Burnup Distribution Research Articles

Uncertainty propagation in the simulation of a nuclear power plant operational transient

With the continuous deployment of various intermittent energy sources on the grid there is an increasing opportunity for nuclear reactors to perform power maneuvers which can help alleviate issues related to supply oscillations during some periods of high renewable output. While utility specific codes can model such transients for safety assessments, there is a need to increase confidence in the application of these codes and to quantify the capabilities and accuracies of models in predicting these transients. In this work a power maneuver from 100 % full power to 59 % full power for a large CANDU reactor was studied using the TRACE-PARCS toolset. The work was computationally expensive as it examined both the effects of i) nuclear data library uncertainty which requires re-generation of the few-group cross sections and regeneration of an equilibrium core using 4 years of synthetic fuelling, and ii) initial core burn-up distribution involving the simulation of online fuelling operations over a period of 1400 days.The figures of merit considered in this work include changes in the average liquid zone controller fill level, individual channel powers, and the timing of adjuster bank withdrawals and reinsertions. Amongst the 100 s of simulated transients, the average time between adjuster bank withdrawals to override the Xenon transient and absolute standard deviations in these timings were found to be consistent between different nuclear datasets. The observed standard deviations were small, suggesting that the sensitivity to both nuclear data and initial core configuration is relatively small for both the adjuster withdrawal phase and the reinsertion phase. The contributions to total uncertainty due to both the core initial conditions and the nuclear data uncertainty were determined. During the early phase of the transient (i.e., adjuster withdrawals) nuclear data uncertainty and initial condition uncertainties were found to contribute nearly equally to total uncertainty, with slightly larger contributions due to nuclear data uncertainty. For adjuster bank reinsertions later in the transient it was observed that the contribution to total uncertainty by initial condition uncertainty was on average twice that of nuclear data uncertainties.The transients were compared to an actual power maneuver in a ∼900 MW CANDU reactor. In all cases, the model’s behaviour, while qualitatively correct, systematically over-predicted the time durations between adjuster movements and this difference exceeded the envelope of simulations that account for nuclear data and initial core configuration. Sensitivity studies performed to investigate the discrepancies suggest that additional refinements to the RRS emulator used in this work are required to match the station RRS more closely and that the transient evolution is highly sensitive to the initial excess reactivity in the core, which was observed to be lower in the station than in the TRACE simulations. Based on the simulation results the combined impact of the emulator responses, initial average zone levels, and incrementals modelling have a larger uncertainty than those related to nuclear data and initial core burnup distribution.

High-Fidelity Monte Carlo Analysis of Highly-Localized Fission Power Peaking near a Flux Trap in an MTR Core

In this study, a high-fidelity Monte Carlo model was utilized to investigate the localized behavior of the power peaking factor in a reactor core. The model considered the effect of water gaps, also known as flux traps, on the local power peaking. The model, developed using the Serpent code, employs a fine spatial mesh to accurately describe the fission power and burnup distribution. The results obtained from the model were validated through comparison with experimental measurements of the power distribution obtained from the IRR1 facility. The study found that the local accumulation of thermal flux caused by enhanced neutron moderation in the flux trap leads to a highly localized increase in power density, affecting the power peaking factor. The quantification of this effect was a key finding of the study. The results obtained from the study were highly dependent on the model’s fidelity, with significant differences being observed between the power peaking factor calculated on a fine mesh as opposed to that calculated at the plate or assembly scale. Furthermore, the experimental validation of the model enabled the prediction of the power peaking factor in other regions within the fuel assembly, which are not accessible to measurement instrumentation, with a high degree of confidence. The study’s findings may be useful for optimizing reactor design and operation and assessing the safety margins in reactors with similar characteristics.

