Effect of Axial Burnup on Power Distribution and Isotope Inventory for a PWR Fuel Assembly

Effect of Axial Burnup on Power Distribution and Isotope Inventory for a PWR Fuel S. M. Reda a1 and E. A. Amin b (a) Physics Department, Faculty of Science, Zagazig University, Egypt (b) Nuclear and Radiological Regulatory Authority, Egypt Received: 22/9/2016 Accepted: 10/11/2016 ABSTRACT Axial burnup is an important factor in criticality safety and thermo-hydraulic calculation. In the present study, the effect of axial distribution of burnup on power distribution and isotope inventory were evaluated using combination of the WIMSD-5B and MCNP5 codes for PWR fuel rods assembly. The fuel rods of assembly were divided into 5, 8 and 10 zones. The system was normalized to the total thermal power 16.89172 MWth, which was derived using the fuel assembly load of 458.599 kg. The MCNP5 code has been used to perform three dimensional neutron physics analysis while WIMSD-5B was used for generation of number densities at various stages of fuel burnup. The results were compared with data from the Takahama-3 Benchmark. The calculated-to-experimental and previous calculated results for ratios of U-235, U-236, U-238 and many important nuclides show good agreement. Both results for the isotopic inventory and the power distribution emphasize the importance of considering the axial variation of burnup. Keywords: PWR axial power/ Axial power distribution/ PWR burnup/ PWR fuel/ MCNP power calculations INTRODUCTION As fuel is burned in a reactor, the burnup of the fuel becomes distributed axially and the reactivity of the fuel decreases. The profile of this axial distribution attains a flattened cosine shape with time, although the exact profile varies significantly with operating history and other effects unique to the individual reactor and fuel assembly. The cosine shape is representative of typical burnup profiles, which shows that the ends of the fuel are less burned than the central region. The ends of the fuel can create positive reactivity relative to the central region, hence the term end-effects (1). In reactor calculations, the same isotopic composition is usually considered axially for the fuel assembly. When the uniform axial isotopic distribution is assumed, the most reactive region of the element is the mean axial plane (2). The dynamics of reactors operations result in non-uniform axialburnup profiles in fuel with any significant burnup (3). In the present work the effect of considering different isotopic compositions for different axial segments is considered with the aim to show the effect of the axial divisions on both power distribution and isotopic inventory. Simulation of the Takahama-3 benchmark assembly is used in the present study. Takahama-3 reactor is a burnup benchmark experiment that can be used to validate codes and burnup calculation techniques. It is a PWR operated by Kansai Electric Power Company of Japan. The irradiation examinations were carried out on two of 157 (17x17 fuel rods) assemblies. Each of the fuel assemblies contains 248 UO 2 rods at 4.1% U-235 enriched, 16 UO 2 -Gd 2 O 3 rods at 2.6% U-235 enriched containing 6% Gd 2 O 3 and 25 control rods guide tubes (4-6). The Takahama-3 assay data and the results of the benchmark studies have potentially important implications for burnup credit in the United States (7). These data have been applied to benchmark the isotopic predictions using the SCALE 4.4a and HELIOS-I.6 code systems (8). A coupled neutronics-thermal hydraulics calculation was carried out to analyze the axial power distribution of the Europe High Performance Light Water Reactor (EHPLWR) fuel assembly (9). The result of this work showed that the axial power distribution of the EHPLWR fuel assembly does not 1 Corresponding author e-mail: sonreda@yahoo.com 123

follow the cosine shape when the burn-up is not taken into account. There were two peaks, the larger one is close to the lower part and the smaller one is close to the upper part of the fuel. Another analysis was carried out with a self-developed Thermohydraulics (T/H) code and MCNP code (10). Only the active part of the fuel assembly is taken into consideration and the result showed that only one power peak which is close to the bottom of the fuel assembly. Furthermore, these results indicated that not only the burnup but also the enrichment has a great influence on the power profile of the EHPLWR fuel assembly. Another study was carried out to analyze the axial power distribution of the SCWR-CANDU fuel assembly (11). The result shows that the density change of the water has little effect on the axial power distribution of the fuel assembly. The power profile follows the cosine shape approximately. The CFX 13.0 code and MCNP4C code were coupled for the axial power distribution analysis of the super critical water reactor assembly (12). The density change effect of the water is taken into account. The burn-up and enrichment of the fuel assembly were not taken into consideration. Moreover, the power distribution was not affected by changing the water density. Monte Carlo burnup simulations are important tools for reference calculations concerning core properties during normal operation (13-16). One of the methods that can give an accurate enough result for problems, involving burnup dependent number densities when using Monte Carlo based codes, is employing lattice codes. These codes like WIMS (17) can be used in conjunction with Monte Carlo codes. Such lattice codes can generate burnup dependent number density values for an equivalent unit cell representative of full geometry (18). In this work, the fuel rods of assembly were divided into 5, 8 and 10 zones. The system was normalized to the total thermal power 16.89172 MWth, which was derived using the fuel assembly load of 458.599 kg. The MCNP5 code has been used to perform three dimensional neutron physics analysis while WIMSD-5B was used for generation of number densities at various stages of fuel burnup. Calculations for the atomic densities of most isotopes of Uranium, Neptunium, Plutonium, Americium, Curium and some fission products were performed. The results were compared with measured and calculated SF95 fuel rod (8) and other two published results (5,7). MATERIAL AND METHODS Monte Carlo burnup simulation for Takahama-3, PWR 17x17 fuel rods assembly, was performed to study the effect of dividing the assembly fuel rods axially in to number of zones on the axial assembly power distribution. The methodology includes dividing the fuel rod into 5, 8, and 10 equal parts. The isotopic inventories for all important isotopes are determined up to 385-day irradiation. The simulation of the assembly performed by MCNP5 is done in full details with different divisions of the axial direction as mentioned earlier in one, five, eight and ten equal segments. The code WIMSD-5B delivers the isotopic inventory for the irradiation level of each segment. UO 2 Fig. (1): UO 2 fuel pin cells model 124

In the WIMSD-5B calculations of both the PWR UO 2 and UO 2 -Gd 2 O 3 fuel rods of the Takahama-3 burnup benchmark are simulated by a simple infinite fuel pin cell model as shown in figure (1) (for UO 2 bin). The main takahama-3 information is given in table (1). The pin irradiation according to UO 2 fuel rod (SF95) of the Takahama-3 burnup benchmark is illustrated in Table (2). Our results of UO 2 fuel bin were compared those of SF95 fuel rod results (Table 7). The MCNP5 fuel rod assembly model is illustrated in Figure (2). The atomic number densities shown in Table (3) refer to the fresh fuels used in power profile calculation at zero burnup. Important nuclides are those that directly or indirectly affect notably the result of a burnup calculation. In the simulations, it was assumed that all the nuclides which the mass fraction or atomic fraction or fission fraction or absorption fraction is higher than 10-4 are important according to Dalle, 2009 (7). The assembly power distribution was performed for each considered case with 0 and after 385 day burnup. In each case, the fuel rods were divided into equal lengths intervals. The irradiation distributions for each case are shown in Tables (4 to 6). The high precision of obtained parameters was assured by performing simulation with 100 inactive and 200 active cycles of 15E+4 neutrons, which gives 45E+6 particle histories. The particle histories are greater than 20E+6, a value recommended by Kepisty and Cetnar (2015) (15). Under these conditions, the relative error of tallies is much below 0.01%, which is sufficient for reliable Monte Carlo simulations. UO 2 fuel rods UO2-Gd2O3 fuel rods Position of Control Rod (fill with coolant) Fig. (2):17 x 17 fuel rods assembly 125

