Second-Order MaxEnt Predictive Modelling Methodology. III: Illustrative Application to a Reactor Physics Benchmark

This work illustrates the innovative results obtained by applying the recently developed the 2nd-order predictive modeling methodology called “2nd- BERRU-PM”, where the acronym BERRU denotes “best-estimate results with reduced uncertainties” and “PM” denotes “predictive modeling.” The physical system selected for this illustrative application is a polyethylene-reflected plutonium (acronym: PERP) OECD/NEA reactor physics benchmark. This benchmark is modeled using the neutron transport Boltzmann equation (involving 21,976 uncertain parameters), the solution of which is representative of “large-scale computations.” The results obtained in this work confirm the fact that the 2nd-BERRU-PM methodology predicts best-estimate results that fall in between the corresponding computed and measured values, while reducing the predicted standard deviations of the predicted results to values smaller than either the experimentally measured or the computed values of the respective standard deviations. The obtained results also indicate that 2nd-order response sensitivities must always be included to quantify the need for including (or not) the 3rd- and/or 4th-order sensitivities. When the parameters are known with high precision, the contributions of the higher-order sensitivities diminish with increasing order, so that the inclusion of the 1st- and 2nd-order sensitivities may suffice for obtaining accurate predicted best- estimate response values and best-estimate standard deviations. On the other hand, when the parameters’ standard deviations are sufficiently large to approach (or be outside of) the radius of convergence of the multivariate Taylor-series which represents the response in the phase-space of model parameters, the contributions stemming from the 3rd- and even 4th-order sensitivities are necessary to ensure consistency between the computed and measured response. In such cases, the use of only the 1st-order sensitivities erroneously indicates that the computed results are inconsistent with the respective measured response. Ongoing research aims at extending the 2nd-BERRU-PM methodology to fourth-order, thus enabling the computation of third-order response correlations (skewness) and fourth-order response correlations (kurtosis).

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.

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.

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.

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.

Development of a dynamics model for graphite-moderated channel-type molten salt reactor

A molten salt reactor(MSR) is one of the six advanced reactor concepts selected by the generation Ⅳ international forum because of its advantages of inherent safety, and the promising capabilities of Th-U breeding and transuranics transmutation. A dynamics model for the channel-type MSR is developed in this work based on a three-dimensional thermal–hydraulic model(3DTH) and a point reactor model. The 3DTH couples a three-dimensional heat conduction model and a one-dimensional single-phase flow model that can accurately consider the heat conduction between different assemblies. The 3DTH is validated by the RELAP5 code in terms of the temperature and mass flow distribution calculation. A point reactor model considering the drift of delayed neutron precursors is adopted in the dynamics model. To verify the dynamics model, three experiments from the molten salt reactor experiment are simulated. The agreement of the experimental data and simulation results was excellent.With the aid of this model, the unprotected step reactivity addition and unprotected loss of flow of the 2 MWt experimental MSR are modeled, and the reactor power and temperature evolution are analyzed.

Modeling-based optimization of a fixed-bed industrial reactor for oxidative dehydrogenation of propane

An industrial scale propylene production via oxidative dehydrogenation of propane(ODHP)in multi-tubular reactors was modeled.Multi-tubular fixed-bed reactor used for ODHP process,employing 10000 of small diameter tubes immersed in a shell through a proper coolant flows.Herein,a theory-based pseudo-homogeneous model to describe the operation of a fixed bed reactor for the ODHP to correspondence ole fin over V_2O_5/γ-Al_2O_3catalyst was presented.Steady state one dimensional model has been developed to identify the operation parameters and to describe the propane and oxygen conversions,gas process and coolant temperatures,as well as other parameters affecting the reactor performance such as pressure.Furthermore,the applied model showed that a double-bed multitubular reactor with intermediate air injection scheme was superior to a single-bed design due to the increasing of propylene selectivity while operating under lower oxygen partial pressures resulting in propane conversion of about 37.3%.The optimized length of the reactor needed to reach 100%conversion of the oxygen was theoretically determined.For the single-bed reactor the optimized length of 11.96 m including 0.5m of inert section at the entrance region and for the double-bed reactor design the optimized lengths of 5.72m for the first and 7.32 m for the second reactor were calculated.Ultimately,the use of a distributed oxygen feed with limited number of injection points indicated a signi ficant improvement on the reactor performance in terms of propane conversion and propylene selectivity.Besides,this concept could overcome the reactor runaway temperature problem and enabled operations at the wider range of conditions to obtain enhanced propylene production in an industrial scale reactor.

