The mixed oxide (MOX) fuel is one of the most important fuels for the advanced reactors in the future. It is flexible to be applied either in the thermal reactor like pressurized water reactor (PWR) or in the fast reactor (FR). This paper compares the two approaches from the view of fuel cost. Two features are involved. (1) The cost of electricity (COE) is investigated based on the simulation of realistic operation of a practical PWR power plant and a typical fast breeder reactor design. (2) A new economic analysis model is established, considering the discount rate and the revenue of the reprocessed plutonium besides the traditional costs in the processes of fuel cycle. The sensitivity of COE to the changing parameters is also analyzed. The results show that, in the closed fuel cycle, the fuel cost of applying MOX fuels in the FBR is about 25% lower than that in the PWR at the current operating and fuel cycle level.
The closed fuel cycle becomes more and more attractive in the fast development of nuclear industry. Many countries have executed or decided to execute such strategy. Especially in China, the nuclear energy expanded rapidly in the past several years. In the future, it is pointed that the nuclear power installation will be over 75 GWe by 2020. Huge amount of natural uranium is required. Large pressure is withstood for the low efficiency of current resources utilization. The closed fuel cycle strategy becomes the necessary choice.
The fabrication, application, and reprocessing of mixed oxide (MOX) fuel is one of the key technologies in the closed fuel cycle. By using the reprocessed plutonium, the utilization efficiency of uranium, which is defined as the mass of uranium consumed duo to per kilowatt hour electricity production, is significantly increased. The previous studies have shown that the utilizing of MOX fuel in the thermal reactors can increase the utilization efficiency by 20%–30% [
In China, the closed fuel cycle strategy and the reusing of the recycled plutonium have been determined by the government. However, the way to reuse the plutonium is still need to be considered further, especially for the investor of nuclear power plant. The cost must be considered seriously. It sometimes dominates the decision. For the nuclear power plant, the MOX fuel can be used in both thermal and fast reactors. Therefore, it is useful to analyze the composition of cost while using the MOX fuel in different reactors and make the comparisons to suggest a better decision from the view of economics besides the technologies, and so forth.
The economic analysis on the fuel cycle has been paid attention to since years ago. In 1991, the Westinghouse applied the minimum revenue requirement method to analysis the economics of open and closed fuel cycles [
In this study, the fuel costs of using the MOX fuels in PWR and FBR are investigated, considering the current design of reactors besides the economic parameters only. The operation of power plant is simulated by the reactor core analysis codes. The comparisons in the current or near future situation are analyzed. Also the sensitivity of the costs is predicted. The results show that the fuel cost of electricity (FCOE) in PWR with MOX fuel loaded is 25% higher than that of in FBR. But the situation will be changed with the burnup and discount rate.
To simulate the operation of PWR with the MOX fuel loaded, the code package CASMO/SIMULATE [
The computational flowchart of reactor core simulation.
To avoid the confusion from the differences of reactors, the fuel cost of electricity (FCOE) evaluated by the cost per kilowatt hour electricity production from the fuel cycle is applied in the analysis. The mass flow of heavy metal (including the uranium and plutonium) in the closed fuel cycle is illustrated in Figure
The mass flow of heavy metal in the closed fuel cycle.
PWR
FBR
Cash flow as in Figure
The cash flow in the closed fuel cycle.
PWR
FBR
The cost of a power plant consists of the capital cost, fuel cost, annual cost, and so forth. This study focuses only on the fuel costs.
For the PWR, due to the limit of loading fraction, two kinds of fuels should be considered together, that is, the UO2 fuel and the MOX fuel. The cost is formulated as:
The costs of UO2 fuel and MOX fuel are obtained according to the material flow and cash flow described above. They are represented as follows:
For the fast breeder reactor, there are also two types of fuel assemblies. The seed assemblies, made from the MOX fuel, produce most of the energy for generating the electricity. The blanket assemblies, which contain only depleted uranium, breed the plutonium with small fraction of electricity production. Therefore, the composition of fuel cost is
For the fast breeder reactor, the discharged plutonium from breeding is very important and can be further used in other fast reactors. It is considered as the potential revenue. The benefit is represented as in (
Additionally, a special issue should be noticed, and the plutonium should be stored for some time before it is fabricated into the new fuel assemblies. However, it is expensive to keep the reprocessed plutonium securely. The additional cost should be involved.