Table (1): Takahama-3 information Total No. of Uranium Reactor Power Uranium Power(MW) Mass (ton) Power (M) (MW) Mass (ton) 2652 157 72 36.8333 16.89171975 0.458599 Table (2). Burnup distributions for the UO 2 fuel rod (SF95) Distance on Z-axis from fuel top (cm) Sample ID From to 1 109.8 183 SF95-1 14.30 2 36.6 109.8 SF95-2 24.35 3-36.6 36.6 SF95-3 35.52 4-109.8-36.6 SF95-4 36.69 5-183 -109.8 SF95-5 30.40 Z- axis intervals Table (3): Atomic densities of the assembly materials Material Isotope Atomic densities (Atoms/barn.cm) Material Isotope Burnup (GWd/MTU) Atomic densities (Atoms/barn.cm) UO2 UO2-Gd2O3 U-234 9.1361e-06 U-234 4.2940e-06 U-235 9.3472e-04 U-235 5.6226e-04 U-238 2.1523e-02 U-238 2.0549e-02 O-16 4.4935e-02 Gd-154 4.6173e-05 Borated water Gd-155 2.9711e-04 H-1 4.8132e-02 Gd-156 4.1355e-04 O-16 2.4066e-02 Gd-157 3.1518e-04 B-10 3.6487e-06 Gd-158 4.9786e-04 B-11 1.4686e-05 Gd-160 4.3764e-04 Zircaloy-4 O16 4.5243e-02 Cr - natural 7.5891e-05 Fe - natural 1.4838e-04 Zr - natural 4.2982e-02 Table (4): Irradiation distributions for the five intervals Z- Intervals Interval Power (Pi) MW (Pfi)Power = (Pi)/Average assembly power Pfi *36.8333 (MWd/ton) Irradiation (GWd/MTU) UO2 1 3.036 0.899 33.102 12.744 2 3.398 1.006 37.046 14.263 3 3.966 1.172 43.171 16.621 4 3.323 0.984 36.227 13.947 5 3.009 0.891 32.801 12.628 UO2-Gd2O3 1 0.030 0.009 0.336 0.127 2 0.034 0.010 0.376 0.142 3 0.046 0.012 0.431 0.166 4 0.033 0.016 0.362 0.139 5 0.030 0.009 0.328 0.126 Total Power = 16.892 MW, Average Power = 3.378 MW 126

Table (5): Irradiation distributions for the 8 intervals Z- Intervals Interval Power (Pi) MW (Pfi)Power = (Pi)/Average assembly power 127 Pfi *36.8333 (MWd/ton) Irradiation (GWd/MTU) UO2 1 1.318 0.624 22.98705 8.850 2 1.813 0.859 31.62307 12.175 3 2.246 1.064 39.17464 15.082 4 2.689 1.274 46.91024 18.060 5 2.797 1.325 48.8004 18.788 6 2.450 1.161 42.74656 16.457 7 2.079 0.985 36.26629 13.963 8 1.332 0.631 23.24332 8.949 UO2-Gd2O3 1 0.013171 0.006 0.230 0.088 2 0.018136 0.009 0.316 0.122 3 0.022482 0.011 0.392 0.151 4 0.026859 0.013 0.469 0.180 5 0.027966 0.013 0.488 0.188 6 0.024442 0.012 0.426 0.164 7 0.020748 0.010 0.362 0.139 8 0.013301 0.006 0.232 0.089 Total Power = 16.892 MW, Average Power = 2.111 MW Table (6): Irradiation distributions for the 10 intervals Z- Intervals Interval Power (Pi) MW (Pfi)Power = (Pi)/Average assembly power Pfi *36.8333 (MWd/ton) Irradiation (GWd/MTU) UO2 1 0.447 0.264 9.737 3.749 2 1.166 0.690 25.427 9.789 3 1.792 1.061 39.066 15.040 4 2.239 1.326 48.832 18.800 5 2.480 1.468 54.089 20.824 6 2.534 1.500 55.258 21.274 7 2.354 1.394 51.336 19.764 8 1.925 1.139 41.967 16.157 9 1.291 0.764 28.148 10.837 10 0.497 0.294 10.837 4.172 UO2-Gd2O3 1 0.005 0.003 0.098 0.0377 2 0.012 0.007 0.254 0.0977 3 0.018 0.011 0.389 0.150 4 0.022 0.013 0.486 0.187 5 0.025 0.015 0.540 0.208 6 0.025 0.015 0.551 0.212 7 0.024 0.014 0.514 0.198 8 0.019 0.011 0.418 0.161 9 0.013 0.008 0.280 0.108 10 0.005 0.003 0.109 0.041 Total Power = 16.892 MW, Average Power = 1.689 MW

RESULTS AND DISCUSSION PWR UO 2 fuel rod of the Takahama-3 burnup benchmark (SF95) was simulated by combination of MCNP5 and WIMSD-5B. The comparison of calculated current results with experimental (C/E) and calculations of Takahama-3 fuel rod (SF95) and another two references (5,7) is illustrated in Table (7). The reported results in Table 7 for all isotopes are given as discharge values (immediately after irradiation). The experimental results for Pu-239 included Np-239 (decay parent) because of the difficulty separating these actinides. Therefore, calculated values of Pu-239 plus Np- 239 were used for comparisons with the experimental values for Pu-239 (Table 7) according to Sanders and Gauld (2003) (8). The calculated-to-experimental ratios for U-235, U-236, U-238 and many important nuclides, listed in Table (7), show a good agreement in the range of ±10%. Similarly, the comparison with the average calculated results (5,7) shows a good agreement for most nuclides. Ratios for some isotopes as Pu-238, Pu-240, Am-242 and Cm-242 show a poor agreement more than ±10%, which indicated some significant discrepancies either in the formation or the destruction path of these isotopes. The different nuclear data libraries used in the supplementary benchmarking studies would be recommended to find source of the discrepancies in accordance of Oettingean and Cetnar (2014) (10). The difference in U-235 nuclide density remarked in the current calculation, in comparison to experimental and other codes calculations might be due to many reasons. This includes: detailed actinides decay chain and the different neutron cross section data libraries (14). The present WIMSD- 5B calculations use the WLUP WIMS library that is based on ENDF/V II. The measured values for the important nuclides in Table (7) were slightly higher than the calculated values, (less than ±10%) except for Pu-238. For Pu-238, the difference between the measured and calculated values was 20%. The reason for the higher values is presumed to be due to background contaminations from the point of view of Kihsoo et al., (2012) (19). As seen in Table (7), the average results are close to the experimental and previous calculated data. The difference between the measured and the calculated results using SAS2H or the Origen-2 code for the Pu isotopes in Takahama-3 reactor ranged from 13 15%. Some of the nuclide C/E ratios of both SCALE 4.4a and HELIOS-1.6 codes were improved compared to earlier results, including those for Cs-134 and Eu-254 (8). Nevertheless, the isotopic data which are widely used to validate the codes and data used for predicting isotopic compositions in spent fuel are generally available only for specific fuel rods (20, 21, 22, 7) and not for the assembly average (20). 128

