PEBBLE FUEL DESIGN FOR THE PB-FHR

PEBBLE FUEL DESIGN FOR THE PB-FHR Anselmo T. Cisneros, Raluca O. Scarlat, Micheal R. Laufer, Ehud Greenspan, and Per F. Peterson University of California Berkeley 4155 Etcheverry Hall MC 1720, Berkeley, CA 94720 Tel: (510)-642-4077, Fax: (510)-643-9685, Email: tommycisneros@berkeley.edu Abstract This paper presents the results of parametric studies of pebble fuel that can guide the design of future PB-FHR cores. The pebble fuel designs are assessed using the following performance characteristics: burnup, reactivity feedback, transient response, timescale to reach equilibrium cycle, and protection of structural components. The performance of a thorium pebble blanket is assessed by comparing against a seed-only system and system that utilizes a graphite pebble reflector instead of a thorium blanket. This paper presents the functional requirements and a methodology to assess these fuel pebble designs. This paper identifies a feasible design space for low enriched uranium pebbles and selected a baseline pebble design for safe, economic energy generation. Furthermore, this study finds a thorium blanket does not increase the performance of the system significantly with respect to a graphite pebble reflector. Therefore, a graphite pebble reflector is recommended in the baseline full-core design to extend the lifetime of the outer solid graphite reflector to the life of plant. I. INTRODUCTION The Annular Pebble Bed FHR (PB-FHR) is a fluoride salt cooled high temperature reactor (FHR) that uses continuously refueled pebble fuel. Recent experimental and numerical simulations have proven the feasibility of maintaining radial zones of different pebble types without physical separation 1. The initial design of the PB-FHR calls for an annulus of low enriched uranium (LEU, 19.9w%) seed pebbles that drive a blanket of fertile thorium pebbles 2. The baseline for both fuel types is a once through fuel cycle; however, the thorium pebbles must breed their own fissile fuel, 233 U. The function of the seed pebbles is to safely and economically produce as much energy as possible prior to discharge. Scoping calculations indicate that the lifetime of the PB-FHR may be limited by neutron damage to graphite structural components. It is envisioned that the inner graphite reflector will be replaced periodically. However, it is easier and desirable to design the outer radial reflector to survive the life of plant. A blanket of thorium pebbles reduces neutron damage in the outer graphite reflector while producing power. Alternatively, an inert graphite pebble reflector could perform this neutron damage mitigating function even more effectively. The objective of this study is to find a feasible LEU seed pebble design and determine whether or not the outer solid graphite reflector must be protected with either a thorium pebble blanket or a graphite pebble reflector. If the outer solid graphite reflector must be protect, what is the best option. The methodology required to assess fuel designs with respect to multiple performance metrics is presented in section II. Section III presents the functional requirements of the LEU seed pebble and the results of a fuel design parametric study used to identify a feasible design space and define a baseline seed pebble fuel design. Likewise, Section IV presents the requirements of the thorium blanket and the results of blanket fuel design parametric study. In addition to comparing the performance blanket fuel designs this section also compares systems with thorium blankets against core configurations without one to determine if a thorium blanket is required in the PB- FHR. II. COMPUTATIONAL MODEL The computational model for this system is discussed in four subsections. The first is a description of the PB- FHR reactor system. The second discusses the neutronics and depletion models used to predict fuel cycle parameters as well as transient response parameters. The third presents the heat transfer model while the fourth describes the fuel economics model. 900

