Thorium utilization in a small and long-life HTR Part III: Composite-rod fuel block

Transcription

1 Thorium utilization in a small and long-life HTR Part III: Composite-rod fuel block Jacques Verrue a,b, Ming Ding b, Jan Leen Kloosterman b a Ecole polytechnique (member of ParisTech), Palaiseau Cedex, France b Delft University of Technology, Mekelweg 15, 2629JB Delft, The Netherlands Abstract The U-Battery is a small long-life high temperature gas-cooled reactor (HTR). In order to increase its lifetime and diminish its reactivity swing, this paper presents the neutronic performances of a fuel block with uranium and thorium in the form of composite rods. In composite-rod fuel block, each fuel compact is made out of either uranium or thorium TRISO particles, and the compacts are assembled in fuel rods. This type of fuel features a specic axial separation between thorium and uranium compacts, which gives more design exibility. The design parameters, investigated by SCALE 6, include the number and spatial distribution of fuel compacts within the rods, the enrichment of uranium, the radii of fuel kernels and fuel compacts and the packing fractions of UO 2 and ThO 2 TRISO particles. A lower moderation ratio and a larger inventory of heavy metal results in a lower reactivity swing. The optimal carbon-to-heavy metal ratio depends on the mass fraction of U-235 and is commonly in the range. The spatial distribution of the fuel compacts within the fuel rods has a great inuence on the energy spectrum in each fuel compact and thus on the beginning-of-life reactivity and the reactivity swing. At end of life, the dierences are smaller due to the ssions of U-233, produced from transmutation of Th-232. It enables to design fuel blocks with very small reactivity swing, down to less than 4% in a 10-year lifetime. Among all types of thorium fuelled U-Battery blocks, the composite-rod fuel block achieves the highest end-of-life reactivity and the lowest reactivity swing. Keywords: Thorium-fuelled reactors, neutronic features, small and long-life reactors, prismatic HTR, U-Battery Preprint submitted to Nuclear Engineering and Design July 22, 2011

2 1. Introduction From the mid 1950s to the mid 1980s, thorium has been tested in HTRs (AVR and THTR in Germany, Fort St Vrain in the USA) in the form of (Th,U)O 2 or (Th,U)C 2. Interest in thorium had several explanations. First, its natural abundance (three to four times as much as uranium) makes it an attractive alternative to uranium resources. Moreover, thorium is not a ssile element but transmutation of Th-232 into ssile U-233 is ecient in thermal and epithermal reactors. Finally, U-233 is considered as the best ssile isotope among U-233, U-235 and Pu-239 in thermal and epithermal spectrum as regards its neutronic properties. Indeed, the number of released neutrons per absorbed neutron,, is 10 to 20% higher than those of U-235 and Pu-239. Since then, thorium has been a matter of interest to support the worldwide development of nuclear energy. Its use is investigated as well in HTRs or molten salt reactors as in water-cooled reactors. In order to extend the potential of thorium and put its breeding capacity in thermal and epithermal spectrum to good use, this paper investigates the neutronic performances of thorium as a nuclear fuel of the U-Battery, which is a 20 MWth long-life block-type HTR. The second part of the paper briey describes the structure of fuel blocks with composite rods. The third part investigates the number of UO 2 fuel compacts. The fourth part discusses the enrichment. The fth part presents a parametric analysis of composite-rod fuel blocks as regards the geometric parameters. The sixth part studies the inuence of the proportion of thorium. The seven part analyses the spatial distribution of UO 2 fuel compacts. The eighth part checks the temperature coecient of reactivity and the ninth part compares the composite-rod fuel block with two other thorium-fuelled U-Battery blocks. 2. Description of the composite-rod fuel block Figure 1 shows a schematic diagram of a U-Battery block fuelled with composite rods (a) and a single composite rod (b). The U-Battery fuel block comprises 216 fuel channels, including 6 xed burnable poison channels which may be lled with fuel. Every fuel channel is lled with 15 fuel compacts, the group of which is called a fuel rod. The fuel compacts are composed of either ThO 2 or UO 2 TRISO particles and assembled in fuel rods according to a given pattern. Moreover, in order to simplify the pattern of fuel blocks, it is assumed that all fuel rods are identical, as shown in Fig. 1 (a). The 2

3 axial and fuel compact-level separation between uranium and thorium is the specicity of this type of fuel block. The spatial distribution of the fuel compacts in a fuel rod is a specic parameter of composite-rod fuel blocks. It determines the number of uranium and thorium fuel compacts in the fuel block and their locations. The locations of uranium and thorium fuel compacts in a fuel rod is sometimes called pattern. Because a composite fuel rod contains 15 fuel compacts, a list of 15 letters is used to represent it. Each letter stands for one fuel compact and the rst letter corresponds to the bottom 1 fuel compact. For instance, the sequence UUTUUTTTTTTTTTT plotted in Fig. 1 indicates that fuel rods are composed of 4 uranium fuel compacts and 11 thorium fuel compacts; starting from the bottom, there are two uranium fuel compacts, one thorium fuel compact, two uranium fuel compacts and ten thorium fuel compacts. Figure 1: 3D schematic diagram of a fuel block with composite rods (a) and one single fuel rod (b). The spatial distribution of the fuel compacts in the rods is UUTU- UTTTTTTTTTT. The number of UO 2 fuel compacts per rod, one composition parameter, ve geometric parameters and the spatial distribution of fuel compacts were 1 This may inuence further investigations, especially when neutronics is coupled with thermal-hydraulics. As regards our neutronic-only approach, calculations showed that the situation was perfectly symmetric between top and bottom. 3

