Validation of LWR fuel depletion calculation module of reactor physics code system CBZ

ABSTRACT This paper presents the results of validation calculations of the nuclear fuel depletion calculation module of the CBZ reactor physics code system, CBZ/Burner. Validation calculations were conducted using the post irradiation examination data obtained at Fukushima-Daini Unit 2 and at Takahama Unit 3. The nuclide number densities calculated with CBZ/Burner were compared with the measurement values, and generally good agreement was obtained. The sensitivity coefficients of the nuclide number densities with respect to nuclear data were calculated for all concerned nuclides with the depletion perturbation calculation capability of CBZ/Burner, and the nuclear data-induced uncertainties of the nuclide number densities were quantified. From the numerical results, we can conclude that the nuclear fuel depletion calculation module for LWR in the CBZ code system was successfully validated.


Introduction
Nuclear fuel depletion is an important phenomenon in nuclear fission reactors that results in compositional changes in irradiated nuclear fuels during reactor operation. Since the fuel composition, i.e. nuclide number densities of the nuclear fuels, significantly affects the behavior of neutrons in a reactor core and hence the neutronic property of the reactor, it is crucial to accurately predict the nuclide number densities of nuclear fuels loaded in a reactor core during reactor operation. Furthermore, after reactor operation, proper management of spent nuclear fuels discharged from the reactor core should be ensured. Since the spent nuclear fuels contain a significant amount of radioactive materials, measures of radiation protection and heat removal from the spent fuels should be carefully considered. Even after the final disposal of the spent fuels such as the geological disposal, potential risks of radioactivity released to the environment should be assessed thoroughly to ensure high-level safety. From these aspects, the nuclide number densities of nuclear fuels are quite important.
Prediction of the nuclide number densities of nuclear fuels relies heavily on the numerical simulation. The change in the nuclide number densities with time, or nuclide transmutation, is generally simulated by solving the governing equation, the well-known Bateman equation. Defining the Bateman equation for the certain problem requires the reaction rates of various nuclides and reaction types, and these are obtained by solving the steady-state neutron transport (or diffusion) equation. These processes are generally called nuclear fuel depletion calculations, and the numerical accuracy of these two kinds of simulation is important for the accurate prediction of the nuclide number densities.
In addition to accurate numerical methods to solve the Bateman equation and the neutron transport equation, accurate nuclear data which are necessary to define these equations are also important. Various kinds of nuclear data are relevant to the nuclear fuel depletion: neutron-nuclide reaction cross sections, radioactive decay data such as decay constants, fission yields defined for each fissionable nuclide with several different neutron energy points inducing the fission reaction, etc. In addition to the accuracy of these data, careful attention should be paid to preparing the energy-averaged data when the deterministic methods, or multi-group methods, are employed.
As described above, accurate numerical methods and nuclear data are essential in numerical simulations for the nuclear fuel depletion calculations, and computer codes for the depletion calculations implementing the advanced methods and nuclear data have been developed. Since the number of these computer codes is large, they are not cited individually here. These codes can be generally categorized into two: those based on the probabilistic methods and the deterministic methods. There are several advantages and disadvantages in both of them, and it has been considered that these are complementary with each other.
At Hokkaido University, two modules for the nuclear fuel depletion calculations have been being developed in the framework of the reactor physics code system CBZ [1], which is based on the deterministic method. Target systems of these modules are  light water reactors (LWR). A module named Burner  can handle simple fuel pin-cell problems comprising  fuel pellet, cladding, and coolant with the periodic  boundary conditions, and a module named MulticellBurner can handle multi-cell problems such as fuel assembly models with the periodic or perfect reflective boundary condition. These two modules employ several advanced numerical methods and recent nuclear data such as the Japanese evaluated nuclear data library, JENDL-4.0 [2]. One of the distinguishing features of these modules is the capability of calculating the sensitivity coefficients of parameters and quantities during fuel depletion with respect to nuclear data. This capability is based on the depletion perturbation theory (DPT) [3,4], which was established many years ago, and has been extended to be combined with the predictor-corrector method [5] for the application to LWR fuel assemblies containing burnable absorbers. The sensitivity coefficients of parameters and quantities for static problems under fixed nuclide number densities to nuclear data can be easily calculated with the classical or generalized perturbation theory, and many existing computer codes have such capabilities. On the other hand, to authors' knowledge, there are no computer codes targeting the LWR fuel assemblies into which DPT has been implemented at present. There have been several works demonstrating the usefulness of the sensitivity coefficients calculated by DPT, and some of these have already been published by us [6][7][8]. One typical example is to quantify the uncertainties of nuclide number densities during depletion induced by the nuclear data uncertainty. Although there have been various works doing the uncertainty quantification of nuclide number densities and their relevant quantities with the Monte Carlo sampling scheme [9][10][11], results that are free from statistical uncertainties have been presented in out previous works.
Whereas several works using the nuclear fuel depletion calculation capabilities of CBZ have been published so far, detailed validation results of these capabilities have not yet been reported in the open literature. The purpose of the present work is the comprehensive validation of these modules. Validation will be conducted against the postirradiation examination (PIE) data on fuel samples irradiated at Fukushima-Daini Unit 2 of the boiling water reactor and at Takahama Unit 3 of the pressurized water reactor [12].
The present paper is organized as follows. In Section 2, numerical methods and data used for these modules are briefly explained. In prior to the validation calculations, comparisons between these modules and the well-verified reference code MVP-BURN [13] based on the continuous-energy Monte Carlo method are made for simple fuel pin-cell problems in order to quantify the numerical accuracy of these modules. These results are described in Section 3. In Section 4, validation works are presented. Results of quantification of the nuclear data-induced uncertainty of nuclide number densities are also presented in this section. Section 5 is our conclusion for the present work and future perspectives.