Table (7): Comparison of current results with experimental (C/E) and calculated results of Takahama-3 SF95 fuel rod and another two references (5,7) Burnup 14.3 24.4 35.4 36.7 30.4 Current (GWd/ton) Average Nuclide C/E C/E C/E C/E C/E C/M Average Takahama (SAS2H) (8) Average Takahama (HEMOS) (8) Average C/E (Dalle 2009) (7) Average C/E (Suyama et al 2002) (5) 234 U 1.137 1.039 1.351 1.326 0.961 1.16 1.12 0.95 1.11 1.04 235 U 1.017 1.033 1.018 1.049 1.049 1.03 0.99 1.01 0.99 1.02 236 U 0.913 0.910 0.945 0.946 0.929 0.93 0.99 0.99 0.98 0.94 238 U 1.002 1.005 1.008 1.007 1.006 1.01 1.00 1.00 1.00 1.00 238 Pu 0.733 0.697 0.832 0.875 0.853 0.80 0.94 0.98 0.78 0.85 239 Pu 0.895 0.890 0.919 0.953 0.970 0.93 0.99 1.04 0.95 1.02 240 Pu 0.845 0.806 0.874 0.897 0.88 0.86 1.02 1.01 1.02 1.01 241 Pu 1.038 0.901 0.875 0.907 0.963 0.94 0.96 1.01 0.89 0.98 242 Pu 0.974 0.879 0.90 0.912 0.951 0.92 1.02 0.93 0.88 0.94 241 Am 0.362 0.811 1.160 1.710 1.042 1.02 1.14 1.16 0.76 1.16 242m Am 0.308 0.517 0.743 0.845 0.775 0.64 1.05 1.02 ND ND 243 Am 0.757 0.808 0.889 0.940 0.952 0.87 1.13 0.98 0.93 0.89 242 Cm 0.400 0.503 0.570 0.524 0.743 0.55 0.66 0.83 0.53 0.68 243 Cm 0.236 0.360 0.551 0.581 0.493 0.44 0.75 0.79 0.46 0.60 244 Cm 0.586 0.589 0.742 0.783 0.849 0.71 0.96 0.91 0.80 0.76 134 Cs 0.926 0.820 0.798 0.802 0.839 0.80 0.85 0.80 0.81 0.88 137 Cs 0.981 0.955 0.958 0.950 0.967 0.96 0.99 0.97 0.91 0.98 154 Eu 0.801 0.763 0.796 0.802 0.842 0.80 0.96 1.05 0.89 0.80 125 Sb 2.128 1.845 2.071 2.515 2.039 2.12 2.05 2.65 ND ND 106 Ru 1.221 1.195 1.118 1.121 1.059 1.14 1.15 1.13 ND ND 143 Nd 0.972 0.967 0.964 0.975 0.977 0.97 0.98 0.98 0.88 0.97 145 Nd 0.983 0.979 0.985 0.984 0.980 0.98 0.81 0.99 0.97 1.00 129

The full Takahama-3 assembly was simulated by MCNP5 to estimate the power distribution at 0 and after 385-day burnup. The power calculations have been done by f4 tally for average neutron flux with 45 million nps. The isotopes atomic densities (g/mgu) for 5, 8 and 10 sections assembly, UO 2 and UO 2 -Gd2O 3 fuel rods are illustrated in Tables (8 to 13). The tabulated data show that the 235 U, 238 U, 155 Gd and 157 Gd isotopes have the same average atomic densities in all 5, 8 and 10 axial zones for UO 2 and UO 2 -Gd2O 3. Table (8): Isotopes Atomic density (g/mgu) for 5 sections UO 2 fuel rods assembly Sections Section 1 Section 2 Section 3 Section 4 Section 5 Burnup (GWd/ton) Nuclide 12.744 14.263 16.621 13.947 12.628 Average Over the five sections 234 U 3.44E+02 3.36E+02 3.27E+02 3.39E+02 3.45E+02 3.37E+02 235 U 2.84E+04 2.72E+04 2.52E+04 2.74E+04 2.85E+04 2.74E+04 236 U 2.23E+03 2.46E+03 2.79E+03 2.41E+03 2.21E+03 2.42E+03 238 U 9.53E+05 9.52E+05 9.51E+05 9.52E+05 9.53E+05 9.52E+05 237 Np 9.85E+01 1.16E+02 1.45E+02 1.12E+02 9.72E+01 1.14E+02 239 Np 6.70E+01 7.11E+01 7.13E+01 7.04E+01 6.13E+01 6.82E+01 238 Pu 9.53E+00 1.29E+01 1.92E+01 1.21E+01 9.30E+00 1.26E+01 239 Pu 3.53E+03 3.83E+03 4.22E+03 3.77E+03 3.51E+03 3.77E+03 240 Pu 5.80E+02 6.78E+02 8.33E+02 6.57E+02 5.73E+02 6.64E+02 241 Pu 3.02E+02 3.60E+02 4.62E+02 3.48E+02 2.98E+02 3.54E+02 242 Pu 2.55E+01 3.64E+01 5.69E+01 3.39E+01 2.48E+01 3.55E+01 241 Am 3.51E+00 4.88E+00 7.36E+00 4.58E+00 3.42E+00 4.75E+00 242m Am 3.77E-02 5.61E-02 9.16E-02 5.19E-02 3.65E-02 5.47E-02 243 Am 1.25E+00 2.13E+00 4.18E+00 1.92E+00 1.19E+00 2.14E+00 242 Cm 3.83E-01 6.04E-01 1.08E+00 5.53E-01 3.69E-01 5.97E-01 243 Cm 1.94E-03 3.64E-03 8.01E-03 3.22E-03 1.84E-03 3.73E-03 244 Cm 8.61E-02 1.70E-01 4.12E-01 1.49E-01 8.14E-02 1.80E-01 154 Gd 6.67E-02 9.34E-02 1.49E-01 8.73E-02 6.49E-02 9.23E-02 155 Gd 1.46E-02 1.59E-02 1.95E-02 1.56E-02 1.46E-02 1.60E-02 156 Gd 2.94E+00 3.43E+00 4.26E+00 3.33E+00 2.90E+00 3.37E+00 157 Gd 3.57E-02 3.74E-02 4.09E-02 3.70E-02 3.60E-02 3.74E-02 158 Gd 2.37E+00 2.81E+00 3.56E+00 2.72E+00 2.34E+00 2.76E+00 106 Ru 4.76E+01 5.45E+01 6.54E+01 5.31E+01 4.71E+01 5.35E+01 125 Sb 2.79E+00 3.14E+00 3.69E+00 3.07E+00 2.76E+00 3.09E+00 134 Cs 1.76E+01 2.19E+01 2.92E+01 2.10E+01 1.73E+01 2.14E+01 137 Cs 4.75E+02 5.32E+02 6.20E+02 5.21E+02 4.71E+02 5.24E+02 143 Nd 4.09E+02 4.52E+02 5.15E+02 4.43E+02 4.06E+02 4.45E+02 145 Nd 2.95E+02 3.28E+02 3.78E+02 3.21E+02 2.92E+02 3.23E+02 154 Eu 2.64E+00 3.42E+00 4.77E+00 3.25E+00 2.58E+00 3.33E+00 130

