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Investigating the Performance and safety features of Pressurized water reactors using the burnable poisons
Annals of Nuclear Energy 141 (2020) 107354
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Annals of Nuclear Energy journal homepage: www.elsevier.com/locate/anucene
Investigating the Performance and safety features of Pressurized water reactors using the burnable poisons Sonia M. Reda a,b,⇑, S.S. Mustafa b, Nourhan A. Elkhawas c a
Physics Department, College of Science, Jouf University, P.O. Box: 2014, Sakaka, Saudi Arabia Physics Department, Faculty of Science, Zagazig University, Zagazig, Egypt c Zagazig Higher Institute for Engineering and Technology, Zagazig, Egypt b
a r t i c l e
i n f o
Article history: Received 21 September 2019 Received in revised form 17 January 2020 Accepted 20 January 2020
Keywords: Burnable Poisons Burnable absorbers Vera core benchmark Keff MCNPX Code
a b s t r a c t Investigating the performance and safety features of Pressurized water reactors (PWRs) using the burnable poisons (BPs) are evaluated in this paper. Modeling and simulating of PWR assembly from Vera core physics benchmark are carried out using the MCNPX code. The effect of using different burnable poisons (eight) on the neutronic parameters are studied. Moreover, the types of BPs either as integral burnable absorbers (IBAs) or as burnable poison rods (BPRs) are investigated. The effect of these poisons on the effective multiplication factor is the first parameter that simulated. Gadolinium oxide (Gd2O3) and Erbium oxide (Er2O3) are used as IBAs that mixed homogenously with uranium fuel. The results indicated that Erbium is more effective than Gadolinium due to the fast depletion of gadolinium that shortens the core life. Zirconium diboride (ZrB2), Lutetium Oxide (Lu2O3) and Protactinium Oxide (PaO2) are also investigated as IBAs that are used as coating the outer surface of fuel rod. The results demonstrated that Protactinium is more effective than other poisons. Moreover, the impact of Pyrex (SiO2-B2O3), WABA (Al2O3-B4C) and Hafnium di-boride (HfB2) are included and analyzed. Effective multiplication factor and beta effective are evaluated at the beginning of life of reactor operation. Finally, via the Pin by pin power distribution at BOC and EOC on the assembly level, maximum and minimum power values for the different cases are compared. Ó 2020 Elsevier Ltd. All rights reserved.
1. Introduction Safety features of nuclear power plants are very serious to avoid the nuclear accidents. These accidents not only affect the environment by releasing radioactive materials but also damage humanity life (Awan et al., 2017). Pressurized water reactors (PWRs) are the most widely used nuclear reactors to generate electric energy. Nuclear energy can be controlled in predictable manner by using Burnable Poisons (BPs) materials which improve the performance of reactor (Rouf and Suud, 2016). Burnable Absorber (BA) is a high neutron absorber nuclide that has high absorption cross section and changes to an isotope with a lower absorption after capturing a neutron (Závorka and Škoda, 2016). Burnable Poisons have some advantages, they increase core life without any reduction in control safety improve core power distributions if they are located in a proper fashion, suppress the excess reactivity (at BOC) and harden the neutron spectrum producing more Pu-239. The most common ⇑ Corresponding author at: Physics Department, Faculty of Science, Zagazig University, Zagazig, Egypt E-mail addresses: [email protected], [email protected] (S.M. Reda). https://doi.org/10.1016/j.anucene.2020.107354 0306-4549/Ó 2020 Elsevier Ltd. All rights reserved.
burnable poison isotopes used in PWR assemblies are boron 10, Gadolinium 157 and Erbium-167. Boron can be used as IFBA which consists of Zrb2 layer around fuel pellets and as BPRs in form of B4C/Al2O3. Solublity of high concentration of boron in water participates in a positive temperature coefficient for the reactor core. The Gadolinium and erbium are mixed in the oxide form within fuel pellets. Other isotopes with high absorption cross section are Europium, Dysprosium, Hafnium, Lutetium, Protactinium and palladium (Khoshahval et al., 2016). The operation of the reactor depends on many factors as number of poison rods, rod positions and the concentration of poisons that make the best use of the utilization of the fuel (Galahom, 2017). As the fuel enrichment increases, the amount of BP and soluble boron are required to increase the control of the excess reactivity. High boron concentration makes the moderator temperature coefficient (MTC) less negative or slightly positive that can reduce the safety of reactor. If the amount of BA increases, it will cause short cycle length due to the reduced amount of fuel and penalty of residual (Choe et al., 2016). Table 1 shows some of the physical properties of BPs. It is obvious that Gadolinium has the highest absorption cross section than
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Table 1 Physical properties of BPs. BP material
Gd2O3
Er2O3
Hfb2
Zrb2
PaO2
Lu2O3
Dy2O3
Sm2O3
Main absorbing nuclide Density(g/cm3) Cross section (Barns) Melting temperature (°c)
Gd-155 Gd-157 7.4 60900 ± 500 254000 ± 815 2350
Er-167 8.64 649 ± 8 2355
Hf-177B-11 10.5 373 ± 10 5.5 ± 3.3 3250
b-11 6.08 5.5 ± 3.3 3000
Pa-231 8.9 293 1572
Lu-176 9.420 2090 ± 70 2490
Dy-161 Dy-164 7.81 600 ± 25 2650 ± 70 2340
Sm-149 8.35 40140 ± 600 2325
other materials (Mughabghab, 2003). The melting point of the boride compounds is higher than that of the oxide forms. Two categories of burnable absorbers (BAs) can be used with PWR fuels: (i) Integral Burnable Absorbers (IBAs) (ii) Discrete Burnable Poison Rods (BPRs) 1.1. Integral burnable absorbers IBAs are neutron absorbing materials that can be mixed homogenously with fuel rod components or coated the fuel matrix and located symmetrically within the fuel assembly (Khoshahval et al., 2016; Nguyen et al., 1154). Several different types of IBAs are used in PWR fuel. Neutron absorbers such as Gadolinia (Gd2O3), Erbia (Er2O3) or Europium Oxide (Eu2O3) are mixed with Uranium Dioxide (UO2) fuel in selected rod locations within an assembly. The Westinghouse – designed Integral Fuel Burnable Absorber (IFBA) rods contain a thin layer of neutron absorber material in form of Zirconium Diboride (Zrb2) coating the outer surface of fuel rod. Also, Lutetium and Protactinium in the oxide form can be used as IFBA coating fuel matrix. Other integral absorbers consist of Boron Carbide (B4C). In addition, Alumina Oxide (Al2O3) can be placed in rods that replace approximately 20 Uranium Oxide fuel rods in some control element (CE) designed fuel assemblies (Khoshahval et al., 2016). For PWR reactors, without using IBAs, the reactivity reduces with burnup in a nearly linear fashion. In contrast, the significant use of IBAs that reactivity increases as fuel burns until reaching maximum value where poison is approximately depleted then decreases with burnup. Furthermore, other designs of fuel assembly make modest use of IBAs , reactivity remains constant or slowly decreases with burnup up to the point where the IBAs is nearly depleted and then decreases with burnup (Galahom, 2016). 1.2. Burnable poison rods BPRs are rods composed of high absorption cross-section materials that can be loaded in guide tubes of PWR assembly. This type of burnable absorbers has been only applied in PWR fuel (O’Leary and Pitts, 2001). BPRs consisting of B4C/Al2O3 pellets with Zircaloy coating are used in framatome cogema fuels (FCF) (Khoshahval et al., 2016). Westinghouse has manufactured two types of BPRs: (1) Wet Annular Burnable Absorbers (WABAs). (2) Pyrex Burnable Absorbers Assemblies (BAAs). Wet Annular Burnable Absorbers is a discrete burnable absorber that consists of (Al2O3-B4C) composite ceramic pellets in annular design with wet central region filled in water and Zircaloy-4 cladding (Wagner and Parks, 2000). Alumina Oxide (Al2O3) and Boron Carbide (B4C) can be bounded and strengthened together to form Alumina – Boron – Carbide mixture (Al2O3-B4C) (14% wt. B4C with 0.1% C) by sintering process which has a low density 2.593 gm/cm3 and temperature 1600 °C (Cavdar et al., 2018). Advantages of using WABAs in PWR assemblies are to minimize the excess of reactivity
and decrease the concentration of boron at the begin of cycle but also has disadvantages such as high costs of manufacture for the annular rod (Carolina and Karve, 2003). Pyrex glass (SiO2-B2O3 with 12.5% wt. B2O3) is modeled in the assembly as a borosilicate tube with void central region and surrounded by stainless steel304 (Wagner and Parks, 2000). Borosilicate has high thermal, chemical and mechanical resistance, and low coefficient of expansion and density of 2.23 g/cm3 (Zhang et al., 2018). Both types of BAs are manufactured to operate during the first cycle of fuel assembly. After one cycle, the BPRs are replaced by the coolant to occupy the guide tube volume. In the case of IBAs, the poison materials remain in the fuel assembly throughout its lifetime and produce small penalty of reactivity at the end of life due to the incomplete depletion of the neutron absorber material. 2. Materials Different Burnable Poison components have been investigated to find the optimal BP material. Eight materials are evaluated as BAs in PWR assemblies in this research. Gadolinia and Erbia are used as IBs that mixed with Uranium fuel. Protactinium Oxide, Lutetium Oxide and Zirconium Diboride are used as IBs coating the fuel rods. Also, Pyrex alloys (SiO2/B2O3), Ceramic alloys (B4C/Al2O3) and Hafnium Diboride are applied as BPRs to the guide tubes of PWR assembly. 2.1. Gadolinium One of the most widely rare earth elements that can be used in both Pressurized Water Reactors (PWRs) and Boiling Water Reactors (BWRs) is Gadolinium. It contains two high thermal neutron absorbers isotopes (Gd-155 and Gd-157) and large natural abundance equals 15% and 16% respectively (Khoshahval et al., 2016). Gadolinia (Gd2O3) is used as an integral burnable absorber by mixing Gadolinium Oxide with the selected fuel rods (UO2). The number of fuel rods bearing Gadolinium are small because of its large absorption cross section which causes self-shielding and participates in avoiding the fast burnout of fuel. Mostly, the Gadolinium rods are located near the water holes to decrease the power peaking of assembly (Galahom, 2016; Oettingen and Cetnar, 2014). 2.2. Erbium Natural Erbium contains six isotopes from which Er-167 has large thermal neutron absorption cross section but smaller than that of other poisons such as Boron (B-10) and Gadolinium (Gd155, Gd-157). Erbia (Er2O3) is used in PWR by mixing Erbium Oxide homogenously with Uranium fuel (UO2) and using this mixture leads to reduce the cycle length (Galahom, 2016; Refeat, 2016). Using Erbia reduces the reactivity, soluble boron concentration and the value of MTC (Franceschini and Petrovic´, 2009). 2.3. Protactinium Oxide Protactinium serves as neutron absorber during the first cycle to compensate for the excess reactivity (Riyana and Ud, 2005).
