- Email: [email protected]
MCNPX–BUCAL1 code to code verification through burnup analysis
Annals of Nuclear Energy 60 (2013) 242–247
Contents lists available at SciVerse ScienceDirect
Annals of Nuclear Energy journal homepage: www.elsevier.com/locate/anucene
MCNPX–BUCAL1 code to code verification through burnup analysis B. El Bakkari a,b,⇑, T. El Bardouni b, B. Nacir a, C. El Younoussi a,b, Y. Boulaich a,b, H. Boukhal b a b
Reactor Operating Unit (UCR), National Centre of Sciences, Energy and Nuclear Techniques (CNESTEN/CENM), POB 1382, Rabat, Morocco ERSN–LMR, Department of Physics, Faculty of Sciences, POB 2121, Tetuan, Morocco
a r t i c l e
i n f o
Article history: Received 28 January 2013 Received in revised form 24 April 2013 Accepted 30 April 2013 Available online 6 June 2013 Keywords: MCNPX2.7 BUCAL1 Burnup Verification TRIGA reactor ENDF/B-VII.0
a b s t r a c t The availability of accurate burnup data is an essential first step in any systematic approach to enhancement of economics, safety and performance of a research reactor. This first step requires the utilization of a well verified burnup code system. In this work a newly home-developed burnup code called BUCAL1 is presented. The code provides the full capabilities of the Monte Carlo neutron and photon transport code MCNP (version 5c). BUCAL1 has the capability of using several depletion calculation schemes that do not exist in several other burnup code systems such as: shuffling, refueling and multicycles burnup calculation, in an automatic way. The accuracy and precision of BUCAL1 were tested for U-Zrh fuels, by a code to code verification with MCNPX2.7, by predicting the burnup parameters of the 2 MW TRIGA Mark II Moroccan research reactor. Continuous energy cross section data from the more recent nuclear data evaluation ENDF/B-VII.0 as well as S(a, b) thermal neutron scattering functions distributed with the MCNP code were used. Analysis of the verification results shows that BUCAL1 is enough accurate to be used in burnup calculations. Ó 2013 Elsevier Ltd. All rights reserved.
1. Introduction Several codes or combination of codes have been developed to perform Monte Carlo depletion analysis. In these burnup codes the main approach is to use neutron absorption and fission reaction information generated via neutronics codes to determine the nuclide composition at a next time step. This kind of model allows the integration of all neutron flux information into the calculation without post-processing and additional manipulation of neutron flux and cross-sections set. Neutron absorption and fission reaction data for individual nuclides are available as output from the Monte Carlo codes like MCNP through the use of tallies. The only requirement is point wise energy-dependent cross section set which is available for each nuclide of interest at required temperature. This paper presents a new home-developed burnup code, BUCAL1, coupled with MCNP (version 5c) Monte Carlo code (X-5 Monte Carlo Team, 2003). MCNP can model extremely complex three-dimensional geometries. So, BUCAL1 is quite accurate over a given region because MCNP-generated reaction rates are integrated over the continuous-energy nuclear data and the space within the region. Thus, any oddly or regularly shaped region in MCNP can be depleted. The mean features of BUCLA1, regarding
⇑ Corresponding author at: Reactor Operating Unit (UCR), National Centre of Sciences, Energy and Nuclear Techniques (CNESTEN/CENM), POB 1382, Rabat, Morocco. Tel.: +212 668782702; fax: +212 537803326. E-mail address: [email protected] (B. El Bakkari). 0306-4549/$ - see front matter Ó 2013 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.anucene.2013.04.037
