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Assembly design of a fluoride salt-cooled high temperature commercial-scale reactor: Neutronics evaluation and parametric analysis
Annals of Nuclear Energy 141 (2020) 107288
Contents lists available at ScienceDirect
Annals of Nuclear Energy journal homepage: www.elsevier.com/locate/anucene
Assembly design of a fluoride salt-cooled high temperature commercial-scale reactor: Neutronics evaluation and parametric analysis Vitesh Krishna, Ching Hiong Yap, Sicong Xiao ⇑ Singapore Nuclear Research and Safety Initiative, National University of Singapore, 1 Create Way, Create Tower, Singapore 138602, Singapore
a r t i c l e
i n f o
Article history: Received 24 August 2019 Received in revised form 27 November 2019 Accepted 23 December 2019
Keywords: Flouride salt-cooled high temperature reactors Commercial power Assembly design Neutronic study
a b s t r a c t In this study, a novel assembly design is proposed for a fluoride salt-cooled high-temperature commercial-scale (FHCR) reactor. It employs tristructural isotropic (TRISO) fuel particles nestled within removable cylindrical beryllium carbide (Be2C) moderator blocks, which are further contained within prismatic graphite blocks. As the name implies, the FHCR is a preconception of a 3400 MW(t) commercial power reactor that uses FLiBe (LiF-BeF2) as the primary coolant of choice. This paper uses the SERPENT 2 code to conduct a parametric neutronics study on the two-dimensional lattice assembly design of the FHCR. The calculations examine the effects of various fuel enrichment levels, TRISO particle packing fractions, fuel compacts’ pitch sizes, and moderating materials on the cycle length, while also determining the neutron spectrum and various nuclide inventories. Finally, a preliminary core is modeled based on the study conducted on the assembly design. Based on the negative values of the fuel temperature coefficients (FTC), moderator temperature coefficients (MTC), and coolant temperature coefficients (CTC) obtained, the design is determined to be safe. This new assembly design is also able to achieve keff > 1 for approximately 3.55 years, translating to a burn-up of 160.6 MWd/KgU. Ó 2019 Elsevier Ltd. All rights reserved.
1. Introduction The fluoride salt-cooled high temperature reactor (FHR) is a solid-fueled variant of the Gen IV class of reactor concept known as the molten salt reactor (MSR). Molten salt coolants in FHRs offer much higher heat capacities, better thermal conductivity, and near atmospheric pressure operational advantages, thus overcoming the limitations of gaseous or helium coolants employed in conventional high temperature gas-cooled reactors (HTGRs) whilst offering an additional layer of inherent safety (Gentry, 2017). In addition, the passive decay heat removal systems ensure that FHRs remain severe-accident proof, especially during Beyond Design Basis Accidents (BDBA) (Nakata, 2019). While there is ample research dedicated to various core designs and fuel optimization strategies for FHRs (Scarlat, 2014), most have been conceived as demonstration reactors (DRs) for establishing baseline engineering feasibility, or as small modular reactors (SMRs) targeted at remote communities (Andreades and Peterson, 2017; Louis Qualls, 2017; Sun et al., 2016). As such, they are not intended to be large scale commercial baseload nuclear
power plants (NPPs) to replace the existing aging fleet of light water reactors (LWR) and other commercial gas-cooled reactors (West et al., 2011). Other FHR designs propose online refuelling strategies that involve the removal of entire hexagonal fuel assemblies. By contrast, in this FHCR design, the central region containing the moderator and fuel compacts (see Fig. 1) permits an alternative online refueling strategy since they can be removed from the hexagonal graphite reflector fixture, thus reducing the volume of radioactive graphite waste. The remainder of this paper is organized as follows. In Section 2, the FHCR assembly design is shown and the input parameters in Serpent 2 is discussed. In Section 3, the results and discussions are given, including the parametric analysis, moderator study, isotopic evolution, and reactivity coefficients of the assembly design. A preliminary core is modeled and its cycle length is assessed. Finally, the conclusions are given in Section 4.
2. FHCR assembly design and calculation setup 2.1. Assembly design
⇑ Corresponding author. E-mail addresses: [email protected] (V. Krishna), [email protected] (C.H. Yap), [email protected] (S. Xiao). https://doi.org/10.1016/j.anucene.2019.107288 0306-4549/Ó 2019 Elsevier Ltd. All rights reserved.
Fig. 1 shows the FHCR assembly consisting of 312 cylindrical graphite matrix fuel compacts (in black) and 157 coolant channels
2
V. Krishna et al. / Annals of Nuclear Energy 141 (2020) 107288
Fig. 1. Assembly layout of the FHCR. The magnified image on the right shows a thin layer of FLiBe surrounding the fuel and Be2C region of the fuel assembly.
