therefore, the optimization started with the maximum uranium enrichment of 20% and then decreased the enrichment stepwise. The calculated conditions of several cases for the PBR with 3-g HM loading in a pebble, at different pebble velocities (corresponding to discharge burnup) and uranium enrichments, are shown in Table 3. In cases 1, 2 and 3, a maximum 20% of uranium enrichment was used to determine the maximum discharge burnup, in which the reactor could become critical at equilibrium conditions. The remaining analyses (cases 4, 5 and 6) with lower enrichment of uranium were then performed to find the highest FIFA value. After determining the optimal fuel composition for the PBR with 3-g HM loading in a pebble, the same procedures were implemented for different amounts of HM loading, from 1.5 to 4.5 g. In this study, the reactor power was set at 300 MWth. At the initial condition, the active core was filled by fresh fuel pebbles. The calculation was started from the initial condition until the neutron flux and nuclide density reached equilibrium, where the keff, discharge burnup and FIFA were estimated.
Table 3. The reactor could not reach criticality when the discharge burnup was larger than 130 GWd/t-HM, even if the enrichment of uranium was set to a maximum of 20%. Case 4 was implemented with the same discharge burnup of 130 GWd/t-HM, but with lower uranium enrichment than in case 3. From Table 3, a lower enrichment of uranium, with the same discharge burnup, gave a higher FIFA value as well as a higher peak pebble power (maximum power of a pebble in the core). For example, the FIFA value and peak pebble power (in cases 3 and 4) increased from 66.8% to 79.5% and 3.9 to 4.7 KW, respectively, if the fuel enrichment decreased from 20% to 17%. Because, to produce the same discharge burnup at the same power, the reactors in cases 3 and 4 had to have almost the same number of fission reactions. The fuel enrichment in case 4 was lower than that in case 3; this required the FIFA in case 4 to be higher than that in case 3 to produce the same number of fission reactions. It also can be seen that case 4, with 17% of fuel enrichment, yielded the highest burnup of 130 GWd/t-HM and the highest FIFA of 79.5%. However, case 4 could not be accepted due to the fact that the peak pebble power should be less than the limit of 4.5 kW to maintain the integrity of the fuel pebbles during operation (Bende, 1999). Only case 3 and 5 could be satisfied with the peak pebble power limit. Therefore, when considering both the discharge burnup and FIFA factors between cases 3 and 5, case 5 was considered the optimal fuel composition for 3-g HM loading, with a discharge burnup of 125 GWd/t-HM and a FIFA of 76.7%. Fig. 6 shows a comparison of the axial power density in the center core for various fuel compositions in the case of 3-g HM loading. It can be seen that, as is generally true for OTTO cycle pebble bed reactors, the peak power density appears at the top region, while it becomes very small at the bottom of the core.
4.2. Results The analysis results in the case of 3-g HM loading with different uranium enrichments and different residence times are shown in
Fig. 6. Axial power density profile at center of the OTTO PBRs for the same 3-g HM loading scheme.
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Fig. 7. Power density distribution (a) and thermal neutron flux (b) in the OTTO PBR with 3-g HM loading and 17% uranium enrichment.
Case 1 produced the highest peak power density because of its highest discharge burnup while the optimal case 5 gave about 23 W/cm3 in peak power density. Fig. 7a shows the power density distribution in the optimal reactor (case 5) in case of 3 g HM loading per pebble. The peak power density appeared at the top region, because fresh fuel pebbles were deposited onto the top of the core and the spent fuel pebbles were discharged from the bottom of the core during operation. Fig. 7b shows the thermal neutron flux (E < 1.86 eV) distribution in the core. The variations were similar to the power density profile, since the reaction rate was mainly attributed to the thermal flux. It can be seen that the power density peaks (corresponding to thermal flux peaks) at the top of the core appeared adjacent to inner core and side reflector regions. The reflection of thermal neutron flux at side reflector is the reason for the increase of power density in this region. The radial thermal flux gradually became flat when the fuel pebbles moving to bottom core, because the bottom region contained the pebbles with a very low fissile content. After finishing optimization of the fuel composition for the PBR with 3-g HM loading in a pebble, the same procedures were implemented while changing the HM loading from 1.5 to 4.5 g. The optimization results for these other HM-loading schemes are summarized in Table 4. In case of 1.5-g HM loading with 19% uranium enrichment, the reactor could achieve a discharge burnup of 120 GWd/t-HM with a FIFA of about 66%. The reactor with 4.5-g HM loading per pebble, in fact, could give a higher burnup value than 110 GWd/t-HM as shown in Table 4. However, the peak pebble power exceeded the limit of 4.5 KW if the discharge burnup was larger than 110 GWd/t-HM. Table 4 also shows that most of the cases had almost the same FIFA value, with 2-g HM loading giving the highest discharge burnup value, approximately Table 4 Burnup performance for different HM-loading schemes per fuel ball. HM loading [g] Uranium enrichment [%] Residence time of fuel balls [days]
1.5 19 229
2 20 369
3 17 476
3.5 16 534
4.5 15 629
keff Max. discharge burnup [GWd/t-HM] FIMA [%] FIFA [%] Peak pebble power [KW]
1.028 120 12.6 66.1 3.7
1.027 145 15.1 75.7 4.5
1.025 125 13.0 76.7 4.3
1.016 120 12.5 77.9 4.4
1.010 110 11.5 76.5 4.4
Fig. 8. Axial power density profile at the center of the reactors for various fuel compositions.