Steady-state analysis of ROSTOV-2 benchmark problem using SERPENT-2 and PARCS codes

Recently, a new benchmark problem has been introduced by the OECD/NEA on the Rostov-2 reactor to address the verification and validation of novel High-Fidelity Multi-Physics tools. In line with the first phase of this benchmark, the current research was dedicated to the steady state reactor physics analysis, using “traditional multi-physics” codes for further and future comparisons. A set of homogenized two-group cross-section libraries were developed using SERPENT-2 Monte Carlo code. Some sophisticated techniques have been employed for detailed consideration of radial as well as axial reflectors, spacer grids and assembly discontinuity factor evaluation. Since PARCS code requires the group constants in PMAXS format, the generated libraries were re-formatted using the GenPMAXS interface. The PMAXS library verification, as well as the steady state analysis have been conducted in three operational states of the reactor using PARCS nodal diffusion code, independent SERPENT-2 Monte Carlo simulation and some available reference data. A set of criticality calculations have been conducted to evaluate the total reactivity worth of different control rod groups, the group #10 integral reactivity curve, fuel temperature coefficient and the critical boron concentration in Hot Zero Power (HZP) and Hot Full Power (HFP) states. The maximum reactivity difference between PARCS and SERPENT-2 simulations was less than 100 pcm in all criticality calculations. In HFP state, the relative power distribution in radial and axial directions were calculated and compared. The maximum Power Peaking Factors (PPFs) and the location of the “hot assembly” from PARCS and SERPENT-2 are in good agreement with each other. Finally, the burn-up calculation was conducted with PARCS code to evaluate neutronic parameters at some specific burn-up values. The calculated reactor physics parameters including the critical boron concentration, the power peaking factors, the power and burn-up distributions at the Beginning of Experiment (BOE) were consistent with available reference data.

A comparison study on the burnup of HTR-10 fuels using radiometric and mass spectrometric methods

Online burnup measurement of a single irradiated spherical fuel element using gamma spectrometry has been applied for years on HTR-10. This reactor has a complex operation history for varies experiments, which raises the uncertainty over the non-destructive measured burnup. In this research, three irradiated spherical fuel elements with different burnup were deconsolidated, and their coated particles were analysed by both radiometric methods based on Cs-137 activity and mass spectrometric methods based on neodymium and actinide mass. The burnup distribution in each spherical fuel element was indicated by fractional U-235 burnup of particles from various radii and relatively uniform. The inventory of Cs-137 in one spherical fuel element was measured by on- and off-line gamma spectrometry and results showed tiny differences. Destructively measured Cs-137 activities from particles indicate negligible portion of Cs-137 in the graphite matrix. Burnup calculated from Cs-137 by radiometric method and Nd-148 by mass spectrometric method were compared. Results showed that the two values were not significantly different for fuels with a clear radiation history, but differences were observed in the fuel with a complex radiation history.

Method Research on Data Assimilation for Burnup Distribution of PWR Based on Three=dimensional Variation and Neutral Network Algorithm

Method Research on Data Assimilation for Burnup Distribution of PWR Based on Three=dimensional Variation and Neutral Network Algorithm

Data assimilation for the burnup distribution applying the three-dimensional variational and artificial neutral network algorithm

In this paper, a data-assimilation method has been proposed and applied for the burnup distribution of PWR. The burnup distribution is significant for the safety and economy of the reactor, as it is essential for the fuel-reloading design and optimization. Due to the fact that the burnup distribution cannot be measured directly during the reactor operation, the numerical simulation is widely applied in reactor engineering. However, there definitely exist differences between the numerical simulation and the actual core due to some unavoidable factors, such as component manufacturing deviation, uneven flow distribution and so on. These differences would induce the errors to the simulation values of power distributions and hence to the burnup distributions. Therefore, a data-assimilation method for the burnup distribution has been proposed, aiming at reducing the burnup-distribution errors with application of the power-distribution measurements. In our research, the three-dimensional variational (3DVAR) algorithm was applied for burnup-distribution calibration and the artificial neutral network (ANN) algorithm was applied to establish the complex relations between burnup distribution and power distribution. As engineering verification, the proposed data-assimilation method has been applied to the CNP1000 PWR operated in China. The numerical results indicated that the burnup-distribution errors can be reduced notably, as the maximum value of relative errors for power distribution can be reduced from 9.53% to 5.11%.

