Abstract

Small modular reactors (SMRs) based on high-temperature gas-cooled reactor (HTGR) technology are being developed for providing high-temperature process heat and high-efficiency (>40%) electrical power generation. However, most of the HTGR-SMR concepts require high assay low enriched uranium (HALEU) fuel, with enrichments typically above 10 wt.% 235U/U, to get sufficiently high burnup levels and fuel lifetime. The goal of this study is to identify alternative fuel concepts for HTGRs that can achieve sufficiently high burnup and low temperature reactivity coefficients while using uranium with 5 wt.% 235U/U. A previous study has shown that a modified prismatic HTGR fuel assembly with hydrogen-based moderator (7LiH) and cylindrical fuel elements of 5 wt.% 235U/U enriched uranium can greatly reduce fuel consumption of an HTGR. However, such a design concept could lead to positive temperature reactivity coefficients (TRCs), making reactor control more challenging, with reduced passive safety. In this study, variations of the hydrogen-based moderator in this alternative fuel assembly concept are evaluated to identify configurations that achieve negative TRCs, thus improving passive safety characteristics. Calculation results demonstrate that negative TRCs can be achieved with reduced hydrogen mass such that natural uranium consumption is substantially less than that of the tristructural isotropic (TRISO) fuel concept, with comparable or longer core life.

1 Introduction

There is interest among governments, industry, and reactor vendors in the deployment of small modular high-temperature gas-cooled reactors (SM-HTGRs, or HTGR-SMRs) [14] for various applications. Most HTGRs that are currently under development use helium gas as the primary coolant and are moderated using graphite. Thus, HTGRs can operate at temperatures (≥700 °C) that are much higher than in water-cooled reactors such as pressurized water reactors (PWRs) and pressure tube heavy water reactors (PT-HWRs). With high operating temperatures, HTGRs are well-suited for providing heat for a wider range of industrial processes and for higher efficiency electrical power generation. However, HTGRs require high assay low enriched uranium (HALEU) fuel, with enrichments typically between 10 wt.% 235U and 19.75 wt.% 235U, to get sufficiently high burnup levels and fuel residence time/operating life. Reliance on HALEU presents challenges with respect to supply since there is no fully developed and operational commercial market for HALEU at the time of this publication. The use of HALEU also presents greater issues with respect to nonproliferation relative to uranium with lower enrichments.

The need for HALEU is primarily a consequence of the low volumetric density of fissionable material in tristructural isotropic (TRISO) fuel particles, and the use of graphite as a moderator/reflector. HTGR fuel is typically in the form of a fuel compact (analogous to a fuel pellet) with TRISO particles embedded in a graphite or silicon carbide (SiC) matrix. Because of the multiple layers of buffer graphite, pyrolytic carbon (PyC) and SiC that are used to coat the central fuel kernel (typically made of UO2, or UCO) in a TRISO particle, ∼12 vol. % of a TRISO particle is fuel. The rest of the volume is occupied by structural materials. In addition, the packing fraction of TRISO fuel particles in a fuel compact with a graphite or SiC matrix is typically less than 52 vol. % (the theoretical maximum of spheres packed in a cubic array), and usually in the range between 30 vol. % and 40 vol. %. Thus, the total volume of the fuel compact occupied by fuel could be less than 5 vol. %. To compensate for the low volumetric density of fissionable material, a higher fissile concentration in the fuel is required. Furthermore, the longer slowing-down distance of neutrons in graphite relative to hydrogen requires that the core be surrounded by a large reflector to improve neutron moderation and reduce neutron leakage in order to achieve acceptable fuel burnup. The use of HALEU helps minimize the required size of the reflector.

The uranium enrichment required to achieve acceptable burnup in an HTGR can be reduced by introducing a hydrogen-based moderator to the reactor [5]. This moderator would need to be able to retain hydrogen at high temperatures within an HTGR core. Such moderator materials, including 7LiH [6,7], ZrH1.6 [8], YH2 [5], 7LiOH, and NaOH [10], have been investigated for use in high-temperature reactors.

Alternatives to TRISO fuel particles embedded in fuel compacts in prismatic graphite blocks have been proposed that can reduce the required uranium enrichment by replacing the TRISO particle-embedded compacts with cylindrical fuel pellets that resemble conventional pressurized water reactor and PT-HWR fuel [7,11]. Furthermore, a cylindrical, SiC, clad fuel pellet concept is being developed for a fast-spectrum HTGR [12,13]. The results presented in Ref. [7] indicate that the use of cylindrical fuel pellets of low-enriched uranium (LEU) at 5 wt.% 235U/U, combined with the inclusion of 7LiH moderator in the fuel assembly can reduce fissile consumption by 49%, and extend the fuel residence time by more than 9 years. Unfortunately, a tradeoff of this concept is that the inclusion of hydrogen moderator in the fuel assembly can result in large positive temperature reactivity coefficients (TRCs), which is undesirable with respect to reactor safety. This issue with positive TRCs with solid hydrogen-based moderators has been encountered in other studies [9]. However, it was anticipated that these positive TRCs could be reduced, and perhaps even be made slightly negative, by reducing the mass of hydrogen in the assembly. Negative TRCs provide a passive feedback mechanism that regulates reactor temperature, in that an increase in temperature causes a decrease in power, which then reduces temperature.

The purpose of this study is to evaluate design variants of the multilayer annular fuel pellet concept proposed previously in Ref. [7] to identify those that reduce TRCs, thus improving its passive safety characteristics. Specifically, the volume and type of hydrogen-based moderator will be varied to determine the effect on TRCs and fuel cycle performance (e.g., burnup and fuel lifetime). In addition to 7LiH, two other candidate moderator materials, 7LiOH and NaOH, will be investigated in this study.

2 High Temperature Gas-Cooled Reactor Fuel Models

The HTGR fuel concepts that are evaluated in this study are the reference, TRISO particle-based fuel, and the annular fuel concept with alternative moderator configurations, the models of which are described in this section.

2.1 Reference Fuel Concept.

The prismatic fuel assembly models analyzed in Ref. [7] are based on the MHTGR-350 benchmark [14] design concept, a 350 MWth/165-MWel reactor that includes blocks made of graphite (1850 kg/m3) with holes for coolant (such as helium) and holes for TRISO particle-embedded fuel compacts. A radial view of the reference MHTGR-350 fuel assembly model is shown in Fig. 1. The uranium in the reference fuel concept is 15.5 wt.% 235U/U.

Fig. 1
Reference fuel block layout (adapted from Fig. 2-2 from Ref. [14]). *Note: there are 102 large coolant holes (0.793 cm in diameter), and 6 small coolant holes (0.635 cm in diameter). There are 210 fuel holes, each 0.635 cm in diameter. To a first approximation, there is one coolant hole for every two fuel holes.
Fig. 1
Reference fuel block layout (adapted from Fig. 2-2 from Ref. [14]). *Note: there are 102 large coolant holes (0.793 cm in diameter), and 6 small coolant holes (0.635 cm in diameter). There are 210 fuel holes, each 0.635 cm in diameter. To a first approximation, there is one coolant hole for every two fuel holes.
Close modal

2.2 Annular Fuel Concept.

In the modified fuel assembly that was introduced in Ref. [7], the fuel compacts of the reference fuel assembly are replaced with multiclad, annular fuel elements in which the fuel is in the form of two concentric, hollow cylinders as is shown in Fig. 2. The materials that comprise the fuel element layers are listed in Table 1. The annular fuel elements are enclosed in multiple layers, analogous to those of TRISO fuel particles, to prevent fission product (FP) migration at high temperatures. In this fuel element, the 0.6-mm thick SiC cladding, sandwiched between two pyrolytic carbon (PyC) layers, extends from the bottom to the top of the 79-cm high prismatic graphite block and encloses a stack of annular fuel pellets, which are each 0.04928 m long. The fabrication process of the multilayered cladding (i.e., SiC cladding between two PyC layers) will be modified compared to the process used for TRISO particle manufacture because of the larger size/thickness and nonspherical geometry of the SiC cladding. The fuel element is sealed by two SiC endcaps affixed onto the SiC fuel element cladding. The fuel element includes a central void region and porous buffer carbon to accommodate gaseous FPs, although future research is needed to determine if these are sufficient to limit pressure-induced strain on the cladding to acceptable levels.

