Abstract

Fluoride-salt-cooled high temperature reactor (FHR) effectively combines the solid fuel and moderator design of high-temperature gas-cooled reactor (HTGR) technology with the fluoride salt coolant (LiF-BeF2, FLiBe) of molten salt reactor (MSR) technology, enabling low-pressure (∼1 atm, 101.325 kPa), and high-temperature (∼700 °C) operations. The design and operational features of the FHR make it a potentially attractive option for a small modular reactor (SMR), provided that it can be modified and made physically small and operate at a low-enough power level (<350 MWth/<150 MWel). Most FHR-SMR designs use high-assay low enriched uranium (HALEU) fuel in the form of tri-structural isotropic (TRISO) fuel particles, combined with the use of a graphite moderator. However, there are alternative design concepts for an FHR-SMR that may offer superior performance characteristics, while utilizing an alternative fissile fuel supply option. In this exploratory study, lattice physics calculations were performed with Serpent to evaluate an alternative FHR-SMR prismatic fuel block design concept using coated annular fuel pellets instead of TRISO-particle fuel compacts, along with the use of hydrogen-based solid moderator rods made of 7LiH. In initial studies, it was found that fuel blocks with 120 moderator rods made of 7LiH tended to have large positive temperature reactivity coefficients (TRCs), which is undesirable for safety reasons. However, reducing the number of moderator rods to 90 or 54, while increasing the number of fuel rods and coolant holes led to low or negative temperature coefficients. For a prismatic fuel block design with 54-7LiH moderator rods, the isothermal temperature coefficient of reactivity (Isothermal TRC), with simultaneous changes in the fuel (F), graphite (G), hydrogen (H), and coolant (C) temperatures, ranges between −0.159 mk/K and −0.054 mk/K, depending on the operating temperature and fuel burnup. Such alternative FHR-SMR fuels could achieve a single-batch core life of ∼10 years with low enriched uranium (LEU) fuel, and ∼45 years with HALEU, in a 350-MWth reactor core.

1 Introduction

1.1 Background.

The concept of the fluoride-salt-cooled high temperature reactor (FHR) has been under development over the last 20 years, with strong interest by a number of universities, government laboratories, and small modular reactor (SMR) vendors [13]. The FHR was proposed by Oak Ridge National Laboratory (ORNL) in 2003 and other institutions [35]. The original FHR concept uses graphite and tri-structural isotropic (TRISO) fuel particles [6], similar to what is used in HTGR, but uses a fluoride-based molten salt (such as FLiBe) as a coolant instead of helium for improved heat transfer, and the ability to operate without pressurization [7,8]. As stated by Jiang and Zhang [2], “FHR effectively combines the high-temperature and high-burnup fuel technology of a HTGR, the low-pressure and high-temperature molten salt cooling technology of MSR, and the passive safety technology of liquid metal cooled fast reactors. Compared with the MSR, the coolant of FHR does not possess high radiation, and it can reduce the requirement of structural materials.”

The FHR operates at temperatures (typically between 600 °C and 700 °C) [2,3,5]) that are much higher than in water-cooled reactors, such as pressurized water reactors (280 °C–315 °C) and pressure tube heavy water reactors (250 °C–310 °C). During operation, the nuclear energy generated by the reactor core is transferred to the fluoride salt and is removed through the primary heat exchangers. Various energy conversion systems can be coupled with the FHR, and the thermal interface required for high temperature processing can be provided with the added advantage of a heat storage facility and molten salt energy storage pool. Therefore, the FHR system can provide integrated energy solutions to users, including electricity and heat for high-temperature processing [9,10]. For example, Greene [5] and Forsberg [9] and others [10,11] have indicated that a number of crude oil recovery methods, petrochemical refining process such as thermal-cracking and distillation of heavy crude oil, bitumen (from oilsands), shale oil, and soft coal can be carried out successfully if the process heat is the range of 600 °C–700 °C.

The design and operational features of the FHR make it a potentially attractive option for SMR applications [12], provided that it can be modified and redesigned such that it can be made physically small and operate at a low-enough power level (typically in the range of 20 MWel–300 MWel). It will also be desirable for an FHR-SMR to have a relatively long operating life (>10 years) before it requires refueling. In addition, such a modified FHR design should have inherent or natural safety features, such as near-zero or negative temperature coefficients of reactivity, which will make the FHR easier to control under normal operating conditions and postulated accident scenarios. Of course, such features are also desirable/required for large-scale reactors.

1.2 Motivation.

The purpose of this study is to evaluate the performance characteristics (k-inf, k-eff, neutron leakage, exit burnup) and safety characteristics (temperature coefficients of reactivity) of an alternative fuel design for a FHR, based on modifications to an alternative HTGR fuel design investigated in a previous study at Canadian Nuclear Laboratories (CNL) [13].

In this study, “FLiBe” (a eutectic mixture of LiF + BeF2) is used as a coolant instead of helium. The alternative FHR fuel design differs from more conventional FHR design concepts developed by ORNL and Kairos Power [35,8] in that it uses a multilayer annular fuel pellet instead of a TRISO particle fuel compact and it also uses a hydrogen-based moderator (in the form of solid 7LiH rods) instead of graphite. The proposed annular fuel pellet is analyzed with two levels of uranium enrichment 5 wt.% U-235/U and 19.75 wt.% U-235/U, which are representative of low enriched uranium (LEU) and high-assay LEU (HALEU), respectively.

The previous FHR-SMR design concept of the small modular advanced high temperature reactor [5] that was completed by ORNL and other collaborators in 2010 selected FLiBe as its primary coolant. FLiBe coolant has the advantage of a lower melting temperature (732 K/459 °C) and melts viscosity [5]. Kairos Power's KP-FHR concept proposed in 2018 [8] combines the use of TRISO particles in fuel pebbles (instead of fuel compacts) with FLiBe coolant.

It is anticipated that FLiBe, as a low-pressure coolant, will have fewer occupational hazards (namely, risk of fire) as a primary coolant than a liquid alkali metal, such as sodium, which is much more chemically reactive. In the unlikely event that fuel is damaged, and fission products are able to escape from the fuel, it is expected that the majority of fission products will stay contained in the FLiBe, with the exception of tritium and noble gases, such as xenon and krypton [7].

However, it is recognized the manufacturing of FLiBe salt will entail different risks due to the use of beryllium in BeF2, where beryllium is a toxic metal, and FLiBe itself will toxic [14,15]. There will also be the issue of tritium production due to neutron reactions on Li, Be, and F, and that is why it will be necessary to use lithium enriched to 99.975 at% Li-7/Li, to minimize tritium (H-3) production from reactions on Li-6 (n + Li-6 → H-3 + He-4). The chemical toxicity of FLiBe due to BeF2 and the radiotoxicity of FLiBe when activated due to production of trace amounts of tritium are tradeoffs [3,5].

1.3 Other Studies of Interest for Fluoride-Salt-Cooled High Temperature Reactors.

Although the focus of this work was to modify and adapt an existing alternative HTGR prismatic fuel block design concept explored recently at CNL [13], it is recognized that other research groups within the international community have also carried out similar studies exploring alternative FHR fuel design concepts, such as those at Cambridge University [1619] and Massachusetts Institute of Technology [20], where the idea of adapting advanced gas-cooled reactor (United Kingdom) technology with a molten salt coolant was considered.

2 Description of Fluoride-Salt-Cooled High Temperature Reactor-Small Modular Reactor Alternative Fuel Design Concept to Be Assessed

2.1 Use of Coated, Multi-Layer Annular Fuel Pellets Instead of Tri-Structural Isotropic –Based Fuel Compacts.

While TRISO fuel particles in the form of fuel compacts or fuel pebbles are proposed typically for the majority of HTGR and FHR concepts, a different and potentially superior design concept is considered in this study, a concept that could permit higher fuel burnup, improved uranium and fissile utilization, and longer core life [13,2123]. Instead, a multilayer annular fuel pellet that is similar to the structure of a conventional fuel element used in pressurized water reactors, pressure tube heavy water reactors, and British advanced gas-cooled reactors is proposed, as an alternative to TRISO particle fuel compacts. Such a concept was also investigated as an alternative fuel for HTGRs, as discussed in the previous lattice physics studies by Wojtaszek and Bromley [13]. The anticipated advantage of this design concept is that it can allow a higher fissile loading density (fissile atoms/cm3) in the fuel than that found in TRISO-type fuels, which have most of their volume (more than 50%) occupied by nonfuel structural materials, such as graphite, pyrolytic carbon (PyC), and silicon carbide (SiC). The other advantage is that this design concept can incorporate some of the protective features of TRISO-type fuels, and accident-tolerant fuels with multiple coating layers, making the fuel more durable and robust. Similar ideas for non-TRISO fuels for use in high-temperature reactors have been proposed other research groups [5,2123].