Numerical methods and data
In this section, numerical methods and data employed in the fuel depletion calculation modules for LWR, Burner and MulticellBurner, are described. These modules were developed in the framework of the reactor physics code system CBZ. All programs in CBZ are written with the C++ computer language, and methods and data are defined as classes. Both the Burner and MulticellBurner modules are also classes, and the main characteristics of them are inherited from a base class GeneralBurner. Since it is not important to distinguish one from the other, we refer to these modules as CBZ/Burner in the following. When the Bateman equation and the multi-group neutron transport equation are solved numerically, corresponding classes of CBZ are utilized inside CBZ/Burner. Thus, the validation of CBZ/Burner includes those of each class used in CBZ/Burner.

Numerical methods
Nuclear fuel depletion calculations based on the deterministic method can be separated into three parts: the resonance treatment part, the neutron transport calculation part, and the nuclide transmutation calculation part. Each part is described below.
The purpose of the resonance treatment part is to obtain multi-group cross sections of media comprising the target system. In CBZ/Burner, multi-group cross sections are calculated from the infinite dilution cross sections and the self-shielding factors based on the advanced Bondarenko model [14]. This model has been developed for resonance calculations of LWR fuel pins. Its features are an optimized set of Bell factor values in the one-term rational approximation for the neutron escape probability, resonance interference treatment with R-parameters, and correction to the current-weighted total cross section to mitigate the energy condensation errors. This model has much less computational burden than the calculation method solving neutron slowing-down problems with the ultra-fine energy group which has been adopted in many other codes. The resonance calculations are carried out for the square fuel pin-cell geometry, and the background cross sections in a heterogeneous system are evaluated by the Dancoff factor method in conjunction with the enhanced neutron current method [15] based on the fixed-source neutron transport calculations.
In the neutron transport calculation part, the twodimensional multi-group neutron transport equation is numerically solved using the method of characteristics (MOC). The periodic or perfect reflective boundary condition is exactly considered using the cyclic trajectory method [16], and the two-point Tabuchi-Yamamoto optimized set [17] is used for polar-angle discretization. The standard step characteristics scheme is adopted for the spatial integration. The numerical conditions in the MOC calculations are as follows: the fuel pellet region is divided into three or four spatial meshes; the number of azimuthal-angle directions is 64 for 2π; the width of trajectories is around 0.02 cm. The scattering anisotropy is considered by the P0 transport approximation.
In the nuclide transmutation calculation part, the Bateman equation is solved by the Mini-Max Polynomial Approximation method (MMPA) [18,19], which is applicable to the problems involving short half-lived nuclides. For problems containing burnable absorber pins like typical LWR fuel assemblies, the advanced optimally weighted predictorcorrector (AOWPC) method [20] is adopted to reduce the computational burden. Burnup periods per one burnup step were set less than 2.0 GWD/t. Constant values are used for the energy released per a fission of actinoids.
The sensitivity coefficients of parameters and quantities during fuel depletion are calculated with the DPT capability of CBZ/Burner. The adjoint equations to the Bateman equation and the neutron transport equation are defined and solved with the same numerical methods adopted to the corresponding forward equations. It should be noted that the implicit sensitivities [21] are not accounted for in CBZ/Burner; the sensitivity coefficients with respect to the infinite dilution cross sections are calculated. Although all kinds of nuclear data are accounted for in the static components of sensitivity coefficients, only the (n,f), (n,γ), and (n,2n) reaction cross sections are accounted for in the burnup components of sensitivity coefficients. This treatment is expected reasonable for LWR analyses. The uncertainty propagation calculations are carried out using the sensitivity coefficients and covariance data of the nuclear data. The details of the uncertainty propagation calculations can be found in our previous paper [6]. The sensitivity coefficients are calculated not only to reaction cross sections but also to decay constants, decay branching ratios, and fission yields.