The M310-type PWR is chosen in the simulation for its common installation. However, limited by the safety factors, the fraction of MOX fuel in the reactor core should not exceed 30% due to the change by the plutonium [
In the original reactor core, only the UO2 fuel assemblies are loaded. The MOX fuel assemblies are imported batch by batch. The plutonium in MOX fuel is reprocessed from the current PWR spent fuels. The composition is given as in Table
The composition of reprocessed plutonium.
Isotopes | 238Pu | 239Pu | 240Pu | 241Pu | 242Pu |
---|---|---|---|---|---|
Mass percent/% | 2.85 | 52.28 | 23.33 | 15.20 | 6.34 |
The refueling scheme is illustrated as in Figure
The reactor core performance of PWR with MOX fuel loaded.
Items | Value |
---|---|
Length of cycle (EFPD1) | 480 |
Maximum burnup of UO2 assembly (GWd/tHM2) | 53.02 |
Maximum burnup of MOX assembly (GWd/tHM) | 49.56 |
Average burnup of UO2 assembly (GWd/tHM) | 46.69 |
Average burnup of MOX assembly (GWd/tHM) | 47.11 |
Critical concentration of boric solution, BOL (ppm3) | 1773 |
Enthalpy rising factor, BOL4/EOL5 | 1.51/1.34 |
Axial power peak factor, BOL/EOL | 1.47/1.33 |
Radial power peak factor, BOL/EOL | 1.34/1.17 |
1Effective full power day. 2Tons of heavy metal. 3Parts per million. 4Beginning of life. 5End of life.
The loading pattern of fuel assemblies in the PWR.
The BN600-type fast reactor is chosen as the basis for its success operation experience [
There are two options in developing a fast reactor, one is called the breeder reactor, and the other is called the burner reactor. In this study, the breeder reactor is investigated only since the economics of the burner is not so meaningful. From this point, the core design is improved from the current BN600’s. The radial blanket is added to enhance the breeding and make the conversion ratio bigger than 1.0. The loading pattern is illustrated as in Figure
The loading pattern of fuel assemblies in the fast reactor.
The out-in refueling scheme is designed. Figure
The reactor performances are simulated by using PIJ/CITATION. After 10 batches of refueling, the equilibrium cycle can be obtained. The parameters are obtained as in Table
The reactor core performance of FBR with MOX fuel loaded.
Items | Value |
---|---|
Length of cycle (EFPD) | 225 |
Reactivity loss (Δk/k%) | 4.25 |
Average burnup (GWd/tHM) | 105.19 |
Max. burnup (GWd/tHM) | 113.13 |
Mass of plutonium loading (ton) | 0.6 |
Mass of discharged plutonium from blankets each cycle (ton) | 0.192 |
Power fraction in the seed assemblies, BOC/EOC (%) | 96.62/93.78 |
Axial power peak factor, BOC/EOC | 1.239/1.199 |
Axial power peak factor, BOC/EOC | 1.197/1.197 |
Max. linear power density (kw/m) | 38.9 |
Conversion ratio, BOC/EOC | 1.09/1.137 |
Based on the simulation, the mass balance can be obtained from the following economic analysis. Besides, the discharging parameters are also necessary to analyze the FCOE. Since all the core performances in PWR and FBR do not deviate from the traditional conditions of current UO2-fueled reactors, no excess changes should be considered further in operating the reactors due to loading the MOX fuel.
The price in the processes of fuel cycle is the most important economic parameter. The price used in this study is cited from the website
The price of processing techniques and its change interval in the fuel cycle.
