Reactor Kinetics Research Articles

Design of Fractional‐Order Sliding Mode Controller for an Unstable Three‐State Model Jacketed CSTR

ABSTRACTControl of a jacketed continuous stirred tank reactor (CSTR) is challenging due to nonlinear dynamics, complexity, and rapid reactor dynamics under imperfect mixing in the jacket. Current controller designs mainly focus on the two‐state model, neglecting the potential of three‐state models in scenarios with nonperfect mixing and fast reactor dynamics. This study proposes a sliding mode controller (SMC) design scheme based on the transfer function model using a newly developed jellyfish optimisation algorithm. Further, a fractional‐order sliding mode control (FO‐SMC) strategy is proposed, which integrates modifications to the SMC to mitigate chattering, enhance control robustness, and provide better disturbance rejection capability. PID and fractional‐order PID (FOPID) controllers were also designed for comparative analysis. The simulation results demonstrated that FO‐SMC outperformed other designed controllers, shown by a 37.14% reduction in settling time, 10.69% reduction in integral absolute error (IAE), and 19.06% reduction in time‐weighted absolute error (ITAE) compared to SMC and various other improved performance indicators. Parameter variation and noise analysis highlighted the ability of the controller to maintain stability and performance under dynamic conditions.

Integrated learning‐based estimation and nonlinear predictive control of an ammonia synthesis reactor

AbstractThis paper presents an advanced machine learning‐based framework designed for predictive modeling, state estimation, and feedback control of ammonia synthesis reactor dynamics. A high‐fidelity two‐dimensional multiphysics model is employed to generate a comprehensive dataset that captures variable dynamics under various operational conditions. Surrogate long short‐term memory neural networks are trained to enable real‐time predictions and model‐based control. Additionally, a feedforward neural network is developed to estimate the outlet ammonia concentration and hotspot temperature using spatially distributed temperature readings, thereby addressing the challenges associated with real‐time concentration and maximum temperature measurements. The machine learning‐based predictive modeling and state estimation methods are integrated into a model predictive control architecture to regulate ammonia synthesis. Simulation results demonstrate that the machine learning surrogates accurately represent the nonlinear process dynamics with minimal discrepancy while reducing optimization costs compared to the high‐fidelity model, ensuring adaptability and effective guidance of the reactor to desired set points.

Dynamics and control of a parallel-plates reactor for ethanol steam reforming thermally coupled with catalytic ethanol combustion

Dynamics and control of a parallel-plates reactor for ethanol steam reforming thermally coupled with catalytic ethanol combustion

Critical impact of inter-electrode spacing on RF discharge dynamics in ICP plasma reactors: strategies for enhanced plasma performance

Critical impact of inter-electrode spacing on RF discharge dynamics in ICP plasma reactors: strategies for enhanced plasma performance

Fractional Order ANFIS Sliding Mode Controller for Two-Time Scale Dynamics in PWR

In this research work, a novel model of Pressurized Water Reactor (PWR) dynamics is developed with special emphasis on nuclear fuel burn-up or fuel depletion dynamics. PWR dynamics is identified and decomposed into fast and slow dynamic modes for the first time in this research work. The stiff two-time scale reactor dynamics problem is addressed, and a new sophisticated fractional order two-time scale sliding mode controller is designed. The PWR dynamics is uncertain due to three distinct operating conditions of nuclear reactor core as Beginning of Core (BOC), Middle of Core (MOC) and End of Core (EOC) synthesizing a variable structure model. The model uncertainties are estimated using Adaptive Neuro-Fuzzy Inference System (ANFIS) while different reactivity components are addressed as active disturbance or measurement noise. The novel robust control design problem is a big challenge in this research. The proposed controller is designed, tested and validated against benchmark data and found excellent in performance.