(in yellow) contained within a cylindrical beryllium carbide (Be2C) moderator (in blue), which is further embedded within a prismatic graphite block (in green), with the two structures separated by a circumferential coolant channel (in yellow). This unique feature not only assists in decreasing temperatures at the peripheries of the fueled regions where there are more fuel compacts to coolant channels but also allows for the possibility of online refueling since the cylindrical Be2C moderator block (containing the fuel compacts) can be detached, shuffled or replaced with relative ease. Furthermore, the fact that the graphite reflector blocks remain in the reactor during online refueling serve to minimize the production of radioactive waste. The TRISO uranium dioxide fuel kernels are enriched to 19.5% with packing fractions of 0.495 in each compact. The FHCR assembly design parameters are defined in Table 1. The specific power density, also reflected in Table 1, is calculated based on 265 fuel assemblies that constitute the FHCR core (See Table 5). The primary loop coolant for the FHCR uses FLiBe (LiF-BeF2). Be2C is chosen as the moderating material for housing the fuel compacts owing to its high thermal conductivity as well as refractory properties that can withstand temperatures well exceeding 1000 °C (melting point 2150 °C). As such, Be2C has been suggested as a possible material for nuclear reactor cores (Hehr et al., 2010; Schwartz, 1965). However, the fact that Be2C is easily hydrolyzed by water vapor even at room temperatures makes it unsuitable for use in LWR systems (Weber et al., 1957). Nevertheless, this
Table 1 Fuel assembly design parameters. Parameter
Value
Fuel enrichment Fuel pitch Packing fraction Coolant channel diameter Cylindrical fuel compact diameter Inner cylindrical Be2C region diameter Outer cylindrical coolant channel thickness Hexagonal assembly radius Outer Hexagonal coolant channel thickness Specific power density Thermal power
19.5 wt% 235U 1.8 cm 49:5% 0.7 cm 1.245 cm 48.2 cm 0.1 cm 26 cm 0.1 cm 0.1238 kW/g 3400 MW
disadvantage is mitigated in high temperature reactors like the FHRs which can prevent moisture formation. Furthermore, Be2C is also a superior neutron moderator compared to graphite, thus improving the neutron economy in a commercial reactor. 2.2. Calculation setup Calculations on the FHCR model are performed using the Serpent 2 code (Leppänen et al., 2015) with reflective boundary conditions to simulate a 2D infinite lattice assembly. In Monte Carlo simulation, 50 inactive cycles and 100 active cycles are used in which 2000 source neutrons are utilized in each cycle. The statistical error is approximately 0.002 and 0.0009 for both the analog and implicit infinite multiplication values in each respective burn up step. Finally, nuclear data for cross sections, fissions, and decays are obtained from the ENDF-VII.0 libraries. 3. Results and discussions 3.1. Parametric analysis The basic assembly design is modeled in Serpent with the specifications listed in Table 1. Therefore, a parametric study is done to evaluate the effects of certain parameters on the overall burn-up of a 2D infinite lattice assembly. The parameters that are assessed include, TRISO packing fraction (PF), fuel enrichment (FE) and fuel pitch (FP). Four different values for each parameter are chosen prior to analysis, which are listed in Table 2. As the specific power density changes when either the TRISO PF or fuel enrichment is varied, each scenario involving these parameters the power density is also computed accordingly.
Table 2 Parameters studied in this paper. TRISO Packing Fraction 19:5% 29:5% 39:5% 49:5%
Fuel Enrichment 13.5 15.5 17.5 19.5
wt% wt% wt% wt%
235
U U U 235 U 235 235
Fuel Pitch 1.3 1.4 1.6 1.8
cm cm cm cm
V. Krishna et al. / Annals of Nuclear Energy 141 (2020) 107288
Base case is selected to ensure appropriate comparison within the various values of each parameter. For instance, while varying PF in the TRISO PF analysis, the fuel enrichment and fuel pitch are kept constant throughout. Similarly, in fuel enrichment analysis, the packing fraction and fuel pitch are kept constant. In fuel pitch study, the packing fraction and fuel enrichment are kept constant. The burn-up calculation is performed for 1357 days. The results are given in Fig. 2. In Fig. 2, the legend key described as ‘standard’ is a reference mark for keff ¼ 1. Increasing the TRISO packing fraction has a positive impact on the overall cycle length, as seen in Fig. 2. With reference from Fig. 2, the different values of PF record different initial keff values. The lower the TRISO packing fraction, the higher the initial keff but the cycle length is shortened. As the TRISO PF is increased, the fuel loading increases. A higher fuel loading results in longer cycle lengths. However, other reports have suggested there is a threshold limit for the TRISO packing factor (Powers, 2013). This threshold limit is not studied here as this is just a preliminary investigation. Moreover, based on Fig. 2, the cycle
3
length progressively increases from lowest to highest packing fraction. Hence, the threshold limit should be beyond 49.5%. From Fig. 2, one can also find that the fuel pitch size has a small effect on the cycle length for the selected fuel pitch range. Fuel pitch greater than 1.8 cm is not studied as it would require dimension alterations to the fuel assembly and the comparison across the different fuel pitches will not longer be accurate. In fuel enrichment analysis, increasing the fissile content in the fuel extends the cycle length. Evident from Fig. 2, the highest fuel enrichment yields the longest cycle length. Therefore, 19.5 wt% 235 U is selected as the highest enrichment in this study due to the global consensus that nuclear fuel for civil purposes must not exceed 20 wt%. The preliminary parametric study of the FHR shed valuable insights on how the cycle length changes. Although this study only assesses the individual contribution of these parameters to the cycle length, a combined contribution is yet to be assessed. Future work could involve, studying other parameters, selecting the optimal value of each parameter and studying the combined effect on cycle length. However, based on the parametric study done
Fig. 2. Parametric study of (a) TRISO packing fraction. (b) Fuel pitch. (c) Fuel enrichment.