Fig. 2
Radial cross section view of fuel element geometry (half element is shown not to scale). *Note: Diagram is not to scale. The radial thickness of various coatings and clad regions and other nonfuel regions are exaggerated for better visual clarity (actual thickness of each layer is shown in brackets).
Fig. 2
Radial cross section view of fuel element geometry (half element is shown not to scale). *Note: Diagram is not to scale. The radial thickness of various coatings and clad regions and other nonfuel regions are exaggerated for better visual clarity (actual thickness of each layer is shown in brackets).
Close modal
Table 1

Description of regions in heterogeneous annular fuel element (cladding + fuel meat)

RegionMaterialsDensity (kg/m3)Outer radius (m)Thickness (m)Purpose
1. Outer clad coatingPyrolytic carbon (OPyC)19006.25 × 10–34.00 × 10–5• Gaseous FP retention
2. Main cladSilicon carbide (SiC)32006.21 × 10–36.00 × 10–4• Fuel element protection cladding
Nongaseous FP retention
3. Inner clad coatingPyrolytic carbon (IPyC)19005.61 × 10–34.00 × 10–5• Gaseous FP retention
1. Buffer layerLow-density carbon buffer10005.57 × 10–31.00 × 10–4• Space for gas accumulation
• Accommodation for fission recoils
2. Outer fuel annulusUO210,3005.47 × 10–31.30 × 10–3• Option for heterogeneous fuel
3. Fuel interface layerLow-density carbon buffer10004.17 × 10–34.00 × 10–5• Space for gas accumulation
• Accommodation for fission recoils
4. Inner fuel annulusUO210,3004.13 × 10–32.00 × 10–3• Option for heterogeneous fuel
5. Inner fuel coatingPyrolytic carbon19002.13 × 10–34.00 × 10–5• Gaseous FP retention
6. Inner void spaceVacuum02.09 × 10–31.00 × 10–3• Space for gas accumulation
7. Fission product getter materialPorous graphite10001.09 × 10–31.09 × 10–3• Capture gaseous FP
RegionMaterialsDensity (kg/m3)Outer radius (m)Thickness (m)Purpose
1. Outer clad coatingPyrolytic carbon (OPyC)19006.25 × 10–34.00 × 10–5• Gaseous FP retention
2. Main cladSilicon carbide (SiC)32006.21 × 10–36.00 × 10–4• Fuel element protection cladding
Nongaseous FP retention
3. Inner clad coatingPyrolytic carbon (IPyC)19005.61 × 10–34.00 × 10–5• Gaseous FP retention
1. Buffer layerLow-density carbon buffer10005.57 × 10–31.00 × 10–4• Space for gas accumulation
• Accommodation for fission recoils
2. Outer fuel annulusUO210,3005.47 × 10–31.30 × 10–3• Option for heterogeneous fuel
3. Fuel interface layerLow-density carbon buffer10004.17 × 10–34.00 × 10–5• Space for gas accumulation
• Accommodation for fission recoils
4. Inner fuel annulusUO210,3004.13 × 10–32.00 × 10–3• Option for heterogeneous fuel
5. Inner fuel coatingPyrolytic carbon19002.13 × 10–34.00 × 10–5• Gaseous FP retention
6. Inner void spaceVacuum02.09 × 10–31.00 × 10–3• Space for gas accumulation
7. Fission product getter materialPorous graphite10001.09 × 10–31.09 × 10–3• Capture gaseous FP

Note: The grey-shaded rows in this table correspond to layers in the 0.79 m long cladding.

The unshaded rows in this table correspond to layers in each annular fuel pellet.

The configuration of these layers represents an initial concept for the purpose of lattice physics evaluation, which may be modified based on future studies to evaluate and improve performance (e.g., FP retention under accident conditions), manufacturability, and cost, while maintaining the fuel cycle advantages of the annular fuel concept presented in this study.

The fuel is in the form of UO2, the composition of which is provided in Table 2. The lattice physics model comprises a 0.04928 m long midsection of this element (the typical length of a single fuel compact), which excludes the endcaps. The volume of UO2 fuel in the annular fuel pellet is greater than that of the UCO fuel kernels in TRISO particles in a MHTGR-350 fuel compact by a factor of 14.9.

Table 2

Uranium dioxide isotopic composition (kg/m3)

NuclideUO2 5 wt.% U-235/U (kg/m3)
U-2343.46
U-23545.5
U-2388650
O-161220
O-170.495
Total10,300
NuclideUO2 5 wt.% U-235/U (kg/m3)
U-2343.46
U-23545.5
U-2388650
O-161220
O-170.495
Total10,300

The modified fuel assembly that has been studied in Ref. [7] includes 120 hydrogen-based moderator rods to compensate for the increased volume of fuel, which provides sufficient additional moderation to achieve high fissile utilization. This modified fuel assembly is shown in Fig. 3. The moderator rods are composed of lithium hydride (7LiH), with the lithium enriched to 99.995 at. % 7Li/Li. Each moderator element comprises a cylindrical 7LiH pellet (0.0073 m radius) encased in SiC cladding (0.00794 m outer radius).

Fig. 3
Modified HTGR fuel assembly concept with 120 moderator elements. *Moderator rods represent fuel and coolant holes that have been filled with a hydrogen-based moderator, such as 7LiH. There are 108 Moderator rods on the periphery and 12 Moderator rods near the middle. **There are 132 fuel holes, and 66 coolant holes. The fuel holes are filled with heterogeneous, annular fuel pellets instead of TRISO-based fuel compacts.
Fig. 3
Modified HTGR fuel assembly concept with 120 moderator elements. *Moderator rods represent fuel and coolant holes that have been filled with a hydrogen-based moderator, such as 7LiH. There are 108 Moderator rods on the periphery and 12 Moderator rods near the middle. **There are 132 fuel holes, and 66 coolant holes. The fuel holes are filled with heterogeneous, annular fuel pellets instead of TRISO-based fuel compacts.
Close modal

The nominal reference temperatures of the assembly materials are listed in Table 3.

Table 3

Reference material temperatures

MaterialTemperaturea (K)
Fuel element (including all layers)875
Helium in gap surrounding fuel compacts855
Block graphite835
Helium in coolant channelsb750
MaterialTemperaturea (K)
Fuel element (including all layers)875
Helium in gap surrounding fuel compacts855
Block graphite835
Helium in coolant channelsb750
a

Note: Temperature data are taken from Ref. [14], which are averaged and rounded to the nearest 5 K.

b

Note: Nominal helium coolant inlet temperature is ∼532 K and the nominal exit temperature is ∼960 K, with a simple average temperature of ∼746 K, which is close to the 750 K value used in the previous benchmark study [14].

2.3 Alternative Moderator Configurations.

In the current study, an exploratory analysis is conducted to determine the effects of varying moderator configurations on burnup and TRCs of the annular fuel concept with 5 wt.% 235U/U enriched uranium fuel. Two alternative configurations of hydrogen-based moderator rods are tested: an assembly with 90 moderator rods (Fig. 4), and an assembly with 54 moderator rods (Fig. 5). Furthermore, two alternative, hydrogen-based, moderator materials are tested: 7LiOH and NaOH, which a recent study has shown could be attractive moderator materials for compact SMRs [10]. As is the case with 7LiH, the lithium in 7LiOH is 99.995 at. % 7Li/Li. The compositions of the moderators are listed in Table 4. It is expected that reducing the quantity of hydrogen in the fuel assembly will reduce the TRCs while also reducing the attainable burnup.