Table (9): Isotopes Atomic density (g/mgu) for 5 sections UO 2 -Gd 2 O 3 fuel rods assembly Sections Section 1 Section 2 Section 3 Section 4 Section 5 Burnup (GWd/ton) Nuclide 12.744 14.263 16.621 13.947 12.628 Average Over the five sections 234 U 1.87E+02 1.87E+02 1.87E+02 1.87E+02 1.87E+02 1.87E+02 235 U 2.46E+04 2.46E+04 2.46E+04 2.46E+04 2.46E+04 2.46E+04 236 U 3.19E+01 3.58E+01 4.17E+01 3.50E+01 3.18E+01 3.52E+01 238 U 9.16E+05 9.16E+05 9.16E+05 9.16E+05 9.16E+05 9.16E+05 237 Np 3.40E-01 4.22E-01 5.64E-01 4.05E-01 3.37E-01 4.14E-01 239 Np 1.57E+02 1.67E+02 1.80E+02 1.65E+02 1.56E+02 1.65E+02 238 Pu 8.73E-04 1.22E-03 1.91E-03 1.14E-03 8.59E-04 1.20E-03 239 Pu 9.21E+01 1.12E+02 1.44E+02 1.08E+02 9.13E+01 1.09E+02 240 Pu 5.80E-01 7.32E-01 1.00E+00 7.00E-01 5.74E-01 7.17E-01 241 Pu 1.32E-02 1.86E-02 2.96E-02 1.74E-02 1.30E-02 1.83E-02 242 Pu 1.06E-05 1.68E-05 3.13E-05 1.54E-05 1.04E-05 1.69E-05 241 Am 1.46E-06 2.32E-06 4.31E-06 2.12E-06 1.43E-06 2.33E-06 242m Am 5.97E-10 1.06E-09 2.30E-09 9.48E-10 5.81E-10 1.10E-09 243 Am 1.28E-08 2.27E-08 4.94E-08 2.03E-08 1.24E-08 2.35E-08 242 Cm 3.49E-09 6.21E-09 1.35E-08 5.55E-09 3.39E-09 6.43E-09 243 Cm 8.31E-13 1.46E-12 3.40E-12 1.30E-12 8.11E-13 1.56E-12 244 Cm 3.31E-11 6.54E-11 1.66E-10 5.74E-11 3.20E-11 7.07E-11 154 Gd 1.33E+03 1.33E+03 1.33E+03 1.33E+03 1.33E+03 1.33E+03 155 Gd 8.46E+03 8.44E+03 8.42E+03 8.45E+03 8.46E+03 8.45E+03 156 Gd 1.22E+04 1.22E+04 1.23E+04 1.22E+04 1.22E+04 1.22E+04 157 Gd 8.88E+03 8.83E+03 8.76E+03 8.84E+03 8.88E+03 8.84E+03 158 Gd 2.81E+04 2.81E+04 2.82E+04 2.81E+04 2.81E+04 2.81E+04 106 Ru 5.62E-01 6.31E-01 7.37E-01 6.17E-01 5.59E-01 6.21E-01 125 Sb 2.53E-02 2.84E-02 3.32E-02 2.78E-02 2.52E-02 2.80E-02 134 Cs 7.80E-03 9.77E-03 1.33E-02 9.36E-03 7.71E-03 9.58E-03 137 Cs 4.50E+00 5.05E+00 5.89E+00 4.94E+00 4.48E+00 4.97E+00 143 Nd 4.15E+00 4.64E+00 5.42E+00 4.54E+00 4.12E+00 4.57E+00 145 Nd 2.96E+00 3.31E+00 3.86E+00 3.24E+00 2.94E+00 3.26E+00 154 Eu 1.12E-03 1.40E-03 1.91E-03 1.34E-03 1.10E-03 1.37E-03 131

Table (10): Isotopes Atomic density (g/mgu) for 8 zones UO 2 fuel rods assembly Sections Section 1 Section 2 Section 3 Section 4 Section 5 Section 6 Section 7 Section 8 Average over the eight sections Burnup (GWd/ton) 8.949 13.962 16.457 18.788 18.060 15.082 12.175 8.850 Nuclide 234 U 3.60E+02 3.38E+02 3.27E+02 3.17E+02 3.20E+02 3.33E+02 3.46E+02 3.60E+02 3.37E+02 235 U 3.17E+04 2.73E+04 2.53E+04 2.35E+04 2.40E+04 2.64E+04 2.88E+04 3.18E+04 2.74E+04 236 U 1.67E+03 2.44E+03 2.79E+03 3.10E+03 3.00E+03 2.60E+03 2.18E+03 1.65E+03 2.43E+03 238 U 9.54E+05 9.52E+05 9.51E+05 9.49E+05 9.50E+05 9.51E+05 9.53E+05 9.54E+05 9.52E+05 237 Np 5.81E+01 1.12E+02 1.43E+02 1.73E+02 1.64E+02 1.26E+02 9.18E+01 5.72E+01 1.16E+02 239 Np 6.51E+01 6.99E+01 7.18E+01 7.38E+01 7.27E+01 7.11E+01 6.79E+01 6.14E+01 6.92E+01 238 Pu 4.02E+00 1.25E+01 1.90E+01 2.66E+01 2.41E+01 1.52E+01 8.83E+00 3.91E+00 1.43E+01 239 Pu 2.89E+03 3.94E+03 4.34E+03 4.65E+03 4.56E+03 4.13E+03 3.61E+03 2.86E+03 3.87E+03 240 Pu 3.68E+02 6.87E+02 8.57E+02 1.02E+03 9.68E+02 7.63E+02 5.68E+02 3.62E+02 6.99E+02 241 Pu 1.38E+02 3.35E+02 4.48E+02 5.60E+02 5.25E+02 3.84E+02 2.59E+02 1.35E+02 3.48E+02 242 Pu 7.78E+00 3.26E+01 5.32E+01 7.79E+01 6.96E+01 4.11E+01 2.13E+01 7.49E+00 3.88E+01 241 Am 1.12E+00 4.40E+00 6.94E+00 9.81E+00 8.86E+00 5.47E+00 2.95E+00 1.07E+00 5.08E+00 242m Am 9.79E-03 5.04E-02 8.56E-02 1.27E-01 1.13E-01 6.49E-02 3.14E-02 9.36E-03 6.15E-02 243 Am 2.60E-01 1.99E+00 3.97E+00 6.80E+00 5.80E+00 2.76E+00 1.09E+00 2.46E-01 2.86E+00 242 Cm 8.70E-02 5.41E-01 1.00E+00 1.60E+00 1.40E+00 7.25E-01 3.16E-01 8.29E-02 7.19E-01 243 Cm 3.03E-04 3.35E-03 7.58E-03 1.42E-02 1.18E-02 4.94E-03 1.65E-03 2.84E-04 5.52E-03 244 Cm 1.22E-02 1.65E-01 4.06E-01 8.21E-01 6.67E-01 2.52E-01 7.59E-02 1.14E-02 3.01E-01 154 Gd 2.36E-02 9.10E-02 1.51E-01 2.25E-01 2.00E-01 1.15E-01 5.98E-02 2.28E-02 1.11E-01 155 Gd 1.01E-02 1.59E-02 1.97E-02 2.38E-02 2.25E-02 1.75E-02 1.36E-02 1.00E-02 1.66E-02 156 Gd 1.83E+00 3.36E+00 4.25E+00 5.15E+00 4.86E+00 3.75E+00 2.78E+00 1.81E+00 3.47E+00 157 Gd 3.01E-02 3.81E-02 4.14E-02 4.42E-02 4.34E-02 3.95E-02 3.55E-02 3.01E-02 3.78E-02 158 Gd 1.43E+00 2.75E+00 3.54E+00 4.36E+00 4.09E+00 3.10E+00 2.24E+00 1.40E+00 2.86E+00 106 Ru 3.15E+01 5.38E+01 6.55E+01 7.67E+01 7.32E+01 5.90E+01 4.56E+01 3.11E+01 5.46E+01 125 Sb 1.94E+00 3.10E+00 3.68E+00 4.23E+00 4.06E+00 3.36E+00 2.68E+00 1.92E+00 3.12E+00 134 Cs 9.15E+00 2.14E+01 2.91E+01 3.72E+01 3.46E+01 2.48E+01 1.66E+01 8.95E+00 2.27E+01 137 Cs 3.38E+02 5.25E+02 6.18E+02 7.05E+02 6.78E+02 5.67E+02 4.58E+02 3.34E+02 5.28E+02 143 Nd 3.01E+02 4.47E+02 5.14E+02 5.73E+02 5.55E+02 4.77E+02 3.96E+02 2.98E+02 4.45E+02 145 Nd 2.13E+02 3.23E+02 3.77E+02 4.25E+02 4.10E+02 3.48E+02 2.85E+02 2.10E+02 3.24E+02 154 Eu 1.33E+00 3.43E+00 4.84E+00 6.35E+00 5.85E+00 4.04E+00 2.57E+00 1.29E+00 3.71E+00 132

