Burnup Calculations Research Articles

The effect of errors in the neutron flux density on the uncertainties of nuclear concentrations of nuclides arising during the calculation of fuel burnup in cells with different neutron spectra

Computational studies have been carried out showing the complex time dependence of uncertainties in nuclear concentrations of various nuclides arising from the propagation of the neutron flux density errors in the burnup calculation process in cells with different neutron spectra on the above errors. It is found that these uncertainties not only depend on the burnup time in a complex way, but also depend on the spectrum of the cell. The variants of the cell with thermal and fast neutron spectra were considered. The calculations were performed using the VisualBurnOut program (Kolesov et al. 2009), which makes it possible to estimate these uncertainties arising due to errors in the input parameters of the burnup problem (reaction rates, neutron flux density, etc.). The influence of the number of calculated burnup points on the results of burnup calculations by the Monte Carlo method was investigated. Uncertainties arising in nuclear concentrations at intermediate calculation steps due to errors in nuclear concentrations appearing at the previous step were taken into account in the calculations.

Evaluation of the impact of the nuclear data library cinder.dat in MCNP burn-up calculations

Burn-up calculations with the MCNP code are based on the cinder.dat library, which includes the information of the cross-sections, the fission product yields and the decay data necessary to perform the depletion (among others). This library is based mainly on ENDF/B-VI.0 and has been enhanced with other databases, but no version based on other libraries (like JEFF or JENDL) is available in the bibliography or supplied with the MCNP code. This creates an inconsistency when other libraries are used for transport since the information of different libraries is mixed in the burn-up process.This study aims to evaluate the impact of the use of the cinder.dat library when other libraries are desired for transport and of the full replacement of the library file. In this paper, a new library has been developed and proposed to replace cinder.dat when coherent calculations using JEFF-3.3 for transport and burn-up are desired.

Uncertainty Propagation of Fission Product Yields from Uranium and Plutonium in Pebble-Bed HTGR Burnup Calculation

Quantifying fission product yield uncertainty contribution to reactor burnup calculation is an important aspect of pebble-bed High Temperature Gas-cooled Reactor (pebble-bed HTGR) uncertainty analysis. In this work, uncertainty propagation of fission product yield to pebble-bed HTGR burnup calculation is conducted. Uncertainty of fission product yields from four fissile isotopes, namely 233U, 235U, 239Pu and 241Pu, are considered. The stochastic sampling-based uncertainty analysis method is adopted and fission product yield covariance matrices are estimated from ENDF/B-VII.1. The covariance matrix for each fissile actinide is estimated based on the Bayesian method and fission product yields are assigned with log-normal distribution in the sampling process with the Latin Hypercube Sampling (LHS) method. Since the fission fraction from 239Pu plays an important role in fissions of fuels with high burnup value in pebble-bed HTGR, the fission product yield uncertainty contribution from 239Pu is highlighted in this work. The result shows that, in the burnup equilibrium state of pebble-bed HTGR, fission product yield uncertainty contributions from 235U and 239Pu to relative uncertainty of keff are 0.027% and 0.026%, respectively. The overall uncertainty contribution from four fissile isotopes (233U, 235U, 239Pu and 241Pu) to relative uncertainty of equilibrium core keff is 0.038%. Furthermore, fission product yield uncertainty has an important contribution to the nuclide density uncertainty of fission products. The most relative uncertainty, 10.82%, is observed in 109Ag contributed from the fission product yield uncertainty of 239Pu at the burnup equilibrium state. This indicates the uncertainty contribution from the fission product yield of 239Pu cannot be neglected in pebble-bed HTGR burnup uncertainty analysis.