4 Table 1: Reference values of the investigation parameters. Parameter Reference value Number of UO 2 fuel compacts (n UO2 ) 4 Enrichment of uranium (E) 20% Radius of fuel compacts (R) cm Radius of UO 2 kernels (r U ) cm Radius of ThO 2 kernels (r T ) cm UO 2 TRISO particles packing fraction (PFU) ThO 2 TRISO particles packing fraction (PFT) Thorium mass fraction 82.74% Spatial distribution TTTTTTTTTTTUUUU investigated in order to analyse the neutronic performances of composite-rod fuel blocks. The mass fraction of thorium is investigated as well. Although this parameter is not independent from the others, its investigation shows the benets of adding thorium in the fuel block, with respect to the U-Battery low-enriched uranium (LEU) reference fuel block [1]. All the investigation parameters and their reference values are presented in Table 1. A set of values for these parameters is called a conguration. When all parameters are equal to their references values, the fuel block is called reference conguration. During parametric investigations, by default and unless something else is mentioned, the parameters are equal to their reference values. All calculations were performed on a single fuel block with reective boundary conditions and implemented in the TRITON module of SCALE 6 [2]. This module mainly calls four function modules. BONAMI and CENTRM process the resonance cross-sections of the material and cells. KENO-VI is a 3D Monte Carlo criticality code and provides the innite multiplication factor of the fuel blocks. Finally, ORIGEN-S performs point depletion calculation. The temperature of all material is 300 K and the upper boundary of the thermal energy domain is 3 ev. Unless anything else is mentioned, the uncertainty of the k calculations is lower than Number of UO 2 fuel compacts The number of UO 2 fuel compacts (n UO2 ) acts both as a geometric and as a composition parameter for it changes the volume allocated to each fuel type (uranium or thorium), the masses of heavy metals in the fuel block and 4

5 the mass fraction of thorium. In this section only, parameter values of uranium and thorium fuel compacts are the same and correspond to reference design values of the U-Battery. The enrichment of uranium is 12%, the radii of uranium and thorium fuel kernels are cm, both packing fractions are 0.3 and the radius of fuel compacts is cm [1]. As well, the density dierence between UO 2 and ThO 2 is neglected so that replacing a UO 2 fuel compact by a ThO 2 fuel compact would not change the total mass of heavy metal nor the moderation (or carbon-to-heavy metal) ratio N C =N HM. All uranium fuel compacts are at the top end of rods and all thorium fuel compacts at the bottom end of rods, as it is in the reference conguration. The dierence is that there are more or less uranium and thorium fuel compacts. Figure 2: k at BOL and EOL as a function of the number of UO 2 fuel compacts per rod and as a function of the total mass of U-235 in the fuel block. Figure 2 shows the innite multiplication factor as a function of the number of UO 2 fuel compacts per rod, at beginning of life (BOL) and after 10 eective full power years (EFPYs), which is the end of life (EOL). The top axis indicates the corresponding mass of U-235 in the fuel block. k mainly increases with n UO2. When the number of UO 2 fuel compacts is less than 5

6 7, which corresponds to a U-235 mass of 486 g, the fuel block is sub-critical at EOL because there are not enough ssile isotopes. Moreover, the neutron mean free path has the same order of magnitude than the characteristic length of a fuel compact. Thus, a small number of UO 2 fuel compacts increases the leakage probability of neutrons from UO 2 regions. As thorium has a higher capture cross-section than U-238 at thermal energies, the required initial mass of ssile material is higher. The conguration with n UO2 = 2 is an interesting case because the total mass of ssile isotopes is the same at BOL and at EOL. Yet the reactivity increases. This is because the ssile isotope amount at EOL includes U- 233, which has the best neutronic properties among all ssile isotopes. It especially releases more neutrons than U-235 when ssioned, so has a higher and leads to a higher k. This is conrmed by the high proportion of U-233 in the fuel block, as shown in the bottom subgure of Fig. 3. When n UO2 increases, there is more uranium and less thorium in the fuel block. It leads to an increase of k at BOL because of more ssile material. It also leads to an increase of reactivity swing, because the decrease of k with time is less counterbalanced by the increase of as there is less thorium. The reactivity swing is dened as follows: k = kbol k EOL k BOL The top and bottom subgures of Fig. 3 respectively show the conversion ratios of dierent regions and the mass fractions of ssile isotopes in the fuel block as a function of the number of UO 2 fuel compacts per rod. The top axis gives the corresponding mass of U-235 in the fuel block. According to the top subgure of Fig. 3, the conversion ratio of the whole fuel block behaves like that of the thorium region when there are few UO 2 fuel compacts and like that of the uranium region when there are few ThO 2 fuel compacts. Since Th-232 has a larger radiative capture cross-section than U-238 in the thermal energy domain, the total conversion ratio increases while n UO2 decreases. When n UO2 is low, the total conversion ratio is high as well as the mass fraction of U-233, as respectively indicated in the top and bottom subgure of Fig. 3. This shows that ssions of U-233 dominate the ssion reactions in the fuel block. Given that thorium is in excess with respect to uranium, this is why k EOL is almost constant when there is less than 3 UO 2 fuel compacts. On the contrary, when n UO2 is high, the mass fraction of U-233 is very low, the 6

7 Figure 3: Conversion ratio (top) and mass fractions of ssile isotopes (bottom) at EOL as a function of the number of UO 2 fuel compacts per rod and as a function of the total mass of U

