Conceptual Design of a Micro Nuclear Reactor for Canadian Arctic Communities

Abstract Small Canadian arctic communities rely on diesel generators for their electricity needs. Providing such generators with fuel year round presents logistical challenges because of inclement weather and the long transportation distances involved. This work presents the conceptual design of a 10-MW(thermal) microreactor that can be used to provide 3.5 MW of electricity as well as district heating to arctic communities. The reactor has a lead-cooled and graphite-moderated core with 13 vertical fuel channels containing high-assay low-enriched uranium fuel enriched to 10%. The core is enclosed in a unpressurized reactor vessel and is passively cooled through natural convection. Stirling engines are used to drive the electrical generators. The hot cylinders of the Stirling engines are located in the unpressurized reactor vessel and are heated directly by the primary coolant. Preliminary neutronic and thermal-hydraulic analyses of the core indicate that the design is technically feasible and that the reactor can function for 2 years and 9 months without refueling.


I. INTRODUCTION
Most Canadian arctic communities use diesel generators as their main source of electrical power since they are not connected to any major electricity grid. The average electrical generating capacity of a remote arctic community in Canada is 3.5 MW(electric) (Ref. 1). A recent study by Natural Resources Canada in collaboration with provincial and territorial governments found the price of unsubsidized electricity in remote arctic communities to be as high as $1.14/kWh (Ref. 1), approximately 10 times higher than in highpopulation centers connected to the main electricity grid.
The bulk of the price differential comes from fuel transportation costs. It is therefore desirable to replace diesel generation with generation based on very high energy density fuel, such as nuclear generation. This work presents the conceptual design of a 10-MW(thermal) micro nuclear reactor, dubbed the ZAN4e (Zero-degree Arctic Natural-circulation 4-MW electric), that can be used to generate electricity with residual heat being available for district heating.

II. MAIN DESIGN FEATURES AND CORE PARAMETERS
The ZAN4e reactor is intended to operate in isolated locations, far from bodies of water or any industrial water source, at low ambient temperatures (as low as −50°C) and without access to grid power. In such conditions, water-based technology does not offer the usual advantage of easy availability, and in fact, poses additional challenges because of the freezing risk during shutdown since water expands when freezing and can damage system components. The freezing risk applies not only to the water used as coolant or moderator, but also to the water in steam turbines. Maintenance, both preventative and corrective, can present challenges, and hence, a simple design with few system components is preferable.
The ZAN4e reactor is unpressurized, lead cooled, graphite moderated, and uses high-assay low-enriched uranium (HALEU) fuel. Stirling engines heated directly by the primary-circuit lead coolant are used to convert heat to work and drive the electrical generators, without the need for a secondary circuit. Coolant circulation is achieved by natural convection without the use of pumps.
The use of graphite as moderator avoids possible core damage resulting from the volume increase of water when freezing, 2 an important consideration for the arctic climate. The lead coolant can withstand high temperatures without boiling (boiling point is 1737°C), leading to the improved efficiency of the Stirling engines, and compared to sodium and water, is comparatively benign and does not support chemical interactions that can lead to energy release in the event of accident conditions. 3 As an added advantage, unlike water which expands when solidifying, lead shrinks when solidifying, and therefore does not put any pressure on the boundary of any volume that contains it, thus avoiding potential mechanical damage to the core if the reactor has to be shut down in the absence of external power, a probable scenario in an off-grid arctic location. Once external power (backup diesel generators) is restored, the lead coolant can be brought back to liquid form using electrical heaters and the reactor can be started up. The specific placement and design of such heaters is not considered at this conceptual-design stage.
The ZAN4e core consists of a 1.7-m-tall vertical graphite cylinder pierced axially by 13 vertical cylindrical fuel channels that consist of two concentric tubes separated by a gas gap for thermal insulation. The inner tubes contain the fuel assemblies and natural lead coolant. Fuel channels are arranged in a rectangular array with a pitch of 28.575 cm. The overall reactor diagram is shown in Fig. 1.
The graphite moderator is sealed in a stainless steel vessel in order to avoid contact with air and consequent oxidation. Even in the event of an air-ingress accident (i.e., oxygen entering the reactor core as well the stainless steel vessel), the graphite blocks will oxidize and lose mass, but the unique atomic crystal structure of nuclear-grade graphite will prevent self-sustained burning. 4 The core is located at the bottom of an inner stainless steel reactor vessel, which is cylindrical in shape, taller than the core, and with a hemispheric bottom. The inner reactor vessel has transfer holes both at the bottom and at the top. The hole diameter (20.7 cm) is twice the diameter of the inner tube diameter, which is large enough to present only minimal resistance to coolant circulation. The inner vessel is contained in the outer reactor vessel, which is a cylinder with a larger radius than the inner vessel. The difference in radii is sufficient to accommodate 13 Stirling engine cylinders arranged in a circular array at the top of the two vessels and to present minimal hydraulic resistance to the convection flow of the coolant.
The cooler lead enters the core at the bottom, is heated up in the fuel channels, reaches the plenum at the top of the core, then exits the inner vessel through the top transfer holes whereby it heats up the Stirling engine cylinders. Having transferred heat to the Stirling engine cylinders, the cooler lead moves downward through the downcomer between the two vessels and reenters the inner vessel through the bottom transfer holes, reaching the bottom of the core again.
The fuel assemblies have CANDU-like geometry (i.e., 37-element annular cluster), thus relying on wellestablished technology, and uses HALEU fuel to provide sufficient reactivity for the small core and to ensure a sufficient period of time between refuelings. A cross section through the core is shown in Fig. 1.
The main core and fuel channel parameters are shown in Table I. The masses of various reactor components are shown in Table II.