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The long-lived isotope pa-231 with 32,760 years has high thermal neutron cross section (293 barns) (Rouf and Suud, 2016). On the other hand, the transformation process of pa-nuclide during burnup process through neutron capture would increase the production of U-233 and the core life time (Riyana and Ud, 2005). 2.4. Hafnium Diboride Hafnium Diboride is a very refractory ceramic material which has a brittle mechanical behavior and can be used as neutron absorber due to the presence of high neutron cross section of both Hafnium and Boron-10. This burnable poison in reactor core is carried out with Hafnium cladding and also used FeCrAl cladding instead of the rational clad of Zirconium (Qasim Awan et al., 2018). 2.5. Lutetium Oxide Lutetium (Lu) which has atomic number 71 is one of the most rare earth elements. It has two stable isotopes Lu-175 and Lu176 with natural abundance of 97.4% and 2.6% respectively. Lu177 can be produced by two ways: the first way to obtain it by the 176Lu (n, ɣ) 177Lu reaction of the natural or enriched Lu2O3 (in Lu-176) target, or by (Yb2O3) target followed by the separation of Lu-177 from the isotopes of Ytterbium. The transmutation process and decay of nuclides from Lu-175 ? Lu-176 ? Hf-177 ? Hf178 ? Hf-179 would produce large amount of residual reactivity but enriching Lutetium Oxide (in Lu-176) can reduce the residual reactivity (Renier and Grossbeck, 2001; Pasqualini et al., 2007). 2.6. Zirconium Diboride Zirconium Diboride can act as thin layer of integral burnable poison coating the outer surface of fuel rod and the main neutron absorber is boron 10 that has high neutron cross section. Moreover, there is no residual reactivity and poison isotopes at the end of cycle due to the complete depletion of boron (Franceschini and Petrovic´, 2009). Helium gas can be released by 10 B (n, a) 7Li reaction and creates undesirable internal fuel pin pressure (Renier and Grossbeck, 2001). 3. Design and analysis of fuel assembly The reference core design chosen in this study is a typical Westinghouse 17 X 17 pressurized water reactor (PWR) rated power at 3411 MWth with 157 fuel assemblies (Inoue et al., 2004; Godfrey, ,2014). Each assembly contains 264 fuel pins, 24 guide tubes and one instrumental tube. The reference fuel rod is composed of 3.1% enriched (UO2) uranium dioxide and burned up to 60 GWD/ MTU. Due to the symmetry of the PWR assemblies, one assembly has been evaluated using MCNPX Code. The Vera calculations were carried out with a three – dimensional transport and depletion code –MCNPX version 2.7 and cross section data library from ENDF/BVII.0. The main parameters of fuel assembly design are displayed in Table 2. Fig. 1 shows MCNPX cross sectional view for the different models of PWR assemblies with different cases of BPs materials. Seven types of PWR assemblies are investigated with eight burnable poison materials (Gd2O3, Er2O3, Lu2O3, ZrB2, PaO2, HfB2, Al2O3-B4C, and SiO2-B2O3).. There are four different IBAs configurations, two of them contain 12 or 24 BPs mixed with uranium fuel (Wagner and Parks, 2000). And these configurations are shown in figures (1-b) and (1-c); however, the other two configurations of IFBA that is coating the fuel rods with 0.01 mm of BPs and the number of these poisons in PWR model is 68 or 88 rods (Walker,
Table 2 Benchmark design parameters. Design Parameters
Values
Assembly array size, pins Array geometry Number of fuel rods per assembly Number of guide tubes Number of instrumentation tubes
17 17 square 264 24 1 Fuel rod Uo2 3.1% 1.26 cm 21.50 cm 365.76 cm 0.4096 cm 0.418 cm 0.475 cm 0.561 cm 0.602 cm 0.559 cm 0.605 cm Zircaloy-4 Helium 3411 MW 900 °k 600 °k
Fuel material Fuel enrichment Fuel rod pitch Assembly pitch Fuel rod height Pellet radius Inner clad radius Outer clad radius Inner guide tube radius Outer guide tube radius Inner instrument tube radius Outer instrument tube radius Clad material Gas material Rated core power Fuel temperature Moderator temperature
2015) are shown in figures (1-d) and (1- e). Two different burnable poisons rods configurations are also modeling that contain 12 or 24 rods which replace the guide tubes in fuel assembly (Wagner and Parks, 2000), that are represented in figures (1-f) and (1-g). MCNPX Code is used to determine both the effective multiplication factor and beta effective for the assembly with and without burnable poisons at the beginning of life. Moreover, pin power distributions, reactivity, concentration of fission products and effective multiplication factor have been calculated at the BOC and EOC. 4. Results and discussion 4.1. PWR model validation For validation, PWR fuel assembly was modeled by MCNPX to verify model data by comparison with Vera Core Physics Benchmark. Fuel pin cells were occupied by uranium oxide with 3.1 wt % 235U enrichment. The temperature used was 600 k for fuel and borated water which was used as moderator material. Six problems that contain a single Westinghouse 17X17 type fuel rod cell at Beginning Of Life (BOL) requirements as illustrated in Fig. 1 are chosen for modeling. All edge surfaces were considered as ‘‘reflected surface” to reflect the particles back so that all the neutrons were absorbed in the media, and then k1 could be evaluated. The infinite multiplication factor and pin by pin power distribution were calculated for the six models to study the neutronic effects of burnable poisons (Godfrey, 2014). As seen in Table 3, the values of the infinite multiplication factor at BOL for the assembly simulated by MCNPX Code are compared with the reference values obtained by KENO Code. The results obtained show perfect concurred with reference benchmark results (Godfrey,2014). Tables 4 and 5 represent the maximum and minimum values of pin power for MCNPX Code which coincide with the reference results with average 98% (Godfrey,2014). The results indicate that the assembly which contains IFBA 104 + 20 WABA poisons has the maximum value for pin power but the assembly with 12 rods of Gadolinia has the minimum value of pin power.
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Fig. 1. Horizontal cross section MCNPX computer model of PWR assembly with different cases of BPs materials.
Table 3 Infinite multiplication factor values for modeling and benchmark code. Case
k1 KENO
MCNPX
% error
Vera 2b (without BPs) Gadolinium 12 Gadolinium 24 Pyrex 12 Pyrex 24 IFBA 104 + 20 WABA
1.183360 ± 0.000024
1.18312 ± 0.00015
0.020281
1.047729 0.927410 1.069627 0.976018 0.869615
± ± ± ± ±
0.000024 0.000024 0.000024 0.000026 0.000025
1.04747 0.92671 1.06960 0.97686 0.86941
± ± ± ± ±
0.00033 0.00033 0.00032 0.00035 0.00032
0.024806 0.075479 0.002524 0.086268 0.023573
4.2. Burnup calculation Depletion characteristics of different burnable absorbers are investigated. However, the first parameter determined in this work is the neutron multiplication factor versus burnup.
