Analysis of Fuel Burnup and Transmutations at High Burnup of Sodium Fast Breeder Reactor

: In this paper, the Monte Carlo N-Particle extended computer code (MCNP) were used to design a model of the European Sodium-cooled Fast Reactor. The multiplication factor, conversion factor, delayed neutrons fraction, doppler constant, control rod worth, sodium void worth, masses for major heavy nuclei, radial and axial power distribution at high burnup are studied. The results show that the reactor breeds fissile isotopes with a conversion ratio of 0.994 at fuel burnup 70 (GWd/T), and minor actinides are buildup inside the reactor core. The study aims to check the efficiency of the model on the calculation of the neutronic parameters of the core at high burnup.


Introduction:
The Generation IV (Fourth Generation) International Forum (GIF) roadmap identifies fast reactors as a special, potentially sustainable energy source, especially in waste management and nuclear fuel optimization 1 .For 60 years of technical experience in related projects in many countries, sodium-cooled fast reactors (SFRs) are placed in a unique position among the various systems corroborative by GIF.Many countries have demonstrated significant technological advances in sodium-cooled fast reactors in design and operation terms 2 .The United States (US) Experimental Breeder Reactor (EBR) and Fast Flux Test Facility (FFTF), Russia's BN series reactors, Japan's Monju reactor, and France's Phénix prototype and commercial SuperPhénix have added more than 37 years of reactor operating experience in SFR technology 2 .
The newest examples of sodium-cooled reactors are the recently linked to the net China Experimental Fast Reactor (CEFR) 3 , India's prototype fast breeder reactor (PFBR ) 4 , and the Russian BN-800 reactor under construction 5 .For the Europe community, the "European Sustainable Nuclear Industrial Imitative" (ESNII) planned an industrial project called "Advanced Sodium Technological Reactor" (ASTRID) for many demonstration purposes.In addition to current fast reactor construction projects, many European countries are performing research programmes to develop pioneering fast reactor (GEN-IV) concepts.
The European Fast Sodium Reactor Community Project (CP-ESFR) is part of EURATOM's contribution to the GIF and seeks to create a common European framework to support fast sodium reactor technology.It was launched in the 7th EURATOM Framework Programme, with the aim of 24 European partners to create the technological basis for European fast sodium reactor plants (ESFR) to improve safety performance, resource efficiency, and costefficiency 6 .
The design and safety parameter analysis of the world's nuclear reactors, in normal operation and under accident conditions needs continuous improvement of computational precision.In this study, the Monte Carlo Neutron Transport Code MCNPX 7 was used to design an ESFR core model to analyze and evaluate a set of burnup-related properties.These include the axial and radial power distribution in the SFR core and the isotopic composition of the fuel.In addition, the performance characteristics at the start of cycle (BOC) and end of cycle (EOC) were investigated, considering the changes in the fuel isotopic composition during burnup 8 .The results obtained will serve as an updated analysis for further evaluation of fuel behavior and performance in the SFR core.

