Reduced-order method for nuclear reactor primary circuit calculation

Accurate real-time simulations of nuclear reactor circuit systems are particularly important for system safety analysis and design.To effectively improve computational efficiency without reducing accuracy,this study establishes a thermal-hydraulics reduced-order model(ROM)for nuclear reactor circuit systems.The full-order circuit system calculation model is first established and verified and then used to calculate the thermal-hydraulic properties of the circuit system under different states as snapshots.The proper orthogonal decomposition method is used to extract the basis functions from snapshots,and the ROM is constructed using the least-squares method,effectively reducing the difficulty in constructing the ROM.A comparison between the full-order simulation and ROM prediction results of the AP1000 circuit system shows that the proposed ROM can improve computational efficiency by 1500 times while achieving a maximum relative error of 0.223%.This research develops a new direction and perspective for the digital twin modeling of nuclear reactor system circuits.

An Axial Dispersion Model for Evaporating Bubble Column Reactor

Evaporating bubble column reactor (EBCR) is a kind of aerated reactor in which the reaction heat is removed by the evaporation of volatile reaction mixture. In this paper, a mathematical model that accounts for the gas-liquid exothermic reaction and axial dispersions of both gas and liquid phase is employed to study the performance of EBCR for the process of p-xylene(PX) oxidation. The computational results show that there are remarkable concentration and temperature gradients in EBCR for high ratio of height to diameter (H/DT). The temperature is lower at the bottom of column and higher at the top, due to rapid evaporation induced by the feed gas near the bottom. The concentration profiles in the gas phase are more nonuniform than those (except PX) in the liquid phase, which causes more solvent burning consumption at high H/DT ratio. For p-xylene oxidation, theo ptimal H/DT is around 5.

Intensification of Deep Hydrodesulfurization Through a Two-stage Combination of Monolith and Trickle Bed Reactors

Deep hydrodesulfurization （HDS） is an important process to produce high quality liquid fuels with ultra-low sul- fur. Process intensification for deep HDS could be implemented by developing new active catalysts and/or new types of reactors. In this work, the kinetics of dibenzothiophene （DBT） hydrodesulfurization over Ni-P/SBA-15/ cordierite catalyst was investigated at 340-380 ℃ and 3.0-5.0 MPa. The first-order reaction model with respect to both DBT and H2 was used to fit the kinetics data in a batch recycle operation system. It is found that both the activation energy and rate constant over the Ni-P monolithic catalyst under our operating conditions are close to those over conventionally used HDS catalysts. Comparative performance studies of two types of reactors, i.e., trickle bed reactor and monolithic reactor, were performed based on reactor modeling and simulation. The results indicate that the productivity of the monolithic reactor is 3 times higher than that of the trickle bed reactor on a catalyst weight basis since effective utilization of the catalyst is higher in the monolithic reactor, but the volumetric productivity of the monolithic reactor is lower for HDS of DBT. Based on simulation results, a two- reactor-in-series configuration for hydrodesulfurization is proposed, in which a monolithic reactor is followed by a tickled bed reactor so as to attain intensified performance of the system converting fuel oil of different sulfur-containing compounds. It is illustrated that the two reactor scheme outperforms the trickle bed reactor both on reactor volume and catalyst mass bases while the content of sulfur is reduced from 200 μg·g-1 to about 10 μ·g-1.

Modeling of a slurry bubble column reactor for Fischer-Tropsch syn- thesis

On the basis of the global CO consumption rate model, the lumped product distribution model and the sedimenta- tion-dispersion model of a catalyst, a steady-state, one-dimensional mathematical model of the slurry bubble column reactor for Fischer-Tropsch synthesis were established. The mathematical simulation of the slurry bubble column reactor for Fischer-Tropsch synthesis was carried out under the following typical industrial operating conditions： temperature 230 ℃, pressure 3.0 MPa, gas flow 5x 105 m3/h, catalyst content in slurry phase 30%, reactor diameter 5.0 m and the composition of feed gas： y（H2）=0.60, y（CO）=0.30, y（N2）=0.10. The influences of operating pressure, temperature and re（HE）Ira（CO） in feed gas on the reactor＇s reaction performance were simulated.