145 GWd/t-HM. Therefore, from the viewpoint of discharge burnup and actinides transmutation, 2-g HM loading per pebble with 20% uranium enrichment was the optimal fuel composition for a PBR utilizing the UO2-ROX fuel. Fig. 8 illustrates the power density profile at the center of the optimal reactors for each HM-loading scheme per fuel pebble. The power density profiles were nearly identical for all reactors, with a peak power density of about 25 W/cm3. This value was far beyond the power peak limit for PBMR design of 10 W/cm3. Therefore, in the next section, optimization was performed to reduce this peak power density to below the limit. Thermal (E < 1.86 eV) and fast (E > 0.1 MeV) neutron flux profiles are shown in Fig. 9. The fast neutron flux in the axial direction does not vary between the alternative cases, while differences in the thermal neutron flux can easily be observed: the lower HM loading produced significantly larger thermal neutron flux at the top region of the active core. Because, the reactors with the same power produce equal number of fission reactions. A reactor with lower (higher) fissile density had higher (lower) thermal neutron flux to generate the same power level. As a result, the thermal
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Fig. 9. Axial neutron flux profile (average) in the reactors for various fuel compositions: (a) thermal neutron flux; (b) fast neutron flux.
Table 5 Burnup performance of reactors with different core heights. Core height [cm]
300
400
500
600
1000
Discharge burnup [GWd/t-HM] Residence time [days] keff FIMA [%] FIFA [%] Max. power density [W/cm3]
145 111 0.960 15.1 75.7 26.9
145 147 0.985 15.1 75.5 25.3
145 184 0.997 15.1 75.6 24.4
145 221 1.003 15.1 75.4 24.4
145 369 1.027 15.1 75.7 23.0
neutron flux was largest for 1.5-g HM loading, whereas it became smallest for 4.5-g HM loading. 5. Optimization of the core designs In previous sections, optimization of the fuel composition was performed. The results showed that the core height could be reduced since the impact of the bottom core on burnup performance proved insignificant. Also, the peak power density of the reactor exceeded the limit of that for PBMR design. Hence, in this section, further optimization of core designs will be carried out by changing the core height and reactor power to reduce the construction cost as well as the peak power density. 5.1. Optimization of core height As can be clearly seen from Figs. 8 and 9, the power density and neutron flux at the bottom of the core were very small. Therefore, the impact of the bottom core on burnup performance was insignificant; as a result, it was deduced that the core height could be reduced without changing the burnup performance at equilibrium state. The optimal core in Section 4.2, with 2-g HM loading and 20% uranium enrichment, was used to investigate the effect on burnup performance when changing the core height. The pebble velocity remained constant to achieve the same discharge burnup of 145 GWd/t-HM as before. Table 5 shows the burnup performance results when the core height changed from 3 m to 10 m. According to this table, the reactors could be critical if the core height was greater than 6 m whereas it became subcritical for reactors with a core height of 5 m or less. This phenomenon can be explained from the power density and thermal neutron flux distribution in Fig. 10. In the
cases of PBRs with 65 m core height, the power density and neutron flux were fairly significant at the bottom region. This means that in these cases, the neutron flux in both the top and bottom regions contributed to the criticality of the reactors. Hence, the neutron flux in the top region itself could not make the reactor critical without the bottom region. Conversely, in the case of reactors with core heights of 6 m or more, due to the very small neutron flux and power density at the bottom region, reducing the core height did not decrease the neutron flux greatly; therefore, the reactor could be critical without the bottom region. Table 5 also shows that the main reactor physical parameters were not changed even if the core height decreased from 10 m to 6 m. Reducing the core height also decreased the number of pebbles loaded into the core. For example, a PBR with 10-m core height required approximately 380,000 pebbles in comparison to 230,000 pebbles in the PBR with 6-m core height.
