The development of a waste inventory database and waste treatment technology and the evaluation of the feasibility of each technology and the total system of waste management requires a team composed of system engineers, researchers,

and implementers from the start of R&D. The authors propose an R&D implementation and evaluation team (Fig. 28.2). The role of each member is as follows: researchers conduct laboratory-scale cold and hot tests for collecting basic information on waste inventory and treatment technology, implementers carry out engineering-scale cold and hot tests for commercializing the technol­ogy, and system engineers carry out the system design and cost evaluation of the technology to evaluate the feasibility of the technology. The members of the team should work together on R&D and to check whether the data obtained are sufficient for all members. As a result of this collaboration, it is expected that sufficient data will be obtained to pursue the next phase of testing and to transfer the technical knowledge smoothly to other members. Because the engineering — scale test will be conducted by the implementers, education and training of future operators will be also performed. The team should also evaluate the storage, transportation, and disposal technology. For this purpose, system engineers who perform these evaluations should be involved.

Takanori Kitada, Thanh Mai Vu, and Noboru Dobuchi

Abstract The neutron spectrum of a pulsed neutron reactor at subcritical state is different from that evaluated by k-eigenvalue mode, because of the time needed in the neutron slowing-down process from fast to thermal energy range. The time needed in slowing down does not depend on the degree of subcriticality, but the decreasing speed of neutron flux becomes fast as the subcriticality becomes deep. Therefore, the neutron spectrum becomes soft as the subcriticality becomes deep. This fact suggests to us that group constants to be used in the design study should change with the degree of subcriticality of the target system, even in the case of the same composition.

Keywords ADSR • Alpha-eigenvalue • k-Eigenvalue mode • Neutron spectrum • Subcriticality • Time-dependent mode

13.1 Introduction

The accelerator-driven subcritical reactor (ADSR) is considered as one of the best candidates to annihilate the radioactivity of nuclear waste and has been investigated in many institutes for many years. The ADSR is operated by the pulsed proton beam as an ignition of spallation reaction to produce many neutrons. Kyoto University Critical Assembly (KUCA) is one of the facilities to demonstrate the ADSR by using accelerated protons for the spallation reaction or deuterons for the deuterium — tritium (DT) reaction.

This study focused on the transient behavior of the neutron spectrum in a subcritical system after the injection of DT neutrons to know and discuss the physical behavior of the neutron spectrum in a subcritical system through the analysis of the experiments performed at KUCA. The subcritical system with pulsed neutrons has been widely analyzed in the steady state, although transient behavior of the neutron spectrum after the injection of DT neutrons can be analyzed in the transient state. This chapter focuses on the neutron spectrum evaluated in

T. Kitada (*) • T. M. Vu • N. Dobuchi

Osaka University, Graduate School of Engineering, 2-1 Yamada-oka, Suita,

Osaka 565-0871, Japan

e-mail: kitada@see. eng. osaka-u. ac. jp © The Author(s) 2015

K. Nakajima (ed.), Nuclear Back-end and Transmutation Technology for Waste Disposal, DOI 10.1007/978-4-431-55111-9_13

steady state, and two kinds of calculation modes in steady state are compared and discussed: the k-eigenvalue mode and the alpha-eigenvalue mode.

Chapter 2 shows a brief explanation of KUCA experiments and the major results. Analyses of the experiments and discussion are described in Chap. 3, and the conclusions are summarized in Chap. 4.

This chapter shows a brief explanation of experiments performed at KUCA for the convenience of easy understanding of the analysis described in the next chapter.

Experiments modeled on the ADSR were performed at the A-core with adjacent D+ accelerator. A typical core configuration is shown in Fig. 13.1 for the case of 13 fuel rods. Each square cell is 2 in. x 2 in. in size, with size in the horizontal direction about 1.5 m, composed of a central 40-cm-thick fuel region and upper and lower polyethylene reflector regions. All control rods are inserted through the experiment. Accelerated D+ ions are hit with tritium target, depicted as T-target in Fig. 13.1, and 14 MeV neutrons produced by D-T reaction at T-target are injected into the core region composed of the fuel rods, polyethylene reflector, etc. Neutrons are injected from outside the core region in this experiment.

The target subcriticality was widely changed by changing the number of fuel rods from 19 to 6 to check the validity of the fiber scintillation counter used in the measurement. The subcriticality of the system was evaluated by the so-called extrapolation area ratio method proposed by Gozani [1]. The counters used in the experiments were set at several positions inside the core, and the measured results summarized in Table 13.1 are the results obtained at the core central area, where the most reliable results are expected. Measured subcriticality is from 2.3 [$] (19 fuel rods case) to 49 [$] (6 fuel rods case).

