- Email: [email protected]
Calculation of fuel burn up and radioactive inventory in a CANDU reactor using WIMS-D4 code
Annals of Nuclear Energy 37 (2010) 66–70
Contents lists available at ScienceDirect
Annals of Nuclear Energy journal homepage: www.elsevier.com/locate/anucene
Calculation of fuel burn up and radioactive inventory in a CANDU reactor using WIMS-D4 code Zafar Yasin * Physics Division, PINSTECH, P.O. Nilore, Islamabad, Pakistan
a r t i c l e
i n f o
Article history: Received 27 July 2009 Received in revised form 19 September 2009 Accepted 28 September 2009 Available online 6 November 2009
a b s t r a c t A study of fuel burn up and radioactive inventory for the CANDU reactor is carried out to validate the computer code WIMS-D4 for cluster geometry. The infinite and effective multiplication factors are calculated as a function of burn up and compared with the available results. A good agreement is observed among the present calculations and the previous published results. The code is then used to calculate the 235U and 238U consumed and the 239Pu produced in the fuel bundle. The inventories and the corresponding activities of some important fission products are also calculated. Ó 2009 Elsevier Ltd. All rights reserved.
1. Introduction Due to the unavailability of fusion technology in the coming three to four decades, rise of oil prices in the world market, shortage of water resources, and due to the growing energy needs of the world population, particularly in the developing countries, there is again an increase in trend to use nuclear energy for peaceful purpose. Among the existing technologies of nuclear power plants, Canada Deuterium Uranium (CANDU) reactors rank second place of commercial nuclear power reactors in the world. The main advantages of the CANDU reactors are the on-line fuelling, use of natural uranium as fuel and enhanced neutron economy due to the negligible neutron loss in heavy water. These reactors are more suitable for a country that has lot of reserves of natural uranium and no enrichment facility. The purpose of the present work is to validate the computer code WIMS-D4 (Halsall, 1980) for the cluster type geometry and then to calculate the inventory and the corresponding activities of some important actinides and fission products present in the reactor core. The reactor selected for the analysis is CANDU 600 MWe PHWR, the standard IAEA bench mark, because the published results are available for this reactor and it has been used extensively to validate the computer codes and different fuel compositions (Sahin et al., 2004, 2006). The computer code is validated by calculating the infinite and effective multiplication factors as a function of burn up and by comparing the calculated values with the available data in the literature. After validating the computer code, the radioactive invento-
* Tel.: +92 51 9290231 7; fax: +92 51 922372 7. E-mail addresses: [email protected], [email protected] 0306-4549/$ - see front matter Ó 2009 Elsevier Ltd. All rights reserved. doi:10.1016/j.anucene.2009.09.015
ries and the corresponding activities of various types of actinides and fission products are also calculated, as the severe accident in a nuclear reactor depends upon the amount of the isotopes present in the core. These are also necessary to estimate the strength of the radiological hazards. 2. Reactor descriptions The reactor core contains 380 fuel channels and each fuel channel contains 37-fuel pins. Fig. 1 shows the cross sectional view of a fuel channel, containing a fuel bundle, a pressure tube, a calandria tube, and moderator. Lattice benchmark cell model and lattice benchmark cell model for WIMS-D4 are shown in Figs. 2 and 3, respectively. The data used to model the unit cell is given in Table 1. The values of the radial and axial buckling, calculated from the reactor dimensions, used are 4.1925E 5 and 2.687E 5, respectively. 3. Calculational methodology The WIMS-D4 (Winfrith Improved Multigroup Scheme versionD4) code is used to study the fuel burn up and radioactive inventory of some important isotopes. WIMS-D4 is being used to solve the one dimensional neutron transport for research and power reactors, and the most comprehensive code of its kind. It is a general purpose multigroup transport theory based code and uses different types of libraries available for analysis. For the present analysis, 69 groups neutron cross section library of UK origin is used. The 69 groups consists of 14 fast, 13 resonance and 42 thermal groups. For the present work, the 69 groups in the data set library were collapsed to five-group cross section data set.