Table 4 Maximum Pin by pin power distribution values for the modeled assembly compared with benchmark values. Case
Maximum pin power KENO MCNPX present
% Error
Vera 2b (without BPs) Gadolinium 12 Gadolinium 24 Pyrex 12 Pyrex 24 IFBA 104 + 20 WABA
1.0474 1.1053 1.1688 1.0578 1.1541 1.1661
0.0000 0.45236 3.19986 1.11552 0.66718 4.84521
1.0474 1.1103 1.2062 1.0460 1.1464 1.2226
± ± ± ± ± ±
0.0025 0.0026 0.0029 0.0026 0.0028 0.0029
4.2.1. Effect of using IBAs in PWR assembly Fig. 2 displays the behavior for keff as a function of fuel burnup in the case of IBAs that mixed homogenously with uranium fuel with different number 12 and 24 poison rods for Gadolinia and Erbia. The results indicate that keff for PWR assembly without BPs decreases dramatically due to the production of 135Xe and
S.M. Reda et al. / Annals of Nuclear Energy 141 (2020) 107354 Table 5 Minimum Pin by pin power distribution values for the modeled assembly compared with benchmark values. Case
Vera 2b (without BPs) Gadolinium 12 Gadolinium 24 Pyrex 12 Pyrex 24 IFBA 104 + 20 WABA
Minimum pin power KENO
MCNPX Present
% Error
0.9406 0.21730 0.2431 0.92990 0.90700 0.84670
0.9365 ± 0.0026 0.21587 ± 0.0020 0.24841 ± 0.0021 0.93178 ± 0.0027 0.90678 ± 0.0028 0.74551 ± 0.0029
0.43589 0.65807 2.18428 0.202172 0.024255 11.95110
149 Sm (Galahom, 2016). In addition, keff has a small value for Gadolinia case than other cases. Therefore, as Gadolinia rod number increases in the fuel assembly, keff value decreases in the beginning burnup steps. That’s due to the presence of high absorption cross section Gd-155 and Gd-157 as mentioned in Table 1. The behavior of Gadolinia curve increases until reaching to 10 GWD/MTU at which the absorbing nuclides are nearly depleted then began to decrease linearly. The effect of Gd on Keff values at first steps is larger than erbium, this effect decreases quickly in the case of Gd compared with erbium, this is may be due to the rapidly degradation of Gd compared with Er. The change of effective multiplication factor (Keff) versus fuel burnup for three different poison materials Protactinium Oxide (PaO2), Lutetium Oxide (Lu2O3) and Zirconium Diboride (ZrB2), that coating the outer of fuel rod with a fixed number (68 or 88), are illustrated in Fig. 3. As can be observed, Lutetium has a faster rate of depletion than boron and Protactinium. So, Protactinium Oxide layers is preferable in nuclear reactor applications because they maintain criticality (Keff = 1) at longer periods (approximately 422 days) of reactor operation. In contrast to ZrB2 layers, criticality is maintained for shorter periods (nearly 211 days). In addition, using Protactinium indicate that it’s a good choice for using as IBA due to the transformation process of Pa to U-233 by neutron absorption that can be used as nuclear weapons or as nuclear fuels, that also has half-life of 159,200 years.
4.2.2. Effect of using BPRs in PWR assembly Comparison between three different BPRs (Pyrex-WABA and HfB2) which replace the guide tubes in fuel assembly are given in
5
Fig. 4. The results show that Keff in PWR assembly with BPs are very small compared with Keff of PWR assembly without BPs. This reduction in Keff is due to the ability of BPs to absorb neutrons (Galahom, 2016). In addition, HfB2 is burned out faster than other poisons and has the lowest value of keff at the first burnup steps that’s due to the presence of two high absorption cross section nuclides Hf and B-10 that converts to B-11 by neutron capture so that core life time decreased than other cases. Pyrex has a slightly higher value of keff, so that’s a useful decision for using as BPRs. 4.2.3. The reactivity variation with burnup at different cases of BPs The aim of this section is to evaluate the effect of using BPs on suppressing the reactivity of reactor. In general, the presence of any of the BPRs has a negative effect on the reactivity of the assembly. This effect changes from material to other according to their thermal neutron absorption. The reactivity decreases with the burnup due to the reduction of the fissile material (Galahom, 2017). Dependent upon calculations, reactivity results at BOC, MOC and EOC are tabulated in Table 6. Using Hafnium Diboride gives the highest negative reactivity at both BOC and EOC because of their large cross section and their presence in 24 guide tube location which increasing their concentration in the assembly. Reactivity gives a prediction about neutron population over time and the deviation from criticality case of reactor (DOE-HDBK, 0000).
q¼
keff 1 keff
ð1Þ
From Eq. (1) we can note that q has a positive or negative value of reactivity. This value differs from one material to another based on the thermal neutron absorption cross section and the concentration of the poison on the assembly. 4.2.4. The fuel composition (Actinides and fission Products). Atom densities of fission products and actinides for the different cases of BPs with respect to fuel burnup are presented for Vera assembly. U-235 depleted during the operation of reactor and its concentration decreases. Fissile product Pu-239 is produced after capturing neutron by U-238 which converts to Np-239 then to Pu-239. Some fission products can affect on the neutrons economy by absorbing neutrons. The presence of BAs during depletion process hardens the neutron spectrum, resulting in lower 235U depletion and higher production of fissile plutonium isotopes.
Fig. 2. Multiplication factor variation with burnup at different cases of IBAs.
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Fig. 3. Multiplication factor variation with burnup at different cases of IBAs.
Fig. 4. Multiplication factor variation with burnup at different cases of BPRs.
Table 6 Reactivity values with fuel burnup. case
Reactivity BOC
MOC
EOC
Without poisons Gd 12 Gd 24 Er 12 Er 24 IFBA (Zrb2) 68 IFBA (Zrb2) 88 Lu2o3 (natural) 68 Lu2o3 (enriched) 68 Lu2o3 (enriched) 88 Pao2 68 Pao2 88 Pyrex 12 Pyrex 24 WABA 12 WABA24 Hfb2 12 Hfb2 24
0.148 0.038 0.086 0.125 0.102 0.078 0.048 0.129 0.068 0.037 0.126 0.119 0.058 0.032 0.060 0.027 0.061 0.246
0.003 0.019 0.026 0.013 0.018 0.122 0.159 0.034 0.147 0.202 0.036 0.042 0.085 0.148 0.083 0.148 0.281 0.535
0.127 0.176 0.182 0.170 0.170 0.285 0.307 0.196 0.314 0.347 0.197 0.200 0.222 0.268 0.223 0.270 0.522 0.872
The simultaneous increase in plutonium production and decrease in fission of 235U may increase the reactivity of the fuel at discharging and beyond. An assembly exposed to BAs may have a higher reactivity for a given burnup than that has not. Fission products actinides concentrations differ according to BAs types. BAs that have large thermal neutron absorption cross section, decrease fission process in the core, i.e. consume less fissile materials 235U (Galahom, 2016). Analysis of the comparison for the concentration of U-235 for the different poisons with fuel burnup is shown in Fig. 5. At BOC, U-235 has 7.181E-04 atoms/barn*cm for all cases which indicate that fuel enriched with 3.7% U-235.At EOC, Pyrex that replace the guide tube has the largest value of U-235 atom densities with 6.026E-05and the smallest value for using enriched Lu2O3 with 1.241E-05. Fig. 6 shows the depletion of U-238 during the burnup process which indicates the small depletion of U-238; the atom density at the beginning of cycle is 2.215E-02 and becomes 2.106E-02 at EOC for the HFB2-24 case (the highest value), in case of Lu2O3 it is 2.073E-02 (the lowest value).
S.M. Reda et al. / Annals of Nuclear Energy 141 (2020) 107354
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Fig. 5. Variation of U-235 concentration for different cases with burnup.
Fig. 6. Variation of U-238 concentration for different cases with burnup.
The production of fissile product Pu-239 is given in Fig. 7. There is no Plutonium in core at BOC but its concentration increases with burnup due to the transmutation process of U-238. At the EOC, Using Pyrex gives the largest value for Pu production with
1.456E-04 and HFb2 has the lowest value 8.722E-05. Pyrex-24 has the highest value for Np-237 production at the EOC with 1.903E-05 but Hfb2 has the smallest value with 1.515E-05 as portrayed in Fig. 8.
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Fig. 7. Variation of Pu-239 concentration for different cases with burnup.
Fig. 8. Variation of Np-237 concentration for different cases with burnup.