CTF-PARCS Core Multi-Physics Computational Framework for Efficient LWR Steady-State, Depletion and Transient Uncertainty Quantification

Best Estimate Plus Uncertainty (BEPU) approaches for nuclear reactor applications have been extensively developed in recent years. The challenge for BEPU approaches is to achieve multi-physics modeling with an acceptable computational cost while preserving a reasonable fidelity of the physics modeled. In this work, we present the core multi-physics computational framework developed for the efficient computation of uncertainties in Light Water Reactor (LWR) simulations. The subchannel thermal-hydraulic code CTF and the nodal expansion neutronic code PARCS are coupled for the multi-physics modeling (CTF-PARCS). The computational framework is discussed in detail from the Polaris lattice calculations up to the CTF-PARCS coupling approaches. Sampler is used to perturb the multi-group microscopic cross-sections, fission yields and manufacturing parameters, while Dakota is used to sample the CTF input parameters and the boundary conditions. Python scripts were developed to automatize and modularize both pre- and post-processing. The current state of the framework allows the consistent perturbation of inputs across neutronics and thermal-hydraulics modeling. Improvements to the standard thermal-hydraulics modeling for such coupling approaches have been implemented in CTF to allow the usage of 3D burnup distribution, calculation of the radial power and the burnup profile, and the usage of Santamarina effective Doppler temperature. The uncertainty quantification approach allows the treatment of both scalar and functional quantities and can estimate correlation between the multi-physics outputs of interest and up to the originally perturbed microscopic cross-sections and yields. The computational framework is applied to three exercises of the LWR Uncertainty Analysis in Modeling Phase III benchmark. The exercises cover steady-state, depletion and transient calculations. The results show that the maximum fuel centerline temperature across all exercises is 2474K with 1.7% uncertainty and that the most correlated inputs are the 238U inelastic and elastic cross-sections above 1 MeV.

A Study of Gamma Heating, Neutron Flux, and Gamma Flux Under Several Reactor Core Conditions in the McMaster Nuclear Reactor

Changes in the thermal power of a nuclear research reactor will lead to changes in experimental, irradiation, and testing conditions. Consequently, reactor core parameters are inevitably susceptible to changes. One such parameter is gamma heating (GH), which results from gamma interaction with materials. In this work, a gamma thermometer was used to measure GH over the course of 7 operational days and nights. In addition, the Monte Carlo reactor physics code Serpent-2 was used to evaluate the sensitivity of common detection methods for monitoring reactor core parameters such as neutron fluxes, GH, and gamma flux under the following conditions: reactor core power variation, reactor core fuel shuffling, and detector vicinity fuel assembly shuffling. The GH values obtained through measurements and calculations were linearly proportional to the reactor power. In addition, the Serpent-2 code for the McMaster nuclear reactor showed that despite maintaining the reactor power core at the same level, the fuel burnup distribution could alter the studied parameters.

Data Assimilation for the Burnup Distribution Applying the Three-Dimensional Variational and Artificial Neutral Network Algorithm

Data Assimilation for the Burnup Distribution Applying the Three-Dimensional Variational and Artificial Neutral Network Algorithm

TRANOX: Model for non-isothermal steam oxidation of zircaloy cladding

• Developed a mechanistic oxygen distribution model in steam-oxidized Zircaloy-4. • Experimental validation conducted for ECR, oxygen distribution, and phase thickness. • Providing accurate oxidation prediction in non-isothermal conditions. • Validate the accuracy of CP correlation and provide an advanced mechanistic model. • Explaining effect of hydrogen on oxygen content in zr for highburnup cladding. TRANOX-1.0 (TRANsient OXidation), a mechanistic model that calculates oxygen distribution for isothermal and non-isothermal transients (1000–1250 °C) has been developed. TRANOX solves radial transient diffusion equation using Finite Difference Method (FDM) with spatial phase changes for each time step. Diffusion coefficients of each resulting phase were obtained by searching a combination that best guarantees Equivalent Cladding Reacted (ECR) and α-Zr(O) thickness simultaneously. The model has been extensively validated by overarching experimental campaigns including isothermal and non-isothermal high temperature steam oxidation, and post-metallurgical characterization. Accounting for α+β equilibrium phase, TRANOX gives accurate predictions for ECR, spatially averaged radial oxygen distribution, and thicknesses of each phase. Mechanistically solving the diffusion equation, TRANOX exhibits unbiased predictability for isothermal and non-isothermal transients. TRANOX was used to understand the oxygen distribution of pre-hydrided high burnup fuel cladding. The diffusion resistance behavior of α-Zr(O) and α+β with respect to hydrogen content counteract, neutralizing the overall hydrogen effect on oxygen distribution. The limited hydrogen effect on diffusion resistance during the early stage of steam oxidation further reduces the hydrogen-sensitivity of oxygen profiles. This finding provides a cogent explanation for the effect of hydrogen on oxygen distribution and oxidation kinetics observed by a number of past studies.