Fig. 4
Modified HTGR fuel assembly concept with 90 moderator elements. *Moderator rods represent fuel and coolant holes that have been filled with a hydrogen-based moderator, such as 7LiH. There are 90 Moderator rods on the periphery. **There are 138 fuel holes, and 90 coolant holes. The fuel holes are filled with heterogeneous, annular fuel pellets instead of TRISO-based fuel compacts.
Fig. 4
Modified HTGR fuel assembly concept with 90 moderator elements. *Moderator rods represent fuel and coolant holes that have been filled with a hydrogen-based moderator, such as 7LiH. There are 90 Moderator rods on the periphery. **There are 138 fuel holes, and 90 coolant holes. The fuel holes are filled with heterogeneous, annular fuel pellets instead of TRISO-based fuel compacts.
Close modal
Fig. 5
Modified HTGR fuel assembly concept with 54 moderator elements. *Moderator rods represent fuel and coolant holes that have been filled with a hydrogen-based moderator, such as 7LiH. There are 54 moderator rods on the periphery. **There are 174 fuel holes, and 90 coolant holes. The fuel holes are filled with heterogeneous, annular fuel pellets instead of TRISO-based fuel compacts.
Fig. 5
Modified HTGR fuel assembly concept with 54 moderator elements. *Moderator rods represent fuel and coolant holes that have been filled with a hydrogen-based moderator, such as 7LiH. There are 54 moderator rods on the periphery. **There are 174 fuel holes, and 90 coolant holes. The fuel holes are filled with heterogeneous, annular fuel pellets instead of TRISO-based fuel compacts.
Close modal
Table 4

Moderator material compositions

Molar density (at.·cm–1·barn–1)
Nuclide7LiaH7LiOHNaOH
6Li2.670 × 10–61.730 × 10–6
7Li5.340 × 10–23.459 × 10–2
16O3.459 × 10–22.523 × 10–2
17O1.315 × 10–59.589 × 10–6
23Na2.523 × 10–2
1H5.341 × 10–23.460 × 10–22.523 × 10–2
2H8.011 × 10–65.189 × 10–63.783 × 10–6
Molar density (at.·cm–1·barn–1)
Nuclide7LiaH7LiOHNaOH
6Li2.670 × 10–61.730 × 10–6
7Li5.340 × 10–23.459 × 10–2
16O3.459 × 10–22.523 × 10–2
17O1.315 × 10–59.589 × 10–6
23Na2.523 × 10–2
1H5.341 × 10–23.460 × 10–22.523 × 10–2
2H8.011 × 10–65.189 × 10–63.783 × 10–6
a

Note: the lithium is enriched to 99.995 at. % 7Li/Li.

Although the hydrogen density of 7LiOH is somewhat lower than that of 7LiH, the potential advantage of 7LiOH is its greater chemical stability and retention of its hydrogen atom. Lithium hydroxide is stable in liquid form (melts at 735 K) and does not decompose until it reaches its boiling point (∼1197 K), whereas 7LiH will begin to substantially decompose once it reaches its melting point (∼961 K) [15].

Although sodium hydroxide (NaOH) has an even lower hydrogen density than 7LiOH, it can operate at a much higher temperature before decomposition occurs, with a melting point of 596 K and a boiling point of 1661 K. Sodium hydroxide was considered for application as a combined moderator/coolant for the aircraft nuclear propulsion program in the United States in the 1950s [16]. Although the use of NaOH was abandoned as a coolant due to anticipated problems with corrosion, it is still possible that NaOH could be used in modern reactor concepts as a high-temperature, stagnant, hydrogen-based moderator. A private sector company, Seaborg Technologies, based in Denmark, is considering the use of NaOH as a stagnant moderator for its molten salt reactor concept [17,18]. Furthermore, Na does not require isotopic enrichment, unlike Li, and Na is more abundant than Li, and thus costs less.

The densities of LiH [19], LiOH [20,21], and NaOH [20,22] are temperature dependent, as shown in Fig. 6, which is taken into account in the calculation of TRCs. It is assumed that thermal expansion of these moderator materials is accommodated by the inclusion of void space above the core inside the SiC that encapsulates each moderator rod.

Fig. 6
Density versus temperature of the hydrogen-based moderators
Fig. 6
Density versus temperature of the hydrogen-based moderators
Close modal

3 Evaluation Criteria

The moderator configurations described in Secs. 2.2 and 2.3 are evaluated according to fuel consumption and temperature reactivity coefficients, the calculation of which are described in this section.

3.1 Fuel Consumption.

Annual fuel consumption (QEU) for a full SM-HTGR core is calculated for each concept using Eq. (1). In a three-batch fueling scheme, the mass of fresh fuel that is loaded into the core during refueling is 1/3 of the mass of fuel in the core, and the interval of time between refueling is 1/3 of the fuel lifetime. Equations (2) and (3) are used to calculate the annual natural uranium (NU) consumption (QNU), where R is the NU feed to enriched uranium product ratio
QEU=LEUD
(1)
R=xpxtxfxt
(2)
QNU=QEUR
(3)

where

  1. LEU is the mass, in kg, of enriched uranium that is loaded into the core during refueling (i.e., 1/3 of the core for three batch refueling).

  2. D is the duration, in years, between refueling (i.e., 1/3 of the fuel lifetime for three batch refueling).

  3. xp is the wt.% of 235U in enriched uranium.

  4. xf is the wt.% of 235U in NU, which is assumed to be 0.711 wt.% 235U/U.

  5. xt is the wt.% of 235U in the enrichment tails, which is assumed to be 0.2 wt.% 235U/U.

According to Eq. (2) the feed-to-product ratio (R) for xp = 5 wt.% 235U/U enriched uranium is 9.4.

3.2 Reactivity Coefficients.

Fuel TRCs (FTRCs), graphite TRCs (GTRCs), hydrogen moderator TRCs (HTRCs), and assembly TRCs (ATRCs) are calculated over a range of temperatures and burnups. The data in Table 5 show the burnup fractions and material temperatures at which keff (effective neutron multiplication factor) is calculated. To estimate FTRCs, a calculation of keff is conducted for each combination of burnup fraction (i.e., the associated fuel composition at a given burnup level) and temperature of the material in the right-most column of the corresponding row in Table 5, with the temperatures of all other materials set to their respective reference values. The same procedure is followed to calculate GTRCs, and HTRCs. The ATRCs are estimated by calculating keff for each burnup and temperature, where the temperatures of fuel, graphite, hydrogen moderator, and coolant are all set to the same value in each calculation. The keff is then used to calculate the TRCs over the range of temperatures [T1,T2] = [300 K, 600 K], [600 K, 900 K], [900 K, 1200 K], and [1200 K, 1500 K] at the indicated burnup (BU) using the following equation:
TRC(BU,T1,T2)=keff(BU,T1)keff(BU,T2)T1T2
(4)
Table 5

Burnup fractions and temperatures that are used to calculate reactivity coefficients

MaterialBurnup fractionaMaterial temperatures (K)
Fuel0, 1/3, 2/3, 1300, 600, 900, 1200, 1500
Graphite0, 1/3, 2/3, 1300, 600, 900, 1200
Hb0, 1/3, 2/3, 1300, 600, 900, 1200
He coolant0, 1/3, 2/3, 1300, 600, 900, 1200
MaterialBurnup fractionaMaterial temperatures (K)
Fuel0, 1/3, 2/3, 1300, 600, 900, 1200, 1500
Graphite0, 1/3, 2/3, 1300, 600, 900, 1200
Hb0, 1/3, 2/3, 1300, 600, 900, 1200
He coolant0, 1/3, 2/3, 1300, 600, 900, 1200
a

0 burnup fraction corresponds to fresh fuel, and burnup fraction of 1 corresponds to the exit burnup for three-batch refueling.

b

Hydrogen-based moderator compact.

4 Methods

The criteria described in Sec. 3 are evaluated based on lattice physics calculation of the value of keff and fuel burnup, which in turn is used to calculate exit burnup and core lifetime. This section describes these methods as well as the estimation of full core fuel mass, which is used to calculate fuel consumption.

4.1 Lattice Physics Calculations.

The lattice physics and depletion calculations are performed using the serpent 2 (version 2.1.31) Monte Carlo (MC) neutron transport and burnup/depletion code [23]. All results presented in this document are calculated using the endf/b-vii.0 nuclear data library that is distributed with serpent 2. The serpent lattice physics calculations are performed on Canadian Nuclear Laboratories' Minerva computing cluster using 550 generations (or cycles), with 2 × 106 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.

The cross section and thermal scattering data that are used for the given material temperature are listed in Table 6. Thermal scattering data at temperatures that do not match those in the library are interpolated from data at the nearest lower and higher temperatures.

