Thermal patterns in simple models of cylindrical reactors

The propagation of fronts and the emergence of spatiotemporal patterns on a cylindrically shaped thin catalytic reactor is simulated with a homogeneous model of a fixed catalytic bed, with characteristically large Lewis and Peclet numbers, and a first-order Arrhenius kinetics (i.e., thermokinetic model) which may be coupled with slow changes of catalytic activity (i.e., oscillatory kinetics). Planar fronts of the thermokinetic model may undergo symmetry breaking in the transversal direction only at relatively low Lewis number, but for high Le the front remains flat. Patterns due to oscillatory kinetics in reactors of high Le are shown, for the first time, to undergo symmetry breaking in the azimuthal direction when the perimeter is sufficiently large. The generic regular patterns simulated then are rotating multi-wave patterns of constant rotation-speed and oscillatory-‘firing’ ones, and theirs selection is highly sensitive to governing parameters and initial conditions. The results are organized in bifurcation diagrams showing the coexisting two-dimensional solutions with varying perimeter. Increasing convective velocity or reactor radius leads to symmetry breaking of regular patterns and the system may switch to chaos.     

Transversal patterns in three‐dimensional packed bed reactors: Oscillatory kinetics

Formation of transversal patterns in a 3D cylindrical reactor is studied with a catalytic reactor model in which an exothermic first‐order reaction of Arrhenius kinetics occurs with a variable catalytic activity. Under these oscillatory kinetics, the system exhibits a planar front (1D) solution with the front position oscillating in the axial direction. Three types of patterns were simulated in the 3D system: rotating fronts, oscillating fronts with superimposed transversal (nonrotating) oscillations, and mixed rotating–oscillating fronts. These solutions coexist with the planar front solution and require special initial conditions. We map bifurcation diagrams showing domains of different modes using the reactor radius as a bifurcation parameter. The possible reduction of the 3D model to the 2D cylindrical shell model is discussed. © 2010 American Institute of Chemical Engineers AIChE J, 2010     

Are 3‐D models necessary to simulate packed bed reactors? analysis and 3‐D simulations of adiabatic and cooled reactors

Simulations and analysis of transversal patterns in a homogeneous three‐dimensional (3‐D) model of adiabatic or cooled packed bed reactors (PBRs) catalyzing a first‐order exothermic reaction were presented. In the adiabatic case the simulation verify previous criteria, claiming the emergence of such patterns when (ΔT_ad/ΔT_m)/(Pe_C/Pe_T) surpasses a critical value larger than unity, where ΔT_ad and ΔT_m are adiabatic and maximal temperature rise, respectively. The reactor radius required for such patterns should be larger than a bifurcation value, calculated here from the linear analysis. With increasing radius new patterned branches, corresponding to eigenfunction of the problem emerge, whereas other branches become unstable. The maximal temperature of the 3‐D simulations may exceed the 1‐D prediction, which may affect design procedures. Cooled reactor may exhibit patterns, usually axisymmetric ones that can be characterized by two anomalies: the peak temperature may exceed the corresponding value of an adiabatic reactor and may increase with wall heat‐transfer coefficient, and the peak temperature in a sufficiently wide reactor need not lie at the center but rather on a ring away from it. In conclusions, we argue that transversal patterns are highly unlikely to emerge in practical adiabatic PBRs with a single exothermic reaction, as in practice Pe_C/Pe_T > 1. That eliminates patterns in stationary and downstream‐moving fronts, whereas patterns may emerge in upstream‐moving fronts, as shown here. This conclusion may not hold for microkinetic models, for which stationary modes may be established over a domain of parameters. This suggests that a 1‐D model may be sufficient to analyze a single reaction in an adiabatic reactor and a 2‐D axisymmetric model is sufficient for a cooled reactor. The predictions of a 2‐D cylindrical thin reactor with those of a 3‐D reactor were compared, to show many similarities but some notable differences. © 2012 American Institute of Chemical Engineers AIChE J, 2012     

催化剂填料催化乙酸甲酯水解的动力学研究

采用间歇搅拌釜反应器在40~55的温度范围内以强酸性催化剂填料为催化剂研究了乙酸甲酯的水解动力学规律。实验在原料水与乙酸甲酯的摩尔配比0.5:1~2:1范围内考察了低水浓度时的动力学结果,并采用了较小的粉状催化剂颗粒和较高的搅拌速度以消除内外扩散阻力。实验结果分别用均相动力学模型和基于Langmuir- Hinshelwood 理论的非均相动力学模型进行拟合,得到了两者的模型参数。统计检验发现在水浓度不太高的条件下基于单点吸附理论的表面反应是最关键的控制步骤,此时用非均相动力学方程来拟合实验数据比较准确,而传统上采用的均相动力学方程拟合精度较差,只有在水浓度很高的条件下才能适用。     