the existing other code systems, can be summed up on its capability to do several depletion schemes required for fuel management analysis, such as shuffling and refueling and the calculation of several important burnup parameters needed for reactor and safety analysis: criticality, thermal hydraulic, shielding, etc. The accuracy of BUCAL1 results were tested for different kinds of fuels (MOX, UO2 and ThO2-UO2) with different irradiation conditions in previous published papers (El Bakkari et al., 2009a,b; El Bakkari et al., 2012). In this work, MCNPX2.7 (Pelowitz, 2011) was chosen as a reference code to assess the accuracy of BUCAL1 for U-ZrH fuels, by predicting the burnup parameters of the 2 MW TRIGA Mark II Moroccan research reactor. Neutron cross section evaluations, based on the ENDF/B-VII (Chadwick et al., 2006) nuclear data library, were used. The ENDF/B-VI (McLane, 2001) was used for S(a, b) treatment. 2. BUCAL1 code system BUCAL1 is a FORTRAN computer code designed to aid in analysis, prediction, and optimization of fuel burnup performance in nuclear reactors. The code was developed, at the Laboratory of Matter and Radiation (LMR) of University ABDELMALEK ESSADI Tetuan – Morocco, to incorporate the neutron absorption reaction tally information generated directly by MCNP(5c) code in the calculation of fissioned or neutron-transmuted isotopes for multi-fueled regions. This allows us to benefit of the full capabilities provided by MCNP and to incorporate them into burnup calculations in the aim to perform more accurate and robust treatment of the problem. Neutron
B. El Bakkari et al. / Annals of Nuclear Energy 60 (2013) 242–247 Table 1 MCNP-tallied reactions used in BUCAL1. Reaction type
c) f) 2n) 3n)
Actinides
(n, (n, (n, (n,
Fission products
(n, c)
MCNP reaction identifier 102 6 16 17
243
Using BUCAL1 one can do standard burnup calculation, burnup calculation followed by a space of time of cooling, burnup calculation with shuffling of fueled regions and burnup calculation with reloading of new fresh fuels. Continuation card in BUCAL1 allows users to restart calculations after unwanted stops. In the current version of BUCAL1, the two groups of nuclides under consideration are:
102
transmutation, fission, and radioactive decay are included in the modeling of the production and removal terms for each isotope of interest. For a fueled region, neutron transmutation, fuel depletion, fission-product poisoning, actinide generation, burnable poison loading and depletion effects are included in the calculation. The code uses the fourth order Rung Kutta method with the predictor–corrector approach (El Bakkari et al., 2009a,b) for the resolution of the depletion equation for more than 900 isotopes.
1. Actinides (ACT) that contain heavy metal nuclides with atomic number Z P 90 and their decay daughters, 45 actinides covering the rang from Th-231 to Cf-252. 2. Fission products (FP) produced by fissions and their decay/capture daughters, 859 fission products covering the range from Cr-66 to Yb-172. Specifically, the calculated reaction rates of fission products and actinides are shown in Table 1. Only the neutron capture cross section is considered for fission products since neutron absorption by
Fig. 1. Simplified follow diagram of BUCAL1.
244
B. El Bakkari et al. / Annals of Nuclear Energy 60 (2013) 242–247
Fig. 4. The axial view of the MCNP model of TRIGA reactor.
Fig. 2. Actual core configuration of the Moroccan TRIGA research reactor.
Fig. 5. System keff of TRIGA reactor as a function of burnup (MW h).
quantities of fission products and higher-mass actinides (Xu, 2003). Actually, the LMR team is working on the development of a new version that will take into account of several other reactions, which permit the treatment of non-fuel regions for spent fuel analysis. Fig. 1 gives the simplified follow diagram of BUCAL1. 3. MCNP modeling of TRIGA reactor
Fig. 3. The radial view of the MCNP model of TRIGA reactor.
fission products is primarily via (n, c) reaction. For actinides, four types of reactions are considered including capture, fission, (n, 2n) and (n, 3n) because they lead to the production of significant
The TRIGA reactor is a light water cooled, graphite-reflected one, designed for operation at a steady state thermal power level of 2000 kW. An outstanding feature of the TRIGA reactor is its proven safety, which stems from the large instantaneous negative temperature coefficient of reactivity of its U-ZrH fuel moderatormaterial. The TRIGA core consists of 101 fuel elements, 17 graphite elements, central thimble and a pneumatic transfer tube. Elements are arranged in seven concentric rings in hexagonal geometry and the spaces between the rods are filled with water that acts as coolant and moderator. Fig. 2 gives the actual core configuration.
B. El Bakkari et al. / Annals of Nuclear Energy 60 (2013) 242–247
Fig. 6. Average fuel burnup per core ring.
