Effective Delayed Neutron Fraction Research Articles

Examination of the use of thorium-based fuel for burning minor actinides in European sodium cooled fast reactor

Abstract To reduce the potential and volume of radiotoxicity of radioactive wastes, minor actinides (MAs) elements recovered from discharged fuel are to be recycled. In this context, the main aim of this work is to examine the possibility of using thorium-based fuel for burning extra MAs in the fourth generation European Sodium cooled Fast Reactor (ESFR). For that MCNPX transport code was used to design a representative fuel assembly of this concept. The reference uranium-based fuel was uniformly replaced by thorium mixed with different fractions of MAs and burned for 2050 effective full power days. The influence of MAs on the evolution of reactivity and fuel transmutation is being investigated to ensure the performance of the fuel. Also, different neutronic and safety parameters such as neutron yield, neutron spectrum, neutron flux, effective delayed neutron fraction, Doppler constant, sodium void reactivity coefficient, were computed and their change with MAs content was investigated. Results indicate that recycling of MAs in ESFR using thorium-based fuel has a positive effect on reactivity and transmutation evolution but on other hand has a negative effect on safety parameters.

Extended development of the Monte Carlo code MCNP for effective delayed neutron fraction calculation in molten salt reactors

In this study the Monte Carlo code MCNP is extended to account for the fuel circulation effect in molten salt reactors. An algorithm is created to track delayed neutron precursors and the effective delayed neutron fraction is calculated using predicted fuel velocity fields from the computational fluid dynamics solver. Delayed neutron precursors are monitored throughout various sections of a closed fuel loop in a molten salt reactor. The Moten Salt Fast Reactor is chosen as the benchmark for the extended code, with the calculated multiplication factor and reactivity feedback coefficients agreeing well with referenced results. Dependence of the effective delayed neutron fraction on the fuel flow rate is studied. Validation of the extended code is performed using the Molten Salt Reactor Experiment, showing a good agreement between the calculated delayed neutron fraction loss and the experimental data. These results demonstrate that the extended MCNP code can be reliably used for delayed neutron fraction calculations in both fast and thermal spectrum molten salt reactors.

Development and Verification of Neutron Kinetics Parameter Calculation Program Applicable to Subcritical Systems of Long-Life Reactors

The fundamental prompt neutron delayed constant α, the effective delayed neutron fraction β eff , and the effective neutron generation time Λ eff are important for accurate measurements of keff in subcritical systems. In this paper, based on the open-source program OpenMC, a module with the function of calculating the α-eigenvalue is developed based on the k-α iterative method. Based on the nodal expansion method (NEM), an adjoint neutron flux calculation program was developed, which in turn used the idea of coupling the k-α iterative method with the NEM to obtain the neutron kinetics parameters (α, β eff , and Λ eff ) of the subcritical system and allowed for a more accurate keff under the subcritical system as compared to the traditional k-mode program. In this paper, the results of the α-eigenvalues calculated by the program are validated using the Godiva benchmark and the MUSE-4 device as computational objects. The accuracy of the results for β eff and Λ eff was verified with the KUCA (Kyoto University Critical Assembly) benchmark. The results of the keff calculations using k-mode and α-mode are compared with the ADS benchmark. The results show that the calculation program (α-mode) can obtain keff under the subcritical system more accurately, which makes up for the shortcomings of the traditional program, which cannot be calculated under the deep subcritical system. The relative error between the calculated and reference values was less than 750 pcm at deep subcriticality (keff = 0.899). The error was less than 400 pcm at the deeper subcritical system (keff = 0.952), which can satisfy the demand for neutron dynamics parameters and keff calculation in the subcritical system. The program can also continue to be upgraded in the later stage in the calculation method and other aspects.

Potential of mixed oxide fuel for higher fissile conversion ratio in light water reactors