II.A. System Description The system description of the PB-FHR is presented in the following sections with each section corresponding to a different length scale: a full-core scale, a pebble scale and a TRISO particle scale, respectively (Figure 1). Fig. 1 Geometry of PB-FHR II.A.1 Full-Core Annular PB-FHR Geometry The baseline design of PB-FHR generates power from a packed bed of seed pebbles fueled with LEU that drive a subcritical blanket of thorium-fueled pebbles. Another design variant of the PB-FHR replaces the thorium blanket with a graphite pebble reflector. The primary coolant, flibe (67% molar LiF and 33% molar BeF 2 ), is circulated radially outward into the core from a central channel in the inner graphite reflector that also provides channels for shutdown rod insertion. The seed region of the bed extends from the inner graphite reflector to the blanket region as you continue out radially. The blanket pebbles are ultimately confined radially by the solid outer graphite reflector. The core can be segmented into five axial regions: an entrance region, an expansion region, an active region, a converging region and a defueling chute. The pebble bed floats upward as pebbles are removed from the top of the defueling chute (pebbles are designed to be buoyant in the flibe). Pebbles are initially segregated into their respective radial regions with a physical barrier in the entrance region, but after plug flow is established no barrier is required 1. The lower expansion region connects the entrance region to the active core region. The active region has a large radius to locally increase reactivity and power generation. The defueling chute is connected to the active region by the converging region. Dimensions of the core are presented in Table I. II.A.2 PB-FHR Pebble Geometry The PB-FHR uses pebbles similar to the Pebble Bed Modular Reactor (PBMR) that are spherical compacts of TRISO fuel particles encased in an inert graphite shell. However, the PB-FHR pebbles have a smaller radius to further improve heat transfer 3, and a low-density graphite core to control buoyancy and concentrate the fuel particles as close to the coolant as possible to minimize the temperature differential between the fuel and the coolant 4. Table II presents dimensions of the pebbles. TABLE I Dimensions of Full-Core Annular PB-FHR Core component Inner graphite reflector Pebble bed (entrance) Pebble bed (expansion region) Pebble bed (active region) Pebble bed (converging region) Pebble bed (defueling chute) Outer graphite reflector Pebble component Component dimension Dimensio n value Outer radius (cm) 90 Outer radius (cm) 160 Height (cm) 150 Expansion angle 60 (degrees) Outer radius (cm) 240 Height (cm) 300 Converging angle 45 (degrees) Outer radius (cm) 120 Height (cm) 150 Outer radius (cm) 300 TABLE II Dimensions of PB-FHR Pebble Component dimension Dimensio n value Low Density Graphite Pebble Outer Radius (cm) 0.0-1.31 Core Active Region Outer Radius (cm) 0.09-1.4 Pebble Shell Outer Radius (cm) 1.5 Coolant Pebble Packing Fraction (%) 60 II.A.3 PB-FHR TRISO Particle Geometry 901

The PB-FHR uses TRISO particle fuel similar to that used in HTGRs 5,6,7. The seed pebbles use UC 0.5 O 1.5 enriched to 19.9w% 235 U whereas the blanket pebbles utilize ThO 2 of natural thorium. The spherical fuel kernels are encased in a layer of porous graphite, an inner pyrolytic carbon layer, a silicon carbide layer and an outer pyrolytic carbon layer. The TRISO particles are dispersed in a graphite matrix. Table III presents dimensions of the TRISO particles. TABLE III Dimensions of PB-FHR TRISO Particles TRISO particle component Component dimension Dimension value (seed / blanket) Fuel Kernel Kernel Diameter (µm) 250-1000 / 600 Buffer Layer Thickness (µm) 100 /64 Inner Pyrolytic Carbon Layer Thickness (µm) 35 / 26 Silicon Carbide Layer Thickness (µm) 35 / 31 Outer Pyrolytic Carbon Layer Thickness (µm) 35 / 55 Graphite TRISO Packing matrix Fraction (%) <40% II.B. Neutronics Model The continuous energy Monte Carlo neutron transport code, MCNP5 version 1.51, is used to perform neutron transport simulation 8. Fuel kernels are modeled explicitly on a simple cubic lattice to correctly account for the double heterogeneity of the pebble-bed fuel. However, the TRISO layers are homogenized together with the graphite matrix to accelerate the computation without sacrificing accuracy 9. Two models are used for this study: a unit cell of LEU pebbles with reflective boundary conditions to represent a large well-mix bed of seed pebbles with different burnup states, and a full-core model of an PB-FHR with an inner LEU pebbles region surrounded by a blanket of fertile thorium pebbles. II.B.1 Pebble