Table 2 Average fuel burnup per core ring at 12,000 MW h.
Ring Ring Ring Ring Ring Ring CRs
B C D E F G
MCNPX (%)
BUCAL1 (%)
24.3 21.5 19.5 16.3 13.1 10.8 19.2
23.9 20.8 18.9 15.5 13.7 10.7 18.5
(BUCAL1-MCNPX)/MCNPX (%) 1.89 3.54 2.99 4.68 4.44 1.37 3.69
245
The reactor was modeled in full 3-D details to minimize geometry approximations. The repeated structure capability of MCNP was used to create a full core 3-D model of TRIGA. The TRIGA lattice can be represented as a hexagonal prism, solids with eight faces. The fuel elements were modeled explicitly specifying the detailed structure of the rod to eliminate any homogenization effects. The tapered end fixtures of stainless steel were also modeled with very little approximation. The power level of the reactor is controlled with five control rods: a regulating rod and four shim safety rods. The control rods were explicitly modeled along the active length containing three vertical sections of boron carbide, fuel follower and void region. The central thimble was considered to be filled with water and the pneumatic tube was considered to be void. The graphite dummy elements are of the same general dimensions and construction as the fuel-moderator elements, except these elements are made of aluminum alloy and filled entirely with graphite. The model was extended up radially containing the graphite reflector and lead shield. An annular well on the inside diameter in the top of the graphite reflector that provides for the rotary specimen rack was also modeled along with the radial and tangential beam ports that serve for experimentations around the TRIGA core. To complete the modeling of all reactor facilities, the thermal column, which is a squared assembly located in the side of the reactor shield structure, is also modeled. It is located between beam ports NB1 and NB4 and the reactor tank that consists of an aluminum vessel installed in the reactor shield structure, this facility serves for the irradiation of large experimental specimens. Figs. 3 and 4 represent the radial and axial view of MCNP5 model of the 2 MW TRIGA MARK II research reactor of CENM.
Fig. 7. Actinides concentrations versus burnup (MW h).
246
B. El Bakkari et al. / Annals of Nuclear Energy 60 (2013) 242–247
Fig. 8. Fission products concentrations versus burnup (MW h).
An essential aspect of developing an accurate reactor physics model is validation. The accuracy of both the neutron transport physics as represented in MCNP and the user-defined model must be assessed. Therefore, to build confidence, all the neutronics parameters including effective multiplication factor, radial and axial power peaking distributions as well as the reactivity worth and integral reactivity curves of the control rods were calculated and compared to the experimental ones and those available at the Final Safety Analysis Report (El Bakkari et al., 2010). 4. Results and discussions The code applicability to reactor calculations must be demonstrated by considering the range of parameters that characterize the role of the code. This means that the boundaries of validity and application for the code need to be rigidly verified. To fulfill these requirements we are trying to test BUCAL1 using several kinds of fuels and under several irradiation conditions (El Bakkari et al., 2009a,b; El Bakkari et al., 2010). In this study, the Moroccan 2 MW TRIGA Mark II research reactor is considered as benchmark. Calculations were done using an HP proliant server IntelÒ Xeon™ CPU 3.40 GHz, 2 GB RAM and 2 Mb Cache Memory under Linux Mandriva operating system. Each MCNP run is done for 6e+6 neutron histories that lead to an eigenvalue statistical error less than 150 pcm.
