Effective Delayed Neutron Fraction Βeff Research Articles

Validation and Neutronic Analysis of the CENM TRIGA MARK II SCALE Research Reactor Model: Computations Versus Experiment

This research analysis is mainly devoted to enhancing the safe and optimum use of the Center des Etudes Nucléaires de la Maâmora (CENM) TRIGA MARK II research reactor. To serve this purpose, various integral neutronic responses, such as the effective multiplication factor keff, the effective delayed neutron fraction βeff, the neutron flux distributions at the beam port entrances and the pneumatic transfer system bottom, the pin power peaking factors, the total excess reactivity, the control rod worth, the shutdown margin, and the worth of 11 fuel elements taken from different TRIGA core positions are calculated in order to evaluate the accuracy and the reliability of the developed TRIGA SCALE reactor model. The aim has been fulfilled by comparing the TRIGA SCALE results with those obtained by the MCNP TRIGA model, as well as with some recent experimental measurements from 2021. In general, all the obtained results reveal a good consistency between the SCALE and MCNP TRIGA models studied in this paper. The results analysis indicates also that the B-2 fuel element (Ring B) is the hottest rod among the 101 fuel rods existing in the TRIGA reactor core, which releases a maximum power of 31.67 kW. Furthermore, the total control rod worth, the total core excess reactivity, and the shutdown margin results are also closer to the experimental measurements.

Preservation of kinetics parameters generated by Monte Carlo calculations in two-step deterministic calculations

The generation of accurate kinetic parameters such as mean generation time Λ and effective delayed neutron fraction βeff via Monte Carlo codes is established. Employing these in downstream deterministic codes warrants another step to ensure no additional error is introduced by the low-order transport operator when computing forward and adjoint fluxes for bilinear weighting of these parameters. Another complexity stems from applying superhomogenization (SPH) equivalence in non-fundamental mode approximations, where reference and low-order calculations rely on a 3D full core model. In these cases, SPH factors can optionally be computed for only part of the geometry while preserving reaction rates and K-effective, but the impact of such approximations on kinetics parameters has not been thoroughly studied. This paper aims at studying the preservation of bilinearly-weighted quantities in the Serpent–Griffin calculation procedure. Diffusion and transport evaluations of IPEN/MB-01, Godiva, and Flattop were carried out with the Griffin reactor physics code, testing available modeling options using Serpent-generated multigroup cross sections and equivalence data. Verifying Griffin against Serpent indicates sensitivities to multigroup energy grid selection and regional application of SPH equivalence, introducing significant errors; these were demonstrated to be reduced through the use of a transport method together with a finer energy grid.

Calculation of kinetic parameters βeff and Λ with modified open source Monte Carlo code OpenMC(TD)

This work presents the methodology used to expand the capabilities of the Monte Carlo code OpenMC for the calculation of reactor kinetic parameters: effective delayed neutron fraction βeff and neutron generation time Λ. The modified code, OpenMC(Time-Dependent) or OpenMC(TD), was then used to calculate the effective delayed neutron fraction by using the prompt method, while the neutron generation time was estimated using the pulsed method, fitting Λ to the decay of the neutron population. OpenMC(TD) is intended to serve as an alternative for the estimation of kinetic parameters when licensed codes are not available. The results obtained are compared to experimental data and MCNP calculated values for 18 benchmark configurations.

Explore the possible advantages of using thorium-based fuel in a pressurized water reactor (PWR) Part 1: Neutronic analysis

