Nuclide Depletion Research Articles

Numerical simulation of Delayed-SPND response current in NECP-Bamboo

Self-Powered Neutron Detectors (SPNDs) are widely used in Gen-III commercial PWR cores to simultaneously and continuously measure the in-core neutron flux density. A response current simulation module has been designed, developed and validated in the NECP-Bamboo code for delayed-SPNDs. First, neutron transport and nuclide depletion simulation are carried out in Bamboo-Lattice to obtain the variation of nuclide composition and the few-group constants. Next, a Monte-Carlo code is employed to calculate the electron escape probability and gamma sensitivity of SPND for each depleted lattice. Finally, the electron escape probability, gamma sensitivity and the few-group constants are regarded as input parameters for the core simulation. The response current is calculated in the Bamboo-Core code during the simulation of core operation. The methodology and the code were verified against measured values on Vanadium and Rhodium SPND. In addition, the response current of Vanadium SPND in the AP1000 core was simulated and validated.

Development and verification of code IMPC-Depletion for nuclide depletion calculation

Simulation of nuclide inventory evolution in the reactor during the entire irradiation history is of significance to the design of fuel component and core layout scheme and nuclear waste disposal. To perform accurate burnup calculations for fast reactor systems such as accelerator-driven sub-critical reactors, a nuclide depletion code IMPC-Depletion has been developed. Depletion of reactor material is described by thousands of coupled first-order ordinary differential equations, which is the stiff ODEs system. For IMPC-Depletion, algorithms including Chebyshev Rational Approximation Method (CRAM) and Transmutation Trajectory Analysis method (TTA) are implemented to solve Bateman equations. The parameter-extended XML file format is used as standard input. Decay, constant flux and power modes are supported. To verify IMPC-Depletion code, decay of Ra228, fixed-flux irradiation of Zircaloy-4 and 2.4% UO2, fixed-power irradiation of 3.2% UO2 are tested. Results are basically consistent with those of ORIGEN2.1. In addition to independent nuclides inventory analysis, IMPC-Depletion can also be coupled with Monte Carlo neutron transport code to solve burnup problem. Here, simple MOX pin cell and OECD/NEA fast reactor burnup benchmarks are employed to verify the Out-coupling Monte Carlo burnup code system IMPC-Burnup2.1, which couples OpenMC and IMPC-Depletion. Result parameters such as keff, reactivity changes and nuclides inventory values are reliable when compared with other participants.

Validation of nuclide depletion capabilities in Monte Carlo code MCS

In this work, the depletion capability implemented in Monte Carlo code MCS is investigated to predict the isotopic compositions of spent nuclear fuel (SNF). By comparison of MCS calculation results to post irradiation examination (PIE) data obtained from one pressurized water reactor (PWR), the validation of this capability is conducted. The depletion analysis is performed with the ENDF/B-VII.1 library and a fuel assembly model. The transmutation equation is solved by the Chebyshev Rational Approximation Method (CRAM) with a depletion chain of 3820 isotopes. 18 actinides and 19 fission products are analyzed in 14 SNF samples. The effect of statistical uncertainties on the calculated number densities is discussed. On average, most of the actinides and fission products analyzed are predicted within ±6% of the experiment. MCS depletion results are also compared to other depletion codes based on publicly reported information in literature. The code-to-code analysis shows comparable accuracy. Overall, it is demonstrated that the depletion capability in MCS can be reliably applied in the prediction of SNF isotopic inventory.

