Reactor Kinetics Research Articles

Swine wastewater treatment using combined up-flow anaerobic sludge blanket and anaerobic membrane bioreactor: Performance and microbial community diversity

To address the existing economic and environmental issues associated with swine wastewater (SW) treatment, a process combining up-flow anaerobic sludge blanket (UASB) and anaerobic membrane bioreactor (AnMBR) was developed and continuously operated for 137 d. Bioreactor conversion and microbial community dynamics in reactors were analyzed. The UASB–AnMBR process yielded excellent pollutants removal efficiencies of 96% and 63% for chemical oxygen demand (COD) and total phosphorous (TP), respectively. More than 60% of Firmicutes (Terrisporobacter, Turicibacter, and Clostridium sensu stricto 1), which were dominated by Methanosaeta and Methanobacterium with relative abundances of 58.6% and 36.8% in the UASB and 22.5% and 40.3% in the AnMBR, respectively, converted complex compounds into organic acids for methanogenesis. This research presented an analysis of pollutants removal and microbial dynamics of UASB–AnMBR, which significantly affected the large-scale application of UASB–AnMBR process.

On the cyclic change in the dynamics of the IBR-2M pulsed reactor

It is shown that in the IBR-2M reactor by the end of the reactor cycle, changes in dynamics are observed associated with a strong weakening of the fast power feedback (PF), as a result of which the reactor becomes oscillatorily unstable. After each week of zero-power operation the negative changes in reactor dynamics disappear and the stability of the reactor is restored. Thus, the reactor undergoes cyclic changes in the oscillatory instability. The correlation between of a fast PF and a slow PF is experimentally observed, which makes it possible to almost completely eliminate the cyclic component of instability by changing the control mode of rods of the control system.

Analysis of LBLOCA of APR1400 with 3D RPV model using TRACE

It is very difficult to capture the multi-dimensional phenomena such as asymmetric flow and temperature distributions with the one-dimensional (1D) model, obviously, due to its inherent limitation. In order to overcome such a limitation of the 1D representation, many state-of-the-art system codes have equipped a three-dimensional (3D) component for multi-dimensional analysis capability. In this study, a standard multi-dimensional analysis model of APR1400 (Advanced Power Reactor 1400) has been developed using TRACE (TRAC/RELAP Advanced Computational Engine). The entire reactor pressure vessel (RPV) of APR1400 has been modeled using a single 3D component. The fuels in the reactor core have been described with detailed and coarse representations, respectively, to figure out the impact of the fuel description. Using both 3D RPV models, a comparative analysis has been performed postulating a double-ended guillotine break at a cold leg. Based on the results of comparative analysis, it is revealed that both models show no significant difference in general plant behavior and the model with coarse fuel model could be used for faster transient analysis without reactor kinetics coupling. The analysis indicates that the asymmetric temperature and flow distributions are captured during the transient, and such nonuniform distributions contribute to asymmetric quenching behaviors during blowdown and reflood phases. Such asymmetries are directly connected to the figure of merits in the LBLOCA analysis. Therefore, it is recommended to employ a multi-dimensional RPV model with a detailed fuel description for a realistic safety analysis with the consideration of the spatial configuration of the reactor core.

CFD modeling of the ethylene–vinyl acetate copolymerization autoclave reactor: Effects of comonomer ratio on reactor dynamics and copolymer properties

Computational fluid dynamics (CFD) modeling of an industrial ethylene–vinyl acetate autoclave copolymerization reactor was conducted to evaluate the effects of comonomer ratios on reactor dynamics and product properties, including the molecular weight distribution (MWD), and copolymer composition. To accurately predict the MWD of copolymer chains under highly nonideal mixing conditions at a reduced computational cost, the CFD-multicompartment model and probability generating function (PGF) transform were applied. The effectiveness of the developed model was validated by the satisfactorily consistent plant data and simulated results. The model revealed that an increase in the vinyl acetate (VA) content significantly decreased the temperature, promoting combinational termination and chain transfer to polymer reaction for a broad copolymer MWD. The pseudo-kinetic-based analysis showed that VA was consumed more slowly than ethylene, resulting in its lower value in the copolymer composition than that of the comonomer ratios. However, despite nonideal mixing, the copolymer composition was maintained to be uniform for the copolymers produced over the entire reactor volume. In conclusion, the proposed model can be used to understand the governing behaviors of copolymerization under nonideal mixing conditions, design commercial copolymerization reactors, and predict copolymer product qualities.