The prospect of adopting various mixed oxide fuels to increase the conversion ratio (CR) of conventional LWRs has been explored in this study. The Westinghouse AP1000 fuel assembly (FA) was taken as the reference design. While the geometry of the FA was kept the same, five assembly models were constructed utilizing different MOX fuels in the fuel rods. Depleted UO2 was mixed with PuO2 for the first model, the next two models featured a combination of UO2 with ThO2, the fourth one utilized a mixture of PuO2 and ThO2, and the final model employed a combination of UO2, PuO2, and ThO2. Depletion analysis of these fuel assembly models was then carried out using the lattice physics code Dragon 5. The burnup-dependent infinite multiplication factor and reactivity were determined and a significant improvement in cycle length was observed at the end of the burnup period because of fertile to fissile conversion. A higher fast fission rate was obtained for plutonium-based fuel models compared to the reference, whereas the thorium-based fuel models demonstrated higher thermal fission rates. The linear reactivity model (LRM) was utilized to calculate fuel cycle performance for a three-batch refueling scheme. The three fuel models utilizing PuO2 achieved improved discharge burnup and cycle length, and required lower charge fuel mass to obtain the same thermal power. All of the five proposed models attained higher conversion ratios compared to the reference, while the highest increment in CR was obtained for the last model utilizing all three oxides. The CR of conventional UO2 fuel in AP1000 was 0.64, whereas it was calculated to be 0.73 for Model 5. Key safety parameters including the fuel and moderator temperature coefficients of reactivity and the effective delayed neutron fraction of the models were also determined. Finally, the isotopic evolution of minor actinides and fission product poisons of the models were analyzed as a function of burnup and compared with the reference.

Implementation and Testing of Generalized Perturbation Theory Capabilities in TRIPOLI-4®

In this paper, we describe the implementation, verification, and numerical validation of Generalized Perturbation Theory (GPT) capabilities in the TRIPOLI4® Monte Carlo code. The GPT is applied to reaction rate ratios (linear forms) and effective kinetics parameters (bilinear forms). For these latter, we focus in particular on the effective neutron generation time Λ eff , the effective prompt lifetime ℓ eff , and the effective delayed neutron fraction β eff . Verification is achieved comparing the results obtained using TRIPOLI-4® to benchmarks where analytical solutions are available. Numerical validation is performed with respect to independent Monte Carlo calculations using the SCALE 6.2.4 and SERPENT 2.2 codes, to published results, and to direct perturbations. Finally, a comparison with respect to the APOLLO3® deterministic code is performed for the EPICURE experimental configuration of the water-moderated EOLE reactor core, formerly operated at CEA.

Evaluation of Kinetic Parameters RSG-GAS Reactor Equilibrium Silicide Core Using Continuous-Energy Monte Carlo Serpent 2 Code

The purpose of this study is to determine the kinetic parameters of the RSG-GAS equilibrium core. The calculated kinetic parameters are the effective delayed neutron fraction βeff, the neutron generation time Ʌ, and the prompt neutron lifetime ℓ since they are related to the safety of nuclear operations. The kinetic parameters were calculated using the Serpent 2 code with the ENDF/B-VII.1 and ENDF/B-VIII.0 nuclear data libraries. Calculations were performed using various adjoint-weighted methods such as Meulekamp’s method, Nauchi’s method, the Iterated Fission Probability method, and the Perturbation Technique. The calculated results of the six-group delayed neutron fraction by the Meulekamp and the IFP methods showed no significant difference. Choosing the IFP method as the reference, the maximum difference for βeff (694 pcm) is 0.73%, and the maximum difference for Ʌ and ℓ is 1.89%. The calculated kinetic parameters with ENDF/B-VII.1 and ENDF/B-VIII.0 are quite close, with a maximum difference of 0.9%. The sensitivity analysis results indicate several nuclides and reaction types that dominantly affect the βeff and Λ. The results of the kinetic parameter calculations can be used for the safety analysis of the RSG-GAS equilibrium core.

Sensitivity and Uncertainty Calculations in Support of the Noise Analysis of the TAPIRO Reactor

In the framework of an assessment of the application of neutron noise methodologies to the TAPIRO reactor, sensitivity and uncertainty analyses on impacting nuclear data for this experimental reactor have been performed using the Serpent Monte Carlo code. Integral parameters relevant to the noise analysis of TAPIRO have been investigated, namely the effective multiplication factor, the effective delayed neutron fraction and the effective generation time. The nuclear data uncertainty has been assessed using different data libraries (ENDF/B-VIII.0 and JEFF-3.3), different energy grids (ECCO-33 and XMAS- 172) and different techniques (Generalised Perturbation Theory and Unscented Transform). A ranking of the most impacting nuclides and reactions in terms of uncertainties has been performed, pointing out that the impact of nuclear data uncertainties on the responses is non-negligible and must be taken into account also in the noise analysis of the reactor.

