Pin Cell Model Research Articles

ANALYSIS OF THORIUM PIN CELL BURN UP OF THE PWR USING WIMS CODE

A thorium-fueled benchmark comparison was made in this study between state-of-the-art codes, WIMSD-5B code to MOCUP (MCNP4B + ORIGEN2), and CASMO-4 for burnup calculations as part of efforts to examine the possible benefits of using thorium in PWR fuel. WIMSD-5B calculations employ the same model as a reference, MOCUP, and CASMO, however, there are some variances in methodology and cross-section libraries. On a PWR pin cell model, eigenvalue and isotope concentrations were examined up to high burnup. The eigenvalue comparison as a function of burnup is good, with a maximum difference of less than 5% and an average absolute difference of less than 1%. The isotope concentration comparisons outperform a set of ThO2-UO2 fuel benchmarks and are comparable to a set of uranium fuel benchmarks previously published in the literature. As a function, the eigenvalue comparison The actinide and fission product data sources for a typical thorium fuel are reported in the WIMSD-5B burnup calculations. The reasons for discrepancies in coding are examined and explored.Keywords: Thorium, PWR Fuel, Burn up, Pin Cell, WIMSD-5B

Performing linear regression with responses calculated using Monte Carlo transport codes

In many of the complex systems modeled in the field of nuclear engineering, it is often useful to use linear regression-based analyses to analyze relationships between model parameters and responses of interests. In cases where the response of interest is calculated by a simulation which uses Monte Carlo methods, there will be some uncertainty in the responses. Further, the reduction of this uncertainty increases the time necessary to run each calculation. This paper presents some discussion on how the Monte Carlo error in the response of interest influences the error in computed linear regression coefficients. A mathematical justification is given that shows that when performing linear regression in these scenarios, the error in regression coefficients can be largely independent of the Monte Carlo error in each individual calculation. This condition is only true if the total number of calculations are scaled to have a constant total time, or amount of work, for all calculations. An application with a simple pin cell model is used to demonstrate these observations in a practical problem.

On the use of criticality and depletion benchmarks for verification of nuclear data

The problem of calculating sensitivity coefficients to nuclear data in burnup problems is addressed. A non-intrusive method based on the random sampling of nuclear data and on linear regression is proposed to overcome the limitations of dealing with a complex coupled problem. Sensitivity plots are reported for the actinide concentrations that build up in irradiated fuel and that have the largest impact for the safe and economical management of spent nuclear fuel. Despite using a simplified pincell model, the range of applicability of the calculated sensitivities is further discussed. The sensitivity study is corroborated by an analysis of how different nuclear data libraries perform in the prediction of the neutron multiplication factor in a burnup problem. The origin of the discrepancies between the results obtained using the JEFF-3.3 and ENDF/B-VIII.0 nuclear data libraries are investigated.

Calculation of PWR Thorium Pin Cell Burnup and Isotope Prediction Using WIMSD-5B Code

The amount of thorium in the world is very abundant and the benefits of using thorium as fuel for nuclear reactors such as PWR are increasingly widespread, so it needs to be analyzed. In the initial phase, the PWR pin cell fuel analysis was carried out using the WIMSD-5B code. The PWR ThO2-UO2 fuel in the cladding with the fuel assembly model 17 x 17 is analyzed by its fuel burn up, neutron flux and isotope composition after maximum operation. The pin cell model consisting of fuel, cladding and coolant with a square pitch of 12.6 cm are calculated using different libraries. Eigenvalues, neutron fluxes and isotope concentrations were compared with the PWR pin cell model to high burnup. The eigenvalues and flux neutron as a function of burnup are good, the maximum difference is within 7.41% and the mean absolute difference is less than 3.12 %. The best comparison of fission product isotope concentrations is to use the ENDFB7.1 library with Thorium fuel and is comparable to the uranium fuel reported in the literature. Data sources for actinides and fission products used infuel depletion calculations for thorium fuel are all documented.

