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Criticality and burnup analyses of a PBMR-400 full core using Monte Carlo calculation method
Annals of Nuclear Energy 38 (2011) 298–301
Contents lists available at ScienceDirect
Annals of Nuclear Energy journal homepage: www.elsevier.com/locate/anucene
Criticality and burnup analyses of a PBMR-400 full core using Monte Carlo calculation method Adem Acır a,⇑, Hasan Cosßkun b, Hacı Mehmet Sß ahin a, Özgür Erol c a
Gazi University, Technical Education Faculty, Energy Division, Teknikokullar, Ankara, Turkey Gazi University, Institute of Science and Technology, Ankara, Turkey c Baskent University, Faculty of Engineering, Department of Mechanical Engineering, Etimesgut, Ankara, Turkey b
a r t i c l e
i n f o
Article history: Received 20 May 2010 Received in revised form 4 October 2010 Accepted 18 October 2010 Available online 12 November 2010 Keywords: Monte Carlo MONTEBURNS PBMR-400 Criticality Burnup analysis Packing fraction
a b s t r a c t In this study, the criticality and burnup analyses have been performed for full core model of Pebble Bed Modular Reactors, such as PBMR-400, using the computer codes MCNP5.1.4 and MONTEBURNS 2.0. Three different pebble distributions, namely; Body Centered Cubic (BCC) (packing fraction = 68%), Random Packing (RP) (packing fraction = 61%) and Simple Cubic (SC) (packing fraction = 52%) were selected for the analyses. The calculated core effective multiplication factor, keff, for BCC, RP and SC came to be 1.2395, 1.2357 and 1.2223, respectively. The core life for these distributions were calculated as 1200, 1000, and 800 Effective Full Power Days (EFPDs), whereas, the corresponding burnups came out to be 99,000, 92,000 and 86,000 MWD/T, respectively, for end of life keff set equal to 1.02. Ó 2010 Elsevier Ltd. All rights reserved.
1. Introduction In today’s technological advances, nuclear reactor designs are tending towards smaller, safer, friendlier to environment and more economical. According to these criteria, Pebble Bed Reactors (PBRs) have great advantages over the other traditional fission reactors. PBRs have increased safety associated with the fuel type that is used in these reactors. In PBRs TRISO type fuel is used. In a TRISO particle fuel is packed in a silicon carbide and three pyrocarbon layers. These layers prohibits the leakage of the fission products from the fuel. This safety feature enables us to store the spent fuel in the places that have less radiation protection compared to the traditional reactor fuel waste storages. Low construction costs, high efficiency and online refueling features make these reactors economical (Kadak, 2005). In addition to this, by using helium, a noble gas, as coolant, very high reactor outlet temperatures can be achieved without increasing the pressure in these reactors. This high outlet temperature of the coolant would result in increased efficiency of the power station and/or can be used for the other applications such as hydrogen production. Because of the peculiar nature of the fuel and core geometry, special modeling and computational techniques are required for the design and analysis of PBRs. Various worldwide research cen⇑ Corresponding author. Tel.: +90 312 212 86 82. E-mail address: [email protected] (A. Acır). 0306-4549/$ - see front matter Ó 2010 Elsevier Ltd. All rights reserved. doi:10.1016/j.anucene.2010.10.013
ters are developing and testing models and methods against the PBR’s benchmarks (Bakhshayesh and Vosoughi, 2009; S ß eker and Çolak, 2003). Kim et al. (2007) performed benchmark calculations for PBMR-400, reactor developed in South Africa, by using the Monte Carlo method. Bomboni et al. (2010) carried out the depletion calculation for the same reactor by making use of the computer codes MONTEBURNS 2.0, MCNPX2.6 and BGCore. It was observed that the BGCore code exhibits good computational performance. In present study the analytical methodology and the validity of the computer codes MONTEBURNS 2.0 (Trellue, 2003), MCNP5.1.4 (X-5 Monte Carlo Team, 2005) and ORIGEN2 (Croff, 1980; Ludwig, 2002) has been analysed. The PBMR-400 was taken as reference reactor. Time dependent variations of multiplication factor keff and other parameters were investigated for 9.6% enriched UO2 for different packing fractions. The calculated results were compared with those available in the literature. 2. Reactor description PBMR is a 400 MWth reactor, that utilize TRISO type fuel, has a vertical steel reactor pressure vessel, 6.2 m in inner diameter (Kim et al., 2007). Reactor core is composed of an inner graphite moderator surrounded by an annular fuel zone. The fuel zone is surrounded by an annular graphite zone as shown in Figs. 1 and 2. The main characteristics of the reactor are given in the Table 1. A
299
A. Acır et al. / Annals of Nuclear Energy 38 (2011) 298–301
Reserve Shutdown System Hole (8) Gas Riser (36) Fuel Region Side Reflector
Inner Reflector Control Rod Channel (24)
Central Hole
Fig. 1. Vertical view of the PBMR-400 model (Cosßkun, 2010).