5.2. Power peak reduction Previous studies show that although the effects of a DLOFC accident are limited by the negative reactivity feedback and the capability of the reactor to transfer the decay heat from the core, fuel temperatures are considerably higher compared to normal operating conditions. With the peak power density larger than 10 W/cm3, the fuel temperature in a PBMR can exceed the temperature limit of 1600 °C in a depressurization accident (Boer et al., 2009; Tran and Kato, 2009; Tran et al., 2008). Therefore, in this study the maximum power density was set to less than 10 W/cm3, to keep the fuel temperature below the maximum permissible temperature of the reference PBMR design during normal operation and during a DLOFC transient. For the previous optimal reactor in Section 5.1, the peak power density was approximately 24.4 W/cm3, about 2.5 orders larger than limit. Hence, in order to reduce the peak power density, the reactor power was decreased from 300 to 120 MW as presented in Table 6. The pebble velocity was also decreased, which resulted in an extended residence time of the fuel, to maintain the discharge burnup target and uranium transmutation ratio. The maximum power density could be reduced to 9.6 W/cm3 when the reactor power was set to 120 MW. Fig. 11 presents the power density distribution and thermal neutron flux for ultimately optimal core. It can be seen that the final optimal core gave a high burnup of
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Fig. 10. Axial power density profile (a) and axial thermal neutron flux profile (b) in 300-MWth reactors with various core heights.
Table 6 Burnup performance of 6-m-core-height reactors with different powers.
Table 7 Temperature coefficients for optimal reactor design.
Reactor power [MWth]
300
200
150
120
Temperature [K]
Temperature coefficient [pcm/K]
Discharge burnup [GWd/t-HM] Residence time [days] keff FIMA [%] FIFA [%] Max. power density [W/cm3]
145 221 1.003 15.1 75.4 24.4
145 332 1.006 15.1 75.6 16.1
145 442 1.005 15.1 75.5 12.1
145 553 1.007 15.1 75.4 9.6
300–400 600–700 900–1000
16.5 6.6 5.2
145 GWd/t-HM along with keeping the peak power density smaller than limit of 10 W/cm3. 6. Temperature coefficient In general, a change in the temperature leads to a change in multiplication factor and thereby alters the reactivity of the system. This effect should be thoroughly considered as it has an important bearing on the operation of a reactor, and ultimately on the safety of the system. For thermal reactors in general and
PBRs in particular, the negative temperature coefficient is a required parameter to ensure stability during both normal operation and accident conditions. This analysis estimated the temperature coefficient for the ultimately optimal core in Section 5.2 with 6 m in core height and 120 MW in reactor power. The core composition at equilibrium state was used to calculate the keff by changing the core (fuel and moderator) and reflector temperature from 300 K to 1000 K. Table 7 demonstrates the negative temperature coefficient for the optimal reactor design. Furthermore, the temperature coefficient became more negative with a decreasing core temperature.
Fig. 11. Power density distribution (a) and thermal neutron flux (b) in ultimately optimal PBR with 120-MWth power.
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7. Discussion An analysis for cell calculation was performed to determine the optimal fuel composition. The highest 20% enrichment of uranium with 3-g HM loading in a pebble could give a discharge burnup of about 135 GWd/t-HM and FIFA of 75%. This means that even if the ROX fuel has low fissile density, the UO2-ROX fuel PBR can be expected to achieve high burnup when fuel with high uranium enrichment is used. By adopting OTTO fuel management for the fuel pebbles, the reactor could achieve higher burnup and FIFA values. For example, 2-g HM loading in a pebble and 20% of uranium enrichment gave a discharge burnup of 145 GWd/t-HM and a FIFA of 75% in the optimal case. However, the OTTO cycle made the power density shift to the top region of the core, and as a result, the peak power density became quite high, about 24.4 W/cm3. This value was far beyond the power peak limit for PBMR design of 10 W/cm3. The peak in the power profile can be reduced to 9.6 W/cm3 if the reactor power decreases from 300 MW to 120 MW. Therefore, if the power peak is to remain below 10 W/cm3, a further increase of the reactor power is unattractive for OTTO fuel management. In case of multi-pass fuel management, the reactor power can be increased, as the axial power density is flattened and the power peak is reduced compared to a PBR with OTTO fuel cycle. However, a PBR with a multi-pass cycle may not achieve as high a burnup as a PBR with an OTTO fuel cycle. From the viewpoint of economy issues, it was found that the reactor power as well as burnup performance do not change much, even if the core height decreases from 10 m to 6 m, even as the construction cost is considerably reduced. Decreasing the core height also significantly decreases the amount of fuel pebbles required for loading into the core. For example, a 10-m-tall PBR core required approximately 380,000 pebbles in comparison to 230,000 pebbles for 6-m core. In the multi-pass cycle, the power density profile is flatter, resulting in a higher power density at the bottom region; thus, reducing the core height becomes infeasible due to the effects on the burnup profile. Regarding the temperature coefficient, the ROX fuel reactor had a negative temperature coefficient, required for the passive safety feature of the pebble bed reactor. 8. Conclusion The purpose of this study was to introduce the design concept of a small PBR with ROX fuel and optimize the ROX fuel composition, so that the reactor can achieve as high a burnup as possible without any failure of the spent fuel in a once-though OTTO cycle.
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