Neutronics modelling of control rod compensation operation in small modular fast reactor using OpenMC

The small modular liquid-metal fast reactor (SMFR) is an important component of advanced nuclear systems. SMFRs exhibit relatively low breeding capability and constraint space for control rod installation. Consequently, control rods are deeply inserted at beginning and are withdrawn gradually to compensate for large burnup reactivity loss in a long lifetime. This paper is committed to investigating the impact of control rod compensation operation on core neutronics characteristics. This paper presents a whole core fine depletion model of long lifetime SMFR using OpenMC and the influence of depletion chains is verified. Three control rod position schemes to simulate the compensation process are compared. The results show that the fine simulation of the control rod compensation process impacts significantly the fuel burnup distribution and absorber consumption. A control rod equivalent position scheme proposed in this work is an optimal option in the trade-off between computation time and accuracy. The control position is crucial for accurate power distribution and void feedback coefficients in SMFRs. The results in this paper also show that the pin level power distribution is important due to the heterogeneous distribution in SMFRs. The fuel burnup distribution at the end of core life impacts the worth of control rods.

PBMR-400 BENCHMARK SOLUTION OF EXERCISE 1 AND 2 USING THE MOOSE BASED APPLICATIONS: MAMMOTH, PRONGHORN

High temperature gas cooled reactors (HTGR) are a candidate for timely Gen-IV reactor technology deployment because of high technology readiness and walk-away safety. Among HTGRs, pebble bed reactors (PBRs) have attractive features such as low excess reactivity and online refueling. Pebble bed reactors pose unique challenges to analysts and reactor designers such as continuous burnup distribution depending on pebble motion and recirculation, radiative heat transfer across a variety of gas-filled gaps, and long design basis transients such as pressurized and depressurized loss of forced circulation. Modeling and simulation is essential for both the PBR’s safety case and design process. In order to verify and validate the new generation codes the Nuclear Energy Agency (NEA) Data bank provide a set of benchmarks data together with solutions calculated by the participants using the state of the art codes of that time. An important milestone to test the new PBR simulation codes is the OECD NEA PBMR-400 benchmark which includes thermal hydraulic and neutron kinetic standalone exercises as well as coupled exercises and transients scenarios. In this work, the reactor multiphysics code MAMMOTH and the thermal hydraulics code Pronghorn, both developed by the Idaho National Laboratory (INL) within the multiphysics object-oriented simulation environment (MOOSE), have been used to solve Phase 1 exercises 1 and 2 of the PBMR-400 benchmark. The steady state results are in agreement with the other participants’ solutions demonstrating the adequacy of MAMMOTH and Pronghorn for simulating PBRs.

Burnup Credit Evaluation for BWR Spent Fuel from Full Core Calculations

Due to the challenges of spent fuel accumulation, the nuclear industry is exploring more cost-effective solutions for spent fuel management. The burnup-credit method, in application for storage and transport of the spent fuel, gained traction over recent decades since it can remove the over-conservatism of the “fresh-fuel” approach. The presented research is focused on creating an innovative, best estimate approach of the burnup-credit method for boiling water reactor (BWR) spent fuel based on the results of neutronic/thermal-hydraulic coupled full core simulations. The analysis is performed using a Polaris/DYN3D sequence. Four different shuffling procedures were used to estimate the possible range of the BWR fuel discharged burnup variation. The results showed a strong influence of the shuffling procedure on the final burnup distribution. Moreover, a comparison of the 2D lattice and 3D coupled nodal approaches was conducted for the criticality estimation of single fuel assemblies. The analysis revealed substantial improvement in criticality curves obtained with the full-core model. Finally, it was shown that the benefit from the burnup-credit method is larger in the case of more optimal fuel utilisation-based shuffling procedures. The new approach developed here delivers a promising basis for future industrial optimisation procedures and thus cost optimisation.

