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In this study, the transient response of a reactor in the case of reactivity insertion with and without reactivity feedback was explored. The uncertainties resulting from using various numerical solvers to simulate the reactor response using the point reactor kinetics model were investigated.
Solution of reactor kinetics equation numerically unconditionally stable for all values of reactivity or integration step size
The conventional kinetics equations for reactors in which fuel is stationary are derived without approximation from the time-dependent transport equation. The utility of the precise form which results is discussed, first generally, then with reference to the detailed analysis of two typical experiments. In this study, it is shown that the analysis required for a precise interpretation of kinetics experiments can generally be made using the same techniques employed in the computation of criticality for stationary cases.
This memo reviews analysis of the kinetics behavior of the INL NRAD reactor.
The KIR computer code intended for calculations of nuclear reactor kinetics using the Monte Carlo method is described. The algorithm implemented in the code is described in detail. Some results of test calculations are given.
Interest in circulating fuel reactors (CFRs), particularly molten salt reactors (MSRs) of the fluid fuel type, has been growing in the last two decades. Starting with a resurgence of interest in Europe, there have been a growing number of methods proposed and codes developed to model the kinetics of CFRs, which is a capability essential to the design and evaluation of such reactors. This work first reviews the physical phenomena unique to CFRs in light of current research and how CFR kinetics are impacted by these considerations. In general, it is found that the movement of delayed neutron precursors (DNPs) through the primary loop has significant impacts on transients at low reactor powers or those with significant spatial components such as a change in the primary loop mass flow rate. Effects on the neutron flux are exceedingly minimal and entirely negligible. An extensive review of published models and methods for simulating CFR kinetics is presented, along with transient simulations in fast and thermal neutron flux systems using representative codes from each of the main modeling categories. Comparisons among methods are presented as are recommendations for their use or nonuse in various transient and work-flow scenarios. In general, it is recommended that time-resolved, multigroup neutron diffusion approaches be used to establish ranges of applicability for point reactor kinetics (PRK)–based approaches that themselves may not be applicable for all modeling situations. In such cases, it is suggested that quasi-static approaches be used where PRK-based approaches cannot be used. Finally, a review of common assumptions used in these models is presented, along with an evaluation of their impact on model performance. It is found that neglecting turbulent diffusion in open core–type CFRs is a poor assumption that leads to an underestimation of the reduction of the delayed neutron fraction. Furthermore, it is seen that exclusion of secondary heat transfer loops in models leads to underestimation of transient peaks and troughs.
The system analysis of anticipated operating occurrences and design basis accident for pebblebed reactor systems requires knowledge of the neutron kinetic parameters. These parameters take into account various types of feedback from the pebble-bed core and are typically integrated into system analysis tools such as the System Analysis Module (SAM) in the Nuclear Energy Advanced Modeling and Simulation (NEAMS) tool package. These parameters are typically generated by a higher fidelity full-core coupled neutronics/thermal fluids analysis, such as using Griffin and Pronghorn, in 2D or 3D. The delayed neutron fractions (beta) and the neutron lifetimes (lambda) are typically generated by applying the adjoint solution of the neutron flux. Temperature reactivity coefficients are the most important feedback for all anticipated operating occurrences and design basis accident, then depending on the transient other effects might be important as rector control system worth, s-curves, and Xenon generation. This work package will establish a methodology and process for calculating the reactor kinetics parameters for high-temperature gas-cooled reactor and provide them in a suitable form for system level analyses of typical anticipated operating occurrences and design basis accident.
Phenolic commodity chemicals were produced from lignin with high yield and selectivity in a flow reactor, valorizing the biorefinery process.
The reduction kinetics of hematite iron ore fines to metallic iron by hydrogen using a laboratory fluidized bed reactor were investigated in a temperature range between 873 K and 1073 K, by measuring the weight change of the sample portion during reduction. The fluidization conditions were checked regarding plausibility within the Grace diagram and the measured pressure drop across the material during experiments. The apparent activation energy of the reduction was determined against the degree of reduction and varied along an estimated two-peak curve between 11 and 55 kJ mol{sup −1}. Conventional kinetic analysis for the reduction of FeO to metallic iron, using typical models to describe gas–solid reactions, does not show results with high accuracy. Multistep kinetic analysis, using the Johnson–Mehl–Avrami model, shows that the initial stage of reduction from Fe{sub 2}O{sub 3} to Fe{sub 3}O{sub 4}, and partly to FeO, is controlled by diffusion and chemical reaction, depending on the temperature. Further reduction can be described by a combination of nucleation and chemical reaction, whereby the influence of nucleation increases with an increasing reduction temperature. The results of the kinetical analysis were linked to the shape of the curve from apparent activation energy against the degree of reduction.
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 239 Pu nuclear data to reduce nuclear-data induced uncertainties in the effective neutron multiplication 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 239 Pu nuclear data.