Modeling nonlinear fractional-order subdiffusive dynamics in nuclear reactor with artificial neural networks.

This paper presents the development and analysis of artificial neural network (ANN) models for the nonlinear fractional-order (FO) point reactor kinetics model, FO Nordheim-Fuchs model, inverse FO point reactor kinetics model and FO constant delayed neutron production rate approximation model. These models represent the dynamics of a nuclear reactor with neutron transport modeled as subdiffusion. These FO models are nonlinear in nature, are comprised of a system of coupled fractional differential equations and integral equations, and are considered to be difficult for solving both analytically and numerically. The ANN models were developed using the data generated from these models. The work involves the iterative process of ANN learning with different combinations of layers and neurons. It is shown through extensive simulation studies that the developed ANN models faithfully capture the transient and steady-state dynamics of these FO models, thereby providing a satisfactory representation for the nonlinear subdiffusive process of neutron transport in a nuclear reactor.

On the concept of “effective delayed neutron fraction”

The article considers methodological issues related to the conceptual and terminological apparatus of the dynamics of nuclear reactors. Based on an elementary analysis of the standard point reactor kinetics equations, the author shows that it is necessary to clarify the physical meaning of the parameter β included in the equations, which is traditionally interpreted as the “effective delayed neutrons fraction” (EDNF). It follows directly from the kinetics equations that the parameter β, which appears in these equations as the EDNF, is, from the point of view of the neutron balance, the fraction of prompt neutrons consumed for the generation of delayed neutron precursors (DNPs), and, from the point of view of the DNP balance, the DNP yield per prompt neutron in a single fission event. With these interpretations taken into account, the role of the β parameter is considered in situations related with its adjustment by multiplying it by the “delayed neutron efficiency factor” and with the establishment of the actual fractions of prompt and delayed neutrons. In particular, it is shown that: the statement “if the delayed neutron fraction is β, then the prompt neutron fraction is equal to 1 – β”, used in the problems of analyzing the nuclear reactor dynamics as a starting position, cannot be considered applicable to any reactor conditions; an increase in the β parameter by multiplying it by the “delayed neutron efficiency factor” leads, contrary to traditional interpretations, not to an increase but to a decrease in neutron reproduction in a supercritical reactor. The proposed clarifications are appropriate both in terms of more adequate descriptions of processes in nuclear reactors and in relation to the formulations of nuclear safety requirements.

Extension of the DYN3D/ATHLET code system to SFR applications: models description and initial validation

DYN3D is a 3D reactor dynamics code originally developed for Light Water Reactors (LWRs) analyses. In recent years, the applicability range of DYN3D was extended to coupled 3D neutronics/thermal-hydraulics (TH) simulations of steady-states and transients in Sodium cooled Fast Reactors (SFRs) at reactor core level.The main objective of this study is to scale up the simulation capabilities of DYN3D from SFR core to system level by coupling DYN3D with a TH system code ATHLET capable of sodium flow modeling. The paper describes the adaption and extension of the existing LWR-oriented DYN3D/ATHLET coupling to SFR analysis. This includes a description of the coupling techniques used to integrate DYN3D with ATHLET and a summary of modifications required to enable the modeling of SFR specific phenomena. The paper also presents the approach to the modeling of reactivity effects caused by the thermal expansions of the reactor components located outside the reactor core, such as reactor vessel, core support structure (strongback), control rod drive lines (CRDLs), etc. The paper also includes the description of the initial verification and validation activities of the extended DYN3D/ATHLET code system. The unprotected stage of the Phenix End-Of-Life natural convection test is used as a test case for this purpose.