This study discusses the effect of using 232Th instead of 238U on the neutronic characteristics and the main operating parameters of the pressurized water reactor (PWR). MCNPX version 2.7 was used to compare the neutronic characteristics of UO2 with (Th, 235U)O2 and (Th, 233U) O2. Firstly, the infinity multiplication factor (Kinf), thermal neutron flux, and power distribution have been studied for the investigated fuel types. Secondly, the effect of Gd2O3 and Er2O3 on the Kinf and on the radial thermal neutron flux and thermal power has been investigated to distinguish which of them is more suitable than the other in reactivity management. Thirdly, to illustrate the effectiveness of 232Th in decreasing the inventory of both the actinides and non-actinides, the concentration of plutonium (Pu) isotopes and minor actinides (MAs) has been simulated with the fuel burnup. Besides, due to their large thermal neutron absorption cross-section, the concentrations of 135Xe, 149Sm, and 151Sm with the fuel burnup have been investigated. Finally, the main safety parameters such as the reactivity worth of the control rods (ρCR), the effective delayed neutron fraction βeff, and the Doppler reactivity coefficient (DRC) were calculated to determine to which extent these fuel types achieve the acceptable limits.

Analysis of OECD/NEA medium 1000 MWth sodium-cooled fast reactor using the Monte Carlo serpent code and ENDF/B-VIII.0 nuclear data library

This study presents a benchmark evaluation of the new ENDF/B-VIII.0 nuclear data library for the Organization for Economic Co-operation and Development/Nuclear Energy Agency Medium 1000 MWth sodium-cooled fast reactor (SFR). The study presented herein covers both SFR core types, i.e., metallic fueled (MET-1000) and oxide fueled (MOX-1000), simulated using the continuous-energy Monte Carlo Serpent2 code. The neutronics performances of the ENDF/B-VIII.0-based simulations were compared mainly to two libraries: ENDF/B-VII.1 and JENDL-4.0. The comparison includes several neutronics parameters evaluated for the beginning and end of the cycle conditions. These parameters include the effective multiplication factor keff, total effective delayed neutron fraction βeff, sodium void reactivity (∆ρNa), Doppler constant (∆ρDoppler), and control rod worth (∆ρCR). In addition, a sensitivity study was used to reveal the major isotope/reaction pairs contributing to the discrepancy observed in the performance of the three libraries using 33 and 44-energy-group structures.

Validation of CASMO5 neutron kinetics parameters

Studsvik’s CASMO5 lattice physics code is validated against neutron kinetics experiments performed at the Tank-Type Critical Assembly (TCA) and the IPEN/MB-01 reactor. For the TCA measurements, CASMO5 agreed with βeff/Λ within 3%. For the IPEN/MB-01 measurements, CASMO5 computed the effective delayed neutron fraction βeff and the mean neutron generation time Λ to within 3.6σ of the measurement error. The ENDF/B-VII.1 and JENDL-4.0 delayed neutron data gave the best results for βeff, followed by Tuttle and then the eight-group JEFF-3.2. CASMO5′s predicted reactivity ρ versus reactor period was mostly within 5% using Tuttle, JENDL-4.0, or JEFF-3.2 delayed neutron data. However, using ENDF/B-VII.1 resulted in poorer reactivity predictions, with errors up to 50%. All CASMO5 kinetics parameters are based on a recently-developed transport-based adjoint capability, which relies on the Method of Characteristics with Linear Source approximation for the solution of the two-dimensional transport equation.

Improvement of the VVER-1200 Fuel Cycle by Introducing Thorium with Different Fissile Material in Blanket-Seed Assembly

This work presents a comparison between the homogeneous and heterogeneous [seed-blanket (SB)] fuel assembly used in the VVER-1200 core. The MCNPX 2.7 code with the ENDF/B-VII.0 data library was used to investigate the possible advantages that can be achieved when the SB assembly is used instead of homogeneous assembly. Thorium-232 was used as a fertile material in the blanket region and different fissile materials were investigated in the seed region. The neutronic characteristics of the presented designs were investigated by comparing four different combinations of fissile materials with (Th,U)O2 that were distributed uniformly through the whole assembly. The radial power distribution was investigated in both homogeneous and SB assemblies. The power distribution is flatter in the homogeneous assembly than the heterogeneous assembly. The suggested fuels in the SB assembly achieved a longer fuel cycle than the homogeneous assembly. Neutronic parameters related to reactor safety operation, such as control rod worth, Doppler reactivity coefficient, and effective delayed neutron fraction βeff have been investigated for the suggested fuel types. The SB assembly achieved a higher conversion ratio than the homogeneous assembly. Therefore, the fissile inventory ratio decreased more slowly with burnup in the case of SB than in the homogeneous assembly. Using 232Th instead of 238U reduced the production of the plutonium and the transuranic atoms.