Dynamics of Molten Salt Reactor with Operating Heaters

Recent interest in molten salt reactors (MSRs) has initiated research projects on their safety and performance compared to light water reactors. Maintaining the fuel salt in a molten state during reactor operation at all power levels is a significant safety concern for these reactors. Various strategies can be used to maintain the fuel salt temperature above its melting point during low-power reactor operation. This study analyzed the impact of using electric heaters on the stability and performance of an operating MSR. For this purpose, a simulation tool was developed for reactor dynamics and stability analysis studies. The simulation tool was validated against the Molten Salt Reactor Experiment reactivity insertion tests. The dynamics of an MSR with and without operating electric heaters at steady state and following initiated transients were investigated and compared. Simulation results showed that the usage of these heaters is more pronounced during transients rather than in the steady-state operation. The stability of the system degraded following transients due to the operation of heaters. However, using heaters remains an alternative strategy to maintain fuel salt molten at low power levels.

Capacitive deionization in water treatment: A review of reactor dynamics, electrode materials, functional membranes, and modeling techniques

Capacitive deionization in water treatment: A review of reactor dynamics, electrode materials, functional membranes, and modeling techniques

Application of the Krylov-Schur method in three-dimensional nuclear reactor discrete ordinates criticality calculations

The accurate and efficient solution of the neutron transport equation is essential in nuclear reactor physics for understanding reactor kinetics, stability, and safety. This study investigates the application of the Krylov-Schur method to three-dimensional neutron transport criticality calculations within the Marvin code, comparing its performance to the traditional Power Iteration (PI) method. Using the Takeda benchmark problems, the Krylov-Schur solver demonstrated high accuracy in eigenvalue calculations and neutron flux distributions, closely matching reference Monte Carlo (MC) results. Additionally, the parallel efficiency of the Krylov-Schur method was evaluated, showing significant speed-up and better scalability compared to the PI method, particularly in large-scale computations. However, the method requires a larger memory footprint due to the need to store multiple Krylov subspace vectors and Schur decompositions. Despite this, the findings highlight the Krylov-Schur method's robustness and computational efficiency, making it a promising tool for neutron transport simulations in complex reactor configurations. Future work will focus on investigating the subtraction of high-order eigenvalues and eigenvectors using the Krylov-Schur method to further enhance neutron transport simulations.

VOF-based modeling study of surface oscillation behavior and gas–liquid stirring dynamics in the bottom-blown reactors

Gas bottom-blown reactors are widely employed in the chemical, metallurgical, and biochemical industries due to their superior mixing capabilities. This study numerically investigates the gas–liquid flow hydrodynamics and bubble dynamics in a bottom-blown system with a circular boundary using the volume of fluid approach. Following the experimental validation of the mathematical model, this study evaluates the effects of gas flow rates, liquid heights, and fluid medium properties on the dynamics of the bubble swarm, as well as on the surface behavior and the mixing characteristics of the flow field. The results indicate that: (1) Rising bubbles disturb the fluid flow, generating numerous vortices that facilitate momentum transfer for effective gas stirring; (2) The height of the liquid surface oscillation during the bottom-blown process exhibits significant temporal variation, with the peak showing clear lateral swings; (3) Due to the nonlinear interactions involving bubble coalescence and breakup during their ascent, along with constructive and destructive interference between liquid surface waves, the liquid surface can exhibit violent fluctuations at certain moments; (4) Bubble size and aspect ratio significantly influence liquid surface oscillations; (5) The bubble rising path displays instability due to vortex shedding, with some vortices forming at locations where the bubble shape changes abruptly. A prediction equation for bubble velocity is proposed: uc=σ5.2737Lcρc4.2737/16156μl9.5475.

Online and Offline Fault Detection and Diagnostics in a Nuclear Power Plant Condenser