Data
The number of energy groups and the group structure in the multi-group cross sections are arbitrary in the CBZ code system. The present work employed the following two energy group structures: the SHEM 361group structure [22] and the SRAC 107-group structure. The former was used to obtain the best-estimate results of CBZ/Burner, and the latter was used to calculate the sensitivity coefficients and to carry out the uncertainty propagation calculations from nuclear data to the target parameters and quantities. The reason why the 361-group library was not used for the sensitivity coefficient calculations is that it is unpractical due to the long computation time and large amount of computer memory. In the resonance treatment part, the 361-and 107-group libraries which were consistently generated from the point-wise crosssection data of JENDL-4.0 with the FRENDY code [23] and the TIMS-1 code [24] were used. When the SHEM 361-group structure was adopted, the advanced Bondarenko method was not used since the energy group structure of SHEM-361 is enough fine not to use this method.
The number of nuclides considered in the nuclide transmutation chain is also arbitrary in the CBZ code system: we can use reference chains consisting of all nuclides defined in the evaluated nuclear data libraries and simplified chains consisting of some specific nuclides which largely contribute to the reactivity during fuel depletion. In the present work, a simplified chain consisting of 22 actinoids and 137 fission products was used to reduce the computational burden, particularly in the sensitivity coefficient calculations with DPT. Generally, 21 actinoids are considered in CBZ/Burner; however, since Cm-247 number densities are included in the PIE data of Takahama Unit 3, Cm-247 was included in the burnup chain in the present work. The 137 fission products are those explicitly treated in the FP-138 chain developed in the previous work [25]; only Rh-105m was ignored to avoid accuracy degradation in the DPT calculations due to its short half-life. The decay data and fission yield data were retrieved from JENDL/FPD-2011 and JENDL/FPY-2011 [26]. On the reaction branching ratio, constant (energy group-independent) values are used. For example, an isomeric branching ratio to the Am-242 meta-stable state for the Am-241 (n,γ) reaction is 0.122017, which is recommended to use in MVP-BURN.
In the uncertainty propagation calculations, covariance data of the multi-group (infinite dilution) cross sections were prepared by the ERRORR module of NJOY2016 [27]. Covariance data of the actinoid nuclear data were taken from JENDL-4.0, and all kinds of the covariance data such as reaction cross sections, � ν values, � μ values, and fission spectra were accounted for. On the other hand, covariance data of the fission products are not provided in JENDL-4.0. In order to quantify the impact of nuclear data uncertainties of the fission products on the final results, covariance data of the fission products were taken from ENDF/B-VIII.0 [28]. Since ENDF/B-VIII.0 does not provide any covariance data to the following fission products, those in TENDL-2019 [29] were used: Ce-144, Sm-147, -148, -150, -153, -154, Eu-154, Cs-134, Nd-144, -147, -150, Pm-148, -148m, and -149. It should be emphasized here that this treatment is tentative since the consistency between the evaluated nuclear data and their uncertainty information is not assured. Regarding the fission yield uncertainties, correlations among the fission products belonging to the same mass chain were considered with the analytical method used by Devillers [30]. It has been shown that this simple treatment yields consistent results with those obtained with more sophisticated methods [7] such as the generalized least-square method considering several physical constraints [31]. The uncertainty in the thermal scattering data is not considered in the present work, but it was recently reported that the impact of the thermal scattering data uncertainty on the nuclide number densities is not significant [32].

Comparison with the continuous-energy Monte Carlo burnup code
In order to quantify the numerical accuracy of CBZ/ Burner, results of CBZ/Burner are compared with results obtained by MVP-BURN, which employs the continuous-energy Monte Carlo particle transport calculations.