Inner Reflector
Gas Riser (36)
Reserve Shutdown System Hole (8)
Side Reflector
Fuel Region Control Rod Channel (24)
Central Hole Fig. 2. Horizontal view of the PBMR-400 model (Cosßkun, 2010).
fuel pebble contains 15,000 TRISO fuel particles. Fuel particles are present in 5 cm diameter graphite matrix, which holds the particles together and acts as a moderator. Uranium dioxide fuel in TRISO particles are surrounded by three pyrolitic carbon (PyC) and a silicon carbide layer. The main characteristics of the fuel pebbles and the TRISO particles, used in this study, are given in Tables 2 and 3, respectively.
3. Numerical calculations The neutron transport calculations were carried out with Monte Carlo methods, using the widely known three dimensional particle transport code MCNP, version 5.1.4 (X-5 Monte Carlo Team, 2005).
MCNP5.1.4 allows the simulation of complex geometrical descriptions limited only with available computational power. MCNP5.1.4 simulation and calculations were made by using the ENDF/B-V continuous energy cross-section libraries. The first step of the computational procedure with MCNP were the definition of the geometry, material and the selection of appropriate tallies to obtain keff value of the reactor core and the flux spectrum. Time dependent burnup and criticality calculations were made by using MONTEBURNS 2.0. (Trellue, 2003), a burnup code, which is a fully automated tool that links the Monte Carlo transport code MCNP with the radioactive decay and burnup code ORIGEN2 (Croff, 1980; Ludwig, 2002). The principle function of MONTEBURNS 2.0 is to transfer one group cross-section and flux values from MCNP to ORIGEN2, and then transfer the resulting material compositions
A. Acır et al. / Annals of Nuclear Energy 38 (2011) 298–301 Table 1 Characteristics of PBMR (400MWth) core (Kim et al., 2007). Properties
110
1.6
100
Values
Thermal power Total volume of fuel region Diameter of inner reflector Diameter of fuel region Diameter of reactor pressure vessel Length of reactor pressure vessel Length of fuel Number of pebbles in fuel region
1.4
400 MW 83.7156 m3 2m 3.7 m 6.2 m 20 m 11.62 m 360,000
90 1.2
80
keff = 1.02
70
1
keff
60 Table 2 Characteristics of the pebbles (Kim et al., 2007).
0.8 50
Properties
Values
Number of TRISO particles per pebble Diameter of the pebble Thickness of the fuel free zone Density of the carbon matrix in pebble Enrichment of the fuel in U – 235 Mass of uranium per pebble
15,000 6 cm 0.5 cm 1.75 g/cm3 9.6% 9 g
0.6
40
Fuel burn-up grade (GW.d/ton)
300
30
0.4
20 0.2
0
Table 3 Characteristics of TRISO particles (Kim et al., 2007).
10
0
200
400
600
800
1000
0 1200
Operation time (days)
Properties
Values
Diameter of the fuel kernel Density of UO2 Coating layers materials (inner to outer) Thicknesses of layers Density of materials in the layers
0.5 mm 10.4 g/cm3 C/C/SiC/C 95/40/35/40 lm 1.05/1.9/3.18/1.90 g/cm3
Fig. 3. Temporal variation of the lattice criticality keff and the fuel burnup grade r: with packing type of SC; s: packing type of RP; t: packing type of BCC.
0.008
0.007
(after irradiation and/or decay) from ORIGEN2 back to MCNP in a repeated cyclic fashion.