Unit Cell Model In a continuously refueled pebble-bed reactor, the integral neutronic parameters of the core, such as k- effective, are dependent on the aggregate fuel composition of all the pebbles in the core. It is assumed that, due to the multi-recycling of the fuel pebbles and continuous refueling each volume element of the core will contain, on average, equal number of pebbles with any burnup level between zero to the discharge burnup. The neutron spectrum the pebbles are exposed to is affected by the pebbles burnup distribution. This burnup dependence is accounted for by using a face-centered cubic unit cell with reflective boundary conditions composed of pebbles of eight burnup states equally spaced from zero to the discharge burnup. For the depletion calculations, effective one group cross sections are generated for each burnup state. A fuel pebble that enters a specific burnup state is depleted with the corresponding set of burnup dependent cross sections until it advances to the next burnup state or is discharged. II.B.2 Full-Core Model The structural design of the PB-FHR originally described by Hong et al. 10 is used as a basis for the fullcore model. The PB-FHR operates at 900 MWth with the power distribution between the seed and blanket determined based on the flux distribution calculated from neutron transport. In the neutron transport model, the seed and blanket regions are populated by lattices of FCC unit cells similar to those described in the previous section. The unit cells of both the seed and the blanket only have four burnup states. Pebbles on opposite faces of the cubic unit cell and in the corners have the same burnup state, so that pebbles have a single burnup state in the global universe of the MCNP model. The interface between the seed and blanket in the PB-FHR model are set to maintain the cross sectional area ratios imposed in the entrance region of the core as predicted by numerical simulations and confirmed in pebble recirculation experiments 1. The volume fraction of the blanket or graphite pebble reflectors analyzed in this study are reduced to 21% (limited by a minimum blanket thickness at the inlet of about 4 pebble diameters required to maintain separate seed and blanket regions) from 61% as in the 2010 feasibility study to improve anticipated transient without scram (ATWS) response 2. II.B.3 Equilibrium Depletion Analysis The neutron transport code MCNP5 is coupled to the depletion analysis code ORIGEN2.2 11 by the Burnup Equilibrium Analysis Utility, BEAU, developed at UC Berkeley. BEAU iteratively searches for the equilibrium fuel cycle parameters subjected to user-specified core power, no excess reactivity at equilibrium and a target blanket discharge burnup using the methodology described by Cisneros et al. 12. Once these conditions are satisfied, BEAU determines power and flux distributions throughout the core, composition evolutions of each fuel type throughout the fuel cycle, and generates an MCNP5 input deck of the core at equilibrium. 902

The concentration of 6 Li in the coolant plays an important role in the neutron economy, tritium production and coolant temperature reactivity feedback in FHRs. Therefore, it is important to determine the system specific equilibrium concentration of 6 Li. Because the equilibrium 6 Li composition depends on the core neutron spectrum, an FHR specific module is implemented in BEAU s depletion analysis sequence to solve for the equilibrium concentration of 6 Li using equation 1 13. II.C Pebble Heat Transfer Model The temperature distribution within a fuel pebble needs to be known in order to accurately account for the density and temperature of the pebble constituents. A simple analytical unit-cell heat transfer model was developed for a single pebble. This model breaks the heat transport problem into two length scales: the pebble scale and the TRISO particle scale as proposed by Stainsby et al.14. At the pebble scale, the power is assumed to be uniform throughout the fuel loaded region of the pebble. The bulk temperature of the coolant and zero heat flux at the insider boundary of the fuel layer are used for the boundary conditions. At the TRISO scale, the power is decomposed into positive power generated in the fuel kernel and negative power generated in the TRISO layers and matrix such that the power sums to zero on this scale as proposed