8 mass fraction of U-235 is high and the total conversion ratio is low. The chain reaction is mostly supported by U-235 and U-238 Pu. 4. Enrichment of uranium The enrichment of uranium is another eective parameter to adjust the criticality of the fuel block. The two following methods of increasing the enrichment were considered: (a) The initial mass of uranium and the initial mass of thorium are constant. This is the classic way of increasing the enrichment, since U-238 is replaced by U-235. In this method, the ratio of ssile isotopes to heavy metal (also called eective enrichment) increases with the enrichment. (b) The initial mass of U-235 is constant. Thus, increasing the enrichment means loading less U-238. So the packing fraction of UO 2 TRISO particles diminishes while the enrichment increases. To keep the total mass of heavy metal constant, the packing fraction of ThO 2 TRISO particles must increase. In short, increasing the enrichment is done by replacing U-238 by Th-232, so that the initial masses of ssile and fertile material are constant. Therefore, the eective enrichment is constant. Both methods keep the total mass of heavy metal constant, as well as the moderation ratio N C =N HM. The innite multiplication factor as a function of the enrichment of uranium is plotted in Fig. 4, respectively in subgures (a) and (b) for methods (a) and (b). In Fig. 4 (a), because of the replacement of fertile by ssile material, the innite multiplication factor increases with the enrichment both at BOL and EOL. When the enrichment is greater than 12%, the reactivity swing becomes positive, reaches a maximum at about 20% and slightly decreases while the enrichment increases. Yet from 12%, the reactivity swing is in the narrow 1-3% range. Thus, the classic enrichment is an ecient way to change the level of reactivity without changing the reactivity swing, although low enriched uranium has a maximum authorised U-235 mass fraction of 20%. In Fig. 4 (b), k BOL still increases but less than in the previous case; on the contrary, k EOL is almost steady. This conrms that k BOL increases with the enrichment of uranium but shows that k EOL mainly increases with the mass of U-235 and not with the enrichment alone. Indeed, if the mass of U-235 is constant, it even decreases from 60%. This slight decrease is due to 8

9 Figure 4: Innite multiplication factor as a function of the enrichment of uranium. The total mass of heavy metal is constant. (a): the total mass of uranium (U U-238) is constant. (b): the mass of U-235 and the total mass of fertile material (U Th-232) are constant. 9

10 a concentration eect. Since U-238 is replaced by Th-232 without changing the spatial distribution of fuel compacts, there is more thorium in thorium fuel compacts and less uranium in uranium fuel compacts. Therefore, the increase of enrichment goes along with an increase of absorption in thorium fuel compacts and a lower resonance escape probability in the fuel block. This is why k EOL decreases and k BOL increases less than in the rst case, although in this case, there is enough U-235 to keep the fuel block critical during at least 10 EFPYs. Moreover, Fig. 4 (b) shows that replacing U-238 by Th-232 as a fertile material makes the reactivity of the fuel block higher at BOL. This is because of Th-232 lower absorption resonance integral compared to that of U-238. In another way, U-238 can be used instead of thorium as a kind of neutronic poison to diminish the initial reactivity along with supporting end-of-life reactivity through transmutation into Pu-239. Nevertheless, the plutonium cycle has many drawbacks that the thorium one does not have as regards proliferation, recycling or waste disposal. Figure 5: Ratio of the mass of ssile isotopes at EOL to that at BOL (left) and reactivity swing (right) as a function of the enrichment of uranium. 10

11 Considering the set of parameters of method (a) (total mass of heavy metals constant, U-235 replaced by U-238), Fig. 5 shows the ratio of the mass of ssile isotopes at EOL to that at BOL and the reactivity swing of the fuel block as a function of the enrichment. The reactivity swing has already been discussed. When the enrichment is low, the mass ratio is greater than one as there are very few ssile isotopes at BOL and U-233 is generated as the burnup increases. Then, the mass ratio decreases with the increase of enrichment, i.e. with the increase of the initial mass of ssile U-235. After 20%, the mass ratio slightly increases again; with the increase of enrichment, the remaining mass of U-235, m 25, becomes the most signicant term of the ratio (m 25 + m 23 + m 49 + m 41 )=m fis (where m ij is the mass of the ssile isotope such that i is the last digit of the number of protons and j the last digit of the number of neutrons). The remaining mass fraction of U-235 increases while the enrichment increases. About 30% of U-235 is still in the fuel block at EOL when the enrichment is 20%, whereas this fraction rises up to about 70% when the enrichment is 95%. In thorium fuelled blocks, the role of U-235 is to ignite the chain reaction in the fuel block. Thus, for neutronic and economic reasons, U-235 should be burnt up as much as possible. This is the case when the enrichment is low. Therefore, a balance must be found between the need of ssile material and the maximum burnup of U Geometric parameters of fuel compacts Since uranium and thorium are located in separate fuel compacts, the radii of fuel kernels and the packing fractions of each type of fuel compacts are independent. The radius of fuel compacts is assumed to be the same for both types, otherwise the geometry and design of fuel rods would be too complex. Table 2 shows the ve investigated geometric parameters and their variation ranges. Only one parameter is changed at a time, the others being equal to their reference values. While investigating the radii of fuel kernels, the thicknesses of coating layers keep constant Radius of fuel compacts The radii of uranium and thorium fuel compacts are identical so that the shape of the fuel rods remains cylindrical. Since the packing fractions are constant, increasing the radius of fuel compacts means loading more uranium 11