Table (11): Isotopes Atomic density (g/mgu) for 8 zones UO 2 -Gd 2 O 3 fuel rods assembly Sections Section 1 Section 2 Section 3 Section 4 Section 5 Section 6 Section 7 Section 8 Average over the eight sections Burnup (GWd/ton) 0.089 0.139 0.164 0.188 0.180 0.151 0.122 0.0885 Nuclide 234 U 1.87E+02 1.87E+02 1.87E+02 1.87E+02 1.87E+02 1.87E+02 1.87E+02 1.87E+02 1.87E+02 235 U 2.47E+04 2.46E+04 2.46E+04 2.46E+04 2.46E+04 2.46E+04 2.46E+04 2.47E+04 2.46E+04 236 U 2.25E+01 3.50E+01 4.12E+01 4.70E+01 4.52E+01 3.79E+01 3.06E+01 2.23E+01 3.52E+01 238 U 9.16E+05 9.16E+05 9.16E+05 9.16E+05 9.16E+05 9.16E+05 9.16E+05 9.16E+05 9.16E+05 237 Np 1.73E-01 4.05E-01 5.52E-01 7.09E-01 6.58E-01 4.71E-01 3.14E-01 1.70E-01 4.31E-01 239 Np 1.26E+02 1.65E+02 1.79E+02 1.90E+02 1.87E+02 1.72E+02 1.53E+02 1.25E+02 1.62E+02 238 Pu 3.09E-04 1.14E-03 1.84E-03 2.72E-03 2.42E-03 1.44E-03 7.71E-04 3.00E-04 1.37E-03 239 Pu 4.97E+01 1.08E+02 1.41E+02 1.76E+02 1.65E+02 1.23E+02 8.57E+01 4.89E+01 1.12E+02 240 Pu 2.83E-01 7.00E-01 9.78E-01 1.29E+00 1.18E+00 8.25E-01 5.32E-01 2.77E-01 7.58E-01 241 Pu 4.52E-03 1.74E-02 2.86E-02 4.29E-02 3.80E-02 2.22E-02 1.16E-02 4.39E-03 2.12E-02 242 Pu 2.56E-06 1.54E-05 2.99E-05 5.14E-05 4.37E-05 2.13E-05 8.97E-06 2.46E-06 2.20E-05 241 Am 3.53E-07 2.13E-06 4.11E-06 7.07E-06 6.01E-06 2.94E-06 1.24E-06 3.40E-07 3.02E-06 242m Am 1.01E-10 9.53E-10 2.17E-09 4.26E-09 3.48E-09 1.43E-09 4.84E-10 9.65E-11 1.62E-09 243 Am 2.16E-09 2.04E-08 4.66E-08 9.17E-08 7.49E-08 3.06E-08 1.04E-08 2.06E-09 3.49E-08 242 Cm 5.90E-10 5.57E-09 1.27E-08 2.50E-08 2.04E-08 8.35E-09 2.83E-09 5.61E-10 9.50E-09 243 Cm 2.69E-13 1.31E-12 3.18E-12 6.92E-12 5.47E-12 2.00E-12 6.88E-13 2.65E-13 2.51E-12 244 Cm 4.10E-12 5.77E-11 1.54E-10 3.47E-10 2.72E-10 9.34E-11 2.57E-11 3.87E-12 1.20E-10 154 Gd 1.33E+03 1.33E+03 1.33E+03 1.33E+03 1.33E+03 1.33E+03 1.33E+03 1.33E+03 1.33E+03 155 Gd 8.51E+03 8.45E+03 8.42E+03 8.39E+03 8.40E+03 8.43E+03 8.47E+03 8.51E+03 8.45E+03 156 Gd 1.22E+04 1.22E+04 1.23E+04 1.23E+04 1.23E+04 1.23E+04 1.22E+04 1.22E+04 1.22E+04 157 Gd 8.99E+03 8.84E+03 8.77E+03 8.69E+03 8.72E+03 8.81E+03 8.89E+03 8.99E+03 8.84E+03 158 Gd 2.79E+04 2.81E+04 2.82E+04 2.82E+04 2.82E+04 2.81E+04 2.80E+04 2.79E+04 2.81E+04 106 Ru 3.94E-01 6.17E-01 7.28E-01 8.35E-01 8.01E-01 6.69E-01 5.38E-01 3.90E-01 6.22E-01 125 Sb 1.78E-02 2.78E-02 3.28E-02 3.76E-02 3.61E-02 3.01E-02 2.43E-02 1.76E-02 2.80E-02 134 Cs 3.86E-03 9.35E-03 1.29E-02 1.69E-02 1.56E-02 1.10E-02 7.15E-03 3.78E-03 1.01E-02 137 Cs 3.17E+00 4.94E+00 5.82E+00 6.66E+00 6.39E+00 5.35E+00 4.32E+00 3.13E+00 4.97E+00 143 Nd 2.92E+00 4.55E+00 5.35E+00 6.12E+00 5.88E+00 4.92E+00 3.97E+00 2.89E+00 4.58E+00 145 Nd 2.08E+00 3.24E+00 3.82E+00 4.37E+00 4.19E+00 3.51E+00 2.83E+00 2.06E+00 3.26E+00 154 Eu 5.51E-04 1.34E-03 1.86E-03 2.43E-03 2.24E-03 1.57E-03 1.02E-03 5.40E-04 1.45E-03 133