2.2 Design and Operational Specifications for Fuel Concept.

This lattice physics study for an alternative FHR-SMR fuel uses the multilayer annular fuel pellet concept, combined with FLiBe coolant, in a hexagonal, prismatic fuel block made of graphite structural material, based on the MHTGR-350 benchmark design concept [24], and similar to that used in the previous study by Wojtaszek and Bromley [13]. The multilayer annular fuel pellet consists of two concentric, hollow cylinders (see Fig. 1) and uses additional protective layers to prevent the migration of fission products.

Fig. 1
Radial cross section view of fuel element geometry
Fig. 1
Radial cross section view of fuel element geometry
Close modal

The lattice physics model is a “standard” (without shutdown rods) prismatic fuel block with a single axial layer of fuel element (4.928 cm), which corresponds to the height of a single fuel compact in the MHTGR-350 benchmark problem design [24]. The total power in the 4.928-cm axial layer for the prismatic fuel block is set to 36 kW, which is the power per compact (172 W) multiplied by the 210 fuel compact locations per fuel block, and rounded to the nearest kW, as found in the original MHTGR-350 benchmark design concept [2427]. As stated in Ref. [13], “the replacement of fuel compacts with annular fuel elements also requires the replacement of several fuel elements and coolant channels with special moderator elements to improve moderation to achieve a fuel block that is supercritical in the core at the beginning of cycle (BOC).” The configuration of moderator elements in the fuel block is shown in Fig. 2. In this configuration, there are 108 moderator holes on the outside, 12 moderator holes on the inside, 132 fuel holes, and 66 coolant holes. The number of fuel and coolant holes have been reduced from the original reference design (210 fuel holes, 108 coolant) holes by approximately 40% (132/210∼0.63; 66/108∼0.61), which suggests an increase in the volumetric power density in the fuel elements of approximately 60%.

Fig. 2
Modified HTGR fuel block concept with 120 moderator rods ([13]) * Outer and inner rods represent fuel and coolant holes that have been filled with a hydrogen-based moderator, such as 7LiH. There are 108 Moderator holes on the outside, and 12 Moderator holes on the inside. ** There are 132 Fuel Holes, and 66 Coolant Holes. The fuel holes are filled with annular fuel pellets instead of TRISO-based fuel compacts.
Fig. 2
Modified HTGR fuel block concept with 120 moderator rods ([13]) * Outer and inner rods represent fuel and coolant holes that have been filled with a hydrogen-based moderator, such as 7LiH. There are 108 Moderator holes on the outside, and 12 Moderator holes on the inside. ** There are 132 Fuel Holes, and 66 Coolant Holes. The fuel holes are filled with annular fuel pellets instead of TRISO-based fuel compacts.
Close modal

In addition, each moderator element comprises a cylindrical 7LiH pellet (0.73-cm radius) encased in SiC cladding (0.794-cm outer radius). Lithium hydride (7LiH) is chosen for the additional moderation since it is a more effective moderator than carbon in graphite, with a much shorter slowing-down distance, due to the use of hydrogen. In addition, the use of a hydrogen-based moderator such as 7LiH will help reduce the migration distance in the prismatic fuel block, which will reduce neutron leakage from the FHR-SMR core. This feature is important in order to achieve compact, small-sized reactor cores, with a long operational life before refueling is required.

With the use 7LiH rods, the moderation of neutrons in the prismatic fuel block will be dominated by the 7LiH, with supplementary moderation provided by the solid graphite, and also by the FLiBe coolant. Thus, the solid graphite in the fuel block serves mainly as a structural component for the different holes containing fuel, coolant or 7LiH. As a structural material, the use of graphite is attractive for use due to its high-temperature stability, and its low neutron absorption cross section, which is preferred for use in HTGRS, FHRs, and MSRs. However, it is possible that alternative structural materials (such as SiC composite) could be considered for the design of such prismatic fuel blocks.

With regards to the feasibility of using 7LiH as a high-temperature moderator, there are a number of factors that can be considered. The average temperature of the FLiBe coolant in the proposed FHR concept will be ∼675 °C = (650 °C + 700 °C)/2, which is below the melting point (∼688 °C) of 7LiH [2830]. It is possible that closer to the core exit, where the coolant is at 700 °C, there could be localized melting of the 7LiH inside the SiC containment tubes, inside the graphite block. However, even at temperatures close to its melting point, 7LiH is relatively stable. At 700 °C, the vapor pressure of 7LiH is just ∼1 mmHg (∼133 Pa) [28]. It is recognized that a more detailed heat transfer analysis will be required in future studies to determine the temperature distribution in the fuel blocks within the FHR core, in order to obtain a better estimate of the potential level of localized melting of the 7LiH.

The Li is enriched to 99.995 at% 7LiH/Li to reduce neutron absorption in 6Li. This approach will also reduce unwanted tritium production. Although use of enriched lithium for the 7LiH moderator rods is recognized as an added complexity and cost, the use of enriched lithium is also needed for FLiBe [35]. While other hydrides could potentially serve as high-temperature moderators, such as ZrH1.6, CaH2, and YH2 [3137], a key advantage of 7LiH made with 99.995 at% 7Li/Li is that the enriched lithium has a lower thermal neutron capture cross section (∼0.092 barns) than zirconium (∼0.196 barns), calcium (∼0.429 barns), or yttrium (1.284 barns), and will permit better neutron economy, more fuel burnup, and a longer core lifetime.

Although not investigated in this study, other potential hydrogen-based high-temperature moderators include ZrH1.6, YH2, CaH2, 7LiOH, and NaOH, which have different advantages and tradeoffs relative to 7LiH. It is recognized that much of the current international work on microreactors for terrestrial and space applications has identified YH2 as a desirable moderator due to its stability at very high temperatures (above 900 °C) [3537], although operation with high assay low-enriched uranium (HALEU, ∼19.75 wt.% U-235/U) will be needed to compensate for the parasitic neutron absorption in yttrium.

The regions and materials that comprise the fuel pellet are listed in Table 1. The nominal reference temperatures of the materials in the fuel block are based on previous thermal-hydraulics calculations [5,2427], and are presented in Table 3. The nominal temperatures used for the different components was set to be the same as those used in the previous HTGR–SMR study by Wojtaszek and Bromley [13], and these numbers are considered an approximation, and suitable for the current exploratory studies. It is recognized that future thermal-hydraulic and heat transfer studies will be required to obtain updates of the component temperatures with FLiBe coolant (ranging from 650 °C inlet to 700 °C exit), and with modified fuel block designs, and associated power distributions.

Table 1

Description of regions in annular fuel pellet

RegionMaterialsOuter radius (cm)Inner radius (cm)
1. Outer clad coatingPyrolytic Carbon (OPyC)0.6250.621
2. Main cladSilicon Carbide (SiC)0.6210.561
3. Inner clad coatingPyrolytic Carbon (IPyC)0.5610.557
4. Buffer layerLow density carbon buffer0.5570.547
5. Outer fuel annulusUO2 (see comments in Table 2)0.5470.417
6. Fuel interface layerLow density carbon buffer0.4170.413
7. Inner fuel annulusUO2 (see comments in Table 2)0.4130.213
8. Inner fuel coatingPyrolytic carbon0.2130.209
9. Inner void spaceVacuum0.2090.109
10. Fission product getter materialPorous graphite0.1090
RegionMaterialsOuter radius (cm)Inner radius (cm)
1. Outer clad coatingPyrolytic Carbon (OPyC)0.6250.621
2. Main cladSilicon Carbide (SiC)0.6210.561
3. Inner clad coatingPyrolytic Carbon (IPyC)0.5610.557
4. Buffer layerLow density carbon buffer0.5570.547
5. Outer fuel annulusUO2 (see comments in Table 2)0.5470.417
6. Fuel interface layerLow density carbon buffer0.4170.413
7. Inner fuel annulusUO2 (see comments in Table 2)0.4130.213
8. Inner fuel coatingPyrolytic carbon0.2130.209
9. Inner void spaceVacuum0.2090.109
10. Fission product getter materialPorous graphite0.1090
Table 3

Nominal/reference material temperatures used in modeling FHR

MaterialTemperature (K)
Fuel compact (annular fuel element and compact graphite)875
Helium in gap surrounding fuel compacts855
Block moderator (graphite and 7LiH)835
Coolant channels (FLiBe, nominal temperature 600 °C)873
MaterialTemperature (K)
Fuel compact (annular fuel element and compact graphite)875
Helium in gap surrounding fuel compacts855
Block moderator (graphite and 7LiH)835
Coolant channels (FLiBe, nominal temperature 600 °C)873

2.3 Insights From Previous Studies.

It was observed in the previous study by Wojtaszek and Bromley [13] that the prismatic fuel block with 120 7LiH moderator rods (108 outer rods and 12 inner rods) gives positive temperature reactivity coefficients (TRC), where the negative fuel temperature coefficient of reactivity (Fuel TRC, F-TRC) is overwhelmed by the large positive hydrogen-based moderator temperature coefficient of reactivity (Hydrogen TRC, H-TRC). As a result of the previous study, it was speculated that the lattice may be “over-moderated.” Therefore, to correct this undesirable feature (a large positive temperature coefficient of reactivity) in this study, the number of moderator holes are reduced from 120 to 90 7LiH holes (see Fig. 3) and then further reduced from 90 to 54 7LiH holes (see Fig. 4).