A variance-reduction strategy for the sensitivity of βeff

The Monte Carlo computation of the GPT-based sensitivity of the effective delayed neutron fraction βeff to nuclear data proves to be quite difficult to converge due to the small amount of delayed neutrons that are sampled in k-eigenvalue calculations. This paper describes a variance-reduction method aimed at efficiently computing the sensitivity coefficients of βeff, reducing the associated Monte Carlo uncertainty and increasing the Figure Of Merit. This variance-reduction technique allows also computing the sensitivities of βj eff for a specific precursor family j. Verification and performance evaluation are achieved using simple configurations admitting analytical solutions and several continuousenergy benchmarks.

The influence of graphite moderator density on the neutronic performance and fuel economy of a Molten Salt Reactor

Typical thermal molten salt reactor (MSR) employs graphite as its neutron moderator, due to its chemical compatibility and low neutron absorption. It is not without issues, however, since graphite provides positive temperature feedback when the MSR is fueled with U-233. Reducing the graphite density can possibly ameliorate this issue, but at the cost of other neutronic parameters, such as fertile conversion into fissile nuclide, and fuel economy, such as fissile makeup cost. This study evaluates the influence of graphite moderator density on the neutronic performance and fuel economy of an MSR. Passive Compact Molten Salt Reactor (PCMSR) design was used as the MSR model. To evaluate the neutronic parameters, MCNP6.2 radiation transport code with ENDF/B-VII.0 neutron cross section library were used. The evaluated neutronic parameters were temperature coefficient of reactivity (TCR), kinetic parameters, and conversion ratio (CR). Meanwhile, the fuel economy evaluation comprised the initial fuel inventory cost and fissile makeup cost. From the calculation results, lowering graphite density remarkably improves TCR, but also decreased CR in a notable amount. While effective delayed neutron fraction (βeff) was not particularly affected, mean neutron generation time (Λ) was reduced in lower graphite density. Considering the fuel economy, initial fuel cost is not significantly affected, but the fissile makeup cost can be sensitive of graphite density.

Research on Neutronics Safety Parameters of the AP1000 Nuclear Reactor under Different Conditions

Changes in temperature during reactor operation may cause changes in physical parameters, leading to core overheating and accidents. It is essential to analyze and assess the safety parameters of the core under different operating conditions. This paper investigates the effects of fuel temperature, moderator density, boron concentration, and control rod state on AP1000 safety parameters. The study uses RMC and NJOY to calculate the changes in reactivity factor, effective delayed neutron fraction, and neutron generation time of the AP1000 reactor under different operating conditions. The changes in reactivity coefficients, neutron fluxes, and relative power densities of AP1000 reactors are analyzed for normal and accidental operating conditions. The results indicated that the reactivity coefficient remained negative under accident conditions, which ensured the safe operation of the reactor. The delayed neutron fraction, neutron flux, and power density distributions are affected by fuel temperature, moderator density, and control rod position. The control rod worth was sufficient for the emergency shutdown of the reactor under accidental conditions. It is demonstrated that the operation of the AP1000 reactor under study conditions is safe and controllable.

Comparative analysis of fuel burnup calculations of fourth-generation European fast reactors

Abstract The sustainability of nuclear energy implies the continuous research and development of fast reactor technology. This work represents a comparative analysis of fuel burnup calculations of three commercial-level fast spectrum concepts which are under research and development in Europe. The investigated designs are the European Sodium-cooled Fast Reactor, the European Lead-cooled Fast Reactor, and the European Gas-cooled Fast Reactor. MCNPX transport code was used to design three representative fuel assemblies of these fourth-generation concepts to analyze and compare their neutronic and safety parameters. The neutronic and safety analysis in this work includes the evolution of infinite multiplication factor and fissile inventory, neutron yield, the average energy of neutrons causing fission, neutron energy spectrum, neutron generation time, Doppler reactivity effect, effective delayed neutron fraction, and coolant void reactivity coefficient. The fuel burnup results showed that the ESFR is superior regarding the reactivity swing and breeding of fissile 239Pu. On the other hand, analysis of safety parameters results showed that they depend mainly on fuel composition rather than on other design specifications.