Neutronic and burn‐up calculations of the ( ThO2‐UO2 ) pin cell benchmark using DRAGON5 and MCNP6 .2 codes with ENDF / B‐VIII .0 nuclear data library

A (ThO2-UO2) fuel pin benchmark, consisting of 75 w/o Th and 25 w/o U, was utilized for analysis of depletion and inventory of the fuel for the pressurized water reactor (PWR) pin-cell model. To perform this study and evaluate cross-section data, the new version VIII.0 of the ENDF/B nuclear data library was utilized to generate a data set in ACE (A Compact ENDF) format at different temperatures (583.1, 600, 621.1, and 900 K), utilizing NJOY2016 and MAKXSF6.2 codes to process the data at the specific temperatures. In this paper, the infinite multiplication factor (kinf), neutron energy flux spectrum (utilizing 172 energy groups), the concentrations and activities of the most important products of fission, the actinide radionuclides accumulated in the pin-cell, and the total radioactivity were calculated and compared, utilizing the MCNP6.2 and DRAGON5 codes. Furthermore, the burn-up (BU) dependent behavior of the PWR thorium pin-cell was validated and compared with the reference results obtained utilizing the CASMO-4, MIT-MOCUP, and INEEL-MOCUP codes. The results of this study show good agreements between all codes analysed.

Development and validation of the depletion capability of the high-fidelity neutronics code NECP-X

The depletion capability of NECP-X is developed. Two depletion libraries are developed for depletion calculations. One full-fidelity depletion library contains 1547 isotopes, and a new compressed depletion library is generated. Cross sections from the EAF-2010 library are integrated into depletion libraries, which give cross sections for reaction channels not included in the ENDF library. For the traditional predictor-corrector method, two transport calculations are conducted during every depletion step, where transport calculation is very time consuming, so a new transport-depletion coupling strategy is developed to reduce calculation time. The VERA depletion benchmark problems are utilized to assess the accuracy of compressed depletion library and new coupling method. The equivalent pin-cell model and assembly model, which are often used for validation, are asserted by comparing to the full-core model. Finally, measurement data for 22 fuel samples are used to validate the depletion capability of NECP-X. The results demonstrate good accuracy of NECP-X.

A Comparison Between the Embedded Self-Shielding Method and the Enhanced Neutron Current Method Based on the Equivalent Pin Cell Model on the Irregular Fuel Lattice Problem

The Embedded Self-Shielding Method (ESSM) coupled with the heterogeneous Resonance Integral tables and the Enhanced Neutron Current Method (ENCM) with equivalent Dancoff factor are reviewed and reformulated to a unified framework by incorporating the ultra-fine-group slowing-down calculation on two-dimensional square pin cell problems. The comparison between the two approaches on the resonance self-shielding calculation of irregular fuel lattices shows that the reformulated ESSM approach will bring errors to the cross-section prediction of fuel pins in the irregular lattice, especially when the moderator density is low. Also, the reformulated ENCM approach is more stable for different configurations. Further numerical tests show that the scalar flux calculated by the ESSM approach is affected by the global neutron balance across the fuel lattice and ESSM is more sensitive to the error brought by the enforced equivalence.

Validation of lattice physics code STREAM for predicting pressurized water reactor spent nuclear fuel isotopic inventory

This work investigates the depletion capability implemented in lattice physics code STREAM for the prediction of pressurized water reactor (PWR) uranium dioxide (UO2) spent nuclear fuel (SNF) isotopic inventory. The validation of this capability is performed by comparison of STREAM calculation results to measured SNF assay data obtained from PWRs Takahama-3, Calvert Cliffs and GKN II. The depletion analysis is conducted with the ENDF/B-VII.0 library and uses a pin cell model of the fuel rods from which the fuel samples were taken. The Chebyshev Rational Approximation Method (CRAM) is used to solve the depletion equation with about 1300–1600 isotopes in the depletion chain. 16 actinides and 23 fission products are analyzed in 14 spent UO2 fuel samples. The actinides are isotopes of uranium, neptunium, plutonium, americium and curium. The fission products nuclides include isotopes of cesium, neodymium, europium, samarium as well as 106Ru, 144Ce, 155Gd, 99Tc, 90Sr, 109Ag, and 103Rh. The sensitivity of some of the nuclides to the details of the power history and the adjustment of the fuel sample burnup is discussed. The impact of using ENDF/B-VII.0 library instead of ENDF/B-VI.8 is also discussed. Most of the nuclides analyzed are well predicted within ±7% of the experiment for actinides and fission products. STREAM depletion results are also compared to the codes SWAT, HELIOS and SCALE results based on publicly available information in literature, to check the performance of STREAM relative to other codes for the prediction of SNF isotopic inventory. The comparison to other code systems shows that the implementation in STREAM is of comparable accuracy. Overall, this paper demonstrates that the depletion capability in STREAM can be reliably applied to predict the isotopic inventory of PWR UO2 SNF for burnup ranging from 14 to 54 GWd/t and initial enrichment ranging from 3.0 to 4.1 wt% 235U.