Z. Yasin / Annals of Nuclear Energy 37 (2010) 66–70
67
Fig. 3. Lattice benchmark cell model for WIMS-D4. Fig. 1. Cross sectional view of the fuel channel (Sahin et al., 2004).
neutron transport equation. For the present analysis, DSN option is used. WIMS-D4 also performs calculations for the important fission product chains and more various absorber event chains are also provided. For burn up calculations, Power C card is used in the input of WIMS-D4 file. The ratio of power in MWt to the amount of initial fuel in tones is required for this card. For the CANDU 600 case, this ratio comes out to be 25.06 MW/ te. The burn up calculations has been performed for the 125 days. The multiplication factors, consumption of 235U and 238U and 239Pu produced as a function of burn up days are calculated. The inventories of some important fission products and their corresponding activities are also calculated. The computer code WIMS-D4 has already been used extensively to model the pin type and slab geometries (Khan et al., 2004; Ahmad and Ahmad, 2004; Saleem et al., 1995). In the present work, it is being used to model the cluster type geometry.
4. Results and discussion
Fig. 2. Latttice benchmark cell model.
The boundaries of the energy shift of these five groups are given in Table 2. The code calculates the cell-averaged diffusion coefficients (D), absorption (Ra), fission cross sections (mRf), the infinite multiplication factor (kinf) and effective multiplication factor keff (if buckling is provided). The code solves the burn up equations for fuel and fission products for a given specific power and then calculates the isotopic compositions and concentrations (gm/cm) of important isotopes present in the reactor core. Several options are available in WIMS-D4, like discrete ordinance (DSN) and collision probability method, for differential and integral solutions of Boltzmann
The variation of the infinite and effective multiplication factors versus the burn up, calculated using the WIMS-D4 model of Fig. 3, are shown in Figs. 4 and 5, respectively. The present values of the multiplication factors are compared with the published results available in Ref Saleem et al. (1995). The comparison of the infinite and effective multiplication factors with the other available results are also shown in Table 3. A good agreement is observed among the present calculations and the previous ones. It is to be noted that the multiplication factors first decrease abruptly and then slowly. The initial fast decrease in the multiplication factors is due to the consumption of 235U and build-up of xenon and samarium and other fission products in the core. The slow or about flat decrease of multiplication factors is due to the production of 239 Pu along with other nuclides. Then there is fast decrease in the multiplication factors is due to the consumption of both 235U and 239Pu, and the accumulation of fission products in the reactor
68
Z. Yasin / Annals of Nuclear Energy 37 (2010) 66–70
Table 1 Basic benchmark cell data.
1.14 1.12 Compacted and sintered natural UO2 pellets 18.7 kg 700 °C (‘‘effective” average) 12.154 mm 480 mm
Fuel bundle assembly Number of elements (rods) Length of bundle
37 495 mm
Outer element ring No. of elements Diameter (nominal, cold)
18 86.61 mm
Intermediate element ring No. of elements Diameter (nominal, cold)
12 57.51 mm
Inter element ring No. of elements Diameter (nominal, cold) Central element Arrangement
6 29.77 1 Fig. 1
Element sheath Material Density Outside diameter Thickness Total Zr mass per bundle
Zirconium 6.51 g/cc 13.08 mm 0.419 mm 2.264
1.08 1.06 PINSTECH KANUPP CNEA KAERI BARC INPR ONTARIOHYDRO
1.04 1.02 1.00 0.98 0.96
0
1000
2000
3000
4000
5000
6000
7000
8000
9000
Burn up (MWD/te) Fig. 4. Infinite multiplication factors as a function of burn up.
1.10 1.08 1.06
Temperature Inside diameter Wall thickness
Zirconium 6.8775 g/cc (The density corresponds to 6.55 normal Zirconium density 1.05 to take into account the presence of Niobium) 209 °C 103 mm 4.34 mm
Calandria tubes Material Density Temperature Inside diameter Wall thickness
Zirconium 6.55 g/cc 680 °C 129 mm 14 mm
Coolant Material Density Temperature Fission bundle power
99.75 w/o D2O 0.804 g/cc 290 °C (‘‘Effective” average) 620 KW
Moderator Material Density Temperature Boron concentration
99.75 w/o D2O 1.0915 g/cc 60 °C 0 mg/kg D2O
k-effective
Pressure tubes Material Density
1.10
k-infinity
Fuel Material Total mass per bundle Temperature Diameter of the pellets Stack length (Average)
1.04 1.02 PINSTECH KANUPP CNEA KAERI BARC INPR ONTARIOHYDRO
1.00 0.98 0.96 0.94 0
1000
2000
3000
4000
5000
6000
7000
8000
9000
Burn up (MWD/te)
Table 2 Broad group energy boundaries for the five groups. Group number
Energy boundaries
1 2 3 4 5
10.0–0.821 MeV 0.821 MeV–5.530 keV 5.530 keV–0.625 eV 0.625 eV–0.140 eV <0.140 eV
core. As the natural uranium is used as fuel, thus during the fuel burn up, 235U is consumed due to fission in 235U by thermal neutrons and 239Pu is produced due to the capturing of neutron by 238 U. The atom densities of 235U, 238U and 239Pu as a function of
Fig. 5. Effective multiplication factors as a function of burn up.