Problem specifications
Eight LWR fuel pin-cell models were used in this comparison. Those were chosen from a set of the pincell models, which were prepared to develop a library for the ORIGEN code [33]. Two of them mimic PWR and the others do BWR. One of the PWR pin-cells is the UO2 fuel whose uranium-235 enrichment is 4.1 wt %, and the other is the MOX fuel whose plutonium enrichment is 10 wt% with the standard plutonium isotopic composition: Pu-238/-239/-240/-241/-242/ Am-241 = 2.1%/54.5%/25.0%/9.3%/6.4%/2.7%. These are referred to as PWR-UO2 and PWR-MOX in the following. For the BWR pin-cells, a model based on the Step-3 type assembly with UO2 and MOX fuels were used. The uranium-235 enrichment of the UO2 fuel is 4.1 wt%, and the plutonium enrichment of the MOX fuel is 4.0 wt% with the standard plutonium isotopic composition: Pu-238/-239/-240/-241/-242/ Am-241 = 1.5%/58.7%/26.6%/8.3%/4.0%/0.8%. On the coolant of the BWR pin-cells, three different void ratios, 0%, 40%, and 70%, were considered for both the UO2 and MOX fuels. These six BWR pin-cells are referred to as BWR-UO2-V0, BWR-UO2-V40, BWR-UO2-V70, BWR-MOX-V0, BWR-MOX-V40, and BWR-MOX-V70. Detailed information on these models, such as the dimensions, compositions, and region-wise temperature, can be found in the original literature [33]. Constant line power of 179 W/cm was assumed and fuel depletion calculations were carried out by fuel burnup of 45 GWd/t.

Results
In both calculations with CBZ/Burner and MVP-BURN, reaction cross-section data of JENDL-4.0 were commonly used. As mentioned in the preceding section, the 361-group library was used to obtain the best-estimate results with CBZ/Burner. The nuclide transmutation chain, ChainJ40, was used in the calculations with MVP-BURN. It consists of 28 actinoids and 197 fission products and adopts the JENDL/FPD-2000 library [34] for decay data and JENDL-4.0 for fission yield data. In order to keep the consistency between CBZ/Burner and MVP-BURN, the same FP-197 chain based on the same nuclear data was prepared and used in the calculations with CBZ/Burner.
In the calculations with MVP-BURN, the number of particles per one batch was set 10,000, the number of total batches was 1,000, and the initial 100 batches were discarded. With this condition, it is expected that the statistical uncertainties in the results of MVP-BURN were negligible. The 1σ statistical uncertainties in the infinite neutron multiplication factor are less than 0.02%Δk=kk 0 during the burnup.
Differences in the infinite neutron multiplication factors obtained with CBZ/Burner to the references are shown in Figure 1. On the UO2 fuels, slight underestimation of approximately 0.1%Δk=kk 0 is systematically observed during the depletion. On the MOX fuels, overestimation of over 0.2%Δk=kk 0 is observed at the beginning of the depletion, and during the depletion this overestimation tends to be small and the maximum difference becomes 0.1%Δk=kk 0 at 45 GWd/t. As a conclusion, the infinite neutron multiplication factors are estimated by CBZ/Burner within approximately 0.2%Δk=kk 0 errors during the fuel depletion of LWR fuel pin-cells. From a viewpoint of practical applications, this error would be insignificant and acceptable. Results obtained with the 107-group library are presented in Figure A1 of the Supplemental Online Material.
Next, nuclide number densities at 20 and 40 GWd/t are assessed. Figure 2 shows relative differences in the actinoid number densities. Errors of CBZ/Burner in the number densities are less than 1.5% for the major actinoids and 2.5% for the minor actiniods. Figure 3 shows relative difference in the number densities of important fission products. Generally, excellent agreement between CBZ/ Burner and MVP-BURN is observed, but relatively large discrepancy over 2% is observed in two fission products, I-130 and Sm-149. These differences  Relative error in number density     Relative error in number density would come from the limitation of the employed numerical methods of CBZ/Burner. The most possible cause is the resonance calculation part, and finer-group libraries should be implemented in order to further increase the accuracy if necessary. Results of the number density calculations obtained with the 107-group library are presented in Figure  A2 for actinoids and in Figure A3 for fission products.