Monte Carlo uncertainty quantification of the effective delayed neutron fraction

ABSTRACT The applicability of Monte Carlo techniques, namely the Monte Carlo sensitivity method and the random-sampling method, for uncertainty quantification of the effective delayed neutron fraction βeff is investigated using the continuous-energy Monte Carlo transport code, MCNP, from the perspective of statistical convergence issues. This study focuses on the nuclear data as one of the major sources of βeff uncertainty. For validation of the calculated βeff, a critical configuration of the VENUS-F zero-power reactor was used. It is demonstrated that Chiba's modified k-ratio method is superior to Bretscher's prompt k-ratio method in terms of reducing the statistical uncertainty in calculating not only βeff but also its sensitivities and the uncertainty due to nuclear data. From this result and a comparison of uncertainties obtained by the Monte Carlo sensitivity method and the random-sampling method, it is shown that the Monte Carlo sensitivity method using Chiba's modified k-ratio method is the most practical for uncertainty quantification of βeff. Finally, total βeff uncertainty due to nuclear data for the VENUS-F critical configuration is determined to be approximately 2.7% with JENDL-4.0u, which is dominated by the delayed neutron yield of 235U.

Sensitivity and uncertainty analysis of βeff for MYRRHA using a Monte Carlo technique

This paper presents a nuclear data sensitivity and uncertainty analysis of the effective delayed neutron fraction βeff for critical and subcritical cores of the MYRRHA reactor using the continuous-energy Monte Carlo N-Particle transport code MCNP. The βeff sensitivities are calculated by the modified k-ratio method proposed by Chiba. Comparing the βeff sensitivities obtained with different scaling factors a introduced by Chiba shows that a value of a = 20 is the most suitable for the uncertainty quantification of βeff. Using the calculated βeff sensitivities and the JENDL-4.0u covariance data, the βeff uncertainties for the critical and subcritical cores are determined to be 2.2 ± 0.2% and 2.0 ± 0.2%, respectively, which are dominated by delayed neutron yield of 239Pu and 238U.

Current Mode Neutron Noise Measurements in the Zero Power Reactor CROCUS

The present article is an overview of developments and results regarding neutron noise measurements in current mode at the CROCUS zero power facility. Neutron noise measurements offer a non-invasive method to determine kinetic reactor parameters such as the prompt decay constant at criticality α = βeff / λ, the effective delayed neutron fraction βeff, and the mean generation time λ for code validation efforts. At higher detection rates, i.e. above 2×104 cps in the used configuration at 0.1 W, the previously employed pulse charge amplification electronics with BF3 detectors yielded erroneous results due to dead time effects. Future experimental needs call for higher sensitivity in detectors, higher detection rates or higher reactor powers, and thus a generally more versatile measurement system. We, therefore, explored detectors operated with current mode acquisition electronics to accommodate the need. We approached the matter in two ways: 1) By using the two compensated 10B-coated ionization chambers available in CROCUS as operational monitors. The compensated current signal of these chambers was extracted from coremonitoring output channels. 2) By developing a new current mode amplification station to be used with other available detectors in core. Characteristics and first noise measurements of the new current system are presented. We implemented post-processing of the current signals from 1)and 2) with the APSD/CPSD method to determine α. At two critical states (0.5 and 1.5 W), using the 10B ionization chambers and their CPSD estimate, the prompt decay constant was measured after 1.5 hours to be α=(156.9 ± 4.3) s-1 (1σ). This result is within 1σ of statistical uncertainties of previous experiments and MCNPv5-1.6 predictions using the ENDF/B-7.1 library. The newsystem connected to a CFUL01 fission chamber using the APSDestimate at 100 mW after 33 min yielded α = (160.8 ± 6.3) s-1, also within 1σ agreement. The improvements to previous neutron noise measurementsinclude shorter measurement durations that can achievecomparable statistical uncertainties and measurements at higherdetection rates.