Spatiotemporal Patterns on a Ring Network of Oscillatory Electrochemical Reaction with Negative Global Feedback

The formation of spatiotemporal patterns in chemical systems can often be attributed to local and global interactions with the nonlinear kinetics, e. g., due to diffusion or an external constraint, respectively. We investigate the dynamics of an oscillatory chemical reaction on a ring of discrete elements, where the positive local coupling and negative global feedback can be varied independently to observe the emerging spatiotemporal patterns. With local coupling, the oscillations exhibit nearly in-phase synchronization. When increasing the global negative feedback, a transition is seen from nearly sinusoidal phase profile oscillations through rotating and standing waves to amplitude death behavior. The experimental studies are interpreted with a kinetic model of nickel electrodissolution. The results demonstrate the presence of rich spatiotemporal patterns that can be obtained in a network with positive local and negative global interactions.     

A PROBABILISTIC MODEL OF THE FISCHER-TROPSCH SYNTHESIS IN A FLOW REACTOR

The Fischer-Tropsch synthesis is usually carried out in flow reactors, such as fluidized-bed and bubble column slurry reactors. The nature of multiphase flow together with the well-known random nature of chemical reactions renders the performances of such flow reactors stochastic. In this work, stochastic processes, more specifically continuous time Markov chains, are employed for analyzing and modeling both the dispersive mixing and chemical kinetics in a flow reactor for the Fischer-Tropsch synthesis. The model predicts the distributions of products inside as well as outside the reactor at any time Under a steady state operation, the model gives rise to the Flory equation. Other results include expressions for predicting the mole fraction of chains with j carbon atoms inside and outside the reactor. This approach can be applied to both time homogeneous and heterogeneous processes.     

Dynamics of catalytic reactions and reactors

Heterogeneous catalytic reactions and catalytic reactors are known to exhibit complex dynamic behavior and significant progress has been made, in the past two decades, in understanding this complexity using the tools of nonlinear dynamics and advanced experimental methods. This article presents an overview of complex dynamic behavior in heterogeneous catalysis and points out their intriguing nature along with practical implications. The issues discussed are the source of oscillatory behavior, classification of complex motions, transitions to chaotic solutions and spatiotemporal patterns in reactors of various geometries.     

A numerical investigation of aerosol dynamics in a wall-less reactor

This paper describes a numerical investigation of aerosol formation during silane decomposition in a wall-less reactor. The wall-less reactor is amenable to numerical investigation because the homogeneous chemical reactions leading to the formation of solid particles are isolated from heterogeneous effects, such as occur at the walls of a laminar flow aerosol reactor. The flow/heat transfer and gas-phase chemical kinetics are simulated utilizing separate one-way coupled models. The aerosol dynamics model is based on a simplified sectional model originally developed by Okuyama et al. This model is modified to allow for the simulation of particle growth via condensation. Simulations have been performed which indicate that particle growth via condensation may be an important process. Additionally, the effects of total reactor pressure, temperature and inlet silane concentration on the dynamics of the aerosol population have been investigated. Conditions which result in the formation of larger and more numerous particles have been identified.     

Analysis of excitable waves and spatio-temporal patterns in fixed-bed reactors

This work develops the methodology for the identification and classification of motions in an one-dimensional fixed-bed reactor with excitable and/or oscillatory kinetics. Pattern selection is determined by phase planes spanned by the reactor. Two different models are used to illustrate the main spatio-temporal patterns.     

Mass transfer in annular cylindrical reactors in laminar flow

Radial diffusional mass transfer is studied in a fluid flowing in fully developed laminar flow in an annular cylindrical reactor in which a first order heterogeneous reaction is taking place at the wall. The asymptotic behaviour of the concentration decrease far from the reactor inlet is especially investigated. Limiting values of Sherwood numbers are numerically determined and represented by semi-empirical expressions. Additivity relationships between homogeneous and heterogeneous contributions are established. Theoretical results are found in excellent agreement with those yielded by a new experimental method based on heterogeneous decomposition of ozone. Annular reactors exhibit a mass transfer efficiency which is noticeably higher than that of empty tubes. This efficiency may be characterized by three criteria related to inner space utilization, catalytic surface utilization and/or mechanical energy degradation.     