Effect of hydrogen combustion reaction on the dehydrogenation of ethane in a fixed-bed catalytic membrane reactor

A two-dimensional non-isothermal mathematical model has been developed for the ethane dehydrogenation reaction in a fixed-bed catalytic membrane reactor. Since ethane dehydrogenation is an equilibrium reaction,removal of produced hydrogen by the membrane shifts the thermodynamic equilibrium to ethylene production.For further displacement of the dehydrogenation reaction, oxidative dehydrogenation method has been used.Since ethane dehydrogenation is an endothermic reaction, the energy produced by the oxidative dehydrogenation method is consumed by the dehydrogenation reaction. The results show that the oxidative dehydrogenation method generated a substantial improvement in the reactor performance in terms of high conversions and signi ficant energy saving. It was also established that the sweep gas velocity in the shell side of the reactor is one of the most important factors in the effectiveness of the reactor.

Modeling and experimental studies of methyl methacrylate polymerization in a tubular reactor

In this study, rheological examination of the mixture of a tubular reactor in which methyl methacrylate was polymerized has been studied. The n(flow behavior index) value of Power Law Model of mixture contained in the reactor has been determined within the span of 0.3492 to 0.9889 by curve fitting. Employing these numerical data for velocity profile, the reactor has been modeled. Moreover, the functions of the reactor have been compared in the three modes of plug, mixed and laminar flow. The results obtained in this research indicate that the polymethyl methacrylate mixture contained in the reactor is pseudo-plastic. Moreover, as the conversion grows, the velocity profile starts as a parabolic profile and approaches the plug mode; although it never reaches the plug. The other conclusions borne in this study indicate that when the reactor's radius is decreased, the conversion rate grows. However, as decreasing the radius would also reduce the productions rate, this procedure is not economical. Finally, in this modeling, the amount of conversion is equal to 56.47% at the end and according to its laboratory proportion which is 55.88%, it has reached the conclusion that the modeling duly undertaken is applicable and valid.

Flow Field and Temperature Field in GaN-MOCVD Reactor Based on Computational Fluid Dynamics Modeling

Metal organic chenlical vapor deposition （AIOCVD） growth systems arc one of the. main types of equipment used for growing single crystal materials, such as GaN. To obtain fihn epitaxial materials with uniform performanee, the flow field and ternperature field in a GaN-MOCVD reactor are investigated by modeling and simulating. To make the simulation results more consistent with the actual situation, the gases in the reactor are considered to be compressible, making it possible to investigate the distributions of gas density and pressure in the reactor. The computational fluid dynamics method is used to stud,v the effects of inlet gas flow velocity, pressure in the reactor, rotational speed of graphite susceptor, and gases used in the growth, which has great guiding~ significance for the growth of GaN fihn materials.

MPC of distillation column with side reactors for methyl acetate

This paper focuses on the dynamic control of distillation column with side reactors(SRC) for methyl acetate production. To obtain the optimum integrated structure and steady state simulation, the systematic design approach based on the concept of independent reaction amount is applied to the process of SRC for methyl acetate production. In addition to the basic control loops, multi-variable model predictive control modular with methyl acetate concentration and temperature of sensitive plate is designed. Then, based on process simulation software Aspen Plus, dynamic simulation of SRC for methyl acetate production is used to verify the effectiveness of the control scheme.

Modeling of C_(8) Aromatics Isomerization in a Radial Bed Reactor

Reactor models were developed to describe the isomerization reaction process of C_(8) aromatics by applying a six-component sequential reaction network.Lab-scale experimental data were used in an axial bed reactor model,and dynamic parameters were fitted by simulated annealing algorithm.In addition,industrial data and calculated dynamic parameters were used to determine the six-component concentration distributions using a radial reactor model.The influence of back-mixing on reaction performance was investigated.It was found that the model considering back-mixing was much closer to the real industrial reaction process.

