**2. Safety of nuclear reactor and breeding**

Passive safety features are preferred for advanced reactor design, such as Economic Simplified Boiling Water Reactor (ESBWR) [2], Advanced Passive 1000 (AP1000) [2], and European Pressurized water Reactor (EPR) [3], to enhance safety and reliability and to reduce human intervention. In Fukushima Daiichi accident on March 11, 2011, passive safety features were desired especially for isolation condenser (IC) systems in unit 1 [4].

In addition, high-temperature gas-cooled reactor (HTGR) attracts attention after the accident due to the inherent safety features for all safety functions of "shutdown," "cooling," and "containment" [5]. As a result, the development of HTGR was recommended in "strategic energy plan," which is formulated by the government of Japan on April 11, 2014 [6].

The fundamental safety features are composed of the three functions of control of reactivity (shutdown), removal of heat from the reactor (cooling), and confinement of radioactive material (containment). In the Fukushima Daiichi accident, the first function "shutdown" was successfully performed. However, the second function "cooling" failed even with the IC systems, which have enough heat removal function for 8 hours per IC system. For the IC systems, passive safety features were desired as described in the previous section. As a result, the final function of "containment" was lost as well.

The first feature of "shutdown" was performed as the automatic scram by detecting the earthquake. For light water reactor (LWR), if the scram would be failed, the reactor power settles down to zero power by moderator reactivity feedback due to the reduced density of the moderator and the Doppler effect due to the increased fuel temperature when heat removal from core is lost.

That is equivalent to inherent safety feature due to self-regulation of power of LWR for normal operation condition. The negative reactivity feedback is caused by expansion of moderator. The moderator temperature coefficient, void coefficient for boiling water reactor (BWR), is designed to be negative as it depends only on the degree of moderation and not on the core size. In other words, the LWR core is designed to be under-moderated [7] such that the neutron moderation is not sufficient to obtain a maximum multiplication factor. At the same time, the multiplication factor is reduced by a moderator density reduction.

For HTGR, the graphite structure is also employed as moderator. The volume ratio of fuel to the moderator, which is an indicator for degree of moderation, is determined by the integrity of core structure and a state of the art of fuel fabrication. Generally, for almost all nuclear reactors, as fuel assembly has more number of fuel pins, the fuel temperature can be reduced to lower because the power-sharing decreases per fuel pin. For HTGR with pin-in-block type fuel, the fuel pins are allocated into the coolant hole in graphite fuel block. The number of fuel pins is restricted by the requirement for the fuel block strength against thermal stress. The fuel pins are composed of coated fuel particles (CFPs). The maximum volume fraction is determined by a state of the art of fuel fabrication to restrict initial failure fraction of the CFPs. To obtain high burnup for long life cycle, the volume fraction prefers the maximum value. Moreover, the moderating power and the absorption cross section of graphite are lower than those of light water. The optimized design for criticality is not preferable from the viewpoint of the long life cycle with considering burnup. According to the result, HTGR's design condition is in the undermoderated region when the core design is reasonable and realistic from the viewpoint of the heat removal, the integrity of structure, and the long life cycle. Moreover, the solid moderator of graphite is never voided. To realize a negative power reactivity coefficient, there are two factors, the Doppler effect of fuel temperature and reactivity feedback of moderator temperature due to neutron spectrum shift of Maxwellian distribution peak [8]. As a result, thermal reactor including LWR and HTGR has the inherent safety feature due to self-regulation of power.

discussed in Section 2. Sustainability of uranium resources and that with plutonium thermal use is discussed in Section 3. Economics of electricity generation with conventional uranium, sweater uranium, and plutonium multi-recycling by FBR is discussed in Section 4. Energy

Passive safety features are preferred for advanced reactor design, such as Economic Simplified Boiling Water Reactor (ESBWR) [2], Advanced Passive 1000 (AP1000) [2], and European Pressurized water Reactor (EPR) [3], to enhance safety and reliability and to reduce human intervention. In Fukushima Daiichi accident on March 11, 2011, passive safety features were

In addition, high-temperature gas-cooled reactor (HTGR) attracts attention after the accident due to the inherent safety features for all safety functions of "shutdown," "cooling," and "containment" [5]. As a result, the development of HTGR was recommended in "strategic

The fundamental safety features are composed of the three functions of control of reactivity (shutdown), removal of heat from the reactor (cooling), and confinement of radioactive material (containment). In the Fukushima Daiichi accident, the first function "shutdown" was successfully performed. However, the second function "cooling" failed even with the IC systems, which have enough heat removal function for 8 hours per IC system. For the IC systems, passive safety features were desired as described in the previous section. As a result, the final

The first feature of "shutdown" was performed as the automatic scram by detecting the earthquake. For light water reactor (LWR), if the scram would be failed, the reactor power settles down to zero power by moderator reactivity feedback due to the reduced density of the moderator and the Doppler effect due to the increased fuel temperature when heat removal from core is lost.