Fissile isotopes density (gr/cm3)
0.006
4. Results and discussion The criticality and burnup calculations for PBMR-400 full core were performed for Random Packing (RP) (packing fraction of 61%), Body Centered Cubic (BCC) (packing fraction of 68%) and Simple Cubic (SC) (packing packing fraction of 52%) distribution of fuel pebbles. The computer codes MCNP5.1.4 and MONTEBURNS 2.0 were used for the analysis. During the course of calculations the reactor power was assumed as 400MWth. In the first series of calculations, the RP distribution with the packing fraction of 61% was selected to validate the neutronic results. In the second phase, the keff and burnup values for the BCC and SC lattice model as well as RP distribution were investigated. Table 4 presents the keff values for the different packing fractions. The table also includes the value of keff given elsewhere (Kim et al., 2007) for comparison. Table 4 depicts that the difference between calculated core excess reactivities, for packing fraction of 61%, is 14%. The difference may be due to the difference in the computational models adopted, etc. As the comparison is between two calculated results (not with the experimental one), therefore, a
235
U
0.005
0.004
0.003
0.002 239
Pu
240
Pu
0.001
241
Pu
0
200
400
600
800
1000
1200
Operation time (days) Fig. 4. Temporal variation of density of the plutonium isotopes in the PBMR-400 fueled with 9.6% enriched in 235U (packing fraction 68%).
Table 4 Multiplication factor calculated by MCNP for various packing fractions. Fuel lattice type
BCC RP SC
Calculated (this study)
Reported (Kim et al., 2007)
keff
Core average reactivity (pcm)
keff
Core average reactivity (pcm)
1.23959 ± 0.00183 1.23571 ± 0.00159 1.22237 ± 0.00174
21,480 21,165 20,080
– 1.2795 ± 0.000551 –
– 24,645 –
A. Acır et al. / Annals of Nuclear Energy 38 (2011) 298–301 0.06
core multiplication factor = 1.02, the core burnup values are approximately 99,000, 92,000 and 86,000 MWD/T for BCC, RP and SC lattice distribution, respectively. The results show that core life and hence the burnup increases with increasing packing fraction. Fig. 4 shows the density variations of the uranium and plutonium isotopes with burnup in the 9.6% enriched UO2 fuel and for BCC lattice distribution. It can be observed that while there is a continuous decrease in 235U, 239Pu production increases slightly during the reactor operation. The production of 239Pu makes a supporting effect to the reactor criticality and contributes to extended fuel utilization. Fig. 5 shows temporal variation of Np, Am and Cm isotopes. The figure shows that the production of these isotopes is very small compared to the plutonium isotopes in the discharged fuel. Fig. 6 demonstrates the variation of all of the fissile isotopes cumulatively as a function of reactor operation time.
Fissile isotopes density (mgr/cm3)
0.05
0.04
0.03
0.02
237
243
Np
Am
5. Conclusion
244 241
Cm
Am
0.01
242
Cm
0
301
0
200
400
600
800
1000
1200
Operation time (days) Fig. 5. Temporal variation of density of Np, Am and Cm isotopes in the PBMR-400 fueled with 9.6% enriched in 235U (packing fraction 68%).
0.008
In this study, time dependent neutronic analyses were performed for PBMR-400 reactor by using the MCNP5.1.4 and MONTEBURNS 2.0 code package. The preliminary results are encouraging; therefore, it is suggested that these computer codes may be utilized for further analysis of the pebble bed reactors. The following conclusions can also be drawn: The core multiplication factor, core burnup and hence the core life increase with increasing the fuel pebbles packing fraction. Values of keff are 1.23959 ± 0.00183, 1.23571 ± 0.00159 and 1.22237 ± 0.00174 whereas the burnup values are about 99,000, 92,000 and 86,000 MWD/T, respectively for BCC, RP and SC fuel pebble distributions, respectively.
Fissile isotopes density (gr/cm3)
0.007
Acknowledgments
0.006
The authors appreciate the constructive comments of the referees that have helped improve the quality of the paper.