Fig. 3
Modified FHR fuel block with 90 7LiH moderator rods * The 90 7LiH moderator rods are in the two outer rings of holes in the graphite block
Fig. 3
Modified FHR fuel block with 90 7LiH moderator rods * The 90 7LiH moderator rods are in the two outer rings of holes in the graphite block
Close modal
Fig. 4
Modified FHR fuel block with 54 7LiH moderator rods * The 54 7LiH moderator rods are in the outer ring of holes in the graphite block, with 9 rods per hexagon side
Fig. 4
Modified FHR fuel block with 54 7LiH moderator rods * The 54 7LiH moderator rods are in the outer ring of holes in the graphite block, with 9 rods per hexagon side
Close modal

2.4 Design Concepts for Current Study.

The lattice concepts that were analyzed in this study are listed in Table 4. They are used to evaluate the effects of replacing coolant material (changing from pressurized helium to FLiBe) and the effect of replacing 7LiH moderator holes with coolant and fuel holes in the FHR-SMR design concept.

Table 4

Description of FHR-SMR fuel assembly/fuel block concepts

Fuel concept (318 holes)Number of moderator holes (7LiH)Number of fuel compact holesNumber of coolant holes (FLiBe)Comments
FHR-90LiH-FA-0019013890Fuel is UO2, U is 5 wt.% U-235/U
FHR-54LiH-FA-0015417490Fuel is UO2, U is 5 wt.% U-235/U
FHR-90LiH -FA-0139013890Fuel is UO2, U is 19.75 wt.% U-235/U
FHR-54LiH-FA-0135417490Fuel is UO2, U is 19.75 wt.% U-235/U
Fuel concept (318 holes)Number of moderator holes (7LiH)Number of fuel compact holesNumber of coolant holes (FLiBe)Comments
FHR-90LiH-FA-0019013890Fuel is UO2, U is 5 wt.% U-235/U
FHR-54LiH-FA-0015417490Fuel is UO2, U is 5 wt.% U-235/U
FHR-90LiH -FA-0139013890Fuel is UO2, U is 19.75 wt.% U-235/U
FHR-54LiH-FA-0135417490Fuel is UO2, U is 19.75 wt.% U-235/U

The four main cases include: (1) FHR-90LiH-FA-001, (2) FHR-54LiH-FA-001, (3) FHR-90LiH-FA-013, and (4) FHR-54LiH-FA-013. The following is an explanation of the naming convention of these four cases. The acronym “FHR” refers to FLiBe salt cooled High temperature Reactor. The numbers “90” and “54” refer to the number of 7LiH moderator holes in the outer region of one hexagonal fuel assembly. As a simplification, the term “LiH” refers to 7LiH moderator rods, where the Li is enriched to 99.995 at% 7Li/Li. From this section on, LiH refers to 7LiH. The acronym “FA” refers to the fuel assembly (or prismatic fuel block). The serial number “001” and “013” refer to specific test cases with a fuel type. The fuel type “001,” refers to UO2 fuel made with uranium enriched to 5 wt.% U-235/U, while fuel type “013” refers to uranium enriched to 19.75 wt.% U-235/U. Although not shown or discussed here, the other serial numbers “002” to “012” refer to other fuel types tested that involved different levels of enrichment or different fuel materials (such as UN, UC, and UCO instead of UO2). The naming convention is similar to that used in the studies by Wojtaszek and Bromley [13]. As an illustrative example, the test case FHR-90LiH-FA-001 refers to the FHR fuel concept with 90 7LiH moderator holes in one hexagonal fuel block/fuel assembly, with fuel made of 5 wt.% U-235/U in the form of UO2.

3 Computational Tool for Lattice Physics Calculations —Serpent

The lattice physics calculations were performed using the Serpent 2 [38] (version 2.1.31) Monte Carlo (MC) neutron transport and burnup/depletion code, which is approved for use at CNL. All results presented in this document are calculated using the ENDF/B-VII.0 nuclear data library that is distributed with Serpent 2. The hexagonal prismatic fuel block was modeled with 12-fold symmetry in Serpent. Each fuel element has two annular fuel zones (inner and outer) that were modeled explicitly.

The calculations were performed on the CNL Minerva cluster using 550 generations (or cycles), with 200,000 neutrons per generation. The first 50 generations are used to achieve convergence of the criticality source calculation and are not included in the calculation of the reaction rates and output data statistics. Previous benchmark studies have determined that the fission source distribution is well converged after 50 generations with at least 50,000 neutrons per generation [27].

The typical statistical uncertainty in the calculation of the infinite multiplication factor (k-infinity) in lattice physics calculations at each burnup step was approximately ±δk-infinity ∼±0.1 mk (1 mk = 100 pcm = 0.001 Δk/k)

4 Performance Metrics

4.1 Multiplication Factor (k-Effective or keff).

In this study, all Serpent lattice physics calculations are conducted using reflective boundary conditions imposed on the 4.928-cm axial segment of the prismatic fuel block/fuel assembly. This axial segment corresponds to the height of a fuel compact, as described in the previous studies for the MHTGR-350 design concept/benchmark problem [2427].

The effective neutron multiplication factor (k-effective or keff) is calculated using a two-group diffusion leakage model with homogenized cross section using the following equation:
keff=νΣf1+νΣf2ΣS(12)(D2B2+ΣR2)(D1B2+ΣR1)ΣS(21)ΣS(12)(D2B2+ΣR2)
(1)

B2 is the geometric buckling, assuming B12=B22.

νΣfn is the fission neutron production cross section for group n.

ΣS(nm) is the neutron scattering cross section from group n to m.

Dn is the diffusion coefficient for group n.

ΣRn is the removal cross section for group n.

The value of B2 is calculated using Eq. (2) for a cylindrical, homogeneous reactor core, with active height (Ha) of 793 cm and an effective radius (Ra) of 153.5 cm
B2=(2.405Ra)2+(πHa)2
(2)

The effective radius is approximated based on the horizontal area of 66 fuel columns (with 10 fuel blocks per column) for a SMR core, based on the studies described previously by Wojtaszek in Ref. [13]. The 66-column core is expected to have a total reactor power of ∼350 MW, based on the MHTGR-350 benchmark design concept [2427]. Each fuel block is hexagonal with a flat-to-flat length of 36 cm, and thus is 1122.4 cm2 in area. A circle with an area of 1122.4 × 66 = 74,076.3 cm2 has an effective radius of 153.5 cm. Thus, the geometric buckling is calculated to be (2.405/153.5)2 + (π/793)2 = 2.61 × 10−4 cm−2. This value of geometric buckling to obtain an estimate of neutron leakage and keff neglects the effect of the inner and outer graphite reflectors in reducing neutron leakage; thus, it is likely an overestimate of the neutron leakage. For the purposes of this exploratory study, this approximate model for the calculation of keff and neutron leakage, making use of homogenized two-group diffusion data from lattice physics calculations with Serpent is considered adequate. Of course, it is recognized that a more accurate value of keff can be calculated using a full core physics model with Serpent (or a deterministic core physics code), which is an anticipated future work activity.

4.2 Exit Burnup/Fuel Residence Time.

In reactor operations, burnup is the multiplication of the thermal power (with units as W, kW, or MW) of the plant and the time (e.g., day) of operation divided by the mass of the initial fuel loading (e.g., kgHM). The exit burnup and fuel residence time correspond to the burnup step in which neutron multiplication factor keff = 1.000. A two-point linear interpolation is used to estimate the exit burnup and fuel residence time that correspond to keff = 1.000 using the values of keff, burnup, and fuel residence time at the last burnup step where keff > 1.000 and at the first burnup step where keff < 1.000. The values of burnup and fuel residence time obtained will be that for single-batch burnup.

4.3 Reactivity Coefficients.

Fuel, graphite, hydrogen and coolant temperature reactivity coefficients (Fuel TRC (F-TRC), Graphite TRC (G-TRC), Hydrogen TRC (H-TRC), and Coolant TRC (C-TRC), respectively) are calculated over a range of burnups and temperatures that are listed in Table 5. The cross section and thermal scattering data that are used for the given material temperatures are listed in Table 6. The thermal scattering data available with Serpent [38] to the authors at the time that this study was performed was based on ENDF-B-VII. The authors did not have access to more recent nuclear data based on ENDF/B-VIII, which would have been useful for SiC and FLiBe [39,40]. Since there was no data available for the thermal scattering of neutrons on hydrogen in LiH, the thermal scattering data for hydrogen in water was used as a first approximation.