Table (12): Isotopes Atomic density (g/mgu) for 10 zones UO 2 fuel rods assembly Sections Burnup (GWd/ton) Nuclide Section 1 Section 2 Section 3 Section 4 Section 5 Section 6 Section 7 Section 8 Section 9 Section 10 4.172 10.837 16.157 19.764 21.274 20.824 18.800 15.040 9.789 3.749 Average over the ten sections 234 U 3.81E+02 3.51E+02 3.28E+02 3.12E+02 3.06E+02 3.08E+02 3.16E+02 3.32E+02 3.55E+02 3.83E+02 3.37E+02 235 U 3.64E+04 3.00E+04 2.56E+04 2.28E+04 2.17E+04 2.21E+04 2.35E+04 2.63E+04 3.10E+04 3.68E+04 2.74E+04 236 U 8.41E+02 1.98E+03 2.75E+03 3.22E+03 3.40E+03 3.34E+03 3.10E+03 2.60E+03 1.81E+03 7.60E+02 2.38E+03 238 U 9.57E+05 9.53E+05 9.51E+05 9.49E+05 9.48E+05 9.48E+05 9.49E+05 9.51E+05 9.54E+05 9.57E+05 9.52E+05 237 Np 1.91E+01 7.82E+01 1.40E+02 1.87E+02 2.08E+02 2.02E+02 1.74E+02 1.26E+02 6.73E+01 1.63E+01 1.22E+02 239 Np 6.46E+01 6.83E+01 7.17E+01 7.41E+01 7.55E+01 7.47E+01 7.23E+01 6.89E+01 6.48E+01 6.15E+01 6.96E+01 238 Pu 6.40E-01 6.74E+00 1.83E+01 3.04E+01 3.67E+01 3.47E+01 2.68E+01 1.53E+01 5.21E+00 4.90E-01 1.75E+01 239 Pu 1.65E+03 3.43E+03 4.35E+03 4.80E+03 4.96E+03 4.91E+03 4.69E+03 4.18E+03 3.20E+03 1.50E+03 3.77E+03 240 Pu 1.10E+02 4.90E+02 8.42E+02 1.09E+03 1.19E+03 1.16E+03 1.02E+03 7.65E+02 4.22E+02 9.13E+01 7.19E+02 241 Pu 1.95E+01 2.07E+02 4.44E+02 6.19E+02 6.91E+02 6.70E+02 5.73E+02 3.94E+02 1.69E+02 1.45E+01 3.80E+02 242 Pu 4.74E-01 1.46E+01 5.06E+01 9.05E+01 1.11E+02 1.05E+02 7.85E+01 4.07E+01 1.04E+01 3.16E-01 5.02E+01 241 Am 7.17E-02 2.07E+00 6.72E+00 1.14E+01 1.36E+01 1.29E+01 1.00E+01 5.50E+00 1.49E+00 4.78E-02 6.38E+00 242m Am 3.64E-04 2.05E-02 8.17E-02 1.50E-01 1.84E-01 1.74E-01 1.30E-01 6.48E-02 1.39E-02 2.22E-04 8.19E-02 243 Am 7.22E-03 6.47E-01 3.65E+00 8.30E+00 1.11E+01 1.02E+01 6.79E+00 2.69E+00 4.03E-01 4.18E-03 4.38E+00 242 Cm 2.62E-03 1.95E-01 9.36E-01 1.93E+00 2.47E+00 2.30E+00 1.62E+00 7.14E-01 1.27E-01 1.56E-03 1.03E+00 243 Cm 4.17E-06 8.87E-04 6.85E-03 1.79E-02 2.52E-02 2.28E-02 1.42E-02 4.79E-03 5.07E-04 2.18E-06 9.32E-03 244 Cm 1.52E-04 3.97E-02 3.63E-01 1.06E+00 1.56E+00 1.39E+00 8.14E-01 2.46E-01 2.21E-02 7.80E-05 5.50E-01 154 Gd 2.46E-03 4.34E-02 1.45E-01 2.66E-01 3.31E-01 3.11E-01 2.29E-01 1.17E-01 3.20E-02 1.79E-03 1.48E-01 155 Gd 5.23E-03 1.21E-02 1.96E-02 2.60E-02 2.88E-02 2.80E-02 2.44E-02 1.81E-02 1.11E-02 4.73E-03 1.78E-02 156 Gd 6.92E-01 2.39E+00 4.17E+00 5.57E+00 6.21E+00 6.02E+00 5.18E+00 3.76E+00 2.08E+00 6.06E-01 3.67E+00 157 Gd 2.14E-02 3.39E-02 4.15E-02 4.58E-02 4.73E-02 4.69E-02 4.49E-02 4.05E-02 3.26E-02 2.03E-02 3.75E-02 158 Gd 4.97E-01 1.90E+00 3.47E+00 4.75E+00 5.33E+00 5.16E+00 4.39E+00 3.11E+00 1.64E+00 4.31E-01 3.07E+00 106 Ru 1.27E+01 4.01E+01 6.46E+01 8.18E+01 8.92E+01 8.70E+01 7.72E+01 5.93E+01 3.54E+01 1.12E+01 5.59E+01 125 Sb 8.68E-01 2.38E+00 3.62E+00 4.46E+00 4.81E+00 4.71E+00 4.24E+00 3.36E+00 2.14E+00 7.76E-01 3.14E+00 134 Cs 2.12E+00 1.34E+01 2.82E+01 4.07E+01 4.66E+01 4.48E+01 3.72E+01 2.47E+01 1.10E+01 1.71E+00 2.50E+01 137 Cs 1.59E+02 4.09E+02 6.07E+02 7.41E+02 7.97E+02 7.80E+02 7.05E+02 5.65E+02 3.70E+02 1.43E+02 5.28E+02 143 Nd 1.48E+02 3.58E+02 5.06E+02 5.97E+02 6.33E+02 6.22E+02 5.73E+02 4.76E+02 3.27E+02 1.34E+02 4.37E+02 145 Nd 1.02E+02 2.55E+02 3.70E+02 4.45E+02 4.75E+02 4.66E+02 4.25E+02 3.46E+02 2.32E+02 9.21E+01 3.21E+02 154 Eu 2.99E-01 2.06E+00 4.68E+00 7.04E+00 8.15E+00 7.81E+00 6.36E+00 4.03E+00 1.66E+00 2.39E-01 4.23E+00 134