4.3. Beginning of life calculations eff
Physical parameters of PWR assembly were simulated by using MCNPX Code. Both KCODE and KSRC cards were used to calculate Keff at beginning of cycle by using both delayed and prompt neutrons. KCODE simulations were performed using 500 cycles with 10,000 particles. The second calculation was the delayed neutron fraction ßeff.
¼
K eff kprompt beff
ð2Þ
From Eq. (2), kprompt is the effective multiplication factor when only prompt neutrons are carried out by using TOTNU card and set its value to NO (Compton, 2015). Table 7 summarizes the results for Keff and ßeff for the different cases of BPs. The result of the comparative calculations shows that Lu2O3 in the natural form and
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S.M. Reda et al. / Annals of Nuclear Energy 141 (2020) 107354 Table 7 Beginning of life calculations for two factors (Keff, ßeff). Case
keff
ßeff
Gd12 Gd24 Er 12 Er 24 IFBA 68 IFBA 88 lu 68 (nat) lu 68 (enr) lu 88 (enr) pa 68 pa 88 Pyrex 12 Pyrex 24 WABA 12 WABA 24 hfb2 12 hfb2 24
1.04747 0.92671 1.15032 1.12126 1.09139 1.05556 1.1568 1.08114 1.04376 1.15177 1.14338 1.0696 0.97686 1.06468 0.98037 0.94743 0.80576
0.007303312 0.006960106 0.006685096 0.006349999 0.006844483 0.006337868 0.006396957 0.007445844 0.0066682 0.006806915 0.007075513 0.006881077 0.006920132 0.007213435 0.005946734 0.007219531 0.007458797
HFB2 have the largest and smallest values for keff respectively. However, HFB2 and WABA 24 have the highest and smallest values for ßeff respectively. 4.4. Pin power distribution at (BOC-EOC) Maximum power distribution and minimum power distribution at the beginning of cycle and at the end of cycle are listed in Table 8. The results showed that at the BOC using Lu2O3 enriched (88 rod) gives the highest value but gadolinium with 12 rod has the lowest value. Also, at the EOC, Lu2O3 enriched (68 rod) gives the maximum and minimum value for power distribution. 5. Conclusion and recommendations The neutronic analysis and burnup calculations for PWR assembly using different burnable absorbers are investigated using MCNPX Code. The results are given briefly in the following conclusions: The results obtained by MCNPX are infinite multiplication factor and Pin by Pin power distribution for the modeled PWR assembly show a good agreement with keno code from Vera core physics benchmark.
Erbium is more effective than Gadolinium as IBAs that mixed with Uranium fuel. Therefore, the applicable trend is favorable for PWRs fueled with UO2-Er2O3 which increases the core life time. Protactinium Oxide is more effective than Integral Fuel Burnable Absorber (IFBA) and Lutetium oxide as IBAs that are coating the outer surface of fuel rod. So, PWR assemblies modeled with UO2 rods surrounded by Protactinium oxide layers is preferable in nuclear reactor applications because they maintain criticality (Keff = 1) at longer periods (approximately 422 days) of reactor operation. In contrast to ZrB2 layers, criticality is maintained for shorter periods (nearly 211 days). Hafnium Diboride gives a high negative reactivity compared with other burnable poisons at BOC and EOC. That’s may be due to the presence of two high absorption cross section nuclides Hf and B-10 (that converts to B-11 by neutron capture) so that core life time decreased than other cases. Moreover, Pyrex has a slightly higher value of keff, so using it guarantees the safe operation of reactor. it is considered one of the models that could be applicable in nuclear reactor applications. Fuel compositions are investigated and the results show that U235 and U-238 concentrations decreases with burnup and Pu239 and Np-237 concentrations increase with fuel depletion. Finally, at the beginning of life calculations, two factors (keff and ßeff) are evaluated and the comparative calculations show that HfB2 has the smallest value for Keff and largest value for ßeff. During the cycle (BOC, EOC) maximum and minimum value for pin by pin power distribution are determined for the different cases. The large value of ßeff increases safety. CRediT authorship contribution statement Sonia M. Reda and S. S. Mustafa shared the presented idea. Nourhan A. khawas and Sonia M. Reda carried out the calculations and wrote the manuscript. All authors discussed the results. Sonia M. Reda and S. S. Mustafa revised the manuscript. Sonia M. reda supervised the findings of this work. Sonia M. reda and Nourhan A. Elkhawas authors contributed to the final version of the manuscript. Sonia M. reda followed up the publication. Declaration of Competing Interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
Table 8 Pin by Pin power distribution values during the cycle. Case
Without poisons Gd12 Gd24 Er 12 Er 24 IFBA 68 IFBA 88 lu 68 (nat) lu 68 (enr) lu 88 (enr) pa 68 pa 88 Pyrex 12 Pyrex 24 WABA 12 WABA 24 hfb2 12 hfb2 24
BOC
EOC
MAX
MIN
MAX
MIN
1.0489 1.1156 1.2094 1.0514 1.0659 1.2549 1.3829 1.0943 1.2960 1.4651 1.1004 1.0926 1.0442 1.1458 1.0398 1.1474 1.1201 1.1468
9.4139E01 2.1714E01 2.4685E01 8.7781E01 8.8948E01 4.0196E01 4.0617E01 8.3103E01 2.9376E01 2.9435E01 8.1324E01 8.6445E01 9.3026E01 9.120E01 9.3384E01 9.1107E01 9.0781E01 8.7564E01
1.05201 1.0463 1.0607 1.0430 1.0626 1.1539 1.1301 1.0704 1.1789 1.1754 1.0778 1.0633 1.0481 1.1324 1.04371 1.1222 1.0846 1.1095
9.3795E01 8.9985E01 9.1302E01 9.3892E01 8.7828E01 6.4048E01 7.3198E01 8.8978E01 5.4670E01 6.1425E01 8.7256E01 9.2111E01 9.4056E01 9.2163E01 9.3528E01 9.3296E01 9.1837E01 9.1616E01
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Acknowledgment We would like to acknowledge Professor Dr. Esmat A Amin, Nuclear and Radiological Regulatory Authority, Cairo, Egypt, for her kind help, valuable scientific comments and for the revision of the final manuscript. Appendix A. Supplementary data Supplementary data to this article can be found online at https://doi.org/10.1016/j.anucene.2020.107354. References Awan, M.Q., Cao, L., Wu, H., 2017. Burnable poisons alternative configurations in ATFCM PWR fuelassembly. ASME. Int. Conf. Nucl. Eng. 3, 6–13. Rouf and Z. Suud, ‘‘Analysis of Burnable Poison Effect on Combined (Th-U)O2 Fuel Cycle Performance in 800 MWt Long-Life PWR,” Indian J. Sci. Technol., vol. 9, no. 28, 2016. Závorka, J., Škoda, R., 2016. Hafnium in nuclear fuel cladding used both as oxidation protection and burnable absorber. ASME Int. Conf. Nucl. Eng. Khoshahval, F., Foroutan, S.S., Zolfaghari, A., Minuchehr, H., 2016. Evaluation of burnable absorber rods effect on neutronic performance in fuel assembly of WWER-1000 reactor. Ann. Nucl. Energy 87, 648–658. Galahom, A.A., 2017. Study of the possibility of using Europium and Pyrex alloy as burnable absorber in PWR. Ann. Nucl. Energy 110, 1127–1133. Choe, J., Shin, H.C., Lee, D., 2016. New burnable absorber for long-cycle low boron operation of PWRs. Ann. Nucl. Energy 88, 272–279. S. F. Mughabghab, ‘‘Thermal neutron capture cross sections resonance in tegrals and G-factors,” INDC Int. Nucl. Data Comm., no. 11376, 2003. X. H. A. Nguyen, P. Venneri, and Y. Kim, ‘‘Burnable absorber optimization in a superflux research burnable absorber optimization in a super-flux research reactor utilizing plate-type fuel,”European Research Reactor Conference (RRFM),pp. 1154, 2016. Galahom, A.A., 2016. Investigation of different burnable absorbers effects on the neutronic characteristics of PWR assembly. Ann. Nucl. Energy 94, 22–31. P. M. O’Leary, M. L. Pitts, ‘‘Effects of Burnable Absorbers on PWR Spent Nuclear Fuel”, MW’01 conference, 25 February - 1 March, 2001. Wagner, J.C., Parks, C.V., 2000. Parametric study of the effect of burnable poison rods for PWR Burnup credit. Office of Nuclear Regulatory Research in NRC Publications.