An Inline Burnup Algorithm

Inline algorithms have been proposed for coupling Monte Carlo neutron transport solvers with several other physics, such as xenon and iodine densities and thermal hydraulics. This paper proposes a new inline algorithm that can be applied to burnup calculations. The algorithm is a modification of the predictor-corrector method, where the corrector-step nuclide densities are converged simultaneously with the fission source. This could, in principle, obviate the need for two full neutronics solutions per time-step while still allowing the accuracy of predictor-corrector methods with improved stability. This paper describes the algorithm and demonstrates its stability properties through a Fourier analysis. Although not unconditionally stable, judicious use of batching and relaxation are shown to greatly improve the algorithm’s stability properties in realistic systems.

Investigation and improvement of the Mini-Max Polynomial Approximation method for solving burnup equations

In this work, a new efficient solution algorithm named Combined Matrix Iterative Algorithm based on the Mini-Max Polynomial Approximation (MMPA) method is proposed for burnup calculations. As a new matrix exponential method in recent years, MMPA method has good numerical stability and computational accuracy, and all calculation are real number operations. As the same with Chebyshev Rational Approximation Method (CRAM) which is widely and successfully used in solving burnup equations, the method can also directly deal with rigid and sparse burnup matrices. Compared with the traditional solution algorithms based on MMPA method, the Combined Matrix Iterative Algorithm (MMPA-CMIA) proposed in this paper can effectively reduce the computational complexity and improve the computational efficiency after equivalently transforming the expression of the MMPA method. Then the MMPA-CMIA is used to theoretically demonstrate and analyze the solution efficiency of random matrices with different orders which has the similar distribution characteristics to burnup matrices. Compared with the 16-order CRAM method and the other two traditional solution algorithms based on MMPA method, the algorithm shows good acceleration effect and computational precision. Finally, the algorithm is used in the actual burnup benchmarks to verify and validate the accuracy and efficiency. The burnup matrices of different orders are constructed through detailed burnup chain and simplified burnup chain. The results show that the algorithm has good accuracy and numerical stability. And comparing with 16-order CRAM, the algorithm can save about 30% of computing time for solving burnup equations. It shows that the algorithm is a potentially powerful method for accelerating the solution of large-scale burnup calculations.

Physics Assessment of the Impact of Modified End Pellets on Axial Power Peaking for Advanced/Nonconventional Uranium-Based Fuels in Pressure Tube Heavy Water Reactors

Abstract Axial power peaking is a phenomenon with safety implications for pressure tube heavy water reactors (PT-HWRs). Since PT-HWRs use shorter (∼50 cm) bundles, there are small axial gaps, which expose the ends of the fuel elements to more neutron flux, and therefore results in higher power density levels occurring in the ends of the fuel elements. Power peaking has the potential to cause fuel damage and failure, if the local linear element rating (LER) exceeds 57 kW/m, and may be of greater concern for advanced, higher burnup fuels. Earlier studies have been done using three-dimensional mcnp models of a PT-HWR fuel bundle with slightly enriched uranium; they demonstrated that ThO2 could be used to reduce axial power peaking in fresh fuel. This result was achieved by replacing some of the UO2 with ThO2 in the last 3 cm of fuel pellets at each end of a fuel bundle. This study extends the previous work by performing 3D neutronics and burnup calculations using serpent, to evaluate how power peaking changes with burnup. In addition, alternative dilution materials (such as depleted UO2, ZrO2, and MgO) were also evaluated. It was found that axial power peaking can be significantly reduced by using the ThO2 dilution material for fresh fuel, while ZrO2 or MgO are even more effective at higher burnup levels. Dilution materials have little impact (less than 2%) on the exit burnup of the fuel.