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V. Krishna et al. / Annals of Nuclear Energy 141 (2020) 107288
Table 3 Parameters chosen to be used in other studies in this research. TRISO Packing Fraction 49:5%
Fuel Enrichment 19.5 wt%
235
U
Fuel Pitch 1.8 cm
above, the following parameters are confirmed for other studies conducted in this research (refer to Table 3).
the amount of moderator. The other two candidates, Be2C and BeO perform as a better moderator than graphite. This is due to the lighter atomic mass compared to graphite. However, the difference in cycle length between using Be2C and BeO is very small. When Be2C is used as the moderator, the cycle length achieved is the longest and is hence the preferred choice of moderator for other studies in this research. Based on the design of the FHCR, Be2C is the most suitable material for a moderator from a neutronics point of view.
3.2. Moderator materials The possibility of using another moderator material other than graphite is studied. Therefore, five different potential materials are chosen (refer to Table 4) to evaluate the impact on the cycle length. The central region in the assembly design that encompasses the fuel compact and coolant channels is where the moderator is located. The outer region of the assembly remains as graphite moderated. Excluding graphite, the other four moderators are selected based on the criteria of low atomic number but higher than hydrogen and to be a solid. Low atomic number is necessary as this implies a higher slowing down power. Fig. 3 shows the impact of the different moderator materials on the cycle length. Silicon carbide and magnesium oxide have the lowest number of days for which the FHCR remained critical. Their performances are much worse than graphite as this could be attributed to the fact that their atomic masses are larger than that of graphite’s, thus requiring more collisions to thermalize neutrons. Therefore, more amounts of SiC and MgO would be required to achieve similar thermalization capacity of a specific amount of graphite. But in this study the moderator volume is fixed, hence it is not feasible to alter Fig. 4. FHCR neutron spectrum. Table 4 Moderators that are studied in this research. Moderator
Density (g=cm3 )
Graphite Beryllium Carbide (Be2C) Beryllium Oxide (BeO) Silicon Carbide (SiC) Magnesium Oxide (MgO)
1.75 1.9 3.01 3.2 3.6
Fig. 3. Moderator material as a function of the cycle length.
Fig. 5. Isotope depletion/formation as a function of burnup. (a) Plutonium isotopes. (b) Fertile and fissile isotopes.
V. Krishna et al. / Annals of Nuclear Energy 141 (2020) 107288
3.3. Neutron spectrum The overall neutron spectrum is generated. As seen from Fig. 4, the neutron flux in the thermal region is significantly higher than the fast region. This phenomena is expected due to the large moderator volume in the design. 3.4. Isotopic evolution Plutonium isotopes are formed from neutron interaction with U. 239Pu is formed prior to the other plutonium isotopes. The rate of formation of these isotopes differs based on either the neutron or fission cross sections of the respective isotopes. 239Pu has the highest density among its isotopes as shown in Fig. 5. In some proportion of cases, not all captures of 239Pu would result in fission. 240 Pu, 241Pu, and 242Pu accumulate as the residence time of fuel in an operating reactor progresses to achieve deep-burn. As seen from Fig. 5, 238U decreases at a slower rate than 235U during burn up due to its relatively smaller total cross section. The total fissile curve in 238
Table 5 Full core specifications. Parameter
Value
Fuel enrichment Fuel pitch Packing fraction No. of fuel rods per assembly No. of fuel assemblies Assembly pitch Axial graphite reflector thickness, Z 1 Flibe channel, Z 2 Core height, Z 3 Core radius, R1 R2 R3 R4
19.5 wt% 1.8 cm 49:5% 312 265 54 cm 50 cm 20 cm 550 cm 580 cm 590 cm 610 cm 635 cm
235
U
5
Fig. 5 represents 235U, 239Pu and 241Pu. It is worth noting that the profile of the total fissile curve is very similar to that of the 235U curve as the conversion ratio is relatively small. Also, the scale of the plot is such that the mass of 238U is much higher than that of 235 U; hence, the depletion of 238U is not very apparent in the same plot. 235U, on the other hand, undergoes fission and is gradually being depleted. As burnup continues, the odd-numbered plutonium isotopes which are fissile would also undergo fission and start to decrease in their respective quantities. By contrast, 240Pu and 242Pu which are not fissile would continue to build up and eventually exceed that of the odd-numbered plutonium isotopes. 3.5. Full core The assembly design is then extended to encompass the entire core with specifications detailed in Table 5 below. The core is designed such that both the radial and axial reflectors are made of graphite. Fig. 6 shows the X-Y or aerial view of the FHCR core while Fig. 7 depicts the Z or axial view. The magnified image to the right of Fig. 6 shows the peripheral graphite blocks surrounding the core that requires replacement after a stipulated duration since they will be subjected to high neutron irradiation over the course of reactor operation. The regions beyond the replaceable graphite are permanent radial graphite reflectors followed by the core barrel (R2 R1 ), FLiBe downcomer (R3 R2 ) and reactor pressure vessel (R4 R3 ) as seen in Fig. 7. Finally, Fig. 8 depicts the cycle length of the FHCR core operating at 3400 MWt, with an effective operating cycle length of 3.55 years prior to refueling. Currently, the design of the FHCR core is in the preliminary stage and does not have any control rods nor burnable poisons. 3.6. Reactivity coefficients The fuel temperature coefficient (FTC), also known as the Doppler temperature coefficient or Doppler effect, measures the
Fig. 6. FHCR full core.