III. CORE ANALYSIS
The core performance is analyzed from neutronics, thermal, and hydraulic perspectives to demonstrate that the design is feasible and that safety limits are not exceeded. Neutronics calculations were performed using the lattice transport code DRAGON (Ref. 5) and the core diffusion code DONJON (Ref. 6). Thermal-hydraulic analysis was performed using well-accepted correlations.

III.A. Overall Plant Energy Balance
The approximate net overall thermal efficiency of the Stirling engines used in the ZAN4e reactor can be evaluated using Eq. (1) (Ref. 7): Assuming the hot-cylinder temperature T H to be equal to the average coolant temperature of 650°C and the coldcylinder temperature T C to be equal to 75°C (necessary to drive the district heating system 8 ), the Stirling engine efficiency is found to be 34%. Ignoring losses, the available electrical power is estimated to be 3.4 MW, and the district heating power is estimated to be 6.6 MW.

III.B. Neutronic Analysis
The aims of the neutronic analysis are fourfold: 1. Determine the core reactivity as a function of the lattice pitch.
2. Determine the fuel burnup as a function of fuel enrichment.
3. Determine the power peaking factors.

Determine the core life.
Neutronics calculations were performed in two steps: a lattice calculation step and a core calculation step. Lattice calculations were performed in two dimensions for a lattice cell consisting of a fuel channel and associated moderator. They produce cell-averaged, burnup-dependent, two-group macroscopic cross sections to be used in the core calculation. All lattice calculations employ the collision probabilities method and were performed using the lattice code DRAGON (Ref. 5) and the WIMS-D Library Update 69group microscopic cross-section library. 9 The lattice cell geometry used in DRAGON is shown in Fig. 2.
All cell boundary conditions are reflective. Core-level calculations used a cell-homogenized reactor model. They employed the finite difference method in two-group diffusion theory in a Cartesian geometry and were performed using the code DONJON (Ref. 6). The geometrical model utilized in DONJON is shown in Fig. 3. The corrugated outer boundary of the axial cross section is designed to enclose an area exactly equal to the area of the true circular boundary of the axial cross section, thus preserving the general neutron absorption

III.B.1. Neutron Spectrum
As can be inferred from Fig. 2 and the data in Table I, 88% of the cell volume is occupied by the graphite moderator. Consequently, the neutron spectrum is well thermalized, as illustrated in Fig. 4, which shows the lethargy spectrum (reference energy 10 MeV) of the proposed design. For comparison, a generic pressurized water reactor (PWR) lattice spectrum is also shown.    MICRO NUCLEAR REACTOR FOR CANADIAN ARCTIC COMMUNITIES · CROWELL and NICHITA 507

III.B.2. Lattice Pitch
The dependence of the fresh-core effective multiplication factor on the lattice pitch is shown in Fig. 5. The results shown in Fig. 5 indicate that the fresh-core multiplication factor increases up to a pitch of 38 cm. However, to limit the size and overall weight of the core, a 28.575-cm pitch, identical to that of the CANDU reactor, is used. As can be seen from Fig. 5, that only results in an approximately 400 pcm penalty in the core reactivity.