Table 6

Cross-section and thermal scattering data used from serpent nuclear data library

Material temperature (K)Cross-section data (temperature)Thermal scattering data (temperature)b
300a.03c (300 K)gre7.00t (294 K), gre7.12t (600 K)
600a.06c (600 K)gre7.12t (600 K)
750a.06c (600 K)gre7.12t (600 K), gre7.18t (800 K)
835, 855, 875a.06c (600 K)gre7.18t (800 K), gre7.22t (1200 K)
900a.09c (900 K)gre7.18t (800 K), gre7.22t (1200 K)
1200a.12c (1200 K)gre7.22t (1200 K)
1500a.15c (1500 K)gre7.22t (1200 K), gre7.24 (1600 K)
Material temperature (K)Cross-section data (temperature)Thermal scattering data (temperature)b
300a.03c (300 K)gre7.00t (294 K), gre7.12t (600 K)
600a.06c (600 K)gre7.12t (600 K)
750a.06c (600 K)gre7.12t (600 K), gre7.18t (800 K)
835, 855, 875a.06c (600 K)gre7.18t (800 K), gre7.22t (1200 K)
900a.09c (900 K)gre7.18t (800 K), gre7.22t (1200 K)
1200a.12c (1200 K)gre7.22t (1200 K)
1500a.15c (1500 K)gre7.22t (1200 K), gre7.24 (1600 K)
a

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

b

Thermal scattering data at two temperatures are used for interpolating at temperatures that do not match that of the available data.

No thermal scattering data is used for hydrogen bound in LiH, LiOH, or NaOH due to there being no such data available. While the impact of thermal scattering is expected to be a second-order effect for the evaluation of fuel burnup and reactivity coefficients, it is anticipated that there is an opportunity for improvement for future work by acquiring such data.

4.2 Calculation of K-Effective.

All serpent calculations of the lattice physics model of a single prismatic fuel assembly are conducted using reflective boundary conditions on a fuel assembly. To calculate the effective neutron multiplication factor (k-effective, or keff) considering expected neutron leakage in a full, finite sized reactor core, a two-group diffusion leakage model with homogenized cross sections generated by serpent 2 is used along with a user-defined geometric buckling value associated with the full finite core geometry. The formula for calculating keff is given in Eq. (5). This calculation provides an approximate value of keff for comparison purposes in this study and has been used in a previous study [7]. A more accurate value of keff will be calculated using a full core physics model in future work
keff=νΣf1+νΣf2ΣS(12)(D2B2+ΣR2)(D1B2+ΣR1)ΣS(21)ΣS(12)(D2B2+ΣR2)
(5)

where

  1. B2 is the geometric buckling, in m−2, assuming B12=B22.

  2. νΣfn is the fission neutron production cross section, in m−1, for group n.

  3. ΣS(nm) is the neutron scattering cross section, in m−1, from group n to m.

  4. Dn is the diffusion coefficient, in m, for group n.

  5. ΣRn is the removal cross section, in m, for group n.

The value of B2 is calculated using Eq. (6), assuming a cylindrical, homogeneous core with an active height (Ha) of 7.93 m [24] and an effective radius (Ra) of 1.535 m. The effective radius is approximated based on the horizontal area of 66 fuel blocks. Each fuel block is hexagonal with a flat-to-flat length of 0.36 m (Fig. 1), and thus is 0.11224 m2 in area. A circle with an area of 0.11224 × 66 = 7.40763 m2 has an effective radius of 1.535 m. Thus, the geometric buckling is calculated to be 2.61 m−2. This value of geometric buckling neglects the effect of the inner and outer graphite reflectors in reducing neutron leakage, thus it is likely an overestimate of the neutron leakage
B2=(2.405Ra)2+(πHa)2
(6)

4.3 Exit Burnup and Core Lifetime.

The single-batch exit burnup and fuel residence time correspond to the burnup step in which keff = 1.000. A two-point linear interpolation is used to estimate the 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. In this study, a three-batch refueling scheme is used, which is also used in previous studies of the MHTGR-350 [7,24]. The linear reactivity model is used to estimate the exit burnup and fuel residence time (lifetime) for a 3-batch refueling scheme, which is 3/2 times the single-batch exit burnup and fuel residence time, respectively. The formula for the linear reactivity model is BU(n) = BU(1) × 2n/(n + 1). For a three batch scheme, n = 3, and BU(3) = BU(1) * 6/4 = 1.5*BU(1).

Thus, for example, if lattice physics calculations with a leakage model imposed determine that keff = 1.000 when BU(1) = 30 MWd/kg, and core life(n = 1) = 10 years, then the three-batch exit burnup will be BU(3) = 45 MWd/kg, with a three-batch core life (n = 3) = 15 years.

4.4 Full Core Fuel Mass Estimation.

The fuel and NU consumption in this study are calculated from the mass of fuel in a core. The total mass of fuel in the core is calculated based on a description of the MHTGR-350 from Ref. [24], which describes the two types of fuel assemblies in the core: a standard assembly and a reserve shutdown control (RSC) assembly, which are referred to as “fuel elements” in that document. The RSC assembly has fewer fuel holes than the standard assembly in order to make room for control devices. In total, there are 660 prismatic fuel assemblies in the MHTGR-350 core. There are 540 (54 fuel columns × 10 assemblies per column) standard and 120 (12 fuel columns × 10 assemblies per column) RSC assemblies in the core, each of which has 210 and 186 fuel holes, respectively, in the reference MHTGR-350 design. Each fuel hole contains 15 fuel compacts in a 79-cm high fuel assembly. Thus, there are 15 × (210 × 540 + 186 × 120) = 2,035,800 fuel compacts in the reference core. Each fuel compact comprises 6416 TRISO particles, which is 0.0024984 kgU/compact. As such, the reference core with TRISO-type fuel contains 5086 kgU.

Due to the replacement of some fuel compacts with moderator elements in the annular fuel assembly, the number of fuel holes depends on the number of moderator elements in the assembly. In a fuel assembly with 120 moderator elements, there are 132 and 110 fuel holes per standard and RSC assembly, respectively. Thus, there are a total of 156 × 540 + 134 × 120 = 100,320 annular fuel elements in the core. The length of an annular fuel element is 0.7392 m, thus, there is 2.91 × 10–5 m3 of fuel in each of the inner and outer annuli of a fuel element. Given the composition of UO2 in Table 2, the total mass of uranium in the core is 44,766 kgU. With 90, and 54 moderator elements, there are 138 and 174 fuel elements in the standard assembly, respectively. Table 7 lists the total core fuel mass for each of the three moderator compact configurations.

Table 7

Annular concepts of core fuel mass

Number of moderator compacts1209054
Number of fuel holes in standard assembly132138174
Number of fuel holes in RSC assembly110116150
Total fuel mass in standard assembly (kgU)74.978.398.8
Total core fuel mass (kgHM)44,76646,86459,328
Specific power (W/kgU)7.77.45.9
Number of moderator compacts1209054
Number of fuel holes in standard assembly132138174
Number of fuel holes in RSC assembly110116150
Total fuel mass in standard assembly (kgU)74.978.398.8
Total core fuel mass (kgHM)44,76646,86459,328
Specific power (W/kgU)7.77.45.9

5 Results

A series of serpent 2 lattice physics calculations were executed for each moderator configuration of the annular fuel concept described in Sec. 2.3, the output of which was used to calculate the fuel consumption and temperature reactivity coefficients via the methods described in Sec. 4. The MC uncertainty in the value of keff calculated by serpent 2 does not exceed 6.0 × 10–2 mk, (±Δk/k ≤±0.00006, ±6 pcm), thus the error in temperature reactivity coefficients is less than ±3.0 × 10–4 mk/K.

5.1 Exploratory Analysis.

The results of the exploratory analysis of moderator configurations show that there are tradeoffs between fuel consumption and TRCs, which are shown in Fig. 7. This plot shows the ATRCs in the temperature range [600 K, 900 K] versus NU consumption. This temperature range includes the reference operating temperatures. Of all the configurations with negative ATRCs in this temperature range, only 54-7LiH and 120-NaOH have lower NU consumption than the reference TRISO fuel concept. However, the 90-7LiOH configuration, with a maximum ATRC of 0.006 mk/K, is close to having solely negative ATRCs while having 37.7% lower NU consumption relative to the TRISO fuel concept. Furthermore, the 90-NaOH configuration has NU consumption that is only 3.3% higher than that of the TRISO fuel concept and ATRCs that do not exceed –0.036 mk/K.

Fig. 7
Maximum ATRC at [600 K, 900 K] versus NU consumption. *The vertical dotted line shows the NU consumption of the reference TRISO fuel concept (47,247 kgU/year). **The horizontal dotted line shows 0.00 mk/K. **Each point is labeled with the corresponding number of moderator rods.
Fig. 7
Maximum ATRC at [600 K, 900 K] versus NU consumption. *The vertical dotted line shows the NU consumption of the reference TRISO fuel concept (47,247 kgU/year). **The horizontal dotted line shows 0.00 mk/K. **Each point is labeled with the corresponding number of moderator rods.
Close modal

Further details of the exploratory analysis results are provided in the remainder of this section.