Utilization of ACE nuclear data file toolkit ACEtk to calculate relative sensitivity coefficients of point-kinetics parameters

Sensitivity and uncertainty methods are quintessential for nuclear criticality safety and experiment design. This type of analysis relies on calculations of sensitivity coefficients; sensitivity coefficients of the effective neutron multiplication factor with respect to some nuclear data are predominantly calculated and used. As a part of the Laboratory Directed Research & Development project EUCLID (Experiments Underpinned by Computational Learning for Improvements in nuclear Data) at Los Alamos National Laboratory, sensitivity coefficients of many radiation detector measurement responses with respect to nuclear data were investigated. Specifically, this paper outlines a method to calculate point-kinetics parameters relative sensitivity coefficients with respect to nuclear data. Point-kinetics parameters such as the prompt neutron decay constant, effective delayed neutron fraction, and neutron generation time are especially important to experimenters and reactor operators designing systems with dynamic neutron populations. This method couples capabilities of the ACE (A Compact ENDF) nuclear data file toolkit, ACEtk, with the ability to load cross sections into the radiation transport code Monte Carlo N-Particle (MCNP). Key aspects of optimizing this method for a particular application and sensitivity profiles of the Jezebel criticality experiment are examined and discussed.

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.

Neutronic analysis of the European sodium cooled fast reactor with Monte Carlo code OpenMC

Abstract The sodium-cooled fast reactor is a Generation-IV International Forum recommended technology, with an aim to improve sustainability, safety, and proliferation resistance. To ensure accurate reactor physics calculation and safety analyses, nuclear data libraries require continuous improvement through modifications based on additional measurements, evaluations, and validation studies with criticality experiments. In this work the Sodium-cooled Fast Reactor Uncertainty Analysis in Modeling (SFR-UAM) benchmark served as a basis to assess differences in nuclear data libraries and estimate variability in criticality and power distribution results. The research has been carried out using the OpenMC code and the study presented here covers two SFR models: MOX-3600 and ABR-1000. The neutronic calculation of numerous parameters in fast spectrum systems including effective multiplication factor (k eff), effective delayed neutron fraction (β eff), sodium void reactivity (Δρ Na), Doppler constant (Δρ Doppler), and control rod (ρ CR) worth were calculated and compared mainly to five libraries: ENDF/B-VII.1, ENDF/B-VIII, JEFF-3.3, JENDL-4.0 and TENDL-2019. In addition, sensitivity calculations using GPT-free method were conducted to understand relevant sensitivities for a given quantity of interest in major isotope/reaction pairs. The major driver of observed uncertainty in k eff are found for the high actinide isotopes mainly capture cross section of 239, 240Pu as well as fission reaction of 239Pu.

Nuclear data uncertainty influence on the breeding ratio in sodium-cooled fast reactor systems

Nuclear data are a main uncertainty source in neutron transport simulations making their consideration in reactor safety necessary. This arises anew with the state-of-the-art reactors known as Generation IV. Some of the reactors suggests providing the reactivity margin below the effective delayed neutron fraction excluding prompt criticality accidents, and the breeding ratio is the key factor in this. Consequently, assessing a degree of the breeding ratio accuracy is of interest. Therefore, in this work, the breeding ratio uncertainties are analyzed by performing a sensitivity and uncertainty analysis of the MET1000 and MOX3600 models with respect to nuclear data using SCALE. As a result, the breeding ratio uncertainties are obtained approximately equal to 2% as the main contributors are 239Pun,γ, 238Un,γ, and 238Un,n'. The uncertainty sources between the models are compared, and 16O preponderantly increases the total uncertainty not directly by its uncertainty but by its impact on the spectrum.

Searching for optimal accident tolerant fuel for the VVER-1200 reactor from the neutronic point of view

ABSTRACT In an attempt to find an optimum fuel, which can withstand the harsh operation condition in the VVER-1200 reactor, different fuel types were investigated in this work. Uranium carbide and uranium nitride are proposed as alternative fuels to UO2. MCNPX 2.7 with cross-section library ENDF/B-VII was used to design 3D model of VVER-1200 to investigate the neutronic properties of the suggested fuel types. The output results of the burnup of the proposed fuels have been analyzed to determine which of them achieves the longest fuel cycle. It was found that UO2 and U12C achieved criticality till 35 GWD/MTHM, while U14N and U15N achieved criticality at 30 GWD/MTHM and 24 GWD/MTHM, respectively. The traditional method of reactivity management has been tested on the proposed fuel to determine to what extent it is valid for them. To ensure the operation safety of the proposed fuel, some safety factors such as moderator temperature coefficient (MTC‎), fuel temperature coefficient (FTC‎), and effective delayed neutron fraction (βeff) have been calculated. The distribution of the thermal neutron flux and normalized power has been displayed to give us a good insight view of the VVER-1200 assembly to determine which of the proposed fuels is optimum compared to UO2.