Comparison of HELIOS-2.1 and SCALE-6.1 codes on pin-cell model

Deterministic HELIOS-2.1 and SCALE-6.1 codes are compared using pin-cell models for light water reactor (LWR) and heavy water reactor (HWR) cases. The main objective of this study is to identify the origins of any discrepancies between compared codes. The infinite multiplication factor kinf, flux distribution, absorption, fission, production reaction rates, and burn-up dependent concentrations of major fuel isotopes, are investigated herein and compared.Comparison of kinf has shown that the codes are in good agreement for both the LWR and HWR cases. The codes showed differences in the isotope number density of up to 6% in the case of prominent isotopes, and for 235U and 239Pu at 60 GWd/tU in the LWR case. These differences were, approximately 20% for 235U and 30% for 239Pu in the HWR case.It is concluded that these discrepancies are attributed to differences in the modelling of the thermalisation process in the HWR case. This needs to be investigated further to determine the root cause. Possible causes could be the neutron group structure, cross section condensation, treatment of up-scatter, angle dependence of scatter, and spatial homogenisation during source iterations.

Ultra-fine-group resonance treatment using equivalent Dancoff-factor cell model in lattice physics code GALAXY

ABSTRACT In order to achieve highly accurate resonance calculations with short computation time , a new ultra-fine-group resonance calculation method is developed. The ultra-fine-group method has a limitation in practical design applications of large and complicated geometries in fuel assembly level due to its long computation time. Therefore, we developed an enhanced one-dimensional (1D) cylindrical pin-cell model to achieve both high calculation accuracy and short computation time. In the enhanced 1D cylindrical pin-cell modeling, moderator radius is adjusted to preserve each fuel pellet's Dancoff factor obtained in the exact 2D fuel lattice arrangement. We call this model the ‘equivalent Dancoff-factor’ cell model. This model can accurately consider heterogeneity effects in PWR fuel assemblies and can represent effective cross sections obtained by the ultra-fine-group calculations in the complicated 2D square lattice arrangements. The present method is implemented with Mitsubishi Heavy Industries, Ltd. lattice physics code GALAXY. From the comparisons of neutron multiplication factors and pin power distributions between GALAXY and a continuous-energy Monte Carlo code, applicability of the present method to lattice physics calculations is confirmed. Application of GALAXY with the present method achieves high accuracy with short computation time in normal operations and accident conditions including low moderator density conditions.

Numerical investigation of the random arrangement effect of coated fuel particles on the criticality of HTTR fuel compact using MCNP6

This study investigated the random arrangement effect of coated fuel particles (CFPs) on the criticality of the fuel compact of the high-temperature engineering test reactor (HTTR). A utility program coupled with MCNP6, namely the realized random packing (RRP) model, was developed to explicitly model the random arrangement of CFPs in a specified fuel compact of the HTTR. The criticality and neutronic calculations for a pin cell model were performed using the Monte Carlo MCNP6 code with ENDF/B-VII.1 neutron library data. The reliability of the RRP model was confirmed by the insignificant variance of the infinite multiplication factor (kinf) among 10 different random arrangements of the CFPs. Next, the criticality of the RRP model was compared with those of a non-truncated uniform packing (NUP) model and an on-the-fly random packing (ORP) model, which is a stochastic geometry capability in MCNP6. The results indicated that there was no substantial difference between the NUP and ORP models. However, the RRP model presented a lower kinf (by about 0.32–0.52%Δk/k) than the NUP model. In addition, the difference in kinf was increased as uranium enrichment decreased. Investigation of the 4-factor formula showed that the difference in kinf was predominantly a result of the resonance escape probability, with the RRP model showing the smallest value.