by Stainsby et al. 14. Zero heat flux at the center of the fuel kernel and zero mean temperature of the TRISO unit cell are taken as the boundary conditions for the model on the TRISO scale. The temperature distribution in this model is taken as the TRISO scale temperature distribution superimposed onto the pebble scale temperature distribution. Heat transfer properties of pebble and TRISO particle constituents are taken from the OECD 15 presented in Table IV; heat transfer properties of the coolant were taken from Williams et al. 16. Thermo-physical properties of thorium are assumed to be the same as LEU properties. Homogenized thermal conductivities of the active region were generated based on the TRISO particle design of each pebble using Maxwell s method. Convection coefficients were generated using Wakao s modified Nusselt assuming a Reynolds number of 1200 17. TABLE IV Thermal Conductivities for Pebble Components 15 (1) Pebble Constituent Thermal Conductivity (W/mK) Shell 15 Active Region (derivative of TRISO design) TRISO Constituent Thermal Conductivity (W/mK) Kernel 3.7 Buffer 0.5 Pyrolytic Carbon 4 Silicon Carbide 16 Matrix 15 II.D Fuel Costs Model This study uses the fuel costs model developed by INL 18. Fuel cycle analysis can determine the flows of uranium ore, required feed, tails to be disposed, separative work required, and waste produced. Estimated specific fuel cycle costs for N th of a kind were taken from Shropshire 19 and inflated to 2012 dollars; see Table IV. Fuel cycle costs for thorium fuel are assumed to be similar to those for uranium where they apply. Fuel costs for an arbitrary amount of fuel are normalized by the energy generated assuming the maximum seed burnup obtained from depletion analysis or the blanket burnup imposed in the depletion calculation definition. The average fuel costs in system with both LEU and thorium pebbles is calculated by weighing these normalized fuel costs by the power fraction of each fuel type. TABLE IV Specific Fuel Costs for PB-FHR Fuel Cycle NOAK Costs LEU Thoriu m Uranium Ore ($/kg) 106 - Uranium Conversion ($/kg) 11 11 Uranium Enrichment ($/SWU) 122 - Tails Disposal ($/kg) 11 - Fuel Fabrication ($/kg) 11600 11600 Spent Fuel Storage ($/kg) 233 233 Spent Fuel Disposition ($/kg) 3293 3293 III. LOW ENRICHED URANIUM PEBBLE FUEL DESIGN A parametric study was undertaken to identify a feasible design space and to select a baseline seed pebble fuel design for the FHR core. The design variables include the kernel diameter, TRISO packing fraction, radius of the low-density graphite pebble core and density of this core. The pebble buoyancy design requirement was satisfied by imposing an average pebble density of 1.745. For this study 35 seed pebble designs were investigated with design parameters (pebble core radius, 903

pebble core density, and TRISO packing fraction) used to impose a C/HM and an III.A. Low Enriched Uranium Pebble Design Objectives Anticipated transient without scram, ATWS, is the most severe beyond design basis event postulated for an FHR. The ATWS hot shut-down coolant outlet (AHSCO) temperature is used as the metric of ATWS response. Feasible LEU pebble fuel designs must have negative fuel and coolant temperature coefficient of reactivity resulting in a low AHSCO temperature. Nickel based alloys to be used for metallic structural components and heat exchangers are limited to 704ºC peak temperature during normal operation 3. These structures will fail as a function of their time integrated temperatures. Therefore this study assumes that peak temperatures of metallic components must not exceed 750ºC in a beyond design basis event like ATWS with loss of forced cooling to avoid performing coupled neutronics and thermal fluids transient analysis. This component of the fuel design study will search for the pebble design offering the highest maximum burnup while meeting these safety requirements. The economics of seed pebbles depends on the uranium fuel cost (ore, conversion, tails-disposal, enrichment), and pebble fabrication cost. In literature, fabrication costs of TRISO particles scale only with the mass of uranium (most likely because of speculative cost models) 18,19. Therefore, maximizing the discharge burnup while maintaining reactor safety minimizes the LEU fuel cycle cost. Fig. 2 Seed Fuel Temperature Reactivity Coefficients as a function