Nuclear power plants (NPPs) face significant financial pressures due to operational and maintenance costs. This research investigates Fault Detection and Diagnostics (FDD) techniques to optimize maintenance schedules and reduce expenses. The NPP condenser plays a critical role in converting turbine exhaust steam back into water for reuse. Condenser tube fouling, a prevalent fault mode, impedes heat transfer efficiency and can lead to decreased plant efficiency and safety risks. This study proposes an FDD framework that leverages raw signal analyses from temperature and pressure monitoring to detect and diagnose condenser tube fouling in both online and offline settings. The online approach facilitates close-to-real-time predictions, enabling proactive maintenance strategies. Additionally, the framework explores incorporating a condenser’s maintenance history for enhanced diagnostics. We employ a dataset obtained from a simulated nuclear power plant condenser using the Asherah Nuclear Power Plant Simulator (ANS). ANS replicates the operational dynamics of a pressurized water reactor (PWR) type NPP. The proposed methodology utilizes an encoder-decoder (E-D) structured 1DCNN model to analyze the raw signals. The research demonstrates consistent and accurate fault detection and diagnostics for condenser tube fouling in both online and offline scenarios. A high potential for generalization to unseen conditions was observed. However, online detection using small data windows necessitates caution due to potential false alarms around the transition points. Our findings pave the way for further exploration of robust diagnostics by accommodating a wider spectrum of fouling rates within degradation classes using ANS. This combined online and offline FDD approach offers a promising solution for promoting operational safety, efficiency, and cost-effectiveness in NPP condensers.

Fluidized Bed Reactors for energy recovery from biomass and wastes: a data-driven approach towards the development of digital twins for real time control and monitoring

Abstract The application of machine learning (ML) techniques for the control and development of digital twins for a fluidized bed reactors represents a significant advancement in process engineering. In this study, the integration of data-driven models trained using computational fluid dynamics (CFD) simulations, is explored for developing and optimizing the lab-scale fluidized bed reactor operations. By leveraging the collection of data generated from CFD simulations, data-driven algorithms, based on the Singular Value Decomposition (SVD) and Gaussian processes for regression, are trained to predict the gas-solid flow patterns under different operating condition. The data-driven models presented, serve as efficient reduced order model (ROM) surrogate for computationally expensive CFD simulations, enabling real-time predictions and control strategies for fluidized bed reactors, facilitating continuous monitoring, optimization, and predictive maintenance. Moreover, the ROM can effectively capture the complex relationships within the reactor system, with an overall error < 10% even without precise knowledge of the underlying physical phenomena. The synergistic combination of ML techniques and CFD simulations offers valuable insights into complex multiphase flow phenomena and reactor dynamics, leading to improved process control, energy efficiency, and overall performance of fluidized bed reactors. This approach holds great promise for accelerating innovation and sustainability in chemical and energy industries.

Evaluation of dynamical behavior of Thorium fueled SMART reactor using lumped parameter dynamic model

The point reactor dynamic model is based on the lumped parameter model and, unlike the traditional reactor kinetics model, takes into account the effects of the fuel and moderator temperature on the system reactivity. This model is a system of nonlinear and nonhomogeneous differential equations and is used in the transient analysis of an initially critical system subjected to any perturbation. In this study, transient analysis of the Th-fueled SMART reactor is performed by the point dynamics model. Initially, the reactor is kept critical using the reactivity control mechanisms such as control rods insertioın and soluble boron addition to the moderator. The required neutronic parameters such as precursors’ parameters, neutron generation time, and reactivity coefficients are calculated using the Serpent 2 Monte Carlo code. The moderator average temperature and system pressure are used as two distinct thermodynamic properties to determine thermal-hydraulic parameters such as heat capacity, conductivity coefficient, convection coefficient, and fuel thermal resistance. For different reactivity insertion scenarios, MATLAB ODE45 suite is used to solve the point dynamic equations. The validity of the provided code is also verified either through comparison with the analytically solvable form of the point dynamic model or by analyzing the asymptotic equilibrium values of the considered parameters. Finally, it is seen that when an initially critical reactor operating at a certain power level undergoes a perturbation, after a short time the system becomes again critical and operates at an almost stable power level different from the pre-perturbation power level. This, in turn, implies that the calculated neutronic and thermal-hydraulic parameters are physically meaningful.