Table (13): Isotopes Atomic density (g/mgu) for 10 zones UO 2 -Gd 2 O 3 fuel rods assembly Sections Section 1 Section 2 Section 3 Section 4 Section 5 Section 6 Section 7 Section 8 Section 9 Section 10 Average over the ten sections Burnup (GWd/ton) 0.042 0.108 0.161 0.198 0.212 0.208 0.187 0.150 0.098 0.038 Nuclide U 1.88E+02 1.87E+02 1.87E+02 1.87E+02 1.86E+02 1.86E+02 1.87E+02 1.87E+02 1.87E+02 1.88E+02 1.87E+02 235 U 2.47E+04 2.46E+04 2.46E+04 2.46E+04 2.46E+04 2.46E+04 2.46E+04 2.46E+04 2.47E+04 2.47E+04 2.46E+04 236 U 1.05E+01 2.72E+01 4.04E+01 4.95E+01 5.30E+01 5.20E+01 4.69E+01 3.76E+01 2.46E+01 9.52E+00 3.51E+01 238 U 9.16E+05 9.16E+05 9.16E+05 9.16E+05 9.16E+05 9.16E+05 9.16E+05 9.16E+05 9.16E+05 9.16E+05 9.16E+05 237 Np 3.89E-02 2.49E-01 5.32E-01 7.79E-01 8.86E-01 8.55E-01 7.04E-01 4.63E-01 2.05E-01 3.17E-02 4.74E-01 239 Np 7.00E+01 1.42E+02 1.77E+02 1.94E+02 1.99E+02 1.98E+02 1.90E+02 1.71E+02 1.33E+02 6.42E+01 1.54E+02 238 Pu 3.19E-05 5.41E-04 1.74E-03 3.15E-03 3.85E-03 3.64E-03 2.69E-03 1.41E-03 4.03E-04 2.33E-05 1.75E-03 239 Pu 1.22E+01 6.95E+01 1.37E+02 1.91E+02 2.13E+02 2.06E+02 1.75E+02 1.21E+02 5.83E+01 1.00E+01 1.19E+02 240 Pu 6.04E-02 4.16E-01 9.40E-01 1.43E+00 1.65E+00 1.58E+00 1.28E+00 8.09E-01 3.39E-01 4.90E-02 8.54E-01 241 Pu 4.51E-04 8.03E-03 2.70E-02 5.02E-02 6.19E-02 5.83E-02 4.24E-02 2.16E-02 5.93E-03 3.29E-04 2.76E-02 242 Pu 1.18E-07 5.51E-06 2.76E-05 6.32E-05 8.37E-05 7.73E-05 5.06E-05 2.06E-05 3.68E-06 7.76E-08 3.32E-05 241 Am 1.63E-08 7.59E-07 3.80E-06 8.70E-06 1.15E-05 1.06E-05 6.96E-06 2.83E-06 5.07E-07 1.07E-08 4.57E-06 242m Am 2.35E-12 2.64E-10 1.97E-09 5.52E-09 7.83E-09 7.09E-09 4.18E-09 1.36E-09 1.59E-10 1.47E-12 2.84E-09 243 Am 4.63E-11 5.65E-09 4.23E-08 1.19E-07 1.69E-07 1.53E-07 9.00E-08 2.93E-08 3.41E-09 2.74E-11 6.11E-08 242 Cm 1.26E-11 1.54E-09 1.15E-08 3.24E-08 4.60E-08 4.16E-08 2.45E-08 7.97E-09 9.28E-10 7.46E-12 1.67E-08 243 Cm 1.95E-13 4.31E-13 2.86E-12 9.36E-12 1.41E-11 1.26E-11 6.77E-12 1.91E-12 3.23E-13 1.95E-13 4.88E-12 244 Cm 2.35E-13 1.25E-11 1.38E-10 4.74E-10 7.21E-10 6.39E-10 3.40E-10 8.86E-11 6.93E-12 2.17E-13 2.42E-10 154 Gd 1.33E+03 1.33E+03 1.33E+03 1.33E+03 1.33E+03 1.33E+03 1.33E+03 1.33E+03 1.33E+03 1.33E+03 1.33E+03 155 Gd 8.57E+03 8.49E+03 8.42E+03 8.38E+03 8.36E+03 8.36E+03 8.39E+03 8.43E+03 8.50E+03 8.57E+03 8.45E+03 156 Gd 1.21E+04 1.22E+04 1.23E+04 1.23E+04 1.23E+04 1.23E+04 1.23E+04 1.23E+04 1.22E+04 1.21E+04 1.22E+04 157 Gd 9.13E+03 8.93E+03 8.77E+03 8.66E+03 8.62E+03 8.63E+03 8.70E+03 8.81E+03 8.97E+03 9.15E+03 8.84E+03 158 Gd 2.78E+04 2.80E+04 2.82E+04 2.83E+04 2.83E+04 2.83E+04 2.82E+04 2.81E+04 2.80E+04 2.78E+04 2.81E+04 106 Ru 1.84E-01 4.76E-01 7.14E-01 8.80E-01 9.46E-01 9.27E-01 8.32E-01 6.63E-01 4.31E-01 1.66E-01 6.22E-01 125 Sb 8.31E-03 2.15E-02 3.22E-02 3.96E-02 4.25E-02 4.17E-02 3.74E-02 2.99E-02 1.94E-02 7.49E-03 2.80E-02 134 Cs 8.43E-04 5.62E-03 1.25E-02 1.87E-02 2.15E-02 2.07E-02 1.68E-02 1.08E-02 4.61E-03 6.86E-04 1.13E-02 137 Cs 1.48E+00 3.83E+00 5.71E+00 7.01E+00 7.52E+00 7.37E+00 6.63E+00 5.30E+00 3.46E+00 1.34E+00 4.97E+00 143 Nd 1.37E+00 3.52E+00 5.25E+00 6.45E+00 6.91E+00 6.78E+00 6.10E+00 4.88E+00 3.19E+00 1.23E+00 4.57E+00 145 Nd 9.74E-01 2.51E+00 3.75E+00 4.60E+00 4.93E+00 4.83E+00 4.35E+00 3.48E+00 2.27E+00 8.79E-01 3.26E+00 154 Eu 1.20E-04 8.05E-04 1.79E-03 2.70E-03 3.10E-03 2.98E-03 2.41E-03 1.55E-03 6.59E-04 9.77E-05 1.62E-03 135

Table (14) gives the variation of keff as a function of the number of axial layers. It is clear from the Table that keff increases with the increase of the nodes number (positive reactivity) at high burnup value. Table (15) gives the isotopic inventory variations with the number of axial nodes at burnup 385 days. The values for the different isotopes in general increase with the increase of nodes number. Table (14): k eff as a function of the number of axial layers Burnup Sections Keff S.D. 0 Day Burnup 385 Day Burnup 1 5 8 10 1 5 8 10 1.16664 0.00012 1.16628 0.00016 1.16657. 0.00016 1.16239 0.00016 1.10944 0.00011 Table (15): Isotopic inventory variations with the axial nodes number Materials Sections Nuclide UO2 1.11112 0.00011 UO2-Gd2O3 1.12644 0.00011 1.13210 0.00012 1 5 8 10 1 5 8 10 234 U 3.39E+02 3.37E+02 3.37E+02 3.37E+02 1.87E+02 1.87E+02 1.87E+02 1.87E+02 235 U 2.74E+04 2.74E+04 2.74E+04 2.74E+04 2.46E+04 2.46E+04 2.46E+04 2.46E+04 236 U 2.40E+03 2.42E+03 2.43E+03 2.38E+03 3.53E+01 3.52E+01 3.52E+01 3.51E+01 238 U 9.52E+05 9.52E+05 9.52E+05 9.52E+05 9.16E+05 9.16E+05 9.16E+05 9.16E+05 237 Np 1.14E+02 1.14E+02 1.16E+02 1.22E+02 4.10E-01 4.14E-01 4.31E-01 4.74E-01 239 Np 6.12E+01 6.82E+01 6.92E+01 6.96E+01 1.66E+02 1.65E+02 1.62E+02 1.54E+02 238 Pu 1.21E+01 1.26E+01 1.43E+01 1.75E+01 1.17E-03 1.20E-03 1.37E-03 1.75E-03 239 Pu 3.69E+03 3.77E+03 3.87E+03 3.77E+03 1.09E+02 1.09E+02 1.12E+02 1.19E+02 240 Pu 6.46E+02 6.64E+02 6.99E+02 7.19E+02 7.10E-01 7.17E-01 7.58E-01 8.54E-01 241 Pu 3.69E+02 3.54E+02 3.48E+02 3.80E+02 1.78E-02 1.83E-02 2.12E-02 2.76E-02 242 Pu 3.48E+01 3.55E+01 3.88E+01 5.02E+01 1.58E-05 1.69E-05 2.20E-05 3.32E-05 241 Am 4.72E+00 4.75E+00 5.08E+00 6.38E+00 2.18E-06 2.33E-06 3.02E-06 4.57E-06 242m Am 5.32E-02 5.47E-02 6.15E-02 8.19E-02 9.82E-10 1.10E-09 1.62E-09 2.84E-09 243 Am 1.88E+00 2.14E+00 2.86E+00 4.38E+00 2.10E-08 2.35E-08 3.49E-08 6.11E-08 242 Cm 5.62E-01 5.97E-01 7.19E-01 1.03E+00 5.75E-09 6.43E-09 9.50E-09 1.67E-08 243 Cm 3.13E-03 3.73E-03 5.52E-03 9.32E-03 1.35E-12 1.56E-12 2.51E-12 4.88E-12 244 Cm 1.44E-01 1.80E-01 3.01E-01 5.50E-01 6.00E-11 7.07E-11 1.20E-10 2.42E-10 154 Gd 8.86E-02 9.23E-02 1.11E-01 1.48E-01 1.33E+03 1.33E+03 1.33E+03 1.33E+03 155 Gd 1.66E-02 1.60E-02 1.66E-02 1.78E-02 8.45E+03 8.45E+03 8.45E+03 8.45E+03 156 Gd 3.34E+00 3.37E+00 3.47E+00 3.67E+00 1.22E+04 1.22E+04 1.22E+04 1.22E+04 157 Gd 3.80E-02 3.74E-02 3.78E-02 3.75E-02 8.84E+03 8.84E+03 8.84E+03 8.84E+03 158 Gd 2.73E+00 2.76E+00 2.86E+00 3.07E+00 2.81E+04 2.81E+04 2.81E+04 2.81E+04 106 Ru 5.32E+01 5.35E+01 5.46E+01 5.59E+01 6.22E-01 6.21E-01 6.22E-01 6.22E-01 125 Sb 3.07E+00 3.09E+00 3.12E+00 3.14E+00 2.80E-02 2.80E-02 2.80E-02 2.80E-02 134 Cs 2.10E+01 2.14E+01 2.27E+01 2.50E+01 9.50E-03 9.58E-03 1.01E-02 1.13E-02 137 Cs 5.21E+02 5.24E+02 5.28E+02 5.28E+02 4.97E+00 4.97E+00 4.97E+00 4.97E+00 143 Nd 4.44E+02 4.45E+02 4.45E+02 4.37E+02 4.58E+00 4.57E+00 4.58E+00 4.57E+00 145 Nd 3.21E+02 3.23E+02 3.24E+02 3.21E+02 3.26E+00 3.26E+00 3.26E+00 3.26E+00 154 Eu 3.17E+00 3.33E+00 3.71E+00 4.23E+00 1.36E-03 1.37E-03 1.45E-03 1.62E-03 136

