2. Block-type HTRs and calculation methodologies

## 2.1. Block-type HTRs and spatial separation levels

## 2.1.1. Block-type HTRs

1. Introduction

98 Recent Improvements of Power Plants Management and Technology

During the mid-1950s to the mid-1970s, some different types of Th/U MOX fuels, for example (Th,U)O2 or (Th,U)C2, were tested and used as fuels in high-temperature gas-cooled reactors (HTRs), like AVR and THTR in Germany [1] and Fort St. Vrain in the USA [2]. Three main reasons inspired them to demonstrate Th-U fuel cycle at that time. First, compared with kwon uranium, thorium is three times more abundant in nature. Second, Th-232 has an attractive potential for breeding to fissile U-233 efficiently in thermal neutron spectrum. U-233 is also considered as the best compared with other two common fissile isotopes, U-235 and Pu-239, in epithermal or thermal spectrum from neutronic point of view because the number of fission neutrons per neutron absorbed is 10–20% higher than that of U-235 and Pu-239. Finally, uranium resources were believed to be insufficient to support the development of nuclear

Besides HTRs, thorium has been an interesting nuclear fuel for various reactor applications [3], such as molten-salt reactors (MSRs) and water-cooled reactors.Especially, combined with molten-salt fuel in MSRs, thorium was used as a necessary composition of the "standard" fuel aiming to converse and even breed Th-232 to U-233 from the 1970s to mid-1980s. In past 20 years, the potential of thorium has been extended to radioactive waste management and plutonium incineration [4]. In this application, Th-232 is considered as a better fertile isotope than U-238 because of a larger net destruction of plutonium, when weapon-grade or reactorgrade plutonium is burned in various nuclear reactors. Furthermore, thorium-fueled reactors

Combined with the commercial purpose and potential application scale, light-water reactors (LWRs) are a natural choice from the reactor point of view in recent years because of a large amount of LWRs all over the world. The seed-and-blanket (S&B) concept has been reexamined for LWR application by the MIT group [5, 6]. The concepts originate from S&B configuration and were developed for the advanced water breeder application (AWBA) program and tested in the light water breeder reactor (LWBR) at Shippingport from 1977 to 1982 [7]. Further work on thorium-fueled LWRs has been pursued by Radkowsky and Galperin [8]. The MIT group proposed the micro-heterogeneous fuel assemblies and the whole assembly seed-and-blanket (WASB) concept. Moreover, compared with the past research, the recent MIT work is all based

Because of the burnup limit of LWRs (usually 50 GWd/tHM), some research showed that the potential of thorium is limited in LWRs, and HTRs are a better choice for thorium-based fuel for higher burnup and harder neutron spectrum. Recently, the concept of S&B fuel blockshas been introducedto the U-battery [9], a small long-life HTR, and a commercial-level GT-MHR [10], as well as advanced high-temperature reactors (AHTRs) [11] with low-pressure liquid-salt (Flibe) as coolant, which enables the design of a high-power (e.g., 2400–4000 MWth), high-temperature (850–950C) reactor with fully passive safety capability and the economic production of electricity

The past studies have shown the distribution of thorium and uranium fuels in space is a very important factor for the performance of thorium-fueled reactors and have proposed some

industries on a large scale at the early period of nuclear energy development.

generate less long-lived radioactive wastes than uranium-fueled ones.

on low-enriched uranium for proliferation resistance.

orhydrogen.

Modular block-type HTRs [12] are one kind of inherently safe reactors, which passively remove decay heat by natural convection, conduction, and radiation from the reactor core and keep the fuel intact. As mentioned in Section 1, the block-type HTRs are a better choice for thorium-based fuel for higher burnup and harder neutron spectrum. Moreover, an advantage of block-type HTRs over pebble-bed HTRs is that the former provides multi-level and fixed spatial distribution of thorium/uranium fuels in the reactor cores.The reactor core of the block-type HTRs investigated, as shown in Figure 1(a), is comprised of an annular fuel zone, inner reflectors, and outer reflectors. The annular fuel zone is comprised of 1980 fuel blocks, as shown in Figure 1(b). The fuel blocks are stacked firmly against each other in columns that form an annulus between an inner and an outer reflector, both of which consist of rings of unfueled graphite blocks. The annular core configuration ensures higher thermal power and inherent safety under most accidents and transient conditions. Each fuel block includes 210 fuel channels, 108 coolant channels, and 6 fixed burnable poison channels which are filled with

Figure 1. Thorium-fueled HTR and fuel block, (a) Reactor core and (b) Fuel block. Does the query aim to use second style for the book?

graphite in the flowing calculations.The cylindrical fuel compacts are stacked inside channels drilled into hexagonal graphite blocks. Other geometrical parameters ofthe fuel blocks are listed in Table 1.