4.1. Core life-time and fuel burnup The variation of the effective multiplication factor (keff) as a function of burnup (MW h) is of primary importance for the determination of the core life-time. Fig. 5 shows this variation for both codes MCNPX and BUCAL1. The beta-effective used to express the reactivity in unit of ($) is 0.007 (Nelkin and Johnson, 1958). In this figure the large Dk differences between the two codes is found to be 0.3%. The estimated life time for the actual core configuration is found to 9600 MW h using MCNPX and BUCAL1, supposing a continuous operation of the reactor at full power. Initial steps are very important for burnup calculation due to the buildup of some equilibrium poisons such as Xe135, especially in case of constant power depletion calculation. The loss of reactivity due to Xe135 effect is found to be 3.55$ and 3.98$ for BUCAL1 and MCNPX, respectively. The estimated value by General Atomics is 3.57$. Comparison of the average fuel burnup per core ring calculated using MCNPX and BUCAL1 is presented in Fig. 6. Table 2 shows the average fuel burnup per core ring after 12,000 MW h. Control rods (CRs) were excluded from ring D and considered as independent, because they do not have the same geometry and fuel concentration as the standard fuel elements. From Fig. 6, it is clearly remarked that MCNPX and BUCAL1 agree well. The difference in
B. El Bakkari et al. / Annals of Nuclear Energy 60 (2013) 242–247 Table 3 Fractional difference in nuclide concentration (at./b-cm) at 12,000 MW h from BUCAL1 in comparison with MCNPX results. Nuclides
MCNPX
U235 U238 U234 U236 Pu239 Pu240 Xe135 Sm149 Ru103 I127 Cs137 Nd147 Pm149
2.1045E 9.9421E 9.7337E 6.3713E 2.9867E 1.913E 1.6401E 1.6565E 2.3897E 4.8155E 2.1195E 4.8065E 4.8487E
BUCAL1 04 04 10 06 06 07 09 08 07 08 06 08 09
2.1097E 9.9425E 9.8143E 6.2952E 2.9809E 1.8569E 1.6338E 1.6776E 2.3747E 5.0121E 2.0598E 4.7195E 4.8423E
(BUCAL1-MCNPX)/MCNPX (%) 04 04 10 06 06 07 09 08 07 08 06 08 09
0.244 0.004 0.827 1.195 0.194 2.931 0.382 1.274 0.627 4.081 2.819 1.810 0.131
the worst case (12,000 MW h) is found to be less than 5%. However, the maximum fuel burnup is found to be around 25% for ring B, due to the relatively higher thermalization of neutrons in the central region of the core. 4.2. Core average isotopic concentration The core averaged isotopic concentration of U234, U235, U236, U238, Pu239, Pu240, Xe135, Sm149, I127, Cs137, Nd147, Pm149 and Ru103 as a function of burnup are shown on Figs. 7 and 8. It is clearly seen that the inventory prediction obtained by BUCAL1 agree well with MCNPX2.7. For more clarity, fractional difference in nuclide concentration at 12,000 MW h from BUCAL1 in comparison with MCNPX is presented in Table 3. The verification shows that the higher difference is found to be 4% for Iodine127, which can be considered very acceptable for BUCAL1. Although, several causes might contribute to this difference, such as neutronic/burnup coupling algorithms, nuclear data precisions and statistical error propagation.
247
5. Conclusion A new developed burnup code system called BUCAL1 has been presented and compared to MCNPX2.7, by predicting the burnup parameters of the 2 MW TRIGA Mark II Moroccan research reactor. The results of analysis show that BUCAL1 is enough accurate and precise to do burnup calculation for several kinds of fuels. BUCAL1 algorithms provide the capability of doing several depletion calculation modules, which enlarge the space of utilization of the code to be able to do several burnup calculations, such as fuel management studies and safety analysis of irradiated and spent fuel, for power as well as light water research reactors.
References Chadwick, M.B. et al., 2006. ENDF/B-VII.0: next generation evaluated nuclear data library for nuclear science and technology. Nuclear Data Sheets 107, 2931– 3060,. El Bakkari, B., El Bardouni, T., Merroun, O., et al., 2009a. Development of an MCNPtally based burnup code and validation through PWR benchmark exercises. Annals of Nuclear Energy 36 (5), 626–633. El Bakkari, B., El Bardouni, T., Merroun, O., et al., 2009b. Validation of a new continuous Monte Carlo burnup code using a MOX fuel assembly. Nuclear Engineering and Design 239 (10), 1828–1838. El Bakkari, B., Nacir, B., El Bardouni, T., et al., 2010. Monte Carlo modeling of TRIGA research reactor. Radiation Physics and Chemistry 79 (10), 1022–1030. El Bakkari, B., El Bardouni, T., Nacir, B., et al., 2012. Accuracy assessment of a new Monte Carlo based burnup computer code. Annals of Nuclear Energy 45, 29–36. McLane, V., 2001. ENDF-102, Data Formats and Procedures for the Valuated Nuclear Data File ENDF-6, BNL-NCS-44945-01/04, revised April 2001. Nelkin, M.S., Johnson, M., 1958. Inhour equation for isotope reactor. General Atomic Inter-Company Communication, GA-P-14-101 22, January 1958. Pelowitz D.B. et al., 2011. MCNPXTM User’s Manual (Version 2.7.0). LA-CP-1100438, April, 2011. X-5 Monte Carlo Team, 2003. MCNP – A General Monte Carlo N-Particle Transport Code, Version5 – Los Alamos National Laboratory. Xu, Zh., 2003. Design strategies for optimizing high burnup fuel in pressurized water reactors. PhD Dissertation, Massachusetts Institute of Technology, January 2003.