NO reduction capacity of four major solid fuels in reburning conditions - Experiments and modeling

The combustion of solid fuels in the rotary kiln and in the calciner of a cement plant generates fuel and thermal NO. This NO can be reduced inside the reducing zone of the calciner. This occurs in two different ways: homogeneous reduction by hydrocarbons and heterogeneous reduction by char. The purpose of this paper is to identify the relative contribution of volatile matters or char on the NO reduction process, which largely depends on the nature of the solid fuel used for reburning.Experiments were undertaken in an Entrained Flow Reactor (EFR), at three temperatures: 800, 900 and 1000 °C. Four major fuels used in the cement production process were studied: a lignite, a coal, an anthracite and a petcoke. Specific experiments were undertaken to determine (i) their devolatilisation kinetics and the gas species released. A wide range of species influencing the NO chemistry was carefully analyzed. Then, (ii) the char oxidation and (iii) the char NO reduction kinetics were characterized. Finally, (iv), the “global” NO reduction capability of each fuel was quantified through experiments during which all phenomena could occur together. This corresponds to the situation of an industrial reactor in reducing conditions. Anthracite and petcoke reduce only very small quantities of NO whereas lignite and coal reduce, respectively, 90% and 80% of the initially present 880 ppm of NO (at 1000 °C after 2 s).The four types of experiments described above were then modeled using a single particle thermo-chemical model that includes heterogeneous reactions and detailed chemistry in the gas phase. This model reveals that both NO reduction on char and NO reduction by volatiles mechanisms contribute significantly to the global NO reduction. After short residence times (several tenth of a second), gas phase reactions reduce NO efficiently; after long residence times (several seconds) the char reduces larger quantities of NO.     

Steady state multiplicity behavior of an isothermal axial dispersion fixed-bed reactor with nonuniformly active catalyst

An isothermal, heterogeneous fixed-bed reactor packed with nonuniformly active catalyst pellets where a biomolecular Langmuir-Hinshelwood reaction occurs, is studied using an axial dispersion model. A catalyst activity distribution given by a Dirac delta function, where the active catalyst is deposited at a specific location within the pellet, is considered. This includes the common case of externally coated pellets with external mass transfer resistance. The steady state multiplicity behavior of this reactor, and its limiting cases: CSTR, PFR and pseudohomogeneous axial dispersion, are examined in detail. The nonlinearity of the reaction kinetics provides two sources of multiplicity, through the heterogeneous nature of the reactor and the presence of axial dispersion in the fluid phase. Their roles in determining reactor multiplicity behavior are fully explored. It is shown that this system can admit at most nine steady state solutions. The limiting behavior of the heterogeneous axial dispersion model as Pe → 0 or ∞ is not represented fully by the CSTR or PFR models because of ignition phenomenon. Finally, the effects of mixing on reactor conversion are discussed.     

Heterogeneous modeling of an autothermal membrane reactor coupling dehydrogenation of ethylbenzene to styrene with hydrogenation of nitrobenzene to aniline: Fickian diffusion model

Coupling of reactions in catalytic membrane reactors provides a route to process intensification. Dehydrogenation of ethylbenzene and hydrogenation of nitrobenzene form a promising pair of processes to be coupled in a membrane reactor. The heat released from the hydrogenation side is utilized to break the endothermality on the dehydrogenation side, while hydrogen produced on the dehydrogenation side permeates through the hydrogen-selective membranes, enhances the equilibrium conversion of ethylbenzene and reacts with nitrobenzene on the permeate side to produce aniline. Mathematical reactor models are excellent tools to evaluate the extent of improvement before experiments are set up. However, a careful selection of phenomena considered by the reactor model is needed in order to obtain accurate model predictions.To investigate the effect of the intraparticle resistances on the performance of the cocurrent configuration of the coupling reactor, a heterogeneous fixed bed reactor model is developed with Fickian diffusion inside the catalyst pellets. For the condition of interest, the styrene yield is found to be 82% by the homogenous model, 73% by the heterogeneous model for isothermal pellets, and 69% by the heterogeneous model with non-isothermal pellets. Hence, the homogeneous model overestimates the yield by 5–15% of their actual values.     

Hydration of propylene oxide using ion-exchange resin catalyst in a slurry reactor

Kinetics of hydration of propylene oxide using an ion-exchange resin catalyst in a slurry reactor was studied. The kinetics of homogeneous, uncatalyzed reaction was studied separately and used to obtain heterogeneous reaction kinetics. The homogeneous reaction was found to be 0.43 order with respect to propylene oxide concentration. The heterogeneous reaction was found to have intraparticle diffusional resistance under certain conditions. The intrinsic kinetic parameters and effective diffusivity were obtained from these data. The heterogeneous reaction was found to be 0.55 order with respect to propylene oxide concentration. The activation energies obtained for homogeneous and heterogeneous reactions were 51.5 and 53.4 kJ/mol, respectively. A theoretical model incorporating all the mass transfer resistances has been proposed.     