Implementation of a Model Predictive Control Strategy to Regulate Temperature Inside Plug-Flow Solar Reactor With Countercurrent Flow

Abstract Solar-driven thermochemical energy storage systems are proven to be promising energy carriers (solar fuels) to utilize solar energy by using reactive solid-state pellets. However, the production of solar fuel requires a quasi-steady-state process temperature, which represents the main challenge due to the transient nature of solar power. In this work, an adaptive model predictive controller (MPC) is presented to regulate the temperature inside a tubular solar reactor to produce solid-state solar fuel for long-term thermal storage systems. The solar reactor system consists of a vertical tube heated circumferentially over a segment of its length by concentrated solar power, and the reactive pellets (MgMn2O4) are fed from the top end and flow downwards through the heated tube. A countercurrent flowing gas supplied from the lower end interacts with flowing pellets to reduce it thermochemically at a temperature range of 1000—1500 °C. A low-order physical model was developed to simulate the dynamics of the solar reactor including the reaction kinetics, and the proposed model was validated numerically by using a 7-kW electric furnace. The numerical model then was utilized to design the MPC controller, where the control system consists of an MPC code linked to an adaptive system identification code that updates system parameters online to ensure system robustness against external disturbances (sudden change in the flow inside the reactor), model mismatches, and uncertainty. The MPC controller parameters are tuned to enhance the system performance with minimum steady-state error and overshoot. The controller is tested to track different temperature ranges between 500 °C and 1400 °C with different particles/gas mass flowrates and ramping temperature profiles. Results show that the MPC controller successfully regulated the reactor temperature within ± 1 °C of its setpoint and maintained robust performance with minimum input effort when subjected to sudden changes in the amount of flowing media and the presence of chemical reaction.

A meta-heuristic algorithm based on Henry's law for the load-following of a two-point PWR model

Henry's law has become the basis of a new meta-heuristic algorithm called Henry gas solubility optimization (HGSO). The novelty of this research is based on the use of this new algorithm in an important issue in nuclear energy, that is, reactor dynamics. The results can signify the validity of HGSO optimization process by comparing with established methods such as particle swarm optimization along with many studies conducted in different sciences. The two-point model of a pressurized light-water nuclear reactor (PWR) is controlled by an HGSO-tuned PID controller based on the integral of the time-weighted absolute error performance index and the axial offset following strategy. A Lyapunov approach guarantees the stability of the tuned PID. Unlike conventional theoretical estimating methods, these algorithms require the least mathematical calculations with the highest accuracy and speed to achieve optimal responses. The results signify the efficiency of this method than an empirically tuned PID, with the least mathematical calculations.

Modeling and Intelligent Controller Design for Reactor Regulating System of Advanced CANDU Reactor (ACR-700) in LabVIEW

In this research work, an Advanced CANDU Reactor of 700 MWe rating (ACR-700) is attempted for Reactor Regulating System (RRS) modeling and intelligent controller design. ACR-700 is a state-of-the-art advanced generation-III reactor. The reactor regulating system is modeled with special emphasis on internal and external reactivity devices. ACR-700 is designed with Liquid Zone Control (LZC) Model, Adjuster Banks Model, Absorber Banks Model and Shutdown Banks Model. The RRS model is a highly sophisticated model developed based on the principle of spatial nuclear reactor dynamics. The RRS model is a multivariable model. The spatial reactor dynamics is modeled based on five internal feedbacks and three feedbacks. The original controller design of RRS is comprised of a PID control algorithm. The control design is reattempted with an advanced intelligent algorithm in which the ANFIS controller is used as a modern control design tool. The new ANFIS controller is basically a multivariable controller. All the modeling of RRS is implemented in Visual Basic (VB) Software while the controller is configured in LabVIEW. A special toolkit is designed for the interfacing of Visual Basic and LabVIEW known as VBLAB. The optimization of intelligent controller parameters is carried out by Genetic Algorithm (GA). The GA-optimized intelligent controller is configured with the VB RRS model. All the variable trends are visualized in the VB environment. The proposed closed-loop ACR-700 RRS control system is tested for small perturbation Analysis and power ramp-down transient and found with excellent behavior well within the design limits. The performance of the suggested ACR-700 RRS controller is compared with the existing conventional controller. The performance of the suggested control scheme is marked with reduced oscillations and faster as compared to the existing control scheme.