Simulation calculation of weapon-grade plutonium production in pressurized water reactor

The nuclear nonproliferation is a common objective for the international society, of which one of the most important issues is the nonproliferation of weapon-grade nuclear material. Plutonium is a by-product when nuclear reactors are operated. If a commercial power nuclear reactor operates without counting its economic benefits, it is possible that weapon-grade plutonium (WGPu) would be produced in the nuclear reactor with using uranium as nuclear fuel. In the paper, we quantitatively study the plutonium isotopic composition and yield of the WGPu produced in a pressurized water reactor (PWR), and thereby investigate the proliferation risk of commercial nuclear reactors. The properties of plutonium produced in the PWR are calculated by MCORGS, which is developed by us to link MCNP and ORIGENS for calculating the transport-burnup. For evaluating the changing behavior of plutonium isotopic ratio dependent on the cooling time after being discharged from a PWR, we add the model of calculating the depletion and decay properties of nuclear fuel into the MCORGS code system. In order to calculate the yield of WGPu produced in the PWR, we carry out the neutron and burnup calculations by using five reactor models. The simulation models and operation history are based on the configuration and parameters of Japanese Takahama-3 unit. According to the positions and proportions of UO2 fuel rods, burnable poison rods and guide tubes in Takahama-3 PWR, we build a PWR model of an infinite heterogeneous 66 pin cell lattice, carry out simulation calculation and explore the condition for WGPu existing in the two kinds of fuel rods. When the burnup of a UO2 fuel rod is no more than 4.7 MWd/kgU, it contains WGPu. When the burnup of a burnable poison rod is no more than 2.7 MWd/kgU, it contains WGPu. Therefore, the issue of WGPu production in PWR is transformed into the research of the spatial distribution of PWR burnup. In order to obtain the axial PWR burnup, we build an infinite fuel pin cell model in which the PWR is divided into 20 equal zones in the axial direction, and calculate PWR axial burnup distribution when it is operated at 9 typical powers of Takahama-3 PWR. It is found that the burnup value of the two ends of 1/20 section is worth 1/3 of the two middle ones. Based on the principle of neutron leakage in a PWR and the simulation results of a fuel assembly, we build a special PWR mode, in which the PWR is divided into 10 zones in radial direction, and obtain the radial distribution of PWR burnup after the first, the second and the third fuel cycle. Based on the WGPu existing condition and the spatial distribution of a PWR burnup, in this paper we present the exact position of WGPu contained in PWR core and the yield of WGPu in UO2 fuel rods. The calculation results indicate that the spent nuclear fuel with low burnup brings huge proliferation risk, of which the supervision should be strengthened.

Study of on-the-fly Doppler broadening in JMCT program

In this paper, we introduce the on-the-fly (OTF) Doppler method which is used to calculate the temperature-dependent cross section. After substituting Adler-Adler multilevel representation into Doppler formulation, the theoretical formulation of temperature dependent cross section is obtained. This theoretical formulation can be approximated by a Taylor series expansion and asymptotic series expansion, which is the base of OTF method. The OTF method can be used to calculate the cross section of any nuclide at any temperature in a range of 300-3000 K based on cross section library of 300 K. For the OTF method, firstly, a series of temperature dependent cross section libraries is produced by NJOY. Secondly, a uniform energy grid is evaluated by the temperature dependent cross section libraries. Thirdly, a polynomial is used to fit the temperature dependent cross section on each energy grid. The coefficient of the polynomial is obtained by single value decomposition algorithm. Finally, the coefficients of the polynomial in all energy grids and the energy grids themselves are written in a text file. To test the cross section polynomial produced by OTF method, we compare the total and absorption cross sections of 238U and 235U calculated by the polynomial with those produced by NJOY. The errors of these cross sections obtained by these two programs are presented in the paper. The text file produced by OTF method can be read by the Monte Carlo code JMCT, which is a coupled neutron/photon transport code developed by IAPCM. After providing the temperature and energy of the particle, the temperature dependent cross sections in two adjacent energy grids are calculated by the polynomial respectively. The cross section of target energy is obtained by linear interpolation. Two benchmarks including a pin-cell model and an assembly model are used to verify the applications of OTF method in JMCT. The results are presented in the paper.

The history-partitioning method for multigroup stochastic cross section generation

A method is detailed for the stochastic generation of multigroup cross sections. This paper describes a solid theoretical framework for development of multigroup (discrete energy) nuclear data from continuous energy evaluated nuclear data files by Monte Carlo means. Included is a novel means of estimating the angular distribution of particles scattered in different energy groups.The method is demonstrated using a highly heterogeneous VHTR pin cell model. Homogenized cross sections are generated for a fuel region consisting of encapsulated fuel particles dispersed in a graphite matrix, placed back into the pin cell problem, and compared to the original continuous energy heterogeneous model. Results show eigenvalue agreement of approximately 100pcm, which is within the estimated uncertainty range of the multigroup data.