12 Table 2: Ranges of investigation for geometric parameters. Parameter Change range N C =N HM Radius of fuel compacts (R) 0.4{0.75 cm 443.2{119.7 Radius of UO 2 kernels (r U ) 0.01{0.06 cm 205.6{140.5 UO 2 packing fraction (PFU) 0.1{ {156.0 Radius of ThO 2 kernels (r T ) 0.01{0.06 cm 671.2{129.3 ThO 2 packing fraction (PFT) 0.1{ {114.5 and thorium in the fuel block. Thus, the moderation ratio N C =N HM decreases as the radius increases. The radius of fuel compacts is not the only parameter that controls the moderation ratio. Indeed, increasing the packing fractions of UO 2 and ThO 2 TRISO particles also makes N C =N HM decrease. These two ways of changing the moderation ratio are compared in Fig. 6, which shows k as a function of N C =N HM. The solid curve is the calculation results with dierent fuel compact radii and constant packing fractions. The open dots are calculated with dierent packing fractions and a constant fuel compact radius. These two series of curves roughly have the same behaviour. Thus, changing the moderation ratio using the fuel compact radius or the packing fractions of UO 2 and ThO 2 TRISO particles hardly makes a dierence. There is only a small deviation however, especially at BOL. This deviation is due to the double heterogeneous eect. Like in all HTRs, U-Battery fuel blocks have two levels of heterogeneity. The rst level lies in the distribution of the TRISO particles inside the fuel compacts. The second level is related to the lattice of fuel compacts in fuel blocks. The radius of fuel compacts aects the second level of heterogeneity. The double heterogeneous eect is less important at EOL because the self-shielding of fuel compacts decreases with burnup. Indeed, the outer part of the fuel compacts, which shield the inner part from resonance energy neutrons, are depleted while burnup increases. There is only a narrow range of moderation ratios, from 160 to 195, which ensure criticality of the fuel block at EOL. This range corresponds to a range of fuel compact radii from 0.65 to 0.59 cm. The increase of the moderation ratio results in a sharp increase of the reactivity swing, insofar as above 195, k EOL increases and k BOL decreases. This is because better moderation favours ssion reactions with respect to radiative captures, since the ratio of Th-232 capture cross-section to U-235 or U-233 ssion cross-section is higher at high energies. 12

13 Figure 6: Innite multiplication factor as a function of the moderation ratio. Solid dots: results when changing the radius of fuel compacts. Open dots: results when changing the packing fractions. 13

14 5.2. Further discussion about the moderation ratio The time-dependant innite multiplication factor strongly depends on the moderation ratio, as shown in Fig. 7, which displays the innite multiplication factor of neutrons as a function of time and with the moderation ratio as a parameter. The input parameters are the composite-rod fuel block reference conguration and the moderation ratio is modied by changing the packing fractions, like the second method of the previous section. According to Fig. 7, there is a great drop of reactivity during the rst 18 days. It is due to the formation of ssion products such as xenon or samarium which are neutron poisons. When the reactivity swing is very low, like curve \195" in Fig. 7, counting the initial drop in the reactivity swing gives a larger estimation of k and thus compensates the bell-shaped evolution of the innite multiplication factor. Moreover, as the mass of heavy metal is small when the moderation ratio is high, the ratio of ssion products to ssile isotopes increases rapidly. This is why a larger and larger initial reactivity drop is observed as the moderation ratio increases. Figure 7: Innite multiplication factor as a function of time and with the moderation ratio as a parameter. The major dierences between the curves of Fig. 7 can be explained 14

15 analysing the mass fractions of isotopes at EOL and the conversion ratios in the dierent regions of the fuel. These data are respectively plotted in the top and bottom subgures of Fig. 8. In the thorium region, there are very few U-235 and Pu isotopes, so the conversion ratio essentially represents the ratio between the production and the loss of U-233 in this region. Moreover, most U-235 atoms are in UO 2 fuel compacts and most U-233 atoms are in ThO 2 fuel compacts. Therefore the mass fraction of U-235 (respectively U-233) is mostly related to UO 2 (respectively ThO 2 ) fuel compacts. As a consequence, these two mass fractions are analysed separately. In the thorium region, as the moderation ratio increases, the mass fraction of U-233 increases while the conversion ratio decreases. This is because a soft spectrum favours U-233 consumption, whereas Th-232 absorption is higher in a hard spectrum. Indeed, the ratio of Th-232 absorption cross-section to U- 233 ssion cross-section is greater at high energies. So when the moderation ratio is high, there is not enough transmutation of Th-232. As regards the uranium region, the remaining mass fraction of U-235 decreases and the conversion ratio increases with the moderation ratio. This means that when the moderation ratio is high, the small initial amount of U-235 supports the ssion reactions in the fuel block at BOL and is rapidly depleted. Combining the depletion of U-235 and not enough generation of U-233 shows why the innite multiplication factor of neutrons sharply decreases with time when the moderation ratio is high. So, the moderation ratio reaches an optimum at about 165. This value enables a small reactivity swing due to a large amount of heavy metal, a relatively low consumption of U-235 and a high conversion ratio in the thorium region which supports the transmutation of thorium into U-233 and helps sustaining the chain reaction Geometric parameters of uranium fuel compacts The geometric parameters specically related to uranium fuel compacts are the radius of UO 2 fuel kernels and the packing fraction of UO 2 TRISO particles. Increasing one of them decreases the moderation ratio N C =N HM because of a larger uranium amount in the fuel block. Figure 9 shows the innite multiplication factor of neutrons at BOL and EOL as a function of the moderation ratio. The solid curve refers to the packing fraction and the open dots refer to the radius of uranium fuel kernels. The two series of curves almost match. So, changing the moderation ratio using the fuel compact radius or the packing fractions of UO 2 and ThO 2 TRISO particles 15

16 Figure 8: Mass fractions of main ssile isotopes (top) and conversion ratio of uranium regions, thorium regions and whole fuel rod (bottom) at EOL and as functions of the moderation ratio. 16

17 hardly makes a dierence. However, there is a small deviation, especially at BOL, as shown in Fig. 9. Like in Sec. 5.1, this deviation is due to the double heterogeneous eect. The radius of fuel kernels aects the rst level of heterogeneity, i.e. the distribution of the TRISO particles within the fuel compacts. When the fuel kernels are larger, the self-shielding is higher [3]. This leads to a higher resonance escape probability of neutrons (p), hence a more ecient moderation and a higher innite multiplication factor. Figure 9: Innite multiplication factor as a function of the moderation ratio of the fuel block. The mass of uranium is changed with PFU and r U (enrichment is constant and equal to its reference value). As shown in Fig. 9, a minimum mass of U-235 is required to make the fuel block critical at BOL and EOL. Then, as the moderation ratio decreases, the reactivity swing decreases and reaches a minimum when N C =N HM is about 155, corresponding to about r U = 0:042 cm. After this point, k BOL decreases because the moderation ratio is too low. This under-moderation results in a hardening of energy spectrum, as conrmed by ux data: the thermal ux in uranium regions at BOL is more than twice as low as in the reference conguration whereas the total ux in those regions only decreases by 16%. A harder spectrum is responsible for decreasing the resonance escape 17