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V. Krishna et al. / Annals of Nuclear Energy 141 (2020) 107288
Fig. 7. FHCR Core from Z view.
Table 6 Reactivity coefficients.
Fig. 8. FHCR full core burnup.
FTC (pcm/K)
MTC (pcm/K)
CTC (pcm/K)
0.96
1.60
0.04
because fuel heating leads to Doppler broadening which implies that more neutrons are susceptible to absorption by 238U at the widened resonance energies, thus decreasing reactivity and stabilizing the reactor. Additionally, as time progresses, the increased production of 240Pu contributes to higher resonance absorption and causes the FTC to become more negative. The moderator temperature coefficient (MTC) is defined as the change in reactivity per degree change in moderator temperature. As shown in Table 6, a perturbation of +100 K gives a negative value for the MTC and a corresponding decrease in keff . The coolant temperature coefficient, by contrast, is slightly negative or even negligible. Although the coefficients are only slightly negative, the presence of the solid moderator and graphite reflectors in the core provide sufficient thermal inertia to retard the rise in core temperatures from reactivity transients.
4. Summary decrease in reactivity for a 1 K change in fuel temperature due to an increase in resonance absorption of neutrons by mainly 238U. As shown in Table 6, a perturbation of +100 K gives a negative value for the FTC and a corresponding decrease in keff . This is
The parametric study conducted in this paper has described design conditions that allow for further optimization of the FHCR assembly in order to extend its operational cycle length. Packing
V. Krishna et al. / Annals of Nuclear Energy 141 (2020) 107288
fractions, levels of enrichment, and fuel pitch lengths are investigated to determine the optimal design values. With that, moderator analysis is performed with Be2C being found to be the most efficient moderator in extending the cycle length (approximately 3.55 years corresponding to a burnup of 160.6 MWd/KgU) as opposed to using graphite in the central region of the assembly. The observable phenomena include reactivity behavior and flux spectrum, with the reactivity coefficients being negative to reflect the main inherent safety feature of FHRs. It should be noted that the results attained in this study are preliminary and represent a proof-of-concept for future studies on this FHCR design. The core configuration displayed in Fig. 6 will be further assessed in future work involving burnable poison analyses as well as thermalhydraulics studies.
CRediT authorship contribution statement Vitesh Krishna: Conceptualization, Formal analysis, Investigation, Methodology, Writing – original draft. Ching Hiong Yap: Conceptualization, Formal analysis, Investigation, Methodology, Writing – original draft. Sicong Xiao: Supervision, Validation, Writing – review & editing.
Acknowledgement The authors would like to thank the anonymous reviewers for their insightful comments which greatly helped to improve the quality of this paper. This work is supported by the National Research Foundation Singapore (R-721-000-002-281). The authors declare that there is no conflict of interest regarding the publication of this paper.