The analysis results of neutron flux distribution and neutron spectrum are summa­rized in this chapter with some discussion. Neutron flux distribution and spectrum in the core are shown in Sects. 13.3.1 and 13.3.2, respectively. All analyses are done by a continuous energy Monte Carlo code named MVP-II [2] with JENDL-4.0 [3] library. The code has the function to simulate the experiment not only in eigenvalue mode but also in time-dependent mode, where the necessary time of neutron flight is used to account for the elapsed time after the injection of DT neutrons.

In this chapter, fast and thermal neutrons are in the energy range less than 4 eV and more than 100 keV, respectively.

Fig. 13.1 Typical core configuration (13 fuel rods case). T-target tritium target

Neutron flux distribution is drastically changed with the change in subcriticality of the system, because of the change in the number of fuel rods in the core. Fig­ures 13.2, 13.3, and 13.4 show the neutron flux distribution along the central line from T-target to core for 13 fuel rods case in eigenvalue mode and time-dependent mode, respectively. Neutron flux distribution evaluated in time-dependent mode changes as a function of elapsed time after the injection of D-T neutrons, and the shape of neutron flux distribution is almost stable after 1e~4 s (Figs. 13.3 and 13.4). The comparison of neutron flux between two modes shows the discrepancy (Figs. 13.5 and 13.6). Thermal neutron flux distribution of the time-dependent mode is smaller at fuel region, but higher at the reflector region, than those of eigenvalue mode, although fast neutron flux distribution is almost the same between the two modes. Figures 13.5 and 13.6 also show that the neutron spectrum is different between two modes, and the details are discussed in the next section.

The neutron spectrum at the fuel region is shown in Figs. 13.7 and 13.8. The neutron spectrum in time-dependent mode changes as a function of elapsed time, although

the neutron spectrum in eigenvalue mode is singular. In addition to this, the neutron spectrum at the fuel region evaluated in eigenvalue mode is almost the same among different subcritical states, because there is no change in fuel composition through the experiment. Neutron spectrum at the fuel region evaluated in time-dependent mode changes as a function of elapsed time after the injection of D-T neutrons, but the shape of the spectrum becomes stable after around 1e~4 s, although the

magnitude of neutron flux decreases with elapsed time (Fig. 13.8). The neutron spectrum is compared between two modes, where the shape of the spectrum in time — dependent mode is almost stable (at 1e~3 s). The comparison of the neutron spectrum is shown in Fig. 13.9. The neutron spectrum in time-dependent mode depends on the subcriticality of the system, and the spectrum becomes soft as the subcriticality becomes deep. This tendency can be understood by considering the following facts. The magnitude of neutron flux decreases as a function of elapsed time in the subcritical system, and the decreasing speed of neutron flux becomes

high for the deep subcritical system. Here the neutrons are slowed down by colliding with the medium in the thermal core, and the time needed in the slowing-down process does not depend on the subcriticality of the system. There­fore, the change in the neutron spectrum is caused by the time delay of decrease in thermal energy range where the neutrons are slowed down compared to that in the fast energy range.

The difference in neutron spectrum will cause the difference in collapsed cross sections widely used in design survey calculations, and the degree of the difference

1E+8

1E+7

1E+6

1E+5

1E+4

1E+3

1E+2

1E+1

1E+0

1E-1

1E-2

1E-3

1E-4

Fig. 13.8 Neutron spectrum at fuel region evaluated in time-dependent mode (13 fuel rods) becomes remarkable as the subcriticality of the system becomes deep. It should be noted that collapsed cross sections depend on the subcriticality of target system because of the difference in neutron spectrum.

There is one recommendation to evaluate the proper neutron spectrum for collapsing. In eigenvalue mode, the k-eigenvalue mode expressed as Eq. (13.13.1) is usually used because the eigenvalue is an unbiased index to recognize the criticality, but there is another eigenvalue mode, named the alpha— eigenvalue mode, expressed as Eq. (13.13.2):

where L is the destruction operator including leakage and absorption reactions, M is the production operator including fission reactions, k is the k-eigenvalue called the effective multiplication factor, a is the alpha-eigenvalue, v is the neutron speed, and фь фа are the neutron fluxes for each mode. Equation (13.1) is derived from a time — dependent equation by eliminating the term of time derivative, but Eq. (13.13.2) is derived by considering the exponential change of neutron flux in time. Usually a subcritical system such as the ADSR is operated not in stable but in transient conditions.