Conceptual design of a 3 MWth yttrium hydride moderated heat pipe cooled micro reactor

Micro reactors are gaining substantial interest worldwide due to their capabilities to deliver power to remote and decentralized areas and their long fuel cycles, making them more attractive than other energy sources. This paper presents a conceptual design and steady-state neutronics and thermal-hydraulics analyses results for a heat pipe cooled yttrium hydride moderated micro reactor. The reactor was designed for both terrestrial and space application purposes; hence, size and weight were important. The neutronics analysis calculations were performed to evaluate key safety parameters such as control devices reactivity worth, temperature reactivity coefficients, and power distribution of the reactor core. Burnup calculations were performed using Monte Carlo code MCNP6.2 and verified against Serpent code results. The thermal-hydraulics analyses calculations were performed to evaluate the temperature distribution in a representative unit cell in the reactor core using the STAR CCM+ multi-physics computational fluid dynamics (CFD) software by utilizing the power distribution obtained from neutronics calculations. It was demonstrated that this reactor could be operated safely for more than 11 years, generating 3 MW of thermal power.

CORE BURN-UP ANALYSIS OF THE RSG-GAS RESEARCH REACTOR USING DETERMINISTIC AND STOCHASTIC METHODSS

Due to several characteristics, such as geometry, compact core, high coolant flow, and high neutron flux, the burn-up study of the RSG-GAS multi-purpose reactor provides challenges when employing a neutronic calculation. For the burn-up analysis, two calculating methodologies are used in the RSG-GAS: deterministic and probabilistic methods. The deterministic codes such as WIMSD-5B and Batan-FUEL are utilized, whereas the continuous-energy Monte Carlo code Serpent 2 is used for the stochastic method. WIMSD-5B is being used to produce a four-group cross-section that is needed by Batan-FUEL to do full core diffusion calculations. Burn-up calculations were performed at the whole fuel assemblies inside the core to see if the deterministic code, WIMSD-5B/Batan-FUEL, could accurately replicate the burn-up behavior of the RSG-GAS research reactor. The Serpent 2 calculation was also done with the exact models to provide a comparison. The results show that both Serpent 2 and WIMSD-5B/Batan-FUEL can perform the RSG-GAS burn-up analysis if appropriate treatments are made to the deterministic codes at both the assembly and core levels. There is a 5% difference in calculated fuel burn-up between deterministic and stochastic approaches.

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

Decay heat calculation for spent fuel pool application

The automatic procedure was developed for fuel assembly decay heat calculation based on PARCS 3D burnup calculation for fuel cycle depletion, and ORIGEN 2.1 calculation during both depletion and fuel cooling. Using appropriate pre-processor and post-processor codes it is possible to calculate fuel assembly decay heat loads for all fuel assemblies discharged from reactor. Simple graphical application is then used to distribute fuel assemblies within fuel pool and to calculate any fuel assembly, SFP rack, or whole pool heat load at arbitrary time. The application can be used for overview of fuel assembly burnups, cooling times or decay heats. Based on given date it is possible to calculate whole pool heat load and time to boiling or time to assembly uncover using simple mass and energy balances. Calculated heat loads can be input to more detailed thermal-hydraulics calculations of spent fuel pool. The demonstration calculation was performed for NPP Krsko spent fuel pool.

Design Study of Small Modular Reactor Class Super Fast Reactor Core for In-Vessel Retention

Abstract The small modular reactor (SMR) class core design concept of once-through supercritical light water-cooled reactor (SCWR) with fast neutron spectrum (super fast reactor (FR)) is being developed at Waseda University. For the 300 MWel class design, complete core meltdown may need to be considered in case of a severe accident. This study proposes the new in-vessel retention (IVR) concept of the SMR class super FR (super FR-IVR), which can avoid recriticality even if the whole core relocates to the lower plenum of the reactor pressure vessel (RPV). The core characteristics with a given set of design specifications and criteria are evaluated based on fully coupled neutronics and thermal-hydraulics core burnup calculations. The debris criticality is evaluated based on Monte Carlo based method to consider the RPV lower plenum and debris configurations. The relationships between the 300 MWel class core design with the inner vessel diameter of 2.32 m and the IVR design are revealed. By reducing the operation cycle length from 720 days to 360 days and increasing the core inlet temperature from 280 °C to 370 °C, the required IVR submergence level could be reduced from 2.18 m to 1.38 m, assuming that the debris bed (melt pool) is homogeneous. However, when fully stratified debris configurations are assumed, the required disperser height and the corresponding IVR submergence level may increase to about 2.70 m.