Reactor Description
The reactor core consists of inner and outer fuel zones.Each zone has a different fuel composition as shown in Fig. 1.There are 225 inner fuel assemblies and 228 outer fuel assemblies 9 .The reactor's control rod system is composed of two main devices: the Primary Control Rod (PCR) and the Secondary Control Rod (SCR).There are 24 SCR assemblies and 24 PCR assemblies 10 .In the designed model, the control assembly consists of a control rod located above the active zone, and the rest of the assembly is filled with sodium.Radial Reflector around the active core consists of 331 assemblies representing three rings around the core.The reflector consists of hexagonal blocks of a homogeneous mixture of 26% Na 74% EM10-like steel (% vol) 11 .Fig. 1, shows three radial zones in the horizontal layout of the core.The three radial zones are the inner core (in blue), the outer core (in orange), and the radial reflector (in yellow).There is one assembly of the reflector located in the center of the inner core.Furthermore, the PCR and SCR rods are dispersed into the two fuel zones.
There are 271 fuel pins in each fuel assembly.These pins are fixed in place by wire spacers and made of mixed oxide fuel (U, Pu)O2 pellets.The cladding is formed from Oxide Strengthened steel (ODS) [11][12][13] .Fig. 2, shows the horizontal section of the fuel assembly and vertical section of the fuel pin.In the horizontal section of the fuel assembly, the blue color refers to the fuel pins, and the red color refers to the coolant, while the orange color indicates the structural materials.
The vertical section of the fuel pin consists of five zones (from the upper to bottom): the first zone is the axial reflector, the second zone is the upper gas plenum, the third zone is the Active core, the fourth zone is the axial reflector, and the fifth zone is the lower gas plenum with dimensions 80.4525 cm, 10.0566 cm, 100.566 cm, 30.1693 cm, and 89.9175 cm, respectively 13 .
The active core is 100.55 cm long and is divided into equally five vertical zones with a length of 20.11 cm.Each vertical zone containes a variuos material composition, and the axial fuel composition has been altered to optimize and flatten axial flux and the axial power distributions [13][14][15] .

MCNPX computer model
Monte Carlo N-Particle Code (MCNP) is a general-purpose and a good computational instrument for Particle transport calculations.MCNPX (MCNP eXtended) is a Fortran90 (F90) Monte Carlo radiation transport computer code that transports many particles over a broad range of energies 7 .
In aim work, a heterogeneous model of the reactor core was designed using MCNPX, as shown in Fig. 1 16 .Results are based on 12 million neutron histories.Calculations are based on the latest version of the ENDF library, which is already included in the MCNP library (ENDF/B-VII).At the burnup card, the fuel burns to 70 (Gwd/T) under normal operating conditions of the ESFR reactor.The cycle time is divided into 16-time steps.

Results and Discussions:
Table.I shows the comparison between MCNPX results and the reference as calculated by (serpent code) 17 .The reactor multiplication factor (Keff ) at (BOC ) beginning of the cycle is 1.02863 and shows good agreement with the reference calculated by Serpent Code.The delayed neutron fraction (eff) for the reactor is 365 pcm which is less than the light water reactor because the fast reactor depends on plutonium as fuel which has a small fraction of delayed neutron fraction.The Doppler coefficient is calculated at fuel temperatures T1 and T2 and is chosen at 1200 ˚K and 1500 ˚K.The difference in results calculated from MCNP and reference for Doppler coefficient is 10 pcm or 1.01% in terms of relative error.It can be seen that the Doppler coefficient has a negative value which is attributed to the resonance crosssection of U-238.As the resonances of U-238 broadened, it reduced the self-shielding effect and resulted in negative feedback on reactivity.
The control rod worth is the reactivity difference between the two states: when all control rods are withdrawn from the core during normal operation and when all control rods are fully inserted.The difference in results calculated from MCNP and reference for Control rod worth is 166 pcm or 2.99%; when the control rods are inserted in the reactor core, the reactivity decrease (the neutron flux decreases) by absorbing neutrons 17 .
The sodium void worth is calculated by replacing all sodium in the active core by void and equaling the reactivity difference between this state and the normal operation state.The sodium void worth is positive.This means that the reactivity increases due to the loss of coolant.Molten sodium works as a coolant for the reactor and also moderates neutrons when the core loses sodium and neutron moderation, neutron spectrum becomes more harder and shifts to higher neutron energy which is the more effective region in a fast reactor 17 .The difference in results calculated from MCNP and reference for Sodium void worth is 22 pcm or 1.27%.Fig. 3, shows Keff versus Burnup (GWd/T) for the present core model.The multiplication factor decreases with burnup due to fuel burnup and consumption.After 70 GWd/T, Keff approach to unity.Fig. 9, illustrates the radial power distribution across the core ( 1/6 of the core).The radial power is calculated at the third zone.The upper number represents the power at BOC, and the lower number refers to power at EOC.The maximum power is 1.567, and the minimum power is 0.107 at BOC.The maximum power is 1.069, and the minimum power is 0.219 at EOC.