Problem specifications
The PIE data of fuel samples irradiated at Fukushima-Daini Unit 2 have been published as the benchmark data [12,35]. Number density data of actinoids and fission products for the 18 irradiated samples are available. The eight samples among them were taken from a normal fuel rod and identified as SF98. The uranium-235 enrichment of this normal fuel rod averaged over axial direction was 3.63 wt%. The other 10 samples were taken from a Gd-bearing fuel rod and identified as SF99. Loaded positions of these fuel rods in a fuel assembly are shown in Figure 4. Since numerical simulations for the Gd-bearing rod are more complicated than those for normal rods which does not contain any burnable absorbers, only the SF98 samples were concerned in the present work. Two samples, SF98-1 and SF98-2, were not treated since those were located near the bottom edge of the fuel rod and two-dimensional calculation model is considered inaccurate. The fuel burnup and void rates of coolant of the concerned six samples were dependent on the axial positions. The estimated fuel burnup [12] and the coolant void rates assumed in the calculations with CBZ/ Burner are shown in Table 1. These void rates were cited from the previous work [36]. The Ru-106 number densities are excluded in the following comparisons due to a potential technical issue in the measurement [12].

Results
C/E values of the nuclide number densities of the six irradiated samples are shown in Figure 5 where error bars depict 1σ measurement errors given in the SF-COMPO2 database [35]. A supplemental figure for actinoids with wide range is also shown in Figure A4 since several C/E values of Cm-242 and -246 are out of the plot range in Figure 5. Calculation results obtained with CBZ/ Burner agree with the measurement data within 30% differences for all actinoids except Cm-242 and -246 and within 10% differences for major actinoids with a few exceptions. Underestimations are systematically observed in Am and Cm isotopes. Regarding the fission products, the calculation and measurement values agree with each other within 20% difference with two exceptions of the Sm-149 data. It should be noted here that underestimation in Pu isotopes, Am-241, and Sm isotopes and scattered behavior of the C/E values in Pu-238 and Sm-149 are also observed in the previous work using the same nuclear data and the same assumption for the coolant void rates [36]. Next, C/E values with nuclear data-induced uncertainties for the SF98-3 sample are shown in Figure 6 where error bars with bold lines depict nuclear data-induced uncertainties of 1σ. Those for the other samples are shown in Figure A5. Differences between the calculation and measurement values in the number densities of U-234 and Cm-242 are much larger than the measurement error and the nuclear datainduced uncertainty. These are also much larger than the numerical errors of CBZ/Burner expected from the benchmark calculation results shown in the preceding section. This result suggests that  there should exist other sources causing uncertainties, which are not accounted for in the present work. Figure 7 shows the correlation matrix of the nuclear data-induced uncertainties for the actinoid number densities of the SF98-3 sample. Strong correlations are observed between nuclides connected via neutron-nuclide reactions and/or radioactive decay. C/E values of the fission product number densities of SF98-3 are shown in Figure 8 with the nuclear data-induced uncertainties. Those for the other samples are shown in Figure A6. On all the fission products, relative uncertainties induced by the decay and fission yield data are less than 1.5%, and large uncertainties over several % observed in Sm-151 and Eu-154 come from the reaction cross-section uncertainties: Sm-150 (n,γ) and Eu-153 (n,γ), respectively. Considering the nuclear data-induced uncertainty and the measurement error, discrepancy of the C/E values from unity is significant in several Sm isotopes. Figure 9 shows the correlation matrix of the nuclear datainduced uncertainties for the fission products of the SF98-3 sample. Strong correlations are observed among the same elements. The same trends as SF98-3 are observed in the correlation matrices of the other samples.
C/E Figure 8. C/E values with nuclear data-induced uncertainties of SF98-3 (fission products).

Problem specifications
The PIE data of the fuel samples irradiated at Takahama Unit 3 have also been published as the benchmark data [12,35]. Number density data of around 30 actinoids and 20 fission products for the 16 irradiated samples are available. These samples were taken from three fuel rods loaded in two different fuel assemblies identified as NT3G23 and NT3G24. Note that these assemblies have the common geometrical specification. Two of these three fuel rods were loaded in the NT3G23 assembly, and the samples from these rods are identified as SF95 and SF96. The remaining fuel rod was loaded in the NT3G24 assembly, and the samples from this rod are identified as SF97. The loaded positions of these fuel rods are shown in Figure 10. Since the SF96 samples were taken from the Gd-bearing fuel rod, those were not concerned in the present work like the SF99 samples in the Fukushima-Daini data. In addition, the SF97-1 sample, which was located near the top edge of the fuel rod, was also excluded from our target. Thus the other ten samples of SF95 and SF97 were concerned in the present work. The initial uranium-235 enrichment of these samples was 4.1 wt%, and the estimated fuel burnup [12] is listed in Table 2. Due to the limitation of the current implementation of CBZ/Burner, the boron concentration was assumed constant during the irradiation. Ru-106 and Sb-125 number densities are excluded in the following comparisons due to a potential technical issue in the measurement [12].