Optimization and burnup calculations of BNPP's reactor core with the new generation fuels (TVS-2M) by artificial neural network

In recent years, many types of research focused on optimizing, modernizing, and developing the fuels for VVER-1000s. A new generation and developed fuel are TVS-2M. Using TVS-2M has many benefits, such as burnup and cycle length increase compared to former fuel assemblies. However, the main issue is to find the best arrangement of the fuel assemblies to increase burnup and safety features. An artificial neural network (ANN) is a powerful tool to predict core burnup for different reactor core configurations in nuclear power plants. One can use ANNs to find the best Fuel arrangement. This article uses a multi-layer neural network to determine the optimum TVS-2M fuel arrangement, which can calculate the burnup of different fuel arrangements. The method utilizes some core parameter data to train a neural network to set up a real-time predicting system for burnup and actinides concentration predictions for different fuel assembly arrangements. The MCNPX code output applies as training data on a multi-layer perceptron neural network. After ensuring the high accuracy of the designed neural network, 20 different arrangements are inserted into the neural network to calculate the burnup parameter for them and select the best arrangement. At last, trained ANN can calculate the actinides concentration and other desired parameters. The results showed that replacing UTVS with TVS-2M FAs, in addition to increasing the length of the operation cycle from 289.6 days to 338.7 days, can increase the cycle's burnup, thus increasing the economic efficiency of the power plant. Also, the results confirm the power of the developed neural networks and approve the use of these networks instead of executing time-consuming codes like MCNPX.

Mitigating the numerical xenon instability in deterministic reactor burnup calculations

Depletion methods used in modern core simulators for thermal-spectrum reactor burnup calculations may be predisposed to activating, under the correct conditions, a numerical instability that presents itself in the form of artificial spatial xenon oscillations. In this paper a three-dimensional pressurised water reactor depletion problem is utilised to demonstrate that one of the most widely used predictor-corrected depletion schemes can be afflicted by numerical xenon instabilities in reactor burnup calculations performed with a state-of-the-art nodal diffusion core simulator. A method which results in tightening the algorithmic coupling between the 135Xe transmutation and the neutron flux computation steps is proposed for mitigating the numerical xenon instability. The method is called the Xenon Transmutation Feedback (XeTF) method because it incorporates 135Xe transmutation in the feedback iterations of a neutronics solver. The effectiveness of the method is verified by numerical evaluation of some typical reactor depletion scenarios.

Development of a Trajectory Period Folding Method for Burnup Calculations

In this paper, we present a trajectory period folding method for numerical modelling of nuclear transformations. The method uses the linear chain method, commonly applied for modelling of isotopic changes in matter. The developed method folds two consecutive periods of time and forms linear chain representations. In the same way as in the linear chain method, the mass flow of straight nuclide-to-nuclide transitions following the formation of nuclide transmutation chains in every step is considered over the total period of interest. Therefore, all quantitative data about the isotopic transformations for the period beyond a particular calculation step are preserved. Moreover, it is possible to investigate the formation history of any isotope from the beginning of irradiation to the arbitrary time step, including cooling periods and multi-recycling for any designed nuclear fuel cycle. We present a case study for the transition from 238U to 239Pu and define the properties of the developed method and its possible applications in reactor physics calculations.