Dynamics of a Centrifugally Confined Fusion Plasma in Space Propulsion Applications

In centrifugal-mirror (CM) confinement, electric and magnetic fields are combined to confine the plasma within a rapidly rotating annulus of burning plasma fixed between two mirror magnets. This confinement scheme can be applied to a direct-fusion-drive propulsion system. Reactor dynamics refers to the thermodynamic and transport characteristics of fusion plasma confined by the centrifugal mirror. The objectives of the paper are to describe 1) the CM well potential and its relation to momentum confinement time, 2) the reactor power balance, 3) the role of electric and magnetic fields in power deposition necessary to affect the plasma rotation, 4) the characteristics and derivation of the critical Mach number for plasma rotation speed, 5) plasma transport in the vicinity of the critical Mach number, and 6) propulsion performance of CM plasmas. The development of these objectives is based on observations and analysis of results from a zero-dimensional (0-D)-model reactor model, where the 0-D model assumes constant properties in the plasma. The principal results are that the power needed to self-power the reactor can be estimated from knowledge of the applied magnetic and electric fields, and the reactor delivers the highest power density when operating near the critical Mach number.

Development of Small Modular Reactor iPWR Dynamics Simulator

Abstract In the energy transition era, nuclear power serves as a significant source of electricity with low emissions, contributing to approximately 10% of the world’s total electricity production. The advanced and distinct features of iPWR-type SMR in the field of nuclear power generation contribute to a greater safety margin. This opens up possibilities for extending the utilization of secure, environmentally friendly, and dependable nuclear energy across various energy sectors. Moreover, the public need to understand the technical performance of the iPWR. To improve understanding of iPWR’s technical performance, a simulator is developed. The simulator is developed to provide a comprehensive study of nuclear reactor transient behavior, to serve as an educational tool for students, and to demonstrate the safety features during accident scenarios. This article introduces a simulator that combines modules of neutronics, reactor thermal-hydraulics, and the NSSS. The simulator uses the design parameters of iPWR with a power capacity of 160 MWt that relies on natural convection. The proposed simulator was developed using LabVIEW software to perform the reactor dynamics calculations. Furthermore, hardware devices for controlling the simulator can be integrated to simulate the control room of an NPP. The calculation was based on the standard lumped parameter point kinetics and thermal-hydraulic equations. To simplify the process and reduce computational cost, several assumptions are incorporated into the equations, including one-group thermal neutron and constant gain thermal power. The simulator development yields preliminary data for reactor calculations, the graphical user interface (GUI) of the simulator, and the Virtual Instruments (VIs) comprising the reactor model. The reactor model comprises multiple components, each represented as a subVI within the LabVIEW environment. This simulator serves as an effective educational and dissemination tool for increasing public acceptance of NPP by providing insights into the behavior of the reactor and facilitating a better understanding of its operation, safety features, and potential benefits.

Exploring thermal flow dynamics in pressurized water reactors using hybrid graphene nanoplatelet coolants

AbstractThis study investigates the impact of hybrid nanoparticles on the temperature of nuclear reactor coolant, with a focus on graphene nanoplatelet (GNP)‐based hybrid nanoparticles. Sixteen different hybrid nanofluids were analyzed, and their performance was compared with a standard water‐based coolant. The criticality values were obtained through MCNP modeling, revealing that higher nanoparticle ratios led to increased criticality, with the highest value of 1.3239 observed in GNP‐Fe3O4 + Al2O3 nanofluids (0.05 wt%) and the lowest value of 1.2935 in GNP–Fe3O4 + SiO2 nanofluids (0.001 wt%). Temperature variations showed that increasing nanoparticle concentrations resulted in slightly higher temperatures, with a maximum of 611.97 K for 0.05 vol.% GNP nanoparticles. Additionally, the departure from nucleate boiling ratio values were consistently above the safety threshold of 2.08, with the lowest value of 3.657 for GNP–Fe3O4 + SiO2 nanofluids (0.05 vol.%). These findings suggest that hybrid nanofluids, particularly those with higher nanoparticle ratios, can enhance the thermal performance and safety margins of nuclear reactor coolants, offering a promising avenue for future research and application.

Two Optimization Approaches for a Small‐Scale Power‐to‐Ammonia Cycle

AbstractAmmonia is a promising carbon‐free energy vector. Small‐scale renewable power‐to‐ammonia (P2A) is particularly suited for isolated agricultural areas where ammonia can be used as fuel and fertilizer. This work compares two approaches to simulate and optimize the steady‐state behavior of a novel small‐scale P2A process: Aspen Plus® and MOSAIC®. Aspen Plus® is a commercial flow sheeting software whereas MOSAIC® is a freeware where equations and thermochemical properties need to be specified by hand. It can be shown that the results of MOSAIC® and Aspen Plus® are qualitatively comparable, but not identical. This suggests that the model in MOSAIC® can be improved further, starting with the implementation of a more accurate numeric reactor kinetics and equation of state.