That is equivalent to inherent safety feature due to self-regulation of power of LWR for normal operation condition. The negative reactivity feedback is caused by expansion of moderator. The moderator temperature coefficient, void coefficient for boiling water reactor (BWR), is designed to be negative as it depends only on the degree of moderation and not on the core size. In other words, the LWR core is designed to be under-moderated [7] such that the neutron moderation is not sufficient to obtain a maximum multiplication factor. At the same time,

For HTGR, the graphite structure is also employed as moderator. The volume ratio of fuel to the moderator, which is an indicator for degree of moderation, is determined by the integrity of core structure and a state of the art of fuel fabrication. Generally, for almost all nuclear reactors, as fuel assembly has more number of fuel pins, the fuel temperature can be reduced to lower because the power-sharing decreases per fuel pin. For HTGR with pin-in-block type fuel, the fuel pins are allocated into the coolant hole in graphite fuel block. The number of fuel pins is

the multiplication factor is reduced by a moderator density reduction.

energy plan," which is formulated by the government of Japan on April 11, 2014 [6].

security for uranium and plutonium utilization is discussed in Section 5.

desired especially for isolation condenser (IC) systems in unit 1 [4].

**2. Safety of nuclear reactor and breeding**

22 Uranium - Safety, Resources, Separation and Thermodynamic Calculation

function of "containment" was lost as well.

On the contrary, many FBR designs allow a positive void reactivity coefficient because of the increase of threshold fission reaction of fertile material with high neutron energy over 1 MeV due to the hard spectrum. **Figure 1** shows the fission and capture cross sections and the ratio of fission cross section to absorption cross section. The ratio stands for the fission probability per neutron absorption reaction. The fission probability also rapidly increases over 1 MeV, and the probability is around unity. Then, when the coolant of sodium is voided, the neutron over 1 MeV increased, and positive reactivity is inserted.

Due to the positive void reactivity coefficient, the coolant is boiled, and the power burst, which melts the fuel pins, occurs upon unprotected loss of coolant flow (ULOF) accident [9]. To prevent the power burst, Integral Fast Reactor (IFR) [10] is designed with a large safety margin for heat removal to avoid coolant boiling instead of inherent safety features of neutronic characteristics for self-regulation due to negative coolant void coefficient. The concept

**Figure 1.** Cross section of 238U and fission probability per neutron absorption.

of the inherent safety feature of IFR was demonstrated using an IFR prototype, Experimental Breeder Reactor No. 2 (EBR-2) [11]. Although IFR allows a positive void coefficient, it was demonstrated that, upon ULOF accident, a reactor operating at full power can be safely shut down using a negative reactivity feedback due to Doppler effect without the need of the scram, other safety systems, or operator actions.

However, the commercial FBRs, such as European fast reactor (EFR) [12], which is one of representative FBRs of Generation IV, have high economy and high breeding ability and cannot have the passive safety feature by the enhanced heat removal function because of its minimal safety margin to obtain high core performance. The safety is guaranteed with a reliable shutdown system in the event of coolant flow loss.

To obtain negative or small positive void coefficient, FBR with large core should be designed with pancake-type core to increase neutron leakage for axial direction when the coolant is voided [13]. However, sodium-cooled FBR cannot obtain the negative void coefficient only with the pancaketype core. Then, the concept of "sodium plenum" [14] was proposed to increase the axial neutron leakage. In this concept, upper axial blanket and upper side of fuel are removed to enhance the neutron leakage when the coolant is voided. Naturally, breeding ability will weaken.

Thus, safety and economy, or breeding ability, are related to the transactions for fast reactors (FRs) including FBR. If core performance is prioritized, the passive safety feature for "shutdown" will be abandoned.

the relation between the market price and the mine exploration and development expenditure [15, 16]. The investment for the exploration and development follows the market price. This

Safety and Economics of Uranium Utilization for Nuclear Power Generation

http://dx.doi.org/10.5772/intechopen.72647

25

The amount of total undiscovered resources in 2013 is approximately 7.7 million tU (7,697,800 tU), which is a marginal decrease from approximately 10 million tU (10,429,100 tU) reported in 2011 [15]. The reason why the resources decrease is that the USA did not report the amount in 2013. Then, I regard the amount of undiscovered resources as the value of 10,429,100 tU reported in 2011. This amount corresponds to approximately 170 years (168.3 years) of the duration period. For the estimation of the amount of conventional uranium resources including the identified and undiscovered resources, the highest cost category, i.e., < 260 \$/kgU, is used. Furthermore, there are other resources called unconventional resources recovered not from uranium mines as uranium ore. The unconventional resources are recovered as minor by-products such as uranium from phosphate rocks, nonferrous ores, carbonatite, black shale, and lignite. The recovery cost from these products is higher because of the low uranium concentration. In the future, these resources would become a viable source when market price of uranium exceeds 260 \$/kgU [15]. The amount of these sources is 7.3–8.4 million tU [15], which corresponds to a duration period of approximately 130 years (117.8–135.5 years). The resources described above can maintain the energy sustainability for the present. However, more resources are

Uranium from seawater, which is also categorized to unconventional resources, amounted to 4.5 billion tU [17] corresponding to a duration period of approximately 72,000 years (72,604 years). The uranium is dissolved in the seawater at a low concentration of 3.3 parts per billion (ppb) [17]. Moreover, the amount of uranium at the surface of the seafloor is approximately a thousand times more than the uranium dissolved in seawater, which is approximately 4.5 trillion tU [18]. The uranium solved in seawater is in an equilibrium state with the uranium contained in

trend is common for other resources, e.g., petroleum and coal.

**Figure 2.** Market price of uranium and mine exploration and development expenditure.

needed to achieve the permanent energy sustainability.