18 probability of neutrons (p) in uranium regions and thus explains the decrease of reactivity at BOL. As discussed in the previous section, a harder spectrum leads to a lower consumption of U-235. The remaining fraction of U-235 indeed increases from 29% when N C =N HM = 178 to 55% when N C =N HM = 152. So, when the moderation ratio is low, the ssion chain reaction is mostly supported by U-233, which comes from transmutation of thorium. This is why k EOL increases when the moderation ratio decreases Geometric parameters of thorium fuel compacts If uranium geometric parameters are xed to their reference value, shown in Table 1, the inuence of those of thorium can be investigated in a similar way. The innite multiplication factor as a function of the moderation ratio, displayed in Fig. 10, enables to draw the same conclusion as in the previous section. In spite of the double heterogeneous eect, the fuel kernel radius and the packing fraction basically have the same inuence on reactivity and the relevant parameter is the moderation ratio (or, here, the mass of thorium). Figure 10: Innite multiplication factor as a function of the moderation ratio of the fuel block. The mass of thorium is changed with PFT and r T. 18

19 When N C =N HM is high, decreasing it lowers the innite multiplication factor at BOL but increases it at EOL. This is respectively due to a worse moderation and a larger amount of thorium to be transmuted. The moderation ratio denes a range of criticality between about 160 and 450. In this range, the larger the amount of thorium, the lower the reactivity swing. Below this range, the reactor is sub-critical anew. This is again because of under-moderation and hard spectrum. Indeed, the average thermal ux in thorium fuel compacts at BOL decreases from 1: n cm 2 s 1 to 1: n cm 2 s 1, which represents a drop of 16.25%, as the moderation ratio decreases from 178 to 114. With respect to the initial mass of Th-232, less U-233 is produced and used, so its contribution to reactivity is not important enough to keep the fuel block critical. 6. Thorium mass fraction Investigating the geometric parameters has highlighted the major role of the moderation ratio. As a complementary approach, the moderation ratio is xed and the proportion of thorium to uranium varies. The packing fractions of UO 2 and ThO 2 TRISO particles are modied in order to investigate the role of the initial thorium mass fraction, dened as m 02 =(m 02 + m 25 + m 28 ); the total mass of heavy metal (hence the moderation ratio) and all other parameters are constant and equal to their reference values. Figure 11 shows k as a function of the mass fraction of thorium. While the fraction of thorium increases, the fraction of uranium decreases. The reactor is sub-critical at EOL from about 83% of thorium. This value obviously depends on other parameters, such as the moderation ratio, as discussed in Sec However, this threshold conrms the need of a minimal mass of uranium 235 to ignite the chain reaction. Indeed, Fig. 11 for high thorium fractions is similar to Fig. 9 for high moderation ratios. They could be interpreted as the evolution of the innite multiplication factor of a fuel block with low amount of uranium. For high thorium mass fractions, the innite multiplication factor at BOL decreases sharply with the decrease of the amount of uranium. k then increases with time and is higher at EOL because of transmutation of thorium into U-233. Nevertheless, as shown in Fig. 11 below 83% (for criticality reasons), the lower the proportion of thorium, the lower the reactivity swing. As discussed in Sec. 5.1, a zero reactivity swing (here occurring at 60%) does not mean that the innite multiplication factor is constant all over fuel block lifetime. For example, at 60%, the innite 19

20 Figure 11: Innite multiplication factor as a function of the mass fraction of thorium at BOL and EOL. 20

21 multiplication factor is at BOL and at EOL but ranges from to during burnup. Yet it is still a promising conguration for it enables to design more simple reactivity control systems and to avoid using xed burnable poisons. Figure 12: Total ( tot, solid dots) and thermal ( th, open dots) neutron ux at EOL in uranium ( U, black squares) and thorium ( T, red circles) regions as a function of the mass fraction of thorium. Figure 12 shows the neutron ux in dierent regions and energy domains as a function of the mass fraction of thorium. While the mass fraction of thorium increases, uranium fuel compacts tend to be pure moderator so the spectrum is softened in those fuel compacts. Indeed, at 97% of thorium, 57% of the ux in this region is thermal whereas this fraction is only 17% in the reference case (83% of thorium). Moreover, since there is less and less uranium in those fuel compacts, most neutron collisions are scattering and the absorption diminishes; this is why the ux increases in spite of less ssile material. A higher and softer ux in uranium fuel compacts favours U-235 consumption. On the contrary, the ux in thorium fuel compacts becomes harder because the total ux increases more than the thermal ux. In those 21