Contents lists available at SciVerse ScienceDirect
Annals of Nuclear Energy journal homepage: www.elsevier.com/locate/anucene
MCNPX–BUCAL1 code to code verification through burnup analysis B. El Bakkari a,b,⇑, T. El Bardouni b, B. Nacir a, C. El Younoussi a,b, Y. Boulaich a,b, H. Boukhal b a b
Reactor Operating Unit (UCR), National Centre of Sciences, Energy and Nuclear Techniques (CNESTEN/CENM), POB 1382, Rabat, Morocco ERSN–LMR, Department of Physics, Faculty of Sciences, POB 2121, Tetuan, Morocco
a r t i c l e
i n f o
Article history: Received 28 January 2013 Received in revised form 24 April 2013 Accepted 30 April 2013 Available online 6 June 2013 Keywords: MCNPX2.7 BUCAL1 Burnup Verification TRIGA reactor ENDF/B-VII.0
a b s t r a c t The availability of accurate burnup data is an essential first step in any systematic approach to enhancement of economics, safety and performance of a research reactor. This first step requires the utilization of a well verified burnup code system. In this work a newly home-developed burnup code called BUCAL1 is presented. The code provides the full capabilities of the Monte Carlo neutron and photon transport code MCNP (version 5c). BUCAL1 has the capability of using several depletion calculation schemes that do not exist in several other burnup code systems such as: shuffling, refueling and multicycles burnup calculation, in an automatic way. The accuracy and precision of BUCAL1 were tested for U-Zrh fuels, by a code to code verification with MCNPX2.7, by predicting the burnup parameters of the 2 MW TRIGA Mark II Moroccan research reactor. Continuous energy cross section data from the more recent nuclear data evaluation ENDF/B-VII.0 as well as S(a, b) thermal neutron scattering functions distributed with the MCNP code were used. Analysis of the verification results shows that BUCAL1 is enough accurate to be used in burnup calculations. Ó 2013 Elsevier Ltd. All rights reserved.