Monte Carlo analysis of KRITZ-2 critical benchmarks on the reactivity temperature coefficient using ENDF/B-VII.1 and JENDL-4.0 nuclear data libraries

A set of KRITZ-2 experiments light water moderated lattices with uranium oxide and mixed-oxide fuel rods, at room and elevated temperatures, performed in the early 1970’s have been assessed. Using the MCNP6.1 code with the most recent cross section libraries: JENDL-4 and ENDF/B-VII.1, the critical experiments KRITZ: 2-1, KRITZ: 2-13, and KRITZ: 2-19 achieved in the Sweden reactor KRITZ were analyzed. We have used the ENDF/B-VII.1 data provided with the MCNP6.1.1 version in ACE format and the Makxsf utility to handle the data in the specific temperatures not available in the MCNP6.1.1 original data. The JENDL-4 evaluations were processed using NJOY99 (update 364) to the temperatures of interest. The detailed comparisons of the calculated and measured (Benchmark, 2005) effective multiplication factors and pin power distributions for UO2 and MOX fuelled cores presented in this work demonstrate a good agreement between calculation and measurements. The maximum deviation of the calculation from the experimental data for keff, is 0.58% (absolute value) obtained for the KRITZ 2:1 at 248.5°C using ENDF/B-VII.1 data.To investigate better the influence of cross sections differences on the reactivity and temperature coefficient, we break down the infinite multiplication factor into its components using a pin cell model. Using this simple model we evaluated the temperature effect on the infinite multiplication factor and the effect on its components.We have also analyzed the temperature effect on the leakage by calculating the non leakage probability and the associated temperature coefficient. The overestimation of the calculated non-leakage probability values using JENDL-4 relatively to the calculated one using ENDF/B-VII.1 for all configurations and all temperatures can be explained by the overestimation of the absorptions in the JENDL-4 library especially in the resonance of the heavy nuclides. We can note that this discrepancy between the libraries decreases in hot conditions.For the reactivity temperature coefficient, our analysis has shown that the tendency of a negative error (overestimation by calculation of the absolute value of the RTC) usually observed when analyzing similar UO2 and MOX LWR lattices is confirmed. However, the level of the calculation error has been reduced significantly by using Monte Carlo modeling associated with the most recent nuclear data libraries.

UO2 versus MOX: Propagated Nuclear Data Uncertainty for keff, with Burnup

Precise assessment of propagated nuclear data uncertainties in integral reactor quantities is necessary for the development of new reactors as well as for modified use, e.g., when replacing UO2 fuel by mixed-oxide (MOX) fuel in conventional thermal reactors.This paper compares UO2 fuel to two types of MOX fuel with respect to propagated nuclear data uncertainty, primarily in keff, by applying the Fast Total Monte Carlo method (Fast TMC) to a typical pressurized water reactor pin cell model in Serpent, including burnup. An extensive amount of nuclear data is taken into account, including transport and activation data for 105 nuclides, fission yields for 13 actinides, and thermal scattering data for H in H2O.There is indeed a significant difference in propagated nuclear data uncertainty in keff; at zero burnup, the uncertainty is 0.6% for UO2 and ˜ 1% for the MOX fuels. The difference decreases with burnup. Uncertainties in fissile fuel nuclides and thermal scattering are the most important for the difference, and the reasons for this are understood and explained.This work thus suggests that there can be an important difference between UO2 and MOX for the determination of uncertainty margins. However, it is difficult to estimate the effects of the simplified model; uncertainties should be propagated in more complicated models of any considered system. Fast TMC, however, allows for this without adding much computational time.

