**3. Sustainability of energy resources**

#### **3.1. Duration period of uranium resources**

Uranium resources should be abundant compared with requirement, and energy security is also necessity to ensure the energy sustainability. The duration period, which is defined as the ratio of available resources to the consumption rate, is employed as a measure of the abundance. The consumption rate is estimated to be approximately 60,000 tU/year (61,980 tU/year) by referring to the measured amount required in the world for electricity capacity of 372 GWe at the end of 2012 [15].

The available resources are categorized to identified resources and undiscovered resources. The identified resources stand for uranium deposits delineated through sufficient direct measurement. The undiscovered resources stand for expected existence on the basis of geological knowledge. Usually, only identified resources are employed to estimate the duration period. However, undiscovered resources and other resources described below also exist and will be available. In the present study, the duration periods except for the identified resources are also evaluated to measure the abundance.

The amount of total identified resources in 2013 is approximately 7.6 million tU (7,635,200 tU) [15]. This amount corresponds to a duration period of approximately 120 years (123.2 years). The resources increased by 7.6% from 2011 by new discoveries owing to the revitalization of investigations on resources with the recent soaring market price of uranium. **Figure 2** shows

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

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

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 shut-

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

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"

Uranium resources should be abundant compared with requirement, and energy security is also necessity to ensure the energy sustainability. The duration period, which is defined as the ratio of available resources to the consumption rate, is employed as a measure of the abundance. The consumption rate is estimated to be approximately 60,000 tU/year (61,980 tU/year) by referring to the measured amount required in the world for electricity capacity of 372 GWe

The available resources are categorized to identified resources and undiscovered resources. The identified resources stand for uranium deposits delineated through sufficient direct measurement. The undiscovered resources stand for expected existence on the basis of geological knowledge. Usually, only identified resources are employed to estimate the duration period. However, undiscovered resources and other resources described below also exist and will be available. In the present study, the duration periods except for the identified resources are

The amount of total identified resources in 2013 is approximately 7.6 million tU (7,635,200 tU) [15]. This amount corresponds to a duration period of approximately 120 years (123.2 years). The resources increased by 7.6% from 2011 by new discoveries owing to the revitalization of investigations on resources with the recent soaring market price of uranium. **Figure 2** shows

the neutron leakage when the coolant is voided. Naturally, breeding ability will weaken.

scram, other safety systems, or operator actions.

24 Uranium - Safety, Resources, Separation and Thermodynamic Calculation

down system in the event of coolant flow loss.

**3. Sustainability of energy resources**

**3.1. Duration period of uranium resources**

also evaluated to measure the abundance.

will be abandoned.

at the end of 2012 [15].

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

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 needed to achieve the permanent energy sustainability.

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 the rock on surface of the seafloor [18]. The concentration of 3.3 ppb is remained because of the equilibrium state. This suggests that not only the amount of the uranium dissolved in seawater but also that in the rock on the surface of the seafloor corresponding to the duration period of approximately 72 million years can be recoverable. In other words, the uranium from seawater is almost an inexhaustible resource.

#### **3.2. Utilization of plutonium**

Plutonium is generated along with burnup of <sup>235</sup>U by conversion of <sup>238</sup>U. Suppress plutonium should be incinerated from the viewpoint of nuclear proliferation. Even when the plutonium is disposed, it is problematic and called a "plutonium mine." As time goes on, the plutonium becomes easy to use. Dose from accompanying fission products (FPs) decays, and a fraction of plutonium fissile (Puf) also increases as shown in **Figure 3**. **Figure 3** shows the change on the fraction of the plutonium fissile in spent fuel of LWR. The peak value of around 0.75 appears at 20,000 years near the half-life of <sup>239</sup>Pu of 24,000 years. In addition, the ability of conversion is measured by conversion ratio (CR). The conversion ratio is defined as follows [19]: CR <sup>=</sup> *Average rate of fissile atom production* \_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_ *Average rate of fissile atom consumption* (1)

$$\text{CR} = \frac{\text{Average rate of fissile atom production}}{\text{Average rate of fissile atom consumption}} \tag{1}$$

The residual plutonium can be also used by mixing fresh plutonium to recover the fraction of fissile plutonium. This concept can be realized by high moderation LWR (HMLWR) [20], which is the full mixed oxide (MOX) fuel reactor concept by using exiting advanced boiling water reactors (ABWRs) and advanced pressurized water reactors (APWRs) without changing the plant system. However, the fuel rod diameter is reduced to increase an atomic number ratio of hydrogen to heavy metal (H/HM) value. The H/HM value is changed from 4.9 to 7.0 for BWR concept and from 4.0 to 6.0 for PWR concept. This is the reason why the concept is named "high moderation." The design change concerning to "high moderation" is necessary

The concept of plutonium recycling is shown in **Figure 4**. In the recycling process, it has been

LWR core and high moderation MOX core provides plutonium. Multi-recycling of Pu in high moderation MOX cores causes degradation of plutonium, while the degradation is prevented by mixing the first plutonium. While repeating this process five times, the plutonium composition is almost saturated and regarded approximately as almost equilibrium state. Using the five times recycled plutonium, the feasibility of reactors was confirmed including safety assessment [20]. This means that multi-recycling of plutonium can be established even in

The Puf consumption rates were evaluated for equilibrium state 39 and 33%, respectively, for the BWR and PWR concept. Those correspond to conversion ratio and/or residual ratio of 0.61 and 0.67, respectively. Here, the conversion ratio is presented by 0.6. With the plutonium consumption of HMLWR, the duration period increases 2.5 times, which can be evaluated as

For the economic electricity generation, it is preferable that uranium recovery cost is cheaper. With the recent price increase in the market, the highest cost category of <260 \$/kgU for conventional uranium resources is added to Red Book 2009 [21]. On the other hand, the recovery cost of unconventional uranium is higher than 260 \$/kgU as mentioned in Section 3.1.

thermal reactor by feeding fresh plutonium from the outside of the cycle.

the sum of the infinite geometric series with the ratio of 0.6.