III.B.3. Enrichment and Fuel Burnup
The CANDU-type fuel assemblies have been shown to operate safely up to a burnup of 20 MWd/kg (Ref. 10). Therefore, the core is assumed not to exceed this maximum assembly burnup. Figure 6 shows the relationship between the core reactivity and the maximum assembly burnup for different levels of enrichment. Core reactivity is found from a full-core, two-group diffusion calculation.
The curves in Fig. 5 include a 7000 pcm reduction in reactivity to account for additional absorbers in the core that are not explicitly modeled, such as structural materials. The value used is based on that for a 660-MW(electric) pressurized heavy water reactor core 11 and is adjusted for the smaller size of the ZAN4e core. It is likely an overestimate of what the real reactivity decrease due to additional absorbers will be. As can be seen from Fig. 6, a 10% fuel enrichment is sufficient to ensure core criticality up to 20 MWd/kgU, and this is the enrichment value chosen for the ZAN4e.

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CROWELL and NICHITA · MICRO NUCLEAR REACTOR FOR CANADIAN ARCTIC COMMUNITIES NUCLEAR TECHNOLOGY · VOLUME 209 · APRIL 2023 The numerator of Eq. (3) represents the maximum linear power of the hot channel, and the denominator represents the average linear power of the hot channel. Finally, the pin power peaking factor Fp is determined as the ratio between the maximum linear pin power density and the average linear pin power density for a fuel assembly, both taken at the same axial position, as expressed by Eq. (4), Within a fuel assembly, the thermal flux, and hence the pin power, increases with the distance between the pin center and the center of the bundle. This is illustrated schematically in Fig. 7, which has been reproduced from Ref. 13. Consequently, the hot pin is found in the outer ring.
The linear power for pin k, q', is determined using the one-group flux φ k , the one-group fission cross section Σ fk , the energy per fission E fk , and the pin cross-section area A p using Eq. (5): Equations (4) and (5) can be combined into The overall power peaking factor of the ZAN4e is simply found by finding the product of the radial power peaking factor, axial power peaking factor, and the pin power peaking factor, as shown in Eq. (7): Table III summarizes all of the power peaking factors calculated for the ZAN4e using DRAGON and DONJON. The overall power peaking factor of the ZAN4e core is smaller than the 3.64 power peaking factor for a theoretical homogeneous, bare cylindrical core (Ref. 12, p. 503). This is due to the neutron-reflecting properties of the graphite and lead surrounding the core both laterally and at the top and bottom. The power peaking factor of the ZAN4e is also competitive with a typical zone-loaded PWR, which is 2.6 (Ref. 12, p. 503).

III.B.5. Core Life
The maximum allowable assembly burnup (B max = 20 MWd/kg), together with the core thermal power (P th = 10 MW), mass of U in fresh fuel m fuel , and the combined axial and radial power peaking factor, F RZ ¼ F R � F Z , determines the core life, as expressed by Eq. (8), Using Eq. (8), the core life is found to be 2.75 years.

III.C.1. Coolant Mass Flow Rate
The mass flow rate in any channel i is determined using Eq. (9), using the channel power q i determined It is assumed that the coolant flow rate through each channel is adjusted (e.g., using diaphragms) so that the inlet and outlet temperatures are the same for all channels. Figure 8 shows the mass flow rate map. The total coolant mass flow rate through the core is determined by summing the mass flow rates through all 13 channels of the core: The value of the total coolant mass flow rate is found to be 140.08 kg/s.

III.C.2. Axial Coolant Temperature and Fuel Temperature Profiles
The bulk coolant temperature is found numerically in 50 axial bins using Eq. (11): where n represents the bin of interest, and q 0 represents the channel linear power density. The centerline fuel temperature is determined using Eq. (12) (Ref. 12, p. 482): The centerline and bulk coolant temperatures for each channel of the core are calculated for a fresh core and an end-of-life core. The axial power profiles for the pin of maximum power are shown in Fig. 9 for both the actual core and a bare (no graphite reflector and no surrounding lead coolant) core. The corresponding fuel centerline temperature profiles for a fresh core and an end-of-life core are shown in Figs. 10 and 11, respectively. Figure 9 illustrates the point at which the low axial power peaking factor of the ZAN4e core is due to the presence of reflector graphite and lead. It also shows that the end-of-life core has a slightly flatter axial power profile due to the higher burnup of the fuel located closer to the midplane of the reactor. Figures 10 and 11 confirm that the calculated coolant mass flow rates result in the desired channel outlet temperature of 900°C. They also show that fuel is expected to remain well below the ~2800°C melting point during normal operation.