Study on Modeling for a New FCC Technique——MIP Riser Reactor

This research work developed a model for the MIP riser reactor using the data collected from an industrial MIP unit.Based on analysis of flow patterns in the reactor,three models were established and a comparison was made on each other.The results indicated that Model Ⅲ,which was assumed a plug flow in the first reaction zone and a gas plug flow and a continuously stirred catalyst flow in the second reaction zone,was the best.The results of this research could offer an information and guidance for optimization and development of MIP unit.

The Statistical Experimental Design for Chemical Reactors Modeling

The Statistical Experimental Design techniques are the most powerful tools for the chemical reactors experimental modeling. Empirical models can be formulated for representing the chemical behavior of reactors with the minimal effort in the necessary number of experimental runs, hence, minimizing the consumption of chemicals and the consumption of time due to the reduction in the number of experimental runs and increasing the certainty of the results. Four types of nonthermal plasma reactors were assayed seeking for the highest efficiency in obtaining hydrogen and ethylene. Three different geometries for AC high voltage driven reactors, and only a single geometry for a DC high voltage pulse driven reactor were studied. According to the fundamental principles of chemical kinetics and considering an analogy among the reaction rate and the applied power to the plasma reactor, the four reactors are modeled following the classical chemical reactors design to understand if the behavior of the nonthermal plasma reactors can be regarded as the chemical reactors following the flow patterns of PFR (Plug Flow Reactor) or CSTR (Continuous Stirred Tank Reactor). Dehydrogenation is a common elimination reaction that takes place in nonthermal plasmas. Owing to this characteristic, a paraffinic heavy oil with an average molecular weight corresponding to C15 was used to study the production of light olefins and hydrogen.

Modeling and Control of a Biodiesel Transesterification Reactor

Dynamic Models for predicting the concentration profiles of the reactants and product in a Continuous Stirred Tank Reactor for the transesterification of used cooking oil (triglyceride) to biodiesel has been developed using the principle of conservation of mass. The developed system of differential equations were integrated numerically using fourth order Runge-Kutta algorithm embedded in ode 45 solver of 7.5 Mathlab program. The models were validated by solving the model equations with kinetic data and other relevant data from literatures. The results and trends were similar and in agreement with those from these literatures. Simulations of the reactor to (±) step changes in the inlet flowrates of the reactants (used cooking oil and methanol) showed great effect on biodiesel production, (instability—oscillations and reduction in output concentration of biodiesel). A feedback control strategy was developed with a Proportional-Integral (PI) Controller and a close loop model was developed for control studies. The closed loop response of the reactor output (biodiesel concentration) showed continuous oscillatory response with offset. Hence the controller parameters (proportional gain Kc and integral time ) were tuned using the “On-Line Trial and Error Method” implemented using MathLab Simulink to obtain optimum values that ensured quick stability of the closed-loop system, reduced or no oscillatory response and no offset. The optimum controller parameters were: proportional gain Kc =8.306 and integral time = 17.157 minutes.

Introducing the nth-Order Features Adjoint Sensitivity Analysis Methodology for Nonlinear Systems (nth-FASAM-N): II. Illustrative Example