burn up days for the fuel bundle of CANDU 600 are shown in Figs. 6–8, respectively. With the passage of time, there is decrease in the number densities, and hence in the concentrations of 235U and 238U and there is increase in the number densities and hence in the concentration of 239Pu. The initial and final (after 125 days) concentrations (gm/cm) and atom densities (#/b.cm) of the most important radionuclides in the reactor core (235U, 238U, 239Pu, 240Pu and 241Pu) are shown in Tables 4 and 5, respectively. The concentration of 235U decreases from 127.3195 gm (2.65249 gm/cm) to 75.5798 (1.57458 gm/cm) and the concentration of 238U decreases from 180,05.664 gm (375.118 gm/cm) to 179,47.200 (373.900 gm/cm). The total amount of 239Pu produced is 32.9088 gm (0.6856 gm/ cm). The radiological hazard due to the severe reactor accidents depends upon the nature, concentrations and the radioactivity of the nuclides produced in the reactor core during burn up process. The concentrations of various important radionuclides, from radiological hazard point of view, are given in Table 6. These values have been calculated during 125 days of fuel burn up. These values are important parameters to estimate the dose or to study the radiological hazard in the case of severe accident which might happen and cause the release of these radionuclides to the environment.
69
Z. Yasin / Annals of Nuclear Energy 37 (2010) 66–70 Table 3 Infinite and effective multiplication factors as a function of burn up. Burn up
PINSTECH (Pakistan)
0 0 800 800 1600 1600 2400 2400 3200 4000 4000 4800 4800 5600 5600 6400 6400 7200 7200 8000 8000
1.1203 1.0946 1.0782 1.0520 1.0765 1.0507 1.0679 1.0426 1.0567 1.0439 1.0194 1.0304 1.0062 1.0166 0.9928 1.0029 0.9795 0.9900 0.9670 0.9773 0.9545
KANUPP* (Pakistan)
CNEA*(Argentina)
KAERI*(Korea)
BARC* (India)
INPR*(Romania)
ONTARIO HYDRO* (Canada)
1.1189 1.0889 1.0855 1.0571 1.0817 1.0537 1.0727 1.0452 1.0612 1.0482 1.0216 1.0345 1.0084 1.0206 0.9948 1.0067 0.9814 0.9931 0.9682 0.9800 0.9554
1.1155 1.0844 1.0767 1.0477 1.0763 1.0478 1.0689 1.0409 1.0581 1.0456 1.0185 1.0321 1.0055 1.0183 0.9920 1.0045 0.9787 0.9909 0.9655 0.9777 0.9527
1.1159 1.0869 1.0751 1.0487 1.0736 1.0470 1.0650 1.0390 1.0535 1.0405 1.0153 1.0267 1.0020 1.0129 0.9886 0.9992 0.9753 0.9859 0.9624 0.9732 0.9501
1.115 1.0840 1.0757 1.0463 1.0737 1.0454 1.0655 1.0377 1.0542 1.0413 1.0145 1.0277 1.0013 1.0139 0.9980 1.0003 0.9748 0.9871 0.9620 0.9749 0.9502
1.1263 1.0918 1.0865 1.0542 1.0862 1.0543 1.0777 1.0465 1.0653 1.0508 1.0207 1.0354 1.0059 1.0198 0.9908 1.0044 0.9759 0.9895 0.9614 0.9753 0.9476
1.0835 1.0513 1.0832 1.0515 1.0749 1.0438 1.0629 1.0488 1.0188 1.0336 1.0042 1.0180 0.9891 1.0023 0.9739 0.9857 0.9509 0.9711 0.9443
Kinf, Keff
From Ref. Saleem et al. (1995).
Table 4 The U235, U238, Pu239, Pu240 and Pu241 concentrations after 125 days of burn up time.
Atom density (#/b.cm)
-4
1.4x10
-4
1.2x10
-4
1.0x10
235
U
-5
8.0x10
-5
6.0x10
0
50
100
150
The element
Initial atom concentration (Gm/cm)
Final atom concentration (Gm/cm)
U235 U238 Pu239 Pu240 Pu241
2.65249E+0 3.75118E+2
1.57458E+00 3.73900E+2 6.85579E 1 1.27038E 1 1.91874E 2
200
Time(days) Fig. 6. Atom densities of
235
U as a function of burn up days.