0.005
References
0.004
0.003
0.002
0.001
0
0
200
400
600
800
1000
1200
Operation time (days) Fig. 6. Temporal variation of density of (235U + 239Pu + 241Pu) isotopes in the PBMR400 fueled with 9.6% enriched in 235U (packing fraction 68%).
difference of 14% may be considered as acceptable. It has also been observed that for an irradiation of 1000 days (approximately 3 years) at full power the value of keff is about 1.02 (Fig. 3) that is comparable to that given by Boer et al. (2009). Table 4 shows that for fresh core the calculated keff values for BCC, RP and SC lattice distributions are, respectively, 1.23959 ± 0.00183, 1.23571 ± 0.00159 and 1.22237 ± 0.00174. Similarly, Fig. 4 depicts that for end of life
Bakhshayesh, K.M., Vosoughi, N., 2009. A simulation of a pebble bed reactor core by the MCNP-4C computer code. Nucl. Technol. Radiat. Prot. 24 (3), 177–182. Boer, B. et al., 2009. In-core fuel management optimization of pebble-bed reactors. Ann. Nucl. Energy 36, 1049–1058. Bomboni, E. et al., 2010. Comparison among MCNP-based depletion codes applied to burnup calculations of pebble-bed HTR lattices. Nucl. Eng. Des. 240 (4), 918– 924. Cosßkun, H., (Supervisor: Assoc. Prof. Dr. Adem Acır), 2010. Neutronic Analysis of Pebble Bed Modular Reactor with Alternative Fuels by Using Monte Carlo Method, Gazi University, Institute of Science and Technology, M.Sc. Thesis, Turkey (in Turkish). Croff, A.G., 1980. A User’s Manual for the ORIGEN2, Computer Code, ORNL/TM-7175. Kadak, A.C., 2005. A future for nuclear energy: pebble bed reactors. Int. J. Crit. Infras. 1 (4), 330–345. Kim, H.C. et al., 2007. Monte Carlo benchmark calculations for 400MWth PBMR Core. In: 13th International Conference on Emerging Nuclear Energy Systems, 03–08 June 2007, Istanbul, Turkey. Ludwig, S., 2002. Revision to ORIGEN2 – Version 2.2, Computer Code, ORNL/TM7175. S ß eker, V., Çolak, Ü., 2003. HTR-10 full core first criticality analysis with MCNP. Nucl. Eng. Des. 222, 263–270. Trellue, H.R., 2003. MONTEBURNS 2.0, An Automated, Multi-Step Monte Carlo Burnup Code System, User’s Manual Version 2.0, Oak Ridge National Laboratory, PSR-455, 2003. X-5 Monte Carlo Team, 2005. MCNP-A General Monte Carlo N-Particle Transport Code, Version 5, vol. II: User’s Guide, LA-CP-03-0245, Los Alamos National Laboratory.
Contents lists available at ScienceDirect
Annals of Nuclear Energy journal homepage: www.elsevier.com/locate/anucene
Criticality and burnup analyses of a PBMR-400 full core using Monte Carlo calculation method Adem Acır a,⇑, Hasan Cosßkun b, Hacı Mehmet Sß ahin a, Özgür Erol c a
Gazi University, Technical Education Faculty, Energy Division, Teknikokullar, Ankara, Turkey Gazi University, Institute of Science and Technology, Ankara, Turkey c Baskent University, Faculty of Engineering, Department of Mechanical Engineering, Etimesgut, Ankara, Turkey b
a r t i c l e
i n f o
Article history: Received 20 May 2010 Received in revised form 4 October 2010 Accepted 18 October 2010 Available online 12 November 2010 Keywords: Monte Carlo MONTEBURNS PBMR-400 Criticality Burnup analysis Packing fraction
a b s t r a c t In this study, the criticality and burnup analyses have been performed for full core model of Pebble Bed Modular Reactors, such as PBMR-400, using the computer codes MCNP5.1.4 and MONTEBURNS 2.0. Three different pebble distributions, namely; Body Centered Cubic (BCC) (packing fraction = 68%), Random Packing (RP) (packing fraction = 61%) and Simple Cubic (SC) (packing fraction = 52%) were selected for the analyses. The calculated core effective multiplication factor, keff, for BCC, RP and SC came to be 1.2395, 1.2357 and 1.2223, respectively. The core life for these distributions were calculated as 1200, 1000, and 800 Effective Full Power Days (EFPDs), whereas, the corresponding burnups came out to be 99,000, 92,000 and 86,000 MWD/T, respectively, for end of life keff set equal to 1.02. Ó 2010 Elsevier Ltd. All rights reserved.