of Seed Fuel Design (pcm/k). All the fuel temperature reactivity coefficients are negative, with the strongest negative feedback occurring for lower C/HM values, that is, harder spectrum. The coolant temperature reactivity coefficients become positive for higher C/HM. Voiding the coolant in the unit cell model has two effects: reducing neutron absorption in, primarily, 7 Li and 6 Li, a strong thermal neutron poison, and spectrum hardening due to removal of neutron moderators 7 Li, 9 Be and 19 F. III.B. Low Enriched Uranium Pebble Parametric Study Results III.B.1 Temperature Reactivity Feedback The fuel temperature reactivity coefficients were determined by using Doppler broadened neutron cross section libraries at 600K, 900K and 1200K. The coolant reactivity coefficients were determined by changing the coolant density 16 according to equation 2 as well as using temperature dependent cross section libraries. The resulting temperature reactivity coefficients are presented in figures 2 and 3 respectively. (2) Fig. 3 Coolant Temperature Reactivity Coefficients as a function of Seed Fuel Design (pcm/k) The coolant is an important moderator in FHRs especially for fuel designs with low C/HM. In these systems, the loss of moderator is the dominant effect and as a result, the coolant temperature reactivity feedback is more negative the lower is C/HM; that is, the more undermoderated the system is. 904

III.B.2 Response to Anticipated Transient Without Scram Since both coolant and fuel reactivity coefficients are required to be negative in credible FHRs designs, a decrease in fuel temperature due to a decrease in power from full power to decay heat is compensated by an increase in coolant temperature such that in ATWS, the reactivity of the system equilibrates to just less than zero. Assuming the core equilibrates to a temperature difference from inlet to outlet of T core at the end of the transient, where this temperature difference creates buoyancy forces sufficient to remove decay heat by natural circulation, the AHSCO temperature can be evaluated approximately using equation 3. Here, Tº fuel and Tº coolant are the average temperature the LEU kernels and the bulk temperature of the coolant respectively at steady state. The core-average initial fuel temperatures are determined using the unit cell heat transfer model previously described in section II.C. For this analysis, the temperature rise across the core required to remove decay heat by natural circulation is assumed to be approximately 100K 21 and the initial average temperature of the fuel and coolant prior to the ATWS transient is calculated assuming a power density of 16.2 MW/m 3 the average core power density if power were only generated in the seed. The equilibrium coolant outlet temperature as a function of fuel design is presented in figure 4. (3) Fig. 4 ATWS hot shutdown coolant outlet temperature as a function of Seed Fuel Design (ºC) Reducing the initial temperature differential between the fuel and the coolant can reduce the potential for coolant temperature increase. Also, stronger negative coolant temperature feedback coefficients keep the ATWS hot shutdown coolant temperature closer to the initial bulk coolant temperature. III.B.3 Maximum Attainable Burnup The maximum attainable discharge burnup was estimated using BEAU as described in the neutronics methodology section. The maximum burnup for each fuel design is presented in figure 5 Fuel designs with low C/HMs (harder neutron spectra), have excellent neutron utilization and a high conversion ratio but low eta, and vice versa for systems with high C/HM. Fuel designs around a C/HM of 400 reach the highest burnups because the spectrum in these systems balances good neutron economy with efficient fuel breeding. The diameter of the fuel kernel affects the degree of spatial self-shielding in the fuel. Neutrons of resonance energies can penetrate into small fuel kernels more than into large ones. Therefore, kernel size can affect the ratio of consumption to breeding of fissile isotopes in the system, though to a lesser extent than C/HM. 905