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Appendix A. Supplementary data Supplementary data associated with this article can be found, in the online version, athttps://doi.org/10.1016/j.anucene.2019. 107288. References Gentry, C. et al., 2017. Neutronic evaluation of a liquid salt-cooled reactor assembly. Nucl. Sci. Eng. 187, 166–184. Nakata, J. et al., 2019. Performance evaluation of decay heat removal systems of Fluoride-salt cooled High-temperature Reactor (FHR). Ann. Nucl. Energy 133, 248–256. Scarlat, R.O. et al., 2014. Design and licensing strategies for the fluoride-salt-cooled, high temperature reactor (FHR) technology. Prog. Nucl. Energy 77, 406–420. Andreades, C., Peterson, P., 2017. Nuclear air Brayton combined cycle and mark 1 pebble bed fluoride-salt-cooled high-temperature reactor economic performance in a regulated electricity market. Nucl. Eng. Des. 323, 474–484. Louis Qualls, A. et al., 2017. Preconceptual design of a fluoride high temperature salt-cooled engineering demonstration reactor: motivation and overview. Ann. Nucl. Energy 107, 144–155. Sun, K., Hu, L.W., Forsberg, C., 2016. Neutronic design features of a transportable fluoride-salt-cooled high-temperature reactor. J. Nucl. Eng. Rad. Sci. 2 (3). 031003-031003-10. West, G.M., McArthur, S.D.J., Towle, D., 2011. Knowledge-directed characterization of nuclear power plant reactor core parameters. Nucl. Eng. Design 241 (9), 4013–4025. Hehr, B.D., Hawari, A.I. Generation of thermal neutron scattering libraries for beryllium carbide. In: 2010 1st International Nuclear & Renewable Energy Conference (INREC), pp. 1–5. Schwartz, M.A., 1965. Method of Vitrifying Ceramic Coatings. United States Patent Office. Weber, W.P. et al., 1957. Properties of Beryllium Oxide and Carbides of Beryllium, Molybdenum, Niobium, Tantalum, and Titanium (Tech. rep.). Battelle Memorial Institute. Leppänen, J. et al., 2015. The Serpent Monte Carlo code: status, development and applications in 2013. Ann. Nucl. Energy 82, 142–150. issn: 0306-4549. Powers, J.J., 2013. Fully Ceramic Microencapsulated (FCM) Replacement Fuel for LWRs (Tech. rep.). Oak Ridge National Laboratory. URL:https://info.ornl.gov/ sites/publications/Files/Pub42476.pdf.
Contents lists available at ScienceDirect
Annals of Nuclear Energy journal homepage: www.elsevier.com/locate/anucene
Assembly design of a fluoride salt-cooled high temperature commercial-scale reactor: Neutronics evaluation and parametric analysis Vitesh Krishna, Ching Hiong Yap, Sicong Xiao ⇑ Singapore Nuclear Research and Safety Initiative, National University of Singapore, 1 Create Way, Create Tower, Singapore 138602, Singapore
a r t i c l e
i n f o
Article history: Received 24 August 2019 Received in revised form 27 November 2019 Accepted 23 December 2019
Keywords: Flouride salt-cooled high temperature reactors Commercial power Assembly design Neutronic study
a b s t r a c t In this study, a novel assembly design is proposed for a fluoride salt-cooled high-temperature commercial-scale (FHCR) reactor. It employs tristructural isotropic (TRISO) fuel particles nestled within removable cylindrical beryllium carbide (Be2C) moderator blocks, which are further contained within prismatic graphite blocks. As the name implies, the FHCR is a preconception of a 3400 MW(t) commercial power reactor that uses FLiBe (LiF-BeF2) as the primary coolant of choice. This paper uses the SERPENT 2 code to conduct a parametric neutronics study on the two-dimensional lattice assembly design of the FHCR. The calculations examine the effects of various fuel enrichment levels, TRISO particle packing fractions, fuel compacts’ pitch sizes, and moderating materials on the cycle length, while also determining the neutron spectrum and various nuclide inventories. Finally, a preliminary core is modeled based on the study conducted on the assembly design. Based on the negative values of the fuel temperature coefficients (FTC), moderator temperature coefficients (MTC), and coolant temperature coefficients (CTC) obtained, the design is determined to be safe. This new assembly design is also able to achieve keff > 1 for approximately 3.55 years, translating to a burn-up of 160.6 MWd/KgU. Ó 2019 Elsevier Ltd. All rights reserved.
1. Introduction The fluoride salt-cooled high temperature reactor (FHR) is a solid-fueled variant of the Gen IV class of reactor concept known as the molten salt reactor (MSR). Molten salt coolants in FHRs offer much higher heat capacities, better thermal conductivity, and near atmospheric pressure operational advantages, thus overcoming the limitations of gaseous or helium coolants employed in conventional high temperature gas-cooled reactors (HTGRs) whilst offering an additional layer of inherent safety (Gentry, 2017). In addition, the passive decay heat removal systems ensure that FHRs remain severe-accident proof, especially during Beyond Design Basis Accidents (BDBA) (Nakata, 2019). While there is ample research dedicated to various core designs and fuel optimization strategies for FHRs (Scarlat, 2014), most have been conceived as demonstration reactors (DRs) for establishing baseline engineering feasibility, or as small modular reactors (SMRs) targeted at remote communities (Andreades and Peterson, 2017; Louis Qualls, 2017; Sun et al., 2016). As such, they are not intended to be large scale commercial baseload nuclear
power plants (NPPs) to replace the existing aging fleet of light water reactors (LWR) and other commercial gas-cooled reactors (West et al., 2011). Other FHR designs propose online refuelling strategies that involve the removal of entire hexagonal fuel assemblies. By contrast, in this FHCR design, the central region containing the moderator and fuel compacts (see Fig. 1) permits an alternative online refueling strategy since they can be removed from the hexagonal graphite reflector fixture, thus reducing the volume of radioactive graphite waste. The remainder of this paper is organized as follows. In Section 2, the FHCR assembly design is shown and the input parameters in Serpent 2 is discussed. In Section 3, the results and discussions are given, including the parametric analysis, moderator study, isotopic evolution, and reactivity coefficients of the assembly design. A preliminary core is modeled and its cycle length is assessed. Finally, the conclusions are given in Section 4.