1. Introduction In today’s technological advances, nuclear reactor designs are tending towards smaller, safer, friendlier to environment and more economical. According to these criteria, Pebble Bed Reactors (PBRs) have great advantages over the other traditional fission reactors. PBRs have increased safety associated with the fuel type that is used in these reactors. In PBRs TRISO type fuel is used. In a TRISO particle fuel is packed in a silicon carbide and three pyrocarbon layers. These layers prohibits the leakage of the fission products from the fuel. This safety feature enables us to store the spent fuel in the places that have less radiation protection compared to the traditional reactor fuel waste storages. Low construction costs, high efficiency and online refueling features make these reactors economical (Kadak, 2005). In addition to this, by using helium, a noble gas, as coolant, very high reactor outlet temperatures can be achieved without increasing the pressure in these reactors. This high outlet temperature of the coolant would result in increased efficiency of the power station and/or can be used for the other applications such as hydrogen production. Because of the peculiar nature of the fuel and core geometry, special modeling and computational techniques are required for the design and analysis of PBRs. Various worldwide research cen⇑ Corresponding author. Tel.: +90 312 212 86 82. E-mail address: [email protected] (A. Acır). 0306-4549/$ - see front matter Ó 2010 Elsevier Ltd. All rights reserved. doi:10.1016/j.anucene.2010.10.013
ters are developing and testing models and methods against the PBR’s benchmarks (Bakhshayesh and Vosoughi, 2009; S ß eker and Çolak, 2003). Kim et al. (2007) performed benchmark calculations for PBMR-400, reactor developed in South Africa, by using the Monte Carlo method. Bomboni et al. (2010) carried out the depletion calculation for the same reactor by making use of the computer codes MONTEBURNS 2.0, MCNPX2.6 and BGCore. It was observed that the BGCore code exhibits good computational performance. In present study the analytical methodology and the validity of the computer codes MONTEBURNS 2.0 (Trellue, 2003), MCNP5.1.4 (X-5 Monte Carlo Team, 2005) and ORIGEN2 (Croff, 1980; Ludwig, 2002) has been analysed. The PBMR-400 was taken as reference reactor. Time dependent variations of multiplication factor keff and other parameters were investigated for 9.6% enriched UO2 for different packing fractions. The calculated results were compared with those available in the literature. 2. Reactor description PBMR is a 400 MWth reactor, that utilize TRISO type fuel, has a vertical steel reactor pressure vessel, 6.2 m in inner diameter (Kim et al., 2007). Reactor core is composed of an inner graphite moderator surrounded by an annular fuel zone. The fuel zone is surrounded by an annular graphite zone as shown in Figs. 1 and 2. The main characteristics of the reactor are given in the Table 1. A
299
A. Acır et al. / Annals of Nuclear Energy 38 (2011) 298–301
Reserve Shutdown System Hole (8) Gas Riser (36) Fuel Region Side Reflector
Inner Reflector Control Rod Channel (24)
Central Hole
Fig. 1. Vertical view of the PBMR-400 model (Cosßkun, 2010).
Inner Reflector
Gas Riser (36)
Reserve Shutdown System Hole (8)
Side Reflector
Fuel Region Control Rod Channel (24)
Central Hole Fig. 2. Horizontal view of the PBMR-400 model (Cosßkun, 2010).
fuel pebble contains 15,000 TRISO fuel particles. Fuel particles are present in 5 cm diameter graphite matrix, which holds the particles together and acts as a moderator. Uranium dioxide fuel in TRISO particles are surrounded by three pyrolitic carbon (PyC) and a silicon carbide layer. The main characteristics of the fuel pebbles and the TRISO particles, used in this study, are given in Tables 2 and 3, respectively.
3. Numerical calculations The neutron transport calculations were carried out with Monte Carlo methods, using the widely known three dimensional particle transport code MCNP, version 5.1.4 (X-5 Monte Carlo Team, 2005).
MCNP5.1.4 allows the simulation of complex geometrical descriptions limited only with available computational power. MCNP5.1.4 simulation and calculations were made by using the ENDF/B-V continuous energy cross-section libraries. The first step of the computational procedure with MCNP were the definition of the geometry, material and the selection of appropriate tallies to obtain keff value of the reactor core and the flux spectrum. Time dependent burnup and criticality calculations were made by using MONTEBURNS 2.0. (Trellue, 2003), a burnup code, which is a fully automated tool that links the Monte Carlo transport code MCNP with the radioactive decay and burnup code ORIGEN2 (Croff, 1980; Ludwig, 2002). The principle function of MONTEBURNS 2.0 is to transfer one group cross-section and flux values from MCNP to ORIGEN2, and then transfer the resulting material compositions
A. Acır et al. / Annals of Nuclear Energy 38 (2011) 298–301 Table 1 Characteristics of PBMR (400MWth) core (Kim et al., 2007). Properties
110
1.6
100
Values
Thermal power Total volume of fuel region Diameter of inner reflector Diameter of fuel region Diameter of reactor pressure vessel Length of reactor pressure vessel Length of fuel Number of pebbles in fuel region