MCS/TH1D analysis of VERA whole-core multi-cycle depletion problems

This paper presents the verification and validation elements of the UNIST in-house Monte Carlo code, MCS, for the multi-cycle and multi-physics analyses of high-fidelity, large-scale commercial pressurized water reactors (PWRs). Analysis on the neutronic performance with thermal/hydraulic (T/H) feedback is the key to detecting the complex behavior of an operating nuclear power reactor. The MCS solutions with T/H feedback, TH1D, of the consortium for advanced simulation of light water reactors (CASL) virtual environment for reactor applications (VERA) core physics benchmark progression problems 6 and 7 showed excellent agreement in eigenvalues, temperature and power profiles with the MC21/COBRA-IE, MC21/CTF and VERA-CS solutions for the single assembly and whole core of Watts Bar Nuclear 1 (WBN1) Cycle 1 under beginning-of-cycle and hot-full-power condition. Furthermore, the core depletion analysis is one of the most compelling advances for reactor analysis. Therefore, this work is significantly focused on the nuclide depletion simulation coupled with TH1D of the first two cycles of WBN1 to address the VERA core physics benchmark problems 9 and 10. MCS is one of the few Monte Carlo codes that have the capability of depletion calculation for both WBN1 Cycles 1 and 2. The accuracy of MCS simulation of WBN1 Cycle 1 is within 40 ppm and 30 ppm in critical boron concentration (CBC) for all burnup points, compared with the measured data and VERA-CS solutions, respectively. To demonstrate the multi-cycle refueling capability of MCS, the WBN1 Cycle 2 is simulated and compared with the solutions of VERA-CS only, because of the lack of available measured data. MCS shows excellent agreement compared with VERA-CS within 30 ppm in CBC, and the average bias for the entire Cycle 2 is approximately 20 ppm. These results provide confidence in MCS’s capability in high-fidelity, multi-cycle calculations of the practical PWR core.

Fuel cycle analysis of molten salt reactors based on coupled neutronics and thermal-hydraulics calculations

A new fuel cycle analysis code named FAMOS was developed for molten salt reactor (MSR) applications by extending the DIF3D code to model the transport of delayed neutron precursors and by coupling the extended DIF3D code with an in-house multi-channel thermal-hydraulics solver and an in-house nuclide depletion solver for the simulation of fuel depletion, reprocessing and feeding. FAMOS can also calculate the effective delayed neutron fraction accounting for the motion of fuel salt, the neutron generation time and the reactivity feedback coefficients. In order to verify the FAMOS code, the molten salt fast reactor (MSFR) proposed in the EVOL (Evaluation and Viability of Liquid Fuel Fast Reactor System) project was analyzed using FAMOS and the calculation results were compared with the reported results. The numerical results indicate that FAMOS is capable of simulating the fuel cycle process of MSRs with good accuracy. FAMOS was applied to the fuel cycle analysis of the molten salt breeder reactor (MSBR) as well. The effects of the temperature distribution and the drift of delayed neutron precursors on the neutronics characteristics and fuel cycle performances of MSBR were evaluated using three different calculation models. The drift of delayed neutron precursors and the temperature distribution shift the axial power distribution upward and downward, respectively, and the latter effect is stronger than the former one. However, the impacts of the temperature distribution and the drift of delayed neutron precursors on the depletion and buildup behaviors of actinides and fission products in MSRs are negligible. It is also possible to achieve a 233U conversion ratio larger than 1.0 without protactinium removal and thus to operate the MSBR by only feeding 232Th, except for the initial start-up stage.

Nuclide depletion capabilities in the Shift Monte Carlo code

A new depletion capability has been developed in the Exnihilo radiation transport code suite. This capability enables massively parallel domain-decomposed coupling between the Shift continuous-energy Monte Carlo solver and the nuclide depletion solvers in ORIGEN to perform high-performance Monte Carlo depletion calculations. This paper describes this new depletion capability and discusses its various features, including a multi-level parallel decomposition, high-order transport-depletion coupling, and energy-integrated power renormalization. Several test problems are presented to validate the new capability against other Monte Carlo depletion codes, and the parallel performance of the new capability is analyzed.