Numerical simulation for the control rod assembly drop time evaluation in a LFR

During scram, the Control Rod Assembly (CRA) is quickly dropped into the core and as well, if any of the operating limits are exceeded, the CRA is dropped into the core within a stipulated time to shut down the reactor power as soon as possible. In this study, the Computational Fluid Dynamics (CFD) approach was used to investigate the CRA drop dynamics of a lead-based research reactor. To simulate the flow field around the CRA in the guide tube, a 3-dimensional model of the CRA in the LBE-filled guide tube was developed and discretized; and the averaged Navier-Stokes equations coupled with the dynamic mesh method were adopted. Considering the large mesh deformation in the LBE coolant domain while the CRA drops, the recently developed FSI method in the CFX code, namely the rigid body approach, was adopted, which falls under the monolithic method. In this method, the translational CRA wall, which is partially immersed in the LBE, was set as a rigid body. It has the advantage of updating and improving the mesh quality through the mesh and re-meshing technique during the process of computation. Compared with the results of the work done in the available literature, the CFD model proved to be applicable and reliable. From the results, the inherent high density among the LBE flow characteristics had the most influence on the drop time. The mass of the CRA impacts its driving force so that the drop time reduces when the CRA mass is increased. In conclusion, the method used in this study can be applied to compute and predict significant parameters which can serve as a reference for a suitable design of the CRA and its drive mechanism in the case of modification for safety.

The optimization study of core power control based on meta-heuristic algorithm for China initiative accelerator driven subcritical system

The core power control is an important issue for the study of dynamic characteristics in China initiative accelerator driven subcritical system (CiADS), which has direct impact on the control strategy and safety analysis process. The CiADS is an experimental facility that is only controlled by the proton beam intensity without considering the control rods in the current engineering design stage. In order to get the optimized operation scheme with the stable and reliable features, the variation of beam intensity using the continuous and periodic control approaches has been adopted, and the change of collimator and the adjusting of duty ratio have been proposed in the power control process. Considering the neutronics and the thermal-hydraulics characteristics in CiADS, the physical model for the core power control has been established by means of the point reactor kinetics method and the lumped parameter method. Moreover, the multi-inputs single-output (MISO) logical structure for the power control process has been constructed using proportional integral derivative (PID) controller, and the meta-heuristic algorithm has been employed to obtain the global optimized parameters for the stable running mode without producing large perturbations. Finally, the verification and validation of the control method have been tested based on the reference scenarios in considering the disturbances of spallation neutron source and inlet temperature respectively, where all the numerical results reveal that the optimization method has satisfactory performance in the CiADS core power control scenarios.

Influence of nanomaterials in biohydrogen production through photo fermentation and photolysis - Review on applications and mechanism

The pressure on reducing greenhouse gas emissions has increased since the focus on climate change mitigation has grown. As the human development index is directly related to per capita energy consumption, sustainable energy production with reduced carbon footprint is the essential pathway for cleaner environment. Over numerous existing biological processes, hydrogen production via photo fermentation and photolysis of water is considered a more sustainable and economical method of hydrogen production. While both biological modes suffer from certain limitations, such as low yields and low production rates, practical implementation is still a long way off due to these limitations. The unique properties of nanomaterials (NMs) can help increase the efficiency of the biomass to biohydrogen process in significant ways. Applications of organic and inorganic nanoparticles in photocatalytic and photo fermentative hydrogen production is discussed in this paper. This review reports a wide range of applications of nanomaterials including the details of photo fermentative microorganisms and their mechanism of action. The maximum photo fermentative bio-H2 production was reported in the presence of SiC–Fe3O4(3.02 mol H2/mol acetate), Ni (41 mol H2/mol sugar), graphite-C3N4 (64.2 mol H2/mol sugar) whereas photocatalytic bio-H2 yield was highest when Pd–Ni/CdS (54 mmol/g.h), Ni-MO/g-C3N4 (1785 mmol/g.h) and CuO/TiO2 (20.3 mmol/g.h) nanoparticles were employed. To design photocatalytic systems for practical and scalable use, the future research should be focused on deeper theoretical knowledge of mechanisms of light harvesting, ± charge separation and transport, surface biochemical reactions, semiconductor–liquid interactions, and reactor dynamics.