-2
Atom density (#/b.cm)
2.2x10
238
-2
U
2.2x10
-2
2.2x10
-2
2.2x10
Table 5 The U235, U238, Pu239, Pu240 and Pu241 atom densities after 125 days of burn up time. The element
Initial atom densities (Atoms/b.cm))
Final atom densities (Atoms/b.cm)
U235 U238 Pu239 Pu240 Pu241
1.5834E 4 2.2110E 2 – – –
9.3995E 2.2038E 4.0226E 7.4103E 1.1146E
5 2 5 6 6
-2
2.2x10
-2
2.2x10
0
50
100
150
200
Time(days) Fig. 7. Atom densities of
Table 6 The values of inventory and activities of fission products and actinides for the UO2 lattice reactor after 125 days. Nuclide
Concentration (Atoms)
Half lives (s)
Activity (Bq)
Activity (Ci)
235
1.96E+23 4.61E+25 8.40E+22 1.55E+22 2.33E+21 9.88E+21 3.24E+21 6.38E+19 2.22E+18 2.56E+19 1.88E+20 3.95E+18 1.59E+19 1.63E+20 4.99E+19 1.71E+19
2.22E+16 1.41E+17 7.61E+11 2.07E+11 4.54E+08 6.72E+12 3.40E+06 1.27E+05 2.90E+23 1.61E+22 6.51E+07 3.27E+04 4.64E+05 2.80E+09 2.71E+08 1.56E+08
6.13E+06 2.26E+08 7.65E+10 5.18E+10 3.55E+12 1.02E+09 6.60E+14 3.47E+14 5.30E 06 1.10E 03 2.00E+12 8.36E+13 2.38E+13 4.04E+10 1.27E+11 7.59E+10
0.000165642 0.00612068 2.068589532 1.398969888 95.8415893 0.027553483 17838.21907 9381.591417 1.43149E 16 2.97992E 14 54.10265742 2260.187 643.0717489 1.092363158 3.441547873 2.051699108
238
U as a function of burn up days. U U 239 Pu 240 Pu 241 Pu 99 Rc 103 Ru 105 Rh 113 Cd 115 In 134 Cs 135 Xe 148 Pm 151 Sm 154 Eu 155 Eu 238
-5
Atom density (#/b.cm)
*
5.0x10
239
Pu
-5
4.0x10
-5
3.0x10
-5
2.0x10
-5
1.0x10
0
Fig. 8. Atom densities of
50 239
100 150 Time(days)
200
Pu as a function of burn up days.
70
Z. Yasin / Annals of Nuclear Energy 37 (2010) 66–70
5. Conclusions
References
The infinite and effective multiplication factors as a function of the burn up are calculated to validate the computer code WIMS-D4 for the cluster geometry. The calculated values are in good agreement with the available results in the literature. The amounts of 235 U and 238U consumed and amount of 239Pu produced are also calculated. The amounts of 235U and 238 U consumed are 51.74 gm and 58.46 gm, respectively while the amount of 239Pu produced is 32.91 gm, in the CANDU 600 fuel bundle after 125 days of reactor operation. The concentrations and the corresponding activities of the most important isotopes in the reactor core are also calculated.
Ahmad, S.I., Ahmad, N., 2004. Effect of new cross sections evaluations on criticality and neutron energy spectrum of a typical material test research reactor. Ann. Nucl. Energy 32, 1867–1881. Halsall, M.J., 1980. Summary of WIMSD4 input options. AEEW-M 1327. Khan, M.J., Aslam, Ahmad, N., 2004. Neutronics analysis of natural uranium fueled, light water cooled, heavy water moderated and graphite reflected nuclear reactors. Ann. Nucl. Energy. 31, 1331–1356. Sahin, Sumer, Yildiz, Kadir, Acir, Adem, 2004. Power flattening in the fuel bundle of a CANDU reactor. Nucl. Eng. Des. 232, 07–11. Sahin, Sumer et al., 2006. An assessment of thorium and spent LWR-fuel utilization potential in CANDU reactors. Energy Convers. Manage. 47, 1661–1675. Saleem, Muhammad, Parvez, Ansar, Arshad, Mohammad, 1995. Calculation of lattice cell constants for the IAEA PHWR benchmark using the computer code WIMS-D/4. The Nucleus 32 (1, 2), 1–11.
Acknowledgements I thank Mr. Mohammad Tayyab and Mr. Bashir for help in this work. I also thank Dr. J.I. Akhter, Dr. Matiullah and Dr. M.I. Shahzad for encouragement and support.