Practical techniques for large-scale Monte Carlo reactor depletion calculatons

This work presents a brief review of numerical methods for nuclide depletion calculations and a summary of several practical techniques for improving computational speed and reducing memory usage in large-scale Monte Carlo reactor depletion calculations. The techniques covered in the paper include: 1) the use of data hierarchy, 2) separation of absorbing and non-absorbing (precursor) nuclides, 3) optimizations for a backward differentiation formula (BDF) numerical solver, 4) the use of simplified (reduced-order) depletion systems, and 5) the use of a residual fission product absorption correction term to account for the cumulative reactivity effect of nuclides that are not explicitly depleted. In addition, the paper describes several implementation and data management strategies used in the MC21 code, which have proven beneficial for large depletion calculations. A description of these various techniques and strategies are presented along with results from scaling studies and representative reactor depletion calculations that demonstrate the effectiveness of these methods. The results from these studies suggest that large-scale MC depletion calculations including tens- to hundreds-of-millions of depletable material compositions are practical on contemporary mid-range computing clusters.

VERA Core Simulator Methodology for Pressurized Water Reactor Cycle Depletion

This paper describes the methodology developed and implemented in the Virtual Environment for Reactor Applications Core Simulator (VERA-CS) to perform high-fidelity, pressurized water reactor (PWR), multicycle, core physics calculations. Depletion of the core with pin-resolved power and nuclide detail is a significant advance in the state of the art for reactor analysis, providing the level of detail necessary to address the problems of the U.S. Department of Energy Nuclear Reactor Simulation Hub, the Consortium for Advanced Simulation of Light Water Reactors (CASL). VERA-CS has three main components: the neutronics solver MPACT, the thermal-hydraulic (T-H) solver COBRA-TF (CTF), and the nuclide transmutation solver ORIGEN. This paper focuses on MPACT and provides an overview of the resonance self-shielding methods, macroscopic-cross-section calculation, two-dimensional/one-dimensional (2-D/1-D) transport, nuclide depletion, T-H feedback, and other supporting methods representing a minimal set of the capabilities needed to simulate high-fidelity models of a commercial nuclear reactor. Results are presented from the simulation of a model of the first cycle of Watts Bar Unit 1. The simulation is within 16 parts per million boron (ppmB) reactivity for all state points compared to cycle measurements, with an average reactivity bias of <5 ppmB for the entire cycle. Comparisons to cycle 1 flux map data are also provided, and the average 2-D root-mean-square (rms) error during cycle 1 is 1.07%. To demonstrate the multicycle capability, a state point at beginning of cycle (BOC) 2 was also simulated and compared to plant data. The comparison of the cycle 2 BOC state has a reactivity difference of +3 ppmB from measurement, and the 2-D rms of the comparison in the flux maps is 1.77%. These results provide confidence in VERA-CS's capability to perform high-fidelity calculations for practical PWR reactor problems.

Improving the Accuracy of the Chebyshev Rational Approximation Method Using Substeps

The Chebyshev rational approximation method (CRAM) for solving the decay and depletion of nuclides is shown to have a remarkable decrease in error when advancing the system with the same time step and microscopic reaction rates as the previous step. This property is exploited here to achieve high accuracy in any end-of-step solution by dividing a step into equidistant substeps. The computational cost of identical substeps can be reduced significantly below that of an equal number of regular steps, as the lower-upper decompositions for the linear solutions required in CRAM need to be formed only on the first substep. The improved accuracy provided by substeps is most relevant in decay calculations, where there have previously been concerns about the accuracy and generality of CRAM. With substeps, CRAM can solve any decay or depletion problem with constant microscopic reaction rates to an extremely high accuracy for all nuclides with concentrations above an arbitrary limit.

