SMR Reactor Simulation Model

A computer model of an exemplary nuclear battery is set up to perform burn-up calculations. As a starting point, the fast, small Toshiba 4S is taken. The reactor model and necessary assumptions are described in the following section. Afterwards, the simulations parameters are introduced.

6.2.1 Description of the Reactor Design

A core model of a small fast reactor was set up for depletion calculations. As far as possible, publicly available technical data for the Toshiba 4S reactor was used. This reactor has an exceptional long lifetime of 30 years without refueling and reshuffling of fuel elements and an electric output of either 10 MWe or 50 MWe (IAEA 2007, p. 395-419; Yacout 2008; Tsuboi et al. 2012). Since the main applications are seen in the smaller version, for the model this version of the reactor with an output of 10 MWe was used. The reactor core would be factory-built, transported to the site, and installed in an underground reactor building. Primary components, such as the heat exchanger, the electromagnetic pumps and the reflector, are located inside the reactor vessel. This setup is referred to as an integral or pool type reactor and is common among SMRs.

II III IV V I Reflector Shutdown Rod Absorber Fuel elements

Figure 6.1.: Movement of the reflector surrounding the reactor core. Before start-up, the reflector is placed below the core. The absorber and shutdown rods are inserted (I). To reach criticality, it is moved upwards (II) and then continues its movement up to the top of the active zone (III). After 15 years, the absorber is withdrawn and the reflector falls back to a lower position (IV). From there it starts its second cycle of upward motion (V).

The long core lifetime is possible due to an adjustable, annular reflector that surrounds the core only partially and a fixed hafnium absorber in the middle of the core. Figure 6.1 shows the different configurations in detail. Before operation, the reflector is placed below the core and the shutdown rod and hafnium absorber are inserted for a sufficient margin to criticality. To start reactor operation, the reflector is lifted to approximately 100 cm and the shutdown rod is withdrawn. At this position, enough neutrons are reflected back into the core that a chain reaction can be sustained. For the following 15 years, the reflector moves continuously upwards, always covering new regions of the core. This is equivalent to adding fresh fuel to the active zone of the core. Since sodium is also a rather good neutron reflector, the volume above the reflecting steel region is filled with inert gas. This prevents that too many neutrons are reflected back into the zone which is not yet due to be burned. With a reflector top position at 175 cm, the replacement of the gas with sodium leads to a small increase in criticality from k_{e f f} = 1.028 to k_{e f f} = 1.032. Hafnium as a neutron poison is particularly qualified for the use in a nuclear battery since the absorption of one neutron leads to the production of another neutron absorbing isotope. This chain continues for five reactions, thus enabling the absorber to work for 15 years (United States

Department of Energy 1993b). Afterwards, the absorber is withdrawn, the reflector falls back to the position where the reactor core barely reaches criticality and starts its second cycle of upward motion.

Originally not planned as a breeder reactor, there are considerations to modify the Toshiba 4S in a way that allows for breeding (Chihara 2010). The main change would be the enlargement of the core diameter to enable the placement of breeding blankets inside the reflector. In the lead-cooled variant of the 4S designed by the Japanese Central Research Institute of Electric Power Industry (4S-LMR for liquid metal reactor) the core diameter is already larger compared to the sodium cooled design (IAEA 2007). In this thesis, the breeder design variant is not further considered. The introduction of breeding blankets would of course lead to an increased plutonium production in the core.

Table 6.1.: Core and element design data for the small, fast reactor model.

Parameter Unit Value Reference

Total Thermal Power MW 30 (Tsuboi et al. 2012) Enrichment of Uranium-235 @ BOL wt% 17.0/19.9 (U.S. DoE 2014) Total Number of Fuel Elements 18 (Tsuboi et al. 2012) Fuel Pins per Element 169 (Tsuboi et al. 2012)

Fuel Element Pitch cm 20.6 (IAEA 2007)

Active Core Height cm 250 (Tsuboi et al. 2012)

Fuel Pin Diameter cm 1.4 (Yacout 2008)

Cladding Thickness cm 0.11 (Yacout 2008)

Pin Pitch (Center to Center) cm 1.51 (Yacout 2008) Element Pitch (Center to Center ) cm 0.25 (Yacout 2008)

Duct to Duct Gap cm 0.22 (Yacout 2008)

In Figure 6.2, cross and vertical section of the reactor core are depicted. The core consists of 19 fuel elements. The central element contains the hafnium absorber and the space for the (emergency) shutdown rod. Uranium-zirconium alloy with 10 wt% zirconium is used as fuel1. The six outermost fuel elements have a higher uranium enrichment of 19.9 % uranium-235, whereas the inner twelve elements contain only 17 % uranium-235 in their uranium fraction (Kilaru et al. 2010; NRC 2012). The inner and outer fuel elements have the same geometry. Each assembly consists of 169 fuel pins. It is surrounded by an HT9-steel duct and completely submerged in sodium. The total heavy metal inventory is 9.24 tons.