Sensitivity of power spectral density techniques to numerical parameters in analyzing neutron noise experiments

Power spectral density (PSD) methods are well-known and widely used for the analysis of neutron noise experiments and obtaining the reactor's integral kinetic parameters, i.e., the effective delayed neutron fraction βeff and the prompt neutron generation time Λ. Many uncertainties are usually associated with PSD methods, e.g., statistical fluctuations in the neutron flux, power drifts, uncertainties in the Diven factor, the integral fission rate, and in the reactivity value. However, the uncertainty associated with the numerical parameters used in the power spectrum calculation procedure is hardly discussed in the literature and generally overlooked.The aim of this paper is to study the uncertainties in the kinetic parameters of a reactor core, obtained by PSD methods, which are associated with the numerical parameters of the method. A comprehensive estimation of the kinetic parameters, including all other uncertainties, is not pursued. In this paper, PSD methods are implemented to analyze critical and subcritical configurations of the MINERVE zero power reactor in order to measure its integral kinetic parameters βeff and Λ. Both cross and auto power spectral densities are calculated and the kinetic parameters are obtained via Lorentzian curve fitting over the calculated PSD. The sensitivity of the obtained kinetic parameters to the choice of numerical parameters used for spectrum calculations is studied and found to be significant with respect to other uncertainties. A novel methodology is proposed for analyzing the kinetic parameters' sensitivity to the PSD calculations and for quantifying the associated uncertainties.

Monte Carlo Approach of Effective Delayed Neutron Fraction by k-Ratio Method with External Neutron Source

In an accelerator-driven system (ADS), the effective delayed neutron fraction βeff is required for subcriticality measurements in order to convert measured reactivity in dollar units into pcm units. Here, an alternative calculation methodology with source-dependent reaction rates is proposed to estimate the subcriticality (pcm units) with an external neutron source for the newly defined parameter. In the proposed methodology, the parameter is obtained by the k-ratio method with reaction rates considering the external neutron source (fixed-source calculation) and is compared with that obtained by the eigenvalue calculations (MCNP6.1). To investigate its applicability to the estimation of subcriticality, subcriticality measurements by the extrapolated area ratio method are carried out in the experiments in ADS at the Kyoto University Critical Assembly, with the variation of subcriticality (pcm units) and the spectrum of the external neutron source. Then, is estimated by the proposed methodology with MCNPX-2.5.0. The measured subcriticality with the use of obtained by the fixed-source calculations shows good agreement with that obtained by the different measurement methodology and MCNPX-2.5.0. Through the subcriticality estimation, the applicability of the proposed methodology is confirmed for different subcriticality levels and the spectrum of the external neutron source.

Measurements of effective delayed neutron fraction in a fast neutron reactor using the perturbation method**Supported by Foundation of Key Laboratory of Neutron Physics, China Academy of Engineering Physics (2012AA01, 2014AA01), National Natural Science Foundation (11375158, 91326104)

A perturbation method is proposed to obtain the effective delayed neutron fraction βeff of a cylindrical highly enriched uranium reactor. Based on reactivity measurements with and without a sample at a specified position using the positive period technique, the reactor reactivity perturbation Δρ of the sample in βeff units is measured. Simulations of the perturbation experiments are performed using the MCNP program. The PERT card is used to provide the difference dk of effective neutron multiplication factors with and without the sample inside the reactor. Based on the relationship between the effective multiplication factor and the reactivity, the equation βeff = dk/Δρ is derived. In this paper, the reactivity perturbations of 13 metal samples at the designable position of the reactor are measured and calculated. The average βeff value of the reactor is given as 0.00645, and the standard uncertainty is 3.0%. Additionally, the perturbation experiments for βeff can be used to evaluate the reliabilities of the delayed neutron parameters. This work shows that the delayed neutron data of 235U and 238U from G.R. Keepin’s publication are more reliable than those from ENDF-B6.0, ENDF-B7.0, JENDL3.3 and CENDL2.2.