In the subcritical system, the alpha-eigenvalue is negative, and the impact of the negative alpha-eigenvalue on neutron flux is remarkable at thermal energy range where the neutron speed is small. Therefore, the neutron spectrum evaluated in alpha-eigenvalue mode is softer than that in k-eigenvalue mode. Similar to this consideration, the difference in neutron spectrum could be observed in the

supercritical state. However, the difference is expected to be not remarkable compared to subcritical state, because excess reactivity is remarkably small com­pared to the subcriticality, as readily expected.

13.2 Conclusions

The neutron flux distribution evaluated in time-dependent mode changes with elapsed time after the ignition of neutrons into the subcritical system, and the neutron distribution in energy and space becomes almost stable in about 1 e~4 s after the ignition.

There is a remarkable difference in neutron spectrum between two results in k-eigenvalue and time-dependent modes. The neutron spectrum (at 1 ps after the ignition) evaluated in time-dependent mode is softer than that in k-eigenvalue mode, and the difference is more remarkable in a deep subcriticality system. This difference is caused by the fact that additional time is necessary to be moderated before decreasing neutron flux in the thermal energy range, and the time is inde­pendent of the subcriticality of the system, depending only on the material compo­sition of the system.

The neutron spectrum of a pulsed neutron reactor is to be evaluated in alpha — eigenvalue mode instead of k-eigenvalue mode to match the neutron spectrum during the decrease with elapsed time after the ignition of pulsed neutrons into the subcritical system.

Open Access This chapter is distributed under the terms of the Creative Commons Attribution Noncommercial License, which permits any noncommercial use, distribution, and reproduction in any medium, provided the original author(s) and source are credited.

Tetsushi Hino, Masaya Ohtsuka, Renzo Takeda, Junichi Miwa, and Kumiaki Moriya

Abstract The RBWR (resource-renewable boiling water reactor) is an innovative BWR that has a capability to breed and burn trans-uranium elements (TRUs) using a multi-recycling process. The RBWR can be used as a long-term energy supply, and it reduces the negative environmental impact that TRUs cause as they are otherwise long-lived radioactive wastes. Various design concepts of the RBWR core have been proposed. The RBWR-AC is a break-even reactor and the RBWR — TB and RBWR-TB2 are TRU burners. The RBWR-TB is designed to burn TRUs from the RBWR-TB itself and to burn almost all the TRUs by repeating their recycling. The RBWR-TB is assumed to be applied for a nuclear power phase-out scenario. The RBWR-TB2 is intended to burn TRUs from LWR spent fuels. The RBWR-TB2 is assumed to be applied for reducing the amount of TRUs to be managed in storage facilities. The RBWR cores achieve their TRU multi-recycling capability under the constraint that the void reactivity coefficient must be negative by introducing the parfait core concept. This chapter reviews details of the specific design and core characteristics of the RBWR.

Keywords Break-even • Burner • BWR • Multi-recycle • TRU • Void reactivity coefficient

14.1 Introduction

Nuclear-generated electrical power is one irreplaceable candidate energy source that responds to the needs for energy security and for reduction of greenhouse-gas emissions. However, there has also been growing concern that significant amounts

T. Hino (*) • M. Ohtsuka • R. Takeda • J. Miwa

Hitachi, Ltd., Hitachi Research Laboratory, 7-1-1, Omika-cho, Hitachi-shi Ibaraki-ken 319-1292, Japan e-mail: tetsushi. hino. kd@hitachi. com

K. Moriya

Hitachi-GE Nuclear Energy, Ltd., 3-1-1, Saiwai-cho, Hitachi-shi, Ibaraki-ken 317-0073, Japan © The Author(s) 2015

K. Nakajima (ed.), Nuclear Back-end and Transmutation Technology for Waste Disposal, DOI 10.1007/978-4-431-55111-9_14

of trans-uranium elements (TRUs) are becoming long-lived radioactive wastes. If TRUs could be recycled as nuclear fuel, the benefits attained from nuclear power would increase as a long-term energy supply and the negative environmental impact of TRUs as radioactive wastes could be greatly reduced. For these purposes many types of innovative reactors, including the sodium-cooled fast reactor (SFR), have been proposed. The resource-renewable BWR (RBWR) has been proposed to achieve the same purposes using concepts based on proven BWR technologies and the BWR capability to control the neutron energy spectrum flexibly [1—3]. A major characteristic of the BWR is “boiling” in the core, which includes water that functions as both a moderator and a coolant. The neutron energy spectrum can be hardened by reducing the hydrogen-to-uranium ratio (H/U) using the two-phase flow and using the hexagonal tight fuel lattice, so that the transmutation of 238U to fissile plutonium is promoted with increasing resonance absorption: this enables the multi-recycling process of both breeding and consuming TRUs. On the other hand, there is a tendency that the harder the neutron spectrum becomes in the TRU-loaded core, the more positive the void reactivity coefficient becomes. The void reactivity coefficient is one of the main safety parameters for light water reactors (LWRs) and must be negative. The RBWR achieves the TRU multi-recycling capability under the constraint of the negative void reactivity coefficient by introducing the parfait core concept [4].