III.C.3. Coolant Circulation Through Natural Convection
An important safety feature in the ZAN4e reactor is its ability to use natural convection for coolant circulation. The physics that allows for natural convection of the lead coolant to occur is the difference in densities of the lead between the high-and low-temperature locations of the reactor. Equation (13)

510
CROWELL and NICHITA · MICRO NUCLEAR REACTOR FOR CANADIAN ARCTIC COMMUNITIES where ΔP stati = static pressure available to push the lead coolant in the core ρ avg = average density in the reactor core ρ L = density of lead at the lowest temperature in the reactor (i.e., 400°C) ρ H = density at the highest temperature in the reactor (i.e., 900°C) g = gravitational acceleration (i.e., 9.81 m/s 2 ) L core = height of the core (i.e., 1.7 m) L above core = height between the top of the core and the bottom of the Stirling engines.
For natural convection to occur in the core, the friction pressure losses in the core need to be less than the available static pressure in the core. The friction pressure loss across a tube with arbitrary-shaped cross section is calculated using Eq. (14), where f is the Fanning friction factor: Using the mass flow rate, the flow velocity is calculated using Eq. (15): The Reynolds number is found using Eq. (16): where μ is the dynamic viscosity of lead in Pa, and D hydraulic is the hydraulic diameter, found according to Ref. 12 as where S is the flow area, and Z is the wetted perimeter of the flow. The hydraulic diameter depends on the size and shape of the tube cross section. For this analysis, five different hydraulic diameters were used, corresponding to a core channel, region above the core, region around each Stirling engine, the downcomer, and region below the core. It should be noted that the pressure drop across one channel was representative of the pressure drop across the core.
The values of the Reynolds number were found to exceed 2100 in all five regions. Consequently, the flow in all five regions was found to be turbulent, and hence, the Fanning friction factor f was found using Blasius' formula (Ref. 12, p. 485): The lead density was found using Eq.
where K L is the loss coefficient based on the flow geometry, ρ is the density of the fluid, and u z is the average velocity of the fluid. The loss coefficient for a 180-deg turn was 0.2. Pressure losses through the transfer holes were estimated by using the formula for the pressure loss induced by an orifice plate in a pipe, as shown by Eq. (22) (Ref. 16): The discharge coefficient decreased slightly as the Reynolds number in the full pipe increased and also decreased slightly as β decreased, reaching a minimum of ~0.6 for Re = ∞ and β ¼ 0 (Ref. 16). The maximum theoretical pressure loss corresponded to the minimum value of the discharge coefficient, namely, C o ¼ 0:6; and to the maximum value of the coefficient 1 À β 4 À � ; namely, 1. It is this maximum theoretical pressure drop, shown in Eq. (23), that was used in this work to estimate the pressure drop through the transfer holes: The parameters used in the determination of the driving static pressure and the friction pressure losses are shown in Table IV. The static pressure was found to be ΔP static ¼ 19; 769 Pa; the determined friction pressure losses are shown in Table V. The values in Table  V include an additional 25% margin over values calculated using Eqs. (14), (21), and (23), respectively. Table V shows that pressure losses were dominated by the pressure loss in the fuel channels, which accounts for more than 99% of the total pressure loss. Consequently, even though the pressure losses for regions of complex geometry, such as the Stirling engine region and the transfer holes, were estimated using relatively coarse approximations, recalculating them using detailed models is not expected to yield substantial changes in the overall result. Because the total pressure loss in Table  V (5257.6 Pa) is much smaller than the static pressure driving the flow (19769 Pa) the condition for natural circulation is satisfied with a large margin.

IV. CONCLUSION AND FUTURE WORK
A graphite-moderated and lead-cooled microreactor with passive coolant circulation can be a viable solution for providing electricity to remote arctic communities. Preliminary analysis indicates that the design is technically feasible. Future efforts will include a more detailed analysis of the natural convection of the coolant using computational fluid dynamics, as well as an analysis of the dynamic behavior of the core, starting with the calculation of reactivity coefficients.
Future investigations could also look at design improvements, such as using 100% 208 Pb coolant to improve neutron economy or using a SiC layer between the graphite blocks and stainless steel vessel to reduce the potential effects of air-ingress accidents. 17 Potential challenges to the adoption of the design include lead-stainless steel chemical interactions and limited availability of HALEU fuel.