Conclusions:
For the ESFR oxide-fuelled core, many fuel burnup-related parameters have been calculated using the Monte Carlo MCNPX computational code.These include the effective neutron multiplication factor (keff), conversion factor, radial and axial power distributions in the ESFR core, and the evolution of fuel composition inside the ESFR core.The axial and radial power have been evaluated for the beginning of the cycle (BOC) and at the end of the cycle (EOC), explicitly taking into account changes in core material composition during burnup.Also, the calculation by MCNPX shows an agreement with reference (SERPENT) for delayed neutrons fraction (eff), Doppler constant, control rod worth, and sodium void worth.By the end of the fuel cycle, the Pu-239 mass is increased, and the total fissile content of the core increases.Also, the conversion factor is higher than 1 during burnup.The obtained results showed that ESFR operates as a breeder with a conversion ratio of 0.994.

Figure 1 .
Figure 1.The horizontal section of the MCNP core model 9 .

Figure 2 .
Figure 2. (a) The horizontal section of the fuel assembly, and (b) The vertical sections of the fuel pin models 9 .

Figure 4 .
Figure 4.The total mass of U-235 (Kg) and Pu-241 for the present model with burnup (GWd/T).

Fig. 5 ,
Fig. 5, shows the total mass of Pu-239 (kg) versus core burnup (GWd/T) during reactor operation for the present model.The results indicate the Pu-239 (with initial mass 5627 Kg) increase during burnup and at 65 GWd/T start to decrease.

Figure 5 .
Figure 5.The total mass of Pu-239 (kg) versus core burnup (GWd/T) during reactor operation for the present model.

Fig. 6 ,
Fig. 6, shows conversion factor versus Burn up (GWd/T) for the core.The conversion factor increases up to 1.003 at 20 (GWd/T) then decreases to 0.9937 at 70 (GWd/T).The conversion factor increases with burnup due to the increase in mass of Pu-239 gradually due to its breeding from the fertile isotopes U-238.As shown in Fig. 4, the masses of U-235 and Pu-241 decrease during burnup through fission or transmutation by neutron capture.After 20 (GWd/T), the conversion factor started to decrease due to the slight decrease in mass of Pu-239 compared to the consumption of U-235 and Pu-241.

Figure 6 .
Figure 6.The conversion factor for the reactor core versus core burnup (GWd/T).

Fig. 7 ,
Fig. 7, shows Pu-238, Pu-240, and Pu-242 and total Plutonium isotopes versus core burnup (GWd/T).The results illustrated that Pu-238 and Pu-242 slightly decreased, while Pu-240 and total Pu isotopes slightly increased.[total Pu isotopes are the summation of all Plutonium isotopes, including Pu-239 and Pu-241, which appeared in the previous figures].The total initial mass of Pu-238 for fresh fuel is 344.6 Kg and at 70 (GWd/T) is 258.8Kg.The total initial mass of Pu-242 for fresh fuel is 1226 Kg and at 70 GWd/T is 1097 Kg.The total initial mass of Pu-240 for fresh fuel is 3524 Kg and at 70 (GWd/T) is 3810 Kg.The total initial mass of Pu isotopes for fresh fuel is 11521.2Kg and at 70 (GWd/T) is 11598.2Kg.

Figure 7 .
Figure 7.The total mass of Pu isotopes (Kg) for the present model with burnup (GWd/T).

Figure 9 .
Figure 9. Radial power distribution across the core for the third zone.

Fig. 10 ,
Fig.10, illustrates the axial power distribution across the axial core distance (cm) for the inner and outer core.The maximum power normalized is 1.4 and 1.2 for the inner and outer core, respectively.

Figure 10 .
Figure 10.Axial power distribution normalized across the core.