This work highlights the unparalleled efficiency of the “nth-Order Function/ Feature Adjoint Sensitivity Analysis Methodology for Nonlinear Systems” (nth-FASAM-N) by considering the well-known Nordheim-Fuchs reactor dynamics/safety model. This model describes a short-time self-limiting power excursion in a nuclear reactor system having a negative temperature coefficient in which a large amount of reactivity is suddenly inserted, either intentionally or by accident. This nonlinear paradigm model is sufficiently complex to model realistically self-limiting power excursions for short times yet admits closed-form exact expressions for the time-dependent neutron flux, temperature distribution and energy released during the transient power burst. The nth-FASAM-N methodology is compared to the extant “nth-Order Comprehensive Adjoint Sensitivity Analysis Methodology for Nonlinear Systems” (nth-CASAM-N) showing that: (i) the 1st-FASAM-N and the 1st-CASAM-N methodologies are equally efficient for computing the first-order sensitivities;each methodology requires a single large-scale computation for solving the “First-Level Adjoint Sensitivity System” (1st-LASS);(ii) the 2nd-FASAM-N methodology is considerably more efficient than the 2nd-CASAM-N methodology for computing the second-order sensitivities since the number of feature-functions is much smaller than the number of primary parameters;specifically for the Nordheim-Fuchs model, the 2nd-FASAM-N methodology requires 2 large-scale computations to obtain all of the exact expressions of the 28 distinct second-order response sensitivities with respect to the model parameters while the 2nd-CASAM-N methodology requires 7 large-scale computations for obtaining these 28 second-order sensitivities;(iii) the 3rd-FASAM-N methodology is even more efficient than the 3rd-CASAM-N methodology: only 2 large-scale computations are needed to obtain the exact expressions of the 84 distinct third-order response sensitivities with respect to the Nordheim-Fuchs model’s parameters when applying the 3rd-FASAM-N methodology, while the application of the 3rd-CASAM-N methodology requires at least 22 large-scale computations for computing the same 84 distinct third-order sensitivities. Together, the nth-FASAM-N and the nth-CASAM-N methodologies are the most practical methodologies for computing response sensitivities of any order comprehensively and accurately, overcoming the curse of dimensionality in sensitivity analysis.

Complementarity of CFD,experimentation and reactor models for solving challenging fluidization problems

Experimentalists, numerical modellers and reactor modellers need to work together, not only just for validation of numerical codes, but also to shed fundamental light on each other＇s problems and underlying assumptions. Several examples are given, Experimental gas axial dispersion data provide a means of choosing the most appropriate boundary condition （no slip, partial slip or full slip） for particles at the wall of fluidized beds. CFD simulations help to identify how close ＂two-dimensional＂ experimental columns are to being truly two-dimensional and to representing three-dimensional columns. CFD also can be used to provide a more rational means of establishing assumptions needed in the modelling of two-phase fluidized bed reactors, for example how to deal with cases where there is a change in molar flow （and hence volumetric flow） as a result of chemical reactions.

Crystal Structure Evolution of the Cu-rich Nano Precipitates from bcc to 9R in Reactor Pressure Vessel Model Steel

The crystal structure evolution of the Cu-rich nano precipitates from bcc to 9R during thermal aging was studied in nuclear reactor pressure vessel （RPV） model steels. The specimens, contained higher copper and nickel contents than commercially available one, were heated at 890 ~C for 0.5 h and then water quenched followed by tempering at 0（50 ~C for I0 h and aging at 400 ~C for 1000 h. It was observed that bcc and 9R orthogonal structure, as well as 9R orthogonal and 9R monoclinic structure, coexist in a single Cu-rich nano precipitate. Further analyses pointed out that Cu-rich nano precipitates of bcc structure were not stable, it may preferentially transform to 9R orthogonal structure and then to 9R monoclinic structure. This results showed that the crystal structure evolution of the Cu-rich nano precipitates was complex.

Modeling of pyridine synthesis process in a coupled fluidized bed reactor

To obtain the optimal operating conditions of a coupled reactor for pyridine synthesis,reactor modeling process is carried out in this paper.During the modeling process,the flow hydrodynamics,heat transfer behavior,inter-phase mass transfer behavior and reaction kinetics were taken into consideration consequently.Further,a regression program based on least square method was proposed to regress the model parameters.The prediction results agreed well with the experimental results with an average deviation of 5.9%.Finally,by setting suitable aim function,the optimal operating conditions of the coupled reactor for pyridine synthesis were determined.