Measurement of delayed neutrons in a thermal nuclear reactor by means of a long run pile noise experiment in sub-critical state

The transfer function of a zero-power thermal reactor was successfully measured thanks to neutron noise techniques from 1 mHz to 160 Hz. During a month-long experimental campaign, the fluctuations of the neutron population in critical and subcritical configurations of the core were acquired using excore fission chambers and analysed through Cross-Power Spectral Density (CPSD) methodology. Firstly, the reactor’s kinetic parameters, i.e. prompt decay constant, effective delayed neutron fraction and generation time, were obtained at critical state. It required calibrating the reactor’s power, which was done by metal foil activation and measurement of the 235U fission rate. Secondly, these parameters were used to estimate the groups’ abundances of delayed neutrons from the CPSD measured in a sub-critical state. Fitting data with a point kinetic model was done with Bayesian inference - CONRAD and Stan programs were used. A very good agreement was found between experimental abundances and the ones computed with TRIPOLI-4 Monte-Carlo transport code and JEFF3.1.1 nuclear data library. Uncertainties on prior abundances between 6 % to 101 %, held mainly by nuclear data, were lowered down to 4 % to 54 %, depending on the delayed group.

Data Assimilation using Non-invasive Monte Carlo Sensitivity Analysis of Reactor Kinetics Parameters

Accurately predicting the criticality of an experiment before interacting with the experimental components is very important for criticality safety. Radiation transport software can be utilized to calculate the effective neutron multiplication factor of a nuclear system. Because of the integral nature of the effective neutron multiplication factor, the value calculated contains various sources of nuclear-data induced uncertainty. The sensitivity analysis and data assimilation technique presented in this paper exhibit one possible method of identifying and reducing the effective neutron multiplication factor nuclear-data induced uncertainty. The results presented in this work show that it is possible to use relative sensitivity coefficients of the prompt neutron decay constant and the effective delayed neutron fraction to 239Pu nuclear data to reduce nuclear-data induced uncertainties in the effective neutron ultiplication factor. This work has been utilized by members of the Los Alamos National Laboratory project EUCLID (Experiments Underpinned by Computational Learning for Improvements in Nuclear Data) for optimally designing a new experiment, which will be used to reduce compensating errors in 239Pu nuclear data.

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.

Minor Actinides Transmutation and 233U Breeding in a Closed Th-U Cycle Based on Molten Chloride Salt Fast Reactor

Long-lived minor actinides (MAs) are one of the primary contributors to the long-term radiological hazards of nuclear waste, and the buildup of MAs is hampering the development of nuclear power. The transmutation of MAs in reactors is regarded as a potential way to replace direct disposal to reduce the impact of MA on the environment and improve the utilization of fuel. Due to its superior features, such as outstanding neutron economy, no fuel assembly fabrication, high neutron flux, and especially online refueling and reprocessing, the molten chloride salt fast reactor (MCFR) is regarded as one of the potential reactors for MA incineration. In this work, MA transmutation capability and 233U breeding performance for an optimized MCFR have been evaluated in different scenarios. The results show that the MA transmutation capability and 233U breeding performance with online transuranic elements (TRU) and 232Th feeding scenario are improved significantly compared with the case in online 233U and 232Th feeding, when the initial MA loading is 5 mol%, the total mass of MA transmutation and MA incineration is 7160 kg and 1759 kg during the whole 100 years operation under online TRU and 232Th feeding scenario, and the corresponding average annual net production of 233U is 450 kg, however, the MA transmutation amount, MA incineration amount and average annual net production of 233U for online 233U and 232Th feeding scenario is 5298 kg, 1315 kg, and 249 kg, respectively. In addition, the research also shows that the increase in initial loading of MA has no obvious effect on the improvement of the 233U breeding performance but can improve the transmutation efficiency of MA under online TRU and 232Th feeding scenarios. Furthermore, if 233U is continuously extracted online from the core during the operation, the 233U breeding performance will be significantly improved, but it will deteriorate the safety performance, such as the fuel temperature coefficient of reactivity (TCR) and the effective delayed neutron fraction (EDNF), more importantly, it will also put forward higher requirements for the immature online reprocessing technology.