This chapter reviews details of the specific design and core characteristics of the RBWR.

14.2.1 Overview

Figure 14.1 shows the reactor pressure vessel (RPV) of the RBWR. The common plant specifications of the RBWR and the latest commercial BWR, the ABWR, are listed in Table 14.1. The rated thermal power, electric power, diameter of the RPV, and core pressure are identical for both reactor plants. Figure 14.2 shows a hori­zontal cross-sectional view of the RBWR core configuration, which is composed of 720 hexagonal fuel bundles and 223 Y-type control rods. The axial configuration uses the parfait core concept in which an internal blanket of depleted uranium oxide is placed between the upper and lower fissile zones of the TRU oxides.

Various design concepts of the RBWR core have been proposed. Recent core designs have focused on TRU management. The RBWR-AC is the break-even reactor that can burn depleted uranium by using TRUs extracted from the spent fuel bundles of LWRs without decreasing the amount of TRUs. The RBWR-TB is the TRU burner that can fission almost all the TRUs, leaving only the minimum critical mass of TRUs, by repeating their recycling and collecting. The RBWR-TB2 is a modified version of the TRU burner. The RBWR-TB2 is designed to be able to burn

Fig. 14.1 Reactor pressure vessel of the resource — renewable boiling water reactor (RBWR) [3]

Reactor pressure vessel

Core (showing some fuel bundles)

Control rod

Table 14.1 Plant specifications [3]

Item RBWR ABWR Thermal power (MWt) 3,926 3,926 Electric power (MWe) 1,356 1,356 RPV diameter (m) 7.1 7.1 Core pressure (MPa) 7.2 7.2 Number of fuel bundles 720 872 Fuel lattice type Hexagonal Square Lattice pitch (mm) 199 155 Number of control rods 223 205 Control rod type Y-type Cross shape

Fig. 14.2 Horizontal cross-sectional view of the RBWR core configuration [3]

Break-even	TRU-burner
BWR/PWR (for RBWR-TB2)
Fig. 14.3 Utilization concept of the RBWR-AC, — TB, and — TB2

TRUs from LWR spent fuels, whereas the RBWR-TB is designed as a burner for the TRUs from the RBWR-TB itself, assuming the RBWR-TB would be utilized when the TRU usefulness is exhausted and almost all should have been fissioned. Figure 14.3 shows the utilization concept of the RBWR-AC, — TB, and — TB2.

In core designs for the RBWR-AC, — TB, and — TB2, keeping charged TRU composition preserved at every operation cycle is mandatory. This criterion ensures the multi-recycling capability, fission, and recycling process of TRUs can be continued while maintaining the criticality and fulfilling the various operation constraints, such as sufficient reactor shutdown margin and negative void reactivity coefficient. As mentioned in the Introduction, the multi-recycling capability is achieved by hardening the neutron energy spectrum and promoting the transmuta­tion of 238U to fissile plutonium using the hexagonal tight fuel lattice, which has a H/U less than that of the conventional BWR square fuel lattice. Figure 14.4 shows the relationship between the volume ratio of water to fuel and the breeding ratio in the RBWR-AC, — TB, — TB2, and the conventional BWR. Because the RBWR-AC and — TB need to continue operation cycles without feeding fissile materials other than those contained in the discharged fuel from themselves, the volume ratios of water to fuel are set lower than those of the RBWR-TB2 and the conventional BWR.

In the following sections, the core calculation method is described first, and then each type of RBWR is described.

An outline of the calculation methods used for the core design is as follows. Group constants of 12 energy groups for the core neutronic calculation were evaluated for the horizontal cross section of the fuel bundle lattice by the Monte Carlo calculation code with 190 energy groups [5]. In the burn-up calculation, 45 actinides from

Volume ratio (H2O/fuel)

* Ratio of discharged amount of fissile materials to charged amount of fissile materials

Fig. 14.4 Relationship between water to fuel volume ratio and fissile breeding ratio

228 253

Th to Es and 84 fission products (83 nuclides treated explicitly and 1 lumped fission product) were treated. In the core neutronic calculation, the 12-energy group, three-dimensional neutron flux was obtained by solving the diffusion equa­tion with 1 mesh for each fuel bundle in the horizontal direction and 34 meshes in the vertical direction.