Kinetic Model of Fixed Bed Reactor with Immobilized Microorganisms for Removing Low-Concentration SO_2

On the basis of the analysis of the process of treating low concentrations of sulfur dioxide （SO2） gas in a fixed bed reactor, a kinetic model is proposed for this process after taking into consideration the effects of internal diffusion, cell concentration, and production yield of microorganisms but ignoring the effect of external diffusion. The results obtained from the model simulation show that this model can indicate the influence of the process factors, Cin, η μmax, Cx, A, h, Kin, and Q, on the removal of SO2 and that the prediction of the results by this model is also satisfactory. This kinetic model can also provide some very important indications regarding the preparation of immobilized microorganisms, selection and domestication of proper species of microorganisms, as well as the design of bioreactors.

Modeling and optimization of industrial Fischer–Tropsch synthesis with the slurry bubble column reactor and iron-based catalyst

To optimize industrial Fischer–Tropsch(FT) synthesis with the slurry bubble column reactor(SBCR) and ironbased catalyst, a comprehensive process model for FT synthesis that includes a detailed SBCR model, gas liquid separation model, simplified CO_2 removal model and tail gas cycle model was developed. An effective iteration algorithm was proposed to solve this process model, and the model was validated by industrial demonstration experiments data(SBCR with 5.8 m diameter and 30 m height), with a maximum relative error b 10% for predicting the SBCR performances. Subsequently, the proposed model was adopted to optimize the industrial SBCR performances simultaneously considering process and reactor parameters variations. The results show that C_(5+) yield increases as catalyst loading increases within 10–70 ton and syngas H_2/CO value decreases within1.3–1.6, but it doesn't increase obviously when the catalyst loading exceeds 45 ton(about 15 wt% concentration).Higher catalyst loading will result in higher difficulty for wax/catalyst separation and higher catalyst cost. Therefore, the catalyst loading(45 ton) is recommended for the industrial demonstration SBCR operation at syngas H_2/CO = 1.3, and the C_(5+) yield is about 402 ton" per day, which has an about 16% increase than the industrial demonstration run result.

Modeling of Fischer-Tropsch Synthesis in a Slurry Reactor with Water Permeable Membrane

Fischer-Tropsch synthesis is an important chemical process for the production of liquid fuels and olefins. In recent years, the abundant availability of natural gas and the increasing demand of olefins, diesel, and waxes have led to a high interest to further develop this process. A mathematical model of a slurry membrane reactor used for syngas polymerization was developed to simulate and compare the maximum yields and operating conditions in the reactor with that in a conventional slurry reactor. The carbon polymerization was studied from a modeling point of view in a slurry reactor with a water permeable membrane and a conventional slurry reactor. Simulation results show that different parameters affect syngas conversion and carbon product distribution, such as the hydrogen to carbon monoxide ratio, and the membrane parameters such as membrane permeance.

Experimental Study and Modeling of an Adiabatic Fixed-bed Reactor for Methanol Dehydration to Dimethyl Ether

One-dimensional heterogeneous plug flow model was employed to model an adiabatic fixed-bed reactor for the catalytic dehydration of methanol to dimethyl ether.Longitudinal temperature and conversion profiles predicted by this model were compared to those experimentally measured in a bench scale reactor.The reactor was packed with 1.5mm γ-Al2O3 pellets as dehydration catalyst and operated in a temperature range of 543-603K at an atmospheric pressure.Also,the effects of weight hourly space velocity(WHSV)and temperature on methanol conversion were investigated.According to the results,the maximum conversion is obtained at 603.15K with WHSV of 72.87h-1.