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Sensitivity coefficients of prompt neutron decay constant (α) and effective delayed neutron fraction (β eff ) to Pu-239 nuclear data were calculated using a newly available tool (ACEtk). Uncertainty calculations showed the following trends: (1) The prompt neutron decay constant can be used to reduce nuclear data-induced uncertainty in Pu-239(n,f) and (2) the effective delayed neutron fraction can be used to effectively reduce nuclear data-induced uncertainty in Pu-239 total fission $\tilde{v}$. Sensitivity/uncertainty analysis can be used to determine optimal experiment/detector setup to identify compensating errors in nuclear data. Upcoming work includes investigating other nuclide-reaction pairs and response sensitivities, such as Δ$\rho$, neutron leakage spectra, and reaction rate measurements to constrain nuclear data of interest.
Abstract not provided.
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The use of electrons as main reagent for the recovery and recycling of critical metals from spent lithium-ion batteries (LIBs) is a process electrification strategy that can be used to close the life-cycle loop of LIBs through more sustainable methods. Electrochemical leaching, a process that uses a reductant that is constantly regenerated electrochemically for the leaching of lithium-ion battery black mass (LIBBM), has shown high extraction efficiencies and sustainable scores. However, slow kinetics, reactor design challenges and lack of deeper understanding of the underlying processes are barriers to the optimization, scale-up, and market adoption of this technology. In this paper, a kinetic study and mathematical model for dissolving LIBBM is presented to better understand the underlying mechanisms aiming to reduce the processing time and make predictions for future design and scale-up. The effect of acid and electrochemically mediated reductant concentrations, LIBBM loading, and cathode/reactor designs were explored. As a result, the leaching time was reduced from 7h to under 1h at a pulp density of 73 g/L, without external heating. A novel reactor with parallel baffle electrodes (PBE) was developed, which significantly reduced the leaching time by improving convection in a stirred slurry electrochemical reactor. Dimensionless numbers were deduced from an unsteady state model, which can be used in dimensional analysis for future process design and scale-up.
The systems analysis of anticipated operating occurrences and design basis accidents for pebble-bed reactor systems requires knowledge of neutron point kinetics equations (PKE) parameters. Typically, the generation of PKE parameters is performed in a global manner using standalone neutronics calculations, without the inclusion of thermal fluid distributions. We utilize Griffin and Pronghorn for generating global and local PKE parameters which includes the use of thermal fluid distributions to account for localized effects. This work establishes a methodology for calculating PKE parameters for a pebble bed reactor with a coupled neutronics/thermal fluids analysis. PKE parameters generated on a global and local basis are compared against a diffusion solve for a typical load-following transient. Locally-generated neutron kinetic parameters are able to reduce the maximum error in the transient power level from 5% to below 1.5%; along with this, bulk temperature errors were reduced from 12 K to 4 K.
Neutron kinetics plays an important role in reactor safety and analysis. The backward Euler method is the most widely used time integration method in the calculation of space-dependent nuclear reactor kinetics. Xia (2006) used this method to discretize the derivative of flux, and adopted the analytic integration to discretize the delayed neutron precursor concentrations. Diagonally Implicit Runge-Kutta (DIRK) method owns high accuracy and excellent stability, and it was applied in the rectangle core for calculating core the nuclear reactor kinetics by Wenbo Zhao (2013). Recently, DIRK was applied to the neutron kinetics for hexagonal-z geometry application (CAI, 2016). As solving the neutron kinetics equations is very time-consuming and the number of available cores continues to increase with parallel architectures evolving, parallel algorithms need to be designed in order to effectively utilize the available resources. However, it is difficult to parallel in time axis because the later moment is strongly dependent on the previous moment. Some methods have been proposed to parallel in time algorithm over the last decades. One of the famous methods to realize time parallelism is the Parareal algorithm (Lions, 2001), which offers a promising approach to increase the degree of concurrency. More than one decade from this method first proposed, this method has been studied and applied in the many fields of applied mathematics, physics, chemistry, parallel computing, etc. Fischer (2014 applied the Parareal method in the field of the Navier-Stokes Equations. Baudron (2014) combined the Parareal method with finite element method to solve the neutron kinetics equations, where the Parareal method was implemented based on the implicit Euler method or method. In this paper, the Parareal method is studied in the hexagonal-z geometry with the help of DIRK developed for neutron kinetics equations (CAI, 2016)
This work applies Lie Group Theory to the nonlinear point-reactor neutron kinetics equations for several reactivity feedback and reactivity insertion models. The goal of this work is to connect known analytical solutions to their corresponding Lie groups as well as to obtain new analytical solutions and the circumstances from which they arise. The reactivity models we consider are the Nordheim-Fuchs Model, an arbitrary-order polynomial reactivity insertion model, and the Fuchs Ramp-Insertion Model. In all three models, we generalize the analysis when possible and obtain analytical solutions in every case. For the first two models, we succeed in finding the Lie groups corresponding to classical solutions and find additional solutions that were otherwise unknown. Finally, for the final model, we obtain a reduced-order nonlinear kinetics equation which is not analytically solvable, but by applying a second-order truncation, we find a novel closed-form solution and demonstrate its validity with a numerical example.