Investigation on long-term daily load follow operation capability of soluble boron-free SMR

Soluble boron-free reactors inherently have larger reactivity feedback than conventional pressurized water reactors during power transients. The purpose of this study is to verify the capability of the long-term load follow operation with only control rods for the soluble boron-free small modular reactors. The effects of the long-term load follow operation on burnup distribution, power distribution, reactivity balance and spatial xenon stability are investigated throughout the whole cycle.The reactivity balance results show that the control rod design of the soluble boron-free SMR successfully manages the reactivity changes introduced by power and xenon changes during the daily load follow operation. The spatial xenon stability analysis demonstrates that the SMR model has enough capability to suppress the axial and quadrant xenon oscillation without a second peak during the load follow operation. The load follow simulation results showed that safety parameters including peaking factor, axial offset and shutdown margin satisfy design limits.

РЕЗУЛЬТАТЫ МОДЕЛИРОВАНИЯ ТЕСТОВОЙ ЗАДАЧИ «BENCHMARK ROSTOV 2» С ИСПОЛЬЗОВАНИЕМ КОМПЛЕКСА ПРОГРАММ САПФИР_95&RC_ВВЭР И КОРСАР

This paper presents the results of “Benchmark Rostov 2” test task simulation using SAPFIR_95&RC_VVER program package; the test task is based on a full-scale experiment performed at the Rostov NPP, where the transition mode with boric acid dilution and a working group insertion to compensate the reactivity were implemented. The purpose of this task is to develop the methods of non-stationary computation of pin-by-pin power energy distribution in calculation programs for neutronic and thermohydraulic characteristics of VVER-type reactors. The SAPFIR_95&RC_VVER program package uses two calculation methods of pin-by-pin power energy distribution: micro- and macro-flux superposition method and combined fine-grid method, where the nodes of radial computational grid in the reactor core coincide with the centers of fuel elements in fuel rod assembly. The combined fine-grid method for calculating pin-by-pin power energy distribution is carried out with the known values of burn-up distributions, fuel temperature, and coolant density obtained from superposition method. Both approaches are used for solving stationary and non-stationary tasks. When simulating the non-stationary processes, the test task can be solved in conjunction with KORSAR thermohydraulic code. This paper describes neutronic models of VVER-1000 reactor core used in “Benchmark Rostov 2” test task for superposition method and combined method. Calculation results for power energy distribution fields are given.

Compression of 3D pin-by-pin burnup data

Several 3D distributions of pin-by-pin data are produced in nodal core calculations. In particular, burnup distributions are used as input of thermo-mechanical computer codes in one-way coupling in order to verify the compliance to safety constraints, either at operation or in accidental transients. Their storage is required because they are computed with restart from previous calculations. Since one value is needed per fuel pin and per axial level, the amount of data to be stored for one reactor configuration is very high. Data compression techniques are very powerful to reduce the storage need. They are proposed in this work to optimise the amount of data saved and processed, without compromising the final accuracy. Specifically, we recommend the Hotelling transform to achieve higher compression performances.

Radiation Shielding Analysis for a Spent Fuel Storage Cask under Normal Storage Conditions

In most cases, gamma radiation is the dominant dose contributor, but in specific configurations, neutron radiation can become significant for the overall dose rate. This occurs for canister storages where the amount of spent fuel is large and thick concrete shields or entry mazes are used for radiation protection. The design of the cask is based on the safety requirements for normal storage conditions under 10 CFR Part 72. A radiation shielding analysis of the spent fuel storage cask optimized for loading design basis fuels was performed for a single cask. For the single cask, dose rates at the external surface of the spent fuel storage cask, some distance away from the cask surface, were evaluated. The results of the shielding analysis for the single cask show that dose rates were considerably higher at the lower side (from the bottom of the cask to the bottom of the neutron shielding) of the cask. However, this is not considered to be a significant issue since additional shielding will be installed at the storage facility. The shielding analysis results showed exponential decrease with distance off the sources. The controlled area boundary was calculated to be approximately 280m from the array, with a dose rate of 20 mrem/yr. Actual dose rates within the controlled area boundary would be lower than 25mrem/yr, due to the decay of radioactivity of spent fuel in storage. Another finding of the study is that the burnup distribution of the spent fuel needs to be taken into account when assessing the yield of the neutron radiation source, because use of the assembly average burnup leads to underestimation of it. Keywords: disposal of spent nuclear fuel, radiation shielding, storage condition, dual-purpose cask, spent fuel assemblies DOI : 10.7176/APTA/79-05 Publication date :September 30 th 2019