1.4
400 MW 83.7156 m3 2m 3.7 m 6.2 m 20 m 11.62 m 360,000
90 1.2
80
keff = 1.02
70
1
keff
60 Table 2 Characteristics of the pebbles (Kim et al., 2007).
0.8 50
Properties
Values
Number of TRISO particles per pebble Diameter of the pebble Thickness of the fuel free zone Density of the carbon matrix in pebble Enrichment of the fuel in U – 235 Mass of uranium per pebble
15,000 6 cm 0.5 cm 1.75 g/cm3 9.6% 9 g
0.6
40
Fuel burn-up grade (GW.d/ton)
300
30
0.4
20 0.2
0
Table 3 Characteristics of TRISO particles (Kim et al., 2007).
10
0
200
400
600
800
1000
0 1200
Operation time (days)
Properties
Values
Diameter of the fuel kernel Density of UO2 Coating layers materials (inner to outer) Thicknesses of layers Density of materials in the layers
0.5 mm 10.4 g/cm3 C/C/SiC/C 95/40/35/40 lm 1.05/1.9/3.18/1.90 g/cm3
Fig. 3. Temporal variation of the lattice criticality keff and the fuel burnup grade r: with packing type of SC; s: packing type of RP; t: packing type of BCC.
0.008
0.007
(after irradiation and/or decay) from ORIGEN2 back to MCNP in a repeated cyclic fashion.
Fissile isotopes density (gr/cm3)
0.006
4. Results and discussion The criticality and burnup calculations for PBMR-400 full core were performed for Random Packing (RP) (packing fraction of 61%), Body Centered Cubic (BCC) (packing fraction of 68%) and Simple Cubic (SC) (packing packing fraction of 52%) distribution of fuel pebbles. The computer codes MCNP5.1.4 and MONTEBURNS 2.0 were used for the analysis. During the course of calculations the reactor power was assumed as 400MWth. In the first series of calculations, the RP distribution with the packing fraction of 61% was selected to validate the neutronic results. In the second phase, the keff and burnup values for the BCC and SC lattice model as well as RP distribution were investigated. Table 4 presents the keff values for the different packing fractions. The table also includes the value of keff given elsewhere (Kim et al., 2007) for comparison. Table 4 depicts that the difference between calculated core excess reactivities, for packing fraction of 61%, is 14%. The difference may be due to the difference in the computational models adopted, etc. As the comparison is between two calculated results (not with the experimental one), therefore, a
235
U
0.005
0.004
0.003
0.002 239
Pu
240
Pu
0.001
241
Pu
0
200
400
600
800
1000
1200
Operation time (days) Fig. 4. Temporal variation of density of the plutonium isotopes in the PBMR-400 fueled with 9.6% enriched in 235U (packing fraction 68%).
Table 4 Multiplication factor calculated by MCNP for various packing fractions. Fuel lattice type
BCC RP SC
Calculated (this study)
Reported (Kim et al., 2007)
keff
Core average reactivity (pcm)
keff
Core average reactivity (pcm)
1.23959 ± 0.00183 1.23571 ± 0.00159 1.22237 ± 0.00174
21,480 21,165 20,080
– 1.2795 ± 0.000551 –
– 24,645 –
A. Acır et al. / Annals of Nuclear Energy 38 (2011) 298–301 0.06
core multiplication factor = 1.02, the core burnup values are approximately 99,000, 92,000 and 86,000 MWD/T for BCC, RP and SC lattice distribution, respectively. The results show that core life and hence the burnup increases with increasing packing fraction. Fig. 4 shows the density variations of the uranium and plutonium isotopes with burnup in the 9.6% enriched UO2 fuel and for BCC lattice distribution. It can be observed that while there is a continuous decrease in 235U, 239Pu production increases slightly during the reactor operation. The production of 239Pu makes a supporting effect to the reactor criticality and contributes to extended fuel utilization. Fig. 5 shows temporal variation of Np, Am and Cm isotopes. The figure shows that the production of these isotopes is very small compared to the plutonium isotopes in the discharged fuel. Fig. 6 demonstrates the variation of all of the fissile isotopes cumulatively as a function of reactor operation time.