**4. Economics of electricity generation**

**4.1. Recovery cost of uranium resources**

cores and MOX cores are coexisting and the reprocessing of both UO<sup>2</sup>

Safety and Economics of Uranium Utilization for Nuclear Power Generation

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

27

because the plutonium fuel hardens neutron spectrum.

**Figure 4.** Plutonium multi-recycling scheme for HMLWR.

assumed that UO<sup>2</sup>

The conversion ratio of LWR is around 0.6 [19]. If the actinoid nuclides are burned as same amount as fissile nuclides in fresh, the conversion ratio coincides with residual ratio (RR), which is defined as the ratio of fissile inventory in discharged fuel to that in fresh fuel. In many designs of LWRs, the fissile inventory and the inventory of burned nuclides are almost same, and conversion ratio can be regarded as residual ratio.

Plutonium can be also used as resources even in thermal reactor, that is, "plutonium thermal use." The duration period increased to 1.6 times, which is the sum of uranium resources of unity and generated plutonium of 0.6, when once-through utilization of plutonium. With considering necessity of reprocessing facility only for spent plutonium fuel, this option can be a realistic candidate.

**Figure 3.** Change on a fraction of fissionable plutonium.

**Figure 4.** Plutonium multi-recycling scheme for HMLWR.

the rock on surface of the seafloor [18]. The concentration of 3.3 ppb is remained because of the equilibrium state. This suggests that not only the amount of the uranium dissolved in seawater but also that in the rock on the surface of the seafloor corresponding to the duration period of approximately 72 million years can be recoverable. In other words, the uranium from seawater

Plutonium is generated along with burnup of <sup>235</sup>U by conversion of <sup>238</sup>U. Suppress plutonium should be incinerated from the viewpoint of nuclear proliferation. Even when the plutonium is disposed, it is problematic and called a "plutonium mine." As time goes on, the plutonium becomes easy to use. Dose from accompanying fission products (FPs) decays, and a fraction of plutonium fissile (Puf) also increases as shown in **Figure 3**. **Figure 3** shows the change on the fraction of the plutonium fissile in spent fuel of LWR. The peak value of around 0.75 appears at 20,000 years near the half-life of <sup>239</sup>Pu of 24,000 years. In addition, the ability of conversion is measured by conversion ratio (CR). The conversion ratio is

CR <sup>=</sup> *Average rate of fissile atom production* \_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_ *Average rate of fissile atom consumption* (1)

The conversion ratio of LWR is around 0.6 [19]. If the actinoid nuclides are burned as same amount as fissile nuclides in fresh, the conversion ratio coincides with residual ratio (RR), which is defined as the ratio of fissile inventory in discharged fuel to that in fresh fuel. In many designs of LWRs, the fissile inventory and the inventory of burned nuclides are almost

Plutonium can be also used as resources even in thermal reactor, that is, "plutonium thermal use." The duration period increased to 1.6 times, which is the sum of uranium resources of unity and generated plutonium of 0.6, when once-through utilization of plutonium. With considering necessity of reprocessing facility only for spent plutonium fuel, this option can be a realistic candidate.

same, and conversion ratio can be regarded as residual ratio.

**Figure 3.** Change on a fraction of fissionable plutonium.

is almost an inexhaustible resource.

26 Uranium - Safety, Resources, Separation and Thermodynamic Calculation

**3.2. Utilization of plutonium**

defined as follows [19]:

The residual plutonium can be also used by mixing fresh plutonium to recover the fraction of fissile plutonium. This concept can be realized by high moderation LWR (HMLWR) [20], which is the full mixed oxide (MOX) fuel reactor concept by using exiting advanced boiling water reactors (ABWRs) and advanced pressurized water reactors (APWRs) without changing the plant system. However, the fuel rod diameter is reduced to increase an atomic number ratio of hydrogen to heavy metal (H/HM) value. The H/HM value is changed from 4.9 to 7.0 for BWR concept and from 4.0 to 6.0 for PWR concept. This is the reason why the concept is named "high moderation." The design change concerning to "high moderation" is necessary because the plutonium fuel hardens neutron spectrum.

The concept of plutonium recycling is shown in **Figure 4**. In the recycling process, it has been assumed that UO<sup>2</sup> cores and MOX cores are coexisting and the reprocessing of both UO<sup>2</sup> LWR core and high moderation MOX core provides plutonium. Multi-recycling of Pu in high moderation MOX cores causes degradation of plutonium, while the degradation is prevented by mixing the first plutonium. While repeating this process five times, the plutonium composition is almost saturated and regarded approximately as almost equilibrium state. Using the five times recycled plutonium, the feasibility of reactors was confirmed including safety assessment [20]. This means that multi-recycling of plutonium can be established even in thermal reactor by feeding fresh plutonium from the outside of the cycle.

The Puf consumption rates were evaluated for equilibrium state 39 and 33%, respectively, for the BWR and PWR concept. Those correspond to conversion ratio and/or residual ratio of 0.61 and 0.67, respectively. Here, the conversion ratio is presented by 0.6. With the plutonium consumption of HMLWR, the duration period increases 2.5 times, which can be evaluated as the sum of the infinite geometric series with the ratio of 0.6.