1. Introduction Several codes or combination of codes have been developed to perform Monte Carlo depletion analysis. In these burnup codes the main approach is to use neutron absorption and fission reaction information generated via neutronics codes to determine the nuclide composition at a next time step. This kind of model allows the integration of all neutron flux information into the calculation without post-processing and additional manipulation of neutron flux and cross-sections set. Neutron absorption and fission reaction data for individual nuclides are available as output from the Monte Carlo codes like MCNP through the use of tallies. The only requirement is point wise energy-dependent cross section set which is available for each nuclide of interest at required temperature. This paper presents a new home-developed burnup code, BUCAL1, coupled with MCNP (version 5c) Monte Carlo code (X-5 Monte Carlo Team, 2003). MCNP can model extremely complex three-dimensional geometries. So, BUCAL1 is quite accurate over a given region because MCNP-generated reaction rates are integrated over the continuous-energy nuclear data and the space within the region. Thus, any oddly or regularly shaped region in MCNP can be depleted. The mean features of BUCLA1, regarding
⇑ Corresponding author at: Reactor Operating Unit (UCR), National Centre of Sciences, Energy and Nuclear Techniques (CNESTEN/CENM), POB 1382, Rabat, Morocco. Tel.: +212 668782702; fax: +212 537803326. E-mail address: [email protected] (B. El Bakkari). 0306-4549/$ - see front matter Ó 2013 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.anucene.2013.04.037
the existing other code systems, can be summed up on its capability to do several depletion schemes required for fuel management analysis, such as shuffling and refueling and the calculation of several important burnup parameters needed for reactor and safety analysis: criticality, thermal hydraulic, shielding, etc. The accuracy of BUCAL1 results were tested for different kinds of fuels (MOX, UO2 and ThO2-UO2) with different irradiation conditions in previous published papers (El Bakkari et al., 2009a,b; El Bakkari et al., 2012). In this work, MCNPX2.7 (Pelowitz, 2011) was chosen as a reference code to assess the accuracy of BUCAL1 for U-ZrH fuels, by predicting the burnup parameters of the 2 MW TRIGA Mark II Moroccan research reactor. Neutron cross section evaluations, based on the ENDF/B-VII (Chadwick et al., 2006) nuclear data library, were used. The ENDF/B-VI (McLane, 2001) was used for S(a, b) treatment. 2. BUCAL1 code system BUCAL1 is a FORTRAN computer code designed to aid in analysis, prediction, and optimization of fuel burnup performance in nuclear reactors. The code was developed, at the Laboratory of Matter and Radiation (LMR) of University ABDELMALEK ESSADI Tetuan – Morocco, to incorporate the neutron absorption reaction tally information generated directly by MCNP(5c) code in the calculation of fissioned or neutron-transmuted isotopes for multi-fueled regions. This allows us to benefit of the full capabilities provided by MCNP and to incorporate them into burnup calculations in the aim to perform more accurate and robust treatment of the problem. Neutron
B. El Bakkari et al. / Annals of Nuclear Energy 60 (2013) 242–247 Table 1 MCNP-tallied reactions used in BUCAL1. Reaction type
c) f) 2n) 3n)
Actinides
(n, (n, (n, (n,
Fission products
(n, c)
MCNP reaction identifier 102 6 16 17
243
Using BUCAL1 one can do standard burnup calculation, burnup calculation followed by a space of time of cooling, burnup calculation with shuffling of fueled regions and burnup calculation with reloading of new fresh fuels. Continuation card in BUCAL1 allows users to restart calculations after unwanted stops. In the current version of BUCAL1, the two groups of nuclides under consideration are:
102
transmutation, fission, and radioactive decay are included in the modeling of the production and removal terms for each isotope of interest. For a fueled region, neutron transmutation, fuel depletion, fission-product poisoning, actinide generation, burnable poison loading and depletion effects are included in the calculation. The code uses the fourth order Rung Kutta method with the predictor–corrector approach (El Bakkari et al., 2009a,b) for the resolution of the depletion equation for more than 900 isotopes.
1. Actinides (ACT) that contain heavy metal nuclides with atomic number Z P 90 and their decay daughters, 45 actinides covering the rang from Th-231 to Cf-252. 2. Fission products (FP) produced by fissions and their decay/capture daughters, 859 fission products covering the range from Cr-66 to Yb-172. Specifically, the calculated reaction rates of fission products and actinides are shown in Table 1. Only the neutron capture cross section is considered for fission products since neutron absorption by
Fig. 1. Simplified follow diagram of BUCAL1.
244
B. El Bakkari et al. / Annals of Nuclear Energy 60 (2013) 242–247
Fig. 4. The axial view of the MCNP model of TRIGA reactor.
Fig. 2. Actual core configuration of the Moroccan TRIGA research reactor.