Neutron-Irradiated Samples as Test Materials for MPEX

Plasma-material interaction is a major concern in fusion reactor design and analysis. The Material Plasma Exposure eXperiment (MPEX) will explore plasma-material interaction under fusion reactor plasma conditions. Samples with accumulated displacement damage (characterized by displacements per atom) produced by fast neutron irradiations in the High Flux Isotope Reactor (HFIR) at Oak Ridge National Laboratory will be studied in the MPEX facility. This paper presents assessments of the calculated induced radioactivity and resulting radiation dose rates of a variety of potential fusion reactor plasma-facing materials, e.g., tungsten. The scientific code packages Monte Carlo N-Particle (MCNP) and Standardized Computer Analyses for Licensing Evaluation (SCALE) were used to simulate irradiation of the samples in HFIR. This included the generation and depletion of nuclides in the material and the subsequent composition, activity levels, gamma radiation fields, and resultant dose rates as a function of cooling time. A challenge of the MPEX project is to minimize the radioactive inventory in the preparation of the samples and the sample dose rates for inclusion in the MPEX facility.

Scavenging of 230Th, 231Pa and 10Be in the Southern Ocean (SW Pacific sector): the importance of particle flux, particle composition and advection

Abstract The scavenging of 230Th, 231Pa and 10Be was studied in the Pacific sector of the Southern Ocean along 170°W using measurements from surface sediments, time-series sediment traps, and the water column. All sediment traps collected an annual flux of 231Pa greater than the integrated rate of production by 235U-decay (up to 5.5 times greater) and a flux of 10Be greater than the global-average deposition rate of 10Be (up to 3.4 times greater). Fluxes of 230Th were on average close to the production rate in the overlying water column. These large fluxes of 231Pa and 10Be, and high unsupported 231Pa/231Th and 10Be/230Th ratios in the sediments, are not associated with depletion of nuclides in the water column, and therefore are not the result of the classical boundary scavenging mechanism. We estimate that of the 231Pa and 230Th advected into the Southern Ocean as part of the large-scale overturning circulation, only those nuclides associated with the “upper limb” of this circulation, i.e. those that pass through the surface as part of the wind-driven Ekman flow, are scavenged efficiently. The majority of the nuclides advected into the Southern Ocean and associated with the “bottom water limb” are not scavenged to the sediments of the Southern Ocean, but are returned northward. Throughout the year, the unsupported 231Pa/230Th and 10Be/230Th ratios of material reaching sediment traps at ∼1000 m at a given site increase with increasing particle flux. This behavior is explained by a conceptual model in which Th, Pa and Be are scavenged reversibly by fine-grained suspended particles at all depths, while Pa and Be are in addition scavenged strongly by diatom-rich aggregates in surface waters. Spatial variability in the annually averaged unsupported 231Pa/230Th and 10Be/230Th ratios of sinking particulate matter reflects primarily the variability in particle composition, and in the ratio and quantity of nuclides upwelled to the mixed layer, rather than variability in particle flux.

A perturbation method for pointwise nuclide depletion calculations

A perturbation method has been developed for computing local nuclide densities to reduce the expense of performing a large number of isotopically detailed depletion calculations. In this method, deviations of local reaction probabilities from node-average values are used to estimate the associated deviations in depleted nuclide densities. The accuracy of the method has been tested by performing several fast reactor numerical calculations. The results indicate that the perturbation method is very accurate for fast reactor applications, while being significantly more efficient. The first and second order perturbation methods are more efficient than the explicit solution of local burnup equations by factors of ∼100 and ∼5, respectively.

Development of a Method for Evaluation of Pin-wise Power Distribution in Fuel Assemblies of Fast Reactors

In the design of fast reactor core with higher burnup and higher linear power, prediction accuracy of burnup history of fuel pin should be upgraded so as to assure fuel integrity without extra design margin under increased neutron fluence and burnup. A method is studied to predict fuel pin-wise power and its burnup history in fast reactors accurately based on an analytic solution of diffusion theory equation on hexagonal geometry with boundary condition from core calculation by finite-differenced diffusion calculation code. The present method is applied to a fast reactor core model, and its accuracy in predicting fuel pin power is tested. The result is compared with the reference solution by the finite difference calculation with very fine mesh. It is found that the present method predicts the power peaking factors in fuel assemblies accurately. The fuel pin-wise nuclide depletion calculation is also done using neutron fluxes for each fuel pin. The result shows that the fuel pin-wise depletion calculation is very important in predicting the burnup history of the fuel assembly in detail.