Table 5

Burnups and temperatures used in calculations of reactivity coefficients

MaterialMaterial temperatures (K)
Fuel300, 600, 900, 1200, 1500
Graphite300, 600, 900, 1200, 1500
H-moderator (7LiH)300, 600, 900, 1200, 1500
Coolant (FLiBe)300, 600, 900, 1200, 1500
Fuel-graphite-H-coolanta300, 600, 900, 1200, 1500
MaterialMaterial temperatures (K)
Fuel300, 600, 900, 1200, 1500
Graphite300, 600, 900, 1200, 1500
H-moderator (7LiH)300, 600, 900, 1200, 1500
Coolant (FLiBe)300, 600, 900, 1200, 1500
Fuel-graphite-H-coolanta300, 600, 900, 1200, 1500
a

In this scenario, the fuel, graphite, hydrogen-based moderator and coolant are all at the same temperature, these perturbations are used for evaluating the isothermal temperature coefficient of reactivity.

Table 6

Cross section and thermal scattering data

Material temperature (K)Cross section data (temperature)*Thermal scattering data (H temperature)Thermal scattering data (graphite temperature)
300a.03c (300 K)lwe7.00t (300 K)gre7.00t (294 K)
600a.06c (600 K)lwe7.12t (600 K)gre7.12t (600 K)
900a.09c (900 K)lwe7.18t (800 K)bgre7.18t (800 K)
1200a.12c (1200 K)lwe7.18t (800 K)gre7.22t (1200 K)b
1500a.15c (1500 K)lwe7.18t (800 K)gre7.22t (1200 K)
Material temperature (K)Cross section data (temperature)*Thermal scattering data (H temperature)Thermal scattering data (graphite temperature)
300a.03c (300 K)lwe7.00t (300 K)gre7.00t (294 K)
600a.06c (600 K)lwe7.12t (600 K)gre7.12t (600 K)
900a.09c (900 K)lwe7.18t (800 K)bgre7.18t (800 K)
1200a.12c (1200 K)lwe7.18t (800 K)gre7.22t (1200 K)b
1500a.15c (1500 K)lwe7.18t (800 K)gre7.22t (1200 K)
a

is the name of the isotope. For example, 92225.03c is the data file for U-235 evaluated at 300 K.

b

It is noted that, for the thermal scattering data for H (in 7LiH), the thermal scattering data for H in H2O (lwe7) are used in this study that are available for the max of 800 K. The thermal scattering data for Graphite (gre7) to the max of 1200 K are used for C in Pyrolytic Carbon, C in SiC, and C in graphite.

Each material temperature matches the temperature at which the corresponding cross section data were evaluated. In case that there is no thermal scattering data available (hydrogen or graphite) at certain temperatures, the thermal scattering data evaluated at the nearest lower temperature is used at these material temperatures.

In addition, the density variations that occur along with temperature changes are considered in this study for 7LiH, FLiBe, and they are listed in Tables 2 and 7, respectively. All other materials have fixed (nominal) densities in these calculations, and assumed to have negligible or relatively small changes with temperature.

Table 2

Sample 7LiH density versus temperature [28]

Temperature (K)300600900961 (solid)961 (liquid)12001500
Density (g/cm3)a0.770.740.700.690.580.580.50b
Temperature (K)300600900961 (solid)961 (liquid)12001500
Density (g/cm3)a0.770.740.700.690.580.580.50b

aThe density variation applied to cases of FHR-90LiH and FHR-54LiH.

bData is result of extrapolation of data curve fit, although decomposition of 7LiH is expected above 1273 K.

Table 7

Sample FLiBe density versus temperature

Temperature (K)30060090012001500
FLiBe density (g/cm3)2.230a2.101a1.938b1.806b1.674b
Temperature (K)30060090012001500
FLiBe density (g/cm3)2.230a2.101a1.938b1.806b1.674b
a

For solid FLiBe (T < 459 °C or 732 K), the density calculation is using formula in Ref. [41].

b

For liquid FLiBe, the density is calculated using formula in Ref. [42].

The keff values are used to calculate temperature reactivity coefficients at the indicated burnup (BU) using Eq. (3), which is a simplified, approximate formula, with coarser changes in material temperatures
TRC(BU,T1,T2)=keff(BU,T1)keff(BU,T2)T1T2
(3)

It is recognized that an alternative approach to evaluating the TRCs would have been to make use of the perturbation capabilities in Serpent [38], rather than making much coarser changes in the material temperatures. The use of Serpent's perturbation capabilities for evaluating TRCs can be considered in future studies.

In this study, in addition to temperature reactivity coefficients for fuel, moderators (graphite and hydrogen), coolant (FLiBe), the isothermal temperature reactivity coefficients (the temperatures of fuel, moderators and coolant are all the same, and are changed simultaneously) are also calculated. The isothermal temperature reactivity coefficient is referred as “FGHC-TRC” or “Isothermal TRC,” indicating changes to all materials (fuel, graphite, hydrogen moderator, and FLiBe coolant). The range of temperatures (T1, T2) are expanded as: (300 K, 600 K), (600 K, 900 K), (900 K, 1200 K), and (1200 K, 1500 K). It is recognized that the calculation of the Isothermal is more relevant at lower temperatures (less than 700 °C/923 K) when 7LiH is in solid form, at or below hot zero power when the FLiBe coolant is in thermal equilibrium with the graphite, hydrogen-based moderator and the fuel. Given that the melting point for 7LiH is ∼961 K and boiling point is ∼1223 K, the evaluation of Isothermal TRC will be less meaningful for temperatures above 1200 K. Similarly, given that FLiBe melts at 459 °C/732 K, the evaluation of the Isothermal TRC will be less relevant at temperatures below 600 K. However, evaluations of Isothermal TRC (and other TRCs) using keff data at operational temperature extremes (300 K, 600 K, and 1500 K) are performed to provide approximate bounding cases and to indicate trends.

5 Computational Lattice Physics Results

5.1 K-infinity, K-Effective, Exit Burnup, and Nominal Core Residence Time.

The single-batch exit burnup, residence time, and specific power for the fuel assembly/fuel block concepts are summarized in Table 8. The plots of kinf, keff, and leakage versus burnup for all four cases (FA-001 and FA-013 variants of FHR-90LiH and FHR-54LiH) are provided in Figs. 57.

Fig. 5
kinf versus Burnup for all test cases
Fig. 5
kinf versus Burnup for all test cases
Close modal
Fig. 6
keff versus Burnup for all test cases * Note: keff was computed using a two-group diffusion leakage model, using an input buckling of 2.61 × 104 cm−2, which corresponds to a bare core with a height of 793 cm and a radius or 153.5 cm, and an assumed zero extrapolation distance
Fig. 6
keff versus Burnup for all test cases * Note: keff was computed using a two-group diffusion leakage model, using an input buckling of 2.61 × 104 cm−2, which corresponds to a bare core with a height of 793 cm and a radius or 153.5 cm, and an assumed zero extrapolation distance
Close modal
Fig. 7
Neutron leakage versus Burnup for all test cases
Fig. 7
Neutron leakage versus Burnup for all test cases
Close modal
Table 8

Exit Burnup of fuel block concepts with different coolant and number of moderator/fuel/coolant holes

Fuel block conceptPower in fuel block (kW/cm)aResidence time (days)Residence time (years)Exit Burnup (MWd/kgHM)Fuel mass (kg)Specific power (kW/kgHM)
FHR-90LiH-FA-0017.3053863.810.628.5324.8757.385
FHR-54LiH-FA-0017.3053599.09.921.0786.1475.857
FHR-90LiH -FA-0137.30516,294.444.6120.3534.8747.386
FHR-54LiH-FA-0137.30517,864.048.9104.6476.1455.858
Fuel block conceptPower in fuel block (kW/cm)aResidence time (days)Residence time (years)Exit Burnup (MWd/kgHM)Fuel mass (kg)Specific power (kW/kgHM)
FHR-90LiH-FA-0017.3053863.810.628.5324.8757.385
FHR-54LiH-FA-0017.3053599.09.921.0786.1475.857
FHR-90LiH -FA-0137.30516,294.444.6120.3534.8747.386
FHR-54LiH-FA-0137.30517,864.048.9104.6476.1455.858
a

The total power in the fuel block for a 4.928-cm axial segment is set to 36 kW.

It can be seen in Table 8 that the exit burnup values for both FA-001 and FA-013 become smaller when the number of LiH moderator holes is reduced from 90 to 54. The exit burnup decreases from ∼28 MWd/kg (for 90 LiH rods) to ∼21 MWd/kg (for 54 LiH rods) for the FA-001 cases, and from ∼120 MWd/kg (for 90 LiH rods) to ∼105 MWd/kg (for 54 LiH rods) for the FA-013 cases. These results occur because 36 of the LiH moderator rods are replaced with fuel holes (increasing from 138 to 174) as shown in Table 4. This change has the effect of reducing the H/U-235 atom ratio, causing the neutron energy spectrum to become harder/faster. The faster neutron energy spectrum causes a reduction in both the neutron multiplication factor and the exit burnup.