Fig. 5. System keff of TRIGA reactor as a function of burnup (MW h).
quantities of fission products and higher-mass actinides (Xu, 2003). Actually, the LMR team is working on the development of a new version that will take into account of several other reactions, which permit the treatment of non-fuel regions for spent fuel analysis. Fig. 1 gives the simplified follow diagram of BUCAL1. 3. MCNP modeling of TRIGA reactor
Fig. 3. The radial view of the MCNP model of TRIGA reactor.
fission products is primarily via (n, c) reaction. For actinides, four types of reactions are considered including capture, fission, (n, 2n) and (n, 3n) because they lead to the production of significant
The TRIGA reactor is a light water cooled, graphite-reflected one, designed for operation at a steady state thermal power level of 2000 kW. An outstanding feature of the TRIGA reactor is its proven safety, which stems from the large instantaneous negative temperature coefficient of reactivity of its U-ZrH fuel moderatormaterial. The TRIGA core consists of 101 fuel elements, 17 graphite elements, central thimble and a pneumatic transfer tube. Elements are arranged in seven concentric rings in hexagonal geometry and the spaces between the rods are filled with water that acts as coolant and moderator. Fig. 2 gives the actual core configuration.
B. El Bakkari et al. / Annals of Nuclear Energy 60 (2013) 242–247
Fig. 6. Average fuel burnup per core ring.
Table 2 Average fuel burnup per core ring at 12,000 MW h.
Ring Ring Ring Ring Ring Ring CRs
B C D E F G
MCNPX (%)
BUCAL1 (%)
24.3 21.5 19.5 16.3 13.1 10.8 19.2
23.9 20.8 18.9 15.5 13.7 10.7 18.5
(BUCAL1-MCNPX)/MCNPX (%) 1.89 3.54 2.99 4.68 4.44 1.37 3.69
245
The reactor was modeled in full 3-D details to minimize geometry approximations. The repeated structure capability of MCNP was used to create a full core 3-D model of TRIGA. The TRIGA lattice can be represented as a hexagonal prism, solids with eight faces. The fuel elements were modeled explicitly specifying the detailed structure of the rod to eliminate any homogenization effects. The tapered end fixtures of stainless steel were also modeled with very little approximation. The power level of the reactor is controlled with five control rods: a regulating rod and four shim safety rods. The control rods were explicitly modeled along the active length containing three vertical sections of boron carbide, fuel follower and void region. The central thimble was considered to be filled with water and the pneumatic tube was considered to be void. The graphite dummy elements are of the same general dimensions and construction as the fuel-moderator elements, except these elements are made of aluminum alloy and filled entirely with graphite. The model was extended up radially containing the graphite reflector and lead shield. An annular well on the inside diameter in the top of the graphite reflector that provides for the rotary specimen rack was also modeled along with the radial and tangential beam ports that serve for experimentations around the TRIGA core. To complete the modeling of all reactor facilities, the thermal column, which is a squared assembly located in the side of the reactor shield structure, is also modeled. It is located between beam ports NB1 and NB4 and the reactor tank that consists of an aluminum vessel installed in the reactor shield structure, this facility serves for the irradiation of large experimental specimens. Figs. 3 and 4 represent the radial and axial view of MCNP5 model of the 2 MW TRIGA MARK II research reactor of CENM.
Fig. 7. Actinides concentrations versus burnup (MW h).
246
B. El Bakkari et al. / Annals of Nuclear Energy 60 (2013) 242–247
Fig. 8. Fission products concentrations versus burnup (MW h).
An essential aspect of developing an accurate reactor physics model is validation. The accuracy of both the neutron transport physics as represented in MCNP and the user-defined model must be assessed. Therefore, to build confidence, all the neutronics parameters including effective multiplication factor, radial and axial power peaking distributions as well as the reactivity worth and integral reactivity curves of the control rods were calculated and compared to the experimental ones and those available at the Final Safety Analysis Report (El Bakkari et al., 2010). 4. Results and discussions The code applicability to reactor calculations must be demonstrated by considering the range of parameters that characterize the role of the code. This means that the boundaries of validity and application for the code need to be rigidly verified. To fulfill these requirements we are trying to test BUCAL1 using several kinds of fuels and under several irradiation conditions (El Bakkari et al., 2009a,b; El Bakkari et al., 2010). In this study, the Moroccan 2 MW TRIGA Mark II research reactor is considered as benchmark. Calculations were done using an HP proliant server IntelÒ Xeon™ CPU 3.40 GHz, 2 GB RAM and 2 Mb Cache Memory under Linux Mandriva operating system. Each MCNP run is done for 6e+6 neutron histories that lead to an eigenvalue statistical error less than 150 pcm.