The vertical section shows that only the lower part of the fuel pins is filled with fuel. The rather high space for fission gases is needed due to the long core lifetime and the subsequent production of fission gases. The fuel pins are surrounded either by the reflecting region or by gas tanks filled with helium. Geometric dimensions for the computer model are summarized in Table 6.1.

The materials and densities as implemented in the model and their respective source are listed in Table 6.2. Isotopic compositions were derived from the Janis data base (NEA 2012b). The temperature gradient in the core is modeled using temperatures of 600 K and 900 K. For these temperatures, cross section data is readily available in VESTA. The outer steel cladding and the inlet sodium have a temperature of 600 K, while the rest of the core is considered to have 900 K. Temperature differences lead to different coolant densities, which are calculated using equation 5.1. In the following calculations a mean value for the sodium density of0.85 g/cm³ is used, since it is shown that the influence on k_{e f f} is negligible compared to calculations with different coolant

1 _{Fractions can either be given in weight percent or atom percent. The more the composites differ in weight, the}

higher is the difference between the two values. 56

100 cm 250 cm 520 cm D=104 cm D=168 cm a) b) Helium Low Enrichment Absorber Steel High Enrichment Coolant Gas Plenum - 50 0 50 - 50 0 50 cm c m - 10 - 5 0 5 10 - 10 - 5 0 5 10 cm c m

Figure 6.2.: Core layout of the small, modular reactor. (a) shows the cross section of the reactor with all 19 fuel elements and the surrounding steel reflector. One fuel element is shown as a close-up, depicting all 169 fuel pins. The inner assembly contains the hafnium absorber and the shutdown rod. The vertical section of the reactor core in (b) depicts the end of the reflecting region at 100 cm and the above placed helium tanks. The figure is adopted from Frieß, Kütt, and Englert (2015).

densities (∆k ≈ 0.00025). The density of the HT9-steel is estimated using the thermal expansion coefficient of steel.

Table 6.2.: Selected material properties as used in the SMR core model. Material Density in g/cm3 Reference

Coolant Sodium 0.87/0.83 (Rouault 2010)

Fuel U-Zr-alloy 15.9 (Yacout 2008)

Cladding, Structure HT9-Steel 7.8 (Brewer 2009) Reflector Stainless Steel 7.92 (Brewer 2009)

Absorber Hafnium 13.31 (Tsuboi et al. 2012)

Gas Helium 1.8· 10−5 (Tsuboi et al. 2012)

Shutdown rod B4C 2.51 (Brewer 2009)

This model is used for all following calculations on the small modular reactor and was extensively described and validated in Fassnacht (2013).

6.2.2 Simulation Parameters

Beside the geometric model, additional data must be provided for the depletion calculation. Most important are the reflector movement and simulated time periods. The core lifetime is set to 30 years, split into time steps of one year each. Comparison runs with shorter steps and therefore more steps in total have shown no significant effect on the material compositions. In fast reactors, there is only minor xenon production, hence no shorter time step of approximately five days at BOL is necessary.

At the EOL, several depletion steps with increasing length were added. During these steps, power output of the reactor is set to zero and only natural decay is calculated. The material to calculate the dose rates from the spent fuel elements after different cooling periods can thus be easily extracted from the output files.

The core was split into ten different burn-up regions for the burn-up calculations. For each of these regions, neutron flux and material composition are constant during one depletion step. Two zones based on the fuel enrichment were defined in radial direction. To properly account for the changing reflector position and resultantly on the highly variable conditions in the different height layers of the core, each of the two radial zones has been further split into five different axial zones.

Preliminary calculations of the criticality in dependency of the reflector position show that criticality is reached when the top of the reflecting region is placed around 120 cm height. After 15 years, when the fixed hafnium absorber is withdrawn, the emerging volume is filled with sodium. The reflector falls back to a position of 157 cm. The higher position in comparison to the initial criticality position is indicated by a figure depicted in IAEA (2007). It seems reasonable because the fuel is already burnt to some degree. The reflector then moves up to its final position at 250 cm with constant velocity, even though the same figure indicates that the constant velocity assumption does not hold true. No more data on this issue could be found in the open literature.

For the simulation, the burn-up code VESTA as described in section 4.2 is used. Cross section data comes from the Joint Evaluated Fission and Fusion Data JEFF-3.1. The power output is set to 30 MWth and assumed to be constant during the complete simulation time.