The most prominent feature of the block-type HTRs is use of tristructural-isotropic (TRISO) particles, which contain five layers from inside to outside: fuel kernel, porous carbon buffer, inner pyrolytic carbon (IPyC), silicon carbide (SiC), and outer pyrolytic carbon (OPyC). The porous carbon buffer layer is provided to protect the dense PyC from fission recoil damage and to provide void volume to limit the fission gas pressure. The dense PyC has good irradiation stability and capability to remain intact to perform fission production retention under severe exposure conditions. Sandwiched between the two PyC layers, the SiC layer provides metallic fission production retention and mechanical strength. TRISO fuel particles are blended and bonded together with a graphite matrix to form fuel compacts. Figure 2 illustrates how the TRISO particles are packaged into the annular core.

## 2.1.2. Definition of multiscale spatial separation

When using thorium in HTRs, two important factors influence nuclear performance. One is the thorium content (the mass ratio of Th-232 to all heavy metal isotopes), meaning the mixed proportion of thorium and uranium. The other is the spatial separation level of thorium and uranium, meaning how thorium and uranium are to be mixed. According to the level of spatial separation, four levels are in a block-type HTR: (1) No separation (Th/U MOX level): with Th/U MOX fuel, the thorium and uranium are mixed in each fuel kernel as a form of (Th,U)O2, as shown in Figure 2(a). Thorium and uranium do not separate in the macrolevel, (2) TRISO-level separation (SBT level): UO2 and ThO2 are made into different TRISO fuel particles (UO2 TRISO and ThO2 TRISO) separately, but the two kinds of TRISO fuel particles are mixed into the same fuel compact, as shown in Figure 2(b), (3) Channel-level separation (SBU level): each fuel channel has only one kind of fuel compacts (UO2 fuel compacts or ThO2 fuel compacts), but a fuel block has both UO2 fuel channels and ThO2 fuel channels, as shown in Figure 2(c), and (4) Block-level separation (WASB level): each fuel block only has a kind of fuel (UO2 or ThO2), but the core has both UO2 fuel blocks and ThO2 fuel blocks, as shown in Figure 2(d).

## 2.2. Calculation and evaluation methods

## 2.2.1. Neutronic calculation method

To only analyze the influence of spatial separation, the other parameters are kept the same including the fuel block geometry, as listed in Table 1, and the fuel shuffling scheme, as shown in Figure 3. A detailed full-core 3D transport calculation in one step will require significant


Table 1. Basic geometrical parameters of fuel blocks in the HTR.

Analysis of the Spatial Separation Effects of Thorium/Uranium Fuels in Block‐Type HTRs http://dx.doi.org/10.5772/intechopen.68671 101

Figure 2. Four levels of spatial separation of thorium/uranium in block-type HTRs.

graphite in the flowing calculations.The cylindrical fuel compacts are stacked inside channels drilled into hexagonal graphite blocks. Other geometrical parameters ofthe fuel blocks are

The most prominent feature of the block-type HTRs is use of tristructural-isotropic (TRISO) particles, which contain five layers from inside to outside: fuel kernel, porous carbon buffer, inner pyrolytic carbon (IPyC), silicon carbide (SiC), and outer pyrolytic carbon (OPyC). The porous carbon buffer layer is provided to protect the dense PyC from fission recoil damage and to provide void volume to limit the fission gas pressure. The dense PyC has good irradiation stability and capability to remain intact to perform fission production retention under severe exposure conditions. Sandwiched between the two PyC layers, the SiC layer provides metallic fission production retention and mechanical strength. TRISO fuel particles are blended and bonded together with a graphite matrix to form fuel compacts. Figure 2 illustrates how the