Results
C/E values of the nuclide number densities of the SF95 and SF97 samples are shown in Figures 11  and 12 where error bars depict 1σ measurement errors given in SF-COMPO2 [35]. Supplemental figures for those of actinoids with wide range are also shown in Figures A7 and A8 since several C/E values are out of the ranges in Figures 11 and 12.
Comparisons with the results of the Fukushima-Daini data would be helpful, and the following observations are obtained: • Calculation results with CBZ/Burner agree with the measurement data within 10% differences for major actinoids.
• Systematic underestimation is observed in several Am and Cm isotopes, but systematic underestimation on Am-241, which was observed in the Fukushima-Daini data, is not observed both in SF95 and SF97.
• Regarding the U-234 number densities, overestimation is observed in some data as the Fukushima-Daini data, but C/E values close to unity are also obtained in the other U-234 data.
• Regarding the Cm-247 number densities, which were measured only in the SF97 samples, significant underestimation of around 30% is observed systematically.
• Regarding the fission products, the calculation and measurement values agree with each other within 10% difference with several exceptions, and the agreement is generally better than that in the   Fukushima-Daini data, whereas systematic underestimation is observed in the Sm isotopes in the Fukushima-Daini data, the same tendency is observed only in Sm-148 and −151 in the Takahama data.
• Significant underestimation is observed in Nd-142 whose PIE data do not exist in the Fukushima-Daini data.
Next, C/E values for actinoids of the SF97-3 sample are shown in Figure 13 where error bars with bold lines depict nuclear data-induced uncertainties of 1σ. Those for the other samples are presented in Figures  A9 and A10. The C/E values, the nuclear data-induced uncertainties, and the measurement errors seem consistent with each other as different from the Fukushima-Daini PIE data. The significant underestimation of Cm-247 can be interpreted by the nuclear data-induced uncertainties. The correlation matrix of actinoids of SF97-3 is shown in Figure 14.
It is quite similar with those of SF98-3 shown in Figure 7, and a strong correlation between Cm-246 and −247 is observed. C/E values of the fission product number densities of SF95-2 are shown in Figure 15 with the nuclear data-induced uncertainties.  densities, the main contributor is the Pr-141 (n,γ) cross sections. The correlation matrix of fission products of SF95-2 is shown in Figure 16. On the correlation matrices for fission products, similar results as the Fukushima-Daini data are obtained.

Conclusion
We have presented the results of validation calculations of the nuclear fuel depletion calculation module of the CBZ reactor physics code system, CBZ/Burner. The target systems of CBZ/Burner are single fuel pin-cell problems and multi-cell problems such as single fuel assemblies of light water reactors. We have briefly described the employed numerical methods for nuclides transmutation calculations and the multi-group neutron transport calculations with the employed nuclear data and nuclide depletion chains.
In prior to the validation calculations, numerical benchmark calculations were carried out through comparisons with the reference results obtained with the continuous-energy Monte Carlo code using the same nuclear data and nuclide transmutation chains. The infinite neutron multiplication factor and the number densities of important actinoids and fission products during fuel depletion were calculated for single fuel pin-cell problems of UO2 and MOX fuels, and generally good agreement between CBZ/Burner and the reference Monte Carlo code was obtained. Regarding the number densities of several nuclides such as Am-242m, I-130, and Sm-149, relatively large errors of over 2% were observed, and these are likely to come from the limitation of the employed numerical methods of CBZ/Burner.
Validation calculations were performed using the post irradiation examination data obtained at Fukushima-Daini Unit 2 and at Takahama Unit 3. The total number of the concerned samples was 15, and the calculated number densities were compared with the measurement values. Generally, good agreement was obtained for actinoids and fission products. The sensitivity coefficients of the nuclide number densities with respect to nuclear data were calculated for all concerned nuclides with the depletion perturbation calculation capability of CBZ/Burner, and the nuclear data-induced uncertainties of the nuclide number densities were quantified.
Based on these results, we can conclude that the nuclear fuel depletion calculation module for LWR in the CBZ code system were successfully validated. The expected future development of this module includes updating with the most recent nuclear data files such as JENDL-5, further speed-up of the numerical simulation by improving the AOWPC method, application to multi-assembly problems, consideration of the uncertainty of the thermal scattering data, implementation of the implicit sensitivity calculation capability, application to PIE analyses for the samples taken from Gd-bearing fuel rods, and use of the further optimization of the group structure based on SHEM-361.