2. FHCR assembly design and calculation setup 2.1. Assembly design
⇑ Corresponding author. E-mail addresses: [email protected] (V. Krishna), [email protected] (C.H. Yap), [email protected] (S. Xiao). https://doi.org/10.1016/j.anucene.2019.107288 0306-4549/Ó 2019 Elsevier Ltd. All rights reserved.
Fig. 1 shows the FHCR assembly consisting of 312 cylindrical graphite matrix fuel compacts (in black) and 157 coolant channels
2
V. Krishna et al. / Annals of Nuclear Energy 141 (2020) 107288
Fig. 1. Assembly layout of the FHCR. The magnified image on the right shows a thin layer of FLiBe surrounding the fuel and Be2C region of the fuel assembly.
(in yellow) contained within a cylindrical beryllium carbide (Be2C) moderator (in blue), which is further embedded within a prismatic graphite block (in green), with the two structures separated by a circumferential coolant channel (in yellow). This unique feature not only assists in decreasing temperatures at the peripheries of the fueled regions where there are more fuel compacts to coolant channels but also allows for the possibility of online refueling since the cylindrical Be2C moderator block (containing the fuel compacts) can be detached, shuffled or replaced with relative ease. Furthermore, the fact that the graphite reflector blocks remain in the reactor during online refueling serve to minimize the production of radioactive waste. The TRISO uranium dioxide fuel kernels are enriched to 19.5% with packing fractions of 0.495 in each compact. The FHCR assembly design parameters are defined in Table 1. The specific power density, also reflected in Table 1, is calculated based on 265 fuel assemblies that constitute the FHCR core (See Table 5). The primary loop coolant for the FHCR uses FLiBe (LiF-BeF2). Be2C is chosen as the moderating material for housing the fuel compacts owing to its high thermal conductivity as well as refractory properties that can withstand temperatures well exceeding 1000 °C (melting point 2150 °C). As such, Be2C has been suggested as a possible material for nuclear reactor cores (Hehr et al., 2010; Schwartz, 1965). However, the fact that Be2C is easily hydrolyzed by water vapor even at room temperatures makes it unsuitable for use in LWR systems (Weber et al., 1957). Nevertheless, this
Table 1 Fuel assembly design parameters. Parameter
Value
Fuel enrichment Fuel pitch Packing fraction Coolant channel diameter Cylindrical fuel compact diameter Inner cylindrical Be2C region diameter Outer cylindrical coolant channel thickness Hexagonal assembly radius Outer Hexagonal coolant channel thickness Specific power density Thermal power
19.5 wt% 235U 1.8 cm 49:5% 0.7 cm 1.245 cm 48.2 cm 0.1 cm 26 cm 0.1 cm 0.1238 kW/g 3400 MW
disadvantage is mitigated in high temperature reactors like the FHRs which can prevent moisture formation. Furthermore, Be2C is also a superior neutron moderator compared to graphite, thus improving the neutron economy in a commercial reactor. 2.2. Calculation setup Calculations on the FHCR model are performed using the Serpent 2 code (Leppänen et al., 2015) with reflective boundary conditions to simulate a 2D infinite lattice assembly. In Monte Carlo simulation, 50 inactive cycles and 100 active cycles are used in which 2000 source neutrons are utilized in each cycle. The statistical error is approximately 0.002 and 0.0009 for both the analog and implicit infinite multiplication values in each respective burn up step. Finally, nuclear data for cross sections, fissions, and decays are obtained from the ENDF-VII.0 libraries. 3. Results and discussions 3.1. Parametric analysis The basic assembly design is modeled in Serpent with the specifications listed in Table 1. Therefore, a parametric study is done to evaluate the effects of certain parameters on the overall burn-up of a 2D infinite lattice assembly. The parameters that are assessed include, TRISO packing fraction (PF), fuel enrichment (FE) and fuel pitch (FP). Four different values for each parameter are chosen prior to analysis, which are listed in Table 2. As the specific power density changes when either the TRISO PF or fuel enrichment is varied, each scenario involving these parameters the power density is also computed accordingly.