5.1.1 Burnup.

Reducing the number of 7LiH rods in the fuel assembly from 120 to either 90 or 54 rods reduces the calculated value of keff at each burnup step, as shown in Fig. 8, which results in reductions in exit burnup of 7.8% and 32.4%, respectively. The slope of keff versus time for the 90 and 54 7LiH rod configurations is less negative than that of the 120 7LiH rod configuration, as is shown in Fig. 9, which is due to their higher fuel mass. Thus, the reduction in fuel lifetimes of the 90 (3.6%) and 54 7LiH (10.8%) rod configurations relative to the 120 7LiH rod configuration are smaller than the percent reductions in burnup. Similarly, the slope of keff versus time for the 90 and 54 7LiOH rod configurations is less negative than that of the 120 7LiOH rod configuration, as is the case for the NaOH rod configurations.

Fig. 8
Effective neutron multiplication factor (keff) versus burnup
Fig. 8
Effective neutron multiplication factor (keff) versus burnup
Close modal
Fig. 9
Effective neutron multiplication factor versus time
Fig. 9
Effective neutron multiplication factor versus time
Close modal

Results of the depletion calculations indicate that the three-batch exit burnups of the annular fuel concepts are much less than that of the TRISO fuel concepts, as is shown in Fig. 10, which is largely due to the annular fuel concepts' lower uranium enrichment (5 wt.% 235U/U) relative to the 15.5 wt.% 235U/U enrichment in TRISO fuel. The data in Fig. 10 also shows that the burnup of the annular fuel concepts correlates with the number of moderator rods and with the hydrogen density in the moderating material.

Fig. 10
Burnup versus number of moderator compacts. *The dotted line shows the exit burnup of the reference, TRISO-fueled MHTGR (80.7 MWd/kgU) that was calculated in a previous study[7].
Fig. 10
Burnup versus number of moderator compacts. *The dotted line shows the exit burnup of the reference, TRISO-fueled MHTGR (80.7 MWd/kgU) that was calculated in a previous study[7].
Close modal

With 120 moderator rods, the difference in burnup between 7LiH and 7LiOH is small (less than 0.5%) relative to their difference in 1H molar density (35%). Changing from 7LiH to 7LiOH has larger effects with fewer moderator rods, where reductions in burnup of 10% and 50% occur with 90 and 54 moderator rods, respectively. Similar results are attained with the substitution of 7LiH for NaOH, which has a 53% lower 1H density, although the reductions in burnup are much greater (34%–82%).

Despite having lower burnups, the higher uranium loading in the annular fuel concepts and the reduced neutron leakage due to the 1H moderator results in longer fuel lifetimes for all but one moderator configurations, as is shown in Fig. 11; the exception being 54-NaOH rods. This figure also shows that fuel lifetime decreases as 1H loading decreases. The data in Fig. 12 shows that six of the configurations tested have lower NU consumption relative to the reference TRISO fuel concept, and that NU consumption increases as 1H loading decreases. The three configurations with higher NU consumption are 54-7LiOH, 54-NaOH, and 90-NaOH, although the latter case is very comparable to the TRISO fuel concept.

Fig. 11
Fuel lifetime versus number of moderator compacts. *The dotted line shows the fuel lifetime of the reference, TRISO-fueled MHTGR (3.2 years) that was calculated in a previous study[7].
Fig. 11
Fuel lifetime versus number of moderator compacts. *The dotted line shows the fuel lifetime of the reference, TRISO-fueled MHTGR (3.2 years) that was calculated in a previous study[7].
Close modal
Fig. 12
NU consumption versus number of moderator compacts. *The dotted line shows the NU consumption of the reference, TRISO fueled MHTGR (47,247 kgU/year) that was calculated in a previous study [7].
Fig. 12
NU consumption versus number of moderator compacts. *The dotted line shows the NU consumption of the reference, TRISO fueled MHTGR (47,247 kgU/year) that was calculated in a previous study [7].
Close modal

5.1.2 Reactivity Coefficients.

The data in Fig. 13 show the hydrogen TRCs versus temperature, where the temperatures are the midpoints between those at which the values of keff are used to calculate the corresponding TRC. For example, a TRC at 750 K is calculated using values of keff at 600 K and 900 K. The error bars in this and all subsequent figures show the range in TRCs across all burnup steps. This figure shows that reducing the number of moderator rods in the fuel assembly reduces the hydrogen temperature reactivity coefficients, although this reduction is insufficient to attain negative HTRCs in some configurations. With 7LiH, 54 moderator rods are the only configuration with negative HTRCs near the operating temperature of 835 K, which is indicated by the vertical dotted line in the figure. The HTRCs in the range [900 K, 1200 K] are even more negative due to the melting point of 7LiH being ∼961 K, which causes a large reduction in density over this temperature range (see Fig. 6).

Fig. 13
HTRC versus temperature. *The vertical dotted line shows the reference moderator rod temperature (835 K). **The horizontal dotted line shows 0.00 mk/K. ***The error bars show the variation in TRCs with burnup.
Fig. 13
HTRC versus temperature. *The vertical dotted line shows the reference moderator rod temperature (835 K). **The horizontal dotted line shows 0.00 mk/K. ***The error bars show the variation in TRCs with burnup.
Close modal

The effects of replacing 7LiH with 7LiOH depend on the moderator temperature. A fuel assembly with 7LiOH moderator rods has lower HTRCs over the range [300 K, 900 K], but higher HTRCs in the range [900 K, 1200 K]. The decrease in HTRCs at lower temperatures is due to the lower density of 1H in 7LiOH, whereas the increases at higher temperatures are primarily due to the larger change in density of 7LiH versus 7LiOH over this range (see Fig. 6). A similar result occurs when the 7LiH rods are replaced with NaOH, except that the HTRCs are a bit lower relative to those of 7LiOH.

Reducing 1H loading reduces the fuel temperature reactivity coefficients, which are less than –0.01 mk/K for all configurations, burnups, and temperatures, as is shown in Fig. 14. The lowest FTRCs are attained with 54 NaOH rods and are between –0.065 mk/K and –0.031 mk/K. For comparison, the FTRCs of the reference TRISO-particle fuel are between –0.088 mk/K and –0.045 mk/K. This figure also shows the reference fuel temperature (875 K) and that FTRCs increase with temperature, with such increase being most pronounced for configurations with 54 moderator rods.

Fig. 14
FTRC versus temperature. *The vertical dotted line shows the reference fuel temperature (875 K). **The error bars show the variation in TRCs with burnup.
Fig. 14
FTRC versus temperature. *The vertical dotted line shows the reference fuel temperature (875 K). **The error bars show the variation in TRCs with burnup.
Close modal

The data in Fig. 15 show that the graphite temperature reactivity coefficients, most of which are positive with 120 moderator rods, decrease with the number of moderator rods. For each of the moderating materials, the GTRCs are mainly negative when there are 54 moderator rods. The effect of moderator material substitution on GTRCs depends on the number of moderator rods. With 90 or 120 moderator rods, swapping 7LiH with either 7LiOH or NaOH reduces the GTRCs, where those of NaOH are lowest. At 54 moderator rods, swapping 7LiH with 7LiOH reduces the maximum GTRCs with respect to burnup at each temperature range, whereas swapping with NaOH increases the GTRCs in the temperature range of [600 K, 1200 K].

Fig. 15
GTRC versus temperature. *The vertical dotted line shows the reference graphite temperature (835 K). **The horizontal dotted line shows 0.00 mk/K. ***The error bars show the variation in TRCs with burnup.
Fig. 15
GTRC versus temperature. *The vertical dotted line shows the reference graphite temperature (835 K). **The horizontal dotted line shows 0.00 mk/K. ***The error bars show the variation in TRCs with burnup.
Close modal

The plots of ATRC versus temperature for each number of moderator rods and each moderator material, which are shown in Fig. 16, look quite like the plots of HTRCs, except that the ATRCs are lower due to the negative FTRCs. This similarity is due to most of the HTRCs being larger in magnitude than the other TRCs.