Experimental estimation of the delayed neutron fraction βeff of the MAESTRO core in the MINERVE zero power reactor

A method for determining the effective delayed neutron fraction βeff using in-pile reactivity oscillations and Fourier analysis is presented. This method is based on measurements of the reactor's power response to small periodic in-pile reactivity perturbations and utilizes Fourier analysis for reconstruction of the reactor zero power transfer function. This approach enables the estimation of βeff using multi-parameter nonlinear weighted least-squares fit. The method extends previous works by accounting for higher harmonics excitation in the frequency domain by the trapezoidal reactivity signal, both in the reactivity perturbation and in the reactor power response. We show that by using this new approach it is possible to obtain the reactor transfer function in a wide range of frequencies, using only a single oscillation frequency. This method is applied to a set of measurements of the MAESTRO core configuration in the MINERVE zero power reactor (ZPR) located at the Cadarache Research Center. The derived value of βeff, using this method, is 711 ± 17 pcm.

Evaluation of βeff Measurements with 252Cf-Source Pseudo-Worth and Noise Methods

The effective delayed neutron fraction βeff is of primary importance for reactivity control of fissile systems and therefore for reactor design and safety analyses. Validation of βeff calculations is complicated by the limited availability of benchmark-quality data. This paper focuses on evaluation and analysis of βeff measurements with 252Cf-source pseudo-worth and noise methods performed at SNEAK 7A and SNEAK 7B assemblies in Germany in the 1970s. The experiments are thoroughly documented in the International Handbook of Evaluated Reactor Physics Benchmark Experiments and briefly presented in this paper. The measurements performed with the two different methods on SNEAK 7A and SNEAK 7B and other facilities systematically produce different values. Given that the noise approach presumes evolution of neutron field fluctuations in a one-point kinetic model, it was assumed that the discrepancies originate from spatial effects. A two-point kinetic model was tested to check this assumption. The paper demonstrates that the βeff measured with the noise method on the SNEAK 7A and SNEAK 7B facilities should be corrected while the 252Cf-source pseudo-worth measurement produces an accurate value.

Calculation of effective delayed neutron fraction with modified library of Monte Carlo code

A new Monte Carlo method is proposed to calculate the effective delayed neutron fraction βeff. Based on perturbation theory, βeff is calculated with modified library of Monte Carlo code. To verify the proposed method, calculations are performed on several benchmarks. The error of the method is analyzed and the way to reduce error is proposed. The results are in good agreement with the reference data.

Monte Carlo and deterministic computational methods for the calculation of the effective delayed neutron fraction

The effective delayed neutron fraction βeff plays an important role in kinetics and static analysis of the reactor physics experiments. It is used as reactivity unit referred to as “dollar”. Usually, it is obtained by computer simulation due to the difficulty in measuring it experimentally. In 1965, Keepin proposed a method, widely used in the literature, for the calculation of the effective delayed neutron fraction βeff. This method requires calculation of the adjoint neutron flux as a weighting function of the phase space inner products and is easy to implement by deterministic codes. With Monte Carlo codes, the solution of the adjoint neutron transport equation is much more difficult because of the continuous-energy treatment of nuclear data. Consequently, alternative methods, which do not require the explicit calculation of the adjoint neutron flux, have been proposed. In 1997, Bretscher introduced the k-ratio method for calculating the effective delayed neutron fraction; this method is based on calculating the multiplication factor of a nuclear reactor core with and without the contribution of delayed neutrons. The multiplication factor set by the delayed neutrons (the delayed multiplication factor) is obtained as the difference between the total and the prompt multiplication factors. Using Monte Carlo calculation Bretscher evaluated the βeff as the ratio between the delayed and total multiplication factors (therefore the method is often referred to as the k-ratio method). In the present work, the k-ratio method is applied by Monte Carlo (MCNPX) and deterministic (PARTISN) codes. In the latter case, the ENDF/B nuclear data library of the fuel isotopes (235U and 238U) has been processed by the NJOY code with and without the delayed neutron data to prepare multi-group WIMSD neutron libraries for the lattice physics code DRAGON, which was used to generate the PARTISN macroscopic cross sections. In recent years Meulekamp and van der Marck in 2006 and Nauchi and Kameyama in 2005 proposed new methods for the effective delayed neutron fraction calculation with only one Monte Carlo computer simulation, compared with the k-ratio method which require two criticality calculations. In this paper, the Meulekamp/Marck and Nauchi/Kameyama methods are applied for the first time by the MCNPX computer code and the results obtained by all different methods are compared.