Table 2 Parameters studied in this paper. TRISO Packing Fraction 19:5% 29:5% 39:5% 49:5%
Fuel Enrichment 13.5 15.5 17.5 19.5
wt% wt% wt% wt%
235
U U U 235 U 235 235
Fuel Pitch 1.3 1.4 1.6 1.8
cm cm cm cm
V. Krishna et al. / Annals of Nuclear Energy 141 (2020) 107288
Base case is selected to ensure appropriate comparison within the various values of each parameter. For instance, while varying PF in the TRISO PF analysis, the fuel enrichment and fuel pitch are kept constant throughout. Similarly, in fuel enrichment analysis, the packing fraction and fuel pitch are kept constant. In fuel pitch study, the packing fraction and fuel enrichment are kept constant. The burn-up calculation is performed for 1357 days. The results are given in Fig. 2. In Fig. 2, the legend key described as ‘standard’ is a reference mark for keff ¼ 1. Increasing the TRISO packing fraction has a positive impact on the overall cycle length, as seen in Fig. 2. With reference from Fig. 2, the different values of PF record different initial keff values. The lower the TRISO packing fraction, the higher the initial keff but the cycle length is shortened. As the TRISO PF is increased, the fuel loading increases. A higher fuel loading results in longer cycle lengths. However, other reports have suggested there is a threshold limit for the TRISO packing factor (Powers, 2013). This threshold limit is not studied here as this is just a preliminary investigation. Moreover, based on Fig. 2, the cycle
3
length progressively increases from lowest to highest packing fraction. Hence, the threshold limit should be beyond 49.5%. From Fig. 2, one can also find that the fuel pitch size has a small effect on the cycle length for the selected fuel pitch range. Fuel pitch greater than 1.8 cm is not studied as it would require dimension alterations to the fuel assembly and the comparison across the different fuel pitches will not longer be accurate. In fuel enrichment analysis, increasing the fissile content in the fuel extends the cycle length. Evident from Fig. 2, the highest fuel enrichment yields the longest cycle length. Therefore, 19.5 wt% 235 U is selected as the highest enrichment in this study due to the global consensus that nuclear fuel for civil purposes must not exceed 20 wt%. The preliminary parametric study of the FHR shed valuable insights on how the cycle length changes. Although this study only assesses the individual contribution of these parameters to the cycle length, a combined contribution is yet to be assessed. Future work could involve, studying other parameters, selecting the optimal value of each parameter and studying the combined effect on cycle length. However, based on the parametric study done
Fig. 2. Parametric study of (a) TRISO packing fraction. (b) Fuel pitch. (c) Fuel enrichment.
4
V. Krishna et al. / Annals of Nuclear Energy 141 (2020) 107288
Table 3 Parameters chosen to be used in other studies in this research. TRISO Packing Fraction 49:5%
Fuel Enrichment 19.5 wt%
235
U
Fuel Pitch 1.8 cm
above, the following parameters are confirmed for other studies conducted in this research (refer to Table 3).
the amount of moderator. The other two candidates, Be2C and BeO perform as a better moderator than graphite. This is due to the lighter atomic mass compared to graphite. However, the difference in cycle length between using Be2C and BeO is very small. When Be2C is used as the moderator, the cycle length achieved is the longest and is hence the preferred choice of moderator for other studies in this research. Based on the design of the FHCR, Be2C is the most suitable material for a moderator from a neutronics point of view.
3.2. Moderator materials The possibility of using another moderator material other than graphite is studied. Therefore, five different potential materials are chosen (refer to Table 4) to evaluate the impact on the cycle length. The central region in the assembly design that encompasses the fuel compact and coolant channels is where the moderator is located. The outer region of the assembly remains as graphite moderated. Excluding graphite, the other four moderators are selected based on the criteria of low atomic number but higher than hydrogen and to be a solid. Low atomic number is necessary as this implies a higher slowing down power. Fig. 3 shows the impact of the different moderator materials on the cycle length. Silicon carbide and magnesium oxide have the lowest number of days for which the FHCR remained critical. Their performances are much worse than graphite as this could be attributed to the fact that their atomic masses are larger than that of graphite’s, thus requiring more collisions to thermalize neutrons. Therefore, more amounts of SiC and MgO would be required to achieve similar thermalization capacity of a specific amount of graphite. But in this study the moderator volume is fixed, hence it is not feasible to alter Fig. 4. FHCR neutron spectrum. Table 4 Moderators that are studied in this research. Moderator
Density (g=cm3 )
Graphite Beryllium Carbide (Be2C) Beryllium Oxide (BeO) Silicon Carbide (SiC) Magnesium Oxide (MgO)
1.75 1.9 3.01 3.2 3.6
Fig. 3. Moderator material as a function of the cycle length.
Fig. 5. Isotope depletion/formation as a function of burnup. (a) Plutonium isotopes. (b) Fertile and fissile isotopes.