Fig. 16
ATRC versus temperature. *The horizontal dotted line shows 0.00 mk/K. **The error bars show the variation in TRCs with burnup.
Fig. 16
ATRC versus temperature. *The horizontal dotted line shows 0.00 mk/K. **The error bars show the variation in TRCs with burnup.
Close modal

With lower, and more negative ATRCs in the temperature range of [900 K, 1200 K], it may be attractive to consider modifying the operating conditions of the HTGR to operate at higher temperatures for the coolant, hydrogen-based moderator, graphite, and fuel. It is evident that above 900 K the ATRC becomes negative for all design concepts, even for 120-7LiH rods. However, changes to the operating temperatures will also impact the exit burnup and core lifetime, which is analyzed and discussed in Sec. 5.2. These negative ATRCs may also permit the addition of more hydrogen-based moderator to increase burnup while maintaining negative ATRCs, which is analyzed in Sec. 5.3.

5.2 Exit Burnup at Higher Operating Temperatures.

Additional calculations have been performed to determine the effects of increasing the operating temperature of a fuel assembly, including fuel, moderator, and coolant, to 1,050 K for the 7LiOH and NaOH configurations that have lower NU consumption at the reference temperatures (∼850 K) relative to the TRISO fuel concept. Configurations with 7LiH are assumed to be unsuitable at 1,050 K since LiH decomposes at 968 K, whereas LiOH and NaOH do not decompose below 1097 K.

The data in Fig. 17 show the impact that increasing temperature to 1,050 K has on the ATRC and NU consumption. The 120-7LiOH configuration at 1,050 K has 2.4% lower burnup and 2.5% greater NU consumption relative to this configuration at the reference temperatures (∼800 K). With 90 7LiOH rods, the burnup and fuel lifetime decrease by 4.7% and the NU consumption increases by 4.9% at the higher temperature. Raising the temperature of the 120-NaOH configuration results in a decrease of 6.6% in burnup and fuel lifetime, and an increase of 7.1% in NU consumption. However, in all cases, the NU consumption at higher operating temperature remains less than that of the TRISO fuel concept.

Fig. 17
ATRC versus NU consumption and temperature. *The vertical dotted line shows the NU consumption of the reference TRISO fuel concept (47,247 kgU/year). **The horizontal dotted line shows 0.00 mk/K. ***Each point is labeled with the number of moderator rods. ****Blue and orange markers correspond to the reference (∼800 K) and higher (1050 K) operating temperatures, respectively.
Fig. 17
ATRC versus NU consumption and temperature. *The vertical dotted line shows the NU consumption of the reference TRISO fuel concept (47,247 kgU/year). **The horizontal dotted line shows 0.00 mk/K. ***Each point is labeled with the number of moderator rods. ****Blue and orange markers correspond to the reference (∼800 K) and higher (1050 K) operating temperatures, respectively.
Close modal

5.3 Impact of Increased Volume of Hydroxide Moderator.

Considering the results presented in Secs. 5.1 and 5.2, it may be possible to increase the volume of hydroxide moderator in the fuel assembly beyond the 120 moderator rods while maintaining negative TRCs when operating at 1050 K, thus increasing burnup. The volume of hydrogen-based moderator in the fuel assembly can be increased by adding a large rod of 7LiOH or NaOH to the center of the fuel assembly, in place of the graphite and inner-most ring of moderator rods; the resulting fuel assembly is shown in Fig. 18.

Fig. 18
Radial view of the fuel assembly concept with large hydroxide rod (120+LCHR)
Fig. 18
Radial view of the fuel assembly concept with large hydroxide rod (120+LCHR)
Close modal

The TRCs with and without the large central hydroxide rod (LCHR) are shown in Figs. 1922 for hydrogen, fuel, graphite, and the assembly, respectively. Points in these plots that correspond to assemblies that have a large, central moderator rod (LCHR) are labeled “120+”. The data in these figures show that the inclusion of a 7LiOH LCHR increases the HTRCs, FTRCs, and ATRCs by as much as 0.01, 0.004, and 0.015 mk/K, respectively. The inclusion of a NaOH LCHR has a larger effect on TRCs with increases in HTRCs, FTRCs, and ATRCs by as much as 0.020, 0.003, and 0.025 mk/K, respectively. The data in Fig. 21 show that the inclusion of a LCHR has negligible effects on GTRCs. With the large central moderator rod, the maximum TRCs at 1050 K are listed in Table 8. For 7LiOH, the maximum HTRC and graphite temperature reactivity coefficient (GTRC) are positive, and the fuel temperature reactivity coefficient (FTRC) and ATRC are negative. For NaOH, all TRCs are negative.

Fig. 19
HTRCs of the hydroxide configurations with (120+LCHR) and without (120) a large, central rod. *The error bars show the variation in TRCs with burnup.
Fig. 19
HTRCs of the hydroxide configurations with (120+LCHR) and without (120) a large, central rod. *The error bars show the variation in TRCs with burnup.
Close modal
Fig. 20
FTRCs of the hydroxide configurations with (120+LCHR) and without (120) a large, central rod. *The error bars show the variation in TRCs with burnup.
Fig. 20
FTRCs of the hydroxide configurations with (120+LCHR) and without (120) a large, central rod. *The error bars show the variation in TRCs with burnup.
Close modal
Fig. 21
GTRCs of the hydroxide configurations with (120+LCHR) and without (120) a large, central rod. *The error bars show the variation in TRCs with burnup.
Fig. 21
GTRCs of the hydroxide configurations with (120+LCHR) and without (120) a large, central rod. *The error bars show the variation in TRCs with burnup.
Close modal
Fig. 22
ATRCs of the hydroxide configurations with (120+LCHR) and without (120) a large, central hydroxide rod. *The error bars show the variation in TRCs with burnup. **Data clearly indicates that it is desirable for reactor to operate above 900 K to ensure a negative temperature coefficient of reactivity.
Fig. 22
ATRCs of the hydroxide configurations with (120+LCHR) and without (120) a large, central hydroxide rod. *The error bars show the variation in TRCs with burnup. **Data clearly indicates that it is desirable for reactor to operate above 900 K to ensure a negative temperature coefficient of reactivity.
Close modal
Table 8

Maximum TRCs with the central hydroxide moderator rod

Value of TRC (mk/K) with a different moderator
Reactivity coefficient7LiOHNaOHa
HTRC0.018–0.006
FTRC–0.013–0.020
GTRC0.0060.000
ATRC–0.005–0.035
Value of TRC (mk/K) with a different moderator
Reactivity coefficient7LiOHNaOHa
HTRC0.018–0.006
FTRC–0.013–0.020
GTRC0.0060.000
ATRC–0.005–0.035
a

It is clear from the tabulated data that the lower hydrogen density in NaOH leads to under-moderation of the lattice, and more negative temperature coefficients, in comparison to 7LiOH.

The data in Fig. 23 shows how adding a large moderator rod to the fuel assembly decreases NU consumption and increases ATRCs. NU consumption decreases by 8% and 12% with the increased hydroxide volume for 7LiOH and NaOH, while increasing the maximum ATRC by 0.013 mk/K and 0.005 mk/K, respectively. This figure also shows that the configuration with a large 7LiOH rod has lower NU consumption than that of the 120 7LiH rod configuration, a decrease of 5%.

Fig. 23
ATRC versus NU consumption and temperature with and without a large, central rod. *The vertical dotted line shows the NU consumption of the reference TRISO fuel concept (47,247 kgU/year). **The horizontal dotted line shows 0.00 mk/K. ***Each point is labeled with the number of moderator rods. ****Blue and orange markers correspond to the reference (∼800 K) and higher (1050 K) operating temperatures, respectively.
Fig. 23
ATRC versus NU consumption and temperature with and without a large, central rod. *The vertical dotted line shows the NU consumption of the reference TRISO fuel concept (47,247 kgU/year). **The horizontal dotted line shows 0.00 mk/K. ***Each point is labeled with the number of moderator rods. ****Blue and orange markers correspond to the reference (∼800 K) and higher (1050 K) operating temperatures, respectively.
Close modal

6 Summary and Conclusions

An exploratory analysis of hydrogen-based moderator configurations has been carried out using lattice physics calculations to evaluate the effects of varying the type and volume of hydride and hydroxide moderator on fuel consumption and temperature reactivity coefficients of a HTGR prismatic fuel assembly concept with 5 wt.% 235U/U enriched uranium, annular fuel elements. Results demonstrate that negative fuel, graphite, and hydrogen TRCs can be achieved while increasing fuel lifetime and reducing natural uranium consumption relative to a graphite-moderated, 15.5 wt.%235U/U enriched uranium, TRISO fuel concept.