Overview of Arbitrarily High-Order Adjoint Sensitivity and Uncertainty Quantification Methodology for Large-Scale Systems

This work reviews from a unified viewpoint the concepts underlying the “nth-Order Comprehensive Adjoint Sensitivity Analysis Methodology for Response-Coupled Forward/Adjoint Linear Systems” (nth-CASAM-L) and the “nth-Order Comprehensive Adjoint Sensitivity Analysis Methodology for Nonlinear Systems” (nth-CASAM-N) methodologies. The practical application of the nth-CASAM-L methodology is illustrated for an OECD/NEA reactor physics benchmark, while the practical application of the nth-CASAM-N methodology is illustrated for a nonlinear model of reactor dynamics that exhibits periodic and chaotic oscillations. As illustrated both by the general theory and by the examples reviewed in this work, both the nth-CASAM-L and nth-CASAM-N methodologies overcome the curse of dimensionality in sensitivity analysis. The availability of efficiently and exactly computed sensitivities of arbitrarily high order can lead to major advances in all areas that need such high-order sensitivities, including data assimilation, model calibration, uncertainty reduction, and predictive modeling.

Design of Fractional Order Sliding Mode Adaptive Fuzzy Switching Controllers for Uncertain ACP1000 Nuclear Reactor Dynamics

Advanced Chinese Pressurized Water Reactor (ACP1000) is a third generation load following nuclear reactor. ACP1000 is designed to control the reactor power by a sophisticated control rod mechanism under the base load normal operation of a nuclear power plant in Mode-G. To extend the normal operation of ACP1000 for load following condition, boron adjustment control is used in manual configuration. In this research work, model based two new controllers are designed for ACP1000 reactor dynamics. A nonlinear two-point reactor kinetics model is developed for two halves of the reactor core designated as top and bottom of reactor core. Reactor feedbacks model for two-point reactor kinetics model is developed with fuel temperature, moderator temperature, Xenon concentration, G-Bank control rod position, R-Bank control rod position and boron concentration feedbacks under normal operation of ACP1000. Two problems of the large reactor core of ACP1000 are Xenon oscillations and axial offset in core power distribution. To address these problems, two new controllers are designed for normal load following operation of ACP1000. One controller is designed to replace G1-Bank and R-Bank in Mode-G for reactor power control. The second controller is designed to replace G2-Bank in Mode-G for reactivity control and axial power distribution control. Originally, both reactor coolant average temperature controller and reactor power controller were adaptive controllers. Therefore, both new controllers are designed based on an optimized sliding algorithm using a dedicated fractional order sliding mode control oriented adaptive fuzzy logic control (FO-SMC-AFLC) synthesis scheme. The performance of the proposed closed loop controllers is evaluated for design step and ramp power transients. Both proposed controllers are validated against benchmark results reported in Preliminary Safety Analysis Report (PSAR) of ACP1000. The novel control design scheme is proved satisfactory for normal load following operation of ACP1000, and all the results are found well within design limits.

Existence of solutions for a quasilinear problem with fast nonlocal terms

In this paper, it is considered the existence of a solution for a nonlocal equation involving the p-Laplacian operator which is related to several applications such as vibration problems, flow of fluids through a homogeneous isotropic rigid porous medium, nuclear reactor's dynamics and in population dynamics. The approach is based on sub-supersolution arguments and Schauder's fixed point theorem. An important fact is that our result is valid for nonlocal terms which may exhibit a growth higher than p.