V. Krishna et al. / Annals of Nuclear Energy 141 (2020) 107288
3.3. Neutron spectrum The overall neutron spectrum is generated. As seen from Fig. 4, the neutron flux in the thermal region is significantly higher than the fast region. This phenomena is expected due to the large moderator volume in the design. 3.4. Isotopic evolution Plutonium isotopes are formed from neutron interaction with U. 239Pu is formed prior to the other plutonium isotopes. The rate of formation of these isotopes differs based on either the neutron or fission cross sections of the respective isotopes. 239Pu has the highest density among its isotopes as shown in Fig. 5. In some proportion of cases, not all captures of 239Pu would result in fission. 240 Pu, 241Pu, and 242Pu accumulate as the residence time of fuel in an operating reactor progresses to achieve deep-burn. As seen from Fig. 5, 238U decreases at a slower rate than 235U during burn up due to its relatively smaller total cross section. The total fissile curve in 238
Table 5 Full core specifications. Parameter
Value
Fuel enrichment Fuel pitch Packing fraction No. of fuel rods per assembly No. of fuel assemblies Assembly pitch Axial graphite reflector thickness, Z 1 Flibe channel, Z 2 Core height, Z 3 Core radius, R1 R2 R3 R4
19.5 wt% 1.8 cm 49:5% 312 265 54 cm 50 cm 20 cm 550 cm 580 cm 590 cm 610 cm 635 cm
235
U
5
Fig. 5 represents 235U, 239Pu and 241Pu. It is worth noting that the profile of the total fissile curve is very similar to that of the 235U curve as the conversion ratio is relatively small. Also, the scale of the plot is such that the mass of 238U is much higher than that of 235 U; hence, the depletion of 238U is not very apparent in the same plot. 235U, on the other hand, undergoes fission and is gradually being depleted. As burnup continues, the odd-numbered plutonium isotopes which are fissile would also undergo fission and start to decrease in their respective quantities. By contrast, 240Pu and 242Pu which are not fissile would continue to build up and eventually exceed that of the odd-numbered plutonium isotopes. 3.5. Full core The assembly design is then extended to encompass the entire core with specifications detailed in Table 5 below. The core is designed such that both the radial and axial reflectors are made of graphite. Fig. 6 shows the X-Y or aerial view of the FHCR core while Fig. 7 depicts the Z or axial view. The magnified image to the right of Fig. 6 shows the peripheral graphite blocks surrounding the core that requires replacement after a stipulated duration since they will be subjected to high neutron irradiation over the course of reactor operation. The regions beyond the replaceable graphite are permanent radial graphite reflectors followed by the core barrel (R2 R1 ), FLiBe downcomer (R3 R2 ) and reactor pressure vessel (R4 R3 ) as seen in Fig. 7. Finally, Fig. 8 depicts the cycle length of the FHCR core operating at 3400 MWt, with an effective operating cycle length of 3.55 years prior to refueling. Currently, the design of the FHCR core is in the preliminary stage and does not have any control rods nor burnable poisons. 3.6. Reactivity coefficients The fuel temperature coefficient (FTC), also known as the Doppler temperature coefficient or Doppler effect, measures the
Fig. 6. FHCR full core.
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V. Krishna et al. / Annals of Nuclear Energy 141 (2020) 107288
Fig. 7. FHCR Core from Z view.
Table 6 Reactivity coefficients.
Fig. 8. FHCR full core burnup.
FTC (pcm/K)
MTC (pcm/K)
CTC (pcm/K)
0.96
1.60
0.04
because fuel heating leads to Doppler broadening which implies that more neutrons are susceptible to absorption by 238U at the widened resonance energies, thus decreasing reactivity and stabilizing the reactor. Additionally, as time progresses, the increased production of 240Pu contributes to higher resonance absorption and causes the FTC to become more negative. The moderator temperature coefficient (MTC) is defined as the change in reactivity per degree change in moderator temperature. As shown in Table 6, a perturbation of +100 K gives a negative value for the MTC and a corresponding decrease in keff . The coolant temperature coefficient, by contrast, is slightly negative or even negligible. Although the coefficients are only slightly negative, the presence of the solid moderator and graphite reflectors in the core provide sufficient thermal inertia to retard the rise in core temperatures from reactivity transients.
4. Summary decrease in reactivity for a 1 K change in fuel temperature due to an increase in resonance absorption of neutrons by mainly 238U. As shown in Table 6, a perturbation of +100 K gives a negative value for the FTC and a corresponding decrease in keff . This is
The parametric study conducted in this paper has described design conditions that allow for further optimization of the FHCR assembly in order to extend its operational cycle length. Packing
V. Krishna et al. / Annals of Nuclear Energy 141 (2020) 107288
fractions, levels of enrichment, and fuel pitch lengths are investigated to determine the optimal design values. With that, moderator analysis is performed with Be2C being found to be the most efficient moderator in extending the cycle length (approximately 3.55 years corresponding to a burnup of 160.6 MWd/KgU) as opposed to using graphite in the central region of the assembly. The observable phenomena include reactivity behavior and flux spectrum, with the reactivity coefficients being negative to reflect the main inherent safety feature of FHRs. It should be noted that the results attained in this study are preliminary and represent a proof-of-concept for future studies on this FHCR design. The core configuration displayed in Fig. 6 will be further assessed in future work involving burnable poison analyses as well as thermalhydraulics studies.
CRediT authorship contribution statement Vitesh Krishna: Conceptualization, Formal analysis, Investigation, Methodology, Writing – original draft. Ching Hiong Yap: Conceptualization, Formal analysis, Investigation, Methodology, Writing – original draft. Sicong Xiao: Supervision, Validation, Writing – review & editing.
Acknowledgement The authors would like to thank the anonymous reviewers for their insightful comments which greatly helped to improve the quality of this paper. This work is supported by the National Research Foundation Singapore (R-721-000-002-281). The authors declare that there is no conflict of interest regarding the publication of this paper.
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