Cavdar, U., Altintasß, A., Karaca, B., 2018. In-situ compaction and sintering of Al2O3B4C composites by using a High-Frequency Induction System. Kovove Mater. 56, 177–181. Carolina S. and Karve A., ‘‘An Advanced Burnable Poison for Pressurized Water Reactors,” Fuel, ANFM, Hilton Head Island, pp. 1–19, 2003. Zhang, Q., Tan, S., Ren, M., Yang, H., Tang, D., Chen, K., Zhang, T., et al., 2018. Effect of Gd2O3 doping on structure and boron volatility of borosilicate glass sealants in solid oxide fuel cells—A study on the La0.6Sr0.4Co0.2Fe0.8O3-D (LSCF) cathode. J. Power Sources 383, 34–41. Oettingen, M., Cetnar, J., 2014. Validation of gadolinium burnout using PWR benchmark specification. Nucl. Eng. Des. 273, 359–366. Refeat, Riham, 2016. Optimum Erbium Isotopes Composition and Distribution for Power Flattening in Advanced PWR Fuel Assembly. J. Mater. Sci. Eng. B 6 (2), 85– 93. Franceschini, F., Petrovic´, B., 2009. Fuel with advanced burnable absorbers design for the IRIS reactor core: Combined Erbia and IFBA. Ann. Nucl. Energy 36 (8), 1201–1207. E. S. Riyana and Z. S. U. Ud, ‘‘Preliminary Design Study of Thorium (Th) and Protactinium (231 Pa) Based Fuel for Tight Lattice Long Life BWR,” Nucl. Phys., no. 509, 2005. Qasim Awan, M., Cao, L., Wu, H., Shen, W., Li, Z., 2018. Neutronic design study of a small modular IPWR loaded with accident tolerant-fully ceramic microencapsulated (AT-FCM) fuel. Nucl. Eng. Des. 335 (28), 18–29. J.-P. A. Renier and M. L. Grossbeck, ‘‘Development of Improved Burnable Poisons for Commerical Nuclear Power Reactors, ” Office of Scientific and Technical Information, 2001. G. Pasqualini, J. Alberto, and O. Junior, ‘‘Study of the production OF 177 Lu through 176 Yb (n , c) 177 Yb ? 177 Lu nuclear reaction,”INAC, International Nuclear Atlantic Conference, pp. 6–11, 2007. Y. Inoue, Z. Xu, and E. E. Pilat, ‘‘Effectiveness of Different Burnable Poisons in a Long Cycle BWR,” ANS, American Nuclear Society pp. 5–12, 2004. A. T. Godfrey, ‘‘VERA Core Physics Benchmark Progression Problem Specifications,” Oak Ridge National Laboratory, Consortium for Advanced Burnable Absorbers Simulation of LWRs (CASL), no. 793,2014. E. D. Walker, ‘‘Modeling Integral Fuel burnable absorbers using the Method of Characteristics,”A thesis presented to university of tennessee in partial fulfillment of the requirements for master degree of science in nuclear engineering,knoxville, 2015. DOE-HDBK-1019/1-93, ‘‘The Nuclear Physics and Reactor Theory”. Handbook(1). W. K. Compton, ‘‘Impact of configuration variations on small modular reactor core performance,”A thesis Presented to the Faculty of the Graduate School of the Missouri University of Science and Technology in Partial Fulfillment of the Requirements for the Degree Master of Science in Nuclear Engineering, 2015.
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Annals of Nuclear Energy journal homepage: www.elsevier.com/locate/anucene
Investigating the Performance and safety features of Pressurized water reactors using the burnable poisons Sonia M. Reda a,b,⇑, S.S. Mustafa b, Nourhan A. Elkhawas c a
Physics Department, College of Science, Jouf University, P.O. Box: 2014, Sakaka, Saudi Arabia Physics Department, Faculty of Science, Zagazig University, Zagazig, Egypt c Zagazig Higher Institute for Engineering and Technology, Zagazig, Egypt b
a r t i c l e
i n f o
Article history: Received 21 September 2019 Received in revised form 17 January 2020 Accepted 20 January 2020
Keywords: Burnable Poisons Burnable absorbers Vera core benchmark Keff MCNPX Code
a b s t r a c t Investigating the performance and safety features of Pressurized water reactors (PWRs) using the burnable poisons (BPs) are evaluated in this paper. Modeling and simulating of PWR assembly from Vera core physics benchmark are carried out using the MCNPX code. The effect of using different burnable poisons (eight) on the neutronic parameters are studied. Moreover, the types of BPs either as integral burnable absorbers (IBAs) or as burnable poison rods (BPRs) are investigated. The effect of these poisons on the effective multiplication factor is the first parameter that simulated. Gadolinium oxide (Gd2O3) and Erbium oxide (Er2O3) are used as IBAs that mixed homogenously with uranium fuel. The results indicated that Erbium is more effective than Gadolinium due to the fast depletion of gadolinium that shortens the core life. Zirconium diboride (ZrB2), Lutetium Oxide (Lu2O3) and Protactinium Oxide (PaO2) are also investigated as IBAs that are used as coating the outer surface of fuel rod. The results demonstrated that Protactinium is more effective than other poisons. Moreover, the impact of Pyrex (SiO2-B2O3), WABA (Al2O3-B4C) and Hafnium di-boride (HfB2) are included and analyzed. Effective multiplication factor and beta effective are evaluated at the beginning of life of reactor operation. Finally, via the Pin by pin power distribution at BOC and EOC on the assembly level, maximum and minimum power values for the different cases are compared. Ó 2020 Elsevier Ltd. All rights reserved.
1. Introduction Safety features of nuclear power plants are very serious to avoid the nuclear accidents. These accidents not only affect the environment by releasing radioactive materials but also damage humanity life (Awan et al., 2017). Pressurized water reactors (PWRs) are the most widely used nuclear reactors to generate electric energy. Nuclear energy can be controlled in predictable manner by using Burnable Poisons (BPs) materials which improve the performance of reactor (Rouf and Suud, 2016). Burnable Absorber (BA) is a high neutron absorber nuclide that has high absorption cross section and changes to an isotope with a lower absorption after capturing a neutron (Závorka and Škoda, 2016). Burnable Poisons have some advantages, they increase core life without any reduction in control safety improve core power distributions if they are located in a proper fashion, suppress the excess reactivity (at BOC) and harden the neutron spectrum producing more Pu-239. The most common ⇑ Corresponding author at: Physics Department, Faculty of Science, Zagazig University, Zagazig, Egypt E-mail addresses: [email protected], [email protected] (S.M. Reda). https://doi.org/10.1016/j.anucene.2020.107354 0306-4549/Ó 2020 Elsevier Ltd. All rights reserved.