22 fuel compacts, the ux increase is due to more U-233 breeding and ssions. Thus, for high thorium mass fractions, the ssion chain reaction is supported by U-233. Yet it is not enough to make the fuel block critical. For very high mass fractions of thorium, a oor can be observed in the ux evolution. Indeed, in the high mass fraction domain, only a slight adjustment of the packing fraction of ThO 2 TRISO particles is necessary to increase the mass fraction of thorium; the situation is opposite in uranium fuel compacts. Therefore, the amount of thorium does not change much with the increase of thorium mass fraction, since it increases by 5% between 90% and 95% of thorium while the amount of uranium is divided by two. Furthermore, uranium fuel compacts tend to be pure graphite. Because of the strong softening of spectrum in uranium fuel compacts when the mass fraction of thorium increases, the EOL reactivity of the fuel block slightly increases when the thorium mass fraction is very high. For lower mass fractions of thorium, the thermal ux in uranium regions decreases more than the total ux in those regions. Since the spectrum is harder, U-235 is relatively less used. Although a maximum burnup of U-235 is preferred, this results in a quite low reactivity swing and saving U-235 can be an advantage if used-fuel reprocessing is possible. On the contrary, the ux in thorium region is softer than for high thorium mass fractions. This shows that the ssion chain reaction is mostly supported by U Spatial distribution of fuel compacts The number of fuel compacts allocated to uranium and thorium is not the only specic feature of composite-rod fuel. Indeed, if it is xed to 4 UO 2 and 11 ThO 2 fuel compacts, for example, there are still 1365 possible patterns because the locations of these fuel compacts are to be determined. There are too many patterns to investigate all of them. The investigated patterns are sorted into groups according to the number of consecutive UO 2 fuel compacts in a fuel rod. Sections 7.1, 7.2 and 7.3 respectively investigate patterns with two, one and four consecutive UO 2 fuel compacts. Following calculations were done with composite-rod fuel block parameter reference values anew, which are presented in Table Grouped patterns In GPD (grouped) patterns, uranium fuel compacts are grouped by pairs. Table 3 shows four patterns and their innite multiplication factor at BOL 22

23 and EOL. k EOL hardly depends on the spatial distribution; the maximum dierence between them is less than 1%. This means that reactivity at EOL is mainly determined by the other parameters of the fuel block. At EOL indeed, the ssion reactions of the reference conguration are maintained by U-233. Since there are 11 ThO 2 fuel compacts in every pattern, similar behaviours at EOL are expected. Because of this similarity, further analysis focuses on BOL. Table 3: Innite multiplication factor and reactivity swing of grouped spatial distributions. k EOL Id Spatial distribution k BOL k [%] GPD 1 UUTTTTTTTTTTTUU GPD 2 TTUUTTTTTTTUUTT GPD 3 TTTTUUTTTUUTTTT GPD 4 TTTTTUUTUUTTTTT Figure 13: Spectrum of several fuel compacts of GPD 3 at BOL. The fuel compacts are labelled by their number (starting from the bottom of the rod) and the composition of the fuel compacts is specied between brackets. Figure 13 displays the energy spectrum of neutrons in several typical fuel compacts of GPD 3. All 15 spectra are not plotted due to clarity reasons. 23

24 The spectrum in uranium fuel compacts is harder than in thorium fuel compacts. The spectrum is hard in uranium fuel compacts because this is where neutrons are produced. On the contrary, the spectrum is softer in thorium fuel compacts because no neutrons are produced at BOL and most neutrons in those fuel compacts have had several scatter collisions with graphite. The spectrum of thorium fuel compacts strongly depends on their location. Thorium fuel compacts very close to uranium fuel compacts almost have the same spectrum as uranium fuel compacts, whereas thorium fuel compacts far from uranium fuel compacts have a much softer spectrum. Figure 14: Total (solid dots) and thermal (open dots) ux at BOL as a function of the fuel compacts of GPD 1, GPD 2, GPD 3 and GPD 4. The thermal and total ux in every fuel compact of GPD 1, GPD 2, GPD 3 and GPD 4 are plotted in Fig. 14. The bottom axis labels refer to the position of the fuel compacts. The bottom (or left) fuel compact has number 1 and the top (or right) fuel compact has number 15. In GPD 2, GPD 3 and GPD 4, the closer uranium fuel compacts are to each other, the lower k BOL is (respectively about 1.09, 1.04, 0.96). Compared to GPD 4, the spectrum of uranium fuel compacts is softer and the spectrum of thorium 24

25 fuel compacts is harder in GPD 2. In terms of four factors, the hardening of spectrum has too opposite eects: a harder spectrum means that the fast ssion factor () is higher and that the resonance escape probability (p) is lower. In thorium fuel compacts, since there is no ssile material at BOL, a harder spectrum results in a higher reactivity because of fast ssions. On the contrary, a soft spectrum in uranium fuel compacts means that is lower and p higher. Given the increase of reactivity that can be observed in case of relatively soft uranium spectra, it can be concluded that the reactivity at BOL is all the higher as the spectrum is relatively hard in thorium fuel compacts and soft in uranium fuel compacts. GPD 1 has a totally dierent behaviour and is under critical at BOL. Since uranium fuel compacts are at both ends of the rod, neutron that leak from one of these fuel compacts have a higher chance to go into another uranium fuel compact because of the reective boundary condition. So the spectrum in uranium fuel compacts is relatively hard, as shown in Fig. 14. This means that the resonance escape probability must be low in these fuel compacts and this results in a low k BOL Spread patterns Table 4 presents ve spread (SPR) patterns and their innite multiplication factor at BOL and EOL. In SPR patterns, uranium fuel compacts are individually scattered over the whole rod. k EOL again hardly depends on the spatial distribution. As regards k BOL, spread patterns can be divided in two groups. The rst group includes SPR 1, SPR 2 and SPR 3 and has a high initial innite multiplication factor. The second group consists of SPR 4 and SPR 5 and has much lower k BOL and reactivity swing. Within each group, k EOL are very close to each other, the dierences being lower than the calculation uncertainty. This is because of geometric similarities. Some uranium fuel compacts are very close to each other (with only one thorium fuel compact in between) in the second group, whereas uranium fuel compacts are more dispersed in the rst group. As shown in Fig. 15, which displays the spectrum of 8 fuel compacts of SPR 1 and of 2 fuel compacts of SPR 4, this dispersion in the rst group results in a homogeneous spectrum since the 8 curves coincide on most of the energy domain. Thus, the total and thermal ux in the fuel rod is homogeneous as well. The comparison with SPR 4, also shown in Fig. 15, indicates that the spectrum of SPR 1 fuel compacts is rather hard because it is closer to the hard spectrum of uranium fuel compacts than to the soft spectrum of 25