An Improved Steady-State and Transient Analysis of the RSG-GAS Reactor Core under RIA Conditions Using MTR-DYN and EUREKA-2/RR Codes

Steady-state and transient analysis of reactor core under Reactivity-Initiated Accident (RIA) conditions are important for reactor operation safety. The reactor dynamics are influenced by neutronic and thermal-hydraulic aspects of the core. In this study, steady-state and transient analysis under RIA conditions of the RSG-GAS multipurpose reactor was carried out using MTR-DYN and EUREKA-2/RR programs. Neutronic calculations were performed using a few group cross-sections generated by Serpent 2 with the latest cross-section data ENDF/B-VIII.0. Steady-state conditions were carried out with a nominal power of 30 MW, while transient under RIA conditions occurred because the control rod was pulled too quickly while the reactor operated. These transient RIA conditions were performed for two cases, during start-up with an initial power of 1 W, and within power range with an initial power of 1 MW. Thermal-hydraulic parameters considered in this study are reactor power, the temperature of the fuel, cladding, and coolant. The calculated maximum fuel temperature at a steady state is 126.02°C. Meanwhile, the calculated maximum fuel temperature during RIA conditions at the initial power of 1 W and 1 MW are 64.38°C and 137.14°C, respectively. There are no significant differences in thermal-hydraulic parameters between each used program. The thermal-hydraulic parameters such as the maximum temperature of the coolant, cladding, and fuel under this postulated RIA condition are within the acceptable reactor operation safety limits.

Passivity-Based Power-Level Control of Nuclear Reactors

Nonlinear power-level control of nuclear reactors can guarantee wide-range closed-loop stability that is positive for plant load-following capability. Nuclear reactor power dynamics are the tight interconnection of both neutron kinetics and thermal hydraulics, which determines that the corresponding control design model is a complex nonlinear system with large uncertainty. Although nuclear reactor dynamics are complex, it is meaningful to develop simple but effective power-level control methods for easy practical implementation and commissioning. In this paper, a passivity-based control (PBC) is proposed for nuclear reactor power-level dynamics, which has a simple form and relies on the measurement of both neutron flux and average primary coolant temperature. By constructing the Lyapunov function based on the shifted ectropies of neutron kinetics and reactor core thermal hydraulics, the sufficient condition for globally asymptotic closed-loop stability is further given. Finally, this PBC is applied to the power-level control of a nuclear heating reactor, and simulation results show the feasibility and satisfactory performance.

Simulation of two-point reactor kinetics model of reflected reactors with Newtonian reactivity feedback

In this study, a non-analog dynamic Monte Carlo method, named Point Kinetics Monte Carlo (PKMC), is developed to solve the one- and two-point reactor kinetic equations for a reflected reactor with six group of delayed neutron precursors with Newtonian reactivity feedback. Dynamic weight window technique is implemented to control neutron and precursor population during the simulation. Moreover, the Stochastic differential equations for Two-Point Reactor Kinetics Model (STPRKM) is developed to determine neutron and precursor population as a function of time. Since, the random fluctuations in the population dynamics carry very often as much information as the mean value, during the derivation of STPRKM, physical nature of the model problem and inherent probabilistic mechanisms are not altered. Using the developed methods, time dependent transient problems of reflected reactors are studied and mean responses and standard deviations determined by these methods are compared with each other and available deterministic results.

State Estimation for Coupled Reaction-Diffusion PDE Systems Using Modulating Functions.

Many systems with distributed dynamics are described by partial differential equations (PDEs). Coupled reaction-diffusion equations are a particular type of these systems. The measurement of the state over the entire spatial domain is usually required for their control. However, it is often impossible to obtain full state information with physical sensors only. For this problem, observers are developed to estimate the state based on boundary measurements. The method presented applies the so-called modulating function method, relying on an orthonormal function basis representation. Auxiliary systems are generated from the original system by applying modulating functions and formulating annihilation conditions. It is extended by a decoupling matrix step. The calculated kernels are utilized for modulating the input and output signals over a receding time window to obtain the coefficients for the basis expansion for the desired state estimation. The developed algorithm and its real-time functionality are verified via simulation of an example system related to the dynamics of chemical tubular reactors and compared to the conventional backstepping observer. The method achieves a successful state reconstruction of the system while mitigating white noise induced by the sensor. Ultimately, the modulating function approach represents a solution for the distributed state estimation problem without solving a PDE online.