burnable poison isotopes used in PWR assemblies are boron 10, Gadolinium 157 and Erbium-167. Boron can be used as IFBA which consists of Zrb2 layer around fuel pellets and as BPRs in form of B4C/Al2O3. Solublity of high concentration of boron in water participates in a positive temperature coefficient for the reactor core. The Gadolinium and erbium are mixed in the oxide form within fuel pellets. Other isotopes with high absorption cross section are Europium, Dysprosium, Hafnium, Lutetium, Protactinium and palladium (Khoshahval et al., 2016). The operation of the reactor depends on many factors as number of poison rods, rod positions and the concentration of poisons that make the best use of the utilization of the fuel (Galahom, 2017). As the fuel enrichment increases, the amount of BP and soluble boron are required to increase the control of the excess reactivity. High boron concentration makes the moderator temperature coefficient (MTC) less negative or slightly positive that can reduce the safety of reactor. If the amount of BA increases, it will cause short cycle length due to the reduced amount of fuel and penalty of residual (Choe et al., 2016). Table 1 shows some of the physical properties of BPs. It is obvious that Gadolinium has the highest absorption cross section than
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Table 1 Physical properties of BPs. BP material
Gd2O3
Er2O3
Hfb2
Zrb2
PaO2
Lu2O3
Dy2O3
Sm2O3
Main absorbing nuclide Density(g/cm3) Cross section (Barns) Melting temperature (°c)
Gd-155 Gd-157 7.4 60900 ± 500 254000 ± 815 2350
Er-167 8.64 649 ± 8 2355
Hf-177B-11 10.5 373 ± 10 5.5 ± 3.3 3250
b-11 6.08 5.5 ± 3.3 3000
Pa-231 8.9 293 1572
Lu-176 9.420 2090 ± 70 2490
Dy-161 Dy-164 7.81 600 ± 25 2650 ± 70 2340
Sm-149 8.35 40140 ± 600 2325
other materials (Mughabghab, 2003). The melting point of the boride compounds is higher than that of the oxide forms. Two categories of burnable absorbers (BAs) can be used with PWR fuels: (i) Integral Burnable Absorbers (IBAs) (ii) Discrete Burnable Poison Rods (BPRs) 1.1. Integral burnable absorbers IBAs are neutron absorbing materials that can be mixed homogenously with fuel rod components or coated the fuel matrix and located symmetrically within the fuel assembly (Khoshahval et al., 2016; Nguyen et al., 1154). Several different types of IBAs are used in PWR fuel. Neutron absorbers such as Gadolinia (Gd2O3), Erbia (Er2O3) or Europium Oxide (Eu2O3) are mixed with Uranium Dioxide (UO2) fuel in selected rod locations within an assembly. The Westinghouse – designed Integral Fuel Burnable Absorber (IFBA) rods contain a thin layer of neutron absorber material in form of Zirconium Diboride (Zrb2) coating the outer surface of fuel rod. Also, Lutetium and Protactinium in the oxide form can be used as IFBA coating fuel matrix. Other integral absorbers consist of Boron Carbide (B4C). In addition, Alumina Oxide (Al2O3) can be placed in rods that replace approximately 20 Uranium Oxide fuel rods in some control element (CE) designed fuel assemblies (Khoshahval et al., 2016). For PWR reactors, without using IBAs, the reactivity reduces with burnup in a nearly linear fashion. In contrast, the significant use of IBAs that reactivity increases as fuel burns until reaching maximum value where poison is approximately depleted then decreases with burnup. Furthermore, other designs of fuel assembly make modest use of IBAs , reactivity remains constant or slowly decreases with burnup up to the point where the IBAs is nearly depleted and then decreases with burnup (Galahom, 2016). 1.2. Burnable poison rods BPRs are rods composed of high absorption cross-section materials that can be loaded in guide tubes of PWR assembly. This type of burnable absorbers has been only applied in PWR fuel (O’Leary and Pitts, 2001). BPRs consisting of B4C/Al2O3 pellets with Zircaloy coating are used in framatome cogema fuels (FCF) (Khoshahval et al., 2016). Westinghouse has manufactured two types of BPRs: (1) Wet Annular Burnable Absorbers (WABAs). (2) Pyrex Burnable Absorbers Assemblies (BAAs). Wet Annular Burnable Absorbers is a discrete burnable absorber that consists of (Al2O3-B4C) composite ceramic pellets in annular design with wet central region filled in water and Zircaloy-4 cladding (Wagner and Parks, 2000). Alumina Oxide (Al2O3) and Boron Carbide (B4C) can be bounded and strengthened together to form Alumina – Boron – Carbide mixture (Al2O3-B4C) (14% wt. B4C with 0.1% C) by sintering process which has a low density 2.593 gm/cm3 and temperature 1600 °C (Cavdar et al., 2018). Advantages of using WABAs in PWR assemblies are to minimize the excess of reactivity
and decrease the concentration of boron at the begin of cycle but also has disadvantages such as high costs of manufacture for the annular rod (Carolina and Karve, 2003). Pyrex glass (SiO2-B2O3 with 12.5% wt. B2O3) is modeled in the assembly as a borosilicate tube with void central region and surrounded by stainless steel304 (Wagner and Parks, 2000). Borosilicate has high thermal, chemical and mechanical resistance, and low coefficient of expansion and density of 2.23 g/cm3 (Zhang et al., 2018). Both types of BAs are manufactured to operate during the first cycle of fuel assembly. After one cycle, the BPRs are replaced by the coolant to occupy the guide tube volume. In the case of IBAs, the poison materials remain in the fuel assembly throughout its lifetime and produce small penalty of reactivity at the end of life due to the incomplete depletion of the neutron absorber material. 2. Materials Different Burnable Poison components have been investigated to find the optimal BP material. Eight materials are evaluated as BAs in PWR assemblies in this research. Gadolinia and Erbia are used as IBs that mixed with Uranium fuel. Protactinium Oxide, Lutetium Oxide and Zirconium Diboride are used as IBs coating the fuel rods. Also, Pyrex alloys (SiO2/B2O3), Ceramic alloys (B4C/Al2O3) and Hafnium Diboride are applied as BPRs to the guide tubes of PWR assembly. 2.1. Gadolinium One of the most widely rare earth elements that can be used in both Pressurized Water Reactors (PWRs) and Boiling Water Reactors (BWRs) is Gadolinium. It contains two high thermal neutron absorbers isotopes (Gd-155 and Gd-157) and large natural abundance equals 15% and 16% respectively (Khoshahval et al., 2016). Gadolinia (Gd2O3) is used as an integral burnable absorber by mixing Gadolinium Oxide with the selected fuel rods (UO2). The number of fuel rods bearing Gadolinium are small because of its large absorption cross section which causes self-shielding and participates in avoiding the fast burnout of fuel. Mostly, the Gadolinium rods are located near the water holes to decrease the power peaking of assembly (Galahom, 2016; Oettingen and Cetnar, 2014). 2.2. Erbium Natural Erbium contains six isotopes from which Er-167 has large thermal neutron absorption cross section but smaller than that of other poisons such as Boron (B-10) and Gadolinium (Gd155, Gd-157). Erbia (Er2O3) is used in PWR by mixing Erbium Oxide homogenously with Uranium fuel (UO2) and using this mixture leads to reduce the cycle length (Galahom, 2016; Refeat, 2016). Using Erbia reduces the reactivity, soluble boron concentration and the value of MTC (Franceschini and Petrovic´, 2009). 2.3. Protactinium Oxide Protactinium serves as neutron absorber during the first cycle to compensate for the excess reactivity (Riyana and Ud, 2005).
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The long-lived isotope pa-231 with 32,760 years has high thermal neutron cross section (293 barns) (Rouf and Suud, 2016). On the other hand, the transformation process of pa-nuclide during burnup process through neutron capture would increase the production of U-233 and the core life time (Riyana and Ud, 2005). 2.4. Hafnium Diboride Hafnium Diboride is a very refractory ceramic material which has a brittle mechanical behavior and can be used as neutron absorber due to the presence of high neutron cross section of both Hafnium and Boron-10. This burnable poison in reactor core is carried out with Hafnium cladding and also used FeCrAl cladding instead of the rational clad of Zirconium (Qasim Awan et al., 2018). 2.5. Lutetium Oxide Lutetium (Lu) which has atomic number 71 is one of the most rare earth elements. It has two stable isotopes Lu-175 and Lu176 with natural abundance of 97.4% and 2.6% respectively. Lu177 can be produced by two ways: the first way to obtain it by the 176Lu (n, ɣ) 177Lu reaction of the natural or enriched Lu2O3 (in Lu-176) target, or by (Yb2O3) target followed by the separation of Lu-177 from the isotopes of Ytterbium. The transmutation process and decay of nuclides from Lu-175 ? Lu-176 ? Hf-177 ? Hf178 ? Hf-179 would produce large amount of residual reactivity but enriching Lutetium Oxide (in Lu-176) can reduce the residual reactivity (Renier and Grossbeck, 2001; Pasqualini et al., 2007). 2.6. Zirconium Diboride Zirconium Diboride can act as thin layer of integral burnable poison coating the outer surface of fuel rod and the main neutron absorber is boron 10 that has high neutron cross section. Moreover, there is no residual reactivity and poison isotopes at the end of cycle due to the complete depletion of boron (Franceschini and Petrovic´, 2009). Helium gas can be released by 10 B (n, a) 7Li reaction and creates undesirable internal fuel pin pressure (Renier and Grossbeck, 2001). 3. Design and analysis of fuel assembly The reference core design chosen in this study is a typical Westinghouse 17 X 17 pressurized water reactor (PWR) rated power at 3411 MWth with 157 fuel assemblies (Inoue et al., 2004; Godfrey, ,2014). Each assembly contains 264 fuel pins, 24 guide tubes and one instrumental tube. The reference fuel rod is composed of 3.1% enriched (UO2) uranium dioxide and burned up to 60 GWD/ MTU. Due to the symmetry of the PWR assemblies, one assembly has been evaluated using MCNPX Code. The Vera calculations were carried out with a three – dimensional transport and depletion code –MCNPX version 2.7 and cross section data library from ENDF/BVII.0. The main parameters of fuel assembly design are displayed in Table 2. Fig. 1 shows MCNPX cross sectional view for the different models of PWR assemblies with different cases of BPs materials. Seven types of PWR assemblies are investigated with eight burnable poison materials (Gd2O3, Er2O3, Lu2O3, ZrB2, PaO2, HfB2, Al2O3-B4C, and SiO2-B2O3).. There are four different IBAs configurations, two of them contain 12 or 24 BPs mixed with uranium fuel (Wagner and Parks, 2000). And these configurations are shown in figures (1-b) and (1-c); however, the other two configurations of IFBA that is coating the fuel rods with 0.01 mm of BPs and the number of these poisons in PWR model is 68 or 88 rods (Walker,
Table 2 Benchmark design parameters. Design Parameters
Values
Assembly array size, pins Array geometry Number of fuel rods per assembly Number of guide tubes Number of instrumentation tubes
17 17 square 264 24 1 Fuel rod Uo2 3.1% 1.26 cm 21.50 cm 365.76 cm 0.4096 cm 0.418 cm 0.475 cm 0.561 cm 0.602 cm 0.559 cm 0.605 cm Zircaloy-4 Helium 3411 MW 900 °k 600 °k
Fuel material Fuel enrichment Fuel rod pitch Assembly pitch Fuel rod height Pellet radius Inner clad radius Outer clad radius Inner guide tube radius Outer guide tube radius Inner instrument tube radius Outer instrument tube radius Clad material Gas material Rated core power Fuel temperature Moderator temperature
2015) are shown in figures (1-d) and (1- e). Two different burnable poisons rods configurations are also modeling that contain 12 or 24 rods which replace the guide tubes in fuel assembly (Wagner and Parks, 2000), that are represented in figures (1-f) and (1-g). MCNPX Code is used to determine both the effective multiplication factor and beta effective for the assembly with and without burnable poisons at the beginning of life. Moreover, pin power distributions, reactivity, concentration of fission products and effective multiplication factor have been calculated at the BOC and EOC. 4. Results and discussion 4.1. PWR model validation For validation, PWR fuel assembly was modeled by MCNPX to verify model data by comparison with Vera Core Physics Benchmark. Fuel pin cells were occupied by uranium oxide with 3.1 wt % 235U enrichment. The temperature used was 600 k for fuel and borated water which was used as moderator material. Six problems that contain a single Westinghouse 17X17 type fuel rod cell at Beginning Of Life (BOL) requirements as illustrated in Fig. 1 are chosen for modeling. All edge surfaces were considered as ‘‘reflected surface” to reflect the particles back so that all the neutrons were absorbed in the media, and then k1 could be evaluated. The infinite multiplication factor and pin by pin power distribution were calculated for the six models to study the neutronic effects of burnable poisons (Godfrey, 2014). As seen in Table 3, the values of the infinite multiplication factor at BOL for the assembly simulated by MCNPX Code are compared with the reference values obtained by KENO Code. The results obtained show perfect concurred with reference benchmark results (Godfrey,2014). Tables 4 and 5 represent the maximum and minimum values of pin power for MCNPX Code which coincide with the reference results with average 98% (Godfrey,2014). The results indicate that the assembly which contains IFBA 104 + 20 WABA poisons has the maximum value for pin power but the assembly with 12 rods of Gadolinia has the minimum value of pin power.