TABLE V Selected Design Values for Baseline LEU Fuel Pebble Parameter Value Carbon to heavy metal ratio 300 Fuel kernel diameter (µm) 400 TRISO packing fraction (%) 40 Pebble core radius (cm) 1.12 Pebble core density (g/cc) 1.54 IV. BLANKET DESIGN IV.A. Blanket Design Objectives Fig. 5 Maximum Attainable Burnup in Seed Pebble as a function of Seed Fuel Design (MWd/MT) III.B.4 Baseline Low Enriched Uranium Pebble Fuel Design Description The negative coolant reactivity coefficients and maximum AHSCO temperature constraint limits the feasible design space. Figure 6 shows the maximum burnup plot over which the ATWS dictated feasible design space imposed. Fig. 6 Feasible Design Space on a Map of Investigated Design Space. The fuel design with the maximum burnup with in this feasible design space is taken as the baseline seed fuel design (C/HM: 300 kernel diameter: 400µm); this seed fuel design will be used for the rest of this study. The engineering parameters that fully define this fuel design are presented in table V. An outer thorium blanket can capture high-energy neutrons leaked from the seed region to mitigate neutron damage to the outer graphite reflector, which needs to last the lifetime of the plant, thereby beneficially utilizing neutrons that would otherwise be wasted breeding 233 U. Pebbles containing un-irradiated thorium are loaded into the outer blanket zone. These pebbles capture high-energy neutrons at resonance energies to breed 233 U. This way the flux of fast neutrons that the outer solid reflector is exposed to is greatly reduced. The effect of radiation damage to structural graphite (volume, strength, thermal conductivity, etc) is dependent on the techniques used during fabrication and operating conditions 20. For this study, a neutron-damage limit of 15 DPA 20 is assumed for the outer solid graphite reflector. The desirable operating lifetime for this reflector is at least 60 years. The thorium blanket can reduce the fuel costs of the system by generating energy from fuel that is significantly less expensive than the LEU seed pebbles; this costs savings is maximized for blankets that produce more power. Blanket pebbles are susceptible to long residence times because they have high fuel loadings, require high burnups (~100 GWd/MT) before they start to generate power and are in the low average neutron flux. Long residence times are undesirable for a number of reasons: long time to reach equilibrium, more expensive to qualify fuel, increased pebble erosion, etc. This study limits residence time in the blanket to less than 6 years. Additionally, the same safety requirements of negative reactivity coefficients and gentle ATWS response from the LEU fuel design parametric study apply to full-core PB- FHR model. IV.B. Thorium Pebble Parametric Study Results For this study, four blanket fuel loadings were investigated. The design variables used to impose a C/HM and an average density of 1.745 g/cc are pebble 906

core radius, pebble core density, and TRISO packing fraction. and the target discharge burnups of 100, 150, 200 and 250 GWd/MT. This parametric study determines the equilibrium state of the PB-FHR assuming each blanket fuel design in the blanket region and the baseline LEU seed fuel design in the seed region to assess full-core performance parameters. This blanket parametric study assesses the system performance with various thorium blanket pebble designs to determine whether there is a thorium pebble design space that significantly outperforms full-core configurations without thorium blankets. IV.B.1 Neutron Damage to Outer Graphite Reflector The outer reflector lifetimes are presented as a function of blanket fuel design in table VI. Alternatively, the extension of reflector lifetime can be achieved using a graphite pebble reflector. Therefore, the reflector lifetime of the PB-FHR with a thorium blanket is also compared against a system where the thorium blanket is replaced by graphite pebble reflector, in addition to a system with no blanket. TABLE VI Outer Graphite Reflector Lifetimes PB-FHR Core Configuration Lifetime of outer graphite reflector (EFPY) Seed Only 19 Blanket with C/HM: 100 37 Blanket with C/HM: 200 48 Blanket with C/HM: 300 61 Blanket with C/HM: 400 68 Graphite Pebble Reflector 170 Either a thorium blanket or graphite pebble reflector can extend the lifetime of the outer graphite reflector beyond the life of the reactor 60 EFPY. IV.B.2 Temperature Reactivity Feedback The fuel temperature reactivity coefficient was divided into two components one for the temperature change in the seed and another for the blanket. The coolant temperature reactivity