As shown in Table 8 and Fig. 8, the single-batch core life time ranges from ∼9.9 years (with LEU) to ∼48.9 years (with HALEU). Although the FHR-54LiH-FA fuels have lower burnup levels than the FHR-90LiH-FA fuels, the lower specific power level (with a greater fuel mass) results in a longer core lifetime. Being able to achieve such large single-batch core lifetime is a significant advantage over the use of conventional TRISO-based fuel particles and graphite moderator. For example, the MHTGR-350, which uses TRISO-based fuel compacts, with an enrichment of ∼15.5 wt.% U-235/U, has a typical single-batch core burnup of ∼80 MWd/kg, and a core life time of ∼3.0–3.5 years [2427]. In applications where long core life before refueling is required, or highly desired, such as remote mining operations and communities [12], the higher performance of the modified FHR-SMR fuel (with ∼10 years with just LEU fuel) is potentially very attractive, and worth any potential additional costs due to design modifications.

Fig. 8
keff versus Time (year) for all test cases
Fig. 8
keff versus Time (year) for all test cases
Close modal

A number of key observations can be made regarding the data shown in Figs. 5 and 6, including the following:

  • kinf values for FA-013 cases are higher than those for FA-001. This result is simply due to the higher content of fissile fuel in FA-013 (19.75 wt.% U-235/U) than that in FA-001 (5 wt.% U-235/U).

  • kinf values for FA-013 cases decreases almost linearly with burnup, but nonlinearly for FA-001. The kinf values for FA-001 cases decrease faster for early burnup than those at higher burnup stage. In FA-013, most of the fissions are occurring in the U-235, with less conversion of U-238 to Pu-239 and Pu-241. In FA-001, at higher burnup levels, there is more breeding of Pu-239 and Pu-241. If the FA-013 cases were pushed to much higher burnup levels, it is expected that it would have a curve similar to that of FA-001.

  • kinf values for 54LiH are lower than those for 90LiH cases before reaching the exit burnup step. For FA-001 at the exit burnup of ∼30 MWd/kgHM, the difference is ∼50 mk (1 mk = 100 pcm = 0.001 dk/k). For FA-013 at the exit burnup of at ∼110 MWd/kgHM, the difference is ∼65 mk. The difference is due to the presence of more fuel and coolant holes (and less moderator holes) in the periphery area for 54LiH, which will harden the neutron energy spectrum, and reduce k-infinity.

  • The neutron leakage ranges from approximately 60 mk for fresh fuel, and then drops down to ∼30 mk for high-burnup fuel. The neutron leakage values are lower for cases with 90 LiH than the neutron leakage for the cases with 54 LiH moderator rods. This result can be explained by the increased neutron absorption with the increased volume of fuel in the 54-LiH-moderator rod cases. It appears that the uranium enrichment level (5 wt.% U-235/U in FA-001 versus. 19.75 wt.% U-235/U in FA-013 has an effect on the leakage level. With a higher fissile content and a reduced ratio of H/U-235 atoms, the neutron energy spectrum will be faster and harder, and the leakage of fast neutrons will be increased.

It is noted that in this study, the linear power of the fuel assembly is set to be the same 36 kW/4.928 cm ∼= 7.305 kW/cm for both FA-90LiH and FA-54LiH; thus, the power per fuel element for the FA-90LiH cases will be higher than that of FA-54LiH cases since there are fewer fuel compacts in the FA-90LiH cases than in the FA-54LiH cases. The linear power of the fuel assembly can be set to be proportional to the number of fuel locations (using same power per fuel compact) in future studies.

5.2 Comparison of Temperature Reactivity Coefficient Data.

In this section, FHR-90LiH and FHR-54LiH are compared in terms of TRC data including the isothermal temperature reactivity coefficient (FGHC-TRC/Isothermal TRC), and the TRCs of individual materials where only the temperature (and density if it is LiH or FLiBe) of one of these material changes, such as fuel (Fuel TRC/F-TRC), graphite (Graphite TRC/G-TRC), hydrogen (Hydrogen TRC/H-TRC), and coolant (Coolant TRC/C-TRC). In cases where the calculated exit burnup was higher, additional reactivity coefficients were calculated at these levels.

As shown previously in Table 8, the exit burnup values of FHR-54LiH cases are 15–25% lower than those of FHR-90LiH cases. For a better comparison of TRC data between the different cases, TRC data at higher burnup values are also included in the comparison in Tables 913. The data plots associated with the TRCs are provided in Figs. 918.

Fig. 9
Isothermal TRC versus Burnup with (a) 90 and (a) 54 7LiH moderator rods for FA-001 with FLiBe coolant (a) 90 7LiH moderator rods, FLiBe coolant and (b) 54 7LiH moderator rods, FLiBe coolant
Fig. 9
Isothermal TRC versus Burnup with (a) 90 and (a) 54 7LiH moderator rods for FA-001 with FLiBe coolant (a) 90 7LiH moderator rods, FLiBe coolant and (b) 54 7LiH moderator rods, FLiBe coolant
Close modal
Fig. 10
Isothermal TRC versus Burnup with (a) 90 and (b) 54 7LiH moderator rods for FA-013 with FLiBe coolant (a) 90 7LiH moderator rods, FLiBe coolant and (b) 54 7LiH moderator rods, FLiBe coolant
Fig. 10
Isothermal TRC versus Burnup with (a) 90 and (b) 54 7LiH moderator rods for FA-013 with FLiBe coolant (a) 90 7LiH moderator rods, FLiBe coolant and (b) 54 7LiH moderator rods, FLiBe coolant
Close modal
Fig. 11
Fuel TRC versus Burnup with (a) 90 and (b) 54 7LiH moderator rods for FA-001 with FLiBe coolant (a) 90 7LiH moderator rods, FLiBe coolant and (b) 54 7LiH moderator rods, FLiBe coolant
Fig. 11
Fuel TRC versus Burnup with (a) 90 and (b) 54 7LiH moderator rods for FA-001 with FLiBe coolant (a) 90 7LiH moderator rods, FLiBe coolant and (b) 54 7LiH moderator rods, FLiBe coolant
Close modal
Fig. 12
Fuel TRC versus Burnup with (a) 90 and (b) 54 7LiH moderator rods for FA-013 with FLiBe coolant (a) 90 7LiH moderator rods, FLiBe coolant and (b) 54 7LiH moderator rods, FLiBe coolant
Fig. 12
Fuel TRC versus Burnup with (a) 90 and (b) 54 7LiH moderator rods for FA-013 with FLiBe coolant (a) 90 7LiH moderator rods, FLiBe coolant and (b) 54 7LiH moderator rods, FLiBe coolant
Close modal
Fig. 13
Graphite TRC versus Burnup with (a) 90 and (b) 54 7LiH moderator rods for FA-001 with FLiBe coolant (a) 90 7LiH moderator rods, FLiBe coolant and (b) 54 7LiH moderator rods, FLiBe coolant
Fig. 13
Graphite TRC versus Burnup with (a) 90 and (b) 54 7LiH moderator rods for FA-001 with FLiBe coolant (a) 90 7LiH moderator rods, FLiBe coolant and (b) 54 7LiH moderator rods, FLiBe coolant
Close modal
Fig. 14
Graphite TRC versus Burnup with (a) 90 and (b) 54 7LiH moderator rods for FA-013 with FLiBe coolant (a) 90 7LiH moderator rods, FLiBe coolant and (b) 54 7LiH moderator rods, FLiBe coolant
Fig. 14
Graphite TRC versus Burnup with (a) 90 and (b) 54 7LiH moderator rods for FA-013 with FLiBe coolant (a) 90 7LiH moderator rods, FLiBe coolant and (b) 54 7LiH moderator rods, FLiBe coolant
Close modal
Fig. 15
Hydrogen TRC versus Burnup with (a) 90 and (b) 54 7LiH moderator rods for FA-001 with FLiBe coolant (a) 90 7LiH moderator rods, FLiBe coolant and (b) 54 7LiH moderator rods, FLiBe coolant
Fig. 15
Hydrogen TRC versus Burnup with (a) 90 and (b) 54 7LiH moderator rods for FA-001 with FLiBe coolant (a) 90 7LiH moderator rods, FLiBe coolant and (b) 54 7LiH moderator rods, FLiBe coolant
Close modal
Fig. 16
Hydrogen TRC versus Burnup with (a) 90 and (b) 54 7LiH moderator rods for FA-013 with FLiBe coolant (a) 90 7LiH moderator rods, FLiBe coolant and (b) 54 7LiH moderator rods, FLiBe coolant
Fig. 16
Hydrogen TRC versus Burnup with (a) 90 and (b) 54 7LiH moderator rods for FA-013 with FLiBe coolant (a) 90 7LiH moderator rods, FLiBe coolant and (b) 54 7LiH moderator rods, FLiBe coolant
Close modal
Fig. 17
Coolant TRC versus Burnup with (a) 90 and (b) 54 7LiH moderator rods for FA-001 with FLiBe coolant (a) 90 7LiH moderator rods, FLiBe coolant and (b) 54 7LiH moderator rods, FLiBe coolant
Fig. 17
Coolant TRC versus Burnup with (a) 90 and (b) 54 7LiH moderator rods for FA-001 with FLiBe coolant (a) 90 7LiH moderator rods, FLiBe coolant and (b) 54 7LiH moderator rods, FLiBe coolant
Close modal
Fig. 18
Coolant TRC versus Burnup with (a) 90 and (b) 54 7LiH moderator rods for FA-013 with FLiBe coolant (a) 90 7LiH moderator rods, FLiBe coolant and (b) 54 7LiH moderator rods, FLiBe coolant
Fig. 18
Coolant TRC versus Burnup with (a) 90 and (b) 54 7LiH moderator rods for FA-013 with FLiBe coolant (a) 90 7LiH moderator rods, FLiBe coolant and (b) 54 7LiH moderator rods, FLiBe coolant
Close modal
Table 9