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Fig. 1. Horizontal cross section MCNPX computer model of PWR assembly with different cases of BPs materials.
Table 3 Infinite multiplication factor values for modeling and benchmark code. Case
k1 KENO
MCNPX
% error
Vera 2b (without BPs) Gadolinium 12 Gadolinium 24 Pyrex 12 Pyrex 24 IFBA 104 + 20 WABA
1.183360 ± 0.000024
1.18312 ± 0.00015
0.020281
1.047729 0.927410 1.069627 0.976018 0.869615
± ± ± ± ±
0.000024 0.000024 0.000024 0.000026 0.000025
1.04747 0.92671 1.06960 0.97686 0.86941
± ± ± ± ±
0.00033 0.00033 0.00032 0.00035 0.00032
0.024806 0.075479 0.002524 0.086268 0.023573
4.2. Burnup calculation Depletion characteristics of different burnable absorbers are investigated. However, the first parameter determined in this work is the neutron multiplication factor versus burnup.
Table 4 Maximum Pin by pin power distribution values for the modeled assembly compared with benchmark values. Case
Maximum pin power KENO MCNPX present
% Error
Vera 2b (without BPs) Gadolinium 12 Gadolinium 24 Pyrex 12 Pyrex 24 IFBA 104 + 20 WABA
1.0474 1.1053 1.1688 1.0578 1.1541 1.1661
0.0000 0.45236 3.19986 1.11552 0.66718 4.84521
1.0474 1.1103 1.2062 1.0460 1.1464 1.2226
± ± ± ± ± ±
0.0025 0.0026 0.0029 0.0026 0.0028 0.0029
4.2.1. Effect of using IBAs in PWR assembly Fig. 2 displays the behavior for keff as a function of fuel burnup in the case of IBAs that mixed homogenously with uranium fuel with different number 12 and 24 poison rods for Gadolinia and Erbia. The results indicate that keff for PWR assembly without BPs decreases dramatically due to the production of 135Xe and
S.M. Reda et al. / Annals of Nuclear Energy 141 (2020) 107354 Table 5 Minimum Pin by pin power distribution values for the modeled assembly compared with benchmark values. Case
Vera 2b (without BPs) Gadolinium 12 Gadolinium 24 Pyrex 12 Pyrex 24 IFBA 104 + 20 WABA
Minimum pin power KENO
MCNPX Present
% Error
0.9406 0.21730 0.2431 0.92990 0.90700 0.84670
0.9365 ± 0.0026 0.21587 ± 0.0020 0.24841 ± 0.0021 0.93178 ± 0.0027 0.90678 ± 0.0028 0.74551 ± 0.0029
0.43589 0.65807 2.18428 0.202172 0.024255 11.95110
149 Sm (Galahom, 2016). In addition, keff has a small value for Gadolinia case than other cases. Therefore, as Gadolinia rod number increases in the fuel assembly, keff value decreases in the beginning burnup steps. That’s due to the presence of high absorption cross section Gd-155 and Gd-157 as mentioned in Table 1. The behavior of Gadolinia curve increases until reaching to 10 GWD/MTU at which the absorbing nuclides are nearly depleted then began to decrease linearly. The effect of Gd on Keff values at first steps is larger than erbium, this effect decreases quickly in the case of Gd compared with erbium, this is may be due to the rapidly degradation of Gd compared with Er. The change of effective multiplication factor (Keff) versus fuel burnup for three different poison materials Protactinium Oxide (PaO2), Lutetium Oxide (Lu2O3) and Zirconium Diboride (ZrB2), that coating the outer of fuel rod with a fixed number (68 or 88), are illustrated in Fig. 3. As can be observed, Lutetium has a faster rate of depletion than boron and Protactinium. So, Protactinium Oxide layers is preferable in nuclear reactor applications because they maintain criticality (Keff = 1) at longer periods (approximately 422 days) of reactor operation. In contrast to ZrB2 layers, criticality is maintained for shorter periods (nearly 211 days). In addition, using Protactinium indicate that it’s a good choice for using as IBA due to the transformation process of Pa to U-233 by neutron absorption that can be used as nuclear weapons or as nuclear fuels, that also has half-life of 159,200 years.
4.2.2. Effect of using BPRs in PWR assembly Comparison between three different BPRs (Pyrex-WABA and HfB2) which replace the guide tubes in fuel assembly are given in
5
Fig. 4. The results show that Keff in PWR assembly with BPs are very small compared with Keff of PWR assembly without BPs. This reduction in Keff is due to the ability of BPs to absorb neutrons (Galahom, 2016). In addition, HfB2 is burned out faster than other poisons and has the lowest value of keff at the first burnup steps that’s due to the presence of two high absorption cross section nuclides Hf and B-10 that converts to B-11 by neutron capture so that core life time decreased than other cases. Pyrex has a slightly higher value of keff, so that’s a useful decision for using as BPRs. 4.2.3. The reactivity variation with burnup at different cases of BPs The aim of this section is to evaluate the effect of using BPs on suppressing the reactivity of reactor. In general, the presence of any of the BPRs has a negative effect on the reactivity of the assembly. This effect changes from material to other according to their thermal neutron absorption. The reactivity decreases with the burnup due to the reduction of the fissile material (Galahom, 2017). Dependent upon calculations, reactivity results at BOC, MOC and EOC are tabulated in Table 6. Using Hafnium Diboride gives the highest negative reactivity at both BOC and EOC because of their large cross section and their presence in 24 guide tube location which increasing their concentration in the assembly. Reactivity gives a prediction about neutron population over time and the deviation from criticality case of reactor (DOE-HDBK, 0000).
q¼
keff 1 keff
ð1Þ
From Eq. (1) we can note that q has a positive or negative value of reactivity. This value differs from one material to another based on the thermal neutron absorption cross section and the concentration of the poison on the assembly. 4.2.4. The fuel composition (Actinides and fission Products). Atom densities of fission products and actinides for the different cases of BPs with respect to fuel burnup are presented for Vera assembly. U-235 depleted during the operation of reactor and its concentration decreases. Fissile product Pu-239 is produced after capturing neutron by U-238 which converts to Np-239 then to Pu-239. Some fission products can affect on the neutrons economy by absorbing neutrons. The presence of BAs during depletion process hardens the neutron spectrum, resulting in lower 235U depletion and higher production of fissile plutonium isotopes.
Fig. 2. Multiplication factor variation with burnup at different cases of IBAs.
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Fig. 3. Multiplication factor variation with burnup at different cases of IBAs.
Fig. 4. Multiplication factor variation with burnup at different cases of BPRs.