26 Table 4: Innite multiplication factor and reactivity swing of spread spatial distributions. k EOL Id Spatial distribution k BOL k [%] SPR 1 UTTTTUTTTUTTTTU SPR 2 TUTTTUTTTUTTTUT SPR 3 TTUTTUTTTUTTUTT SPR 4 TTTTUTUTUTUTTTT SPR 5 UTUTTTTTTTTTUTU Figure 15: Spectrum of the fuel compacts of SPR 1 bottom half-rod and spectrum of two fuel compacts of SPR 4 at BOL. The fuel compacts are labelled by their number (starting from the bottom of the rod) and the composition of the fuel compacts is specied between brackets. 26

27 thorium fuel compacts. As explained previously, a harder spectrum in thorium fuel compacts and a softer spectrum in uranium fuel compacts increase the reactivity because of more Th-232 fast ssions and a higher resonance probability escape in uranium fuel compacts Inuence of boundary conditions All patterns analysed in Secs. 7.1 and 7.2 were symmetric. Thus, no discussion was needed about boundary conditions since a reective and a periodic boundary condition are equivalent. All calculations were performed on a single fuel block with reective boundary conditions and it is assumed that it is representative of a whole core situation. However, for the patterns such as the reference conguration (REF) and the patterns shown in Table 5, in which all four UO 2 fuel compacts are adjacent, a reective boundary condition is no longer equivalent to a periodic boundary condition because they are not symmetric. Table 5: Innite multiplication factor and reactivity swing of localised spatial distributions. k EOL Id Spatial distribution k BOL k [%] REF TTTTTTTTTTTUUUU LOC 1 TTTTTTTTTTUUUUT LOC 2 TTTTTTTTTUUUUTT LOC 3 TTTTTTTTUUUUTTT LOC 4 TTTTTTTUUUUTTTT LOC 5 TTTTTTUUUUTTTTT In a reactor core, in which a lot of fuel blocks are assembled in a periodic pattern, one would expect all congurations of Table 5 to behave the same way. The patterns only dier by a shift indeed, and this shift would no longer make eect in a periodic disposition. Spectrum analysis of congurations LOC 1 to LOC 5 shows that the further uranium fuel compacts are from the boundary of the rod, the harder the spectrum is in these fuel compacts. This is due to a lower thermal ux. When uranium fuel compacts are close to the boundary, slowed neutrons can be reected at the end of the rod and come back into uranium fuel compacts. This is why the spectrum is softer. So is lower but p is higher, which explains that k BOL is higher. In thorium fuel compacts, the spectrum is softer when the uranium fuel compacts are further from the end of the rod. As previously explained, this also diminishes and k BOL. 27

28 However, as regards reactivity results shown in Table 5, this explanation is not enough to analyse the reference conguration. REF indeed has a lower k BOL than LOC 1. Calculation results show that the spectrum in REF uranium fuel compacts is harder than in LOC 1 uranium fuel compacts. Although REF uranium fuel compacts have less leakage because of the reective boundary condition, neutrons that leak towards the top of the rod are less slowed down because they come back in the top uranium fuel compact immediately. This is why the spectrum in uranium fuel compacts is harder and k BOL is lower in the reference case. However, in the centre of a real core, this edge eect would not happen. 8. Temperature coecient of reactivity A negative temperature coecient of reactivity is an inherent safety feature of all reactors, since a temperature or power increase would result in a decrease of reactivity. To calculate the temperature coecient, the following formula [3] is used at 300 and 1100 K: CT = T The temperature step is 200 K and the uncertainty on k is lower than , which leads to a maximum uncertainty of 0:5 pcm/k on the temperature coecient of reactivity. Table 6 shows the temperature coef- cient of reactivity of the reference fuel block (fuel and moderator) as a function of temperature for the fuel block. Table 6: Temperature coecient of reactivity [pcm/k] of the reference fuel block at BOL and EOL. T [ C] EFPYs EFPYs In the whole range of investigation, the temperature coecient is negative. Though, the absolute value of the temperature coecient is lower than that of a uranium-only fuel block [4]. Indeed, the Doppler eect of Th-232 is smaller than that of U-238 because of a three times smaller absorption resonance integral [5]. Thus, the temperature coecient is all the smaller as the mass fraction of thorium is high. Safety requirements are an additional restriction to the amount of thorium loaded in the fuel block. 28

29 9. Comparison of three thorium fuelled U-Battery blocks There are several possibilities to add thorium into U-Battery fuel blocks. Composite-rod fuel blocks are one of them; they feature an axial separation between uranium and thorium. If uranium and thorium are not separated axially but radially, the fuel type is called Seed-and-blanket (S&B) [6]. In this type of fuel block, the fuel rods are exclusively made of either UO 2 or ThO 2 fuel compacts. Thorium rods are located in the outer layers of the block and uranium rods in the inner layers. Finally, a third possibility is not to separate uranium and thorium at all. Thus, uranium and thorium are mixed within the fuel kernels in the form of (Th,U)O 2. This type of fuel block is called MOX fuel block because the fuel kernel is a mixture of UO 2 and ThO 2, like pressurised water reactor (PWR) MOX fuel [4]. In order to compare the neutronic performances of these three types of fuel blocks, the parameter values are the same for the three types and correspond to the U- Battery reference design. There are 216 fuel rods made of 15 fuel compacts each. The enrichment is 12%; the radii of fuel kernels and fuel compacts are respectively 0.25 mm and cm; the packing fractions of UO 2 and ThO 2 TRISO particles are 0.3. The innite multiplication factor of the three fuel block types is shown in Fig. 16 as a function of the initial mass of U-235. As regards the MOX fuel block, the initial mass of U-235 determines the masses of U-238 and Th-232 if the geometric parameters and the enrichment are xed. As regards the S&B fuel block, the mass of U-235 is determined by the number of UO 2 rods. Finally, as regards the composite-rod fuel block, the mass of U-235 is determined by the number of UO 2 fuel compacts, exactly like in Sec. 3. For all fuel blocks, the total mass of heavy metal keeps constant and so does the moderation ratio. Since all fuel block types have identical geometric and composition parameters, the only dierence between them is the location of UO 2 and ThO 2 within the fuel block. According to Fig. 16, the spatial dierences between the three fuel types have more inuence at BOL than at EOL. This is because both U-233 and U-235 take part in the chain reaction at EOL, so there are ssile elements all over the fuel block whatever the initial type is. Yet, separation between thorium and uranium (composite rods and S&B) results in a higher k EOL, so a better utilisation of thorium, especially when the initial mass of U- 235 is higher than 375 g. At BOL, the situation is not so clear, for the k BOL of composite-rod and seed-and-blanket fuel blocks are on both sides 29