When using thorium in HTRs, two important factors influence nuclear performance. One is the thorium content (the mass ratio of Th-232 to all heavy metal isotopes), meaning the mixed proportion of thorium and uranium. The other is the spatial separation level of thorium and uranium, meaning how thorium and uranium are to be mixed. According to the level of spatial separation, four levels are in a block-type HTR: (1) No separation (Th/U MOX level): with Th/U MOX fuel, the thorium and uranium are mixed in each fuel kernel as a form of (Th,U)O2, as shown in Figure 2(a). Thorium and uranium do not separate in the macrolevel, (2) TRISO-level separation (SBT level): UO2 and ThO2 are made into different TRISO fuel particles (UO2 TRISO and ThO2 TRISO) separately, but the two kinds of TRISO fuel particles are mixed into the same fuel compact, as shown in Figure 2(b), (3) Channel-level separation (SBU level): each fuel channel has only one kind of fuel compacts (UO2 fuel compacts or ThO2 fuel compacts), but a fuel block has both UO2 fuel channels and ThO2 fuel channels, as shown in Figure 2(c), and (4) Block-level separation (WASB level): each fuel block only has a kind of fuel (UO2 or ThO2), but

the core has both UO2 fuel blocks and ThO2 fuel blocks, as shown in Figure 2(d).

To only analyze the influence of spatial separation, the other parameters are kept the same including the fuel block geometry, as listed in Table 1, and the fuel shuffling scheme, as shown in Figure 3. A detailed full-core 3D transport calculation in one step will require significant

Values 36 79.3 1.27/210 1.588/102, 1.27/6 500 100/35/35/40 1.05/1.9/3.2/

Diameter/number of coolant channels [cm/]

Diameter of kernels [μm]

Thickness of TRISO layers [μm]

Density of TRISO layers [g/cm<sup>3</sup> ]

1.9

listed in Table 1.

TRISO particles are packaged into the annular core.

100 Recent Improvements of Power Plants Management and Technology

2.1.2. Definition of multiscale spatial separation

2.2. Calculation and evaluation methods

Height of block [cm]

Table 1. Basic geometrical parameters of fuel blocks in the HTR.

Diameter/ number of fuel channels [cm/]

2.2.1. Neutronic calculation method

Parameters Width

across flat [cm]

Figure 3. Reactor core calculation model for 1/6th core.

memory and a central processing unit (CPU) time as utilities in producing calculations or even in laboratories for design purposes. Therefore, a two-step calculation scheme is typical: (1) a detailed calculation at the assembly level with reflective boundary conditions, which gives homogenized cross-sections for the assemblies, condensed to a certain number of groups (lattice calculation step) and (2) a second calculation at the core level with homogenized properties in each assembly and usually small number of groups (full-core calculation step).

In this chapter, the traditional two-step calculation scheme is constructed based on the DRAGON V4 code system [13], as shown in Figure 4. An attractive feature of the DRAGON code is its ability to treat particle fuel in a graphite matrix in a full-assembly calculation. It provides the possibility to define a stochastic mixture of spherical micro-structures that can be distributed inside composite mixtures of the current macro-geometry using the Hebert doubleheterogeneity model [14] or Sanchez-Pogroming double-heterogeneity model [15].

In step (a) in Figure 4, a 2D fuel block is modeled including the structure of the TRISO particle. The method of characteristics (MOC) and 295-group cross-section library (http://www. polymtl.ca/merlin/libraries.htm) are used to solve the transport equation. Then, the energy groups of the cross-sections are condensed to 26 groups during the homogenization of the fuel block. In step (b), a 1D annular core is modeled, comprising a homogenized fuel zone and two reflector zones. The homogenized cross-sections of the fuel block generated in step (a) are used for the fuel zone in this step, and the cross-sections of the graphite generated in step (a) are used for the reflectors of the 1D reactor model. The 1D transport calculations are executed by the discrete ordinate (SN) method. Only the reflectors are homogenized to generate the Analysis of the Spatial Separation Effects of Thorium/Uranium Fuels in Block‐Type HTRs http://dx.doi.org/10.5772/intechopen.68671 103

Figure 4. A schematic diagram of the two-step calculation scheme.

cross-sections of the reflector for the following full-core calculations. In step (c), the 2D full-core calculations are executed by the interface current (IC) method. The cross-sections of fuel blocks in this step come from the step (a), while the cross-sections of reflectors come from step (b).