Development of a Method for Evaluation of Pin-wise Power Distribution in Fuel Assemblies of Fast Reactors.

In the design of fast reactor core with higher burnup and higher linear power, prediction accuracy of burnup history of fuel pin should be upgraded so as to assure fuel integrity without extra design margin under increased neutron fluence and burnup. A method is studied to predict fuel pin-wise power and its burnup history in fast reactors accurately based on an analytic solution of diffusion theory equation on hexagonal geometry with boundary condition from core calculation by finite-differenced diffusion calculation code. The present method is applied to a fast reactor core model, and its accuracy in predicting fuel pin power is tested. The result is compared with the reference solution by the finite difference calculation with very fine mesh. It is found that the present method predicts the power peaking factors in fuel assemblies accurately. The fuel pin-wise nuclide depletion calculation is also done using neutron fluxes for each fuel pin. The result shows that the fuel pin-wise depletion calculation is very important in predicting the burnup history of the fuel assembly in detail.

A linear time-dependent flux approximation for nuclide depletion based on a perturbation method

A method was developed for solving the coupled neutron/nuclide field equations using a linear time-dependent flux approximation that does not require an iterative solution. A perturbation method is used to form the first-order expansion of the time-dependent flux. Solutions of the resulting burnup equations are found to be computationally more efficient than current constant flux or linear flux approximation methods based on an iterative solution. The methods proposed here were validated using a multigroup, zero-dimensional calculation for a fast reactor core model.

Vaiidition of ORIGEN Computer Code by Measurements on Nuclear Fuels of JPDR-1

The depletion and production amounts of U, Pu, transplutonium nuclides and fission products (FPs) measured on the fuel of JPDR-1 were corrected to take account of the performance history of irradiation and cooling using the results of three-dimensional nuclear-thermo-hydrodynamic and nuclide depletion and production calculations. Except a few nuclides, the corrected values proved to agree well with the values calculated by the ORIGEN computer code. Further enhancement of calculational accuracy calls for systematic re-evaluation of neutron cross sections on the basis of neutron spectrum in nuclear fuel.

Validition of ORIGEN computer code by measurements on nuclear fuels of JPDR-1.

The depletion and production amounts of U, Pu, transplutonium nuclides and fission products (FPs) measured on the fuel of JPDR-1 were corrected to take account of the performance history of irradiation and cooling using the results of three-dimensional nuclear-thermo-hydrodynamic and nuclide depletion and production calculations. Except a few nuclides, the corrected values proved to agree well with the values calculated by the ORIGEN computer code. Further enhancement of calculational accuracy calls for systematic re-evaluation of neutron cross sections on the basis of neutron spectrum in nuclear fuel.

New approach to neutron-induced transmutation, radioactivity and afterheat calculations and its application to fusion reactors.

A new method and an accompanying computer code CINAC have been developed for the calculation of neutron-induced transmutation, radioactivity and afterheat. In the method, the generation and depletion of nuclides during and after reactor operation are described in a matrix form in which the arrangement of nuclides is determined systematically. The solutions are obtained by an eigenvalue analysis of the matrix without any time steps or iterative schemes which would increase the computational time. The method can treat any type of activation chains equally, and it gives analytical solutions for linear chains. The CINAC code, coupled with the radiation transport codes ANISN and DOT3.5, can also calculate the dose distribution at any time after shutdown in a one- or two-dimensional geometry of fusion reactors. Two calculations were carried out using CINAC to confirm its validity. The results were compared to those calculated by the THIDA code system which is based on a matrix exponential method. The new method...