Items | Unit ($/kgHM) | Time lag (month) | Material loss (%) | |
---|---|---|---|---|
Current level | Reference change interval | |||
Price of original uranium | 109.2 | 80~300 | −18 | |
Price of chemical conversion | 9.23 | 6.42~12.84 | −12 | 0.5 |
Price of UO2 fuel fabrication | 275 | 200~350 | −6 | 1.0 |
Price of UO2 spent fuel reprocessing | 2107 | 940~3712 | −24 | 0.5 |
Price of reprocessed uranium (RU) | 20 | 0~100 | −24 | |
Price of plutonium storage/$/kgy | 1200 | 1000~1300 | −24~−6 | |
Price of tails | 12 | 7~36 | −12 | |
Price of depleted uranium | 6 | 0~100 | −12 | |
Price of MOX fuel fabrication for PWR | 2215 | 838~2754 | −6 | 0.5 |
Price of MOX fuel fabrication for FBR | 2400 | 1435~3350 | −6 | 0.5 |
Price of blanket fuel fabrication for FBR | 275 | 200~350 | −6 | 0.5 |
Price of MOX spent fuel storage | 470 | 360~580 | 54 | |
Price of recycled plutonium from FBR | 2347 | 1060~4072 | 60 | |
Discount rate | 5% | 2%~8% |
According to the simulation on the M310-type PWR and BN600-like fast breeder reactor, the mass balance based on the mass flow as in Figure
The mass balance of heavy metal in the closed fuel cycle.
PWR
Fast reactor
For the PWR loaded with MOX fuel (up to 30%), the amount of required plutonium equals to the reprocessed mass from three PWR in the same scale. In this case, the uranium resources can be saved over 10%. If the currently reserved PWR spent fuels are used, the fraction will be increased to over 30%.
The final price of MOX fuel reaches 22720 dollar per kilogram ($/kgHM), which is about 8.5 times higher than the one of current UO2 fuel. Figure
The cost compositions of UO2 and MOX fuels.
UO2 fuel
MOX fuel
The final FCOE of PWR is 2.43
The FCOE composition of using MOX fuel in the PWR.
The FCOE composition of using MOX fuel in the FBR.
In this study, the typical design of a breeder reactor is investigated. Without considering the revenue in some fast reactors like ABR [
For the economic analysis, the uncertainty of parameters is quite important due to many complicated factors. The sensitivity analysis is necessary. In this study, the sensitivity is investigated by defining the coefficient of elasticity as:
Among the costs in the fuel cycle, the reprocessing cost accounts for the largest proportion, either in PWR or in FBR. Figure
The changes of FCOE with reprocessing cost.
The practical design and operation of reactors also impact heavily on the costs. For FCOE, the coefficients of elasticity are −0.99 for both PWR and FBR. It means that 1% increase of burnup contributes about 0.99% decrease of the FCOE, which is more attractive in PWR for its higher FCOE at current value. Figure
The changes of FCOE with burnup.
PWR
FBR
The discount rate is very important for the FBR, because the FCOE of FBR is impacted significantly by the revenue of reprocessed plutonium. Unfortunately, the plutonium cannot be immediately applied. The plutonium should be carefully stored as it costs a lot. Due to the effect of time lag, the cost will be increased. The coefficient of elasticity for the FBR is 0.73, which is 10 times larger than the one of PWR. If the discount rate is greater than 8%, the FCOE of FBR is larger than the one of PWR.
Additionally, the original uranium cost is thought to be sensitive for PWR, since most of the fuels are still the UO2 fuels. However, the analysis indicates that the coefficient of elasticity is only 0.081 at current price of original uranium. This factor becomes insignificant.
In this study, the economics of MOX fuel in the closed fuel cycle is analyzed. Considering the two options of applying the MOX fuel, the cost of PWR and FBR are investigated, respectively. The FCOE is used as the evaluation parameter. To find the valuable conclusion, the operations of a typical PWR and FBR are simulated using the reactor core analysis codes. The economic analysis model is established, considering all the components in the closed fuel cycle, especially the revenue of reprocessed plutonium and capital loss in the time lag.
The FCOE of PWR and of FBR are obtained based on the reactor parameters in the equilibrium cycles. For the PWR, the FCOE is 2.43
Although it is only a part of the whole costs in constructing and operating a power plant, the FCOE is one of the most important influencing factors in the daily operation. This study gives the comparison of FCOE in different MOX fuel-loaded reactors. It will be useful to analyze the effect of utilizing the MOX fuel in the future closed fuel cycle.
This paper was carried out partly under the financial support of the National Natural Science Foundation of China (Approved no. 11105104).