coefficients were determined using the same method for the full-core model as they were in the unit cell model. These reactivity coefficients are presented in Table VII. Seed temperatures reactivity coefficients for all three configurations are similar to the fuel reactivity coefficient for the baseline fuel design predicted in the unit cell model, -4.5 (pcm/k). The blanket temperature reactivity coefficient is small because this region produces little power, so it only has little effect on the aggregate system reactivity. The coolant reactivity is much smaller in the full-core model than the unit cell model because moderation lost due to coolant voiding is offset by increased moderation from the inner and outer reflector enabled by increased neutron streaming. TABLE VII Reactivity Coefficients for Full-Core PB-FHR Model PB-FHR Configuration Seed Temperature Reactivity Coefficient (pcm/k) Seed only -4.7 ± 0.2 With thorium blanket -4.4 ± 0.2 With graphite pebble reflector -4.5 ± 0.2 Blanket Temperature Reactivity Coefficient (pcm/k) With thorium blanket -0.14 ± 0.08 Coolant Temperature Reactivity Coefficient (pcm/k) Seed Only -0.58 ± 0.08 With thorium blanket -0.55 ± 0.08 With graphite pebble reflector -0.49 ± 0.08 IV.B.3 Anticipated Transient Without Scram Response Equation 3 for the AHSCO temperature is updated to incorporate a term for the blanket s contribution to the ATWS response, as shown in equation 4. The initial temperature distribution is calculated based on the average power density of the seed and blanket at the equilibrium state using the unit cell heat transfer model previously described in section II.C. The AHSCO temperatures for each core configuration are presented in Table VIII. TABLE VIII ATWS Hot Shutdown Coolant Outlet Temperature PB-FHR Core Configuration Seed Power Density (MW/m 3 ) (4) ATWS Hot Shutdown Coolant Outlet Temp. (ºC) Seed Only 12.8 743 Blanket with C/HM: 100 14.9 744-745 Blanket with C/HM: 200 15.3 746-749 907

Blanket with C/HM: 300 15.5 747-750 Blanket with C/HM: 400 15.6 751-753 Graphite Pebble Reflector 16.2 755 Since the temperature reactivity coefficients are similar for each core configuration the differences in seed power densities drive the differences in AHSCO temperatures. IV.B.4 Fuel Utilization Traditionally, fuel utilization is measured by average fuel burnup. However, a system with two feed fuels complicates things. To take into account the additional energy generated by a fertile blanket, one can quantify the fuel utilization with an effective burnup 2, as defined in equation 5. This definition treats the fertile material as if it were free. One can also assess the fuel utilization with the fuel costs normalized per unit electricity produced. Normalized fuel costs are a function of all fuel cycle costs in the seed and blanket normalized by the electric energy produced (assuming a thermal efficiency of 46%) and weighted by the amount of power produced by each fuel type. Therefore, it incorporates the benefit of increased blanket burnup and better accounts for the cost of fabricating thorium fuel. Normalized fuel costs are presented as a function of blanket pebble design in figure 7. These fuel costs are compared against systems without a thorium blanket in Table X. (5) The effective burnups for systems with thorium blankets are compared to systems without thorium blankets in Table IX. The reduction in seed burnup is compensated for by increased power generation in the thorium blanket the blanket produces from 8%-4% of the power with blankets with high fuel loading (low C/HM) producing more power. The fraction of power generated in the blanket is not sensitive to its discharge burnup within the range of burnups studied because the concentration of 233 U/Th reaches equilibrium at a burnup of ~100 GWd/MT 2, after which, these systems have roughly the same reactivity. The higher average concentrations of 233 U in high burnup cases are offset by higher concentrations of fission products resulting in similar reactivities for higher burnup blankets. PB-FHR Core Periphery TABLE IX Effective Burnups Seed Burnup (MWd/MT ) Effective Burnup (MWd/MT ) Seed Only 2.21e+5 2.21e+5 Blanket with C/HM: 100 2.10e+5 2.28e+5 Blanket with C/HM: 200 2.11e+5 2.25e+5 Blanket with C/HM: 300 2.13e+5 2.23e+5 Blanket with C/HM: 400 2.14e+5 2.22e+5 Graphite Pebble Reflector 2.16e+5 2.16e+5 Fig. 7 Fuel Costs