Stochastic differential equations for non-analog Monte Carlo model of point kinetics equations

The stochastic form of one-point and two-point reactor kinetics models have been extensively investigated in the literature. We have noticed that, in some studies, the probabilistic nature of neutron interaction mechanisms was not incorporated truly. For instance, in the case of negative reactivity insertions, one of the presented probability functions becomes negative, making the Monte Carlo (MC) simulation impossible. In this manuscript, the non-analog stochastic point reactor kinetics models are developed to simulate the stochastic behavior of nuclear systems. To reduce the imposed variance from the leakage and capture of neurons, both capture and leakage events are sampled implicitly. Precursors are also forced to decay in each simulation step. The true variances of the neutron’s and delayed neutron precursor’s populations are determined from the solution of the developed non-analog stochastic models. Also, they are compared with those of both analog and non-analog Monte Carlo methods. The results show that the analog Monte Carlo (MC) has a larger variance than the non-analog MC.

A multi-objective decision-making method for small modular reactor operation based on A3C algorithm

Small modular reactors (SMRs) are ideal energy sources for remote areas, but they still require operators to make decisions. Due to the harsh working environment, it is difficult to resume operation of small modular reactors once an accident occurs in unmanned application scenarios. Therefore, a multi-objective operation scheme that ensures safety and takes into account the operational task requirements is particularly important. We proposed an artificial intelligence approach for multi-objective optimization and decision-making for SMRs. We used a multi-objective extension of the Asynchronous Advantage Actor-Critic (A3C) algorithm to learn a comprehensive optimization function reflecting the importance of each objective under different tasks. We also used a proxy deep neural network (DNN) simulating the reactor dynamics and speeding up the training process. We tested our approach on a simulated SMR under different scenarios, such as normal operation and fault occurrence. The results showed that our approach can perform well under different conditions and avoid local optima. The verification results showed that the operation limits are not violated in the transient process. Our approach solves a challenging problem and provides a valuable insight for the field of SMRs. It can also be applied to other complex systems that require multi-objective optimization and decision-making.

Nonlinear dynamics of a membrane reactor for hydrogen production: Multiplicity of equilibrium solutions and inhibition effects

Membrane reactors for the production of hydrogen are interesting devices that allow for the decentralized production of pure hydrogen while reducing the energy cost of the traditional steam reforming process. The performance of these systems is strongly dependent on the permeability and selectivity of the membrane employed for the separation of the produced hydrogen. Several studies have shown that the actual rate of hydrogen permeation is lower than the one that would be expected based on studies of membrane permeability carried out with pure hydrogen. This difference has been attributed to the competitive adsorption of other species, specifically CO, on the membrane surface. Here we show that this phenomenon could also lead to steady state multiplicity and analyze the dynamics of membrane reactors in the presence of competitive adsorption by CO. Emphasis has been placed on the effect of temperature and gas composition on possible multistable behavior. The results have been interpreted in terms of a transition between kinetics- and permeation-controlled regimes, in which the behavior of the reactor is limited, respectively, by the rate of the chemical reactions or the rate of hydrogen permeation.

A quasistatic asymptotic limit for reactor kinetics

We propose a “quasistatic” asymptotic limit for reactor kinetics in which the material properties vary much more slowly in time than the solution itself. We further develop an asymptotic approximation of the solution in this limit using the method of multiple scales that, to leading order, takes the form of the product of a function that depends only on time and a function that depends on all independent variables but varies on the same time scale as the material properties. Determining when an approximation of this form is valid is of interest as several methods for performing reactor-kinetics calculation rely on such a representation of the solution. With an example reactor-kinetics problem, we demonstrate our asymptotic approximation becomes more accurate as the material properties vary more slowly in time, as expected.