## 2.2.2. Fuel cost analysis model

memory and a central processing unit (CPU) time as utilities in producing calculations or even in laboratories for design purposes. Therefore, a two-step calculation scheme is typical: (1) a detailed calculation at the assembly level with reflective boundary conditions, which gives homogenized cross-sections for the assemblies, condensed to a certain number of groups (lattice calculation step) and (2) a second calculation at the core level with homogenized properties in each assembly and usually small number of groups (full-core calculation step). In this chapter, the traditional two-step calculation scheme is constructed based on the DRAGON V4 code system [13], as shown in Figure 4. An attractive feature of the DRAGON code is its ability to treat particle fuel in a graphite matrix in a full-assembly calculation. It provides the possibility to define a stochastic mixture of spherical micro-structures that can be distributed inside composite mixtures of the current macro-geometry using the Hebert double-

Figure 3. Reactor core calculation model for 1/6th core.

102 Recent Improvements of Power Plants Management and Technology

heterogeneity model [14] or Sanchez-Pogroming double-heterogeneity model [15].

In step (a) in Figure 4, a 2D fuel block is modeled including the structure of the TRISO particle. The method of characteristics (MOC) and 295-group cross-section library (http://www. polymtl.ca/merlin/libraries.htm) are used to solve the transport equation. Then, the energy groups of the cross-sections are condensed to 26 groups during the homogenization of the fuel block. In step (b), a 1D annular core is modeled, comprising a homogenized fuel zone and two reflector zones. The homogenized cross-sections of the fuel block generated in step (a) are used for the fuel zone in this step, and the cross-sections of the graphite generated in step (a) are used for the reflectors of the 1D reactor model. The 1D transport calculations are executed by the discrete ordinate (SN) method. Only the reflectors are homogenized to generate the

An evaluation criterion must be in the comparison of different spatial separationlevels. Usually, the fuel cycle cost is one of the criteria. To make a fair comparison, the adoption of a standardized methodology for fuel cycle cost calculations is prerequisite. Therefore, the levelized lifetime cost methodology is used in this study. The levelized lifetime cost methodology was developed by the Organization for Economic Cooperation and Development (OECD) [16], which uses an internationally accepted investment appraisal methodology to analyze the fuel cycle cost.

The cash flow for fuel cycle material and services commences before the reactor starts to generate electricity and continues well after the reactor ceases operation. The exact timing of payments for natural uranium purchase, conversion, enrichment, fabrication, spent fuel storage, and disposal depends on the associated lead and lag times for the fuel cycle components. To calculate the overall fuel cycle cost, the magnitude of each component cost and the appropriate time that it occurs must be identified. Fuel quantities are obtained from reactor neutronic calculations as described in Section 2.2.1. These quantities of materials and services are adjusted to allow for process losses in the various component stages of the nuclear fuel cycle and then multiplied by the unit costs to obtain the component costs. Finally, the total fuel cycle cost is gotten by discounting these component costs to their present values in a specified base year (usually the commission date of reactor), as shown in Figure 5. The levelized lifetime cost methodology provides costs per unit of electricity generated which are the ratios of lifetime expenses to total expected output, expressed in terms of the present value equivalent. This method derives economic merits by comparing their respective average levelized lifetime costs.

The reactor data and fuel cycle cost data for the HTR are shown in Tables 2 and 3, respectively. Table 2 gives the information about the reactor including the power, lifetime, cycle length, and back-end options. Table 3 gives the unit price and lead or lag time for natural uranium

Figure 5. Time flow of nuclear fuel cycle cost with direct disposal option.


Table 2. Reactor operation data for the HTR.


Table 3. Fuel cycle cost data for the HTR.

purchase, thorium purchase, conversion, and enrichment. The price of natural uranium, conversion, and enrichment is the average price of spot market from 2010 to 2015 (http://www. uxc.com/), respectively: 120.9 \$/kg U, 8.75 \$/kg U, and 126.5 \$/SWU. The fabrication cost of 777 \$/kg HM for HTR fuel blocks comes from the Oak Ridge National Laboratory (ORNL)'s report [17]. Others are the same as the OECD's report [16]. Although different fuel separation levels would likely affect unit price related to fabrication and, in particular, storage, and disposal, their fraction in total fuel cycle cost is small, as mentioned in Section 3.4. Moreover, the sensitivity analysis shows that a 50% variation of the price of fabrication, storage, or disposal will lead to a no-more-than 5% variation of fuel cycle cost [18]. Thus, even if different fuel separation levels have a different price of fabrication, storage, and disposal, the analysis in this chapter is still valid.