Cross Section and Fission Yields Induced Uncertainty in the Water–Water Energetic Reactor-440 Burnup Calculation

Abstract The properties of nuclear fuel depend on the actual isotopic composition which develops during a reactor operation. In practice, the prediction accuracy of burnup calculations serves as the basis for the future precise estimation of a core lifetime and other safety-based core characteristics. The present study quantifies nuclear data induced uncertainties of nuclide concentrations and multiplication factors in water–water energetic reactor (VVER)-440 fuel depletion analysis. The well-known SCALE system and the TRITON sequence are used with the NEWT deterministic solver in the SAMPLER module that implements stochastic techniques to assess the uncertainty in computed results. The propagation of uncertainties in neutron cross section and fission yields is studied through the depletion calculation of 2D heterogeneous VVER-440 fuel assembly with an average enrichment of 4.87 wt % of 235U and six gadolinium rods with 3.35% of Gd2O3. In the paper, fixed nominal depletion conditions are based on the real operational data of the Slovak nuclear power plant Bohunice unit 4 during cycle 30. In total, 250 cases with uncertain parameters are computed and the results are evaluated by an auxiliary tool.

Validation of the advanced neutron transport lattice code KYLIN-V2.0 with critical and burnup experiments

KYLIN-V2.0 is an advanced lattice code developed in Nuclear Power Institute of China. The subgroup method, MOC method and Chebyshev rational approximation method (CRAM) are applied in the resonance, transport and burnup calculation to provide the macro cross-section library. In this paper, several critical experiments and burnup benchmarks, including B&W critical experiment, KRITZ critical experiment and Takahama-3 burnup benchmark, are applied in the validation of KYLIN-V2.0. KYLIN-V2.0 is validated by 21 cases in B&W-1484, 23 cases in B&W-1810 and 16 samples in Takahama-3. Eigenvalue, pin power distribution and nuclides density results of these cases show the good consistency compared with measured data. The KYLIN-V2.0 code shows good heterogeneous calculation ability for two-dimensional lattices.

The Effect of Serpent 2 Calculation Parameters on Evaluated Spent Nuclear Fuel Source Term

Abstract The estimation of spent nuclear fuel source term (decay heat, reactivity, nuclide inventory, etc.) has several sources of uncertainty such as uncertainties in nuclear data, uncertainties in the operation history, and choice of calculation parameters. In this work the effect of calculation parameters is studied by estimating the source term with the built-in burnup capability of serpent. The effect of the following parameters is considered: depletion zone division, burnup steps, unresolved resonance probability table sampling, Doppler-Broadening Rejection Correction (DBRC) and energy-dependent branching ratios. As a test case, a 2D Boiling Water Reactor (BWR) fuel assembly was modeled by first running a burnup calculation followed by a decay calculation. The following source term components were considered when investigating the effect of the studied parameters: total decay heat, photon emission rate and spontaneous fission rate. In general, the differences resulting from the use of different parameter variations were small for all three studied source term components. For the decay heat largest absolute relative difference was approximately 0.6% and for the photon emission rate approximately 1.1%. For the spontaneous fission rate maximum absolute relative difference of nearly 8% was observed. For all three components the variation of the depletion zone division resulted in the largest relative differences. Clear differences were also observed for burnup step length and DBRC variations. The use of unresolved resonance probability table sampling and energy-dependent branching ratios had an insignificant effect on the studied source term components.

Neutronics and burnup analysis of VVER-1000 LEU and MOX assembly computational benchmark using OpenMC Code

A handful of computational benchmarks that incorporate VVER-1000 assemblies having low enriched uranium (LEU) and the mixed oxide (MOX) fuel have been put forward by many experts across the world from the Nuclear Energy Agency. To study & scrutinize the characteristics of one of the VVER-1000 LEU & MOX assembly benchmarks in different states were considered. In this work, the VVER-1000 LEU and MOX Assembly computational-benchmark exercises are performed using the OpenMC software. The work was intended to test the preciseness of the OpenMC Monte Carlo code using nuclear data library ENDF/B-VII.1, against a handful of previously obtained solutions with other computer codes. The kinf value obtained was compared with the SERPENT and MCNP result, which presented a very good similarity with very few deviations. The kinf variation with respect to burnup upto 40 MWd/kgHM was obtained for State-5 by using OpenMC code for both the LEU and MOX fuel assembly. The depletion curves of isotope concentrations against burnup upto 40 MWd/kg/HM were also generated for both the LEU and MOX fuel assembly. The OpenMC results are comparable with those of benchmark mean values. The neutron energy vs flux spectrum was also generated by using OpenMC code. Based on the OpenMC results such as kinf, burnup, isotope concentrations and neutron energy spectrum, it is concluded that the OPenMC code with ENDF/B-VII.1 nuclear data library was successfully implemented. It is planned to use OpenMC code for calculation of neutronics and burnup of the VVER-1200 reactor to be commissioned in Bangladesh by 2023/2024.