Isothermal fuel-graphite-hydrogen-coolant temperature reactivity coefficients (isothermal TRC) versus temperature

Isothermal TRC (mk/K)b
Fuel conceptSelected Burnupa (MWd/kgHM)(300 K,600 K)(600 K,900 K)(900 K,1200 K)(1200 K,1500 K)
FHR-90LiH-FA-001280.13490.0471−0.0625−0.0754
FHR-54LiH-FA-00120−0.0091−0.0425−0.1585−0.1302
FHR-54-LiH-FA-001300.0188−0.0258−0.1512−0.1261
FHR-90LiH-FA-0131200.14610.0427−0.0638−0.0708
FHR-54LiH-FA-0131050.0110−0.0287−0.1234−0.0970
FHR-54-LiH-FA-0131550.0537−0.0021−0.1153−0.0969
Isothermal TRC (mk/K)b
Fuel conceptSelected Burnupa (MWd/kgHM)(300 K,600 K)(600 K,900 K)(900 K,1200 K)(1200 K,1500 K)
FHR-90LiH-FA-001280.13490.0471−0.0625−0.0754
FHR-54LiH-FA-00120−0.0091−0.0425−0.1585−0.1302
FHR-54-LiH-FA-001300.0188−0.0258−0.1512−0.1261
FHR-90LiH-FA-0131200.14610.0427−0.0638−0.0708
FHR-54LiH-FA-0131050.0110−0.0287−0.1234−0.0970
FHR-54-LiH-FA-0131550.0537−0.0021−0.1153−0.0969
a

Selected burnup is a value of burnup that is close to the exit burnup for the FHR-90-LiH-FA Case.

b

The statistical uncertainty is between ±1.4 × 10−4 mk/K and ±3.7 × 10−4 mk/K, with smaller TRC values have larger uncertainties.

Table 10

Coolant temperature reactivity coefficients (coolant TRC) versus temperature and Burnup

Coolant TRC (mk/K)b
Fuel conceptSelected Burnupa (MWd/kgHM)(300 K,600 K)(600 K,900 K)(900 K,1200 K)(1200 K,1500 K)
FHR-90LiH-FA-001280.0051290.0062830.0047490.004570
FHR-54LiH-FA-001200.0009800.0015930.0011420.001077
FHR-54LiH-FA-001300.0028410.0030940.0019440.001693
FHR-90LiH-FA-0131200.0054250.0053460.0039860.004043
FHR-54LiH-FA-0131050.0023040.0009950.0015030.000999
FHR-54LiH-FA-0131550.0037250.0038880.0026550.002433
Coolant TRC (mk/K)b
Fuel conceptSelected Burnupa (MWd/kgHM)(300 K,600 K)(600 K,900 K)(900 K,1200 K)(1200 K,1500 K)
FHR-90LiH-FA-001280.0051290.0062830.0047490.004570
FHR-54LiH-FA-001200.0009800.0015930.0011420.001077
FHR-54LiH-FA-001300.0028410.0030940.0019440.001693
FHR-90LiH-FA-0131200.0054250.0053460.0039860.004043
FHR-54LiH-FA-0131050.0023040.0009950.0015030.000999
FHR-54LiH-FA-0131550.0037250.0038880.0026550.002433
a

Selected burnup is a value of burnup that is close to the exit burnup for the FHR-90-LiH-FA cases.

b

The statistical uncertainty is between ±1.4 × 10−4 mk/K and ±3.7 × 10−4 mk/K, with smaller TRC values have larger uncertainties.

5.2.1 Isothermal Temperature Coefficient (Isothermal Temperature Reactivity Coefficient).

The Isothermal TRCs (FGHC-TRC) were evaluated for the different moderator configurations (FHR-54-LiH, and FHR-90-LiH), and it was found that the FHR-54-LiH concept, with a reduced number of moderator rods, can achieve negative temperature coefficients at all temperatures, and almost all levels of burnup, although at nominal operating temperatures, the FHR-90-LiH concept will also have negative TRCs. More context and explanation of these results are discussed below.

As shown in Table 9, the Isothermal TRCs of FHR-54LiH are lower than those of FHR-90LiH due to less moderation when 36 moderator holes are replaced with fuel holes. The Isothermal TRCs values decrease to lower values at higher temperatures for both cases. For example, the Isothermal TRCs changes from ∼+0.019 mk/K to ∼−0.126 mk/K when temperature increases for FHR-54LiH-FA-001 at a burnup of 30 MWd/kg.

At temperatures above 750 K, the Isothermal TRCs decrease and become negative (which is desired) for the FHR-54-LiH cases (see Figs. 9(b) and 10(b)). This characteristic makes the FHR-54-LiH cases inherently stable and easier to control. For the FHR-90-LiH case, the Isothermal TRC transitions from a positive value at 750 K to a negative value at 1050 K as seen in the plots of Isothermal TRC versus temperature (Figs. 9(a) and 10(a)). It appears that there is a slight increase in Isothermal TRCs at high temperature at [1200 K, 1500 k] for FHR-54-LiH cases (less obvious for FHR-90-LiH cases). This situation could occur because of the changes in the resonance absorption at high temperature, and given that the FHR-54-LiH case has more fuel than the FHR-90-LiH cases. It will be prudent to investigate this phenomena more deeply in future studies.

Earlier studies have suggested that a doppler broadening rejection correction method will have a more significant impact at fuel temperatures above 1000 K [4345]. It is also possible that gaps in the data available for thermal neutron scattering for 7LiH, FLiBe, and SiC could be causing such changes in the Isothermal TRCs at the highest temperatures. Li and coworkers developed their own updated nuclear data libraries to account for thermal scattering in FLiBe and also doppler broadening rejection correction corrections, and found that such adjustments had an impact on evaluating reactivity in FHRs [45].

It is very clear from the data shown that at operating temperatures at or above 900 K (627 °C), the Isothermal TRC is negative, even for the FHR-90-LiH cases at exit burnup. Given that the FHR-SMR will operate normally with a FLiBe coolant temperature between 650 °C and 700 °C, and with even higher temperatures for the LiH, graphite, and the fuel when operating at power, it is most likely the FHR-SMR with the proposed advanced fuel concept will be inherently stable using either the FHR-90LiH or FHR-54LiH design concepts. Thus to ensure safe operations, it becomes important to heat up the reactor system with nonnuclear heat to at least 900 K (when using FHR-90LiH fuel), before withdrawing control rods to cause a positive reactivity insertion, and a power level increase.

It is recognized that the results do not yet account for the effects of neutron thermal scattering in SiC or FLiBe, and future work will require updated data for use in Serpent. More recent studies in China by Liu and coworkers modeling different MSR concepts with FLiBe [40] indicate that use of thermal scattering data for FLiBe could lead to systematic differences in the evaluation temperature coefficients, ranging between −0.0009 mk/K to +0.0024 mk/K in the temperature interval of 900 K–1200 K, depending on the MSR design. Such systematic differences are relatively small (less than 4%) in comparison to the smallest magnitude of the isothermal TRC (-0.0625 mk/K) in this study.

5.2.2 Fuel Temperature Coefficient (Fuel Temperature Reactivity Coefficient).

As shown in Table 11 and Figs. 11 and 12, the Fuel TRC values remain negative at all temperatures for both cases, ranging between −0.050 mk/K and −0.010 mk/K. In contrast to the isothermal Isothermal TRCs, the Fuel TRCs become slightly higher (less negative) when the temperature increases, due to reduced neutron resonance absorption in U-238. The Fuel TRC values for FHR-54LiH are slightly lower than those for FHR-90LiH at all temperatures. It can also be seen that, at zero burnup (fresh fuel), the Fuel TRC values are all lower (more negative) than those at the exit burnup.