管锥形填充床生物反应器水力特性及反应动力学分析

以NaCl为示踪剂,应用脉冲信号理论对管锥形填充床生物反应器内的水流流态进行流态分布实验,得出管锥形填料生物膜反应器流态是完全混合式;应用扩散理论以生物膜内的有机底物为去除对象,根据生物膜内微体积元的物料衡算式,对生物膜内有机底物的去除过程建立数学模型,分别得到在不同底物浓度条件下的三种数学模型;通过试验得出管锥形填充床反应器对污水中有机底物的去除符合一级反应动力学模型,由试验数据拟合其动力学模型为:lnC=-3.67Xt+337.04,回归显著性相关系数为:R2=0.8967。     

Modeling of chemical reactors—XXXI: The one-phase backflow cell model used for simulation of tubular adiabatic reactors

The backflow cell model is used to simulate steady state operation of a tubular adiabatic reactor. The model proposed embraces different mechanism of axial dispersion of heat and mass. It will be shown that the backflow cell model may be used for approximation of the dispersion model. While there are differences in qualitative behavior of simple cell and dispersion models, the backflow cell model gives results which are in agreement with the dispersion model. The model may be used for simulation of steady-state behavior of tubular homogeneous and heterogeneous reactors.     

Esterification of acrylic acid with methanol by reactive chromatography: Experiments and simulations

The esterification of acrylic acid with methanol using Amberlyst 15 as a stationary phase has been investigated using a chromatographic reactor. Several experimental runs at various operating conditions have been conducted on a batch column. A classical reactive chromatography model including lumped kinetics, a linear driving force transport model and a heterogeneous kinetic model for the catalytic reaction has been developed. The additional dispersion of concentration fronts due to density gradient effects has been accounted for in the model. The model parameters have been determined in a fast and reliable way by directly fitting the batch column experiments. In general, a good agreement between experimental and calculated results is obtained. The evaluation of the covariance of the fitted model parameters reveals important insights about the system behavior.Based on the detailed batch column model, a complete model of a simulated-moving-bed reactor has been implemented and its optimal point of operation for the synthesis of methyl acrylate from acrylic acid has been determined. Particularly when considering the low-operating temperature, we can regard this process as a possible competition for current technologies.     

多相光催化反应器数学模型研究进展

本文介绍了当前多相光催化反应体系中反应动力学模型以及反应器数模研究领域内的主要方法及成果。反应动力学方面依据反应机理和动力学方程进行了说明 ;反应器模型则按学术团体各自不同的研究思路及方法分别概述 ,并依照反应器内部的各相的情况作了分类 ,扼要介绍了辐射能分布方程。对未来此领域的研究方向作了展望。     

Mathematical models for the transient behavior of a packed bed Reactor

A mathematical model of a packed bed reactor was developed to include radial and axial diffusion within the reactor as well as film and pore resistances to both heat and mass flows. The non-linear partial differential equations which are coupled by a generalized reaction rate expression were finite-differenced and integrated in the time domain. The performance of the detailed model was compared with those predicted for two simpler models: a homogeneous reactor model and a surface resistance reactor model. The range of variables over which these considerations are important is also indicated.     

臭氧氧化动力学模型及反应器建模研究进展

臭氧化技术可以实现对有机污染物的有效去除,同时兼具绿色环保、工艺流程简单等特点而被广泛应用,而臭氧化模型的构建可以实现对污染物减排的有效预测,对于臭氧化处理污水的工程应用意义重大。本文介绍了臭氧化技术的基本原理,并着重综述了臭氧氧化的动力学模型和反应器建模的研究进展。在臭氧氧化模型的建立中,臭氧的传质和反应是两个最重要的因素。本文首先讨论了臭氧的传质过程,并对其气液两相模型进行了阐述。然后针对忽略臭氧传质的液-液或液-固体系,并根据反应机理,分别总结了常规臭氧氧化、均相催化臭氧氧化和非均相催化臭氧氧化的动力学模型。在充分研究了臭氧氧化的动力学模型后,将其应用到具体反应器的建模中,并总结出模型建立的基本假设。最后指出现有模型存在的一些问题并给出相关的建议,提出臭氧化模型构建的出处是优化工业反应器,实现工程应用。