Computational fluid dynamics simulation of hydrodynamics in the riser of an external loop airlift reactor

Local hydrodynamics in the riser of an external loop airlift reactor （EL-ALR） are identified and the performances of three drag models are evaluated in computational fluid dynamics simulation. The simulation results show that the Schiller-Naumann drag model underestimated the local gas holdup at lower superficial gas velocity whereas the Tomiyama drag model overestimated that at higher superficial gas velocity. By contrast, the dual-bubble-size （DBS）-local drag model gave more reasonable radial and axial distri-butions of gas holdup in all cases. The reason is that the DBS-local drag model gave correct values of the lumped parameter, i,e., the ratio of the drag coefficient to bubble diameter, for varying operating conditions and radial positions. This ratio is reasonably expected to decrease with increasing superficial gas velocity and be smaller in the center and larger near the wall. Only the DBS-local drag model correctly reproduced these trends. The radial profiles of the axial velocity of the liquid and gas predicted by the DBS-local model also agreed well with experimental data.

Novel photocatalytic reactor for degradation of DDT in water and its optimization model

A novel photocatalytic reactor was developed to remove （1,1-bis（4-chlorophenyl）-2,2,2-trichloroethane） （DDT） from water. In the reactor, a cenosphere was used to support TiO2 film made by means of sol-gel. Because the cenospheres were coated with TiO2, their specific gravity was slightly increased from the original 0.6-0.8 to 0.8-0.9, so that they were able to be suspended in water. With the mixed operation of a bubbler, the water in the reactor was in a well-fluidized state. The bottom of the reactor is a sand filter bed, which can be used to prevent the photocatalyst from being lost. A mathematical model of the reactor has been developed in the two primary influential factors： ultraviolet （UV） light intensity and photocatalyst concentration. With such a model, the reactor can be designed more reasonably.

Modeling of fixed bed reactor for coal tar hydrogenation via the kinetic lumping approach

Hydrogenation technology is an indispensable chemical upgrading process for converting the heavy feedstock into favorable lighter products.In this work,a new kinetic model containing four hydrocarbon lumps(feedstock,diesel,gasoline,cracking gas)was developed to describe the coal tar hydrogenation process,the Levenberg–Marquardt’s optimization algorithm was used to determine the kinetic parameters by minimizing the sum of square errors between experimental and calculated data,the predictions from model validation showed a good agreement with experimental values.Subsequently,an adiabatic reactor model based on proposed lumped kinetic model was constructed to further investigate the performance of hydrogenation fixed-bed units,the mass balance and energy balance within the phases in the reactor were taken into accounts in the form of ordinary differential equation.An application of the reactor model was performed for simulating the actual bench-scale plant of coal tar hydrogenation,the simulated results on the products yields and temperatures distribution along with the reactor are shown to be good consistent with the experimental data.

Modeling and simulation of circulating fluidized bed reactors applied to a carbonation/calcination loop

A fluid dynamic model for a gas-solid circulating fluidized bed （CFB） designed using two coupled riser reactors is developed and implemented numerically with code programmed in Matlab. The fluid dynamic model contains heat and species mass balances to calculate temperatures and compositions for a carbonation/calcination loop process. Because of the high computational costs required to resolve the three-dimensional phenomena, a model representing a trade-offbetween computational time requirements and accuracy is developed. For dynamic processes with a solid flux between the two reactor units that depends on the fluid dynamics of both risers, a dynamic one-dimensional two-fluid model is sufficient. A two-fluid model using the constant particle viscosity closure for the stress term is used for the solid phase, and an algebraic turbulence model is applied to the gas phase. The numerical model implementa- tion is based on the finite volume method with a staggered grid scheme. The exchange of solids between the reactor units constituting the circulating fluidized bed （solid flux） is implemented through additional mass source/sink terms in the continuity equations of the two phases, For model validation, a relevant experimental analysis provided in the literature is reproduced by the numerical simulations, The numerical analysis indicates that sufficient heat integration between the two reactor units is important for the performance of the circulating fluidized bed system, The two-fluid model performs fairly well for this chemical process operated in a CFB designed as two coupled riser reactors. Further analysis and optimization of the solution algorithms and the reactor coupling strategy is warranted.