The improved fuel lifetimes and reduced NU consumption are due to the increased uranium loading (almost by a factor of 10), and the reduced neutron leakage from the use of a hydrogen-based moderator. A tradeoff to using 5 wt.% 235U/U instead of 15.5 wt.% 235U/U enriched uranium is the resulting lower burnup, which is over 40% less than that of the TRISO fuel concept. However, this reduction in burnup may not matter, if there is reduction in the NU consumption, and an increase in the fuel lifetime. The results also show that there is a tradeoff between fuel consumption and TRCs when varying the 1H loading in the fuel assembly, where decreasing 1H mass in the fuel assembly reduces TRCs but increases fuel consumption. The reduced TRCs improve the passive safety characteristics of the reactor by reducing power in response to increasing temperatures during transient events.

The key configurations that resulted in negative TRCs and lower NU consumption relative to the TRISO fuel concept are 54 7LiH rods and 120 NaOH rods. It has been found that lower TRCs can also be achieved by increasing the assembly operating temperatures from ∼800 K to 1050 K, which results in a relatively small (<7.1%) decrease in burnup. At 1050 K, the configurations with negative TRCs and lower NU consumption relative to the TRISO fuel concept are 120-7LiOH, 90-7LiOH, and 120-NaOH rods. This result demonstrates a benefit of using 7LiOH or NaOH as the moderator, since neither of them decomposes at temperatures below 1,197 K, whereas 7LiH begins to decompose at its melting point of 961 K, and fully decomposes when it reaches its boiling point (∼1173 K). Furthermore, increasing 7LiOH or NaOH volume beyond that of 120 moderator rods at 1050 K reduced fuel consumption by 12% and 8%, respectively, and resulted in negative TRCs. The resulting NU consumption is 51% and 26% less than that of the TRISO fuel concept for 7LiOH and NaOH, respectively.

7 Options for Future Work and Improvements

Based on what has been learned from the current studies of hydrogen-based moderator configurations in modified prismatic HTGR fuel assemblies with annular-type fuel pellets (instead of conventional TRISO-based fuel compacts), the following are potential options for future work:

  • Investigate the effects of using improved thermal scattering data of 1H in 7LiH, 7LiOH, and NaOH, on the calculated burnup and temperature reactivity coefficients. This investigation can only be done when such data becomes available.

  • Investigate alternative ceramic fuel forms, such as oxycarbides, carbides, and nitrides. Fuels such as UCO, uranium carbide (UC), and uranium nitride (UN) have a higher uranium loading density and a higher thermal conductivity.

  • Investigate alternative fuels, such as thorium-based fuels (U,Th) and (Pu,Th). The use of thorium-based fuels has the potential to make fuel temperature coefficients more negative relative to uranium-based fuels [25].

  • Evaluate the use of alternative structural materials for containing 7LiH to prevent the leakage of hydrogen when operating at temperatures above 900 K. Partial decomposition of 7LiH while it is above its melting point (962 K/689 °C) may be tolerable if the released hydrogen gas can be contained in sealed moderator rods with a suitable barrier to prevent the diffusion of hydrogen. Similar problems arise for other hydrides (such as ZrH1.6, CaH2, and YH2) proposed for use as moderators in high-temperature microreactor design concepts [26,27].

  • Carry out full-core physics calculations of an HTGR core with a number of selected annular-type fuel concepts to get a better estimate of the power distributions and the exit burnup of the fuel. Full core modeling will provide a better estimate of the effects of radial and axial reflectors, neutron leakage, and the effect of control rods used for excess reactivity control and adjusting power distributions.

  • Carry out thermal-hydraulic and heat transfer calculations to obtain better estimates of temperature distributions in the fuel and moderator with annular-type fuel pellets and hydrogen-based moderator rods.

  • Investigate the replacement of fuel assembly graphite with materials that are more resistant to radiation damage.

  • Carry out fuel performance calculations to evaluate the fission product retention capability of the annular fuel concept, with the use of multiple layers of coating and cladding, particularly those with SiC, PyC, and buffer carbon. Ultimately, such studies may reveal that fuel design simplification can be made to reduce the number and thickness of such protective layers.

  • Investigate the processes required to fabricate the annular fuel concept. The challenge will involve fabricating the PyC and SiC layers in the cladding, the PyC layer between the inner fuel annulus and the void region, and the carbon buffer at the center of the fuel. It is possible that modifications to the annular fuel concept may be required to make its fabrication feasible and economical, while having marginal effect on fuel cycle performance.

Acknowledgment

The authors would like to thank Gerhard Strydom, Rike Bostelmann, Pascal Rouxelin, and Nick Brown for sharing their expertise on HTGRs.

The authors also recognize the oversight, help, and assistance provided by the following staff at Canadian Nuclear Laboratories (CNL): Ali Siddiqui, Ashlea V. Colton, Sam Kelly, Huiping V. Yan, Cathy Thiriet, Peter Pfeiffer, Jonathan McKay, and Tina Wilson.

Funding Data

  • Atomic Energy of Canada Limited (AECL), under the auspices of the Federal Nuclear Science and Technology (FST) Program (Grant No.: FST-51120.0.A049; Funder ID: 10.13039/501100004953).

Nomenclature

B2 =

geometric buckling for a core; ((2.405Ra)2+(πHa)2), m–2

BU(n) =

exit burnup for n batch refueling, MWd/kg

Dn =

diffusion coefficient for group n, m

Ha =

effective height of the cylindrical core, m

LEU =

mass of enriched uranium that is loaded into the core during refueling, kg

mk =

unit for the difference between two values of neutron multiplication factors; (10–3 Δk)

MWd =

derived unit of energy; (106·24·3600), J

QEU =

annual fuel consumption; (LEUT), kg/y

QNU =

annual natural uranium consumption; (QEUR), kg/y

Ra =

effective radius of the cylindrical core, m

T =

duration between refueling, s

TRC(BU,T1,T2) =

temperature coefficient of reactivity at burnup B, between temperatures T1 and T2; (kinf(BU,T1)kinf(BU,T2)T1T2), mk/K

y =

derived unit of time; (3600·24·365), s

Greek Symbols
ΣRn =

removal cross section for group n, m–1

ΣS(nm) =

neutron scattering cross section from group n to m, m–1

νΣfn= =

fission neutron production cross section for group n, m–1

Nondimensional Numbers
keff =

neutron multiplication factor for a finite core; (νΣf1+νΣf2ΣS(12)(D2B2+ΣR2)(D1B2+ΣR1)ΣS(21)ΣS(12)(D2B2+ΣR2))

kinf =

neutron multiplication factor on an infinite lattice

R =

ratio of natural uranium feed to enriched uranium product; (xpxtxfxt)