30 Figure 16: Comparison of the k of MOX, composite-rod and S&B fuel blocks at BOL and EOL. 30

31 of that of MOX fuel block between 375 and 830 g. To explain the higher BOL reactivity of S&B, the fuel block is divided into a uranium area and a thorium area. In S&B fuel block, the uranium area is a hexagonal prism as high as the fuel block and located at its centre. In composite-rod fuel block, the uranium area is a hexagonal prism as wide as the fuel block and located at its bottom. Because of the central reective graphite area in each fuel block (Fig. 1), there is more graphite in S&B uranium area. Moreover, more uranium fuel compacts of S&B fuel block are located next to this inner graphite reector. This increases the resonance escape probability and thus the innite multiplication factor of neutrons in the fuel block. The same argument can explain why composite-rod fuel block has a higher k EOL than S&B fuel block when the initial mass of U-235 is lower than 500 g. As previously discussed, for low U-235 mass fractions, the chain reaction is supported by U-233. Because the thorium area includes more graphite and thorium compacts are closer to the inner graphite reector, the resonance escape probability in thorium regions increases and so does k EOL. The combination of a low k BOL and a high k EOL results in a lower reactivity swing of the composite-rod fuel block. The conversion ratios of the three fuel blocks at EOL are displayed in Fig. 17. As for MOX fuel, since there is no thorium region, the thorium CR is calculated as the ratio of the amount of generated U-233 to the loss of U-233. Indeed, as discussed in Sec. 5.2, the conversion ratio in thorium regions is approximately equal to this ratio. For all types of fuel blocks, the conversion ratio decreases with the increase of the mass of U-235 because of a lower production of ssile elements, since the fraction of fertile element in the fuel block decreases and Th-232 has a higher absorption cross-section than U-238 in thermal energies. In MOX fuel block, thorium is spread through the whole fuel block, so the capture probability of thorium is higher than in the two fuel block types which feature separation of uranium and thorium. This explains the higher conversion ratio of thorium in MOX fuel block. The conversion ratio of the thorium area in composite-rod fuel block is lower than the two others, especially from about 500 g of U-235. As the mass of U-235 increases, the interface between uranium and thorium regions becomes larger in S&B fuel block, whereas it is constant in composite-rod fuel block. Thus, although the conversion ratio still slightly increases with the mass of U-235, less thorium is transmuted in composite-rod fuel block than in the two other types. 31

32 Figure 17: Comparison of conversion ratios of MOX, composite-rod and S&B fuel blocks at EOL. 32

33 10. Conclusions In order to enhance the U-Battery performances and simplify the design of reactivity control equipments, the neutronic design of composite-rod fuel blocks has been investigated in this paper. The calculations showed that the specic axial separation between thorium and uranium enables to reach a small reactivity swing. Although adding thorium to the fuel blocks reduces the negative temperature feedback of the fuel because of the decrease of U-238 amount, the temperature coecient of reactivity remains negative. The geometric parameters analysed include the radii of fuel kernels and fuel compacts, and the packing fractions of UO 2 and ThO 2 TRISO particles; the composition parameters consist of the enrichment. The radii of fuel kernels and the packing fractions are equivalent ways to change the innite multiplication factor. These parameters can be unied in one: the moderation ratio. Because of the double heterogeneous eect, which tends to disappear at EOL, using large kernels slightly improves the reactivity of the fuel block. A lower moderation ratio and a larger inventory of heavy metal lead to a lower reactivity swing. On the other hand, the fuel block becomes sub-critical below a moderation threshold. This threshold depends on the mass fraction of U-235 and is commonly in the range. A strong relationship between the mass ratio of ssile isotopes at EOL and BOL and the reactivity swing has been made clear. This relationship is still to investigate, in order to understand in which way the mass ratio can be controlled. The spatial parameters investigated are the number and the spatial distribution of the fuel compacts within a rod. The number of UO 2 fuel compacts changes the total mass of uranium but also the volumes allocated to uranium and thorium. The volumes play an important role as regards the probability of rst-ight escape. Moreover, the spatial distribution of the fuel compacts within a fuel rod has a great inuence on the spectrum in each fuel compact and thus on the reactivity at BOL and the reactivity swing. As regards symmetric spatial distributions, GPD 3 achieves 1.89% reactivity swing because of a relatively hard spectrum in ThO 2 fuel compacts and a relatively soft spectrum in UO 2 fuel compacts. Some composite-rod fuel block congurations present very low reactivity swing, down to less than 1%. Although the reactivity swing denition only takes k BOL and k EOL into account, the maximum dierence of reactivity of such a conguration is less than 4% within 10 EFPYs. Featuring a low reactivity swing is a denite advantage of composite-rod fuel blocks with respect to other U-Battery fuel blocks, such 33