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.

Mathematical Model and Advanced Control for Gas-phase Olefin Polymerization in Fluidized-bed Catalytic Reactors

在这研究，在为煤气阶段的催化石蜡聚合建模的开发用 Ziegler-Natta 催化剂的使流体化床的反应堆(FBR ) 被介绍。在乳剂阶段说明在稳固的粒子和包围气体之间的质量和传热的修改数学模型在这个工作被开发包括地点激活反应。在现在的学习开发的这个模型是随后与著名模型相比，也就是水泡生长，混合得好并且为多孔、非多孔的催化剂的模子常数水泡尺寸模型。我们从模型获得了的结果离经常的水泡尺寸模型很靠近，在反应的开始的混合得好的模型和水泡生长模型但是它的全面行为变化了并且在半工作时间以后与水泡生长模型和经常的水泡尺寸模型相比接近混合得好的模型。神经网络的基于的预兆的控制器被实现控制系统，给可接受的结果并且与常规 PID 控制器相比。

Periodic Packing Mode for Trickle-Bed Reactors: Experiments and Modeling

A periodic packing mode of trickle-bed reactor (TBR) for the gas limited reaction was proposed. Hydrogenation of 2-ethylanthraquinone over Pd/A12Oa in a laboratory-scale TBR was taken as a test reaction for determining whether the periodic packing mode is advantageous. The effects of operating conditions and packing type on TBR performance were experimentally examined to demonstrate the cause-effect relationships. A mathematic model of TBR considering axial dispersion and fractional wetting was developed to quantitatively illuminate the reason of performance enhancement.

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.

Modeling and Control of a Continuous Stirred Tank Reactor Based on a Mixed Logical Dynamical Model

A novel control strategy for a continuous stirred tank reactor(CSTR)system,which has the typical characteristic of strongly pronounced nonlinearity,multiple operating points,and a wide operating range,is initiated from the point of hybrid systems.The proposed scheme makes full use of the modeling power of mixed logical dy- namical(MLD)systems to describe the highly nonlinear dynamics and multiple operating points in a unified framework as a hybrid system,and takes advantage of the good control quality of model predictive control(MPC) to design a controller.Thus,this approach avoids oscillation during switching between sub-systems,helps to relieve shaking in transition,and augments the stability robustness of the whole system,and finally achieves optimal(i.e. fast and smooth)transition between operating points.The simulation results demonstrate that the presented ap- proach has a satisfactory performance.

Cold Model Study and Commercial Test on Novel Vapor-Liquid Distributor of Hydroprocessing Reactor

一个新奇蒸汽液体经销商在在处理反应堆的水疗院使用的存在经销商上根据足够的学习被开发。冷模型测试数据证明新奇蒸汽液体分发者的液体分发表演比传统的显然好。新分发者的商业测试在在西诺佩克·昌灵·布朗奇同伴对待反应堆的 300kt/a 气体油水疗院被执行，证明 newvapor 液体分发者能改进液体分发，支持对待效率的水疗院并且导致比传统的更好的性能。

Developing a Mathematical Model for Hydrate Formation in a Spray Batch Reactor

The formation of methane hydrate was undertaken in this research. The purpose of this work was to model the methane hydrate formation with a hydrate-water–methane system in a semi-batch reactor under steady–state, isothermal and isobaric conditions. Obtained results were validated with experiments conducted in a semi-batch spray reactor at low temperatures and high pressures. The investigated formation of gas hydrate from pure methane required physical constants of these materials which were determined through experimental data. The experiments hence, the theoretical calculations were conducted with pure methane and carried out in a spray reactor at 273.95K and 8705kPa to determine the actual amount of hydrate formation in such reactor. Ultimately;the comparison of the results generated from the developed mathematical model with those of experimental data of others indicated a very satisfactory agreement obtained.