Table 6 Reactivity values with fuel burnup. case
Reactivity BOC
MOC
EOC
Without poisons Gd 12 Gd 24 Er 12 Er 24 IFBA (Zrb2) 68 IFBA (Zrb2) 88 Lu2o3 (natural) 68 Lu2o3 (enriched) 68 Lu2o3 (enriched) 88 Pao2 68 Pao2 88 Pyrex 12 Pyrex 24 WABA 12 WABA24 Hfb2 12 Hfb2 24
0.148 0.038 0.086 0.125 0.102 0.078 0.048 0.129 0.068 0.037 0.126 0.119 0.058 0.032 0.060 0.027 0.061 0.246
0.003 0.019 0.026 0.013 0.018 0.122 0.159 0.034 0.147 0.202 0.036 0.042 0.085 0.148 0.083 0.148 0.281 0.535
0.127 0.176 0.182 0.170 0.170 0.285 0.307 0.196 0.314 0.347 0.197 0.200 0.222 0.268 0.223 0.270 0.522 0.872
The simultaneous increase in plutonium production and decrease in fission of 235U may increase the reactivity of the fuel at discharging and beyond. An assembly exposed to BAs may have a higher reactivity for a given burnup than that has not. Fission products actinides concentrations differ according to BAs types. BAs that have large thermal neutron absorption cross section, decrease fission process in the core, i.e. consume less fissile materials 235U (Galahom, 2016). Analysis of the comparison for the concentration of U-235 for the different poisons with fuel burnup is shown in Fig. 5. At BOC, U-235 has 7.181E-04 atoms/barn*cm for all cases which indicate that fuel enriched with 3.7% U-235.At EOC, Pyrex that replace the guide tube has the largest value of U-235 atom densities with 6.026E-05and the smallest value for using enriched Lu2O3 with 1.241E-05. Fig. 6 shows the depletion of U-238 during the burnup process which indicates the small depletion of U-238; the atom density at the beginning of cycle is 2.215E-02 and becomes 2.106E-02 at EOC for the HFB2-24 case (the highest value), in case of Lu2O3 it is 2.073E-02 (the lowest value).
S.M. Reda et al. / Annals of Nuclear Energy 141 (2020) 107354
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Fig. 5. Variation of U-235 concentration for different cases with burnup.
Fig. 6. Variation of U-238 concentration for different cases with burnup.
The production of fissile product Pu-239 is given in Fig. 7. There is no Plutonium in core at BOC but its concentration increases with burnup due to the transmutation process of U-238. At the EOC, Using Pyrex gives the largest value for Pu production with
1.456E-04 and HFb2 has the lowest value 8.722E-05. Pyrex-24 has the highest value for Np-237 production at the EOC with 1.903E-05 but Hfb2 has the smallest value with 1.515E-05 as portrayed in Fig. 8.
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Fig. 7. Variation of Pu-239 concentration for different cases with burnup.
Fig. 8. Variation of Np-237 concentration for different cases with burnup.
4.3. Beginning of life calculations eff
Physical parameters of PWR assembly were simulated by using MCNPX Code. Both KCODE and KSRC cards were used to calculate Keff at beginning of cycle by using both delayed and prompt neutrons. KCODE simulations were performed using 500 cycles with 10,000 particles. The second calculation was the delayed neutron fraction ßeff.
¼
K eff kprompt beff
ð2Þ
From Eq. (2), kprompt is the effective multiplication factor when only prompt neutrons are carried out by using TOTNU card and set its value to NO (Compton, 2015). Table 7 summarizes the results for Keff and ßeff for the different cases of BPs. The result of the comparative calculations shows that Lu2O3 in the natural form and
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S.M. Reda et al. / Annals of Nuclear Energy 141 (2020) 107354 Table 7 Beginning of life calculations for two factors (Keff, ßeff). Case
keff
ßeff
Gd12 Gd24 Er 12 Er 24 IFBA 68 IFBA 88 lu 68 (nat) lu 68 (enr) lu 88 (enr) pa 68 pa 88 Pyrex 12 Pyrex 24 WABA 12 WABA 24 hfb2 12 hfb2 24
1.04747 0.92671 1.15032 1.12126 1.09139 1.05556 1.1568 1.08114 1.04376 1.15177 1.14338 1.0696 0.97686 1.06468 0.98037 0.94743 0.80576
0.007303312 0.006960106 0.006685096 0.006349999 0.006844483 0.006337868 0.006396957 0.007445844 0.0066682 0.006806915 0.007075513 0.006881077 0.006920132 0.007213435 0.005946734 0.007219531 0.007458797
HFB2 have the largest and smallest values for keff respectively. However, HFB2 and WABA 24 have the highest and smallest values for ßeff respectively. 4.4. Pin power distribution at (BOC-EOC) Maximum power distribution and minimum power distribution at the beginning of cycle and at the end of cycle are listed in Table 8. The results showed that at the BOC using Lu2O3 enriched (88 rod) gives the highest value but gadolinium with 12 rod has the lowest value. Also, at the EOC, Lu2O3 enriched (68 rod) gives the maximum and minimum value for power distribution. 5. Conclusion and recommendations The neutronic analysis and burnup calculations for PWR assembly using different burnable absorbers are investigated using MCNPX Code. The results are given briefly in the following conclusions: The results obtained by MCNPX are infinite multiplication factor and Pin by Pin power distribution for the modeled PWR assembly show a good agreement with keno code from Vera core physics benchmark.
Erbium is more effective than Gadolinium as IBAs that mixed with Uranium fuel. Therefore, the applicable trend is favorable for PWRs fueled with UO2-Er2O3 which increases the core life time. Protactinium Oxide is more effective than Integral Fuel Burnable Absorber (IFBA) and Lutetium oxide as IBAs that are coating the outer surface of fuel rod. So, PWR assemblies modeled with UO2 rods surrounded by Protactinium oxide layers is preferable in nuclear reactor applications because they maintain criticality (Keff = 1) at longer periods (approximately 422 days) of reactor operation. In contrast to ZrB2 layers, criticality is maintained for shorter periods (nearly 211 days). Hafnium Diboride gives a high negative reactivity compared with other burnable poisons at BOC and EOC. That’s may be due to the presence of two high absorption cross section nuclides Hf and B-10 (that converts to B-11 by neutron capture) so that core life time decreased than other cases. Moreover, Pyrex has a slightly higher value of keff, so using it guarantees the safe operation of reactor. it is considered one of the models that could be applicable in nuclear reactor applications. Fuel compositions are investigated and the results show that U235 and U-238 concentrations decreases with burnup and Pu239 and Np-237 concentrations increase with fuel depletion. Finally, at the beginning of life calculations, two factors (keff and ßeff) are evaluated and the comparative calculations show that HfB2 has the smallest value for Keff and largest value for ßeff. During the cycle (BOC, EOC) maximum and minimum value for pin by pin power distribution are determined for the different cases. The large value of ßeff increases safety. CRediT authorship contribution statement Sonia M. Reda and S. S. Mustafa shared the presented idea. Nourhan A. khawas and Sonia M. Reda carried out the calculations and wrote the manuscript. All authors discussed the results. Sonia M. Reda and S. S. Mustafa revised the manuscript. Sonia M. reda supervised the findings of this work. Sonia M. reda and Nourhan A. Elkhawas authors contributed to the final version of the manuscript. Sonia M. reda followed up the publication. Declaration of Competing Interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
Table 8 Pin by Pin power distribution values during the cycle. Case
Without poisons Gd12 Gd24 Er 12 Er 24 IFBA 68 IFBA 88 lu 68 (nat) lu 68 (enr) lu 88 (enr) pa 68 pa 88 Pyrex 12 Pyrex 24 WABA 12 WABA 24 hfb2 12 hfb2 24
BOC
EOC
MAX
MIN
MAX
MIN
1.0489 1.1156 1.2094 1.0514 1.0659 1.2549 1.3829 1.0943 1.2960 1.4651 1.1004 1.0926 1.0442 1.1458 1.0398 1.1474 1.1201 1.1468
9.4139E01 2.1714E01 2.4685E01 8.7781E01 8.8948E01 4.0196E01 4.0617E01 8.3103E01 2.9376E01 2.9435E01 8.1324E01 8.6445E01 9.3026E01 9.120E01 9.3384E01 9.1107E01 9.0781E01 8.7564E01
1.05201 1.0463 1.0607 1.0430 1.0626 1.1539 1.1301 1.0704 1.1789 1.1754 1.0778 1.0633 1.0481 1.1324 1.04371 1.1222 1.0846 1.1095
9.3795E01 8.9985E01 9.1302E01 9.3892E01 8.7828E01 6.4048E01 7.3198E01 8.8978E01 5.4670E01 6.1425E01 8.7256E01 9.2111E01 9.4056E01 9.2163E01 9.3528E01 9.3296E01 9.1837E01 9.1616E01
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