Calculation of LWR βeff kinetic parameters: Validation on the MISTRAL experimental program

This paper presents the analysis of the MISTRAL experimental program in EOLE on the determination of the effective delayed neutron fraction βeff for UO2 and MOX Light Water Reactor cores using the APOLLO2.8 code and JEFF-3.1.1 nuclear data library. The objective was to verify if the new 8 time-groups data in JEFF3 library (instead of the classical 6 groups) allow to reduce the calculation – experiment discrepancy observed using ENDF/B-VII.0 or the previous JEF-2.2 library. The present analysis has shown that the C/E bias is reduced from +2.8% with JEF2.2 to +0.8±1.6% for the UO2 cores and from +0.8% (with JEF2.2) to +0.2±1.6% for the MOX cores, using Discrete Ordinates 2D core calculations. The introduction of Method of Characteristics (MOC) in the flux calculation, through so-called Reference “SHEM-MOC” (281-groups – P3 for scattering) and optimized ”LWR2005” (26-groups – P3 and corrected P0 for scattering) calculation schemes improve slightly the results, with C/E discrepancies of +0.2±1.5% and +0.0±1.5% respectively for UO2, and +0.1±1.6% and −0.1±1.6% respectively for MOX.

JENDL-4.0 Benchmarking for Effective Delayed Neutron Fraction of Fast Neutron Systems

The performance of the latest Japanese evaluated nuclear data library JENDL-4.0 for the prediction of effective delayed neutron fraction βeff is assessed using experimental data of a wide range of fast neutron systems. Covariance data of JENDL-4.0 are used to quantify nuclear-data-induced uncertainties. Calculations with other libraries, JENDL-3.3, ENDF/B-VII.0, and JEFF-3.1, are also carried out for a quantitative comparison. JENDL-4.0 results in good agreement between calculation and experimental values within total uncertainties, and consistency between the differential nuclear data and integral experimental data is confirmed. While the other libraries also show good performance for βeff prediction, there are small differences in the predicted values of βeff among different libraries and ENDF/B-VII.0 gives the most stable results. Furthermore, a simple and convenient procedure to calculate sensitivity profiles of βeff to nuclear data is proposed.

Calculation of the effective delayed-neutron fraction and prompt-neutron lifetime in IBR-2M

The main parameters of IBR-2M are presented: the effective delayed-neutron fraction βeff and the promptneutron lifetime τ, calculated using the DORT two-dimensional multigroup neutron-transport compute code and the SCALE4 code with a system of multigroup nuclear constants. For a regular IBR-2M regime βeff = 0.00216 ± 0.00007, τ = (6.5 ± 0.5)·10–8 sec, the delay-neutron value γ = 0.980, the prompt-neutron decay constant in the critical state α = 3.5·104 sec–1. The calculations showed that the effective delayed-neutron fraction for IBR-2M is identical, within the error limits, to the measured value for IBR-2, the prompt-neutron lifetime is approximately 5% longer (βeff = 0.00216, τ = (6.2 ± 0.2)·10–8 sec). It is shown that βeff and τ increase somewhat as the IBR-2 core size increases in the radial direction.