4.1. Core life-time and fuel burnup The variation of the effective multiplication factor (keff) as a function of burnup (MW h) is of primary importance for the determination of the core life-time. Fig. 5 shows this variation for both codes MCNPX and BUCAL1. The beta-effective used to express the reactivity in unit of ($) is 0.007 (Nelkin and Johnson, 1958). In this figure the large Dk differences between the two codes is found to be 0.3%. The estimated life time for the actual core configuration is found to 9600 MW h using MCNPX and BUCAL1, supposing a continuous operation of the reactor at full power. Initial steps are very important for burnup calculation due to the buildup of some equilibrium poisons such as Xe135, especially in case of constant power depletion calculation. The loss of reactivity due to Xe135 effect is found to be 3.55$ and 3.98$ for BUCAL1 and MCNPX, respectively. The estimated value by General Atomics is 3.57$. Comparison of the average fuel burnup per core ring calculated using MCNPX and BUCAL1 is presented in Fig. 6. Table 2 shows the average fuel burnup per core ring after 12,000 MW h. Control rods (CRs) were excluded from ring D and considered as independent, because they do not have the same geometry and fuel concentration as the standard fuel elements. From Fig. 6, it is clearly remarked that MCNPX and BUCAL1 agree well. The difference in
B. El Bakkari et al. / Annals of Nuclear Energy 60 (2013) 242–247 Table 3 Fractional difference in nuclide concentration (at./b-cm) at 12,000 MW h from BUCAL1 in comparison with MCNPX results. Nuclides
MCNPX
U235 U238 U234 U236 Pu239 Pu240 Xe135 Sm149 Ru103 I127 Cs137 Nd147 Pm149
2.1045E 9.9421E 9.7337E 6.3713E 2.9867E 1.913E 1.6401E 1.6565E 2.3897E 4.8155E 2.1195E 4.8065E 4.8487E
BUCAL1 04 04 10 06 06 07 09 08 07 08 06 08 09
2.1097E 9.9425E 9.8143E 6.2952E 2.9809E 1.8569E 1.6338E 1.6776E 2.3747E 5.0121E 2.0598E 4.7195E 4.8423E
(BUCAL1-MCNPX)/MCNPX (%) 04 04 10 06 06 07 09 08 07 08 06 08 09
0.244 0.004 0.827 1.195 0.194 2.931 0.382 1.274 0.627 4.081 2.819 1.810 0.131
the worst case (12,000 MW h) is found to be less than 5%. However, the maximum fuel burnup is found to be around 25% for ring B, due to the relatively higher thermalization of neutrons in the central region of the core. 4.2. Core average isotopic concentration The core averaged isotopic concentration of U234, U235, U236, U238, Pu239, Pu240, Xe135, Sm149, I127, Cs137, Nd147, Pm149 and Ru103 as a function of burnup are shown on Figs. 7 and 8. It is clearly seen that the inventory prediction obtained by BUCAL1 agree well with MCNPX2.7. For more clarity, fractional difference in nuclide concentration at 12,000 MW h from BUCAL1 in comparison with MCNPX is presented in Table 3. The verification shows that the higher difference is found to be 4% for Iodine127, which can be considered very acceptable for BUCAL1. Although, several causes might contribute to this difference, such as neutronic/burnup coupling algorithms, nuclear data precisions and statistical error propagation.
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5. Conclusion A new developed burnup code system called BUCAL1 has been presented and compared to MCNPX2.7, by predicting the burnup parameters of the 2 MW TRIGA Mark II Moroccan research reactor. The results of analysis show that BUCAL1 is enough accurate and precise to do burnup calculation for several kinds of fuels. BUCAL1 algorithms provide the capability of doing several depletion calculation modules, which enlarge the space of utilization of the code to be able to do several burnup calculations, such as fuel management studies and safety analysis of irradiated and spent fuel, for power as well as light water research reactors.
References Chadwick, M.B. et al., 2006. ENDF/B-VII.0: next generation evaluated nuclear data library for nuclear science and technology. Nuclear Data Sheets 107, 2931– 3060,