Normalized by Electric Energy as a Function of Blanket Design (cents/kwhr-e) According to the economic model, thorium fuel pebbles are expected to have drastically lower normalized fuel costs, (less than 1.3 mil per kwhr-e), because thorium ore is assumed to have no cost and requires no enrichment. Blanket designs with higher fuel loadings produce more power, so fuel costs are weighted by a larger power fraction. Furthermore, thorium pebbles discharged at higher burnups produce more energy for the same fuel costs, further reducing fuel costs. However, using a thorium blanket only reduces the fuel costs by 2-4%. TABLE X Normalized Fuel Costs PB-FHR Core Configuration Fuel Costs (cents/kwhr-e) Seed Only 2.98 Blanket with C/HM: 100 2.91-3.01 Blanket with C/HM: 200 2.95-3.01 Blanket with C/HM: 300 2.98-3.01 Blanket with C/HM: 400 2.99-3.01 Graphite Pebble Reflector 3.04 908

IV.B.5 Thorium Pebble Residence Time Residence time of the blanket pebbles is a function of discharge burnup, fuel loading (C/HM) and power levels in the blanket; see Figure 8. The minimum residence time is greater than the limit established for this study. Fortunately, the systems with the shortest residence times correspond to the longest reflector lifetime (the primary objective of the blanket is to extend the lifetime of the outer reflector). Increasing the power of the whole core can shorten these cycle lengths or using fuel designs with even lower fuel loadings (higher C/HM). identified for the LEU seed pebble fuel design from which a baseline fuel design was selected. This LEU seed pebble design was implemented into a full-core model of the PB- FHR to determine if there was a design space where a fertile thorium blanket would significantly outperform a graphite pebble reflector with respect to extending the lifetime of the outer solid graphite reflector, fuel utilization and transient response. This study concludes that the contribution of the thorium blanket to the reactor power is too small to justify its use. A graphite pebble reflector is the preferred approach for extending the life of the solid graphite reflector to the reactor lifetime. The baseline LEU seed pebble fuel design and graphite pebble reflector core configuration will be adopted as the baseline design in future studies of the PB- FHR. ACKNOWLEDGMENTS This material is based upon work supported under a Department of Energy Nuclear Energy University Programs Graduate Fellowship. Any opinions, findings, conclusions or recommendations expressed in this publication are those of the author(s) and do not necessarily reflect the views of the Department of Energy Office of Nuclear Energy. Fig. 8 Blanket Residence Time as function of Blanket Design (EFPY) IV.B.6 Baseline PB-FHR core configuration Either a thorium blanket or graphite pebble reflector must be implemented in a PB-FHR to extend the lifetime of the outer graphite reflector to the life of plant. However, none of the thorium blanket pebble fuel designs investigated in this study significantly increase the performance of the core with respect to fuel utilization or transient response compared to the case with a graphite pebble reflector. Furthermore, the long residence times of the fertile pebbles will make the approach to the equilibrium state arduous if not impractical. Therefore, this study recommends implementing a graphite pebble reflector rather than a fertile thorium blanket. IV. CONCLUSIONS This study presented the functional requirements of fuel designs for seed and blanket pebbles as well as a methodology to assess candidate fuel designs. Using these requirements and methods a feasible design space was REFERENCES 1. J. BICKLE, A. CISNEROS, M. LAUFER, L. LI, P. F. PETERSON, Conceptual Design, Experiments, and Analysis for the Core of a FHR Test Reactor, ICAPP 2010, San Diego, California, June 13-17, (2010). 2. A. CISNEROS, E. GREENSPAN, P. F. PETERSON, Use of Thorium Blankets in a Pebble Bed Advanced High Temperature Reactor, ICAPP 2010, San Diego, California, June 13-17, (2010). 3. P. BARDET et al., "Design, Analysis and Development of the Modular PB-AHTR," Proceedings of the 2008 International Congress on Advances in Nuclear Power Plants, ICAPP'08, p. 161-178 (2008). 4. A. GRIVEAU et al., "Transient Thermal Response of the PB-AHTR to Loss of Forced Cooling," 909

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