Contents lists available at ScienceDirect
Annals of Nuclear Energy journal homepage: www.elsevier.com/locate/anucene
Calculation of fuel burn up and radioactive inventory in a CANDU reactor using WIMS-D4 code Zafar Yasin * Physics Division, PINSTECH, P.O. Nilore, Islamabad, Pakistan
a r t i c l e
i n f o
Article history: Received 27 July 2009 Received in revised form 19 September 2009 Accepted 28 September 2009 Available online 6 November 2009
a b s t r a c t A study of fuel burn up and radioactive inventory for the CANDU reactor is carried out to validate the computer code WIMS-D4 for cluster geometry. The infinite and effective multiplication factors are calculated as a function of burn up and compared with the available results. A good agreement is observed among the present calculations and the previous published results. The code is then used to calculate the 235U and 238U consumed and the 239Pu produced in the fuel bundle. The inventories and the corresponding activities of some important fission products are also calculated. Ó 2009 Elsevier Ltd. All rights reserved.
1. Introduction Due to the unavailability of fusion technology in the coming three to four decades, rise of oil prices in the world market, shortage of water resources, and due to the growing energy needs of the world population, particularly in the developing countries, there is again an increase in trend to use nuclear energy for peaceful purpose. Among the existing technologies of nuclear power plants, Canada Deuterium Uranium (CANDU) reactors rank second place of commercial nuclear power reactors in the world. The main advantages of the CANDU reactors are the on-line fuelling, use of natural uranium as fuel and enhanced neutron economy due to the negligible neutron loss in heavy water. These reactors are more suitable for a country that has lot of reserves of natural uranium and no enrichment facility. The purpose of the present work is to validate the computer code WIMS-D4 (Halsall, 1980) for the cluster type geometry and then to calculate the inventory and the corresponding activities of some important actinides and fission products present in the reactor core. The reactor selected for the analysis is CANDU 600 MWe PHWR, the standard IAEA bench mark, because the published results are available for this reactor and it has been used extensively to validate the computer codes and different fuel compositions (Sahin et al., 2004, 2006). The computer code is validated by calculating the infinite and effective multiplication factors as a function of burn up and by comparing the calculated values with the available data in the literature. After validating the computer code, the radioactive invento-
* Tel.: +92 51 9290231 7; fax: +92 51 922372 7. E-mail addresses: [email protected], [email protected] 0306-4549/$ - see front matter Ó 2009 Elsevier Ltd. All rights reserved. doi:10.1016/j.anucene.2009.09.015
ries and the corresponding activities of various types of actinides and fission products are also calculated, as the severe accident in a nuclear reactor depends upon the amount of the isotopes present in the core. These are also necessary to estimate the strength of the radiological hazards. 2. Reactor descriptions The reactor core contains 380 fuel channels and each fuel channel contains 37-fuel pins. Fig. 1 shows the cross sectional view of a fuel channel, containing a fuel bundle, a pressure tube, a calandria tube, and moderator. Lattice benchmark cell model and lattice benchmark cell model for WIMS-D4 are shown in Figs. 2 and 3, respectively. The data used to model the unit cell is given in Table 1. The values of the radial and axial buckling, calculated from the reactor dimensions, used are 4.1925E 5 and 2.687E 5, respectively. 3. Calculational methodology The WIMS-D4 (Winfrith Improved Multigroup Scheme versionD4) code is used to study the fuel burn up and radioactive inventory of some important isotopes. WIMS-D4 is being used to solve the one dimensional neutron transport for research and power reactors, and the most comprehensive code of its kind. It is a general purpose multigroup transport theory based code and uses different types of libraries available for analysis. For the present analysis, 69 groups neutron cross section library of UK origin is used. The 69 groups consists of 14 fast, 13 resonance and 42 thermal groups. For the present work, the 69 groups in the data set library were collapsed to five-group cross section data set.
Z. Yasin / Annals of Nuclear Energy 37 (2010) 66–70
67
Fig. 3. Lattice benchmark cell model for WIMS-D4. Fig. 1. Cross sectional view of the fuel channel (Sahin et al., 2004).
neutron transport equation. For the present analysis, DSN option is used. WIMS-D4 also performs calculations for the important fission product chains and more various absorber event chains are also provided. For burn up calculations, Power C card is used in the input of WIMS-D4 file. The ratio of power in MWt to the amount of initial fuel in tones is required for this card. For the CANDU 600 case, this ratio comes out to be 25.06 MW/ te. The burn up calculations has been performed for the 125 days. The multiplication factors, consumption of 235U and 238U and 239Pu produced as a function of burn up days are calculated. The inventories of some important fission products and their corresponding activities are also calculated. The computer code WIMS-D4 has already been used extensively to model the pin type and slab geometries (Khan et al., 2004; Ahmad and Ahmad, 2004; Saleem et al., 1995). In the present work, it is being used to model the cluster type geometry.