Axial Power (MW) Arab Journal of Nuclear Science and Applications, 50 (2), (123-141) 2017 The axial Power Distributions for the five, eight and ten axial intervals at 0 and after 385- day burnup are shown in Figures (3 to 8) respectively. Figures (3, 5 and 7) represent the power distributions of the fresh fuel assembly used in this study (0 burnup). The sum of all power fractions is 100%, which mean the total power of the assembly. From these figures, one can remark that the greatest power fractions are concentrated in assembly center in spite of the fuel compositions are the same in each zone (9,10). It is clear that the power decreases near the assembly boundary with the number of axial zones increase. Nuclear effects which cause variations in the axial power profile include moderator density, Doppler Effect on resonance absorption, spatial distribution of xenon, burnup, and finally the axial distribution of fuel enrichment and burnable absorber (23). Figures (4, 6 and 8) represent the power distributions corresponding to each irradiated zones. Based on these figures, and because of the computer time constraint, burnup calculations with MCNP5 were done for just one assembly with different fuel irradiation zones. For a detailed evaluation it is still necessary to perform a neutron flux mapping by means of adequate measurements. The neutron flux mapping in the whole assembly was performed in MCNP5 3D geometry with high spatial resolution (8). The results of such calculations are representative of the neutron physics and thermal hydraulic conditions in the assembly. These calculations form the basis for the assembly design validation and evaluation of assembly performance. Due to the variation of the power peaks with the burnup progresses, the power decreases in the assembly center and increases gradually directing to the assembly boundary at all. The results are in accordance with De Hart et al., (2008) (1). It is clear from Figures (4, 6 and 8) that the power decreases in the assembly center and increases near the assembly boundary with increasing the number of axial zones. It means that, the greater axial zones number the smallest the power at the assembly center and vice versa. Considering that the power summation equals 100% and considering also, that the cores of LWR are large relative to the neutron diffusion length, the local neutron flux and the power density measurements are not basically constant. In these reactors, the systems for determining the axial power profile or the local power density play a major role. A PWR employing fixed in-core detector in experimental work, have thus, power density measurements with higher accuracies (16). On the other hand, the inserted reactivity by the boron cloud, which is made of the contributions from prompt and delayed neutrons, could have an effect on the calculation of power density. Those contributions are not constant, but they change with the time according to the nuclear reactor dynamics equations (24). MCNP5 code allows only static calculations in which the time dependent effect of delayed and prompt neutrons cannot be resolved. However, a short range of applicability was found resolving the reactivity inserted by the prompt and delayed neutrons (25). 4 3.5 3 2.5 2 1.5 1 0.5 0 0 1 2 3 4 5 Z-Axis from fuel top Fig. (3): 5- Zone power distribution with 0 day burnup 137

Axial Power (MW) Axial Power (MW) Axial Power (MW) Arab Journal of Nuclear Science and Applications, 50 (2), (123-141) 2017 6 5 4 3 2 1 0 0 1 2 3 4 5 Z-Axis from fuel top Fig. (4): 5-Zone power distribution after 385 day burnup 3 2.5 2 1.5 1 0.5 0 0 1 2 3 4 5 6 7 8 Z-Axis from fuel top Fig. (5): 8- Zone power distribution with 0 day burnup 6 5 4 3 2 1 0 0 1 2 3 4 5 6 7 8 Z-Axis from fuel top Fig. (6): 8- Zone power distribution with 385 day burnup 138

Axial Power (MW) Axial Power (MW) Arab Journal of Nuclear Science and Applications, 50 (2), (123-141) 2017 3 2.5 2 1.5 1 0.5 0 0 1 2 3 4 5 6 7 8 9 10 Z-Axis from fuel top Fig. (7): 10- Zone power distribution with 0 day burnup 6 5 4 3 2 1 0 0 1 2 3 4 5 6 7 8 9 10 Z-Axis from fuel top Fig. (8): 10- Zone power distribution with 385 day burnup CONCLUSION The methodology presented in this study allows a comprehensive assessment of the average and maximum axial power distribution for pressurized water reactor assembly. The present Monte Carlo MCNP5 and WIMSD-5B calculations were validated by comparison with the published experimental and calculated data for Takahama-3 reactor and other publications (5,7). The observed axial power distribution reflected mainly the effect of different irradiation in each fuel zone. Due to the variation of the power peaks with the burnup progresses, the power decreases in the assembly center and increases gradually directing to the assembly boundary as well as with the zones number increase, considering constant assembly power. k eff and the values for the different isotopes increase with the increase of nodes number. Both results for the isotopic inventory and the power distribution emphasize the importance of considering the axial variation of burnup. REFERENCES (1) De Hart, M.D., Gauld, I.C. and Suyama, K., Three-dimensional depletion analysis of the axial end of a Takahama fuel rod. International Conference on the Physics of Reactors Nuclear Power: A Sustainable Resource. Casino-Kursaal Conference Center, Interlaken, Switzerland. September 14-19 (2008). 139

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