In the thermal hydraulic calculation, the in-channel coolant flow rate, the two-phase flow pressure drop, and the axial void fraction distribution were calcu­lated based on the power distribution obtained by the core neutronic calculation, so that the pressure drops between fuel bundles were balanced. The core neutronic calculation and the thermal hydraulic calculation were iterated until the power distribution and in-channel coolant flow distribution converged.

The void reactivity coefficient was evaluated by decreasing the core coolant flow rate to 95 % of the rated flow and dividing the change of the neutron multiplication factor by the change of core averaged void fraction, from the respective values at the rated flow.

The axial fuel bundle configuration of the RBWR-AC is shown in Fig. 14.5. The axial configuration is the parfait core, where an internal blanket (520 mm) of depleted uranium oxide is placed between two fissile zones (upper, 280 mm; lower, 193 mm). The upper and lower blankets (70 and 280 mm) are attached above and below the upper and lower fissile zones, respectively.

The neutron absorber zones are placed above and below the fuel zone (fissile and blanket) to increase the margin to maintain the negative void reactivity coefficient. The upper neutron absorber zone is composed of the neutron absorber rods placed between the plenums, which are connected to the fuel rods. The neutron absorber rods are filled with B4C pellets in a sealed tube with an outside diameter of 7.7 mm.

Plenum and holder

500mm

Plenum and neutron absorberrod 500mm

Plenum 300mm Upper blanket "0mm

Upper fissile zone

2S0mm

Intemalblanket

520mm

Lower fissile zone

193mm

Lowerblanket 2S0mm Lower neutron absorption zone ‘0mm

Each neutron absorber rod is attached to support rods fixed with the upper tie-plate of the fuel bundle. The neutron absorber rods are installed in a ratio of one per one fuel rod. Each neutron absorber rod is 500 mm long, and the distance between the upper end of the fuel zone and the lower end of the neutron absorber rod is 300 mm. The lower neutron absorber zone is composed of B4C pellets filled in the fuel cladding. The length of the lower neutron absorber zone is 70 mm.

Figure 14.6 shows a horizontal cross-sectional view of the configuration of the RBWR-AC fuel bundle and its fissile Pu enrichment distribution. The lattice pitches of the fuel bundles are 199.2 mm on the side with the control rod and 194.7 mm on the side without it. The channel box of the fuel bundle is hexagonal with an inner width of 189.1 mm, and its wall thickness is 2.4 mm. The control rod is 6.5 mm thick, and the gap between the rod outer surface and the channel box is 1.6 mm on each side; the gap between channel boxes on the side without the control rod is

0. 8 mm.

The fuel rod gap and pitch are 1.3 and 11.4 mm, respectively. For the equilib­rium core of the RBWR-AC, the bundle-averaged fissile plutonium enrichment is

15.7 wt% for the upper fissile zone (Fig. 14.6a) and 20.1 wt% for the lower fissile zone (Fig. 14.6b). Both the upper and lower fissile zones utilize five different fissile Pu enrichments.

The main core specifications and performance values of the RBWR-AC in the equilibrium core are shown in Table 14.2. The core coolant flow is 2.6 x 104 t/h at a subcooling temperature of 5 K at the entrance and has a steam quality of 35 w/o at the core exit. The void fraction of core coolant is about 30 % at the bottom of the lower fissile zone because of heating in the lower blanket; it reaches 80 % at the top of the core. A breeding ratio of 1.01 is achievable under a 45 GWd/t exposure

Average fissile Puenrichment

15.7 wt%

Number of fuel rods 271

Fuel rod diameter 10.1mm

Fuel rod gap 1.3mm

Thickness of control rod 6.5mm

Average fissile Puenrichment
20.1 wt%

Number of fuel rods 271

Fuel rod diameter 10.1 mm

Fuel rod gap 1.3 mm

Thickness of control rod 6.5 mm

Lower fissile zone

averaged with the upper, internal, and lower blankets. Here the breeding ratio is defined as the number of atoms of fissile plutonium left in the discharged fuel bundles per fissile plutonium loaded in the initial charged fuel bundles.

The loading pattern of the fuel bundles in the equilibrium core adopts zone loading with the reflective boundary condition of 60 ° in the azimuthal direction. After the control rod scheduling is done, the radial power peaking factor is about 1.2 and the axial power peaking factor is about 1.8, including the blanket zones, which results in the minimum critical power ratio of 1.3 and the maximum linear heat­generating rate of 47 kW/m.

The RBWR-AC has a void reactivity coefficient of —2.4 x 10—4 Ak/k/%void, which is comparable with that of the current BWR, about —7 x 10—4 Ak/k/%void.