Radial distributions of power and fuel temperature in annular U3Si2 fuel with FeCrAl cladding

The present work performs systematic study on neutronic properties of annular fuel due to its high efficiency in heat transfer and low peak fuel temperature. Recent physical experiment on annular fuel indicates the present neutronic study is urgent and necessary. The present work concentrates on the investigations on the reactivity and radial distributions of power and fuel temperature for various annular fuels with different moderator to fuel ratios and different inner to outer coolant ratios. An analytical formula fx,s including fuel exposure (s) and relative radial (x) is proposed to describe the radial power distributions. fx,s has a second order polynomial dependence on s with coefficients following a double exponential form versus x. Monte Carlo simulations show that the suggested function fx,s gives a nice description on simulation data with rather small deviations and can immediately provide radial distribution of power and burnup at any fuel exposure and relative radius. The present analytical formula can be directly used for determining radial fuel temperature distribution. Numerical results based on radial power distributions show that about 150 K peak fuel temperature is reduced by dual-coolant annular design. In addition, the radial fuel temperature distributions in annular fuels are quite flatter than that in cylindric fuel rod.

Modification and update of FROBA-ROD code and its applications in fuel rod behavior analysis for PWRs

To analyze the behavior of PWRs fuel rods under steady operation conditions, some models such as modified Forsberg-Massih model and TUBRNP model were applied to FROBA-ROD code, which was developed by Xi'an Jiaotong University in 2012. Then more significant fuel rod behaviors could be simulated by FROBA-ROD code, which facilitated the safety analysis of fuel elements especially under accident conditions. To conduct transient thermal calculations and to improve the simulation accuracy, existing thermal models in FROBA were modified with the new fuel rod thermal conductivity model and burnup distribution model. The new models were validated by comparing it with the results of authorized commercial codes FRAPCON-4.0 and ABQUS and by comparing it with IFA-432 Rod 1 experimental benchmark data conducted by Oak Ridge National Laboratory. The relative calculation errors of centerline temperature calculated by modified FROBA-ROD, original FROBA-ROD and FRAPCON were 5.44%, 11.68% and 9.47% separately, which indicated that the modification and update of FROBA-ROD were valid. Modified FROBA-ROD code was applied to perform the behavior analysis of the AP1000 fuel rod. The simulation results indicated that there were enough safety margins for fuel rod behavior of AP1000 at rated operation conditions. The maximum oxidation thickness of cladding appeared at the upper part of the cladding tube in AP1000, which indicated that this area suffered a higher risk of cladding failure. Modified FROBA-ROD code is expected to deal with fuel rod scenarios under accident conditions after some additions of transient models.

Burnup Calculation Study of Pebble Bed Equilibrium Core

Reaktor Daya Eksperimental (RDE) is a high temperature gas-cooled reactor (HTGR) producing a 10 MW thermal with a pebble bed fuels which being developed by BATAN. The purpose of this paper is to study the burnup distribution and characteristic in the equilibrium core for different multipass recirculation method. Understanding the reactor physics, in particular the burnup, is important for optimum design and safety analysis of nuclear reactor. Related with the design approval phase of RDE, this study provides a design data which needed for the RDE’s safety analysis report, e.g. fuel pebble performance analysis. Analysis in this study was performed using PEBBED diffusion code. PEBBED is designed to solve the neutronics and thermalhydraulics parameter cases for high temperature pebble bed reactors for different fuel recirculation including once-through-then-out (OTTO) and multipass scheme. The reactor core calculation was performed by applying multipass scheme with variation from 5 passes up to 15 passes. With energy and power as inputs, the calculations produce the burnup fraction at the end of the cycle and the fast and thermal neutron fluxes in 8 energy groups. The calculation results showed that the lowest 5 passes fuel recirculation pattern has the highest and lowest minimum discharged burnup value. This is related to the average power distribution in the core which means more passes will flatter the burnup distribution including the power distribution and also seen in the value of flux and power peaking factor produced. power peaking factor produced.