Table 11

Fuel temperature reactivity coefficients (fuel TRC) versus temperature

Fuel TRC (mk/K)b
Fuel TRC (mk/K)Selected Burnupa (MWd/kgHM)(300 K, 600 K)(600 K,900 K)(900 K,1200 K)(1200 K,1500 K)
FHR-90LiH-FA-0010−0.0359−0.0259−0.0277−0.0153
FHR-90LiH-FA-00128−0.0261−0.0188−0.0194−0.0139
FHR-54LiH-FA-0010−0.0522−0.0359−0.0338−0.0237
FHR-54LiH-FA-00120−0.0433−0.0315−0.0296−0.0219
FHR-54LiH-FA-00130−0.0365−0.0271−0.0241−0.0203
FHR-90LiH-FA-0130−0.0284−0.0198−0.0175−0.0126
FHR-90LiH-FA-013120−0.0231−0.0166−0.0174−0.0119
FHR-54LiH-FA-0130−0.0420−0.0290−0.0238−0.0185
FHR-54LiH-FA-013105−0.0345−0.0252−0.0221−0.0168
FHR-54LiH-FA-013155−0.0255−0.0174−0.0149−0.0129
Fuel TRC (mk/K)b
Fuel TRC (mk/K)Selected Burnupa (MWd/kgHM)(300 K, 600 K)(600 K,900 K)(900 K,1200 K)(1200 K,1500 K)
FHR-90LiH-FA-0010−0.0359−0.0259−0.0277−0.0153
FHR-90LiH-FA-00128−0.0261−0.0188−0.0194−0.0139
FHR-54LiH-FA-0010−0.0522−0.0359−0.0338−0.0237
FHR-54LiH-FA-00120−0.0433−0.0315−0.0296−0.0219
FHR-54LiH-FA-00130−0.0365−0.0271−0.0241−0.0203
FHR-90LiH-FA-0130−0.0284−0.0198−0.0175−0.0126
FHR-90LiH-FA-013120−0.0231−0.0166−0.0174−0.0119
FHR-54LiH-FA-0130−0.0420−0.0290−0.0238−0.0185
FHR-54LiH-FA-013105−0.0345−0.0252−0.0221−0.0168
FHR-54LiH-FA-013155−0.0255−0.0174−0.0149−0.0129
a

Selected nonzero burnup is a value of burnup that is close to the exit burnup for the FHR-90-LiH-FA-XXX case.

b

The statistical uncertainty is between ±1.4 × 10−4 mk/K and ±3.7 × 10−4 mk/K, with smaller TRC values have larger uncertainties.

5.2.3 Graphite Temperature Coefficient (Graphite Temperature Reactivity Coefficient).

As shown in Table 12, Figs. 13 and 14, the Graphite TRC values are positive, but very small, typically ranging from +0.0050 mk/K to −0.0005 mk/K, approaching zero values at high operating temperatures (above 1200 K). At very high burnups, the Graphite TRC becomes slightly more positive for the FHR-90-LiH cases at lower temperatures ranging from +0.005 mk/K to +0.015 mk/K. However, such high burnups would only be possible if a three-batch refueling scheme was employed, and in such scenarios, the larger positive Graphite TRC values for the high-burnup fuel would be offset by the smaller Graphite TRC values of the lower burnup fuel in the other batches.

Table 12

Graphite temperature reactivity coefficients (Graphite TRC) versus temperature

Graphite TRC (mk/K)b
Fuel conceptSelected Burnupa (MWd/kgHM)(300 K,600 K)(600 K,900 K)(900 K,1200 K)(1200 K,1500 K)
FHR-90LiH-FA-001280.004990.003720.005770.00031
FHR-54LiH-FA-001200.001000.000890.000060.00047
FHR-54LiH-FA-001300.002390.002400.001790.00053
FHR-90LiH-FA-0131200.004340.003270.00507−0.00053
FHR-54LiH-FA-0131050.001480.000280.00055−0.00004
FHR-54LiH-FA-0011550.004890.003160.003710.00045
Graphite TRC (mk/K)b
Fuel conceptSelected Burnupa (MWd/kgHM)(300 K,600 K)(600 K,900 K)(900 K,1200 K)(1200 K,1500 K)
FHR-90LiH-FA-001280.004990.003720.005770.00031
FHR-54LiH-FA-001200.001000.000890.000060.00047
FHR-54LiH-FA-001300.002390.002400.001790.00053
FHR-90LiH-FA-0131200.004340.003270.00507−0.00053
FHR-54LiH-FA-0131050.001480.000280.00055−0.00004
FHR-54LiH-FA-0011550.004890.003160.003710.00045
a

Selected burnup is a value of burnup that is close to the exit burnup for the FHR-90-LiH-FA cases.

b

The statistical uncertainty is between ±1.4 × 10−4 mk/K and ±3.7 × 10−4 mk/K, with smaller TRC values have larger uncertainties.

5.2.4 Hydrogen Temperature Coefficient (Hydrogen Temperature Reactivity Coefficient).

As shown in Table 13 and Figs. 15 and 16, the Hydrogen TRC values display a very similar trend as Isothermal TRCs for both cases (FHR-90LiH and FHR-54LiH), with values ranging between −0.13 mk/K and +0.15 mk/K. The Hydrogen TRC values of FHR-54LiH are slightly lower than those of FHR-90LiH at all temperatures. The Hydrogen TRC values also become lower and more negative at higher temperatures. These results are explained by a number of processes. One is the reduced neutron moderation by hydrogen at higher temperatures, due to the drop in the hydrogen density. The other related process is the impact in the shift in the neutron energy spectrum, which causes changes in the neutron resonance absorption in U-238, and other isotopes in high-burnup fuel, at higher hydrogen temperatures.

Table 13

Hydrogen temperature reactivity coefficients (hydrogen TRC) versus temperature

Hydrogen TRC (mk/K)b
Fuel conceptSelected Burnupa (MWd/kgHM)(300 K,600 K)(600 K,900 K)(900 K,1200 K)(1200 K,1500 K)
FHR-90LiH-FA-001280.14900.0504−0.0536−0.0603
FHR-54LiH-FA-001200.0282−0.0161−0.1280−0.1038
FHR-54LiH-FA-001300.0422−0.0086−0.1274−0.1024
FHR-90LiH-FA-0131200.14400.0444−0.0557−0.0586
FHR-54LiH-FA-0131050.0330−0.0099−0.1001−0.0780
FHR-54LiH-FA-0131550.05660.0034−0.1031−0.0798
Hydrogen TRC (mk/K)b
Fuel conceptSelected Burnupa (MWd/kgHM)(300 K,600 K)(600 K,900 K)(900 K,1200 K)(1200 K,1500 K)
FHR-90LiH-FA-001280.14900.0504−0.0536−0.0603
FHR-54LiH-FA-001200.0282−0.0161−0.1280−0.1038
FHR-54LiH-FA-001300.0422−0.0086−0.1274−0.1024
FHR-90LiH-FA-0131200.14400.0444−0.0557−0.0586
FHR-54LiH-FA-0131050.0330−0.0099−0.1001−0.0780
FHR-54LiH-FA-0131550.05660.0034−0.1031−0.0798
a

Selected burnup is a value of burnup that is close to the exit burnup for the FHR-90-LiH-FA cases.

b

The statistical uncertainty is between ±1.4 × 10−4 mk/K and ±3.7 × 10−4 mk/K, with smaller TRC values have larger uncertainties.

5.2.5 Coolant Temperature Coefficient (Coolant Temperature Reactivity Coefficient).

In Table 10 and Figs. 17 and 18, the Coolant TRC values are slightly positive but smaller at higher temperatures, ranging typically between −0.001 mk/K and +0.006 mk/K, depending on burnup, temperature, lattice type, and enrichment. Higher Coolant TRC values are possible for the FHR-90Li fuels at higher burnup levels, for three-batch refueling. The Coolant TRC values for FHR-54LiH are slightly lower than those of FHR-90LiH, due to changes in the neutron energy spectrum. As the FLiBe coolant heats up, the changes in the coolant density impacts the absorption, scattering, and thermalization of neutrons by the Li and Be. Subsequently, changes in the neutron energy spectrum will impact the resonance absorption of neutrons in U-238, and other actinides created in higher burnup fuels.

6 Summary and Conclusions

Lattice physics calculations have been carried out with Serpent 2.1.31 (approved for use at CNL) to evaluate the performance characteristics (exit burnup, core residence time) and safety characteristics (TRC) of proposed prismatic fuel block designs for a FLiBe-cooled FHR that could be a potentially attractive design option for a SMR.

The FHR-SMR fuel design concepts were based on modifications to a previous HTGR–SMR design concept, [13], which itself was a modification of the earlier MHTGR-350 benchmark design concept [2427]. The key changes involve replacing the conventional TRISO-filled fuel compacts with multilayer annular fuel pellets, and replacing a number of fuel and coolant holes with solid hydrogen-based moderator (7LiH) holes. The design concept in this study replaces the Helium coolant with FLiBe coolant, and further modifications are made to the number of moderator rods (decrease from 108 to 90, and then to 54 moderator rods), the number of fuel holes, and the number of coolant holes to achieve less positive/more negative temperature reactivity coefficients.