xf =

weight % 235U/U in natural uranium feed

xp =

weight % 235U/U in enriched uranium product

xt =

weight % 235U/U in depleted uranium tails

Subscripts or Superscripts
eff =

effective

EU =

enriched uranium

f =

feed or fission

inf =

infinite

NU =

natural uranium

p =

product

t =

tails

Abbreviations
ATRC =

assembly temperature reactivity coefficient

FP =

fission products

FTRC =

fuel temperature reactivity coefficient

GTRC =

graphite temperature reactivity coefficient

MC =

Monte Carlo

NU =

natural uranium

PT-HWR =

pressure tube heavy water reactor

RSC =

reserve shutdown control

SM-HTGR =

small modular high-temperature gas-cooled reactor

TRISO =

tristructural isotropic

wt.% =

weight percent

References

1.
World Nuclear Association,
2023
, “
Small Nuclear Power Reactors
,” World Nuclear Association, London, UK, accessed June 10, 2023, https://www.world-nuclear.org/information-library/nuclear-fuel-cycle/nuclear-power-reactors/small-nuclear-power-reactors.aspx
2.
Wojtaszek
,
D. T.
,
2019
, “
Potential Off-Grid Markets for SMRs in Canada
,”
CNL Nucl. Rev.
,
8
(
2
), pp.
87
96
.10.12943/CNR.2017.00007
3.
IAEA
,
2022
, “
Advances in Small Modular Reactor Technology Developments a Supplement to: IAEA Advanced Reactors Information System (ARIS)
,”
International Atomic Energy Agency (IAEA)
, Vienna, Austria, accessed June 10, 2023, https://aris.iaea.org/Publications/SMR_booklet_2022.pdf
4.
Canadian Nuclear Safety Commission (CNSC),
2023
, “
Pre-Licensing Vendor Design Review
,”
Canadian Nuclear Safety Commission (CNSC)
, Ottawa, ON, Canada, accessed June 10, 2023, https://nuclearsafety.gc.ca/eng/reactors/power-plants/pre-licensing-vendor-design-review/
5.
Shivprasad
,
A.
,
Torres
,
J.
,
Cutler
,
T.
,
Jewell
,
J.
, and
Mehta
,
V. K.
,
2022
, “
Advanced Moderator Material Handbook
,”
Los Alamos National Laboratory
,
Los Alamos, NM
, Report No. LA-UR-22-30557.
6.
Alhammadi
,
A.
,
Alhoti
,
W.
, and
Hartanto
,
D.
,
2022
, “
Neutronics Design Study of Nuclear Thermal Rocket Using Low Enriched Uranium Fuel
,”
Arab. J. Nucl. Sci. Appl.
,
55
(
2
), pp.
135
145
.10.21608/AJNSA.2022.95984.1511
7.
Wojtaszek
,
D. T.
, and
Bromley
,
B. P.
,
2023
, “
Physics Evaluation of Alternative Uranium-Based Oxy-Carbide Annular Fuel Concepts for Potential Use in Compact High-Temperature Gas-Cooled Reactors
,”
ASME J. Nucl. Eng. Radiat. Sci.
,
9
(
1
), p.
011504
.10.1115/1.4055009
8.
Nam
,
S. H.
,
Venneri
,
P.
,
Kim
,
Y.
,
Chang
,
S. H.
, and
Jeong
,
Y. H.
,
2016
, “
Preliminary Conceptual Design of a New Moderated Reactor Utilizing an LEU Fuel for Space Nuclear Thermal Propulsion
,”
Prog. Nucl. Energy
,
91
, pp.
183
207
.10.1016/j.pnucene.2016.02.008
9.
Ade
,
B. J.
,
Betzler
,
B. R.
,
Burns
,
J. R.
,
Chapman
,
C. W.
, and
Hu
,
J.
,
2022
, “
Reactor Physics Considerations for Use of Yttrium Hydride Moderator
,”
Nucl. Sci. Eng.
,
196
(
12
), pp.
1539
1558
.10.1080/00295639.2022.2035157
10.
Bromley
,
B. P.
,
2022
, “
Initial Exploratory Reactor Physics Assessment of Non-Conventional Fuel Concepts for Very Compact Small Modular Reactors Using Hydroxides as Coolants and/or Moderators
,”
ANS Nucl. Technol. J.
,
208
(
1
), pp.
160
191
.10.1080/00295450.2021.1874778
11.
Sterbentz
,
J. W.
,
2007
, “
Low-Enriched Fuel Design Concept for the Prismatic Very High Temperature Reactor Core
,”
Proceedings of International Congress on Advances in Nuclear Power Plants
, Nice, France, May 13–18, Paper No. 7098, p.
10
.
12.
Choi
,
H.
,
Schleicher
,
R. W.
, and
Bolin
,
J.
,
2020
, “
Performance Analysis of Silicon Carbide Composite Clad Uranium Carbide Fuel for a Long-Life Gas-Cooled Fast Reactor Under Normal Operation—Part I: Design Criteria and Material Data
,”
Nucl. Technol.
,
206
(
7
), pp.
993
1009
.10.1080/00295450.2019.1698936
13.
Choi
,
H.
, and
Bolin
,
J.
,
2020
, “
Performance Analysis of Silicon Carbide Composite Clad Uranium Carbide Fuel for a Long-Life Gas-Cooled Fast Reactor Under Normal Operation—Part II: Modeling and Simulation
,”
Nucl. Technol.
,
206
(
7
), pp.
1010
1018
.10.1080/00295450.2019.1699008
14.
Bostelmann
,
F.
,
Strydom
,
G.
,
Yoon
,
S.
,
2015
, “
Results for Phase I of the IAEA Coordinated Research Program on HTGR Uncertainties
,”
Idaho National Laboratory
,
Idaho Falls, ID
, No. INL/EXT-14-32944.
15.
Messer
,
C. E.
,
1960
, “
A Survey Report on Lithium Hydride
,”
Atomic Energy Commission
, Washington, DC, Report No. NYO-9470.
16.
Bogart
,
D.
, and
Valerino
,
M. F.
,
1953
, “
The Sodium Hydroxide Reactor: Effect of Reactor Variables on Criticality and Fuel Element Temperature Requirements for Sub-Sonic and Supersonic Aircraft Nuclear Propulsion
,”
National Advisory Committee for Aeronautics
, Washington, DC, NACA Research Memorandum No. RM E-52-I-19.
17.
Seaborg Technologies
,
2023
, “
Our Technology
,”
Seaborg Technologies
, Copenhagen, Denmark, accessed June 10, 2023, https://www.seaborg.com/the-reactor
18.
Pater
,
M.
,
Klinkby
,
E. B.
,
Cooper
,
D.
,
2022
, “
Molten Salt Revisited: The CMSR
,”
Nuclear Engineering International
, London, UK, accessed Jan. 24, 2022, https://www.neimagazine.com/features/featuremolten-salt-revisited-the-cmsr-9423379/
19.
Smith
,
R. L.
, and
Miser
,
J. W.
,
1972
, “
Compilation of the Properties of Lithium Hydride
,” NASA Lewis Research Center (Now NASA Glenn Research Center),
Brook Park
,
OH
, Technical Memorandum No. X-483.
20.
Haynes
,
W. M.
,
2015
,
CRC Handbook of Chemistry and Physics
, 95th ed.,
CRC Press
,
Hoboken, NJ
.
21.
Claes
,
P.
, and
Glibert
,
J.
,
1985
, “
Electrical Conductivity and Specific Mass of the Molten LiOH–LiNO3, NaOH–NaNO3, and KOH–KNO3 Mixtures
,”
J. Electrochem. Soc.
,
132
(
4
), pp.
857
862
.10.1149/1.2113973
22.
Bogart
,
D.
,
1954
, “
Densities of Molten Sodium and Rubidium Hydroxides
,”
J. Phys. Chem.
,
58
(
12
), pp.
1168
1169
.10.1021/j150522a026
23.
Leppänen
,
J.
,
Pusa
,
M.
,
Viitanen
,
T.
,
Valtavirta
,
V.
, and
Kaltiaisenaho
,
T.
,
2015
, “
The Serpent Monte Carlo Code: Status, Development and Applications in 2013
,”
Ann. Nucl. Energy
,
82
, pp.
142
150
.10.1016/j.anucene.2014.08.024
24.
Pope
,
M. A.
,
2012
, “
Transmutation Analysis of Enriched Uranium and Deep Burn High Temperature Reactors
,”
Idaho National Laboratory
,
Idaho Falls
, ID, INL/EXT-12-26423, FCR&D-Fco-2012-000149.
25.
Colton
,
A. V.
, and
Bromley
,
B. P.
,
2018
, “
Lattice Physics Evaluation of 35-Element Mixed Oxide Thorium-Based Fuels for Use in Pressure Tube Heavy Water Reactors
,”
Ann. Nucl. Energy
,
117
, pp.
259
276
.10.1016/j.anucene.2018.03.010
26.
Hu
,
X.
,
Schappel
,
D.
,
Silva
,
C. M.
, and
Terrani
,
K. A.
,
2020
, “
Fabrication of Yttrium Hydride for High-Temperature Moderator Application
,”
J. Nucl. Mater.
,
539
, p.
152335
.10.1016/j.jnucmat.2020.152335
27.
Miao
,
Y. N.
,
Stauff
,
N.
,
Bhattacharya
,
S.
,
Yacout
,
A.
, and
Kim
,
T. K.
,
2020
, “
Advanced Moderation Module: Moderation Module for High-Temperature Micro-Reactor Applications
,”
Argonne National Laboratory
,
Lemont, IL
, Report No. ANL/CFCT-20/19.