MCNPX Monte Carlo burnup simulations of the isotope correlation experiments in the NPP Obrigheim

This paper describes the simulation work of the Isotope Correlation Experiment (ICE) using the MCNPX Monte Carlo computer code package. The Monte Carlo simulation results are compared with the ICE-Experimental measurements for burnup up to 30 GWD/t. The comparison shows the good capabilities of the MCNPX computer code package for predicting the depletion of the uranium fuel and the buildup of the plutonium isotopes in a PWR thermal reactor. The Monte Carlo simulation results show also good agreements with the experimental data for calculating several long-lived and stable fission products. However, for the americium and curium actinides, it is difficult to judge the predication capabilities for these actinides due to the large uncertainties in the ICE-Experimental data. In the MCNPX numerical simulations, a pin cell model is utilized to simulate the fuel lattice of the nuclear power reactor. Temperature dependent libraries based on JEFF3.1 nuclear data files are utilized for the calculations. In addition, temperature dependent libraries based ENDF/B-VII nuclear data files are utilized and the obtained results are very close to the JEFF3.1 results, except for ∼10% differences in the prediction of the minor actinide isotopes buildup.

Corrections to the 148Nd method of evaluation of burnup for the PIE samples from Mihama-3 and Genkai-1 reactors

The value of the burnup is one of the most important parameters of samples taken by post-irradiation examination (PIE). Generally, it is evaluated by the Neodymium-148 method. Precise evaluation of the burnup value requires: (1) an effective fission yield of 148Nd; (2) neutron capture reactions of 147Nd and 148Nd; (3) a conversion factor from fissions per initial heavy metal to the burnup unit GWd/t. In this study, the burnup values of the PIE data from Mihama-3 and Genkai-1 PWRs, which were taken by the Japan Atomic Energy Research Institute, were re-evaluated using more accurate corrections for each of these three items. The PIE data were then re-analyzed using SWAT and SWAT2 code systems with JENDL-3.3 library. The re-evaluation of the effective fission yield of 148Nd has an effect of 1.5–2.0% on burnup values. Considering the neutron capture reactions of 147Nd and 148Nd removes dependence of C/E values of 148Nd on the burnup value. The conversion factor from FIMA(%) to GWd/t changes according to the burnup value. Its effect on the burnup evaluation is small for samples having burnup of larger than 30 GWd/t. The analyses using the corrected burnup values showed that the calculated 148Nd concentrations and the PIE data is approximately 1%, whereas this was 3–5% in prior analyses. This analysis indicates that the burnup values of samples from Mihama-3 and Genkai-1 PWRs should be corrected by 2–3%. The effect of re-evaluation of the burnup value on the neutron multiplication factor is an approximately 0.6% change in PIE samples having the burnup of larger than 30 GWd/t. Finally, comparison between calculation results using a single pin-cell model and an assembly model is carried out. Because the results agreed with each other within a few percent, we concluded that the single pin-cell model is suitable for the analysis of PIE samples and that the underestimation of plutonium isotopes, which occurred in the previous analyses, does not result from a geometry model.

Comparison between HELIOS critical-depletion calculations and a PWR thorium cell burnup benchmark

A comparison between the HELIOS computer code and a pin cell burnup benchmark is presented in this paper. The benchmark is based on a thorium fuel pin cell moderated with light water. The burn-up dependent eigenvalue and isotopes concentrations obtained with HELIOS were compared with those obtained with state-of-the-art transport codes (MOCUP, INEEL-MOCUP and CASMO4). The pin cell model considers eight azimuthal regions in the moderator zone and two radial regions in the fuel. The analysis with HELIOS was carried out with cross section libraries of 35 and 190 energy groups. The HELIOS results showed that the average absolute difference as a function of burnup were less than 1% δk/ k in the eigenvalue and an average absolute difference of around 5% in the isotopes concentration, with respect to CASMO4 code.

A Combined Method to Evaluate the Resonance Self Shielding Effect in Power Fast Reactor Fuel Assembly Calculation

A combined method for evaluating the resonance self shielding effect in a two-dimensional power fast reactor fuel assembly is proposed. This method uses the sub-group method to evaluate the self shielding effect of heterogeneous cell and collision probability method in the ultra-fine energy groups to deal with the resonance interference effect between different resonant nuclides. In the present paper, a comparison between the table look-up method and the sub-group method is carried out and it is shown that the latter is superior to the former in a view of evaluating the resonance self shielding effect. These methods have a common defect that it is impossible to treat the resonance interference effect between different resonant nuclides. It can be overcome by using “a correction factor of the resonance interference effect” obtained by the collision probability calculation in the ultra-fine energy groups in a single fuel pin cell model. The microscopic effective cross section obtained by this proposed method agrees well with that by continuous energy Monte Carlo code within 5% relative difference above 100 eV. The k ∞ value is affected about 0.1%Δk/k by the use of the correction factor.