Supplementing fuel behaviour analyses via coupled Monte Carlo neutronics and fission product solution

The accuracy of power distribution solution and burnup algorithms in standalone fuel behaviour codes is limited. For improved accuracy, fuel behaviour codes can be coupled with external reactor physics solvers. A coupled calculation system between the Monte Carlo neutronics and burnup calculation solver Serpent and the fuel behaviour solver TRANSURANUS was developed in an earlier work. The data exchanged between the solvers included fuel pin axial and radial power and temperature distributions, the axial fast flux distribution in the cladding and the changes in the pin radii. In this work the coupling was further improved by developing the capability to transfer and utilize Serpent calculated nuclide compositions in TRANSURANUS within the coupled calculations. Additionally, support for corrector type burnup algorithms in the coupled solution was now implemented for increased accuracy of the nuclide solution. The new capabilities were demonstrated with a coupled single rod burnup calculation utilizing power and coolant history data from the Loviisa nuclear power plant. The focus at this stage was on fission product nuclides as their accumulation adversely affects the fuel performance, making their accurate solution important to ensure safe yet economical use of fuel. The demonstration showed small but visible differences when compared to simulations that were run without using fission products calculated by Serpent. The developed capabilities will now facilitate import of further fission product nuclides to be taken into account in TRANSURANUS.

Efficient Monte Carlo algorithm of time-dependent particle transport problem in multi-physics coupling calculation

Multi-physics coupling calculation has applications in many important research fields. If particle transport process is included in this calculation, Monte Carlo method is often used to simulate this process and usually a large amount of calculation time is needed. So, efficient Monte Carlo algorithm for time-dependent particle transport problem is important for an efficiently coupling calculation, which inevitably relies on large-scale parallel calculation. Based on the characteristic of time-dependent particle transport problem, two methods are proposed in this paper to achieve high- efficiency calculation. One is a tally-reducing algorithm which is used in the coupling of transport simulation and burnup calculation. By reducing the quantity of data which should be reduced necessarily, this method can reduce the calculation time largely. It can be seen that a new coupling mode for these two processes in MPI environment has a larger value when model scale is larger than the sample size. The other method is an adaptive method of setting the sample size of Monte Carlo simulation. The law of large number assures that the Monte Carlo method will obtain an exact solution when the sample scale tends to infinity. But generally, no one knows which sample scale is big enough for obtaining a solution with target precision in advance. So, the common strategy is to set a huge-enough sample scale by experience and conduct the posterior check for all results. Apparently, this way cannot be efficient because the calculation will go on after the precision of solution has reached an object value. Another popular method is to set the sample size to rely on the relative error of some single calculation. The sample size is enlarged without a break until the relative error is less than some presetting value. This method is not suitable either, because Monte Carlo particle transport simulation will gives feedbacks to other process which is composed of many tallies. It is inappropriate to adjust the sample size according to the relative error of any calculation. Relying on the generalization of the Shannon entropy concept and an on-the-fly diagnosis rule for a entropy value sequence, the adaptive method proposed in this paper can reduce the original huge sample scale to a reasonable level. By numerically testing some non-trivial examples, both algorithms can reduce the calculation time largely, with the results kept almost unchanged, so the efficiency is high in these cases.