4. Results and discussion
Fig. 2. Latttice benchmark cell model.
The boundaries of the energy shift of these five groups are given in Table 2. The code calculates the cell-averaged diffusion coefficients (D), absorption (Ra), fission cross sections (mRf), the infinite multiplication factor (kinf) and effective multiplication factor keff (if buckling is provided). The code solves the burn up equations for fuel and fission products for a given specific power and then calculates the isotopic compositions and concentrations (gm/cm) of important isotopes present in the reactor core. Several options are available in WIMS-D4, like discrete ordinance (DSN) and collision probability method, for differential and integral solutions of Boltzmann
The variation of the infinite and effective multiplication factors versus the burn up, calculated using the WIMS-D4 model of Fig. 3, are shown in Figs. 4 and 5, respectively. The present values of the multiplication factors are compared with the published results available in Ref Saleem et al. (1995). The comparison of the infinite and effective multiplication factors with the other available results are also shown in Table 3. A good agreement is observed among the present calculations and the previous ones. It is to be noted that the multiplication factors first decrease abruptly and then slowly. The initial fast decrease in the multiplication factors is due to the consumption of 235U and build-up of xenon and samarium and other fission products in the core. The slow or about flat decrease of multiplication factors is due to the production of 239 Pu along with other nuclides. Then there is fast decrease in the multiplication factors is due to the consumption of both 235U and 239Pu, and the accumulation of fission products in the reactor
68
Z. Yasin / Annals of Nuclear Energy 37 (2010) 66–70
Table 1 Basic benchmark cell data.
1.14 1.12 Compacted and sintered natural UO2 pellets 18.7 kg 700 °C (‘‘effective” average) 12.154 mm 480 mm
Fuel bundle assembly Number of elements (rods) Length of bundle
37 495 mm
Outer element ring No. of elements Diameter (nominal, cold)
18 86.61 mm
Intermediate element ring No. of elements Diameter (nominal, cold)
12 57.51 mm
Inter element ring No. of elements Diameter (nominal, cold) Central element Arrangement
6 29.77 1 Fig. 1
Element sheath Material Density Outside diameter Thickness Total Zr mass per bundle
Zirconium 6.51 g/cc 13.08 mm 0.419 mm 2.264
1.08 1.06 PINSTECH KANUPP CNEA KAERI BARC INPR ONTARIOHYDRO
1.04 1.02 1.00 0.98 0.96
0
1000
2000
3000
4000
5000
6000
7000
8000
9000
Burn up (MWD/te) Fig. 4. Infinite multiplication factors as a function of burn up.
1.10 1.08 1.06
Temperature Inside diameter Wall thickness
Zirconium 6.8775 g/cc (The density corresponds to 6.55 normal Zirconium density 1.05 to take into account the presence of Niobium) 209 °C 103 mm 4.34 mm
Calandria tubes Material Density Temperature Inside diameter Wall thickness
Zirconium 6.55 g/cc 680 °C 129 mm 14 mm
Coolant Material Density Temperature Fission bundle power
99.75 w/o D2O 0.804 g/cc 290 °C (‘‘Effective” average) 620 KW
Moderator Material Density Temperature Boron concentration
99.75 w/o D2O 1.0915 g/cc 60 °C 0 mg/kg D2O
k-effective
Pressure tubes Material Density
1.10
k-infinity
Fuel Material Total mass per bundle Temperature Diameter of the pellets Stack length (Average)
1.04 1.02 PINSTECH KANUPP CNEA KAERI BARC INPR ONTARIOHYDRO
1.00 0.98 0.96 0.94 0
1000
2000
3000
4000
5000
6000
7000
8000
9000
Burn up (MWD/te)
Table 2 Broad group energy boundaries for the five groups. Group number
Energy boundaries
1 2 3 4 5
10.0–0.821 MeV 0.821 MeV–5.530 keV 5.530 keV–0.625 eV 0.625 eV–0.140 eV <0.140 eV
core. As the natural uranium is used as fuel, thus during the fuel burn up, 235U is consumed due to fission in 235U by thermal neutrons and 239Pu is produced due to the capturing of neutron by 238 U. The atom densities of 235U, 238U and 239Pu as a function of
Fig. 5. Effective multiplication factors as a function of burn up.