The annular fuel simulated is made of uranium oxide with different levels of enrichment: 5 wt.% U-235/U (for lower burnups), and 19.75 wt.% U-235/U (for very high burnup).

The exit burnup was evaluated (the value of burnup when keff = 1.000) using the same assumed core size and associated buckling as in the previous HTGR study. With the high loading of uranium fuel, long core lifetimes with single-batch refueling are possible, ranging from 10 to 11 years for low-enrichment fuel (5 wt.% U-235/U) and from 44 to 49 years for high-enrichment fuel (19.75 wt.% U-325/U).

Switching from 90-LiH moderator rods to 54-LiH moderators hardens the neutron energy spectrum and reduces the exit burnup by modest to substantial amounts (13–26%) depending on the enrichment level.

With regards to TRCs, the following key results were obtained:

  • Switching from 90 LiH rods (and 138 fuel holes) to 54 LiH rods (and 174 fuel holes) causes a hardening of the neutron energy spectrum, and a reduction in the TRCs, with less positive and more negative values, particularly for the Isothermal TRC at lower values of burnup, and at higher temperatures (above 900 K).

  • The Fuel TRC remains negative at all temperatures.

  • The Hydrogen TRC is the dominant coefficient. It has much higher magnitude than the TRC contributions from Fuel, Graphite, and Coolant.

  • The Coolant TRCs are relatively small in magnitude.

  • While the use of a higher enrichment of U-235/U increases the exit burnup, it does not appear to have a significant impact on the TRCs.

To achieve a reduction in the TRCs, particularly the Isothermal TRC and the hydrogen temperature coefficient (Hydrogen TRC), it is advantageous to switch from the 90-LiH rod design to the 54-LiH rod design. For the 54-LiH Rod design, the Isothermal TRC ranges between −0.159 mk/K and −0.054 mk/K, depending on the operating temperature and fuel burnup. The use of the 54-LiH rod design concept will extend the temperature range of inherent stability from 900 K down to 450 K, which is actually far below the melting point of FLiBe (∼459 °C/732 K).

However, it is noted again that as long as the FHR operates at temperatures above ∼900 K (627 °C), the Isothermal TRC and the Hydrogen TRC should always be negative, even when using the fuel block design with 90 LiH moderator rods. Given that the coolant will be at ∼650 °C (923 K) when the FHR is operating at hot zero power, it is expected that an FHR using the 90-LiH moderator rod design will be inherently stable. Thus, for startup operations from room temperature (∼20 °C/293 K), it will only be necessary to preheat the FLiBe up to 650 °C before any control rods are withdrawn to cause a positive reactivity insertion and increase reactor power.

For SMR applications where a long core life is desirable, such as remote mining operations and northern communities, the proposed modified FHR–SMR fuel design concept is potentially very attractive in comparison to the alternative of using a more conventional TRISO-based fuel with a graphite moderator in an FHR [5]. It is recognized that the proposed alternative and unconventional FHR concept will require significant further study and development to address various physics and engineering issues before it could be developed commercially and licensed for use.

7 Options for Future Work and Improvements

Based on the results and observations made from this study, the following are potential options for future work and improvements:

With the assessment of both 90LiH and 54LiH setup with the two UO2 fuel concepts for FHR, it will be prudent to investigate the potential use of other types of fuels (UN, UC, UCO), (U,Th), (Pu,Th) that were investigated previously for the HTGR–SMR, as discussed in Ref. [13]. Thorium-based fuels are potentially attractive because they tend to have more negative fuel temperature coefficients of reactivity, and small resonance integrals than uranium-based fuels [46].

While density variations of 7LiH and FLiBe are considered in this study, the impact of density changes for UCO with large temperature changes (such as going from 300 K to 1500 K) can be considered for future studies, For example, for UO2 and UC, the densities change from ∼10.9 g/cm3 and ∼13.5 g/cm3, respectively, at 300 K to ∼10.5 g/cm3 and ∼12.9 g/cm3, respectively, at 1500 K, a density change of less than 5%.

In this study, the thermal scattering data evaluated at the nearest lower temperature is used, in case that there is no thermal scattering data available (hydrogen or graphite) at certain temperatures. For future study, both nearest lower and higher temperature can be provided in Serpent specific format for more accurate simulation. In addition, it will also be desirable to acquire an updated version of Serpent and updates nuclear data based on ENDF/B-VIII.0 [39], to account more accurately for the effects of thermal neutron scattering in 7LiH, SiC, and FLiBe [40,45].

Currently, the temperatures for the different components are using estimated “nominal” values with the temperature variation of Fuel, Moderator (graphite and hydrogen) and Coolant for TRC study. Re-evaluation may need to be performed when better estimates of the temperatures of different components under different operating conditions (inlet temperature, coolant flowrate, power level, etc.) are obtained from in thermal-hydraulic and heat transfer studies in the future.

Instead of the same linear power of 7.305 kW/cm that is used for all fuel assemblies as in this study, the linear power of the fuel assembly that is proportional to the number of fuel locations (using same power per fuel compact) can be set in future studies.

Similar to the previous study of advanced fuel concepts for use in an HTGR–SMR [13], 7LiH was used as a hydrogen-based moderator to help improve neutron moderation, reduce migration distance and reduce neutron leakage to enable compact FHR–SMR cores with a longer core life than by using graphite as a moderator. However, it may be prudent to evaluate the performance and safety characteristics of alternative hydrogen-based moderators, such as YH2, CaH2, 7LiOH, and NaOH, which could have some tradeoffs and advantages relative to 7LiH, depending on the application. Past studies have suggested that hydroxides have the ability to operate at higher temperatures before significant decomposition occurs, and can make very good moderators in combination with molten-salt coolants [47,48].

While graphite is essentially used as a structural material in the FHR concept proposed, it is possible that other structural materials with high-temperature capabilities, and low neutron absorption cross sections could also be considered, such as a composite material made of SiC fibers in a SiC matrix [49].

Acknowledgment

The authors thank the following CNL staff for their assistance: Daniel T. Wojtaszek, Danila Roubtsov, Ashlea V. Colton, Tina H. Wilson, Ali Siddiqui, Crystal Olsheskie, and Rafaele Fiorella.

Funding Data

  • Atomic Energy of Canada Limited (AECL), under the auspices of the Federal Nuclear Science and Technology (FNST) Work Plan (award ID: FST-51120.0.A049; Funder ID: 10.13039/501100004953).

Data Availability Statement

The authors attest that all data for this study are included in the paper.

Nomenclature

B2 =

geometric buckling

Dn =

diffusion coefficient for neutron group n

Ha =

active core height

keff =

effective neutron multiplication factor, also keff or k-effective

kinf =

infinite neutron multiplication factor, also kinf or k-infinity

Ra =

active core radius

Greek Symbols
νΣfn =

fission neutron production cross section for group n

Σs (n → m) =

neutron scattering cross section from group n to m

ΣRn =

removal cross section for neutron group n

Subscripts or Superscripts
el =

electrical

eff =

effective

inf =

infinite

th =

thermal

Acronyms and Abbreviations
AECL =

atomic energy of Canada Limited

AR =

advanced reactor

ATF =

accident tolerant fuel

BOC =

beginning of cycle

BU =

Burnup

BWR =

boiling water reactor

CANDU =

Canada Deuterium Uranium

CNL =

Canadian nuclear laboratories

C-TRC =

coolant temperature reactivity coefficient

DBRC =

doppler broadening rejection correction

FA =

fuel assembly

FGHC-TRC =

fuel graphite hydrogen coolant (iso-thermal) temperature reactivity coefficient

FHR =

fluoride-salt high-temperature reactor

FLiBe =

fluoride salt of lithium and beryllium (LiF-BeF2)

FNST =

federal nuclear science and technology

FST =

federal science and technology

F-TRC =

fuel temperature reactivity coefficient

G-TRC =

graphite temperature reactivity coefficient

HALEU =

high assay low enriched uranium

HTGR =

high-temperature gas-cooled reactor

H-TRC =

hydrogen moderator temperature reactivity coefficient

IPyC =

inner pyrolytic carbon

LEU =

low enriched uranium

MC =

Monte Carlo

MHTGR-350 =

modular high temperature gas-cooled reactor, 350 MWth

MIT =

Massachusetts institute of technology

mk =

milli-k (1 mk = 100 pcm = 0.001 Δk/k)

MSR =

molten salt reactor

OPyC =

outer pyrolytic carbon (OPyC)

ORNL =

Oak Ridge national laboratory

pcm =

per cent mille

PT-HWR =

pressure tube heavy water reactor

PWR =

pressurized water reactor

PyC =

pyrolytic carbon

SiC =

silicon carbide

SmAHTR =

small modular advanced high-temperature reactor

SMR =

small modular reactor

TRC =

temperature reactivity coefficient

TRISO =

tri-structural isotropic

VHTR =

very-high temperature reactor

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