Fissile isotopes density (mgr/cm3)
0.05
0.04
0.03
0.02
237
243
Np
Am
5. Conclusion
244 241
Cm
Am
0.01
242
Cm
0
301
0
200
400
600
800
1000
1200
Operation time (days) Fig. 5. Temporal variation of density of Np, Am and Cm isotopes in the PBMR-400 fueled with 9.6% enriched in 235U (packing fraction 68%).
0.008
In this study, time dependent neutronic analyses were performed for PBMR-400 reactor by using the MCNP5.1.4 and MONTEBURNS 2.0 code package. The preliminary results are encouraging; therefore, it is suggested that these computer codes may be utilized for further analysis of the pebble bed reactors. The following conclusions can also be drawn: The core multiplication factor, core burnup and hence the core life increase with increasing the fuel pebbles packing fraction. Values of keff are 1.23959 ± 0.00183, 1.23571 ± 0.00159 and 1.22237 ± 0.00174 whereas the burnup values are about 99,000, 92,000 and 86,000 MWD/T, respectively for BCC, RP and SC fuel pebble distributions, respectively.
Fissile isotopes density (gr/cm3)
0.007
Acknowledgments
0.006
The authors appreciate the constructive comments of the referees that have helped improve the quality of the paper.
0.005
References
0.004
0.003
0.002
0.001
0
0
200
400
600
800
1000
1200
Operation time (days) Fig. 6. Temporal variation of density of (235U + 239Pu + 241Pu) isotopes in the PBMR400 fueled with 9.6% enriched in 235U (packing fraction 68%).
difference of 14% may be considered as acceptable. It has also been observed that for an irradiation of 1000 days (approximately 3 years) at full power the value of keff is about 1.02 (Fig. 3) that is comparable to that given by Boer et al. (2009). Table 4 shows that for fresh core the calculated keff values for BCC, RP and SC lattice distributions are, respectively, 1.23959 ± 0.00183, 1.23571 ± 0.00159 and 1.22237 ± 0.00174. Similarly, Fig. 4 depicts that for end of life
Bakhshayesh, K.M., Vosoughi, N., 2009. A simulation of a pebble bed reactor core by the MCNP-4C computer code. Nucl. Technol. Radiat. Prot. 24 (3), 177–182. Boer, B. et al., 2009. In-core fuel management optimization of pebble-bed reactors. Ann. Nucl. Energy 36, 1049–1058. Bomboni, E. et al., 2010. Comparison among MCNP-based depletion codes applied to burnup calculations of pebble-bed HTR lattices. Nucl. Eng. Des. 240 (4), 918– 924. Cosßkun, H., (Supervisor: Assoc. Prof. Dr. Adem Acır), 2010. Neutronic Analysis of Pebble Bed Modular Reactor with Alternative Fuels by Using Monte Carlo Method, Gazi University, Institute of Science and Technology, M.Sc. Thesis, Turkey (in Turkish). Croff, A.G., 1980. A User’s Manual for the ORIGEN2, Computer Code, ORNL/TM-7175. Kadak, A.C., 2005. A future for nuclear energy: pebble bed reactors. Int. J. Crit. Infras. 1 (4), 330–345. Kim, H.C. et al., 2007. Monte Carlo benchmark calculations for 400MWth PBMR Core. In: 13th International Conference on Emerging Nuclear Energy Systems, 03–08 June 2007, Istanbul, Turkey. Ludwig, S., 2002. Revision to ORIGEN2 – Version 2.2, Computer Code, ORNL/TM7175. S ß eker, V., Çolak, Ü., 2003. HTR-10 full core first criticality analysis with MCNP. Nucl. Eng. Des. 222, 263–270. Trellue, H.R., 2003. MONTEBURNS 2.0, An Automated, Multi-Step Monte Carlo Burnup Code System, User’s Manual Version 2.0, Oak Ridge National Laboratory, PSR-455, 2003. X-5 Monte Carlo Team, 2005. MCNP-A General Monte Carlo N-Particle Transport Code, Version 5, vol. II: User’s Guide, LA-CP-03-0245, Los Alamos National Laboratory.