burn up days for the fuel bundle of CANDU 600 are shown in Figs. 6–8, respectively. With the passage of time, there is decrease in the number densities, and hence in the concentrations of 235U and 238U and there is increase in the number densities and hence in the concentration of 239Pu. The initial and final (after 125 days) concentrations (gm/cm) and atom densities (#/b.cm) of the most important radionuclides in the reactor core (235U, 238U, 239Pu, 240Pu and 241Pu) are shown in Tables 4 and 5, respectively. The concentration of 235U decreases from 127.3195 gm (2.65249 gm/cm) to 75.5798 (1.57458 gm/cm) and the concentration of 238U decreases from 180,05.664 gm (375.118 gm/cm) to 179,47.200 (373.900 gm/cm). The total amount of 239Pu produced is 32.9088 gm (0.6856 gm/ cm). The radiological hazard due to the severe reactor accidents depends upon the nature, concentrations and the radioactivity of the nuclides produced in the reactor core during burn up process. The concentrations of various important radionuclides, from radiological hazard point of view, are given in Table 6. These values have been calculated during 125 days of fuel burn up. These values are important parameters to estimate the dose or to study the radiological hazard in the case of severe accident which might happen and cause the release of these radionuclides to the environment.
69
Z. Yasin / Annals of Nuclear Energy 37 (2010) 66–70 Table 3 Infinite and effective multiplication factors as a function of burn up. Burn up
PINSTECH (Pakistan)
0 0 800 800 1600 1600 2400 2400 3200 4000 4000 4800 4800 5600 5600 6400 6400 7200 7200 8000 8000
1.1203 1.0946 1.0782 1.0520 1.0765 1.0507 1.0679 1.0426 1.0567 1.0439 1.0194 1.0304 1.0062 1.0166 0.9928 1.0029 0.9795 0.9900 0.9670 0.9773 0.9545
KANUPP* (Pakistan)
CNEA*(Argentina)
KAERI*(Korea)
BARC* (India)
INPR*(Romania)
ONTARIO HYDRO* (Canada)
1.1189 1.0889 1.0855 1.0571 1.0817 1.0537 1.0727 1.0452 1.0612 1.0482 1.0216 1.0345 1.0084 1.0206 0.9948 1.0067 0.9814 0.9931 0.9682 0.9800 0.9554
1.1155 1.0844 1.0767 1.0477 1.0763 1.0478 1.0689 1.0409 1.0581 1.0456 1.0185 1.0321 1.0055 1.0183 0.9920 1.0045 0.9787 0.9909 0.9655 0.9777 0.9527
1.1159 1.0869 1.0751 1.0487 1.0736 1.0470 1.0650 1.0390 1.0535 1.0405 1.0153 1.0267 1.0020 1.0129 0.9886 0.9992 0.9753 0.9859 0.9624 0.9732 0.9501
1.115 1.0840 1.0757 1.0463 1.0737 1.0454 1.0655 1.0377 1.0542 1.0413 1.0145 1.0277 1.0013 1.0139 0.9980 1.0003 0.9748 0.9871 0.9620 0.9749 0.9502
1.1263 1.0918 1.0865 1.0542 1.0862 1.0543 1.0777 1.0465 1.0653 1.0508 1.0207 1.0354 1.0059 1.0198 0.9908 1.0044 0.9759 0.9895 0.9614 0.9753 0.9476
1.0835 1.0513 1.0832 1.0515 1.0749 1.0438 1.0629 1.0488 1.0188 1.0336 1.0042 1.0180 0.9891 1.0023 0.9739 0.9857 0.9509 0.9711 0.9443
Kinf, Keff
From Ref. Saleem et al. (1995).
Table 4 The U235, U238, Pu239, Pu240 and Pu241 concentrations after 125 days of burn up time.
Atom density (#/b.cm)
-4
1.4x10
-4
1.2x10
-4
1.0x10
235
U
-5
8.0x10
-5
6.0x10
0
50
100
150
The element
Initial atom concentration (Gm/cm)
Final atom concentration (Gm/cm)
U235 U238 Pu239 Pu240 Pu241
2.65249E+0 3.75118E+2
1.57458E+00 3.73900E+2 6.85579E 1 1.27038E 1 1.91874E 2
200
Time(days) Fig. 6. Atom densities of
235
U as a function of burn up days.
-2
Atom density (#/b.cm)
2.2x10
238
-2
U
2.2x10
-2
2.2x10
-2
2.2x10
Table 5 The U235, U238, Pu239, Pu240 and Pu241 atom densities after 125 days of burn up time. The element
Initial atom densities (Atoms/b.cm))
Final atom densities (Atoms/b.cm)
U235 U238 Pu239 Pu240 Pu241
1.5834E 4 2.2110E 2 – – –
9.3995E 2.2038E 4.0226E 7.4103E 1.1146E
5 2 5 6 6
-2
2.2x10
-2
2.2x10
0
50
100
150
200
Time(days) Fig. 7. Atom densities of
Table 6 The values of inventory and activities of fission products and actinides for the UO2 lattice reactor after 125 days. Nuclide
Concentration (Atoms)
Half lives (s)
Activity (Bq)
Activity (Ci)
235
1.96E+23 4.61E+25 8.40E+22 1.55E+22 2.33E+21 9.88E+21 3.24E+21 6.38E+19 2.22E+18 2.56E+19 1.88E+20 3.95E+18 1.59E+19 1.63E+20 4.99E+19 1.71E+19
2.22E+16 1.41E+17 7.61E+11 2.07E+11 4.54E+08 6.72E+12 3.40E+06 1.27E+05 2.90E+23 1.61E+22 6.51E+07 3.27E+04 4.64E+05 2.80E+09 2.71E+08 1.56E+08
6.13E+06 2.26E+08 7.65E+10 5.18E+10 3.55E+12 1.02E+09 6.60E+14 3.47E+14 5.30E 06 1.10E 03 2.00E+12 8.36E+13 2.38E+13 4.04E+10 1.27E+11 7.59E+10
0.000165642 0.00612068 2.068589532 1.398969888 95.8415893 0.027553483 17838.21907 9381.591417 1.43149E 16 2.97992E 14 54.10265742 2260.187 643.0717489 1.092363158 3.441547873 2.051699108
238
U as a function of burn up days. U U 239 Pu 240 Pu 241 Pu 99 Rc 103 Ru 105 Rh 113 Cd 115 In 134 Cs 135 Xe 148 Pm 151 Sm 154 Eu 155 Eu 238
-5
Atom density (#/b.cm)
*
5.0x10
239
Pu
-5
4.0x10
-5
3.0x10
-5
2.0x10
-5
1.0x10
0
Fig. 8. Atom densities of
50 239
100 150 Time(days)
200
Pu as a function of burn up days.
70
Z. Yasin / Annals of Nuclear Energy 37 (2010) 66–70
5. Conclusions
References
The infinite and effective multiplication factors as a function of the burn up are calculated to validate the computer code WIMS-D4 for the cluster geometry. The calculated values are in good agreement with the available results in the literature. The amounts of 235 U and 238U consumed and amount of 239Pu produced are also calculated. The amounts of 235U and 238 U consumed are 51.74 gm and 58.46 gm, respectively while the amount of 239Pu produced is 32.91 gm, in the CANDU 600 fuel bundle after 125 days of reactor operation. The concentrations and the corresponding activities of the most important isotopes in the reactor core are also calculated.
Ahmad, S.I., Ahmad, N., 2004. Effect of new cross sections evaluations on criticality and neutron energy spectrum of a typical material test research reactor. Ann. Nucl. Energy 32, 1867–1881. Halsall, M.J., 1980. Summary of WIMSD4 input options. AEEW-M 1327. Khan, M.J., Aslam, Ahmad, N., 2004. Neutronics analysis of natural uranium fueled, light water cooled, heavy water moderated and graphite reflected nuclear reactors. Ann. Nucl. Energy. 31, 1331–1356. Sahin, Sumer, Yildiz, Kadir, Acir, Adem, 2004. Power flattening in the fuel bundle of a CANDU reactor. Nucl. Eng. Des. 232, 07–11. Sahin, Sumer et al., 2006. An assessment of thorium and spent LWR-fuel utilization potential in CANDU reactors. Energy Convers. Manage. 47, 1661–1675. Saleem, Muhammad, Parvez, Ansar, Arshad, Mohammad, 1995. Calculation of lattice cell constants for the IAEA PHWR benchmark using the computer code WIMS-D/4. The Nucleus 32 (1, 2), 1–11.
Acknowledgements I thank Mr. Mohammad Tayyab and Mr. Bashir for help in this work. I also thank Dr. J.I. Akhter, Dr. Matiullah and Dr. M.I. Shahzad for encouragement and support.